2022-10-28 23:06:54 +08:00
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2022-11-01 01:03:59 +08:00
< h1 dir = "auto" id = "ensc3016-notes-1" > ENSC3016 notes< / h1 >
2022-10-28 23:06:54 +08:00
< h3 dir = "auto" id = "etc-3" > Etc< / h3 >
< h4 dir = "auto" id = "first-pass-checks-1" > FIRST-PASS CHECKS< / h4 >
< ul dir = "auto" >
< li dir = "auto" > Double check all are in the correct phase! Multiplications and divisions by < span class = "katex" > < span class = "katex-mathml" > < math xmlns = "http://www.w3.org/1998/Math/MathML" > < semantics > < mrow > < msqrt > < mn > 3< / mn > < / msqrt > < / mrow > < annotation encoding = "application/x-tex" > \sqrt{3}< / annotation > < / semantics > < / math > < / span > < span class = "katex-html" aria-hidden = "true" > < span class = "base" > < span class = "strut" style = "height:1.04em;vertical-align:-0.1328em;" > < / span > < span class = "mord sqrt" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:0.9072em;" > < span class = "svg-align" style = "top:-3em;" > < span class = "pstrut" style = "height:3em;" > < / span > < span class = "mord" style = "padding-left:0.833em;" > < span class = "mord" > 3< / span > < / span > < / span > < span style = "top:-2.8672em;" > < span class = "pstrut" style = "height:3em;" > < / span > < span class = "hide-tail" style = "min-width:0.853em;height:1.08em;" > < svg xmlns = "http://www.w3.org/2000/svg" width = '400em' height = '1.08em' viewBox = '0 0 400000 1080' preserveAspectRatio = 'xMinYMin slice' > < path d = 'M95,702
c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14
c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54
c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10
s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429
c69,-144,104.5,-217.7,106.5,-221
l0 -0
c5.3,-9.3,12,-14,20,-14
H400000v40H845.2724
s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7
c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z
M834 80h400000v40h-400000z'/>< / svg > < / span > < / span > < / span > < span class = "vlist-s" > < / span > < / span > < span class = "vlist-r" > < span class = "vlist" style = "height:0.1328em;" > < span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > or < span class = "katex" > < span class = "katex-mathml" > < math xmlns = "http://www.w3.org/1998/Math/MathML" > < semantics > < mrow > < mn > 3< / mn > < / mrow > < annotation encoding = "application/x-tex" > 3< / annotation > < / semantics > < / math > < / span > < span class = "katex-html" aria-hidden = "true" > < span class = "base" > < span class = "strut" style = "height:0.6444em;" > < / span > < span class = "mord" > 3< / span > < / span > < / span > < / span > where necessary must be checked! Try annotating everything that does not have an associated phase.< / li >
< li dir = "auto" > Check conjugate in current. < span class = "katex" > < span class = "katex-mathml" > < math xmlns = "http://www.w3.org/1998/Math/MathML" > < semantics > < mrow > < mover accent = "true" > < mi > S< / mi > < mo > ˉ< / mo > < / mover > < mo > =< / mo > < mover accent = "true" > < mi > V< / mi > < mo > ˉ< / mo > < / mover > < msup > < mover accent = "true" > < mi > I< / mi > < mo > ˉ< / mo > < / mover > < mo > ∗ < / mo > < / msup > < / mrow > < annotation encoding = "application/x-tex" > \bar{S}=\bar{V}\bar{I}^*< / annotation > < / semantics > < / math > < / span > < span class = "katex-html" aria-hidden = "true" > < span class = "base" > < span class = "strut" style = "height:0.8201em;" > < / span > < span class = "mord accent" > < span class = "vlist-t" > < span class = "vlist-r" > < span class = "vlist" style = "height:0.8201em;" > < span style = "top:-3em;" > < span class = "pstrut" style = "height:3em;" > < / span > < span class = "mord mathnormal" style = "margin-right:0.05764em;" > S< / span > < / span > < span style = "top:-3.2523em;" > < span class = "pstrut" style = "height:3em;" > < / span > < span class = "accent-body" style = "left:-0.1667em;" > < span class = "mord" > ˉ< / span > < / span > < / span > < / span > < / span > < / span > < / span > < span class = "mspace" style = "margin-right:0.2778em;" > < / span > < span class = "mrel" > =< / span > < span class = "mspace" style = "margin-right:0.2778em;" > < / span > < / span > < span class = "base" > < span class = "strut" style = "height:0.8201em;" > < / span > < span class = "mord accent" > < span class = "vlist-t" > < span class = "vlist-r" > < span class = "vlist" style = "height:0.8201em;" > < span style = "top:-3em;" > < span class = "pstrut" style = "height:3em;" > < / span > < span class = "mord mathnormal" style = "margin-right:0.22222em;" > V< / span > < / span > < span style = "top:-3.2523em;" > < span class = "pstrut" style = "height:3em;" > < / span > < span class = "accent-body" style = "left:-0.25em;" > < span class = "mord" > ˉ< / span > < / span > < / span > < / span > < / span > < / span > < / span > < span class = "mord" > < span class = "mord accent" > < span class = "vlist-t" > < span class = "vlist-r" > < span class = "vlist" style = "height:0.8201em;" > < span style = "top:-3em;" > < span class = "pstrut" style = "height:3em;" > < / span > < span class = "mord mathnormal" style = "margin-right:0.07847em;" > I< / span > < / span > < span style = "top:-3.2523em;" > < span class = "pstrut" style = "height:3em;" > < / span > < span class = "accent-body" style = "left:-0.1389em;" > < span class = "mord" > ˉ< / span > < / span > < / span > < / span > < / span > < / span > < / span > < span class = "msupsub" > < span class = "vlist-t" > < span class = "vlist-r" > < span class = "vlist" style = "height:0.6887em;" > < span style = "top:-3.063em;margin-right:0.05em;" > < span class = "pstrut" style = "height:2.7em;" > < / span > < span class = "sizing reset-size6 size3 mtight" > < span class = "mbin mtight" > ∗ < / span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < / li >
< li dir = "auto" > Check transformer parameters are referred to the proper side< / li >
< / ul >
< h4 dir = "auto" id = "y-delta-transformation-balanced-case-1" > Y-< span class = "katex" > < span class = "katex-mathml" > < math xmlns = "http://www.w3.org/1998/Math/MathML" > < semantics > < mrow > < mi mathvariant = "normal" > Δ< / mi > < / mrow > < annotation encoding = "application/x-tex" > \Delta< / annotation > < / semantics > < / math > < / span > < span class = "katex-html" aria-hidden = "true" > < span class = "base" > < span class = "strut" style = "height:0.6833em;" > < / span > < span class = "mord" > Δ< / span > < / span > < / span > < / span > transformation (Balanced case)< / h4 >
< p dir = "auto" > < span class = "katex" > < span class = "katex-mathml" > < math xmlns = "http://www.w3.org/1998/Math/MathML" > < semantics > < mrow > < msub > < mi > Z< / mi > < mi mathvariant = "normal" > Δ< / mi > < / msub > < mo > =< / mo > < mn > 3< / mn > < msub > < mi > Z< / mi > < mi > Y< / mi > < / msub > < / mrow > < annotation encoding = "application/x-tex" > Z_\Delta=3Z_Y< / annotation > < / semantics > < / math > < / span > < span class = "katex-html" aria-hidden = "true" > < span class = "base" > < span class = "strut" style = "height:0.8333em;vertical-align:-0.15em;" > < / span > < span class = "mord" > < span class = "mord mathnormal" style = "margin-right:0.07153em;" > Z< / span > < span class = "msupsub" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:0.3283em;" > < span style = "top:-2.55em;margin-left:-0.0715em;margin-right:0.05em;" > < span class = "pstrut" style = "height:2.7em;" > < / span > < span class = "sizing reset-size6 size3 mtight" > < span class = "mord mtight" > Δ< / span > < / span > < / span > < / span > < span class = "vlist-s" > < / span > < / span > < span class = "vlist-r" > < span class = "vlist" style = "height:0.15em;" > < span > < / span > < / span > < / span > < / span > < / span > < / span > < span class = "mspace" style = "margin-right:0.2778em;" > < / span > < span class = "mrel" > =< / span > < span class = "mspace" style = "margin-right:0.2778em;" > < / span > < / span > < span class = "base" > < span class = "strut" style = "height:0.8333em;vertical-align:-0.15em;" > < / span > < span class = "mord" > 3< / span > < span class = "mord" > < span class = "mord mathnormal" style = "margin-right:0.07153em;" > Z< / span > < span class = "msupsub" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:0.3283em;" > < span style = "top:-2.55em;margin-left:-0.0715em;margin-right:0.05em;" > < span class = "pstrut" style = "height:2.7em;" > < / span > < span class = "sizing reset-size6 size3 mtight" > < span class = "mord mathnormal mtight" style = "margin-right:0.22222em;" > Y< / span > < / span > < / span > < / span > < span class = "vlist-s" > < / span > < / span > < span class = "vlist-r" > < span class = "vlist" style = "height:0.15em;" > < span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < / p >
< h3 dir = "auto" id = "types-of-power-factors-from-ensc2003-1" > Types of power factors (From < code > ENSC2003< / code > )< / h3 >
< p dir = "auto" > Where < span class = "katex" > < span class = "katex-mathml" > < math xmlns = "http://www.w3.org/1998/Math/MathML" > < semantics > < mrow > < mover accent = "true" > < mi > S< / mi > < mo > ˉ< / mo > < / mover > < mo > =< / mo > < mi mathvariant = "normal" > ∣ < / mi > < mover accent = "true" > < mi > S< / mi > < mo > ˉ< / mo > < / mover > < mi mathvariant = "normal" > ∣ < / mi > < mi mathvariant = "normal" > ∠< / mi > < mi > φ< / mi > < / mrow > < annotation encoding = "application/x-tex" > \bar{S}=|\bar{S}|\angle\varphi< / annotation > < / semantics > < / math > < / span > < span class = "katex-html" aria-hidden = "true" > < span class = "base" > < span class = "strut" style = "height:0.8201em;" > < / span > < span class = "mord accent" > < span class = "vlist-t" > < span class = "vlist-r" > < span class = "vlist" style = "height:0.8201em;" > < span style = "top:-3em;" > < span class = "pstrut" style = "height:3em;" > < / span > < span class = "mord mathnormal" style = "margin-right:0.05764em;" > S< / span > < / span > < span style = "top:-3.2523em;" > < span class = "pstrut" style = "height:3em;" > < / span > < span class = "accent-body" style = "left:-0.1667em;" > < span class = "mord" > ˉ< / span > < / span > < / span > < / span > < / span > < / span > < / span > < span class = "mspace" style = "margin-right:0.2778em;" > < / span > < span class = "mrel" > =< / span > < span class = "mspace" style = "margin-right:0.2778em;" > < / span > < / span > < span class = "base" > < span class = "strut" style = "height:1.0701em;vertical-align:-0.25em;" > < / span > < span class = "mord" > ∣ < / span > < span class = "mord accent" > < span class = "vlist-t" > < span class = "vlist-r" > < span class = "vlist" style = "height:0.8201em;" > < span style = "top:-3em;" > < span class = "pstrut" style = "height:3em;" > < / span > < span class = "mord mathnormal" style = "margin-right:0.05764em;" > S< / span > < / span > < span style = "top:-3.2523em;" > < span class = "pstrut" style = "height:3em;" > < / span > < span class = "accent-body" style = "left:-0.1667em;" > < span class = "mord" > ˉ< / span > < / span > < / span > < / span > < / span > < / span > < / span > < span class = "mord" > ∣∠< / span > < span class = "mord mathnormal" > φ< / span > < / span > < / span > < / span > :< / p >
< p > < span class = "katex-display" > < span class = "katex" > < span class = "katex-mathml" > < math xmlns = "http://www.w3.org/1998/Math/MathML" display = "block" > < semantics > < mrow > < mi > φ< / mi > < mo > =< / mo > < mi > arctan< / mi > < mo > < / mo > < mrow > < mo fence = "true" > (< / mo > < mfrac > < mi > Q< / mi > < mi > P< / mi > < / mfrac > < mo fence = "true" > )< / mo > < / mrow > < mo > =< / mo > < msub > < mi > θ< / mi > < mi > v< / mi > < / msub > < mo > − < / mo > < msub > < mi > θ< / mi > < mi > i< / mi > < / msub > < / mrow > < annotation encoding = "application/x-tex" > \varphi = \arctan\left(\frac{Q}{P}\right) = \theta_v-\theta_i< / annotation > < / semantics > < / math > < / span > < span class = "katex-html" aria-hidden = "true" > < span class = "base" > < span class = "strut" style = "height:0.625em;vertical-align:-0.1944em;" > < / span > < span class = "mord mathnormal" > φ< / span > < span class = "mspace" style = "margin-right:0.2778em;" > < / span > < span class = "mrel" > =< / span > < span class = "mspace" style = "margin-right:0.2778em;" > < / span > < / span > < span class = "base" > < span class = "strut" style = "height:2.4em;vertical-align:-0.95em;" > < / span > < span class = "mop" > arctan< / span > < span class = "mspace" style = "margin-right:0.1667em;" > < / span > < span class = "minner" > < span class = "mopen delimcenter" style = "top:0em;" > < span class = "delimsizing size3" > (< / span > < / span > < span class = "mord" > < span class = "mopen nulldelimiter" > < / span > < span class = "mfrac" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:1.3603em;" > < span style = "top:-2.314em;" > < span class = "pstrut" style = "height:3em;" > < / span > < span class = "mord" > < span class = "mord mathnormal" style = "margin-right:0.13889em;" > P< / span > < / span > < / span > < span style = "top:-3.23em;" > < span class = "pstrut" style = "height:3em;" > < / span > < span class = "frac-line" style = "border-bottom-width:0.04em;" > < / span > < / span > < span style = "top:-3.677em;" > < span class = "pstrut" style = "height:3em;" > < / span > < span class = "mord" > < span class = "mord mathnormal" > Q< / span > < / span > < / span > < / span > < span class = "vlist-s" > < / span > < / span > < span class = "vlist-r" > < span class = "vlist" style = "height:0.686em;" > < span > < / span > < / span > < / span > < / span > < / span > < span class = "mclose nulldelimiter" > < / span > < / span > < span class = "mclose delimcenter" style = "top:0em;" > < span class = "delimsizing size3" > )< / span > < / span > < / span > < span class = "mspace" style = "margin-right:0.2778em;" > < / span > < span class = "mrel" > =< / span > < span class = "mspace" style = "margin-right:0.2778em;" > < / span > < / span > < span class = "base" > < span class = "strut" style = "height:0.8444em;vertical-align:-0.15em;" > < / span > < span class = "mord" > < span class = "mord mathnormal" style = "margin-right:0.02778em;" > θ< / span > < span class = "msupsub" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:0.1514em;" > < span style = "top:-2.55em;margin-left:-0.0278em;margin-right:0.05em;" > < span class = "pstrut" style = "height:2.7em;" > < / span > < span class = "sizing reset-size6 size3 mtight" > < span class = "mord mathnormal mtight" style = "margin-right:0.03588em;" > v< / span > < / span > < / span > < / span > < span class = "vlist-s" > < / span > < / span > < span class = "vlist-r" > < span class = "vlist" style = "height:0.15em;" > < span > < / span > < / span > < / span > < / span > < / span > < / span > < span class = "mspace" style = "margin-right:0.2222em;" > < / span > < span class = "mbin" > − < / span > < span class = "mspace" style = "margin-right:0.2222em;" > < / span > < / span > < span class = "base" > < span class = "strut" style = "height:0.8444em;vertical-align:-0.15em;" > < / span > < span class = "mord" > < span class = "mord mathnormal" style = "margin-right:0.02778em;" > θ< / span > < span class = "msupsub" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:0.3117em;" > < span style = "top:-2.55em;margin-left:-0.0278em;margin-right:0.05em;" > < span class = "pstrut" style = "height:2.7em;" > < / span > < span class = "sizing reset-size6 size3 mtight" > < span class = "mord mathnormal mtight" > i< / span > < / span > < / span > < / span > < span class = "vlist-s" > < / span > < / span > < span class = "vlist-r" > < span class = "vlist" style = "height:0.15em;" > < span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < / p >
< / math >
< table dir = "auto" >
< thead dir = "auto" >
< tr dir = "auto" >
< th > < / th >
< th > Lagging< / th >
< th > Leading< / th >
< th > Unity< / th >
< / tr >
< / thead >
< tbody dir = "auto" >
< tr dir = "auto" >
< td > Voltage< / td >
< td > Current behind< / td >
< td > Current ahead< / td >
< td > In phase< / td >
< / tr >
< tr dir = "auto" >
< td > Load type< / td >
< td > Inductive< / td >
< td > Capacitive< / td >
< td > Resistive< / td >
< / tr >
< tr dir = "auto" >
< td > < span class = "katex" > < span class = "katex-mathml" > < math xmlns = "http://www.w3.org/1998/Math/MathML" > < semantics > < mrow > < mi > Q< / mi > < / mrow > < annotation encoding = "application/x-tex" > Q< / annotation > < / semantics > < / math > < / span > < span class = "katex-html" aria-hidden = "true" > < span class = "base" > < span class = "strut" style = "height:0.8778em;vertical-align:-0.1944em;" > < / span > < span class = "mord mathnormal" > Q< / span > < / span > < / span > < / span > < / td >
< td > < span class = "katex" > < span class = "katex-mathml" > < math xmlns = "http://www.w3.org/1998/Math/MathML" > < semantics > < mrow > < mi > Q< / mi > < mo > > < / mo > < mn > 0< / mn > < / mrow > < annotation encoding = "application/x-tex" > Q> 0< / annotation > < / semantics > < / math > < / span > < span class = "katex-html" aria-hidden = "true" > < span class = "base" > < span class = "strut" style = "height:0.8778em;vertical-align:-0.1944em;" > < / span > < span class = "mord mathnormal" > Q< / span > < span class = "mspace" style = "margin-right:0.2778em;" > < / span > < span class = "mrel" > > < / span > < span class = "mspace" style = "margin-right:0.2778em;" > < / span > < / span > < span class = "base" > < span class = "strut" style = "height:0.6444em;" > < / span > < span class = "mord" > 0< / span > < / span > < / span > < / span > < / td >
< td > < span class = "katex" > < span class = "katex-mathml" > < math xmlns = "http://www.w3.org/1998/Math/MathML" > < semantics > < mrow > < mi > Q< / mi > < mo > < < / mo > < mn > 0< / mn > < / mrow > < annotation encoding = "application/x-tex" > Q< 0< / annotation > < / semantics > < / math > < / span > < span class = "katex-html" aria-hidden = "true" > < span class = "base" > < span class = "strut" style = "height:0.8778em;vertical-align:-0.1944em;" > < / span > < span class = "mord mathnormal" > Q< / span > < span class = "mspace" style = "margin-right:0.2778em;" > < / span > < span class = "mrel" > < < / span > < span class = "mspace" style = "margin-right:0.2778em;" > < / span > < / span > < span class = "base" > < span class = "strut" style = "height:0.6444em;" > < / span > < span class = "mord" > 0< / span > < / span > < / span > < / span > < / td >
< td > < span class = "katex" > < span class = "katex-mathml" > < math xmlns = "http://www.w3.org/1998/Math/MathML" > < semantics > < mrow > < mi > Q< / mi > < mo > =< / mo > < mn > 0< / mn > < / mrow > < annotation encoding = "application/x-tex" > Q=0< / annotation > < / semantics > < / math > < / span > < span class = "katex-html" aria-hidden = "true" > < span class = "base" > < span class = "strut" style = "height:0.8778em;vertical-align:-0.1944em;" > < / span > < span class = "mord mathnormal" > Q< / span > < span class = "mspace" style = "margin-right:0.2778em;" > < / span > < span class = "mrel" > =< / span > < span class = "mspace" style = "margin-right:0.2778em;" > < / span > < / span > < span class = "base" > < span class = "strut" style = "height:0.6444em;" > < / span > < span class = "mord" > 0< / span > < / span > < / span > < / span > < / td >
< / tr >
< tr dir = "auto" >
< td > < span class = "katex" > < span class = "katex-mathml" > < math xmlns = "http://www.w3.org/1998/Math/MathML" > < semantics > < mrow > < mi > φ< / mi > < / mrow > < annotation encoding = "application/x-tex" > \varphi< / annotation > < / semantics > < / math > < / span > < span class = "katex-html" aria-hidden = "true" > < span class = "base" > < span class = "strut" style = "height:0.625em;vertical-align:-0.1944em;" > < / span > < span class = "mord mathnormal" > φ< / span > < / span > < / span > < / span > < / td >
< td > < span class = "katex" > < span class = "katex-mathml" > < math xmlns = "http://www.w3.org/1998/Math/MathML" > < semantics > < mrow > < mi > φ< / mi > < mo > > < / mo > < mn > 0< / mn > < mi mathvariant = "normal" > °< / mi > < / mrow > < annotation encoding = "application/x-tex" > \varphi> 0°< / annotation > < / semantics > < / math > < / span > < span class = "katex-html" aria-hidden = "true" > < span class = "base" > < span class = "strut" style = "height:0.7335em;vertical-align:-0.1944em;" > < / span > < span class = "mord mathnormal" > φ< / span > < span class = "mspace" style = "margin-right:0.2778em;" > < / span > < span class = "mrel" > > < / span > < span class = "mspace" style = "margin-right:0.2778em;" > < / span > < / span > < span class = "base" > < span class = "strut" style = "height:0.6944em;" > < / span > < span class = "mord" > 0°< / span > < / span > < / span > < / span > < / td >
< td > < span class = "katex" > < span class = "katex-mathml" > < math xmlns = "http://www.w3.org/1998/Math/MathML" > < semantics > < mrow > < mi > φ< / mi > < mo > < < / mo > < mn > 0< / mn > < mi mathvariant = "normal" > °< / mi > < / mrow > < annotation encoding = "application/x-tex" > \varphi< 0°< / annotation > < / semantics > < / math > < / span > < span class = "katex-html" aria-hidden = "true" > < span class = "base" > < span class = "strut" style = "height:0.7335em;vertical-align:-0.1944em;" > < / span > < span class = "mord mathnormal" > φ< / span > < span class = "mspace" style = "margin-right:0.2778em;" > < / span > < span class = "mrel" > < < / span > < span class = "mspace" style = "margin-right:0.2778em;" > < / span > < / span > < span class = "base" > < span class = "strut" style = "height:0.6944em;" > < / span > < span class = "mord" > 0°< / span > < / span > < / span > < / span > < / td >
< td > < span class = "katex" > < span class = "katex-mathml" > < math xmlns = "http://www.w3.org/1998/Math/MathML" > < semantics > < mrow > < mi > φ< / mi > < mo > =< / mo > < mn > 0< / mn > < mi mathvariant = "normal" > °< / mi > < / mrow > < annotation encoding = "application/x-tex" > \varphi=0°< / annotation > < / semantics > < / math > < / span > < span class = "katex-html" aria-hidden = "true" > < span class = "base" > < span class = "strut" style = "height:0.625em;vertical-align:-0.1944em;" > < / span > < span class = "mord mathnormal" > φ< / span > < span class = "mspace" style = "margin-right:0.2778em;" > < / span > < span class = "mrel" > =< / span > < span class = "mspace" style = "margin-right:0.2778em;" > < / span > < / span > < span class = "base" > < span class = "strut" style = "height:0.6944em;" > < / span > < span class = "mord" > 0°< / span > < / span > < / span > < / span > < / td >
< / tr >
< tr dir = "auto" >
< td > PF [Load]< / td >
< td > < span class = "katex" > < span class = "katex-mathml" > < math xmlns = "http://www.w3.org/1998/Math/MathML" > < semantics > < mrow > < mo stretchy = "false" > [< / mo > < mn > 0< / mn > < mo separator = "true" > ,< / mo > < mn > 1< / mn > < mo stretchy = "false" > )< / mo > < / mrow > < annotation encoding = "application/x-tex" > [0,1)< / annotation > < / semantics > < / math > < / span > < span class = "katex-html" aria-hidden = "true" > < span class = "base" > < span class = "strut" style = "height:1em;vertical-align:-0.25em;" > < / span > < span class = "mopen" > [< / span > < span class = "mord" > 0< / span > < span class = "mpunct" > ,< / span > < span class = "mspace" style = "margin-right:0.1667em;" > < / span > < span class = "mord" > 1< / span > < span class = "mclose" > )< / span > < / span > < / span > < / span > < / td >
< td > < span class = "katex" > < span class = "katex-mathml" > < math xmlns = "http://www.w3.org/1998/Math/MathML" > < semantics > < mrow > < mo stretchy = "false" > [< / mo > < mn > 0< / mn > < mo separator = "true" > ,< / mo > < mn > 1< / mn > < mo stretchy = "false" > )< / mo > < / mrow > < annotation encoding = "application/x-tex" > [0,1)< / annotation > < / semantics > < / math > < / span > < span class = "katex-html" aria-hidden = "true" > < span class = "base" > < span class = "strut" style = "height:1em;vertical-align:-0.25em;" > < / span > < span class = "mopen" > [< / span > < span class = "mord" > 0< / span > < span class = "mpunct" > ,< / span > < span class = "mspace" style = "margin-right:0.1667em;" > < / span > < span class = "mord" > 1< / span > < span class = "mclose" > )< / span > < / span > < / span > < / span > < / td >
< td > < span class = "katex" > < span class = "katex-mathml" > < math xmlns = "http://www.w3.org/1998/Math/MathML" > < semantics > < mrow > < mn > 1< / mn > < / mrow > < annotation encoding = "application/x-tex" > 1< / annotation > < / semantics > < / math > < / span > < span class = "katex-html" aria-hidden = "true" > < span class = "base" > < span class = "strut" style = "height:0.6444em;" > < / span > < span class = "mord" > 1< / span > < / span > < / span > < / span > < / td >
< / tr >
< tr dir = "auto" >
< td > PF [Source]< / td >
< td > < span class = "katex" > < span class = "katex-mathml" > < math xmlns = "http://www.w3.org/1998/Math/MathML" > < semantics > < mrow > < mo stretchy = "false" > [< / mo > < mn > 0< / mn > < mo separator = "true" > ,< / mo > < mo > − < / mo > < mn > 1< / mn > < mo stretchy = "false" > )< / mo > < / mrow > < annotation encoding = "application/x-tex" > [0,-1)< / annotation > < / semantics > < / math > < / span > < span class = "katex-html" aria-hidden = "true" > < span class = "base" > < span class = "strut" style = "height:1em;vertical-align:-0.25em;" > < / span > < span class = "mopen" > [< / span > < span class = "mord" > 0< / span > < span class = "mpunct" > ,< / span > < span class = "mspace" style = "margin-right:0.1667em;" > < / span > < span class = "mord" > − < / span > < span class = "mord" > 1< / span > < span class = "mclose" > )< / span > < / span > < / span > < / span > < / td >
< td > < span class = "katex" > < span class = "katex-mathml" > < math xmlns = "http://www.w3.org/1998/Math/MathML" > < semantics > < mrow > < mo stretchy = "false" > [< / mo > < mn > 0< / mn > < mo separator = "true" > ,< / mo > < mo > − < / mo > < mn > 1< / mn > < mo stretchy = "false" > )< / mo > < / mrow > < annotation encoding = "application/x-tex" > [0,-1)< / annotation > < / semantics > < / math > < / span > < span class = "katex-html" aria-hidden = "true" > < span class = "base" > < span class = "strut" style = "height:1em;vertical-align:-0.25em;" > < / span > < span class = "mopen" > [< / span > < span class = "mord" > 0< / span > < span class = "mpunct" > ,< / span > < span class = "mspace" style = "margin-right:0.1667em;" > < / span > < span class = "mord" > − < / span > < span class = "mord" > 1< / span > < span class = "mclose" > )< / span > < / span > < / span > < / span > < / td >
< td > < span class = "katex" > < span class = "katex-mathml" > < math xmlns = "http://www.w3.org/1998/Math/MathML" > < semantics > < mrow > < mo > − < / mo > < mn > 1< / mn > < / mrow > < annotation encoding = "application/x-tex" > -1< / annotation > < / semantics > < / math > < / span > < span class = "katex-html" aria-hidden = "true" > < span class = "base" > < span class = "strut" style = "height:0.7278em;vertical-align:-0.0833em;" > < / span > < span class = "mord" > − < / span > < span class = "mord" > 1< / span > < / span > < / span > < / span > < / td >
< / tr >
< / tbody >
< / table >
< h2 dir = "auto" id = "power-types-in-induction-motor-1" > Power types in induction motor< / h2 >
< table dir = "auto" >
< thead dir = "auto" >
< tr dir = "auto" >
< th > Type< / th >
< th > Description< / th >
< th > Equivalent terms< / th >
< / tr >
< / thead >
< tbody dir = "auto" >
< tr dir = "auto" >
< td > Input power< / td >
< td > Power into machine. < span class = "katex" > < span class = "katex-mathml" > < math xmlns = "http://www.w3.org/1998/Math/MathML" > < semantics > < mrow > < msub > < mi > V< / mi > < mi > T< / mi > < / msub > < mo > =< / mo > < msub > < mi > V< / mi > < mrow > < mn > 3< / mn > < mi > ϕ< / mi > < / mrow > < / msub > < / mrow > < annotation encoding = "application/x-tex" > V_T=V_{3\phi}< / annotation > < / semantics > < / math > < / span > < span class = "katex-html" aria-hidden = "true" > < span class = "base" > < span class = "strut" style = "height:0.8333em;vertical-align:-0.15em;" > < / span > < span class = "mord" > < span class = "mord mathnormal" style = "margin-right:0.22222em;" > V< / span > < span class = "msupsub" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:0.3283em;" > < span style = "top:-2.55em;margin-left:-0.2222em;margin-right:0.05em;" > < span class = "pstrut" style = "height:2.7em;" > < / span > < span class = "sizing reset-size6 size3 mtight" > < span class = "mord mathnormal mtight" style = "margin-right:0.13889em;" > T< / span > < / span > < / span > < / span > < span class = "vlist-s" > < / span > < / span > < span class = "vlist-r" > < span class = "vlist" style = "height:0.15em;" > < span > < / span > < / span > < / span > < / span > < / span > < / span > < span class = "mspace" style = "margin-right:0.2778em;" > < / span > < span class = "mrel" > =< / span > < span class = "mspace" style = "margin-right:0.2778em;" > < / span > < / span > < span class = "base" > < span class = "strut" style = "height:0.9694em;vertical-align:-0.2861em;" > < / span > < span class = "mord" > < span class = "mord mathnormal" style = "margin-right:0.22222em;" > V< / span > < span class = "msupsub" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:0.3361em;" > < span style = "top:-2.55em;margin-left:-0.2222em;margin-right:0.05em;" > < span class = "pstrut" style = "height:2.7em;" > < / span > < span class = "sizing reset-size6 size3 mtight" > < span class = "mord mtight" > < span class = "mord mtight" > 3< / span > < span class = "mord mathnormal mtight" > ϕ< / span > < / span > < / span > < / span > < / span > < span class = "vlist-s" > < / span > < / span > < span class = "vlist-r" > < span class = "vlist" style = "height:0.2861em;" > < span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > , < span class = "katex" > < span class = "katex-mathml" > < math xmlns = "http://www.w3.org/1998/Math/MathML" > < semantics > < mrow > < msub > < mi > I< / mi > < mi > L< / mi > < / msub > < mo > =< / mo > < msub > < mi > I< / mi > < mrow > < mn > 3< / mn > < mi > ϕ< / mi > < / mrow > < / msub > < / mrow > < annotation encoding = "application/x-tex" > I_L=I_{3\phi}< / annotation > < / semantics > < / math > < / span > < span class = "katex-html" aria-hidden = "true" > < span class = "base" > < span class = "strut" style = "height:0.8333em;vertical-align:-0.15em;" > < / span > < span class = "mord" > < span class = "mord mathnormal" style = "margin-right:0.07847em;" > I< / span > < span class = "msupsub" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:0.3283em;" > < span style = "top:-2.55em;margin-left:-0.0785em;margin-right:0.05em;" > < span class = "pstrut" style = "height:2.7em;" > < / span > < span class = "sizing reset-size6 size3 mtight" > < span class = "mord mathnormal mtight" > L< / span > < / span > < / span > < / span > < span class = "vlist-s" > < / span > < / span > < span class = "vlist-r" > < span class = "vlist" style = "height:0.15em;" > < span > < / span > < / span > < / span > < / span > < / span > < / span > < span class = "mspace" style = "margin-right:0.2778em;" > < / span > < span class = "mrel" > =< / span > < span class = "mspace" style = "margin-right:0.2778em;" > < / span > < / span > < span class = "base" > < span class = "strut" style = "height:0.9694em;vertical-align:-0.2861em;" > < / span > < span class = "mord" > < span class = "mord mathnormal" style = "margin-right:0.07847em;" > I< / span > < span class = "msupsub" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:0.3361em;" > < span style = "top:-2.55em;margin-left:-0.0785em;margin-right:0.05em;" > < span class = "pstrut" style = "height:2.7em;" > < / span > < span class = "sizing reset-size6 size3 mtight" > < span class = "mord mtight" > < span class = "mord mtight" > 3< / span > < span class = "mord mathnormal mtight" > ϕ< / span > < / span > < / span > < / span > < / span > < span class = "vlist-s" > < / span > < / span > < span class = "vlist-r" > < span class = "vlist" style = "height:0.2861em;" > < span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < / td >
< td > < span class = "katex" > < span class = "katex-mathml" > < math xmlns = "http://www.w3.org/1998/Math/MathML" > < semantics > < mrow > < msub > < mi > P< / mi > < mtext > in< / mtext > < / msub > < / mrow > < annotation encoding = "application/x-tex" > P_\text{in}< / annotation > < / semantics > < / math > < / span > < span class = "katex-html" aria-hidden = "true" > < span class = "base" > < span class = "strut" style = "height:0.8333em;vertical-align:-0.15em;" > < / span > < span class = "mord" > < span class = "mord mathnormal" style = "margin-right:0.13889em;" > P< / span > < span class = "msupsub" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:0.3175em;" > < span style = "top:-2.55em;margin-left:-0.1389em;margin-right:0.05em;" > < span class = "pstrut" style = "height:2.7em;" > < / span > < span class = "sizing reset-size6 size3 mtight" > < span class = "mord text mtight" > < span class = "mord mtight" > in< / span > < / span > < / span > < / span > < / span > < span class = "vlist-s" > < / span > < / span > < span class = "vlist-r" > < span class = "vlist" style = "height:0.15em;" > < span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > , < span class = "katex" > < span class = "katex-mathml" > < math xmlns = "http://www.w3.org/1998/Math/MathML" > < semantics > < mrow > < msqrt > < mn > 3< / mn > < / msqrt > < msub > < mi > V< / mi > < mi > T< / mi > < / msub > < msub > < mi > I< / mi > < mi > L< / mi > < / msub > < mi > cos< / mi > < mo > < / mo > < mo stretchy = "false" > (< / mo > < mi > θ< / mi > < mo stretchy = "false" > )< / mo > < / mrow > < annotation encoding = "application/x-tex" > \sqrt{3}V_TI_L\cos(\theta)< / annotation > < / semantics > < / math > < / span > < span class = "katex-html" aria-hidden = "true" > < span class = "base" > < span class = "strut" style = "height:1.1572em;vertical-align:-0.25em;" > < / span > < span class = "mord sqrt" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:0.9072em;" > < span class = "svg-align" style = "top:-3em;" > < span class = "pstrut" style = "height:3em;" > < / span > < span class = "mord" style = "padding-left:0.833em;" > < span class = "mord" > 3< / span > < / span > < / span > < span style = "top:-2.8672em;" > < span class = "pstrut" style = "height:3em;" > < / span > < span class = "hide-tail" style = "min-width:0.853em;height:1.08em;" > < svg xmlns = "http://www.w3.org/2000/svg" width = '400em' height = '1.08em' viewBox = '0 0 400000 1080' preserveAspectRatio = 'xMinYMin slice' > < path d = 'M95,702
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M834 80h400000v40h-400000z'/>< / svg > < / span > < / span > < / span > < span class = "vlist-s" > < / span > < / span > < span class = "vlist-r" > < span class = "vlist" style = "height:0.1328em;" > < span > < / span > < / span > < / span > < / span > < / span > < span class = "mord" > < span class = "mord mathnormal" style = "margin-right:0.22222em;" > V< / span > < span class = "msupsub" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:0.3283em;" > < span style = "top:-2.55em;margin-left:-0.2222em;margin-right:0.05em;" > < span class = "pstrut" style = "height:2.7em;" > < / span > < span class = "sizing reset-size6 size3 mtight" > < span class = "mord mathnormal mtight" style = "margin-right:0.13889em;" > T< / span > < / span > < / span > < / span > < span class = "vlist-s" > < / span > < / span > < span class = "vlist-r" > < span class = "vlist" style = "height:0.15em;" > < span > < / span > < / span > < / span > < / span > < / span > < / span > < span class = "mord" > < span class = "mord mathnormal" style = "margin-right:0.07847em;" > I< / span > < span class = "msupsub" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:0.3283em;" > < span style = "top:-2.55em;margin-left:-0.0785em;margin-right:0.05em;" > < span class = "pstrut" style = "height:2.7em;" > < / span > < span class = "sizing reset-size6 size3 mtight" > < span class = "mord mathnormal mtight" > L< / span > < / span > < / span > < / span > < span class = "vlist-s" > < / span > < / span > < span class = "vlist-r" > < span class = "vlist" style = "height:0.15em;" > < span > < / span > < / span > < / span > < / span > < / span > < / span > < span class = "mspace" style = "margin-right:0.1667em;" > < / span > < span class = "mop" > cos< / span > < span class = "mopen" > (< / span > < span class = "mord mathnormal" style = "margin-right:0.02778em;" > θ< / span > < span class = "mclose" > )< / span > < / span > < / span > < / span > < / td >
< / tr >
< tr dir = "auto" >
< td > Output power< / td >
< td > Mechanical output power of the machine, excludes losses< / td >
< td > < span class = "katex" > < span class = "katex-mathml" > < math xmlns = "http://www.w3.org/1998/Math/MathML" > < semantics > < mrow > < msub > < mi > P< / mi > < mtext > out< / mtext > < / msub > < / mrow > < annotation encoding = "application/x-tex" > P_\text{out}< / annotation > < / semantics > < / math > < / span > < span class = "katex-html" aria-hidden = "true" > < span class = "base" > < span class = "strut" style = "height:0.8333em;vertical-align:-0.15em;" > < / span > < span class = "mord" > < span class = "mord mathnormal" style = "margin-right:0.13889em;" > P< / span > < span class = "msupsub" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:0.2806em;" > < span style = "top:-2.55em;margin-left:-0.1389em;margin-right:0.05em;" > < span class = "pstrut" style = "height:2.7em;" > < / span > < span class = "sizing reset-size6 size3 mtight" > < span class = "mord text mtight" > < span class = "mord mtight" > out< / span > < / span > < / span > < / span > < / span > < span class = "vlist-s" > < / span > < / span > < span class = "vlist-r" > < span class = "vlist" style = "height:0.15em;" > < span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > , < span class = "katex" > < span class = "katex-mathml" > < math xmlns = "http://www.w3.org/1998/Math/MathML" > < semantics > < mrow > < msub > < mi > P< / mi > < mtext > load< / mtext > < / msub > < / mrow > < annotation encoding = "application/x-tex" > P_\text{load}< / annotation > < / semantics > < / math > < / span > < span class = "katex-html" aria-hidden = "true" > < span class = "base" > < span class = "strut" style = "height:0.8333em;vertical-align:-0.15em;" > < / span > < span class = "mord" > < span class = "mord mathnormal" style = "margin-right:0.13889em;" > P< / span > < span class = "msupsub" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:0.3361em;" > < span style = "top:-2.55em;margin-left:-0.1389em;margin-right:0.05em;" > < span class = "pstrut" style = "height:2.7em;" > < / span > < span class = "sizing reset-size6 size3 mtight" > < span class = "mord text mtight" > < span class = "mord mtight" > load< / span > < / span > < / span > < / span > < / span > < span class = "vlist-s" > < / span > < / span > < span class = "vlist-r" > < span class = "vlist" style = "height:0.15em;" > < span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < / td >
< / tr >
< tr dir = "auto" >
< td > Converted power< / td >
< td > Total electrical power converted to mechanical power, includes useful power and mechanical losses inside machine< / td >
< td > < span class = "katex" > < span class = "katex-mathml" > < math xmlns = "http://www.w3.org/1998/Math/MathML" > < semantics > < mrow > < msub > < mi > P< / mi > < mtext > conv< / mtext > < / msub > < / mrow > < annotation encoding = "application/x-tex" > P_\text{conv}< / annotation > < / semantics > < / math > < / span > < span class = "katex-html" aria-hidden = "true" > < span class = "base" > < span class = "strut" style = "height:0.8333em;vertical-align:-0.15em;" > < / span > < span class = "mord" > < span class = "mord mathnormal" style = "margin-right:0.13889em;" > P< / span > < span class = "msupsub" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:0.1514em;" > < span style = "top:-2.55em;margin-left:-0.1389em;margin-right:0.05em;" > < span class = "pstrut" style = "height:2.7em;" > < / span > < span class = "sizing reset-size6 size3 mtight" > < span class = "mord text mtight" > < span class = "mord mtight" > conv< / span > < / span > < / span > < / span > < / span > < span class = "vlist-s" > < / span > < / span > < span class = "vlist-r" > < span class = "vlist" style = "height:0.15em;" > < span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > , < span class = "katex" > < span class = "katex-mathml" > < math xmlns = "http://www.w3.org/1998/Math/MathML" > < semantics > < mrow > < msub > < mi > P< / mi > < mtext > converted< / mtext > < / msub > < / mrow > < annotation encoding = "application/x-tex" > P_\text{converted}< / annotation > < / semantics > < / math > < / span > < span class = "katex-html" aria-hidden = "true" > < span class = "base" > < span class = "strut" style = "height:0.8333em;vertical-align:-0.15em;" > < / span > < span class = "mord" > < span class = "mord mathnormal" style = "margin-right:0.13889em;" > P< / span > < span class = "msupsub" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:0.3361em;" > < span style = "top:-2.55em;margin-left:-0.1389em;margin-right:0.05em;" > < span class = "pstrut" style = "height:2.7em;" > < / span > < span class = "sizing reset-size6 size3 mtight" > < span class = "mord text mtight" > < span class = "mord mtight" > converted< / span > < / span > < / span > < / span > < / span > < span class = "vlist-s" > < / span > < / span > < span class = "vlist-r" > < span class = "vlist" style = "height:0.15em;" > < span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > , < span class = "katex" > < span class = "katex-mathml" > < math xmlns = "http://www.w3.org/1998/Math/MathML" > < semantics > < mrow > < msub > < mi > P< / mi > < mtext > mech< / mtext > < / msub > < / mrow > < annotation encoding = "application/x-tex" > P_\text{mech}< / annotation > < / semantics > < / math > < / span > < span class = "katex-html" aria-hidden = "true" > < span class = "base" > < span class = "strut" style = "height:0.8333em;vertical-align:-0.15em;" > < / span > < span class = "mord" > < span class = "mord mathnormal" style = "margin-right:0.13889em;" > P< / span > < span class = "msupsub" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:0.3361em;" > < span style = "top:-2.55em;margin-left:-0.1389em;margin-right:0.05em;" > < span class = "pstrut" style = "height:2.7em;" > < / span > < span class = "sizing reset-size6 size3 mtight" > < span class = "mord text mtight" > < span class = "mord mtight" > mech< / span > < / span > < / span > < / span > < / span > < span class = "vlist-s" > < / span > < / span > < span class = "vlist-r" > < span class = "vlist" style = "height:0.15em;" > < span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > , < span class = "katex" > < span class = "katex-mathml" > < math xmlns = "http://www.w3.org/1998/Math/MathML" > < semantics > < mrow > < msub > < mi > P< / mi > < mtext > developed< / mtext > < / msub > < / mrow > < annotation encoding = "application/x-tex" > P_\text{developed}< / annotation > < / semantics > < / math > < / span > < span class = "katex-html" aria-hidden = "true" > < span class = "base" > < span class = "strut" style = "height:0.9694em;vertical-align:-0.2861em;" > < / span > < span class = "mord" > < span class = "mord mathnormal" style = "margin-right:0.13889em;" > P< / span > < span class = "msupsub" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:0.3361em;" > < span style = "top:-2.55em;margin-left:-0.1389em;margin-right:0.05em;" > < span class = "pstrut" style = "height:2.7em;" > < / span > < span class = "sizing reset-size6 size3 mtight" > < span class = "mord text mtight" > < span class = "mord mtight" > developed< / span > < / span > < / span > < / span > < / span > < span class = "vlist-s" > < / span > < / span > < span class = "vlist-r" > < span class = "vlist" s
< / tr >
< tr dir = "auto" >
< td > Airgap power< / td >
< td > Power transmitted over airgap.< / td >
< td > < span class = "katex" > < span class = "katex-mathml" > < math xmlns = "http://www.w3.org/1998/Math/MathML" > < semantics > < mrow > < msub > < mi > P< / mi > < mtext > AG< / mtext > < / msub > < / mrow > < annotation encoding = "application/x-tex" > P_\text{AG}< / annotation > < / semantics > < / math > < / span > < span class = "katex-html" aria-hidden = "true" > < span class = "base" > < span class = "strut" style = "height:0.8333em;vertical-align:-0.15em;" > < / span > < span class = "mord" > < span class = "mord mathnormal" style = "margin-right:0.13889em;" > P< / span > < span class = "msupsub" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:0.3283em;" > < span style = "top:-2.55em;margin-left:-0.1389em;margin-right:0.05em;" > < span class = "pstrut" style = "height:2.7em;" > < / span > < span class = "sizing reset-size6 size3 mtight" > < span class = "mord text mtight" > < span class = "mord mtight" > AG< / span > < / span > < / span > < / span > < / span > < span class = "vlist-s" > < / span > < / span > < span class = "vlist-r" > < span class = "vlist" style = "height:0.15em;" > < span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > , < span class = "katex" > < span class = "katex-mathml" > < math xmlns = "http://www.w3.org/1998/Math/MathML" > < semantics > < mrow > < msub > < mi > τ< / mi > < mtext > mech< / mtext > < / msub > < mo > × < / mo > < msub > < mi > ω< / mi > < mi > s< / mi > < / msub > < / mrow > < annotation encoding = "application/x-tex" > \tau_\text{mech}\times\omega_s< / annotation > < / semantics > < / math > < / span > < span class = "katex-html" aria-hidden = "true" > < span class = "base" > < span class = "strut" style = "height:0.7333em;vertical-align:-0.15em;" > < / span > < span class = "mord" > < span class = "mord mathnormal" style = "margin-right:0.1132em;" > τ< / span > < span class = "msupsub" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:0.3361em;" > < span style = "top:-2.55em;margin-left:-0.1132em;margin-right:0.05em;" > < span class = "pstrut" style = "height:2.7em;" > < / span > < span class = "sizing reset-size6 size3 mtight" > < span class = "mord text mtight" > < span class = "mord mtight" > mech< / span > < / span > < / span > < / span > < / span > < span class = "vlist-s" > < / span > < / span > < span class = "vlist-r" > < span class = "vlist" style = "height:0.15em;" > < span > < / span > < / span > < / span > < / span > < / span > < / span > < span class = "mspace" style = "margin-right:0.2222em;" > < / span > < span class = "mbin" > × < / span > < span class = "mspace" style = "margin-right:0.2222em;" > < / span > < / span > < span class = "base" > < span class = "strut" style = "height:0.5806em;vertical-align:-0.15em;" > < / span > < span class = "mord" > < span class = "mord mathnormal" style = "margin-right:0.03588em;" > ω< / span > < span class = "msupsub" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:0.1514em;" > < span style = "top:-2.55em;margin-left:-0.0359em;margin-right:0.05em;" > < span class = "pstrut" style = "height:2.7em;" > < / span > < span class = "sizing reset-size6 size3 mtight" > < span class = "mord mathnormal mtight" > s< / span > < / span > < / span > < / span > < span class = "vlist-s" > < / span > < / span > < span class = "vlist-r" > < span class = "vlist" style = "height:0.15em;" > < span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < / td >
< / tr >
< tr dir = "auto" >
< td > Mechanical loss< / td >
< td > Power lost to friction and windage< / td >
< td > < span class = "katex" > < span class = "katex-mathml" > < math xmlns = "http://www.w3.org/1998/Math/MathML" > < semantics > < mrow > < msub > < mi > P< / mi > < mtext > mechanical < / mtext > < / msub > < / mrow > < annotation encoding = "application/x-tex" > P_\text{mechanical loss}< / annotation > < / semantics > < / math > < / span > < span class = "katex-html" aria-hidden = "true" > < span class = "base" > < span class = "strut" style = "height:0.8333em;vertical-align:-0.15em;" > < / span > < span class = "mord" > < span class = "mord mathnormal" style = "margin-right:0.13889em;" > P< / span > < span class = "msupsub" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:0.3361em;" > < span style = "top:-2.55em;margin-left:-0.1389em;margin-right:0.05em;" > < span class = "pstrut" style = "height:2.7em;" > < / span > < span class = "sizing reset-size6 size3 mtight" > < span class = "mord text mtight" > < span class = "mord mtight" > mechanical < / span > < / span > < / span > < / span > < / span > < span class = "vlist-s" > < / span > < / span > < span class = "vlist-r" > < span class = "vlist" style = "height:0.15em;" > < span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > , < span class = "katex" > < span class = "katex-mathml" > < math xmlns = "http://www.w3.org/1998/Math/MathML" > < semantics > < mrow > < msub > < mi > P< / mi > < mrow > < mtext > F< / mtext > < mspace linebreak = "newline" > < / mspace > < mtext > & W< / mtext > < / mrow > < / msub > < / mrow > < annotation encoding = "application/x-tex" > P_\text{F\\\& W}< / annotation > < / semantics > < / math > < / span > < span class = "katex-html" aria-hidden = "true" > < span class = "base" > < span class = "strut" style = "height:0.8333em;vertical-align:-0.15em;" > < / span > < span class = "mord" > < span class = "mord mathnormal" style = "margin-right:0.13889em;" > P< / span > < span class = "msupsub" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:0.3361em;" > < span style = "top:-2.55em;margin-left:-0.1389em;margin-right:0.05em;" > < span class = "pstrut" style = "height:2.7em;" > < / span > < span class = "sizing reset-size6 size3 mtight" > < span class = "mord text mtight" > < span class = "mord mtight" > F< / span > < span class = "mspace mtight newline" > < / span > < span class = "mord mtight" > & W< / span > < / span > < / span > < / span > < / span > < span class = "vlist-s" > < / span > < / span > < span class = "vlist-r" > < span class = "vlist" style = "height:0.15em;" > < span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > , < span class = "katex" > < span class = "katex-mathml" > < math xmlns = "http://www.w3.org/1998/Math/MathML" > < semantics > < mrow > < msub > < mi > P< / mi > < mtext > friction < / mtext > < / msub > < / mrow > < annotation encoding = "application/x-tex" > P_\text{friction and windage}< / annotation > < / semantics > < / math > < / span > < span class = "katex-html" aria-hidden = "true" > < span class = "base" > < span class = "strut" style = "height:0.9694em;vertical-align:-0.2861em;" > < / span > < span class = "mord" > < span class = "mord mathnormal" style = "margin-right:0.13889em;" > P< / span > < span class = "msupsub" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:0.3361em;" > < span style = "top:-2.55em;margin-left:-0.1389em;margin-right:0.05em;" > < span class = "pstrut" style = "height:2.7em;" > < / span > < span class = "sizing reset-size6 size3 mtight" > < span class = "mord text mtight" > < span class = "mord mtight" > friction < / span > < / span > < / span > < / span > < / span > < span class = "vlist-s" > < / span > < / span > < span class = "vlist-r" > < span class = "vlist" style = "height:0.2861em;" > < span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < / td >
< / tr >
< tr dir = "auto" >
< td > Core loss< / td >
< td > Power lost in machine magnetic material due to hysteresis loss and eddy currents< / td >
< td > < span class = "katex" > < span class = "katex-mathml" > < math xmlns = "http://www.w3.org/1998/Math/MathML" > < semantics > < mrow > < msub > < mi > P< / mi > < mtext > core< / mtext > < / msub > < / mrow > < annotation encoding = "application/x-tex" > P_\text{core}< / annotation > < / semantics > < / math > < / span > < span class = "katex-html" aria-hidden = "true" > < span class = "base" > < span class = "strut" style = "height:0.8333em;vertical-align:-0.15em;" > < / span > < span class = "mord" > < span class = "mord mathnormal" style = "margin-right:0.13889em;" > P< / span > < span class = "msupsub" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:0.1514em;" > < span style = "top:-2.55em;margin-left:-0.1389em;margin-right:0.05em;" > < span class = "pstrut" style = "height:2.7em;" > < / span > < span class = "sizing reset-size6 size3 mtight" > < span class = "mord text mtight" > < span class = "mord mtight" > core< / span > < / span > < / span > < / span > < / span > < span class = "vlist-s" > < / span > < / span > < span class = "vlist-r" > < span class = "vlist" style = "height:0.15em;" > < span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < / td >
< / tr >
< tr dir = "auto" >
< td > Rotor copper loss< / td >
< td > Due to resistance of rotor windings< / td >
< td > < span class = "katex" > < span class = "katex-mathml" > < math xmlns = "http://www.w3.org/1998/Math/MathML" > < semantics > < mrow > < msub > < mi > P< / mi > < mi > r< / mi > < / msub > < / mrow > < annotation encoding = "application/x-tex" > P_r< / annotation > < / semantics > < / math > < / span > < span class = "katex-html" aria-hidden = "true" > < span class = "base" > < span class = "strut" style = "height:0.8333em;vertical-align:-0.15em;" > < / span > < span class = "mord" > < span class = "mord mathnormal" style = "margin-right:0.13889em;" > P< / span > < span class = "msupsub" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:0.1514em;" > < span style = "top:-2.55em;margin-left:-0.1389em;margin-right:0.05em;" > < span class = "pstrut" style = "height:2.7em;" > < / span > < span class = "sizing reset-size6 size3 mtight" > < span class = "mord mathnormal mtight" style = "margin-right:0.02778em;" > r< / span > < / span > < / span > < / span > < span class = "vlist-s" > < / span > < / span > < span class = "vlist-r" > < span class = "vlist" style = "height:0.15em;" > < span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > , < span class = "katex" > < span class = "katex-mathml" > < math xmlns = "http://www.w3.org/1998/Math/MathML" > < semantics > < mrow > < msub > < mi > P< / mi > < mtext > RCL< / mtext > < / msub > < / mrow > < annotation encoding = "application/x-tex" > P_\text{RCL}< / annotation > < / semantics > < / math > < / span > < span class = "katex-html" aria-hidden = "true" > < span class = "base" > < span class = "strut" style = "height:0.8333em;vertical-align:-0.15em;" > < / span > < span class = "mord" > < span class = "mord mathnormal" style = "margin-right:0.13889em;" > P< / span > < span class = "msupsub" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:0.3283em;" > < span style = "top:-2.55em;margin-left:-0.1389em;margin-right:0.05em;" > < span class = "pstrut" style = "height:2.7em;" > < / span > < span class = "sizing reset-size6 size3 mtight" > < span class = "mord text mtight" > < span class = "mord mtight" > RCL< / span > < / span > < / span > < / span > < / span > < span class = "vlist-s" > < / span > < / span > < span class = "vlist-r" > < span class = "vlist" style = "height:0.15em;" > < span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < / td >
< / tr >
< tr dir = "auto" >
< td > Stator copper loss< / td >
< td > Due to resistance of stator windings< / td >
< td > < span class = "katex" > < span class = "katex-mathml" > < math xmlns = "http://www.w3.org/1998/Math/MathML" > < semantics > < mrow > < msub > < mi > P< / mi > < mi > s< / mi > < / msub > < / mrow > < annotation encoding = "application/x-tex" > P_s< / annotation > < / semantics > < / math > < / span > < span class = "katex-html" aria-hidden = "true" > < span class = "base" > < span class = "strut" style = "height:0.8333em;vertical-align:-0.15em;" > < / span > < span class = "mord" > < span class = "mord mathnormal" style = "margin-right:0.13889em;" > P< / span > < span class = "msupsub" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:0.1514em;" > < span style = "top:-2.55em;margin-left:-0.1389em;margin-right:0.05em;" > < span class = "pstrut" style = "height:2.7em;" > < / span > < span class = "sizing reset-size6 size3 mtight" > < span class = "mord mathnormal mtight" > s< / span > < / span > < / span > < / span > < span class = "vlist-s" > < / span > < / span > < span class = "vlist-r" > < span class = "vlist" style = "height:0.15em;" > < span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > , < span class = "katex" > < span class = "katex-mathml" > < math xmlns = "http://www.w3.org/1998/Math/MathML" > < semantics > < mrow > < msub > < mi > P< / mi > < mtext > SCL< / mtext > < / msub > < / mrow > < annotation encoding = "application/x-tex" > P_\text{SCL}< / annotation > < / semantics > < / math > < / span > < span class = "katex-html" aria-hidden = "true" > < span class = "base" > < span class = "strut" style = "height:0.8333em;vertical-align:-0.15em;" > < / span > < span class = "mord" > < span class = "mord mathnormal" style = "margin-right:0.13889em;" > P< / span > < span class = "msupsub" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:0.3283em;" > < span style = "top:-2.55em;margin-left:-0.1389em;margin-right:0.05em;" > < span class = "pstrut" style = "height:2.7em;" > < / span > < span class = "sizing reset-size6 size3 mtight" > < span class = "mord text mtight" > < span class = "mord mtight" > SCL< / span > < / span > < / span > < / span > < / span > < span class = "vlist-s" > < / span > < / span > < span class = "vlist-r" > < span class = "vlist" style = "height:0.15em;" > < span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < / td >
< / tr >
< tr dir = "auto" >
< td > Miscellaneous loss< / td >
< td > Add 1% to losses to account for other unmeasured losses< / td >
< td > < span class = "katex" > < span class = "katex-mathml" > < math xmlns = "http://www.w3.org/1998/Math/MathML" > < semantics > < mrow > < msub > < mi > P< / mi > < mtext > misc< / mtext > < / msub > < / mrow > < annotation encoding = "application/x-tex" > P_\text{misc}< / annotation > < / semantics > < / math > < / span > < span class = "katex-html" aria-hidden = "true" > < span class = "base" > < span class = "strut" style = "height:0.8333em;vertical-align:-0.15em;" > < / span > < span class = "mord" > < span class = "mord mathnormal" style = "margin-right:0.13889em;" > P< / span > < span class = "msupsub" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:0.3175em;" > < span style = "top:-2.55em;margin-left:-0.1389em;margin-right:0.05em;" > < span class = "pstrut" style = "height:2.7em;" > < / span > < span class = "sizing reset-size6 size3 mtight" > < span class = "mord text mtight" > < span class = "mord mtight" > misc< / span > < / span > < / span > < / span > < / span > < span class = "vlist-s" > < / span > < / span > < span class = "vlist-r" > < span class = "vlist" style = "height:0.15em;" > < span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > , < span class = "katex" > < span class = "katex-mathml" > < math xmlns = "http://www.w3.org/1998/Math/MathML" > < semantics > < mrow > < msub > < mi > P< / mi > < mtext > stray< / mtext > < / msub > < / mrow > < annotation encoding = "application/x-tex" > P_\text{stray}< / annotation > < / semantics > < / math > < / span > < span class = "katex-html" aria-hidden = "true" > < span class = "base" > < span class = "strut" style = "height:0.9694em;vertical-align:-0.2861em;" > < / span > < span class = "mord" > < span class = "mord mathnormal" style = "margin-right:0.13889em;" > P< / span > < span class = "msupsub" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:0.2806em;" > < span style = "top:-2.55em;margin-left:-0.1389em;margin-right:0.05em;" > < span class = "pstrut" style = "height:2.7em;" > < / span > < span class = "sizing reset-size6 size3 mtight" > < span class = "mord text mtight" > < span class = "mord mtight" > stray< / span > < / span > < / span > < / span > < / span > < span class = "vlist-s" > < / span > < / span > < span class = "vlist-r" > < span class = "vlist" style = "height:0.2861em;" > < span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < / td >
< / tr >
< / tbody >
< / table >
< div dir = "auto" > < / div >
< center > < img src = "2022-10-25-11-33-40.png" width = 400px > < / center >
< p > < span class = "katex-display" > < span class = "katex" > < span class = "katex-mathml" > < math xmlns = "http://www.w3.org/1998/Math/MathML" display = "block" > < semantics > < mtable rowspacing = "0.25em" columnalign = "right left" columnspacing = "0em" > < mtr > < mtd class = "mtr-glue" > < / mtd > < mtd > < mstyle scriptlevel = "0" displaystyle = "true" > < msub > < mi > P< / mi > < mtext > in< / mtext > < / msub > < / mstyle > < / mtd > < mtd > < mstyle scriptlevel = "0" displaystyle = "true" > < mrow > < mrow > < / mrow > < mo > =< / mo > < msub > < mi > P< / mi > < mtext > SCL< / mtext > < / msub > < mo > +< / mo > < msub > < mi > P< / mi > < mtext > RCL< / mtext > < / msub > < mo > +< / mo > < msub > < mi > P< / mi > < mtext > core< / mtext > < / msub > < mo > +< / mo > < msub > < mi > P< / mi > < mrow > < mtext > F< / mtext > < mspace linebreak = "newline" > < / mspace > < mtext > & W< / mtext > < / mrow > < / msub > < mo > +< / mo > < msub > < mi > P< / mi > < mtext > misc< / mtext > < / msub > < mo > +< / mo > < msub > < mi > P< / mi > < mtext > out< / mtext > < / msub > < / mrow > < / mstyle > < / mtd > < mtd class = "mtr-glue" > < / mtd > < mtd class = "mml-eqn-num" > < / mtd > < / mtr > < mtr > < mtd class = "mtr-glue" > < / mtd > < mtd > < mstyle scriptlevel = "0" displaystyle = "true" > < msub > < mi > P< / mi > < mtext > AG< / mtext > < / msub > < / mstyle > < / mtd > < mtd > < mstyle scriptlevel = "0" displaystyle = "true" > < mrow > < mrow > < / mrow > < mo > =< / mo > < msub > < mi > P< / mi > < mtext > RCL< / mtext > < / msub > < mo > +< / mo > < msub > < mi > P< / mi > < mrow > < mtext > F< / mtext > < mspace linebreak = "newline" > < / mspace > < mtext > & W< / mtext > < / mrow > < / msub > < mo > +< / mo > < msub > < mi > P< / mi > < mtext > misc< / mtext > < / msub > < mo > +< / mo > < msub > < mi > P< / mi > < mtext > out< / mtext > < / msub > < / mrow > < / mstyle > < / mtd > < mtd class = "mtr-glue" > < / mtd > < mtd class = "mml-eqn-num" > < / mtd > < / mtr > < mtr > < mtd class = "mtr-glue" > < / mtd > < mtd > < mstyle scriptlevel = "0" displaystyle = "true" > < msub > < mi > P< / mi > < mtext > mech< / mtext > < / msub > < / mstyle > < / mtd > < mtd > < mstyle scriptlevel = "0" displaystyle = "true" > < mrow > < mrow > < / mrow > < mo > =< / mo > < msub > < mi > P< / mi > < mrow > < mtext > F< / mtext > < mspace linebreak = "newline" > < / mspace > < mtext > & W< / mtext > < / mrow > < / msub > < mo > +< / mo > < msub > < mi > P< / mi > < mtext > misc< / mtext > < / msub > < mo > +< / mo > < msub > < mi > P< / mi > < mtext > out< / mtext > < / msub > < / mrow > < / mstyle > < / mtd > < mtd class = "mtr-glue" > < / mtd > < mtd class = "mml-eqn-num" > < / mtd > < / mtr > < / mtable > < annotation encoding = "application/x-tex" >
\begin{align}
P_\text{in}& =P_\text{SCL}+P_\text{RCL}+P_\text{core}+P_\text{F\\\& W}+P_\text{misc}+P_\text{out}\\
P_\text{AG}& =P_\text{RCL}+P_\text{F\\\& W}+P_\text{misc}+P_\text{out}\\
P_\text{mech}& =P_\text{F\\\& W}+P_\text{misc}+P_\text{out}
\end{align}
< / annotation > < / semantics > < / math > < / span > < span class = "katex-html" aria-hidden = "true" > < span class = "base" > < span class = "strut" style = "height:4.5em;vertical-align:-2em;" > < / span > < span class = "mtable" > < span class = "col-align-r" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:2.5em;" > < span style = "top:-4.66em;" > < span class = "pstrut" style = "height:3em;" > < / span > < span class = "mord" > < span class = "mord" > < span class = "mord mathnormal" style = "margin-right:0.13889em;" > P< / span > < span class = "msupsub" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:0.3175em;" > < span style = "top:-2.55em;margin-left:-0.1389em;margin-right:0.05em;" > < span class = "pstrut" style = "height:2.7em;" > < / span > < span class = "sizing reset-size6 size3 mtight" > < span class = "mord text mtight" > < span class = "mord mtight" > in< / span > < / span > < / span > < / span > < / span > < span class = "vlist-s" > < / span > < / span > < span class = "vlist-r" > < span class = "vlist" style = "height:0.15em;" > < span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < span style = "top:-3.16em;" > < span class = "pstrut" style = "height:3em;" > < / span > < span class = "mord" > < span class = "mord" > < span class = "mord mathnormal" style = "margin-right:0.13889em;" > P< / span > < span class = "msupsub" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:0.3283em;" > < span style = "top:-2.55em;margin-left:-0.1389em;margin-right:0.05em;" > < span class = "pstrut" style = "height:2.7em;" > < / span > < span class = "sizing reset-size6 size3 mtight" > < span class = "mord text mtight" > < span class = "mord mtight" > AG< / span > < / span > < / span > < / span > < / span > < span class = "vlist-s" > < / span > < / span > < span class = "vlist-r" > < span class = "vlist" style = "height:0.15em;" > < span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < span style = "top:-1.66em;" > < span class = "pstrut" style = "height:3em;" > < / span > < span class = "mord" > < span class = "mord" > < span class = "mord mathnormal" style = "margin-right:0.13889em;" > P< / span > < span class = "msupsub" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:0.3361em;" > < span style = "top:-2.55em;margin-left:-0.1389em;margin-right:0.05em;" > < span class = "pstrut" style = "height:2.7em;" > < / span > < span class = "sizing reset-size6 size3 mtight" > < span class = "mord text mtight" > < span class = "mord mtight" > mech< / span > < / span > < / span > < / span > < / span > < span class = "vlist-s" > < / span > < / span > < span class = "vlist-r" > < span class = "vlist" style = "height:0.15em;" > < span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < span class = "vlist-s" > < / span > < / span > < span class = "vlist-r" > < span class = "vlist" style = "height:2em;" > < span > < / span > < / span > < / span > < / span > < / span > < span class = "col-align-l" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:2.5em;" > < span style = "top:-4.66em;" > < span class = "pstrut" style = "height:3em;" > < / span > < span class = "mord" > < span class = "mord" > < / span > < span class = "mspace" style = "margin-right:0.2778em;" > < / span > < span class = "mrel" > =< / span > < span class = "mspace" style = "margin-right:0.2778em;" > < / span > < span class = "mord" > < span class = "mord mathnormal" style = "margin-right:0.13889em;" > P< / span > < span class = "msupsub" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:0.3283em;" > < span style = "top:-2.55em;margin-left:-0.1389em;margin-right:0.05em;" > < span class = "pstrut" style = "height:2.7em;" > < / span > < span class = "sizing reset-size6 size3 mtight" > < span class = "mord text mtight" > < span class = "mord mtight" > SCL< / span > < / span > < / span > < / span > < / span > < span class = "vlist-s" > < / span > < / span > < span class = "vlist-r" > < span class = "vlist" style = "height:0.15em;" > < span > < / span > < / span > < / span > < / span > < / span > < / span > < span class = "mspace" style = "margin-right:0.2222em;" > < / span > < span class = "mbin" > +< / span > < span class = "mspace" style = "margin-right:0.2222em;" > < / span > < span class = "mord" > < span class = "mord mathnormal" style = "margin-right:0.13889em;" > P< / span > < span class = "msupsub" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:0.3283em;" > < span style = "top:-2.55em;margin-left:-0.1389em;margin-right:0.05em;" > < span class = "pstr
< / math >
< p dir = "auto" > Note - assume loss is 0 if not mentioned!< / p >
< table dir = "auto" >
< thead dir = "auto" >
< tr dir = "auto" >
< th > Type< / th >
< th > Description< / th >
< th > Symbols< / th >
< / tr >
< / thead >
< tbody dir = "auto" >
< tr dir = "auto" >
< td > Load torque, Shaft torque< / td >
< td > Torque experienced by load after all losses< / td >
< td > < span class = "katex" > < span class = "katex-mathml" > < math xmlns = "http://www.w3.org/1998/Math/MathML" > < semantics > < mrow > < msub > < mi > τ< / mi > < mtext > load< / mtext > < / msub > < / mrow > < annotation encoding = "application/x-tex" > \tau_\text{load}< / annotation > < / semantics > < / math > < / span > < span class = "katex-html" aria-hidden = "true" > < span class = "base" > < span class = "strut" style = "height:0.5806em;vertical-align:-0.15em;" > < / span > < span class = "mord" > < span class = "mord mathnormal" style = "margin-right:0.1132em;" > τ< / span > < span class = "msupsub" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:0.3361em;" > < span style = "top:-2.55em;margin-left:-0.1132em;margin-right:0.05em;" > < span class = "pstrut" style = "height:2.7em;" > < / span > < span class = "sizing reset-size6 size3 mtight" > < span class = "mord text mtight" > < span class = "mord mtight" > load< / span > < / span > < / span > < / span > < / span > < span class = "vlist-s" > < / span > < / span > < span class = "vlist-r" > < span class = "vlist" style = "height:0.15em;" > < span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > , < span class = "katex" > < span class = "katex-mathml" > < math xmlns = "http://www.w3.org/1998/Math/MathML" > < semantics > < mrow > < msub > < mi > τ< / mi > < mtext > shaft< / mtext > < / msub > < / mrow > < annotation encoding = "application/x-tex" > \tau_\text{shaft}< / annotation > < / semantics > < / math > < / span > < span class = "katex-html" aria-hidden = "true" > < span class = "base" > < span class = "strut" style = "height:0.5806em;vertical-align:-0.15em;" > < / span > < span class = "mord" > < span class = "mord mathnormal" style = "margin-right:0.1132em;" > τ< / span > < span class = "msupsub" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:0.3361em;" > < span style = "top:-2.55em;margin-left:-0.1132em;margin-right:0.05em;" > < span class = "pstrut" style = "height:2.7em;" > < / span > < span class = "sizing reset-size6 size3 mtight" > < span class = "mord text mtight" > < span class = "mord mtight" > shaft< / span > < / span > < / span > < / span > < / span > < span class = "vlist-s" > < / span > < / span > < span class = "vlist-r" > < span class = "vlist" style = "height:0.15em;" > < span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < / td >
< / tr >
< / tbody >
< / table >
< h2 dir = "auto" id = "3phi-induction-motor-1" > < span class = "katex" > < span class = "katex-mathml" > < math xmlns = "http://www.w3.org/1998/Math/MathML" > < semantics > < mrow > < mn > 3< / mn > < mi > ϕ< / mi > < / mrow > < annotation encoding = "application/x-tex" > 3\phi< / annotation > < / semantics > < / math > < / span > < span class = "katex-html" aria-hidden = "true" > < span class = "base" > < span class = "strut" style = "height:0.8889em;vertical-align:-0.1944em;" > < / span > < span class = "mord" > 3< / span > < span class = "mord mathnormal" > ϕ< / span > < / span > < / span > < / span > induction motor< / h2 >
< h3 dir = "auto" id = "etc-4" > Etc.< / h3 >
< ul dir = "auto" >
< li dir = "auto" >
< p dir = "auto" > Slip speed < span class = "katex" > < span class = "katex-mathml" > < math xmlns = "http://www.w3.org/1998/Math/MathML" > < semantics > < mrow > < msub > < mi > N< / mi > < mtext > slip< / mtext > < / msub > < mo > =< / mo > < msub > < mi > N< / mi > < mrow > < mi > s< / mi > < mtext > < / mtext > < / mrow > < / msub > < mo > − < / mo > < msub > < mi > N< / mi > < mi > r< / mi > < / msub > < mo > =< / mo > < mi > s< / mi > < msub > < mi > N< / mi > < mrow > < mi > s< / mi > < mtext > < / mtext > < / mrow > < / msub > < / mrow > < annotation encoding = "application/x-tex" > N_\text{slip}=N_{s\text{ (sync)}}-N_r=sN_{s\text{ (sync)}}< / annotation > < / semantics > < / math > < / span > < span class = "katex-html" aria-hidden = "true" > < span class = "base" > < span class = "strut" style = "height:0.9694em;vertical-align:-0.2861em;" > < / span > < span class = "mord" > < span class = "mord mathnormal" style = "margin-right:0.10903em;" > N< / span > < span class = "msupsub" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:0.3361em;" > < span style = "top:-2.55em;margin-left:-0.109em;margin-right:0.05em;" > < span class = "pstrut" style = "height:2.7em;" > < / span > < span class = "sizing reset-size6 size3 mtight" > < span class = "mord text mtight" > < span class = "mord mtight" > slip< / span > < / span > < / span > < / span > < / span > < span class = "vlist-s" > < / span > < / span > < span class = "vlist-r" > < span class = "vlist" style = "height:0.2861em;" > < span > < / span > < / span > < / span > < / span > < / span > < / span > < span class = "mspace" style = "margin-right:0.2778em;" > < / span > < span class = "mrel" > =< / span > < span class = "mspace" style = "margin-right:0.2778em;" > < / span > < / span > < span class = "base" > < span class = "strut" style = "height:1.0385em;vertical-align:-0.3552em;" > < / span > < span class = "mord" > < span class = "mord mathnormal" style = "margin-right:0.10903em;" > N< / span > < span class = "msupsub" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:0.3448em;" > < span style = "top:-2.5198em;margin-left:-0.109em;margin-right:0.05em;" > < span class = "pstrut" style = "height:2.7em;" > < / span > < span class = "sizing reset-size6 size3 mtight" > < span class = "mord mtight" > < span class = "mord mathnormal mtight" > s< / span > < span class = "mord text mtight" > < span class = "mord mtight" > < / span > < / span > < / span > < / span > < / span > < / span > < span class = "vlist-s" > < / span > < / span > < span class = "vlist-r" > < span class = "vlist" style = "height:0.3552em;" > < span > < / span > < / span > < / span > < / span > < / span > < / span > < span class = "mspace" style = "margin-right:0.2222em;" > < / span > < span class = "mbin" > − < / span > < span class = "mspace" style = "margin-right:0.2222em;" > < / span > < / span > < span class = "base" > < span class = "strut" style = "height:0.8333em;vertical-align:-0.15em;" > < / span > < span class = "mord" > < span class = "mord mathnormal" style = "margin-right:0.10903em;" > N< / span > < span class = "msupsub" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:0.1514em;" > < span style = "top:-2.55em;margin-left:-0.109em;margin-right:0.05em;" > < span class = "pstrut" style = "height:2.7em;" > < / span > < span class = "sizing reset-size6 size3 mtight" > < span class = "mord mathnormal mtight" style = "margin-right:0.02778em;" > r< / span > < / span > < / span > < / span > < span class = "vlist-s" > < / span > < / span > < span class = "vlist-r" > < span class = "vlist" style = "height:0.15em;" > < span > < / span > < / span > < / span > < / span > < / span > < / span > < span class = "mspace" style = "margin-right:0.2778em;" > < / span > < span class = "mrel" > =< / span > < span class = "mspace" style = "margin-right:0.2778em;" > < / span > < / span > < span class = "base" > < span class = "strut" style = "height:1.0385em;vertical-align:-0.3552em;" > < / span > < span class = "mord mathnormal" > s< / span > < span class = "mord" > < span class = "mord mathnormal" style = "margin-right:0.10903em;" > N< / span > < span class = "msupsub" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:0.3448em;" > < span style = "top:-2.5198em;margin-left:-0.109em;margin-right:0.05em;" > < span class = "pstrut" style = "height:2.7em;" > < / span > < span class = "sizing reset-size6 size3 mtight" > < span class = "mord mtight" > < span class = "mord mathnormal mtight" > s< / span > < span class = "mord text mtight" > < span class = "mord mtight" > < / span > < / span > < / span > < / span > < / span > < / span > < span class = "vlist-s" > < / span > < / span > < span class = "vlist-r" > < span class = "vlist" style = "height:0.3552em;" > < span > < / span > < / span > < /s
< / li >
< li dir = "auto" >
< p dir = "auto" > " 1/4 of rated load" != " 1/4 times full load" < / p >
< ul dir = "auto" >
< li dir = "auto" > Means 1/4 of full load slip as it is in the linear region. Accounts for the minimum load.< / li >
< / ul >
< / li >
< li dir = "auto" >
< p dir = "auto" > Rated power stated in machine specification refers to the output power < span class = "katex" > < span class = "katex-mathml" > < math xmlns = "http://www.w3.org/1998/Math/MathML" > < semantics > < mrow > < msub > < mi > P< / mi > < mtext > out< / mtext > < / msub > < / mrow > < annotation encoding = "application/x-tex" > P_\text{out}< / annotation > < / semantics > < / math > < / span > < span class = "katex-html" aria-hidden = "true" > < span class = "base" > < span class = "strut" style = "height:0.8333em;vertical-align:-0.15em;" > < / span > < span class = "mord" > < span class = "mord mathnormal" style = "margin-right:0.13889em;" > P< / span > < span class = "msupsub" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:0.2806em;" > < span style = "top:-2.55em;margin-left:-0.1389em;margin-right:0.05em;" > < span class = "pstrut" style = "height:2.7em;" > < / span > < span class = "sizing reset-size6 size3 mtight" > < span class = "mord text mtight" > < span class = "mord mtight" > out< / span > < / span > < / span > < / span > < / span > < span class = "vlist-s" > < / span > < / span > < span class = "vlist-r" > < span class = "vlist" style = "height:0.15em;" > < span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > , and excludes all losses.< / p >
< / li >
< li dir = "auto" >
< p dir = "auto" > Speed regulation using machine speed: < section > < eqn > < span class = "katex-display" > < span class = "katex" > < span class = "katex-mathml" > < math xmlns = "http://www.w3.org/1998/Math/MathML" display = "block" > < semantics > < mrow > < mtext > SR< / mtext > < mo > =< / mo > < mfrac > < mrow > < msub > < mi > N< / mi > < mrow > < mi > r< / mi > < mo separator = "true" > ,< / mo > < mtext > NL< / mtext > < / mrow > < / msub > < mo > − < / mo > < msub > < mi > N< / mi > < mrow > < mi > r< / mi > < mo separator = "true" > ,< / mo > < mtext > FL< / mtext > < / mrow > < / msub > < / mrow > < msub > < mi > N< / mi > < mrow > < mi > r< / mi > < mo separator = "true" > ,< / mo > < mtext > FL< / mtext > < / mrow > < / msub > < / mfrac > < / mrow > < annotation encoding = "application/x-tex" > \text{SR}=\frac{N_{r,\text{NL}}-N_{r,\text{FL}}}{N_{r,\text{FL}}}< / annotation > < / semantics > < / math > < / span > < span class = "katex-html" aria-hidden = "true" > < span class = "base" > < span class = "strut" style = "height:0.68333em;vertical-align:0em;" > < / span > < span class = "mord text" > < span class = "mord" > SR< / span > < / span > < span class = "mspace" style = "margin-right:0.2777777777777778em;" > < / span > < span class = "mrel" > =< / span > < span class = "mspace" style = "margin-right:0.2777777777777778em;" > < / span > < / span > < span class = "base" > < span class = "strut" style = "height:2.332438em;vertical-align:-0.972108em;" > < / span > < span class = "mord" > < span class = "mopen nulldelimiter" > < / span > < span class = "mfrac" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:1.36033em;" > < span style = "top:-2.314em;" > < span class = "pstrut" style = "height:3em;" > < / span > < span class = "mord" > < span class = "mord" > < span class = "mord mathnormal" style = "margin-right:0.10903em;" > N< / span > < span class = "msupsub" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:0.328331em;" > < span style = "top:-2.5500000000000003em;margin-left:-0.10903em;margin-right:0.05em;" > < span class = "pstrut" style = "height:2.7em;" > < / span > < span class = "sizing reset-size6 size3 mtight" > < span class = "mord mtight" > < span class = "mord mathnormal mtight" style = "margin-right:0.02778em;" > r< / span > < span class = "mpunct mtight" > ,< / span > < span class = "mord text mtight" > < span class = "mord mtight" > FL< / span > < / span > < / span > < / span > < / span > < / span > < span class = "vlist-s" > < / span > < / span > < span class = "vlist-r" > < span class = "vlist" style = "height:0.286108em;" > < span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < span style = "top:-3.23em;" > < span class = "pstrut" style = "height:3em;" > < / span > < span class = "frac-line" style = "border-bottom-width:0.04em;" > < / span > < / span > < span style = "top:-3.677em;" > < span class = "pstrut" style = "height:3em;" > < / span > < span class = "mord" > < span class = "mord" > < span class = "mord mathnormal" style = "margin-right:0.10903em;" > N< / span > < span class = "msupsub" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:0.328331em;" > < span style = "top:-2.5500000000000003em;margin-left:-0.10903em;margin-right:0.05em;" > < span class = "pstrut" style = "height:2.7em;" > < / span > < span class = "sizing reset-size6 size3 mtight" > < span class = "mord mtight" > < span class = "mord mathnormal mtight" style = "margin-right:0.02778em;" > r< / span > < span class = "mpunct mtight" > ,< / span > < span class = "mord text mtight" > < span class = "mord mtight" > NL< / span > < / span > < / span > < / span > < / span > < / span > < span class = "vlist-s" > < / span > < / span > < span class = "vlist-r" > < span class = "vlist" style = "height:0.286108em;" > < span > < / span > < / span > < / span > < / span > < / span > < / span > < span class = "mspace" style = "margin-right:0.2222222222222222em;" > < / span > < span class = "mbin" > − < / span > < span class = "mspace" style = "margin-right:0.2222222222222222em;" > < / span > < span class = "mord" > < span class = "mord mathnormal" style = "margin-right:0.10903em;" > N< / span > < span class = "msupsub" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:0.328331em;" > < span style = "top:-2.5500000000000003em;margin-left:-0.10903em;margin-right:0.05em;" > < span class = "pstrut" style = "height:2.7em;" > < / span > < span class = "sizing reset-size6 size3 mtight" > < span class = "mord mtight" > < span class = "mord mathnormal mtight" style = "margin-right:0.02778em;" > r< / span > < span class = "mpunct mtight" > ,< / span > < span class = "mord text mtight" > < span class = "mord mtight" > FL< / span > < / span > < / span > < / span > < / span > < / span > < span
< / li >
< / ul >
< h3 dir = "auto" id = "diagram-7" > Diagram< / h3 >
< div dir = "auto" > < / div >
< center > < img src = "2022-10-26-22-06-19.png" width = 400px > < / center >
< h3 dir = "auto" id = "equivalent-model-1" > Equivalent model< / h3 >
< h4 dir = "auto" id = "assumptions-3" > Assumptions< / h4 >
< ul dir = "auto" >
< li dir = "auto" > < span class = "katex" > < span class = "katex-mathml" > < math xmlns = "http://www.w3.org/1998/Math/MathML" > < semantics > < mrow > < msub > < mi > x< / mi > < mi > m< / mi > < / msub > < mo > ≈< / mo > < msub > < mi > X< / mi > < mi > m< / mi > < / msub > < / mrow > < annotation encoding = "application/x-tex" > x_m\approx X_m< / annotation > < / semantics > < / math > < / span > < span class = "katex-html" aria-hidden = "true" > < span class = "base" > < span class = "strut" style = "height:0.6331em;vertical-align:-0.15em;" > < / span > < span class = "mord" > < span class = "mord mathnormal" > x< / span > < span class = "msupsub" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:0.1514em;" > < span style = "top:-2.55em;margin-left:0em;margin-right:0.05em;" > < span class = "pstrut" style = "height:2.7em;" > < / span > < span class = "sizing reset-size6 size3 mtight" > < span class = "mord mathnormal mtight" > m< / span > < / span > < / span > < / span > < span class = "vlist-s" > < / span > < / span > < span class = "vlist-r" > < span class = "vlist" style = "height:0.15em;" > < span > < / span > < / span > < / span > < / span > < / span > < / span > < span class = "mspace" style = "margin-right:0.2778em;" > < / span > < span class = "mrel" > ≈< / span > < span class = "mspace" style = "margin-right:0.2778em;" > < / span > < / span > < span class = "base" > < span class = "strut" style = "height:0.8333em;vertical-align:-0.15em;" > < / span > < span class = "mord" > < span class = "mord mathnormal" style = "margin-right:0.07847em;" > X< / span > < span class = "msupsub" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:0.1514em;" > < span style = "top:-2.55em;margin-left:-0.0785em;margin-right:0.05em;" > < span class = "pstrut" style = "height:2.7em;" > < / span > < span class = "sizing reset-size6 size3 mtight" > < span class = "mord mathnormal mtight" > m< / span > < / span > < / span > < / span > < span class = "vlist-s" > < / span > < / span > < span class = "vlist-r" > < span class = "vlist" style = "height:0.15em;" > < span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < / span >
< ul dir = "auto" >
< li dir = "auto" > < span class = "katex" > < span class = "katex-mathml" > < math xmlns = "http://www.w3.org/1998/Math/MathML" > < semantics > < mrow > < msub > < mi > R< / mi > < mi > c< / mi > < / msub > < mo > ⋙< / mo > < msub > < mi > X< / mi > < mi > m< / mi > < / msub > < mo > ⇒< / mo > < msub > < mi > r< / mi > < mi > c< / mi > < / msub > < mo > ⋘< / mo > < msub > < mi > x< / mi > < mi > m< / mi > < / msub > < / mrow > < annotation encoding = "application/x-tex" > R_c\ggg X_m\Rightarrow r_c\lll x_m< / annotation > < / semantics > < / math > < / span > < span class = "katex-html" aria-hidden = "true" > < span class = "base" > < span class = "strut" style = "height:0.8333em;vertical-align:-0.15em;" > < / span > < span class = "mord" > < span class = "mord mathnormal" style = "margin-right:0.00773em;" > R< / span > < span class = "msupsub" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:0.1514em;" > < span style = "top:-2.55em;margin-left:-0.0077em;margin-right:0.05em;" > < span class = "pstrut" style = "height:2.7em;" > < / span > < span class = "sizing reset-size6 size3 mtight" > < span class = "mord mathnormal mtight" > c< / span > < / span > < / span > < / span > < span class = "vlist-s" > < / span > < / span > < span class = "vlist-r" > < span class = "vlist" style = "height:0.15em;" > < span > < / span > < / span > < / span > < / span > < / span > < / span > < span class = "mspace" style = "margin-right:0.2778em;" > < / span > < span class = "mrel amsrm" > ⋙< / span > < span class = "mspace" style = "margin-right:0.2778em;" > < / span > < / span > < span class = "base" > < span class = "strut" style = "height:0.8333em;vertical-align:-0.15em;" > < / span > < span class = "mord" > < span class = "mord mathnormal" style = "margin-right:0.07847em;" > X< / span > < span class = "msupsub" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:0.1514em;" > < span style = "top:-2.55em;margin-left:-0.0785em;margin-right:0.05em;" > < span class = "pstrut" style = "height:2.7em;" > < / span > < span class = "sizing reset-size6 size3 mtight" > < span class = "mord mathnormal mtight" > m< / span > < / span > < / span > < / span > < span class = "vlist-s" > < / span > < / span > < span class = "vlist-r" > < span class = "vlist" style = "height:0.15em;" > < span > < / span > < / span > < / span > < / span > < / span > < / span > < span class = "mspace" style = "margin-right:0.2778em;" > < / span > < span class = "mrel" > ⇒< / span > < span class = "mspace" style = "margin-right:0.2778em;" > < / span > < / span > < span class = "base" > < span class = "strut" style = "height:0.6999em;vertical-align:-0.15em;" > < / span > < span class = "mord" > < span class = "mord mathnormal" style = "margin-right:0.02778em;" > r< / span > < span class = "msupsub" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:0.1514em;" > < span style = "top:-2.55em;margin-left:-0.0278em;margin-right:0.05em;" > < span class = "pstrut" style = "height:2.7em;" > < / span > < span class = "sizing reset-size6 size3 mtight" > < span class = "mord mathnormal mtight" > c< / span > < / span > < / span > < / span > < span class = "vlist-s" > < / span > < / span > < span class = "vlist-r" > < span class = "vlist" style = "height:0.15em;" > < span > < / span > < / span > < / span > < / span > < / span > < / span > < span class = "mspace" style = "margin-right:0.2778em;" > < / span > < span class = "mrel amsrm" > ⋘< / span > < span class = "mspace" style = "margin-right:0.2778em;" > < / span > < / span > < span class = "base" > < span class = "strut" style = "height:0.5806em;vertical-align:-0.15em;" > < / span > < span class = "mord" > < span class = "mord mathnormal" > x< / span > < span class = "msupsub" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:0.1514em;" > < span style = "top:-2.55em;margin-left:0em;margin-right:0.05em;" > < span class = "pstrut" style = "height:2.7em;" > < / span > < span class = "sizing reset-size6 size3 mtight" > < span class = "mord mathnormal mtight" > m< / span > < / span > < / span > < / span > < span class = "vlist-s" > < / span > < / span > < span class = "vlist-r" > < span class = "vlist" style = "height:0.15em;" > < span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < / li >
< li dir = "auto" > < span class = "katex" > < span class = "katex-mathml" > < math xmlns = "http://www.w3.org/1998/Math/MathML" > < semantics > < mrow > < msub > < mi > x< / mi > < mi > m< / mi > < / msub > < mo > =< / mo > < mfrac > < msup > < msub > < mi > R< / mi > < mi > c< / mi > < / msub > < mn > 2< / mn > < / msup > < mrow > < msup > < msub > < mi > R< / mi > < mi > c< / mi > < / msub > < mn > 2< / mn > < / msup > < mo > +< / mo > < msup > < msub > < mi > X< / mi > < mi > m< / mi > < / msub > < mn > 2< / mn > < / msup > < / mrow > < / mfrac > < msub > < mi > X< / mi > < mi > m< / mi > < / msub > < mo > ≈< / mo > < mfrac > < menclose notation = "updiagonalstrike" > < msup > < msub > < mi > R< / mi > < mi > c< / mi > < / msub > < mn > 2< / mn > < / msup > < / menclose > < menclose notation = "updiagonalstrike" > < msup > < msub > < mi > R< / mi > < mi > c< / mi > < / msub > < mn > 2< / mn > < / msup > < / menclose > < / mfrac > < msub > < mi > X< / mi > < mi > m< / mi > < / msub > < mo > =< / mo > < msub > < mi > X< / mi > < mi > m< / mi > < / msub > < / mrow > < annotation encoding = "application/x-tex" > x_m=\frac{{R_c}^2}{{R_c}^2+{X_m}^2}X_m\approx\frac{\cancel{{R_c}^2}}{\cancel{{R_c}^2}}X_m=X_m< / annotation > < / semantics > < / math > < / span > < span class = "katex-html" aria-hidden = "true" > < span class = "base" > < span class = "strut" style = "height:0.5806em;vertical-align:-0.15em;" > < / span > < span class = "mord" > < span class = "mord mathnormal" > x< / span > < span class = "msupsub" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:0.1514em;" > < span style = "top:-2.55em;margin-left:0em;margin-right:0.05em;" > < span class = "pstrut" style = "height:2.7em;" > < / span > < span class = "sizing reset-size6 size3 mtight" > < span class = "mord mathnormal mtight" > m< / span > < / span > < / span > < / span > < span class = "vlist-s" > < / span > < / span > < span class = "vlist-r" > < span class = "vlist" style = "height:0.15em;" > < span > < / span > < / span > < / span > < / span > < / span > < / span > < span class = "mspace" style = "margin-right:0.2778em;" > < / span > < span class = "mrel" > =< / span > < span class = "mspace" style = "margin-right:0.2778em;" > < / span > < / span > < span class = "base" > < span class = "strut" style = "height:1.4977em;vertical-align:-0.4637em;" > < / span > < span class = "mord" > < span class = "mopen nulldelimiter" > < / span > < span class = "mfrac" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:1.034em;" > < span style = "top:-2.6364em;" > < span class = "pstrut" style = "height:3em;" > < / span > < span class = "sizing reset-size6 size3 mtight" > < span class = "mord mtight" > < span class = "mord mtight" > < span class = "mord mtight" > < span class = "mord mtight" > < span class = "mord mathnormal mtight" style = "margin-right:0.00773em;" > R< / span > < span class = "msupsub" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:0.1645em;" > < span style = "top:-2.357em;margin-left:-0.0077em;margin-right:0.0714em;" > < span class = "pstrut" style = "height:2.5em;" > < / span > < span class = "sizing reset-size3 size1 mtight" > < span class = "mord mathnormal mtight" > c< / span > < / span > < / span > < / span > < span class = "vlist-s" > < / span > < / span > < span class = "vlist-r" > < span class = "vlist" style = "height:0.143em;" > < span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < span class = "msupsub" > < span class = "vlist-t" > < span class = "vlist-r" > < span class = "vlist" style = "height:0.7908em;" > < span style = "top:-2.8305em;margin-right:0.0714em;" > < span class = "pstrut" style = "height:2.5em;" > < / span > < span class = "sizing reset-size3 size1 mtight" > < span class = "mord mtight" > 2< / span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < span class = "mbin mtight" > +< / span > < span class = "mord mtight" > < span class = "mord mtight" > < span class = "mord mtight" > < span class = "mord mathnormal mtight" style = "margin-right:0.07847em;" > X< / span > < span class = "msupsub" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:0.1645em;" > < span style = "top:-2.357em;margin-left:-0.0785em;margin-right:0.0714em;" > < span class = "pstrut" style = "height:2.5em;" > < / span > < span class = "sizing reset-size3 size1 mtight" > < span class = "mord mathnormal mtight" > m< / span > < / span > < / span > < / span > < span class = "vlist-s" > < / span > < / span > < span class = "vlist-r" > < span class = "vlist" style = "height:0.143em;" > < span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < span class = "msupsub" > < span class = "vlist-t" > < span class = "vlist-r" > < span class = "vlist" style = "height:0.7908em;" > < span style = "top:-2.8305em;margin-right:0.0714em;" > < span class = "pstrut" style = "height:2.5em;" > < / span > <
< / ul >
< / li >
< li dir = "auto" > < span class = "katex" > < span class = "katex-mathml" > < math xmlns = "http://www.w3.org/1998/Math/MathML" > < semantics > < mrow > < msub > < mi > r< / mi > < mi > c< / mi > < / msub > < mo > ≈< / mo > < msup > < msub > < mi > X< / mi > < mi > m< / mi > < / msub > < mn > 2< / mn > < / msup > < mi mathvariant = "normal" > /< / mi > < msub > < mi > R< / mi > < mi > c< / mi > < / msub > < / mrow > < annotation encoding = "application/x-tex" > r_c\approx {X_m}^2/R_c< / annotation > < / semantics > < / math > < / span > < span class = "katex-html" aria-hidden = "true" > < span class = "base" > < span class = "strut" style = "height:0.6331em;vertical-align:-0.15em;" > < / span > < span class = "mord" > < span class = "mord mathnormal" style = "margin-right:0.02778em;" > r< / span > < span class = "msupsub" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:0.1514em;" > < span style = "top:-2.55em;margin-left:-0.0278em;margin-right:0.05em;" > < span class = "pstrut" style = "height:2.7em;" > < / span > < span class = "sizing reset-size6 size3 mtight" > < span class = "mord mathnormal mtight" > c< / span > < / span > < / span > < / span > < span class = "vlist-s" > < / span > < / span > < span class = "vlist-r" > < span class = "vlist" style = "height:0.15em;" > < span > < / span > < / span > < / span > < / span > < / span > < / span > < span class = "mspace" style = "margin-right:0.2778em;" > < / span > < span class = "mrel" > ≈< / span > < span class = "mspace" style = "margin-right:0.2778em;" > < / span > < / span > < span class = "base" > < span class = "strut" style = "height:1.1373em;vertical-align:-0.25em;" > < / span > < span class = "mord" > < span class = "mord" > < span class = "mord" > < span class = "mord mathnormal" style = "margin-right:0.07847em;" > X< / span > < span class = "msupsub" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:0.1514em;" > < span style = "top:-2.55em;margin-left:-0.0785em;margin-right:0.05em;" > < span class = "pstrut" style = "height:2.7em;" > < / span > < span class = "sizing reset-size6 size3 mtight" > < span class = "mord mathnormal mtight" > m< / span > < / span > < / span > < / span > < span class = "vlist-s" > < / span > < / span > < span class = "vlist-r" > < span class = "vlist" style = "height:0.15em;" > < span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < span class = "msupsub" > < span class = "vlist-t" > < span class = "vlist-r" > < span class = "vlist" style = "height:0.8873em;" > < span style = "top:-3.1362em;margin-right:0.05em;" > < span class = "pstrut" style = "height:2.7em;" > < / span > < span class = "sizing reset-size6 size3 mtight" > < span class = "mord mtight" > 2< / span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < span class = "mord" > /< / span > < span class = "mord" > < span class = "mord mathnormal" style = "margin-right:0.00773em;" > R< / span > < span class = "msupsub" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:0.1514em;" > < span style = "top:-2.55em;margin-left:-0.0077em;margin-right:0.05em;" > < span class = "pstrut" style = "height:2.7em;" > < / span > < span class = "sizing reset-size6 size3 mtight" > < span class = "mord mathnormal mtight" > c< / span > < / span > < / span > < / span > < span class = "vlist-s" > < / span > < / span > < span class = "vlist-r" > < span class = "vlist" style = "height:0.15em;" > < span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < / span >
< ul dir = "auto" >
< li dir = "auto" > < span class = "katex" > < span class = "katex-mathml" > < math xmlns = "http://www.w3.org/1998/Math/MathML" > < semantics > < mrow > < msub > < mi > R< / mi > < mi > c< / mi > < / msub > < mo > ⋙< / mo > < msub > < mi > X< / mi > < mi > m< / mi > < / msub > < mo > ⇒< / mo > < msub > < mi > r< / mi > < mi > c< / mi > < / msub > < mo > ⋘< / mo > < msub > < mi > x< / mi > < mi > m< / mi > < / msub > < / mrow > < annotation encoding = "application/x-tex" > R_c\ggg X_m\Rightarrow r_c\lll x_m< / annotation > < / semantics > < / math > < / span > < span class = "katex-html" aria-hidden = "true" > < span class = "base" > < span class = "strut" style = "height:0.8333em;vertical-align:-0.15em;" > < / span > < span class = "mord" > < span class = "mord mathnormal" style = "margin-right:0.00773em;" > R< / span > < span class = "msupsub" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:0.1514em;" > < span style = "top:-2.55em;margin-left:-0.0077em;margin-right:0.05em;" > < span class = "pstrut" style = "height:2.7em;" > < / span > < span class = "sizing reset-size6 size3 mtight" > < span class = "mord mathnormal mtight" > c< / span > < / span > < / span > < / span > < span class = "vlist-s" > < / span > < / span > < span class = "vlist-r" > < span class = "vlist" style = "height:0.15em;" > < span > < / span > < / span > < / span > < / span > < / span > < / span > < span class = "mspace" style = "margin-right:0.2778em;" > < / span > < span class = "mrel amsrm" > ⋙< / span > < span class = "mspace" style = "margin-right:0.2778em;" > < / span > < / span > < span class = "base" > < span class = "strut" style = "height:0.8333em;vertical-align:-0.15em;" > < / span > < span class = "mord" > < span class = "mord mathnormal" style = "margin-right:0.07847em;" > X< / span > < span class = "msupsub" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:0.1514em;" > < span style = "top:-2.55em;margin-left:-0.0785em;margin-right:0.05em;" > < span class = "pstrut" style = "height:2.7em;" > < / span > < span class = "sizing reset-size6 size3 mtight" > < span class = "mord mathnormal mtight" > m< / span > < / span > < / span > < / span > < span class = "vlist-s" > < / span > < / span > < span class = "vlist-r" > < span class = "vlist" style = "height:0.15em;" > < span > < / span > < / span > < / span > < / span > < / span > < / span > < span class = "mspace" style = "margin-right:0.2778em;" > < / span > < span class = "mrel" > ⇒< / span > < span class = "mspace" style = "margin-right:0.2778em;" > < / span > < / span > < span class = "base" > < span class = "strut" style = "height:0.6999em;vertical-align:-0.15em;" > < / span > < span class = "mord" > < span class = "mord mathnormal" style = "margin-right:0.02778em;" > r< / span > < span class = "msupsub" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:0.1514em;" > < span style = "top:-2.55em;margin-left:-0.0278em;margin-right:0.05em;" > < span class = "pstrut" style = "height:2.7em;" > < / span > < span class = "sizing reset-size6 size3 mtight" > < span class = "mord mathnormal mtight" > c< / span > < / span > < / span > < / span > < span class = "vlist-s" > < / span > < / span > < span class = "vlist-r" > < span class = "vlist" style = "height:0.15em;" > < span > < / span > < / span > < / span > < / span > < / span > < / span > < span class = "mspace" style = "margin-right:0.2778em;" > < / span > < span class = "mrel amsrm" > ⋘< / span > < span class = "mspace" style = "margin-right:0.2778em;" > < / span > < / span > < span class = "base" > < span class = "strut" style = "height:0.5806em;vertical-align:-0.15em;" > < / span > < span class = "mord" > < span class = "mord mathnormal" > x< / span > < span class = "msupsub" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:0.1514em;" > < span style = "top:-2.55em;margin-left:0em;margin-right:0.05em;" > < span class = "pstrut" style = "height:2.7em;" > < / span > < span class = "sizing reset-size6 size3 mtight" > < span class = "mord mathnormal mtight" > m< / span > < / span > < / span > < / span > < span class = "vlist-s" > < / span > < / span > < span class = "vlist-r" > < span class = "vlist" style = "height:0.15em;" > < span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < / li >
< li dir = "auto" > < span class = "katex" > < span class = "katex-mathml" > < math xmlns = "http://www.w3.org/1998/Math/MathML" > < semantics > < mrow > < msub > < mi > r< / mi > < mi > c< / mi > < / msub > < mo > =< / mo > < mfrac > < msup > < msub > < mi > X< / mi > < mi > m< / mi > < / msub > < mn > 2< / mn > < / msup > < mrow > < msup > < msub > < mi > R< / mi > < mi > c< / mi > < / msub > < mn > 2< / mn > < / msup > < mo > +< / mo > < msup > < msub > < mi > X< / mi > < mi > m< / mi > < / msub > < mn > 2< / mn > < / msup > < / mrow > < / mfrac > < msub > < mi > R< / mi > < mi > c< / mi > < / msub > < mo > ≈< / mo > < mfrac > < msup > < msub > < mi > X< / mi > < mi > m< / mi > < / msub > < mn > 2< / mn > < / msup > < msup > < msub > < mi > R< / mi > < mi > c< / mi > < / msub > < mn > 2< / mn > < / msup > < / mfrac > < msub > < mi > R< / mi > < mi > c< / mi > < / msub > < mo > =< / mo > < mfrac > < msup > < msub > < mi > X< / mi > < mi > m< / mi > < / msub > < mn > 2< / mn > < / msup > < msub > < mi > R< / mi > < mi > c< / mi > < / msub > < / mfrac > < / mrow > < annotation encoding = "application/x-tex" > r_c=\frac{{X_m}^2}{{R_c}^2+{X_m}^2}R_c\approx\frac{{X_m}^2}{{R_c}^2}R_c=\frac{{X_m}^2}{R_c}< / annotation > < / semantics > < / math > < / span > < span class = "katex-html" aria-hidden = "true" > < span class = "base" > < span class = "strut" style = "height:0.5806em;vertical-align:-0.15em;" > < / span > < span class = "mord" > < span class = "mord mathnormal" style = "margin-right:0.02778em;" > r< / span > < span class = "msupsub" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:0.1514em;" > < span style = "top:-2.55em;margin-left:-0.0278em;margin-right:0.05em;" > < span class = "pstrut" style = "height:2.7em;" > < / span > < span class = "sizing reset-size6 size3 mtight" > < span class = "mord mathnormal mtight" > c< / span > < / span > < / span > < / span > < span class = "vlist-s" > < / span > < / span > < span class = "vlist-r" > < span class = "vlist" style = "height:0.15em;" > < span > < / span > < / span > < / span > < / span > < / span > < / span > < span class = "mspace" style = "margin-right:0.2778em;" > < / span > < span class = "mrel" > =< / span > < span class = "mspace" style = "margin-right:0.2778em;" > < / span > < / span > < span class = "base" > < span class = "strut" style = "height:1.4977em;vertical-align:-0.4637em;" > < / span > < span class = "mord" > < span class = "mopen nulldelimiter" > < / span > < span class = "mfrac" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:1.034em;" > < span style = "top:-2.6364em;" > < span class = "pstrut" style = "height:3em;" > < / span > < span class = "sizing reset-size6 size3 mtight" > < span class = "mord mtight" > < span class = "mord mtight" > < span class = "mord mtight" > < span class = "mord mtight" > < span class = "mord mathnormal mtight" style = "margin-right:0.00773em;" > R< / span > < span class = "msupsub" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:0.1645em;" > < span style = "top:-2.357em;margin-left:-0.0077em;margin-right:0.0714em;" > < span class = "pstrut" style = "height:2.5em;" > < / span > < span class = "sizing reset-size3 size1 mtight" > < span class = "mord mathnormal mtight" > c< / span > < / span > < / span > < / span > < span class = "vlist-s" > < / span > < / span > < span class = "vlist-r" > < span class = "vlist" style = "height:0.143em;" > < span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < span class = "msupsub" > < span class = "vlist-t" > < span class = "vlist-r" > < span class = "vlist" style = "height:0.7908em;" > < span style = "top:-2.8305em;margin-right:0.0714em;" > < span class = "pstrut" style = "height:2.5em;" > < / span > < span class = "sizing reset-size3 size1 mtight" > < span class = "mord mtight" > 2< / span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < span class = "mbin mtight" > +< / span > < span class = "mord mtight" > < span class = "mord mtight" > < span class = "mord mtight" > < span class = "mord mathnormal mtight" style = "margin-right:0.07847em;" > X< / span > < span class = "msupsub" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:0.1645em;" > < span style = "top:-2.357em;margin-left:-0.0785em;margin-right:0.0714em;" > < span class = "pstrut" style = "height:2.5em;" > < / span > < span class = "sizing reset-size3 size1 mtight" > < span class = "mord mathnormal mtight" > m< / span > < / span > < / span > < / span > < span class = "vlist-s" > < / span > < / span > < span class = "vlist-r" > < span class = "vlist" style = "height:0.143em;" > < span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < span class = "msupsub" > < span class = "vlist-t" > < span class = "vlist-r" > < span class = "vlist" style = "height:0.7908em;" > < span style = "top:-2.8305em;margin-right:0.0714em;" > < span class = "pstrut" style = "height:2.5em;"
< / ul >
< / li >
< / ul >
< h3 dir = "auto" id = "diagram-8" > Diagram< / h3 >
< div dir = "auto" > < / div >
< center > < img src = "2022-10-26-21-53-13.png" width = 400px > < / center >
< h3 dir = "auto" id = "dc-test-1" > DC test< / h3 >
< h4 dir = "auto" id = "delta-machine-1" > < span class = "katex" > < span class = "katex-mathml" > < math xmlns = "http://www.w3.org/1998/Math/MathML" > < semantics > < mrow > < mi mathvariant = "normal" > Δ< / mi > < / mrow > < annotation encoding = "application/x-tex" > \Delta< / annotation > < / semantics > < / math > < / span > < span class = "katex-html" aria-hidden = "true" > < span class = "base" > < span class = "strut" style = "height:0.6833em;" > < / span > < span class = "mord" > Δ< / span > < / span > < / span > < / span > machine< / h4 >
< p > < span class = "katex-display" > < span class = "katex" > < span class = "katex-mathml" > < math xmlns = "http://www.w3.org/1998/Math/MathML" display = "block" > < semantics > < mrow > < msub > < mi > R< / mi > < mi > s< / mi > < / msub > < mo > =< / mo > < mfrac > < mn > 3< / mn > < mn > 2< / mn > < / mfrac > < mo > ⋅< / mo > < mfrac > < msub > < mi > V< / mi > < mrow > < mtext > DC< / mtext > < mo separator = "true" > ,< / mo > < mn > 3< / mn > < mi > ϕ< / mi > < / mrow > < / msub > < msub > < mi > I< / mi > < mrow > < mtext > DC< / mtext > < mo separator = "true" > ,< / mo > < mn > 3< / mn > < mi > ϕ< / mi > < / mrow > < / msub > < / mfrac > < / mrow > < annotation encoding = "application/x-tex" > R_s=\frac{3}{2}\cdot\frac{V_{\text{DC},3\phi}}{I_{\text{DC},3\phi}}< / annotation > < / semantics > < / math > < / span > < span class = "katex-html" aria-hidden = "true" > < span class = "base" > < span class = "strut" style = "height:0.8333em;vertical-align:-0.15em;" > < / span > < span class = "mord" > < span class = "mord mathnormal" style = "margin-right:0.00773em;" > R< / span > < span class = "msupsub" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:0.1514em;" > < span style = "top:-2.55em;margin-left:-0.0077em;margin-right:0.05em;" > < span class = "pstrut" style = "height:2.7em;" > < / span > < span class = "sizing reset-size6 size3 mtight" > < span class = "mord mathnormal mtight" > s< / span > < / span > < / span > < / span > < span class = "vlist-s" > < / span > < / span > < span class = "vlist-r" > < span class = "vlist" style = "height:0.15em;" > < span > < / span > < / span > < / span > < / span > < / span > < / span > < span class = "mspace" style = "margin-right:0.2778em;" > < / span > < span class = "mrel" > =< / span > < span class = "mspace" style = "margin-right:0.2778em;" > < / span > < / span > < span class = "base" > < span class = "strut" style = "height:2.0074em;vertical-align:-0.686em;" > < / span > < span class = "mord" > < span class = "mopen nulldelimiter" > < / span > < span class = "mfrac" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:1.3214em;" > < span style = "top:-2.314em;" > < span class = "pstrut" style = "height:3em;" > < / span > < span class = "mord" > < span class = "mord" > 2< / span > < / span > < / span > < span style = "top:-3.23em;" > < span class = "pstrut" style = "height:3em;" > < / span > < span class = "frac-line" style = "border-bottom-width:0.04em;" > < / span > < / span > < span style = "top:-3.677em;" > < span class = "pstrut" style = "height:3em;" > < / span > < span class = "mord" > < span class = "mord" > 3< / span > < / span > < / span > < / span > < span class = "vlist-s" > < / span > < / span > < span class = "vlist-r" > < span class = "vlist" style = "height:0.686em;" > < span > < / span > < / span > < / span > < / span > < / span > < span class = "mclose nulldelimiter" > < / span > < / span > < span class = "mspace" style = "margin-right:0.2222em;" > < / span > < span class = "mbin" > ⋅< / span > < span class = "mspace" style = "margin-right:0.2222em;" > < / span > < / span > < span class = "base" > < span class = "strut" style = "height:2.3324em;vertical-align:-0.9721em;" > < / span > < span class = "mord" > < span class = "mopen nulldelimiter" > < / span > < span class = "mfrac" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:1.3603em;" > < span style = "top:-2.314em;" > < span class = "pstrut" style = "height:3em;" > < / span > < span class = "mord" > < span class = "mord" > < span class = "mord mathnormal" style = "margin-right:0.07847em;" > I< / span > < span class = "msupsub" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:0.3361em;" > < span style = "top:-2.55em;margin-left:-0.0785em;margin-right:0.05em;" > < span class = "pstrut" style = "height:2.7em;" > < / span > < span class = "sizing reset-size6 size3 mtight" > < span class = "mord mtight" > < span class = "mord text mtight" > < span class = "mord mtight" > DC< / span > < / span > < span class = "mpunct mtight" > ,< / span > < span class = "mord mtight" > 3< / span > < span class = "mord mathnormal mtight" > ϕ< / span > < / span > < / span > < / span > < / span > < span class = "vlist-s" > < / span > < / span > < span class = "vlist-r" > < span class = "vlist" style = "height:0.2861em;" > < span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < span style = "top:-3.23em;" > < span class = "pstrut" style = "height:3em;" > < / span > < span class = "frac-line" style = "border-bottom-width:0.04em;" > < / span > < / span > < span style = "top:-3.677em;" > < span class = "pstrut" style = "height:3em;" > < / span > < span class = "mord" > < span class = "mord" > < span class = "mord mathnormal" style = "margin-right:0.22222em;" > V< / span > < span class = "msupsub" > < span class = "vlist-t vlist-t2" > < s
< / math >
< div dir = "auto" > < / div >
< center > < img src = "2022-10-26-22-43-25.png" width = 400px > < / center >
< h4 dir = "auto" id = "y-machine-1" > Y machine< / h4 >
< p > < span class = "katex-display" > < span class = "katex" > < span class = "katex-mathml" > < math xmlns = "http://www.w3.org/1998/Math/MathML" display = "block" > < semantics > < mrow > < msub > < mi > R< / mi > < mi > s< / mi > < / msub > < mo > =< / mo > < mfrac > < mn > 1< / mn > < mn > 2< / mn > < / mfrac > < mo > ⋅< / mo > < mfrac > < msub > < mi > V< / mi > < mrow > < mtext > DC< / mtext > < mo separator = "true" > ,< / mo > < mn > 3< / mn > < mi > ϕ< / mi > < / mrow > < / msub > < msub > < mi > I< / mi > < mrow > < mtext > DC< / mtext > < mo separator = "true" > ,< / mo > < mn > 3< / mn > < mi > ϕ< / mi > < / mrow > < / msub > < / mfrac > < / mrow > < annotation encoding = "application/x-tex" > R_s=\frac{1}{2}\cdot\frac{V_{\text{DC},3\phi}}{I_{\text{DC},3\phi}}< / annotation > < / semantics > < / math > < / span > < span class = "katex-html" aria-hidden = "true" > < span class = "base" > < span class = "strut" style = "height:0.8333em;vertical-align:-0.15em;" > < / span > < span class = "mord" > < span class = "mord mathnormal" style = "margin-right:0.00773em;" > R< / span > < span class = "msupsub" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:0.1514em;" > < span style = "top:-2.55em;margin-left:-0.0077em;margin-right:0.05em;" > < span class = "pstrut" style = "height:2.7em;" > < / span > < span class = "sizing reset-size6 size3 mtight" > < span class = "mord mathnormal mtight" > s< / span > < / span > < / span > < / span > < span class = "vlist-s" > < / span > < / span > < span class = "vlist-r" > < span class = "vlist" style = "height:0.15em;" > < span > < / span > < / span > < / span > < / span > < / span > < / span > < span class = "mspace" style = "margin-right:0.2778em;" > < / span > < span class = "mrel" > =< / span > < span class = "mspace" style = "margin-right:0.2778em;" > < / span > < / span > < span class = "base" > < span class = "strut" style = "height:2.0074em;vertical-align:-0.686em;" > < / span > < span class = "mord" > < span class = "mopen nulldelimiter" > < / span > < span class = "mfrac" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:1.3214em;" > < span style = "top:-2.314em;" > < span class = "pstrut" style = "height:3em;" > < / span > < span class = "mord" > < span class = "mord" > 2< / span > < / span > < / span > < span style = "top:-3.23em;" > < span class = "pstrut" style = "height:3em;" > < / span > < span class = "frac-line" style = "border-bottom-width:0.04em;" > < / span > < / span > < span style = "top:-3.677em;" > < span class = "pstrut" style = "height:3em;" > < / span > < span class = "mord" > < span class = "mord" > 1< / span > < / span > < / span > < / span > < span class = "vlist-s" > < / span > < / span > < span class = "vlist-r" > < span class = "vlist" style = "height:0.686em;" > < span > < / span > < / span > < / span > < / span > < / span > < span class = "mclose nulldelimiter" > < / span > < / span > < span class = "mspace" style = "margin-right:0.2222em;" > < / span > < span class = "mbin" > ⋅< / span > < span class = "mspace" style = "margin-right:0.2222em;" > < / span > < / span > < span class = "base" > < span class = "strut" style = "height:2.3324em;vertical-align:-0.9721em;" > < / span > < span class = "mord" > < span class = "mopen nulldelimiter" > < / span > < span class = "mfrac" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:1.3603em;" > < span style = "top:-2.314em;" > < span class = "pstrut" style = "height:3em;" > < / span > < span class = "mord" > < span class = "mord" > < span class = "mord mathnormal" style = "margin-right:0.07847em;" > I< / span > < span class = "msupsub" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:0.3361em;" > < span style = "top:-2.55em;margin-left:-0.0785em;margin-right:0.05em;" > < span class = "pstrut" style = "height:2.7em;" > < / span > < span class = "sizing reset-size6 size3 mtight" > < span class = "mord mtight" > < span class = "mord text mtight" > < span class = "mord mtight" > DC< / span > < / span > < span class = "mpunct mtight" > ,< / span > < span class = "mord mtight" > 3< / span > < span class = "mord mathnormal mtight" > ϕ< / span > < / span > < / span > < / span > < / span > < span class = "vlist-s" > < / span > < / span > < span class = "vlist-r" > < span class = "vlist" style = "height:0.2861em;" > < span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < span style = "top:-3.23em;" > < span class = "pstrut" style = "height:3em;" > < / span > < span class = "frac-line" style = "border-bottom-width:0.04em;" > < / span > < / span > < span style = "top:-3.677em;" > < span class = "pstrut" style = "height:3em;" > < / span > < span class = "mord" > < span class = "mord" > < span class = "mord mathnormal" style = "margin-right:0.22222em;" > V< / span > < span class = "msupsub" > < span class = "vlist-t vlist-t2" > < s
< / math >
< div dir = "auto" > < / div >
< center > < img src = "2022-10-26-22-48-09.png" width = 400px > < / center >
< h3 dir = "auto" id = "no-load-test-1" > No-load test< / h3 >
< h4 dir = "auto" id = "assumptions-4" > Assumptions< / h4 >
< ul dir = "auto" >
< li dir = "auto" > < span class = "katex" > < span class = "katex-mathml" > < math xmlns = "http://www.w3.org/1998/Math/MathML" > < semantics > < mrow > < msub > < mi > P< / mi > < mtext > out< / mtext > < / msub > < mo > =< / mo > < mn > 0< / mn > < / mrow > < annotation encoding = "application/x-tex" > P_\text{out}=0< / annotation > < / semantics > < / math > < / span > < span class = "katex-html" aria-hidden = "true" > < span class = "base" > < span class = "strut" style = "height:0.8333em;vertical-align:-0.15em;" > < / span > < span class = "mord" > < span class = "mord mathnormal" style = "margin-right:0.13889em;" > P< / span > < span class = "msupsub" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:0.2806em;" > < span style = "top:-2.55em;margin-left:-0.1389em;margin-right:0.05em;" > < span class = "pstrut" style = "height:2.7em;" > < / span > < span class = "sizing reset-size6 size3 mtight" > < span class = "mord text mtight" > < span class = "mord mtight" > out< / span > < / span > < / span > < / span > < / span > < span class = "vlist-s" > < / span > < / span > < span class = "vlist-r" > < span class = "vlist" style = "height:0.15em;" > < span > < / span > < / span > < / span > < / span > < / span > < / span > < span class = "mspace" style = "margin-right:0.2778em;" > < / span > < span class = "mrel" > =< / span > < span class = "mspace" style = "margin-right:0.2778em;" > < / span > < / span > < span class = "base" > < span class = "strut" style = "height:0.6444em;" > < / span > < span class = "mord" > 0< / span > < / span > < / span > < / span >
< ul dir = "auto" >
< li dir = "auto" > No output power as no load.< / li >
< / ul >
< / li >
< li dir = "auto" > < span class = "katex" > < span class = "katex-mathml" > < math xmlns = "http://www.w3.org/1998/Math/MathML" > < semantics > < mrow > < msub > < mi > R< / mi > < mi > r< / mi > < / msub > < mi mathvariant = "normal" > /< / mi > < mi > s< / mi > < mo > =< / mo > < mi mathvariant = "normal" > ∞< / mi > < / mrow > < annotation encoding = "application/x-tex" > R_r/s=\infty< / annotation > < / semantics > < / math > < / span > < span class = "katex-html" aria-hidden = "true" > < span class = "base" > < span class = "strut" style = "height:1em;vertical-align:-0.25em;" > < / span > < span class = "mord" > < span class = "mord mathnormal" style = "margin-right:0.00773em;" > R< / span > < span class = "msupsub" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:0.1514em;" > < span style = "top:-2.55em;margin-left:-0.0077em;margin-right:0.05em;" > < span class = "pstrut" style = "height:2.7em;" > < / span > < span class = "sizing reset-size6 size3 mtight" > < span class = "mord mathnormal mtight" style = "margin-right:0.02778em;" > r< / span > < / span > < / span > < / span > < span class = "vlist-s" > < / span > < / span > < span class = "vlist-r" > < span class = "vlist" style = "height:0.15em;" > < span > < / span > < / span > < / span > < / span > < / span > < / span > < span class = "mord" > /< / span > < span class = "mord mathnormal" > s< / span > < span class = "mspace" style = "margin-right:0.2778em;" > < / span > < span class = "mrel" > =< / span > < span class = "mspace" style = "margin-right:0.2778em;" > < / span > < / span > < span class = "base" > < span class = "strut" style = "height:0.4306em;" > < / span > < span class = "mord" > ∞< / span > < / span > < / span > < / span > and < span class = "katex" > < span class = "katex-mathml" > < math xmlns = "http://www.w3.org/1998/Math/MathML" > < semantics > < mrow > < msub > < mi > I< / mi > < mi > r< / mi > < / msub > < mo > =< / mo > < mn > 0< / mn > < / mrow > < annotation encoding = "application/x-tex" > I_r=0< / annotation > < / semantics > < / math > < / span > < span class = "katex-html" aria-hidden = "true" > < span class = "base" > < span class = "strut" style = "height:0.8333em;vertical-align:-0.15em;" > < / span > < span class = "mord" > < span class = "mord mathnormal" style = "margin-right:0.07847em;" > I< / span > < span class = "msupsub" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:0.1514em;" > < span style = "top:-2.55em;margin-left:-0.0785em;margin-right:0.05em;" > < span class = "pstrut" style = "height:2.7em;" > < / span > < span class = "sizing reset-size6 size3 mtight" > < span class = "mord mathnormal mtight" style = "margin-right:0.02778em;" > r< / span > < / span > < / span > < / span > < span class = "vlist-s" > < / span > < / span > < span class = "vlist-r" > < span class = "vlist" style = "height:0.15em;" > < span > < / span > < / span > < / span > < / span > < / span > < / span > < span class = "mspace" style = "margin-right:0.2778em;" > < / span > < span class = "mrel" > =< / span > < span class = "mspace" style = "margin-right:0.2778em;" > < / span > < / span > < span class = "base" > < span class = "strut" style = "height:0.6444em;" > < / span > < span class = "mord" > 0< / span > < / span > < / span > < / span >
< ul dir = "auto" >
< li dir = "auto" > Infinite rotor resistance, ignore rotor path.< / li >
< / ul >
< / li >
< / ul >
< h4 dir = "auto" id = "diagram-9" > Diagram< / h4 >
< p dir = "auto" > Using assumptions, remove rotor part of circuit and only consider stator and magnetizing path.< / p >
< div dir = "auto" > < / div >
< center > < img src = "2022-10-25-11-45-26.png" width = 400px > < / center >
< h3 dir = "auto" id = "blocked-rotor-test-1" > Blocked rotor test< / h3 >
< h4 dir = "auto" id = "assumptions-5" > Assumptions< / h4 >
< ul dir = "auto" >
< li dir = "auto" > Ignore magnetizing path, < span class = "katex" > < span class = "katex-mathml" > < math xmlns = "http://www.w3.org/1998/Math/MathML" > < semantics > < mrow > < msub > < mi > I< / mi > < mi > m< / mi > < / msub > < mo > =< / mo > < mn > 0< / mn > < / mrow > < annotation encoding = "application/x-tex" > I_m=0< / annotation > < / semantics > < / math > < / span > < span class = "katex-html" aria-hidden = "true" > < span class = "base" > < span class = "strut" style = "height:0.8333em;vertical-align:-0.15em;" > < / span > < span class = "mord" > < span class = "mord mathnormal" style = "margin-right:0.07847em;" > I< / span > < span class = "msupsub" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:0.1514em;" > < span style = "top:-2.55em;margin-left:-0.0785em;margin-right:0.05em;" > < span class = "pstrut" style = "height:2.7em;" > < / span > < span class = "sizing reset-size6 size3 mtight" > < span class = "mord mathnormal mtight" > m< / span > < / span > < / span > < / span > < span class = "vlist-s" > < / span > < / span > < span class = "vlist-r" > < span class = "vlist" style = "height:0.15em;" > < span > < / span > < / span > < / span > < / span > < / span > < / span > < span class = "mspace" style = "margin-right:0.2778em;" > < / span > < span class = "mrel" > =< / span > < span class = "mspace" style = "margin-right:0.2778em;" > < / span > < / span > < span class = "base" > < span class = "strut" style = "height:0.6444em;" > < / span > < span class = "mord" > 0< / span > < / span > < / span > < / span >
< ul dir = "auto" >
< li dir = "auto" > < span class = "katex" > < span class = "katex-mathml" > < math xmlns = "http://www.w3.org/1998/Math/MathML" > < semantics > < mrow > < msub > < mi > I< / mi > < mi > r< / mi > < / msub > < mo > ⋙< / mo > < msub > < mi > I< / mi > < mi > m< / mi > < / msub > < / mrow > < annotation encoding = "application/x-tex" > I_r\ggg I_m< / annotation > < / semantics > < / math > < / span > < span class = "katex-html" aria-hidden = "true" > < span class = "base" > < span class = "strut" style = "height:0.8333em;vertical-align:-0.15em;" > < / span > < span class = "mord" > < span class = "mord mathnormal" style = "margin-right:0.07847em;" > I< / span > < span class = "msupsub" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:0.1514em;" > < span style = "top:-2.55em;margin-left:-0.0785em;margin-right:0.05em;" > < span class = "pstrut" style = "height:2.7em;" > < / span > < span class = "sizing reset-size6 size3 mtight" > < span class = "mord mathnormal mtight" style = "margin-right:0.02778em;" > r< / span > < / span > < / span > < / span > < span class = "vlist-s" > < / span > < / span > < span class = "vlist-r" > < span class = "vlist" style = "height:0.15em;" > < span > < / span > < / span > < / span > < / span > < / span > < / span > < span class = "mspace" style = "margin-right:0.2778em;" > < / span > < span class = "mrel amsrm" > ⋙< / span > < span class = "mspace" style = "margin-right:0.2778em;" > < / span > < / span > < span class = "base" > < span class = "strut" style = "height:0.8333em;vertical-align:-0.15em;" > < / span > < span class = "mord" > < span class = "mord mathnormal" style = "margin-right:0.07847em;" > I< / span > < span class = "msupsub" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:0.1514em;" > < span style = "top:-2.55em;margin-left:-0.0785em;margin-right:0.05em;" > < span class = "pstrut" style = "height:2.7em;" > < / span > < span class = "sizing reset-size6 size3 mtight" > < span class = "mord mathnormal mtight" > m< / span > < / span > < / span > < / span > < span class = "vlist-s" > < / span > < / span > < span class = "vlist-r" > < span class = "vlist" style = "height:0.15em;" > < span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > as < span class = "katex" > < span class = "katex-mathml" > < math xmlns = "http://www.w3.org/1998/Math/MathML" > < semantics > < mrow > < msub > < mi > R< / mi > < mi > r< / mi > < / msub > < mi mathvariant = "normal" > /< / mi > < mi > s< / mi > < mo > ⋙< / mo > < msub > < mi > Z< / mi > < mi > m< / mi > < / msub > < / mrow > < annotation encoding = "application/x-tex" > R_r/s\ggg Z_m< / annotation > < / semantics > < / math > < / span > < span class = "katex-html" aria-hidden = "true" > < span class = "base" > < span class = "strut" style = "height:1em;vertical-align:-0.25em;" > < / span > < span class = "mord" > < span class = "mord mathnormal" style = "margin-right:0.00773em;" > R< / span > < span class = "msupsub" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:0.1514em;" > < span style = "top:-2.55em;margin-left:-0.0077em;margin-right:0.05em;" > < span class = "pstrut" style = "height:2.7em;" > < / span > < span class = "sizing reset-size6 size3 mtight" > < span class = "mord mathnormal mtight" style = "margin-right:0.02778em;" > r< / span > < / span > < / span > < / span > < span class = "vlist-s" > < / span > < / span > < span class = "vlist-r" > < span class = "vlist" style = "height:0.15em;" > < span > < / span > < / span > < / span > < / span > < / span > < / span > < span class = "mord" > /< / span > < span class = "mord mathnormal" > s< / span > < span class = "mspace" style = "margin-right:0.2778em;" > < / span > < span class = "mrel amsrm" > ⋙< / span > < span class = "mspace" style = "margin-right:0.2778em;" > < / span > < / span > < span class = "base" > < span class = "strut" style = "height:0.8333em;vertical-align:-0.15em;" > < / span > < span class = "mord" > < span class = "mord mathnormal" style = "margin-right:0.07153em;" > Z< / span > < span class = "msupsub" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:0.1514em;" > < span style = "top:-2.55em;margin-left:-0.0715em;margin-right:0.05em;" > < span class = "pstrut" style = "height:2.7em;" > < / span > < span class = "sizing reset-size6 size3 mtight" > < span class = "mord mathnormal mtight" > m< / span > < / span > < / span > < / span > < span class = "vlist-s" > < / span > < / span > < span class = "vlist-r" > < span class = "vlist" style = "height:0.15em;" > < span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < / li >
< / ul >
< / li >
< li dir = "auto" > < span class = "katex" > < span class = "katex-mathml" > < math xmlns = "http://www.w3.org/1998/Math/MathML" > < semantics > < mrow > < msub > < mi > R< / mi > < mi > r< / mi > < / msub > < mi mathvariant = "normal" > /< / mi > < mi > s< / mi > < mo > =< / mo > < msub > < mi > R< / mi > < mi > r< / mi > < / msub > < / mrow > < annotation encoding = "application/x-tex" > R_r/s=R_r< / annotation > < / semantics > < / math > < / span > < span class = "katex-html" aria-hidden = "true" > < span class = "base" > < span class = "strut" style = "height:1em;vertical-align:-0.25em;" > < / span > < span class = "mord" > < span class = "mord mathnormal" style = "margin-right:0.00773em;" > R< / span > < span class = "msupsub" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:0.1514em;" > < span style = "top:-2.55em;margin-left:-0.0077em;margin-right:0.05em;" > < span class = "pstrut" style = "height:2.7em;" > < / span > < span class = "sizing reset-size6 size3 mtight" > < span class = "mord mathnormal mtight" style = "margin-right:0.02778em;" > r< / span > < / span > < / span > < / span > < span class = "vlist-s" > < / span > < / span > < span class = "vlist-r" > < span class = "vlist" style = "height:0.15em;" > < span > < / span > < / span > < / span > < / span > < / span > < / span > < span class = "mord" > /< / span > < span class = "mord mathnormal" > s< / span > < span class = "mspace" style = "margin-right:0.2778em;" > < / span > < span class = "mrel" > =< / span > < span class = "mspace" style = "margin-right:0.2778em;" > < / span > < / span > < span class = "base" > < span class = "strut" style = "height:0.8333em;vertical-align:-0.15em;" > < / span > < span class = "mord" > < span class = "mord mathnormal" style = "margin-right:0.00773em;" > R< / span > < span class = "msupsub" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:0.1514em;" > < span style = "top:-2.55em;margin-left:-0.0077em;margin-right:0.05em;" > < span class = "pstrut" style = "height:2.7em;" > < / span > < span class = "sizing reset-size6 size3 mtight" > < span class = "mord mathnormal mtight" style = "margin-right:0.02778em;" > r< / span > < / span > < / span > < / span > < span class = "vlist-s" > < / span > < / span > < span class = "vlist-r" > < span class = "vlist" style = "height:0.15em;" > < span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > , < span class = "katex" > < span class = "katex-mathml" > < math xmlns = "http://www.w3.org/1998/Math/MathML" > < semantics > < mrow > < mi > s< / mi > < mo > =< / mo > < mn > 1< / mn > < / mrow > < annotation encoding = "application/x-tex" > s=1< / annotation > < / semantics > < / math > < / span > < span class = "katex-html" aria-hidden = "true" > < span class = "base" > < span class = "strut" style = "height:0.4306em;" > < / span > < span class = "mord mathnormal" > s< / span > < span class = "mspace" style = "margin-right:0.2778em;" > < / span > < span class = "mrel" > =< / span > < span class = "mspace" style = "margin-right:0.2778em;" > < / span > < / span > < span class = "base" > < span class = "strut" style = "height:0.6444em;" > < / span > < span class = "mord" > 1< / span > < / span > < / span > < / span >
< ul dir = "auto" >
< li dir = "auto" > Slip is < span class = "katex" > < span class = "katex-mathml" > < math xmlns = "http://www.w3.org/1998/Math/MathML" > < semantics > < mrow > < mn > 1< / mn > < / mrow > < annotation encoding = "application/x-tex" > 1< / annotation > < / semantics > < / math > < / span > < span class = "katex-html" aria-hidden = "true" > < span class = "base" > < span class = "strut" style = "height:0.6444em;" > < / span > < span class = "mord" > 1< / span > < / span > < / span > < / span > as rotor is blocked.< / li >
< / ul >
< / li >
< li dir = "auto" > < span class = "katex" > < span class = "katex-mathml" > < math xmlns = "http://www.w3.org/1998/Math/MathML" > < semantics > < mrow > < msub > < mi > x< / mi > < mi > s< / mi > < / msub > < mo > =< / mo > < msubsup > < mi > x< / mi > < mi > r< / mi > < mo mathvariant = "normal" lspace = "0em" rspace = "0em" > ′ < / mo > < / msubsup > < / mrow > < annotation encoding = "application/x-tex" > x_s=x_r' < / annotation > < / semantics > < / math > < / span > < span class = "katex-html" aria-hidden = "true" > < span class = "base" > < span class = "strut" style = "height:0.5806em;vertical-align:-0.15em;" > < / span > < span class = "mord" > < span class = "mord mathnormal" > x< / span > < span class = "msupsub" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:0.1514em;" > < span style = "top:-2.55em;margin-left:0em;margin-right:0.05em;" > < span class = "pstrut" style = "height:2.7em;" > < / span > < span class = "sizing reset-size6 size3 mtight" > < span class = "mord mathnormal mtight" > s< / span > < / span > < / span > < / span > < span class = "vlist-s" > < / span > < / span > < span class = "vlist-r" > < span class = "vlist" style = "height:0.15em;" > < span > < / span > < / span > < / span > < / span > < / span > < / span > < span class = "mspace" style = "margin-right:0.2778em;" > < / span > < span class = "mrel" > =< / span > < span class = "mspace" style = "margin-right:0.2778em;" > < / span > < / span > < span class = "base" > < span class = "strut" style = "height:0.9989em;vertical-align:-0.247em;" > < / span > < span class = "mord" > < span class = "mord mathnormal" > x< / span > < span class = "msupsub" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:0.7519em;" > < span style = "top:-2.453em;margin-left:0em;margin-right:0.05em;" > < span class = "pstrut" style = "height:2.7em;" > < / span > < span class = "sizing reset-size6 size3 mtight" > < span class = "mord mathnormal mtight" style = "margin-right:0.02778em;" > r< / span > < / span > < / span > < span style = "top:-3.063em;margin-right:0.05em;" > < span class = "pstrut" style = "height:2.7em;" > < / span > < span class = "sizing reset-size6 size3 mtight" > < span class = "mord mtight" > < span class = "mord mtight" > ′ < / span > < / span > < / span > < / span > < / span > < span class = "vlist-s" > < / span > < / span > < span class = "vlist-r" > < span class = "vlist" style = "height:0.247em;" > < span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < / span >
< ul dir = "auto" >
< li dir = "auto" > Same number of turns in stator and rotor< / li >
< / ul >
< / li >
< li dir = "auto" > and < span class = "katex" > < span class = "katex-mathml" > < math xmlns = "http://www.w3.org/1998/Math/MathML" > < semantics > < mrow > < msub > < mi > x< / mi > < mi > r< / mi > < / msub > < mo > =< / mo > < msub > < mi > f< / mi > < mn > 0< / mn > < / msub > < mi mathvariant = "normal" > /< / mi > < msub > < mi > f< / mi > < mtext > BL< / mtext > < / msub > < mo > × < / mo > < msubsup > < mi > x< / mi > < mi > r< / mi > < mo mathvariant = "normal" lspace = "0em" rspace = "0em" > ′ < / mo > < / msubsup > < / mrow > < annotation encoding = "application/x-tex" > x_r=f_0/f_\text{BL} \times x_r' < / annotation > < / semantics > < / math > < / span > < span class = "katex-html" aria-hidden = "true" > < span class = "base" > < span class = "strut" style = "height:0.5806em;vertical-align:-0.15em;" > < / span > < span class = "mord" > < span class = "mord mathnormal" > x< / span > < span class = "msupsub" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:0.1514em;" > < span style = "top:-2.55em;margin-left:0em;margin-right:0.05em;" > < span class = "pstrut" style = "height:2.7em;" > < / span > < span class = "sizing reset-size6 size3 mtight" > < span class = "mord mathnormal mtight" style = "margin-right:0.02778em;" > r< / span > < / span > < / span > < / span > < span class = "vlist-s" > < / span > < / span > < span class = "vlist-r" > < span class = "vlist" style = "height:0.15em;" > < span > < / span > < / span > < / span > < / span > < / span > < / span > < span class = "mspace" style = "margin-right:0.2778em;" > < / span > < span class = "mrel" > =< / span > < span class = "mspace" style = "margin-right:0.2778em;" > < / span > < / span > < span class = "base" > < span class = "strut" style = "height:1em;vertical-align:-0.25em;" > < / span > < span class = "mord" > < span class = "mord mathnormal" style = "margin-right:0.10764em;" > f< / span > < span class = "msupsub" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:0.3011em;" > < span style = "top:-2.55em;margin-left:-0.1076em;margin-right:0.05em;" > < span class = "pstrut" style = "height:2.7em;" > < / span > < span class = "sizing reset-size6 size3 mtight" > < span class = "mord mtight" > 0< / span > < / span > < / span > < / span > < span class = "vlist-s" > < / span > < / span > < span class = "vlist-r" > < span class = "vlist" style = "height:0.15em;" > < span > < / span > < / span > < / span > < / span > < / span > < / span > < span class = "mord" > /< / span > < span class = "mord" > < span class = "mord mathnormal" style = "margin-right:0.10764em;" > f< / span > < span class = "msupsub" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:0.3283em;" > < span style = "top:-2.55em;margin-left:-0.1076em;margin-right:0.05em;" > < span class = "pstrut" style = "height:2.7em;" > < / span > < span class = "sizing reset-size6 size3 mtight" > < span class = "mord text mtight" > < span class = "mord mtight" > BL< / span > < / span > < / span > < / span > < / span > < span class = "vlist-s" > < / span > < / span > < span class = "vlist-r" > < span class = "vlist" style = "height:0.15em;" > < span > < / span > < / span > < / span > < / span > < / span > < / span > < span class = "mspace" style = "margin-right:0.2222em;" > < / span > < span class = "mbin" > × < / span > < span class = "mspace" style = "margin-right:0.2222em;" > < / span > < / span > < span class = "base" > < span class = "strut" style = "height:0.9989em;vertical-align:-0.247em;" > < / span > < span class = "mord" > < span class = "mord mathnormal" > x< / span > < span class = "msupsub" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:0.7519em;" > < span style = "top:-2.453em;margin-left:0em;margin-right:0.05em;" > < span class = "pstrut" style = "height:2.7em;" > < / span > < span class = "sizing reset-size6 size3 mtight" > < span class = "mord mathnormal mtight" style = "margin-right:0.02778em;" > r< / span > < / span > < / span > < span style = "top:-3.063em;margin-right:0.05em;" > < span class = "pstrut" style = "height:2.7em;" > < / span > < span class = "sizing reset-size6 size3 mtight" > < span class = "mord mtight" > < span class = "mord mtight" > ′ < / span > < / span > < / span > < / span > < / span > < span class = "vlist-s" > < / span > < / span > < span class = "vlist-r" > < span class = "vlist" style = "height:0.247em;" > < span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < / span >
< ul dir = "auto" >
< li dir = "auto" > Note: < span class = "katex" > < span class = "katex-mathml" > < math xmlns = "http://www.w3.org/1998/Math/MathML" > < semantics > < mrow > < msubsup > < mi > x< / mi > < mi > r< / mi > < mo mathvariant = "normal" lspace = "0em" rspace = "0em" > ′ < / mo > < / msubsup > < / mrow > < annotation encoding = "application/x-tex" > x_r' < / annotation > < / semantics > < / math > < / span > < span class = "katex-html" aria-hidden = "true" > < span class = "base" > < span class = "strut" style = "height:0.9989em;vertical-align:-0.247em;" > < / span > < span class = "mord" > < span class = "mord mathnormal" > x< / span > < span class = "msupsub" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:0.7519em;" > < span style = "top:-2.453em;margin-left:0em;margin-right:0.05em;" > < span class = "pstrut" style = "height:2.7em;" > < / span > < span class = "sizing reset-size6 size3 mtight" > < span class = "mord mathnormal mtight" style = "margin-right:0.02778em;" > r< / span > < / span > < / span > < span style = "top:-3.063em;margin-right:0.05em;" > < span class = "pstrut" style = "height:2.7em;" > < / span > < span class = "sizing reset-size6 size3 mtight" > < span class = "mord mtight" > < span class = "mord mtight" > ′ < / span > < / span > < / span > < / span > < / span > < span class = "vlist-s" > < / span > < / span > < span class = "vlist-r" > < span class = "vlist" style = "height:0.247em;" > < span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > is the inductance at < span class = "katex" > < span class = "katex-mathml" > < math xmlns = "http://www.w3.org/1998/Math/MathML" > < semantics > < mrow > < msub > < mi > f< / mi > < mtext > BL< / mtext > < / msub > < / mrow > < annotation encoding = "application/x-tex" > f_\text{BL}< / annotation > < / semantics > < / math > < / span > < span class = "katex-html" aria-hidden = "true" > < span class = "base" > < span class = "strut" style = "height:0.8889em;vertical-align:-0.1944em;" > < / span > < span class = "mord" > < span class = "mord mathnormal" style = "margin-right:0.10764em;" > f< / span > < span class = "msupsub" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:0.3283em;" > < span style = "top:-2.55em;margin-left:-0.1076em;margin-right:0.05em;" > < span class = "pstrut" style = "height:2.7em;" > < / span > < span class = "sizing reset-size6 size3 mtight" > < span class = "mord text mtight" > < span class = "mord mtight" > BL< / span > < / span > < / span > < / span > < / span > < span class = "vlist-s" > < / span > < / span > < span class = "vlist-r" > < span class = "vlist" style = "height:0.15em;" > < span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > , the blocked rotor test frequency which is less than the nominal frequency < span class = "katex" > < span class = "katex-mathml" > < math xmlns = "http://www.w3.org/1998/Math/MathML" > < semantics > < mrow > < msub > < mi > f< / mi > < mn > 0< / mn > < / msub > < / mrow > < annotation encoding = "application/x-tex" > f_0< / annotation > < / semantics > < / math > < / span > < span class = "katex-html" aria-hidden = "true" > < span class = "base" > < span class = "strut" style = "height:0.8889em;vertical-align:-0.1944em;" > < / span > < span class = "mord" > < span class = "mord mathnormal" style = "margin-right:0.10764em;" > f< / span > < span class = "msupsub" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:0.3011em;" > < span style = "top:-2.55em;margin-left:-0.1076em;margin-right:0.05em;" > < span class = "pstrut" style = "height:2.7em;" > < / span > < span class = "sizing reset-size6 size3 mtight" > < span class = "mord mtight" > 0< / span > < / span > < / span > < / span > < span class = "vlist-s" > < / span > < / span > < span class = "vlist-r" > < span class = "vlist" style = "height:0.15em;" > < span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < / li >
< / ul >
< / li >
< / ul >
< h4 dir = "auto" id = "diagram-10" > Diagram< / h4 >
< p dir = "auto" > Ignore magnetizing path< / p >
< div dir = "auto" > < / div >
< center > < img src = "2022-10-25-11-46-04.png" width = 400px > < / center >
< hr dir = "auto" >
< h2 dir = "auto" id = "single-phase-induction-motor-1" > Single-phase induction motor< / h2 >
< h3 dir = "auto" id = "diagram-11" > Diagram< / h3 >
< div dir = "auto" > < / div >
< center > < img src = "2022-10-26-21-47-29.png" width = 400px > < / center >
< h3 dir = "auto" id = "blocked-rotor-1" > Blocked-rotor< / h3 >
< h4 dir = "auto" id = "diagram-12" > Diagram< / h4 >
< div dir = "auto" > < / div >
< center > < img src = "2022-10-26-21-48-00.png" width = 400px > < / center >
< h3 dir = "auto" id = "no-load-1" > No-load< / h3 >
< h4 dir = "auto" id = "diagram-13" > Diagram< / h4 >
< div dir = "auto" > < / div >
< center > < img src = "2022-10-26-21-47-49.png" width = 400px > < / center >
< h2 dir = "auto" id = "synchronous-machine-1" > Synchronous machine< / h2 >
< h3 dir = "auto" id = "etc-5" > Etc< / h3 >
< p > < span class = "katex-display" > < span class = "katex" > < span class = "katex-mathml" > < math xmlns = "http://www.w3.org/1998/Math/MathML" display = "block" > < semantics > < mrow > < msub > < mi > E< / mi > < mi > A< / mi > < / msub > < mo > =< / mo > < msub > < mi > V< / mi > < mrow > < mn > 1< / mn > < mi > ϕ< / mi > < / mrow > < / msub > < mo > − < / mo > < msub > < mi > I< / mi > < mi > A< / mi > < / msub > < mo stretchy = "false" > (< / mo > < msub > < mi > R< / mi > < mi > A< / mi > < / msub > < mo > +< / mo > < mi > j< / mi > < msub > < mi > X< / mi > < mi > s< / mi > < / msub > < mo stretchy = "false" > )< / mo > < / mrow > < annotation encoding = "application/x-tex" > E_A=V_{1\phi}-I_A(R_A+j X_s)< / annotation > < / semantics > < / math > < / span > < span class = "katex-html" aria-hidden = "true" > < span class = "base" > < span class = "strut" style = "height:0.8333em;vertical-align:-0.15em;" > < / span > < span class = "mord" > < span class = "mord mathnormal" style = "margin-right:0.05764em;" > E< / span > < span class = "msupsub" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:0.3283em;" > < span style = "top:-2.55em;margin-left:-0.0576em;margin-right:0.05em;" > < span class = "pstrut" style = "height:2.7em;" > < / span > < span class = "sizing reset-size6 size3 mtight" > < span class = "mord mathnormal mtight" > A< / span > < / span > < / span > < / span > < span class = "vlist-s" > < / span > < / span > < span class = "vlist-r" > < span class = "vlist" style = "height:0.15em;" > < span > < / span > < / span > < / span > < / span > < / span > < / span > < span class = "mspace" style = "margin-right:0.2778em;" > < / span > < span class = "mrel" > =< / span > < span class = "mspace" style = "margin-right:0.2778em;" > < / span > < / span > < span class = "base" > < span class = "strut" style = "height:0.9694em;vertical-align:-0.2861em;" > < / span > < span class = "mord" > < span class = "mord mathnormal" style = "margin-right:0.22222em;" > V< / span > < span class = "msupsub" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:0.3361em;" > < span style = "top:-2.55em;margin-left:-0.2222em;margin-right:0.05em;" > < span class = "pstrut" style = "height:2.7em;" > < / span > < span class = "sizing reset-size6 size3 mtight" > < span class = "mord mtight" > < span class = "mord mtight" > 1< / span > < span class = "mord mathnormal mtight" > ϕ< / span > < / span > < / span > < / span > < / span > < span class = "vlist-s" > < / span > < / span > < span class = "vlist-r" > < span class = "vlist" style = "height:0.2861em;" > < span > < / span > < / span > < / span > < / span > < / span > < / span > < span class = "mspace" style = "margin-right:0.2222em;" > < / span > < span class = "mbin" > − < / span > < span class = "mspace" style = "margin-right:0.2222em;" > < / span > < / span > < span class = "base" > < span class = "strut" style = "height:1em;vertical-align:-0.25em;" > < / span > < span class = "mord" > < span class = "mord mathnormal" style = "margin-right:0.07847em;" > I< / span > < span class = "msupsub" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:0.3283em;" > < span style = "top:-2.55em;margin-left:-0.0785em;margin-right:0.05em;" > < span class = "pstrut" style = "height:2.7em;" > < / span > < span class = "sizing reset-size6 size3 mtight" > < span class = "mord mathnormal mtight" > A< / span > < / span > < / span > < / span > < span class = "vlist-s" > < / span > < / span > < span class = "vlist-r" > < span class = "vlist" style = "height:0.15em;" > < span > < / span > < / span > < / span > < / span > < / span > < / span > < span class = "mopen" > (< / span > < span class = "mord" > < span class = "mord mathnormal" style = "margin-right:0.00773em;" > R< / span > < span class = "msupsub" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:0.3283em;" > < span style = "top:-2.55em;margin-left:-0.0077em;margin-right:0.05em;" > < span class = "pstrut" style = "height:2.7em;" > < / span > < span class = "sizing reset-size6 size3 mtight" > < span class = "mord mathnormal mtight" > A< / span > < / span > < / span > < / span > < span class = "vlist-s" > < / span > < / span > < span class = "vlist-r" > < span class = "vlist" style = "height:0.15em;" > < span > < / span > < / span > < / span > < / span > < / span > < / span > < span class = "mspace" style = "margin-right:0.2222em;" > < / span > < span class = "mbin" > +< / span > < span class = "mspace" style = "margin-right:0.2222em;" > < / span > < / span > < span class = "base" > < span class = "strut" style = "height:1em;vertical-align:-0.25em;" > < / span > < span class = "mord mathnormal" style = "margin-right:0.05724em;" > j< / span > < span class = "mord" > < span class = "mord mathnormal" style = "margin-right:0.07847em;" > X< / span > < span class = "msupsub" > < span class = "vlist
< / math >
< p > < span class = "katex-display" > < span class = "katex" > < span class = "katex-mathml" > < math xmlns = "http://www.w3.org/1998/Math/MathML" display = "block" > < semantics > < mrow > < msub > < mi > I< / mi > < mi > A< / mi > < / msub > < mo > =< / mo > < mtext > CONJUGATE< / mtext > < mrow > < mo fence = "true" > (< / mo > < mfrac > < mrow > < mi mathvariant = "normal" > ∣ < / mi > < msub > < mi > S< / mi > < mrow > < mn > 3< / mn > < mi > ϕ< / mi > < / mrow > < / msub > < mi mathvariant = "normal" > ∣ < / mi > < mi mathvariant = "normal" > ∠< / mi > < mi > arccos< / mi > < mo > < / mo > < mo stretchy = "false" > (< / mo > < mi > x< / mi > < mo stretchy = "false" > )< / mo > < / mrow > < mrow > < mn > 3< / mn > < msub > < mi > V< / mi > < mrow > < mn > 1< / mn > < mi > ϕ< / mi > < / mrow > < / msub > < / mrow > < / mfrac > < mo fence = "true" > )< / mo > < / mrow > < mo separator = "true" > ,< / mo > < mrow > < mo fence = "true" > {< / mo > < mtable rowspacing = "0.36em" columnalign = "left left" columnspacing = "1em" > < mtr > < mtd > < mstyle scriptlevel = "0" displaystyle = "false" > < mrow > < mi > x< / mi > < mo > =< / mo > < mo > +< / mo > < mtext > PF< / mtext > < / mrow > < / mstyle > < / mtd > < mtd > < mstyle scriptlevel = "0" displaystyle = "false" > < mrow > < / mrow > < / mstyle > < / mtd > < mtd > < mstyle scriptlevel = "0" displaystyle = "false" > < mtext > lagging< / mtext > < / mstyle > < / mtd > < / mtr > < mtr > < mtd > < mstyle scriptlevel = "0" displaystyle = "false" > < mrow > < mi > x< / mi > < mo > =< / mo > < mo > − < / mo > < mtext > PF< / mtext > < / mrow > < / mstyle > < / mtd > < mtd > < mstyle scriptlevel = "0" displaystyle = "false" > < mrow > < / mrow > < / mstyle > < / mtd > < mtd > < mstyle scriptlevel = "0" displaystyle = "false" > < mtext > leading< / mtext > < / mstyle > < / mtd > < / mtr > < / mtable > < / mrow > < / mrow > < annotation encoding = "application/x-tex" > I_A=\text{CONJUGATE}\left(\frac{|S_{3\phi}|\angle\arccos(x)}{3V_{1\phi}}\right), \begin{cases}x=+\text{PF} & & \text{lagging} \\ x=-\text{PF} & & \text{leading}\end{cases}< / annotation > < / semantics > < / math > < / span > < span class = "katex-html" aria-hidden = "true" > < span class = "base" > < span class = "strut" style = "height:0.8333em;vertical-align:-0.15em;" > < / span > < span class = "mord" > < span class = "mord mathnormal" style = "margin-right:0.07847em;" > I< / span > < span class = "msupsub" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:0.3283em;" > < span style = "top:-2.55em;margin-left:-0.0785em;margin-right:0.05em;" > < span class = "pstrut" style = "height:2.7em;" > < / span > < span class = "sizing reset-size6 size3 mtight" > < span class = "mord mathnormal mtight" > A< / span > < / span > < / span > < / span > < span class = "vlist-s" > < / span > < / span > < span class = "vlist-r" > < span class = "vlist" style = "height:0.15em;" > < span > < / span > < / span > < / span > < / span > < / span > < / span > < span class = "mspace" style = "margin-right:0.2778em;" > < / span > < span class = "mrel" > =< / span > < span class = "mspace" style = "margin-right:0.2778em;" > < / span > < / span > < span class = "base" > < span class = "strut" style = "height:3em;vertical-align:-1.25em;" > < / span > < span class = "mord text" > < span class = "mord" > CONJUGATE< / span > < / span > < span class = "mspace" style = "margin-right:0.1667em;" > < / span > < span class = "minner" > < span class = "mopen delimcenter" style = "top:0em;" > < span class = "delimsizing size3" > (< / span > < / span > < span class = "mord" > < span class = "mopen nulldelimiter" > < / span > < span class = "mfrac" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:1.427em;" > < span style = "top:-2.314em;" > < span class = "pstrut" style = "height:3em;" > < / span > < span class = "mord" > < span class = "mord" > 3< / span > < span class = "mord" > < span class = "mord mathnormal" style = "margin-right:0.22222em;" > V< / span > < span class = "msupsub" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:0.3361em;" > < span style = "top:-2.55em;margin-left:-0.2222em;margin-right:0.05em;" > < span class = "pstrut" style = "height:2.7em;" > < / span > < span class = "sizing reset-size6 size3 mtight" > < span class = "mord mtight" > < span class = "mord mtight" > 1< / span > < span class = "mord mathnormal mtight" > ϕ< / span > < / span > < / span > < / span > < / span > < span class = "vlist-s" > < / span > < / span > < span class = "vlist-r" > < span class = "vlist" style = "height:0.2861em;" > < span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < span style = "top:-3.23em;" > < span class = "pstrut" style = "height:3em;" > < / span > < span class = "frac-line" style = "border-bottom-width:0.04em;" > < / span > < / span > < span style = "top:-3.677em;" > < span class = "pstrut" style = "height:3em;" > < / span > < span class = "mord" > < s
< / math >
< h3 dir = "auto" id = "voltage-regulation-2" > Voltage regulation< / h3 >
< p > < span class = "katex-display" > < span class = "katex" > < span class = "katex-mathml" > < math xmlns = "http://www.w3.org/1998/Math/MathML" display = "block" > < semantics > < mrow > < mtext > VR< / mtext > < mo > =< / mo > < mfrac > < mrow > < mi mathvariant = "normal" > ∣ < / mi > < msub > < mi > V< / mi > < mtext > NL< / mtext > < / msub > < mi mathvariant = "normal" > ∣ < / mi > < mo > − < / mo > < mi mathvariant = "normal" > ∣ < / mi > < msub > < mi > V< / mi > < mtext > FL< / mtext > < / msub > < mi mathvariant = "normal" > ∣ < / mi > < / mrow > < mrow > < mi mathvariant = "normal" > ∣ < / mi > < msub > < mi > V< / mi > < mtext > FL< / mtext > < / msub > < mi mathvariant = "normal" > ∣ < / mi > < / mrow > < / mfrac > < mo > =< / mo > < mfrac > < mrow > < mi mathvariant = "normal" > ∣ < / mi > < msub > < mi > E< / mi > < mi > A< / mi > < / msub > < mi mathvariant = "normal" > ∣ < / mi > < mo > − < / mo > < mi mathvariant = "normal" > ∣ < / mi > < msub > < mi > V< / mi > < mrow > < mn > 1< / mn > < mi > ϕ< / mi > < mo separator = "true" > ,< / mo > < mtext > rated< / mtext > < / mrow > < / msub > < mi mathvariant = "normal" > ∣ < / mi > < / mrow > < mrow > < mi mathvariant = "normal" > ∣ < / mi > < msub > < mi > V< / mi > < mrow > < mn > 1< / mn > < mi > ϕ< / mi > < mo separator = "true" > ,< / mo > < mtext > rated< / mtext > < / mrow > < / msub > < mi mathvariant = "normal" > ∣ < / mi > < / mrow > < / mfrac > < / mrow > < annotation encoding = "application/x-tex" > \text{VR}=\frac{|V_\text{NL}|-|V_\text{FL}|}{|V_\text{FL}|}=\frac{|E_A|-|V_{1\phi,\text{rated}}|}{|V_{1\phi,\text{rated}}|}< / annotation > < / semantics > < / math > < / span > < span class = "katex-html" aria-hidden = "true" > < span class = "base" > < span class = "strut" style = "height:0.6833em;" > < / span > < span class = "mord text" > < span class = "mord" > VR< / span > < / span > < span class = "mspace" style = "margin-right:0.2778em;" > < / span > < span class = "mrel" > =< / span > < span class = "mspace" style = "margin-right:0.2778em;" > < / span > < / span > < span class = "base" > < span class = "strut" style = "height:2.363em;vertical-align:-0.936em;" > < / span > < span class = "mord" > < span class = "mopen nulldelimiter" > < / span > < span class = "mfrac" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:1.427em;" > < span style = "top:-2.314em;" > < span class = "pstrut" style = "height:3em;" > < / span > < span class = "mord" > < span class = "mord" > ∣ < / span > < span class = "mord" > < span class = "mord mathnormal" style = "margin-right:0.22222em;" > V< / span > < span class = "msupsub" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:0.3283em;" > < span style = "top:-2.55em;margin-left:-0.2222em;margin-right:0.05em;" > < span class = "pstrut" style = "height:2.7em;" > < / span > < span class = "sizing reset-size6 size3 mtight" > < span class = "mord text mtight" > < span class = "mord mtight" > FL< / span > < / span > < / span > < / span > < / span > < span class = "vlist-s" > < / span > < / span > < span class = "vlist-r" > < span class = "vlist" style = "height:0.15em;" > < span > < / span > < / span > < / span > < / span > < / span > < / span > < span class = "mord" > ∣ < / span > < / span > < / span > < span style = "top:-3.23em;" > < span class = "pstrut" style = "height:3em;" > < / span > < span class = "frac-line" style = "border-bottom-width:0.04em;" > < / span > < / span > < span style = "top:-3.677em;" > < span class = "pstrut" style = "height:3em;" > < / span > < span class = "mord" > < span class = "mord" > ∣ < / span > < span class = "mord" > < span class = "mord mathnormal" style = "margin-right:0.22222em;" > V< / span > < span class = "msupsub" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:0.3283em;" > < span style = "top:-2.55em;margin-left:-0.2222em;margin-right:0.05em;" > < span class = "pstrut" style = "height:2.7em;" > < / span > < span class = "sizing reset-size6 size3 mtight" > < span class = "mord text mtight" > < span class = "mord mtight" > NL< / span > < / span > < / span > < / span > < / span > < span class = "vlist-s" > < / span > < / span > < span class = "vlist-r" > < span class = "vlist" style = "height:0.15em;" > < span > < / span > < / span > < / span > < / span > < / span > < / span > < span class = "mord" > ∣ < / span > < span class = "mspace" style = "margin-right:0.2222em;" > < / span > < span class = "mbin" > − < / span > < span class = "mspace" style = "margin-right:0.2222em;" > < / span > < span class = "mord" > ∣ < / span > < span class = "mord" > < span class = "mord mathnormal" style = "margin-right:0.22222em;" > V< / span > < span class = "msupsub" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:0.3283em;" > < span style = "top:-2.55em;margin-left:-0.2222em;margin-right:0.05em;" > < span class = "pstrut" style = "height:2.7em;" > < / span > < span class = "si
< / math >
< ul dir = "auto" >
< li dir = "auto" > < span class = "katex" > < span class = "katex-mathml" > < math xmlns = "http://www.w3.org/1998/Math/MathML" > < semantics > < mrow > < msub > < mi > V< / mi > < mtext > FL< / mtext > < / msub > < / mrow > < annotation encoding = "application/x-tex" > V_\text{FL}< / annotation > < / semantics > < / math > < / span > < span class = "katex-html" aria-hidden = "true" > < span class = "base" > < span class = "strut" style = "height:0.8333em;vertical-align:-0.15em;" > < / span > < span class = "mord" > < span class = "mord mathnormal" style = "margin-right:0.22222em;" > V< / span > < span class = "msupsub" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:0.3283em;" > < span style = "top:-2.55em;margin-left:-0.2222em;margin-right:0.05em;" > < span class = "pstrut" style = "height:2.7em;" > < / span > < span class = "sizing reset-size6 size3 mtight" > < span class = "mord text mtight" > < span class = "mord mtight" > FL< / span > < / span > < / span > < / span > < / span > < span class = "vlist-s" > < / span > < / span > < span class = "vlist-r" > < span class = "vlist" style = "height:0.15em;" > < span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > is the full-load voltage which is the full-load/maximum rated voltage at the output terminal.< / li >
< li dir = "auto" > Calculate < span class = "katex" > < span class = "katex-mathml" > < math xmlns = "http://www.w3.org/1998/Math/MathML" > < semantics > < mrow > < msub > < mi > E< / mi > < mi > A< / mi > < / msub > < / mrow > < annotation encoding = "application/x-tex" > E_A< / annotation > < / semantics > < / math > < / span > < span class = "katex-html" aria-hidden = "true" > < span class = "base" > < span class = "strut" style = "height:0.8333em;vertical-align:-0.15em;" > < / span > < span class = "mord" > < span class = "mord mathnormal" style = "margin-right:0.05764em;" > E< / span > < span class = "msupsub" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:0.3283em;" > < span style = "top:-2.55em;margin-left:-0.0576em;margin-right:0.05em;" > < span class = "pstrut" style = "height:2.7em;" > < / span > < span class = "sizing reset-size6 size3 mtight" > < span class = "mord mathnormal mtight" > A< / span > < / span > < / span > < / span > < span class = "vlist-s" > < / span > < / span > < span class = "vlist-r" > < span class = "vlist" style = "height:0.15em;" > < span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > at full load by calculating the current as shown above.< / li >
< li dir = "auto" > < span class = "katex" > < span class = "katex-mathml" > < math xmlns = "http://www.w3.org/1998/Math/MathML" > < semantics > < mrow > < msub > < mi > V< / mi > < mtext > NL< / mtext > < / msub > < / mrow > < annotation encoding = "application/x-tex" > V_\text{NL}< / annotation > < / semantics > < / math > < / span > < span class = "katex-html" aria-hidden = "true" > < span class = "base" > < span class = "strut" style = "height:0.8333em;vertical-align:-0.15em;" > < / span > < span class = "mord" > < span class = "mord mathnormal" style = "margin-right:0.22222em;" > V< / span > < span class = "msupsub" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:0.3283em;" > < span style = "top:-2.55em;margin-left:-0.2222em;margin-right:0.05em;" > < span class = "pstrut" style = "height:2.7em;" > < / span > < span class = "sizing reset-size6 size3 mtight" > < span class = "mord text mtight" > < span class = "mord mtight" > NL< / span > < / span > < / span > < / span > < / span > < span class = "vlist-s" > < / span > < / span > < span class = "vlist-r" > < span class = "vlist" style = "height:0.15em;" > < span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > is the no-load voltage, which in the no-load case will be < span class = "katex" > < span class = "katex-mathml" > < math xmlns = "http://www.w3.org/1998/Math/MathML" > < semantics > < mrow > < msub > < mi > E< / mi > < mi > A< / mi > < / msub > < / mrow > < annotation encoding = "application/x-tex" > E_A< / annotation > < / semantics > < / math > < / span > < span class = "katex-html" aria-hidden = "true" > < span class = "base" > < span class = "strut" style = "height:0.8333em;vertical-align:-0.15em;" > < / span > < span class = "mord" > < span class = "mord mathnormal" style = "margin-right:0.05764em;" > E< / span > < span class = "msupsub" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:0.3283em;" > < span style = "top:-2.55em;margin-left:-0.0576em;margin-right:0.05em;" > < span class = "pstrut" style = "height:2.7em;" > < / span > < span class = "sizing reset-size6 size3 mtight" > < span class = "mord mathnormal mtight" > A< / span > < / span > < / span > < / span > < span class = "vlist-s" > < / span > < / span > < span class = "vlist-r" > < span class = "vlist" style = "height:0.15em;" > < span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > .< / li >
< / ul >
< table dir = "auto" >
< thead dir = "auto" >
< tr dir = "auto" >
< th > No-load< / th >
< th > Full-load< / th >
< / tr >
< / thead >
< tbody dir = "auto" >
< tr dir = "auto" >
< td > < center > < img src = "2022-10-27-20-15-13.png" width = 300px > < / center > < / td >
< td > < center > < img src = "2022-10-27-20-19-47.png" width = 300px > < / center > < / td >
< / tr >
< / tbody >
< / table >
< table dir = "auto" >
< thead dir = "auto" >
< tr dir = "auto" >
2022-11-01 01:03:59 +08:00
< th > PF< / th >
< th > Lagging< / th >
< th > Unity< / th >
< th > Leading< / th >
2022-10-28 23:06:54 +08:00
< / tr >
< / thead >
< tbody dir = "auto" >
< tr dir = "auto" >
2022-11-01 01:03:59 +08:00
< td > VR< / td >
2022-10-28 23:06:54 +08:00
< td > Positive< / td >
< td > Near 0< / td >
< td > Negative< / td >
< / tr >
< / tbody >
< / table >
< h3 dir = "auto" id = "open-and-short-circuit-test-1" > Open and short circuit test< / h3 >
< h4 dir = "auto" id = "note---double-check-if-the-axis-refers-to-per-phase-or-line-voltagecurrent-1" > < strong > Note< / strong > - double-check if the axis refers to per-phase or line voltage/current.< / h4 >
< table dir = "auto" >
< thead dir = "auto" >
< tr dir = "auto" >
< th > Open-circuit test< / th >
< th > Short-circuit test< / th >
< / tr >
< / thead >
< tbody dir = "auto" >
< tr dir = "auto" >
< td > < center > < img src = "2022-10-27-15-31-49.png" width = 300px > < / center > < / td >
< td > < center > < img src = "2022-10-27-15-32-07.png" width = 300px > < / center > < / td >
< / tr >
< / tbody >
< / table >
< h3 dir = "auto" id = "power-flow-1" > Power flow< / h3 >
< p dir = "auto" > < span class = "katex" > < span class = "katex-mathml" > < math xmlns = "http://www.w3.org/1998/Math/MathML" > < semantics > < mrow > < msub > < mi > P< / mi > < mtext > out< / mtext > < / msub > < / mrow > < annotation encoding = "application/x-tex" > P_\text{out}< / annotation > < / semantics > < / math > < / span > < span class = "katex-html" aria-hidden = "true" > < span class = "base" > < span class = "strut" style = "height:0.8333em;vertical-align:-0.15em;" > < / span > < span class = "mord" > < span class = "mord mathnormal" style = "margin-right:0.13889em;" > P< / span > < span class = "msupsub" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:0.2806em;" > < span style = "top:-2.55em;margin-left:-0.1389em;margin-right:0.05em;" > < span class = "pstrut" style = "height:2.7em;" > < / span > < span class = "sizing reset-size6 size3 mtight" > < span class = "mord text mtight" > < span class = "mord mtight" > out< / span > < / span > < / span > < / span > < / span > < span class = "vlist-s" > < / span > < / span > < span class = "vlist-r" > < span class = "vlist" style = "height:0.15em;" > < span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > is the rated power< / p >
< p > < span class = "katex-display" > < span class = "katex" > < span class = "katex-mathml" > < math xmlns = "http://www.w3.org/1998/Math/MathML" display = "block" > < semantics > < mrow > < msub > < mi > P< / mi > < mtext > out< / mtext > < / msub > < mo > =< / mo > < msub > < mi > S< / mi > < mtext > rated< / mtext > < / msub > < mo > × < / mo > < mtext > PF< / mtext > < / mrow > < annotation encoding = "application/x-tex" > P_\text{out}=S_\text{rated}\times \text{PF}< / annotation > < / semantics > < / math > < / span > < span class = "katex-html" aria-hidden = "true" > < span class = "base" > < span class = "strut" style = "height:0.8333em;vertical-align:-0.15em;" > < / span > < span class = "mord" > < span class = "mord mathnormal" style = "margin-right:0.13889em;" > P< / span > < span class = "msupsub" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:0.2806em;" > < span style = "top:-2.55em;margin-left:-0.1389em;margin-right:0.05em;" > < span class = "pstrut" style = "height:2.7em;" > < / span > < span class = "sizing reset-size6 size3 mtight" > < span class = "mord text mtight" > < span class = "mord mtight" > out< / span > < / span > < / span > < / span > < / span > < span class = "vlist-s" > < / span > < / span > < span class = "vlist-r" > < span class = "vlist" style = "height:0.15em;" > < span > < / span > < / span > < / span > < / span > < / span > < / span > < span class = "mspace" style = "margin-right:0.2778em;" > < / span > < span class = "mrel" > =< / span > < span class = "mspace" style = "margin-right:0.2778em;" > < / span > < / span > < span class = "base" > < span class = "strut" style = "height:0.8333em;vertical-align:-0.15em;" > < / span > < span class = "mord" > < span class = "mord mathnormal" style = "margin-right:0.05764em;" > S< / span > < span class = "msupsub" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:0.3361em;" > < span style = "top:-2.55em;margin-left:-0.0576em;margin-right:0.05em;" > < span class = "pstrut" style = "height:2.7em;" > < / span > < span class = "sizing reset-size6 size3 mtight" > < span class = "mord text mtight" > < span class = "mord mtight" > rated< / span > < / span > < / span > < / span > < / span > < span class = "vlist-s" > < / span > < / span > < span class = "vlist-r" > < span class = "vlist" style = "height:0.15em;" > < span > < / span > < / span > < / span > < / span > < / span > < / span > < span class = "mspace" style = "margin-right:0.2222em;" > < / span > < span class = "mbin" > × < / span > < span class = "mspace" style = "margin-right:0.2222em;" > < / span > < / span > < span class = "base" > < span class = "strut" style = "height:0.6833em;" > < / span > < span class = "mord text" > < span class = "mord" > PF< / span > < / span > < / span > < / span > < / span > < / span > < / p >
< / math >
< p > < span class = "katex-display" > < span class = "katex" > < span class = "katex-mathml" > < math xmlns = "http://www.w3.org/1998/Math/MathML" display = "block" > < semantics > < mtable rowspacing = "0.25em" columnalign = "right left" columnspacing = "0em" > < mtr > < mtd class = "mtr-glue" > < / mtd > < mtd > < mstyle scriptlevel = "0" displaystyle = "true" > < msub > < mi > P< / mi > < mtext > in< / mtext > < / msub > < / mstyle > < / mtd > < mtd > < mstyle scriptlevel = "0" displaystyle = "true" > < mrow > < mrow > < / mrow > < mo > =< / mo > < msub > < mi > P< / mi > < mtext > copper< / mtext > < / msub > < mo > +< / mo > < msub > < mi > P< / mi > < mtext > core< / mtext > < / msub > < mo > +< / mo > < msub > < mi > P< / mi > < mrow > < mtext > F< / mtext > < mspace linebreak = "newline" > < / mspace > < mtext > & W< / mtext > < / mrow > < / msub > < mo > +< / mo > < msub > < mi > P< / mi > < mtext > misc< / mtext > < / msub > < mo > +< / mo > < msub > < mi > P< / mi > < mtext > out< / mtext > < / msub > < / mrow > < / mstyle > < / mtd > < mtd class = "mtr-glue" > < / mtd > < mtd class = "mml-eqn-num" > < / mtd > < / mtr > < mtr > < mtd class = "mtr-glue" > < / mtd > < mtd > < mstyle scriptlevel = "0" displaystyle = "true" > < msub > < mi > P< / mi > < mtext > mech< / mtext > < / msub > < / mstyle > < / mtd > < mtd > < mstyle scriptlevel = "0" displaystyle = "true" > < mrow > < mrow > < / mrow > < mo > =< / mo > < msub > < mi > P< / mi > < mrow > < mtext > F< / mtext > < mspace linebreak = "newline" > < / mspace > < mtext > & W< / mtext > < / mrow > < / msub > < mo > +< / mo > < msub > < mi > P< / mi > < mtext > misc< / mtext > < / msub > < mo > +< / mo > < msub > < mi > P< / mi > < mtext > out< / mtext > < / msub > < / mrow > < / mstyle > < / mtd > < mtd class = "mtr-glue" > < / mtd > < mtd class = "mml-eqn-num" > < / mtd > < / mtr > < / mtable > < annotation encoding = "application/x-tex" >
\begin{align}
P_\text{in}& =P_\text{copper}+P_\text{core}+P_\text{F\\\& W}+P_\text{misc}+P_\text{out}\\
P_\text{mech}& =P_\text{F\\\& W}+P_\text{misc}+P_\text{out}
\end{align}
< / annotation > < / semantics > < / math > < / span > < span class = "katex-html" aria-hidden = "true" > < span class = "base" > < span class = "strut" style = "height:3em;vertical-align:-1.25em;" > < / span > < span class = "mtable" > < span class = "col-align-r" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:1.75em;" > < span style = "top:-3.91em;" > < span class = "pstrut" style = "height:3em;" > < / span > < span class = "mord" > < span class = "mord" > < span class = "mord mathnormal" style = "margin-right:0.13889em;" > P< / span > < span class = "msupsub" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:0.3175em;" > < span style = "top:-2.55em;margin-left:-0.1389em;margin-right:0.05em;" > < span class = "pstrut" style = "height:2.7em;" > < / span > < span class = "sizing reset-size6 size3 mtight" > < span class = "mord text mtight" > < span class = "mord mtight" > in< / span > < / span > < / span > < / span > < / span > < span class = "vlist-s" > < / span > < / span > < span class = "vlist-r" > < span class = "vlist" style = "height:0.15em;" > < span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < span style = "top:-2.41em;" > < span class = "pstrut" style = "height:3em;" > < / span > < span class = "mord" > < span class = "mord" > < span class = "mord mathnormal" style = "margin-right:0.13889em;" > P< / span > < span class = "msupsub" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:0.3361em;" > < span style = "top:-2.55em;margin-left:-0.1389em;margin-right:0.05em;" > < span class = "pstrut" style = "height:2.7em;" > < / span > < span class = "sizing reset-size6 size3 mtight" > < span class = "mord text mtight" > < span class = "mord mtight" > mech< / span > < / span > < / span > < / span > < / span > < span class = "vlist-s" > < / span > < / span > < span class = "vlist-r" > < span class = "vlist" style = "height:0.15em;" > < span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < span class = "vlist-s" > < / span > < / span > < span class = "vlist-r" > < span class = "vlist" style = "height:1.25em;" > < span > < / span > < / span > < / span > < / span > < / span > < span class = "col-align-l" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:1.75em;" > < span style = "top:-3.91em;" > < span class = "pstrut" style = "height:3em;" > < / span > < span class = "mord" > < span class = "mord" > < / span > < span class = "mspace" style = "margin-right:0.2778em;" > < / span > < span class = "mrel" > =< / span > < span class = "mspace" style = "margin-right:0.2778em;" > < / span > < span class = "mord" > < span class = "mord mathnormal" style = "margin-right:0.13889em;" > P< / span > < span class = "msupsub" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:0.1514em;" > < span style = "top:-2.55em;margin-left:-0.1389em;margin-right:0.05em;" > < span class = "pstrut" style = "height:2.7em;" > < / span > < span class = "sizing reset-size6 size3 mtight" > < span class = "mord text mtight" > < span class = "mord mtight" > copper< / span > < / span > < / span > < / span > < / span > < span class = "vlist-s" > < / span > < / span > < span class = "vlist-r" > < span class = "vlist" style = "height:0.2861em;" > < span > < / span > < / span > < / span > < / span > < / span > < / span > < span class = "mspace" style = "margin-right:0.2222em;" > < / span > < span class = "mbin" > +< / span > < span class = "mspace" style = "margin-right:0.2222em;" > < / span > < span class = "mord" > < span class = "mord mathnormal" style = "margin-right:0.13889em;" > P< / span > < span class = "msupsub" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:0.1514em;" > < span style = "top:-2.55em;margin-left:-0.1389em;margin-right:0.05em;" > < span class = "pstrut" style = "height:2.7em;" > < / span > < span class = "sizing reset-size6 size3 mtight" > < span class = "mord text mtight" > < span class = "mord mtight" > core< / span > < / span > < / span > < / span > < / span > < span class = "vlist-s" > < / span > < / span > < span class = "vlist-r" > < span class = "vlist" style = "height:0.15em;" > < span > < / span > < / span > < / span > < / span > < / span > < / span > < span class = "mspace" style = "margin-right:0.2222em;" > < / span > < span class = "mbin" > +< / span > < span class = "mspace" style = "margin-right:0.2222em;" > < / span > < span class = "mord" > < span class = "mord mathnormal" style = "margin-right:0.13889em;" > P< / span > < span class = "msupsub" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:0.3361em;" > < span style = "top:-2.55em;margin-left
< / math >
< hr dir = "auto" >
< h3 dir = "auto" id = "magnetic-circuit-analogy-1" > Magnetic circuit analogy< / h3 >
< table dir = "auto" >
< thead dir = "auto" >
< tr dir = "auto" >
< th > Magnetic circuit< / th >
< th > name< / th >
< th > < / th >
< th > Electrical circuit< / th >
< th > name< / th >
< / tr >
< / thead >
< tbody dir = "auto" >
< tr dir = "auto" >
< td > < section > < eqn > < span class = "katex-display" > < span class = "katex" > < span class = "katex-mathml" > < math xmlns = "http://www.w3.org/1998/Math/MathML" display = "block" > < semantics > < mrow > < mi mathvariant = "script" > F< / mi > < / mrow > < annotation encoding = "application/x-tex" > \mathcal F< / annotation > < / semantics > < / math > < / span > < span class = "katex-html" aria-hidden = "true" > < span class = "base" > < span class = "strut" style = "height:0.68333em;vertical-align:0em;" > < / span > < span class = "mord mathcal" style = "margin-right:0.09931em;" > F< / span > < / span > < / span > < / span > < / span > < / eqn > < / section > < / td >
< td > Magnetomotive force [A-turn]< / td >
< td > < / td >
< td > < section > < eqn > < span class = "katex-display" > < span class = "katex" > < span class = "katex-mathml" > < math xmlns = "http://www.w3.org/1998/Math/MathML" display = "block" > < semantics > < mrow > < mi mathvariant = "script" > E< / mi > < / mrow > < annotation encoding = "application/x-tex" > \mathcal E< / annotation > < / semantics > < / math > < / span > < span class = "katex-html" aria-hidden = "true" > < span class = "base" > < span class = "strut" style = "height:0.68333em;vertical-align:0em;" > < / span > < span class = "mord mathcal" style = "margin-right:0.08944em;" > E< / span > < / span > < / span > < / span > < / span > < / eqn > < / section > < / td >
< td > Electromotive force [V]< / td >
< / tr >
< tr dir = "auto" >
< td > < section > < eqn > < span class = "katex-display" > < span class = "katex" > < span class = "katex-mathml" > < math xmlns = "http://www.w3.org/1998/Math/MathML" display = "block" > < semantics > < mrow > < mi mathvariant = "script" > R< / mi > < / mrow > < annotation encoding = "application/x-tex" > \mathcal R< / annotation > < / semantics > < / math > < / span > < span class = "katex-html" aria-hidden = "true" > < span class = "base" > < span class = "strut" style = "height:0.68333em;vertical-align:0em;" > < / span > < span class = "mord mathcal" > R< / span > < / span > < / span > < / span > < / span > < / eqn > < / section > < / td >
< td > Reluctance [1/H]< / td >
< td > < / td >
< td > < section > < eqn > < span class = "katex-display" > < span class = "katex" > < span class = "katex-mathml" > < math xmlns = "http://www.w3.org/1998/Math/MathML" display = "block" > < semantics > < mrow > < mi > R< / mi > < / mrow > < annotation encoding = "application/x-tex" > R< / annotation > < / semantics > < / math > < / span > < span class = "katex-html" aria-hidden = "true" > < span class = "base" > < span class = "strut" style = "height:0.68333em;vertical-align:0em;" > < / span > < span class = "mord mathnormal" style = "margin-right:0.00773em;" > R< / span > < / span > < / span > < / span > < / span > < / eqn > < / section > < / td >
< td > Resistance [< span class = "katex" > < span class = "katex-mathml" > < math xmlns = "http://www.w3.org/1998/Math/MathML" > < semantics > < mrow > < mi mathvariant = "normal" > Ω< / mi > < / mrow > < annotation encoding = "application/x-tex" > \Omega< / annotation > < / semantics > < / math > < / span > < span class = "katex-html" aria-hidden = "true" > < span class = "base" > < span class = "strut" style = "height:0.6833em;" > < / span > < span class = "mord" > Ω< / span > < / span > < / span > < / span > ]< / td >
< / tr >
< tr dir = "auto" >
< td > < section > < eqn > < span class = "katex-display" > < span class = "katex" > < span class = "katex-mathml" > < math xmlns = "http://www.w3.org/1998/Math/MathML" display = "block" > < semantics > < mrow > < mi mathvariant = "normal" > Φ< / mi > < / mrow > < annotation encoding = "application/x-tex" > \Phi< / annotation > < / semantics > < / math > < / span > < span class = "katex-html" aria-hidden = "true" > < span class = "base" > < span class = "strut" style = "height:0.68333em;vertical-align:0em;" > < / span > < span class = "mord" > Φ< / span > < / span > < / span > < / span > < / span > < / eqn > < / section > < / td >
< td > Magnetic flux [Wb]< / td >
< td > < / td >
< td > < section > < eqn > < span class = "katex-display" > < span class = "katex" > < span class = "katex-mathml" > < math xmlns = "http://www.w3.org/1998/Math/MathML" display = "block" > < semantics > < mrow > < mi > I< / mi > < / mrow > < annotation encoding = "application/x-tex" > I< / annotation > < / semantics > < / math > < / span > < span class = "katex-html" aria-hidden = "true" > < span class = "base" > < span class = "strut" style = "height:0.68333em;vertical-align:0em;" > < / span > < span class = "mord mathnormal" style = "margin-right:0.07847em;" > I< / span > < / span > < / span > < / span > < / span > < / eqn > < / section > < / td >
< td > Current [A]< / td >
< / tr >
< tr dir = "auto" >
< td > < section > < eqn > < span class = "katex-display" > < span class = "katex" > < span class = "katex-mathml" > < math xmlns = "http://www.w3.org/1998/Math/MathML" display = "block" > < semantics > < mrow > < mi mathvariant = "script" > P< / mi > < mo > =< / mo > < mfrac > < mn > 1< / mn > < mi mathvariant = "script" > R< / mi > < / mfrac > < / mrow > < annotation encoding = "application/x-tex" > \mathcal P=\frac{1}{\mathcal R}< / annotation > < / semantics > < / math > < / span > < span class = "katex-html" aria-hidden = "true" > < span class = "base" > < span class = "strut" style = "height:0.68333em;vertical-align:0em;" > < / span > < span class = "mord mathcal" style = "margin-right:0.08222em;" > P< / span > < span class = "mspace" style = "margin-right:0.2777777777777778em;" > < / span > < span class = "mrel" > =< / span > < span class = "mspace" style = "margin-right:0.2777777777777778em;" > < / span > < / span > < span class = "base" > < span class = "strut" style = "height:2.00744em;vertical-align:-0.686em;" > < / span > < span class = "mord" > < span class = "mopen nulldelimiter" > < / span > < span class = "mfrac" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:1.32144em;" > < span style = "top:-2.314em;" > < span class = "pstrut" style = "height:3em;" > < / span > < span class = "mord" > < span class = "mord mathcal" > R< / span > < / span > < / span > < span style = "top:-3.23em;" > < span class = "pstrut" style = "height:3em;" > < / span > < span class = "frac-line" style = "border-bottom-width:0.04em;" > < / span > < / span > < span style = "top:-3.677em;" > < span class = "pstrut" style = "height:3em;" > < / span > < span class = "mord" > < span class = "mord" > 1< / span > < / span > < / span > < / span > < span class = "vlist-s" > < / span > < / span > < span class = "vlist-r" > < span class = "vlist" style = "height:0.686em;" > < span > < / span > < / span > < / span > < / span > < / span > < span class = "mclose nulldelimiter" > < / span > < / span > < / span > < / span > < / span > < / span > < / eqn > < / section > < / td >
< td > Permeance [H]< / td >
< td > < / td >
< td > < section > < eqn > < span class = "katex-display" > < span class = "katex" > < span class = "katex-mathml" > < math xmlns = "http://www.w3.org/1998/Math/MathML" display = "block" > < semantics > < mrow > < mi > G< / mi > < mo > =< / mo > < mfrac > < mn > 1< / mn > < mi > R< / mi > < / mfrac > < / mrow > < annotation encoding = "application/x-tex" > G=\frac{1}{R}< / annotation > < / semantics > < / math > < / span > < span class = "katex-html" aria-hidden = "true" > < span class = "base" > < span class = "strut" style = "height:0.68333em;vertical-align:0em;" > < / span > < span class = "mord mathnormal" > G< / span > < span class = "mspace" style = "margin-right:0.2777777777777778em;" > < / span > < span class = "mrel" > =< / span > < span class = "mspace" style = "margin-right:0.2777777777777778em;" > < / span > < / span > < span class = "base" > < span class = "strut" style = "height:2.00744em;vertical-align:-0.686em;" > < / span > < span class = "mord" > < span class = "mopen nulldelimiter" > < / span > < span class = "mfrac" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:1.32144em;" > < span style = "top:-2.314em;" > < span class = "pstrut" style = "height:3em;" > < / span > < span class = "mord" > < span class = "mord mathnormal" style = "margin-right:0.00773em;" > R< / span > < / span > < / span > < span style = "top:-3.23em;" > < span class = "pstrut" style = "height:3em;" > < / span > < span class = "frac-line" style = "border-bottom-width:0.04em;" > < / span > < / span > < span style = "top:-3.677em;" > < span class = "pstrut" style = "height:3em;" > < / span > < span class = "mord" > < span class = "mord" > 1< / span > < / span > < / span > < / span > < span class = "vlist-s" > < / span > < / span > < span class = "vlist-r" > < span class = "vlist" style = "height:0.686em;" > < span > < / span > < / span > < / span > < / span > < / span > < span class = "mclose nulldelimiter" > < / span > < / span > < / span > < / span > < / span > < / span > < / eqn > < / section > < / td >
< td > Conductivity [< span class = "katex" > < span class = "katex-mathml" > < math xmlns = "http://www.w3.org/1998/Math/MathML" > < semantics > < mrow > < mi mathvariant = "normal" > ℧< / mi > < / mrow > < annotation encoding = "application/x-tex" > \mho< / annotation > < / semantics > < / math > < / span > < span class = "katex-html" aria-hidden = "true" > < span class = "base" > < span class = "strut" style = "height:0.6889em;" > < / span > < span class = "mord amsrm" > ℧< / span > < / span > < / span > < / span > ]< / td >
< / tr >
< tr dir = "auto" >
< td > < section > < eqn > < span class = "katex-display" > < span class = "katex" > < span class = "katex-mathml" > < math xmlns = "http://www.w3.org/1998/Math/MathML" display = "block" > < semantics > < mrow > < mi mathvariant = "script" > F< / mi > < mo > =< / mo > < mi mathvariant = "normal" > Φ< / mi > < mi mathvariant = "script" > R< / mi > < / mrow > < annotation encoding = "application/x-tex" > \mathcal F=\Phi\mathcal R< / annotation > < / semantics > < / math > < / span > < span class = "katex-html" aria-hidden = "true" > < span class = "base" > < span class = "strut" style = "height:0.68333em;vertical-align:0em;" > < / span > < span class = "mord mathcal" style = "margin-right:0.09931em;" > F< / span > < span class = "mspace" style = "margin-right:0.2777777777777778em;" > < / span > < span class = "mrel" > =< / span > < span class = "mspace" style = "margin-right:0.2777777777777778em;" > < / span > < / span > < span class = "base" > < span class = "strut" style = "height:0.68333em;vertical-align:0em;" > < / span > < span class = "mord" > Φ< / span > < span class = "mord mathcal" > R< / span > < / span > < / span > < / span > < / span > < / eqn > < / section > < / td >
< td > Hopkinson's law< / td >
< td > < / td >
< td > < section > < eqn > < span class = "katex-display" > < span class = "katex" > < span class = "katex-mathml" > < math xmlns = "http://www.w3.org/1998/Math/MathML" display = "block" > < semantics > < mrow > < mi > V< / mi > < mo > =< / mo > < mi > I< / mi > < mi > R< / mi > < / mrow > < annotation encoding = "application/x-tex" > V=IR< / annotation > < / semantics > < / math > < / span > < span class = "katex-html" aria-hidden = "true" > < span class = "base" > < span class = "strut" style = "height:0.68333em;vertical-align:0em;" > < / span > < span class = "mord mathnormal" style = "margin-right:0.22222em;" > V< / span > < span class = "mspace" style = "margin-right:0.2777777777777778em;" > < / span > < span class = "mrel" > =< / span > < span class = "mspace" style = "margin-right:0.2777777777777778em;" > < / span > < / span > < span class = "base" > < span class = "strut" style = "height:0.68333em;vertical-align:0em;" > < / span > < span class = "mord mathnormal" style = "margin-right:0.07847em;" > I< / span > < span class = "mord mathnormal" style = "margin-right:0.00773em;" > R< / span > < / span > < / span > < / span > < / span > < / eqn > < / section > < / td >
< td > Ohm's law< / td >
< / tr >
< tr dir = "auto" >
< td > < section > < eqn > < span class = "katex-display" > < span class = "katex" > < span class = "katex-mathml" > < math xmlns = "http://www.w3.org/1998/Math/MathML" display = "block" > < semantics > < mrow > < mi mathvariant = "script" > R< / mi > < mo > =< / mo > < mfrac > < mi > l< / mi > < mrow > < mi > μ< / mi > < mi > A< / mi > < / mrow > < / mfrac > < / mrow > < annotation encoding = "application/x-tex" > \mathcal R=\frac{l}{\mu A}< / annotation > < / semantics > < / math > < / span > < span class = "katex-html" aria-hidden = "true" > < span class = "base" > < span class = "strut" style = "height:0.68333em;vertical-align:0em;" > < / span > < span class = "mord mathcal" > R< / span > < span class = "mspace" style = "margin-right:0.2777777777777778em;" > < / span > < span class = "mrel" > =< / span > < span class = "mspace" style = "margin-right:0.2777777777777778em;" > < / span > < / span > < span class = "base" > < span class = "strut" style = "height:2.25188em;vertical-align:-0.8804400000000001em;" > < / span > < span class = "mord" > < span class = "mopen nulldelimiter" > < / span > < span class = "mfrac" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:1.37144em;" > < span style = "top:-2.314em;" > < span class = "pstrut" style = "height:3em;" > < / span > < span class = "mord" > < span class = "mord mathnormal" > μ< / span > < span class = "mord mathnormal" > A< / span > < / span > < / span > < span style = "top:-3.23em;" > < span class = "pstrut" style = "height:3em;" > < / span > < span class = "frac-line" style = "border-bottom-width:0.04em;" > < / span > < / span > < span style = "top:-3.677em;" > < span class = "pstrut" style = "height:3em;" > < / span > < span class = "mord" > < span class = "mord mathnormal" style = "margin-right:0.01968em;" > l< / span > < / span > < / span > < / span > < span class = "vlist-s" > < / span > < / span > < span class = "vlist-r" > < span class = "vlist" style = "height:0.8804400000000001em;" > < span > < / span > < / span > < / span > < / span > < / span > < span class = "mclose nulldelimiter" > < / span > < / span > < / span > < / span > < / span > < / span > < / eqn > < / section > < / td >
< td > < / td >
< td > < / td >
< td > < section > < eqn > < span class = "katex-display" > < span class = "katex" > < span class = "katex-mathml" > < math xmlns = "http://www.w3.org/1998/Math/MathML" display = "block" > < semantics > < mrow > < mi > R< / mi > < mo > =< / mo > < mfrac > < mi > l< / mi > < mrow > < mi > σ < / mi > < mi > A< / mi > < / mrow > < / mfrac > < / mrow > < annotation encoding = "application/x-tex" > R=\frac{l}{\sigma A}< / annotation > < / semantics > < / math > < / span > < span class = "katex-html" aria-hidden = "true" > < span class = "base" > < span class = "strut" style = "height:0.68333em;vertical-align:0em;" > < / span > < span class = "mord mathnormal" style = "margin-right:0.00773em;" > R< / span > < span class = "mspace" style = "margin-right:0.2777777777777778em;" > < / span > < span class = "mrel" > =< / span > < span class = "mspace" style = "margin-right:0.2777777777777778em;" > < / span > < / span > < span class = "base" > < span class = "strut" style = "height:2.05744em;vertical-align:-0.686em;" > < / span > < span class = "mord" > < span class = "mopen nulldelimiter" > < / span > < span class = "mfrac" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:1.37144em;" > < span style = "top:-2.314em;" > < span class = "pstrut" style = "height:3em;" > < / span > < span class = "mord" > < span class = "mord mathnormal" style = "margin-right:0.03588em;" > σ < / span > < span class = "mord mathnormal" > A< / span > < / span > < / span > < span style = "top:-3.23em;" > < span class = "pstrut" style = "height:3em;" > < / span > < span class = "frac-line" style = "border-bottom-width:0.04em;" > < / span > < / span > < span style = "top:-3.677em;" > < span class = "pstrut" style = "height:3em;" > < / span > < span class = "mord" > < span class = "mord mathnormal" style = "margin-right:0.01968em;" > l< / span > < / span > < / span > < / span > < span class = "vlist-s" > < / span > < / span > < span class = "vlist-r" > < span class = "vlist" style = "height:0.686em;" > < span > < / span > < / span > < / span > < / span > < / span > < span class = "mclose nulldelimiter" > < / span > < / span > < / span > < / span > < / span > < / span > < / eqn > < / section > < / td >
< td > < / td >
< / tr >
< / tbody >
< / table >
< hr dir = "auto" >
< h3 dir = "auto" id = "transformers-1" > Transformers< / h3 >
< p > < span class = "katex-display" > < span class = "katex" > < span class = "katex-mathml" > < math xmlns = "http://www.w3.org/1998/Math/MathML" display = "block" > < semantics > < mrow > < msub > < mi > Z< / mi > < mi > P< / mi > < / msub > < mo > =< / mo > < msub > < mi > Z< / mi > < mi > S< / mi > < / msub > < msup > < mrow > < mo fence = "true" > (< / mo > < mfrac > < msub > < mi > N< / mi > < mi > P< / mi > < / msub > < msub > < mi > N< / mi > < mi > S< / mi > < / msub > < / mfrac > < mo fence = "true" > )< / mo > < / mrow > < mn > 2< / mn > < / msup > < mo > =< / mo > < msub > < mi > Z< / mi > < mi > S< / mi > < / msub > < msup > < mi > n< / mi > < mn > 2< / mn > < / msup > < / mrow > < annotation encoding = "application/x-tex" > Z_P=Z_S\left(\frac{N_P}{N_S}\right)^2=Z_S n^2< / annotation > < / semantics > < / math > < / span > < span class = "katex-html" aria-hidden = "true" > < span class = "base" > < span class = "strut" style = "height:0.8333em;vertical-align:-0.15em;" > < / span > < span class = "mord" > < span class = "mord mathnormal" style = "margin-right:0.07153em;" > Z< / span > < span class = "msupsub" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:0.3283em;" > < span style = "top:-2.55em;margin-left:-0.0715em;margin-right:0.05em;" > < span class = "pstrut" style = "height:2.7em;" > < / span > < span class = "sizing reset-size6 size3 mtight" > < span class = "mord mathnormal mtight" style = "margin-right:0.13889em;" > P< / span > < / span > < / span > < / span > < span class = "vlist-s" > < / span > < / span > < span class = "vlist-r" > < span class = "vlist" style = "height:0.15em;" > < span > < / span > < / span > < / span > < / span > < / span > < / span > < span class = "mspace" style = "margin-right:0.2778em;" > < / span > < span class = "mrel" > =< / span > < span class = "mspace" style = "margin-right:0.2778em;" > < / span > < / span > < span class = "base" > < span class = "strut" style = "height:2.604em;vertical-align:-0.95em;" > < / span > < span class = "mord" > < span class = "mord mathnormal" style = "margin-right:0.07153em;" > Z< / span > < span class = "msupsub" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:0.3283em;" > < span style = "top:-2.55em;margin-left:-0.0715em;margin-right:0.05em;" > < span class = "pstrut" style = "height:2.7em;" > < / span > < span class = "sizing reset-size6 size3 mtight" > < span class = "mord mathnormal mtight" style = "margin-right:0.05764em;" > S< / span > < / span > < / span > < / span > < span class = "vlist-s" > < / span > < / span > < span class = "vlist-r" > < span class = "vlist" style = "height:0.15em;" > < span > < / span > < / span > < / span > < / span > < / span > < / span > < span class = "mspace" style = "margin-right:0.1667em;" > < / span > < span class = "minner" > < span class = "minner" > < span class = "mopen delimcenter" style = "top:0em;" > < span class = "delimsizing size3" > (< / span > < / span > < span class = "mord" > < span class = "mopen nulldelimiter" > < / span > < span class = "mfrac" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:1.3603em;" > < span style = "top:-2.314em;" > < span class = "pstrut" style = "height:3em;" > < / span > < span class = "mord" > < span class = "mord" > < span class = "mord mathnormal" style = "margin-right:0.10903em;" > N< / span > < span class = "msupsub" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:0.3283em;" > < span style = "top:-2.55em;margin-left:-0.109em;margin-right:0.05em;" > < span class = "pstrut" style = "height:2.7em;" > < / span > < span class = "sizing reset-size6 size3 mtight" > < span class = "mord mathnormal mtight" style = "margin-right:0.05764em;" > S< / span > < / span > < / span > < / span > < span class = "vlist-s" > < / span > < / span > < span class = "vlist-r" > < span class = "vlist" style = "height:0.15em;" > < span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < span style = "top:-3.23em;" > < span class = "pstrut" style = "height:3em;" > < / span > < span class = "frac-line" style = "border-bottom-width:0.04em;" > < / span > < / span > < span style = "top:-3.677em;" > < span class = "pstrut" style = "height:3em;" > < / span > < span class = "mord" > < span class = "mord" > < span class = "mord mathnormal" style = "margin-right:0.10903em;" > N< / span > < span class = "msupsub" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:0.3283em;" > < span style = "top:-2.55em;margin-left:-0.109em;margin-right:0.05em;" > < span class = "pstrut" style = "height:2.7em;" > < / span > < span class = "sizing reset-size6 size3 mtight" > < span class = "mord mathnormal mtight" style = "margin-right:0.13889em;" > P< / span > < / span > < / span > < / span > < span class = "vlist-s" > < / span > < /s
< / math >
< h4 dir = "auto" id = "maximum-power-1" > Maximum power.< / h4 >
< p dir = "auto" > If load is resistive (< span class = "katex" > < span class = "katex-mathml" > < math xmlns = "http://www.w3.org/1998/Math/MathML" > < semantics > < mrow > < mi > j< / mi > < msub > < mi > X< / mi > < mtext > load< / mtext > < / msub > < mo > =< / mo > < mn > 0< / mn > < / mrow > < annotation encoding = "application/x-tex" > jX_\text{load}=0< / annotation > < / semantics > < / math > < / span > < span class = "katex-html" aria-hidden = "true" > < span class = "base" > < span class = "strut" style = "height:0.8778em;vertical-align:-0.1944em;" > < / span > < span class = "mord mathnormal" style = "margin-right:0.05724em;" > j< / span > < span class = "mord" > < span class = "mord mathnormal" style = "margin-right:0.07847em;" > X< / span > < span class = "msupsub" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:0.3361em;" > < span style = "top:-2.55em;margin-left:-0.0785em;margin-right:0.05em;" > < span class = "pstrut" style = "height:2.7em;" > < / span > < span class = "sizing reset-size6 size3 mtight" > < span class = "mord text mtight" > < span class = "mord mtight" > load< / span > < / span > < / span > < / span > < / span > < span class = "vlist-s" > < / span > < / span > < span class = "vlist-r" > < span class = "vlist" style = "height:0.15em;" > < span > < / span > < / span > < / span > < / span > < / span > < / span > < span class = "mspace" style = "margin-right:0.2778em;" > < / span > < span class = "mrel" > =< / span > < span class = "mspace" style = "margin-right:0.2778em;" > < / span > < / span > < span class = "base" > < span class = "strut" style = "height:0.6444em;" > < / span > < span class = "mord" > 0< / span > < / span > < / span > < / span > ) then for maximum power transfer:< / p >
< p > < span class = "katex-display" > < span class = "katex" > < span class = "katex-mathml" > < math xmlns = "http://www.w3.org/1998/Math/MathML" display = "block" > < semantics > < mrow > < msub > < mi > R< / mi > < mtext > load< / mtext > < / msub > < mo > =< / mo > < mi mathvariant = "normal" > ∣ < / mi > < msup > < msub > < mi > R< / mi > < mtext > src< / mtext > < / msub > < mn > 2< / mn > < / msup > < mo > +< / mo > < mi > j< / mi > < msup > < msub > < mi > X< / mi > < mtext > src< / mtext > < / msub > < mn > 2< / mn > < / msup > < mi mathvariant = "normal" > ∣ < / mi > < / mrow > < annotation encoding = "application/x-tex" > R_\text{load}=|{R_\text{src}}^2+j{X_\text{src}}^2|< / annotation > < / semantics > < / math > < / span > < span class = "katex-html" aria-hidden = "true" > < span class = "base" > < span class = "strut" style = "height:0.8333em;vertical-align:-0.15em;" > < / span > < span class = "mord" > < span class = "mord mathnormal" style = "margin-right:0.00773em;" > R< / span > < span class = "msupsub" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:0.3361em;" > < span style = "top:-2.55em;margin-left:-0.0077em;margin-right:0.05em;" > < span class = "pstrut" style = "height:2.7em;" > < / span > < span class = "sizing reset-size6 size3 mtight" > < span class = "mord text mtight" > < span class = "mord mtight" > load< / span > < / span > < / span > < / span > < / span > < span class = "vlist-s" > < / span > < / span > < span class = "vlist-r" > < span class = "vlist" style = "height:0.15em;" > < span > < / span > < / span > < / span > < / span > < / span > < / span > < span class = "mspace" style = "margin-right:0.2778em;" > < / span > < span class = "mrel" > =< / span > < span class = "mspace" style = "margin-right:0.2778em;" > < / span > < / span > < span class = "base" > < span class = "strut" style = "height:1.1373em;vertical-align:-0.25em;" > < / span > < span class = "mord" > ∣ < / span > < span class = "mord" > < span class = "mord" > < span class = "mord" > < span class = "mord mathnormal" style = "margin-right:0.00773em;" > R< / span > < span class = "msupsub" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:0.1514em;" > < span style = "top:-2.55em;margin-left:-0.0077em;margin-right:0.05em;" > < span class = "pstrut" style = "height:2.7em;" > < / span > < span class = "sizing reset-size6 size3 mtight" > < span class = "mord text mtight" > < span class = "mord mtight" > src< / span > < / span > < / span > < / span > < / span > < span class = "vlist-s" > < / span > < / span > < span class = "vlist-r" > < span class = "vlist" style = "height:0.15em;" > < span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < span class = "msupsub" > < span class = "vlist-t" > < span class = "vlist-r" > < span class = "vlist" style = "height:0.8873em;" > < span style = "top:-3.1362em;margin-right:0.05em;" > < span class = "pstrut" style = "height:2.7em;" > < / span > < span class = "sizing reset-size6 size3 mtight" > < span class = "mord mtight" > 2< / span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < span class = "mspace" style = "margin-right:0.2222em;" > < / span > < span class = "mbin" > +< / span > < span class = "mspace" style = "margin-right:0.2222em;" > < / span > < / span > < span class = "base" > < span class = "strut" style = "height:1.1373em;vertical-align:-0.25em;" > < / span > < span class = "mord mathnormal" style = "margin-right:0.05724em;" > j< / span > < span class = "mord" > < span class = "mord" > < span class = "mord" > < span class = "mord mathnormal" style = "margin-right:0.07847em;" > X< / span > < span class = "msupsub" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:0.1514em;" > < span style = "top:-2.55em;margin-left:-0.0785em;margin-right:0.05em;" > < span class = "pstrut" style = "height:2.7em;" > < / span > < span class = "sizing reset-size6 size3 mtight" > < span class = "mord text mtight" > < span class = "mord mtight" > src< / span > < / span > < / span > < / span > < / span > < span class = "vlist-s" > < / span > < / span > < span class = "vlist-r" > < span class = "vlist" style = "height:0.15em;" > < span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < span class = "msupsub" > < span class = "vlist-t" > < span class = "vlist-r" > < span class = "vlist" style = "height:0.8873em;" > < span style = "top:-3.1362em;margin-right:0.05em;" > < span class = "pstrut" style = "height:2.7em;" > < / span > < span class = "sizing reset-size6 size3 mtight" > < span class = "mord mtight" > 2< / span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < span class = "mord" > ∣ < / span > < / span > < / span > < / span > < / span > < / p >
< / math >
< h4 dir = "auto" id = "parameter-identification-1" > Parameter identification< / h4 >
< div dir = "auto" > < / div >
< center > < img src = "2022-10-28-15-52-14.png" width = 400px > < / center >
< table dir = "auto" >
< thead dir = "auto" >
< tr dir = "auto" >
< th > Open-circuit test< / th >
< th > Short-circuit test< / th >
< / tr >
< / thead >
< tbody dir = "auto" >
< tr dir = "auto" >
< td > < center > < img src = "2022-10-28-15-53-29.png" width = 300px > < / center > < / td >
< td > < center > < img src = "2022-10-28-15-52-58.png" width = 300px > < / center > < / td >
< / tr >
< / tbody >
< / table >
< h4 dir = "auto" id = "voltage-regulation-3" > Voltage regulation< / h4 >
< p > < span class = "katex-display" > < span class = "katex" > < span class = "katex-mathml" > < math xmlns = "http://www.w3.org/1998/Math/MathML" display = "block" > < semantics > < mrow > < mtext > VR< / mtext > < mo > =< / mo > < mfrac > < mrow > < mi mathvariant = "normal" > ∣ < / mi > < msub > < mi > V< / mi > < mtext > NL,P< / mtext > < / msub > < mi mathvariant = "normal" > ∣ < / mi > < mo > − < / mo > < mi mathvariant = "normal" > ∣ < / mi > < msub > < mi > V< / mi > < mtext > rated,P< / mtext > < / msub > < mi mathvariant = "normal" > ∣ < / mi > < / mrow > < mrow > < mi mathvariant = "normal" > ∣ < / mi > < msub > < mi > V< / mi > < mtext > rated,P< / mtext > < / msub > < mi mathvariant = "normal" > ∣ < / mi > < / mrow > < / mfrac > < mo > =< / mo > < mfrac > < mrow > < mi mathvariant = "normal" > ∣ < / mi > < msub > < mi > V< / mi > < mtext > in< / mtext > < / msub > < mi mathvariant = "normal" > ∣ < / mi > < mo > − < / mo > < mi mathvariant = "normal" > ∣ < / mi > < msub > < mi > V< / mi > < mtext > rated,P< / mtext > < / msub > < mi mathvariant = "normal" > ∣ < / mi > < / mrow > < mrow > < mi mathvariant = "normal" > ∣ < / mi > < msub > < mi > V< / mi > < mtext > rated,P< / mtext > < / msub > < mi mathvariant = "normal" > ∣ < / mi > < / mrow > < / mfrac > < / mrow > < annotation encoding = "application/x-tex" > \text{VR}=\frac{|V_\text{NL,P}|-|V_\text{rated,P}|}{|V_\text{rated,P}|}=\frac{|V_\text{in}|-|V_\text{rated,P}|}{|V_\text{rated,P}|}< / annotation > < / semantics > < / math > < / span > < span class = "katex-html" aria-hidden = "true" > < span class = "base" > < span class = "strut" style = "height:0.6833em;" > < / span > < span class = "mord text" > < span class = "mord" > VR< / span > < / span > < span class = "mspace" style = "margin-right:0.2778em;" > < / span > < span class = "mrel" > =< / span > < span class = "mspace" style = "margin-right:0.2778em;" > < / span > < / span > < span class = "base" > < span class = "strut" style = "height:2.3991em;vertical-align:-0.9721em;" > < / span > < span class = "mord" > < span class = "mopen nulldelimiter" > < / span > < span class = "mfrac" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:1.427em;" > < span style = "top:-2.314em;" > < span class = "pstrut" style = "height:3em;" > < / span > < span class = "mord" > < span class = "mord" > ∣ < / span > < span class = "mord" > < span class = "mord mathnormal" style = "margin-right:0.22222em;" > V< / span > < span class = "msupsub" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:0.3361em;" > < span style = "top:-2.55em;margin-left:-0.2222em;margin-right:0.05em;" > < span class = "pstrut" style = "height:2.7em;" > < / span > < span class = "sizing reset-size6 size3 mtight" > < span class = "mord text mtight" > < span class = "mord mtight" > rated,P< / span > < / span > < / span > < / span > < / span > < span class = "vlist-s" > < / span > < / span > < span class = "vlist-r" > < span class = "vlist" style = "height:0.2861em;" > < span > < / span > < / span > < / span > < / span > < / span > < / span > < span class = "mord" > ∣ < / span > < / span > < / span > < span style = "top:-3.23em;" > < span class = "pstrut" style = "height:3em;" > < / span > < span class = "frac-line" style = "border-bottom-width:0.04em;" > < / span > < / span > < span style = "top:-3.677em;" > < span class = "pstrut" style = "height:3em;" > < / span > < span class = "mord" > < span class = "mord" > ∣ < / span > < span class = "mord" > < span class = "mord mathnormal" style = "margin-right:0.22222em;" > V< / span > < span class = "msupsub" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:0.3283em;" > < span style = "top:-2.55em;margin-left:-0.2222em;margin-right:0.05em;" > < span class = "pstrut" style = "height:2.7em;" > < / span > < span class = "sizing reset-size6 size3 mtight" > < span class = "mord text mtight" > < span class = "mord mtight" > NL,P< / span > < / span > < / span > < / span > < / span > < span class = "vlist-s" > < / span > < / span > < span class = "vlist-r" > < span class = "vlist" style = "height:0.2861em;" > < span > < / span > < / span > < / span > < / span > < / span > < / span > < span class = "mord" > ∣ < / span > < span class = "mspace" style = "margin-right:0.2222em;" > < / span > < span class = "mbin" > − < / span > < span class = "mspace" style = "margin-right:0.2222em;" > < / span > < span class = "mord" > ∣ < / span > < span class = "mord" > < span class = "mord mathnormal" style = "margin-right:0.22222em;" > V< / span > < span class = "msupsub" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:0.3361em;" > < span style = "top:-2.55em;margin-left:-0.2222em;margin-right:0.05em;" > < span class = "pstrut" style = "height:2.7em;" > < / span > < span class = "sizing reset-size6 size3 mtight" > < span class = "mord text mtight" > < span class = "mor
< / math >
< p dir = "auto" > Ignore shunt resistance. Refer from primary side. Use KVL to determine < span class = "katex" > < span class = "katex-mathml" > < math xmlns = "http://www.w3.org/1998/Math/MathML" > < semantics > < mrow > < msub > < mi > V< / mi > < mtext > in< / mtext > < / msub > < / mrow > < annotation encoding = "application/x-tex" > V_\text{in}< / annotation > < / semantics > < / math > < / span > < span class = "katex-html" aria-hidden = "true" > < span class = "base" > < span class = "strut" style = "height:0.8333em;vertical-align:-0.15em;" > < / span > < span class = "mord" > < span class = "mord mathnormal" style = "margin-right:0.22222em;" > V< / span > < span class = "msupsub" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:0.3175em;" > < span style = "top:-2.55em;margin-left:-0.2222em;margin-right:0.05em;" > < span class = "pstrut" style = "height:2.7em;" > < / span > < span class = "sizing reset-size6 size3 mtight" > < span class = "mord text mtight" > < span class = "mord mtight" > in< / span > < / span > < / span > < / span > < / span > < span class = "vlist-s" > < / span > < / span > < span class = "vlist-r" > < span class = "vlist" style = "height:0.15em;" > < span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > .< / p >
< p dir = "auto" > Voltage regulation is typically small.< / p >
< p > < span class = "katex-display" > < span class = "katex" > < span class = "katex-mathml" > < math xmlns = "http://www.w3.org/1998/Math/MathML" display = "block" > < semantics > < mrow > < mi mathvariant = "normal" > ∣ < / mi > < msub > < mi > V< / mi > < mtext > in< / mtext > < / msub > < mi mathvariant = "normal" > ∣ < / mi > < mo > =< / mo > < mi mathvariant = "normal" > ∣ < / mi > < msub > < mi > V< / mi > < mtext > rated,P< / mtext > < / msub > < mo > +< / mo > < msub > < mi > I< / mi > < mtext > L,P< / mtext > < / msub > < mo > ⋅< / mo > < mover accent = "true" > < mi > Z< / mi > < mo > ˉ< / mo > < / mover > < mi mathvariant = "normal" > ∣ < / mi > < / mrow > < annotation encoding = "application/x-tex" > |V_\text{in}|=|V_\text{rated,P}+I_\text{L,P}\cdot\bar Z|< / annotation > < / semantics > < / math > < / span > < span class = "katex-html" aria-hidden = "true" > < span class = "base" > < span class = "strut" style = "height:1em;vertical-align:-0.25em;" > < / span > < span class = "mord" > ∣ < / span > < span class = "mord" > < span class = "mord mathnormal" style = "margin-right:0.22222em;" > V< / span > < span class = "msupsub" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:0.3175em;" > < span style = "top:-2.55em;margin-left:-0.2222em;margin-right:0.05em;" > < span class = "pstrut" style = "height:2.7em;" > < / span > < span class = "sizing reset-size6 size3 mtight" > < span class = "mord text mtight" > < span class = "mord mtight" > in< / span > < / span > < / span > < / span > < / span > < span class = "vlist-s" > < / span > < / span > < span class = "vlist-r" > < span class = "vlist" style = "height:0.15em;" > < span > < / span > < / span > < / span > < / span > < / span > < / span > < span class = "mord" > ∣ < / span > < span class = "mspace" style = "margin-right:0.2778em;" > < / span > < span class = "mrel" > =< / span > < span class = "mspace" style = "margin-right:0.2778em;" > < / span > < / span > < span class = "base" > < span class = "strut" style = "height:1.0361em;vertical-align:-0.2861em;" > < / span > < span class = "mord" > ∣ < / span > < span class = "mord" > < span class = "mord mathnormal" style = "margin-right:0.22222em;" > V< / span > < span class = "msupsub" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:0.3361em;" > < span style = "top:-2.55em;margin-left:-0.2222em;margin-right:0.05em;" > < span class = "pstrut" style = "height:2.7em;" > < / span > < span class = "sizing reset-size6 size3 mtight" > < span class = "mord text mtight" > < span class = "mord mtight" > rated,P< / span > < / span > < / span > < / span > < / span > < span class = "vlist-s" > < / span > < / span > < span class = "vlist-r" > < span class = "vlist" style = "height:0.2861em;" > < span > < / span > < / span > < / span > < / span > < / span > < / span > < span class = "mspace" style = "margin-right:0.2222em;" > < / span > < span class = "mbin" > +< / span > < span class = "mspace" style = "margin-right:0.2222em;" > < / span > < / span > < span class = "base" > < span class = "strut" style = "height:0.9694em;vertical-align:-0.2861em;" > < / span > < span class = "mord" > < span class = "mord mathnormal" style = "margin-right:0.07847em;" > I< / span > < span class = "msupsub" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:0.3283em;" > < span style = "top:-2.55em;margin-left:-0.0785em;margin-right:0.05em;" > < span class = "pstrut" style = "height:2.7em;" > < / span > < span class = "sizing reset-size6 size3 mtight" > < span class = "mord text mtight" > < span class = "mord mtight" > L,P< / span > < / span > < / span > < / span > < / span > < span class = "vlist-s" > < / span > < / span > < span class = "vlist-r" > < span class = "vlist" style = "height:0.2861em;" > < span > < / span > < / span > < / span > < / span > < / span > < / span > < span class = "mspace" style = "margin-right:0.2222em;" > < / span > < span class = "mbin" > ⋅< / span > < span class = "mspace" style = "margin-right:0.2222em;" > < / span > < / span > < span class = "base" > < span class = "strut" style = "height:1.0701em;vertical-align:-0.25em;" > < / span > < span class = "mord accent" > < span class = "vlist-t" > < span class = "vlist-r" > < span class = "vlist" style = "height:0.8201em;" > < span style = "top:-3em;" > < span class = "pstrut" style = "height:3em;" > < / span > < span class = "mord mathnormal" style = "margin-right:0.07153em;" > Z< / span > < / span > < span style = "top:-3.2523em;" > < span class = "pstrut" style = "height:3em;" > < / span > < span class = "accent-body" style = "left:-0.1667em;" > < span class = "mord" > ˉ< / span > < / span > < / span > < / span > < / span > < / span > < / span > < span class = "mord" > ∣ < / span > < / span > < / span > < / span > < / span > < / p >
< / math >
< div dir = "auto" > < / div >
< center > < img src = "2022-10-28-16-30-51.png" width = 400px > < / center >
< h3 dir = "auto" id = "dc-machine-1" > DC machine< / h3 >
< table dir = "auto" >
< thead dir = "auto" >
< tr dir = "auto" >
< th > Separately excited machine< / th >
< th > Shunt excited< / th >
< th > Series excited< / th >
< / tr >
< / thead >
< tbody dir = "auto" >
< tr dir = "auto" >
< td > < center > < img src = "2022-10-28-18-21-53.png" > < / center > < / td >
< td > < center > < img src = "2022-10-28-18-22-17.png" > < / center > < / td >
< td > < center > < img src = "2022-10-28-18-28-51.png" > < / center > < / td >
< / tr >
< tr dir = "auto" >
< td > < / td >
< td > Similar torque-speed characteristic to separately-excited machine< / td >
< td > High torque per ampere. Used in high-torque applications< / td >
< / tr >
< tr dir = "auto" >
< td > Requires two independent voltage sources< / td >
< td > < / td >
< td > Do not run unloaded - infinite speed at 0 torque as < span class = "katex" > < span class = "katex-mathml" > < math xmlns = "http://www.w3.org/1998/Math/MathML" > < semantics > < mrow > < mi > ω< / mi > < mo > ∝< / mo > < mn > 1< / mn > < mi mathvariant = "normal" > /< / mi > < msqrt > < mi > τ< / mi > < / msqrt > < / mrow > < annotation encoding = "application/x-tex" > \omega\propto 1/\sqrt{\tau}< / annotation > < / semantics > < / math > < / span > < span class = "katex-html" aria-hidden = "true" > < span class = "base" > < span class = "strut" style = "height:0.4306em;" > < / span > < span class = "mord mathnormal" style = "margin-right:0.03588em;" > ω< / span > < span class = "mspace" style = "margin-right:0.2778em;" > < / span > < span class = "mrel" > ∝< / span > < span class = "mspace" style = "margin-right:0.2778em;" > < / span > < / span > < span class = "base" > < span class = "strut" style = "height:1.0503em;vertical-align:-0.25em;" > < / span > < span class = "mord" > 1/< / span > < span class = "mord sqrt" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:0.8003em;" > < span class = "svg-align" style = "top:-3em;" > < span class = "pstrut" style = "height:3em;" > < / span > < span class = "mord" style = "padding-left:0.833em;" > < span class = "mord mathnormal" style = "margin-right:0.1132em;" > τ< / span > < / span > < / span > < span style = "top:-2.7603em;" > < span class = "pstrut" style = "height:3em;" > < / span > < span class = "hide-tail" style = "min-width:0.853em;height:1.08em;" > < svg xmlns = "http://www.w3.org/2000/svg" width = '400em' height = '1.08em' viewBox = '0 0 400000 1080' preserveAspectRatio = 'xMinYMin slice' > < path d = 'M95,702
c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14
c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54
c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10
s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429
c69,-144,104.5,-217.7,106.5,-221
l0 -0
c5.3,-9.3,12,-14,20,-14
H400000v40H845.2724
s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7
c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z
M834 80h400000v40h-400000z'/>< / svg > < / span > < / span > < / span > < span class = "vlist-s" > < / span > < / span > < span class = "vlist-r" > < span class = "vlist" style = "height:0.2397em;" > < span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < / td >
< / tr >
< tr dir = "auto" >
< td > Motor control using < span class = "katex" > < span class = "katex-mathml" > < math xmlns = "http://www.w3.org/1998/Math/MathML" > < semantics > < mrow > < msub > < mi > R< / mi > < mi > f< / mi > < / msub > < / mrow > < annotation encoding = "application/x-tex" > R_f< / annotation > < / semantics > < / math > < / span > < span class = "katex-html" aria-hidden = "true" > < span class = "base" > < span class = "strut" style = "height:0.9694em;vertical-align:-0.2861em;" > < / span > < span class = "mord" > < span class = "mord mathnormal" style = "margin-right:0.00773em;" > R< / span > < span class = "msupsub" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:0.3361em;" > < span style = "top:-2.55em;margin-left:-0.0077em;margin-right:0.05em;" > < span class = "pstrut" style = "height:2.7em;" > < / span > < span class = "sizing reset-size6 size3 mtight" > < span class = "mord mathnormal mtight" style = "margin-right:0.10764em;" > f< / span > < / span > < / span > < / span > < span class = "vlist-s" > < / span > < / span > < span class = "vlist-r" > < span class = "vlist" style = "height:0.2861em;" > < span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < / td >
< td > Motor control using < span class = "katex" > < span class = "katex-mathml" > < math xmlns = "http://www.w3.org/1998/Math/MathML" > < semantics > < mrow > < msub > < mi > R< / mi > < mi > F< / mi > < / msub > < / mrow > < annotation encoding = "application/x-tex" > R_F< / annotation > < / semantics > < / math > < / span > < span class = "katex-html" aria-hidden = "true" > < span class = "base" > < span class = "strut" style = "height:0.8333em;vertical-align:-0.15em;" > < / span > < span class = "mord" > < span class = "mord mathnormal" style = "margin-right:0.00773em;" > R< / span > < span class = "msupsub" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:0.3283em;" > < span style = "top:-2.55em;margin-left:-0.0077em;margin-right:0.05em;" > < span class = "pstrut" style = "height:2.7em;" > < / span > < span class = "sizing reset-size6 size3 mtight" > < span class = "mord mathnormal mtight" style = "margin-right:0.13889em;" > F< / span > < / span > < / span > < / span > < span class = "vlist-s" > < / span > < / span > < span class = "vlist-r" > < span class = "vlist" style = "height:0.15em;" > < span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < / td >
< td > Motor control using < span class = "katex" > < span class = "katex-mathml" > < math xmlns = "http://www.w3.org/1998/Math/MathML" > < semantics > < mrow > < msub > < mi > V< / mi > < mi > T< / mi > < / msub > < / mrow > < annotation encoding = "application/x-tex" > V_T< / annotation > < / semantics > < / math > < / span > < span class = "katex-html" aria-hidden = "true" > < span class = "base" > < span class = "strut" style = "height:0.8333em;vertical-align:-0.15em;" > < / span > < span class = "mord" > < span class = "mord mathnormal" style = "margin-right:0.22222em;" > V< / span > < span class = "msupsub" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:0.3283em;" > < span style = "top:-2.55em;margin-left:-0.2222em;margin-right:0.05em;" > < span class = "pstrut" style = "height:2.7em;" > < / span > < span class = "sizing reset-size6 size3 mtight" > < span class = "mord mathnormal mtight" style = "margin-right:0.13889em;" > T< / span > < / span > < / span > < / span > < span class = "vlist-s" > < / span > < / span > < span class = "vlist-r" > < span class = "vlist" style = "height:0.15em;" > < span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > .< / td >
< / tr >
< / tbody >
< / table >
< h4 dir = "auto" id = "starting-dc-motors-1" > Starting DC motors< / h4 >
< p dir = "auto" > < span class = "katex" > < span class = "katex-mathml" > < math xmlns = "http://www.w3.org/1998/Math/MathML" > < semantics > < mrow > < msub > < mi > R< / mi > < mi > A< / mi > < / msub > < / mrow > < annotation encoding = "application/x-tex" > R_A< / annotation > < / semantics > < / math > < / span > < span class = "katex-html" aria-hidden = "true" > < span class = "base" > < span class = "strut" style = "height:0.8333em;vertical-align:-0.15em;" > < / span > < span class = "mord" > < span class = "mord mathnormal" style = "margin-right:0.00773em;" > R< / span > < span class = "msupsub" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:0.3283em;" > < span style = "top:-2.55em;margin-left:-0.0077em;margin-right:0.05em;" > < span class = "pstrut" style = "height:2.7em;" > < / span > < span class = "sizing reset-size6 size3 mtight" > < span class = "mord mathnormal mtight" > A< / span > < / span > < / span > < / span > < span class = "vlist-s" > < / span > < / span > < span class = "vlist-r" > < span class = "vlist" style = "height:0.15em;" > < span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > might need to be adjusted so it is high initially in large DC motors, as the starting current is high since there is no back-emf created by < span class = "katex" > < span class = "katex-mathml" > < math xmlns = "http://www.w3.org/1998/Math/MathML" > < semantics > < mrow > < msub > < mi > E< / mi > < mi > A< / mi > < / msub > < / mrow > < annotation encoding = "application/x-tex" > E_A< / annotation > < / semantics > < / math > < / span > < span class = "katex-html" aria-hidden = "true" > < span class = "base" > < span class = "strut" style = "height:0.8333em;vertical-align:-0.15em;" > < / span > < span class = "mord" > < span class = "mord mathnormal" style = "margin-right:0.05764em;" > E< / span > < span class = "msupsub" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:0.3283em;" > < span style = "top:-2.55em;margin-left:-0.0576em;margin-right:0.05em;" > < span class = "pstrut" style = "height:2.7em;" > < / span > < span class = "sizing reset-size6 size3 mtight" > < span class = "mord mathnormal mtight" > A< / span > < / span > < / span > < / span > < span class = "vlist-s" > < / span > < / span > < span class = "vlist-r" > < span class = "vlist" style = "height:0.15em;" > < span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > .< / p >
< h4 dir = "auto" id = "magnetizating-curve-1" > Magnetizating curve< / h4 >
< p dir = "auto" > When a question specifies the field current or < span class = "katex" > < span class = "katex-mathml" > < math xmlns = "http://www.w3.org/1998/Math/MathML" > < semantics > < mrow > < msub > < mi > R< / mi > < mtext > adj< / mtext > < / msub > < / mrow > < annotation encoding = "application/x-tex" > R_\text{adj}< / annotation > < / semantics > < / math > < / span > < span class = "katex-html" aria-hidden = "true" > < span class = "base" > < span class = "strut" style = "height:0.9694em;vertical-align:-0.2861em;" > < / span > < span class = "mord" > < span class = "mord mathnormal" style = "margin-right:0.00773em;" > R< / span > < span class = "msupsub" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:0.3361em;" > < span style = "top:-2.55em;margin-left:-0.0077em;margin-right:0.05em;" > < span class = "pstrut" style = "height:2.7em;" > < / span > < span class = "sizing reset-size6 size3 mtight" > < span class = "mord text mtight" > < span class = "mord mtight" > adj< / span > < / span > < / span > < / span > < / span > < span class = "vlist-s" > < / span > < / span > < span class = "vlist-r" > < span class = "vlist" style = "height:0.2861em;" > < span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > , refer to magnetization curve. Magnetizating curve is valid at a specific speed < span class = "katex" > < span class = "katex-mathml" > < math xmlns = "http://www.w3.org/1998/Math/MathML" > < semantics > < mrow > < msub > < mi > n< / mi > < mrow > < mi > m< / mi > < mn > 1< / mn > < / mrow > < / msub > < / mrow > < annotation encoding = "application/x-tex" > n_{m1}< / annotation > < / semantics > < / math > < / span > < span class = "katex-html" aria-hidden = "true" > < span class = "base" > < span class = "strut" style = "height:0.5806em;vertical-align:-0.15em;" > < / span > < span class = "mord" > < span class = "mord mathnormal" > n< / span > < span class = "msupsub" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:0.3011em;" > < span style = "top:-2.55em;margin-left:0em;margin-right:0.05em;" > < span class = "pstrut" style = "height:2.7em;" > < / span > < span class = "sizing reset-size6 size3 mtight" > < span class = "mord mtight" > < span class = "mord mathnormal mtight" > m< / span > < span class = "mord mtight" > 1< / span > < / span > < / span > < / span > < / span > < span class = "vlist-s" > < / span > < / span > < span class = "vlist-r" > < span class = "vlist" style = "height:0.15em;" > < span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > , and the curve is used to find < span class = "katex" > < span class = "katex-mathml" > < math xmlns = "http://www.w3.org/1998/Math/MathML" > < semantics > < mrow > < msub > < mi > E< / mi > < mrow > < mi > A< / mi > < mn > 1< / mn > < / mrow > < / msub > < / mrow > < annotation encoding = "application/x-tex" > E_{A1}< / annotation > < / semantics > < / math > < / span > < span class = "katex-html" aria-hidden = "true" > < span class = "base" > < span class = "strut" style = "height:0.8333em;vertical-align:-0.15em;" > < / span > < span class = "mord" > < span class = "mord mathnormal" style = "margin-right:0.05764em;" > E< / span > < span class = "msupsub" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:0.3283em;" > < span style = "top:-2.55em;margin-left:-0.0576em;margin-right:0.05em;" > < span class = "pstrut" style = "height:2.7em;" > < / span > < span class = "sizing reset-size6 size3 mtight" > < span class = "mord mtight" > < span class = "mord mathnormal mtight" > A< / span > < span class = "mord mtight" > 1< / span > < / span > < / span > < / span > < / span > < span class = "vlist-s" > < / span > < / span > < span class = "vlist-r" > < span class = "vlist" style = "height:0.15em;" > < span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > . Using the load condition to find the armature current < span class = "katex" > < span class = "katex-mathml" > < math xmlns = "http://www.w3.org/1998/Math/MathML" > < semantics > < mrow > < msub > < mi > I< / mi > < mi > A< / mi > < / msub > < mo > =< / mo > < msub > < mi > τ< / mi > < mtext > ind< / mtext > < / msub > < mi mathvariant = "normal" > /< / mi > < mo stretchy = "false" > (< / mo > < mi > K< / mi > < mi > Φ< / mi > < mo stretchy = "false" > )< / mo > < / mrow > < annotation encoding = "application/x-tex" > I_A=\tau_\text{ind}/(K\varPhi)< / annotation > < / semantics > < / math > < / span > < span class = "katex-html" aria-hidden = "true" > < span class = "base" > < span class = "strut" style = "height:0.8333em;vertical-align:-0.15em;" > < / span > < span class = "mord" > < span class = "mord mathnormal" style = "margin-right:0.07847em;" > I< / span > < span class = "msupsub" > < span class = "vlist-t vlist-t2" > < span
< h4 dir = "auto" id = "idk-1" > Idk< / h4 >
< p > < span class = "katex-display" > < span class = "katex" > < span class = "katex-mathml" > < math xmlns = "http://www.w3.org/1998/Math/MathML" display = "block" > < semantics > < mrow > < msub > < mi > P< / mi > < mtext > mech< / mtext > < / msub > < mo > =< / mo > < msub > < mi > E< / mi > < mi > A< / mi > < / msub > < msub > < mi > I< / mi > < mi > A< / mi > < / msub > < / mrow > < annotation encoding = "application/x-tex" > P_\text{mech}=E_AI_A< / annotation > < / semantics > < / math > < / span > < span class = "katex-html" aria-hidden = "true" > < span class = "base" > < span class = "strut" style = "height:0.8333em;vertical-align:-0.15em;" > < / span > < span class = "mord" > < span class = "mord mathnormal" style = "margin-right:0.13889em;" > P< / span > < span class = "msupsub" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:0.3361em;" > < span style = "top:-2.55em;margin-left:-0.1389em;margin-right:0.05em;" > < span class = "pstrut" style = "height:2.7em;" > < / span > < span class = "sizing reset-size6 size3 mtight" > < span class = "mord text mtight" > < span class = "mord mtight" > mech< / span > < / span > < / span > < / span > < / span > < span class = "vlist-s" > < / span > < / span > < span class = "vlist-r" > < span class = "vlist" style = "height:0.15em;" > < span > < / span > < / span > < / span > < / span > < / span > < / span > < span class = "mspace" style = "margin-right:0.2778em;" > < / span > < span class = "mrel" > =< / span > < span class = "mspace" style = "margin-right:0.2778em;" > < / span > < / span > < span class = "base" > < span class = "strut" style = "height:0.8333em;vertical-align:-0.15em;" > < / span > < span class = "mord" > < span class = "mord mathnormal" style = "margin-right:0.05764em;" > E< / span > < span class = "msupsub" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:0.3283em;" > < span style = "top:-2.55em;margin-left:-0.0576em;margin-right:0.05em;" > < span class = "pstrut" style = "height:2.7em;" > < / span > < span class = "sizing reset-size6 size3 mtight" > < span class = "mord mathnormal mtight" > A< / span > < / span > < / span > < / span > < span class = "vlist-s" > < / span > < / span > < span class = "vlist-r" > < span class = "vlist" style = "height:0.15em;" > < span > < / span > < / span > < / span > < / span > < / span > < / span > < span class = "mord" > < span class = "mord mathnormal" style = "margin-right:0.07847em;" > I< / span > < span class = "msupsub" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:0.3283em;" > < span style = "top:-2.55em;margin-left:-0.0785em;margin-right:0.05em;" > < span class = "pstrut" style = "height:2.7em;" > < / span > < span class = "sizing reset-size6 size3 mtight" > < span class = "mord mathnormal mtight" > A< / span > < / span > < / span > < / span > < span class = "vlist-s" > < / span > < / span > < span class = "vlist-r" > < span class = "vlist" style = "height:0.15em;" > < span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < / p >
< / math >
< p dir = "auto" > No-load separately excited machine. Assuming no mechanical losses.< / p >
< p > < span class = "katex-display" > < span class = "katex" > < span class = "katex-mathml" > < math xmlns = "http://www.w3.org/1998/Math/MathML" display = "block" > < semantics > < mrow > < msub > < mi > E< / mi > < mi > A< / mi > < / msub > < mo > =< / mo > < msub > < mi > V< / mi > < mi > A< / mi > < / msub > < mtext > < / mtext > < / mrow > < annotation encoding = "application/x-tex" > E_A=V_A\text{ (No load)}< / annotation > < / semantics > < / math > < / span > < span class = "katex-html" aria-hidden = "true" > < span class = "base" > < span class = "strut" style = "height:0.8333em;vertical-align:-0.15em;" > < / span > < span class = "mord" > < span class = "mord mathnormal" style = "margin-right:0.05764em;" > E< / span > < span class = "msupsub" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:0.3283em;" > < span style = "top:-2.55em;margin-left:-0.0576em;margin-right:0.05em;" > < span class = "pstrut" style = "height:2.7em;" > < / span > < span class = "sizing reset-size6 size3 mtight" > < span class = "mord mathnormal mtight" > A< / span > < / span > < / span > < / span > < span class = "vlist-s" > < / span > < / span > < span class = "vlist-r" > < span class = "vlist" style = "height:0.15em;" > < span > < / span > < / span > < / span > < / span > < / span > < / span > < span class = "mspace" style = "margin-right:0.2778em;" > < / span > < span class = "mrel" > =< / span > < span class = "mspace" style = "margin-right:0.2778em;" > < / span > < / span > < span class = "base" > < span class = "strut" style = "height:1em;vertical-align:-0.25em;" > < / span > < span class = "mord" > < span class = "mord mathnormal" style = "margin-right:0.22222em;" > V< / span > < span class = "msupsub" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:0.3283em;" > < span style = "top:-2.55em;margin-left:-0.2222em;margin-right:0.05em;" > < span class = "pstrut" style = "height:2.7em;" > < / span > < span class = "sizing reset-size6 size3 mtight" > < span class = "mord mathnormal mtight" > A< / span > < / span > < / span > < / span > < span class = "vlist-s" > < / span > < / span > < span class = "vlist-r" > < span class = "vlist" style = "height:0.15em;" > < span > < / span > < / span > < / span > < / span > < / span > < / span > < span class = "mord text" > < span class = "mord" > < / span > < / span > < / span > < / span > < / span > < / span > < / p >
< / math >
< p > < span class = "katex-display" > < span class = "katex" > < span class = "katex-mathml" > < math xmlns = "http://www.w3.org/1998/Math/MathML" display = "block" > < semantics > < mrow > < msub > < mi > I< / mi > < mi > A< / mi > < / msub > < mo > =< / mo > < mn > 0< / mn > < mtext > < / mtext > < / mrow > < annotation encoding = "application/x-tex" > I_A=0\text{ (No load)}< / annotation > < / semantics > < / math > < / span > < span class = "katex-html" aria-hidden = "true" > < span class = "base" > < span class = "strut" style = "height:0.8333em;vertical-align:-0.15em;" > < / span > < span class = "mord" > < span class = "mord mathnormal" style = "margin-right:0.07847em;" > I< / span > < span class = "msupsub" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:0.3283em;" > < span style = "top:-2.55em;margin-left:-0.0785em;margin-right:0.05em;" > < span class = "pstrut" style = "height:2.7em;" > < / span > < span class = "sizing reset-size6 size3 mtight" > < span class = "mord mathnormal mtight" > A< / span > < / span > < / span > < / span > < span class = "vlist-s" > < / span > < / span > < span class = "vlist-r" > < span class = "vlist" style = "height:0.15em;" > < span > < / span > < / span > < / span > < / span > < / span > < / span > < span class = "mspace" style = "margin-right:0.2778em;" > < / span > < span class = "mrel" > =< / span > < span class = "mspace" style = "margin-right:0.2778em;" > < / span > < / span > < span class = "base" > < span class = "strut" style = "height:1em;vertical-align:-0.25em;" > < / span > < span class = "mord" > 0< / span > < span class = "mord text" > < span class = "mord" > < / span > < / span > < / span > < / span > < / span > < / span > < / p >
< / math >
< p dir = "auto" > Armature reaction causes increase in speed and causes instability as the core saturates near the poles. Can be reduced with compensating winding which is in series with the armature coil.< / p >
< p > < span class = "katex-display" > < span class = "katex" > < span class = "katex-mathml" > < math xmlns = "http://www.w3.org/1998/Math/MathML" display = "block" > < semantics > < mrow > < mi > K< / mi > < mi mathvariant = "normal" > Φ< / mi > < mi > ω< / mi > < mo > =< / mo > < msub > < mi > E< / mi > < mi > A< / mi > < / msub > < / mrow > < annotation encoding = "application/x-tex" > K\Phi\omega=E_A< / annotation > < / semantics > < / math > < / span > < span class = "katex-html" aria-hidden = "true" > < span class = "base" > < span class = "strut" style = "height:0.6833em;" > < / span > < span class = "mord mathnormal" style = "margin-right:0.07153em;" > K< / span > < span class = "mord" > Φ< / span > < span class = "mord mathnormal" style = "margin-right:0.03588em;" > ω< / span > < span class = "mspace" style = "margin-right:0.2778em;" > < / span > < span class = "mrel" > =< / span > < span class = "mspace" style = "margin-right:0.2778em;" > < / span > < / span > < span class = "base" > < span class = "strut" style = "height:0.8333em;vertical-align:-0.15em;" > < / span > < span class = "mord" > < span class = "mord mathnormal" style = "margin-right:0.05764em;" > E< / span > < span class = "msupsub" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:0.3283em;" > < span style = "top:-2.55em;margin-left:-0.0576em;margin-right:0.05em;" > < span class = "pstrut" style = "height:2.7em;" > < / span > < span class = "sizing reset-size6 size3 mtight" > < span class = "mord mathnormal mtight" > A< / span > < / span > < / span > < / span > < span class = "vlist-s" > < / span > < / span > < span class = "vlist-r" > < span class = "vlist" style = "height:0.15em;" > < span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < / p >
< / math >
< p > < span class = "katex-display" > < span class = "katex" > < span class = "katex-mathml" > < math xmlns = "http://www.w3.org/1998/Math/MathML" display = "block" > < semantics > < mrow > < mi > K< / mi > < mi mathvariant = "normal" > Φ< / mi > < msub > < mi > I< / mi > < mi > A< / mi > < / msub > < mo > =< / mo > < mi > τ< / mi > < / mrow > < annotation encoding = "application/x-tex" > K\Phi I_A=\tau< / annotation > < / semantics > < / math > < / span > < span class = "katex-html" aria-hidden = "true" > < span class = "base" > < span class = "strut" style = "height:0.8333em;vertical-align:-0.15em;" > < / span > < span class = "mord mathnormal" style = "margin-right:0.07153em;" > K< / span > < span class = "mord" > Φ< / span > < span class = "mord" > < span class = "mord mathnormal" style = "margin-right:0.07847em;" > I< / span > < span class = "msupsub" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:0.3283em;" > < span style = "top:-2.55em;margin-left:-0.0785em;margin-right:0.05em;" > < span class = "pstrut" style = "height:2.7em;" > < / span > < span class = "sizing reset-size6 size3 mtight" > < span class = "mord mathnormal mtight" > A< / span > < / span > < / span > < / span > < span class = "vlist-s" > < / span > < / span > < span class = "vlist-r" > < span class = "vlist" style = "height:0.15em;" > < span > < / span > < / span > < / span > < / span > < / span > < / span > < span class = "mspace" style = "margin-right:0.2778em;" > < / span > < span class = "mrel" > =< / span > < span class = "mspace" style = "margin-right:0.2778em;" > < / span > < / span > < span class = "base" > < span class = "strut" style = "height:0.4306em;" > < / span > < span class = "mord mathnormal" style = "margin-right:0.1132em;" > τ< / span > < / span > < / span > < / span > < / span > < / p >
< / math >
< p dir = "auto" > For shunt motor< / p >
< p > < span class = "katex-display" > < span class = "katex" > < span class = "katex-mathml" > < math xmlns = "http://www.w3.org/1998/Math/MathML" display = "block" > < semantics > < mrow > < mi > K< / mi > < mi mathvariant = "normal" > Φ< / mi > < mo > =< / mo > < mfrac > < mrow > < msub > < mi > V< / mi > < mi > T< / mi > < / msub > < mo > − < / mo > < msub > < mi > R< / mi > < mi > A< / mi > < / msub > < msub > < mi > I< / mi > < mi > A< / mi > < / msub > < / mrow > < mi > ω< / mi > < / mfrac > < / mrow > < annotation encoding = "application/x-tex" > K\Phi=\frac{V_T-R_AI_A}{\omega}< / annotation > < / semantics > < / math > < / span > < span class = "katex-html" aria-hidden = "true" > < span class = "base" > < span class = "strut" style = "height:0.6833em;" > < / span > < span class = "mord mathnormal" style = "margin-right:0.07153em;" > K< / span > < span class = "mord" > Φ< / span > < span class = "mspace" style = "margin-right:0.2778em;" > < / span > < span class = "mrel" > =< / span > < span class = "mspace" style = "margin-right:0.2778em;" > < / span > < / span > < span class = "base" > < span class = "strut" style = "height:2.0463em;vertical-align:-0.686em;" > < / span > < span class = "mord" > < span class = "mopen nulldelimiter" > < / span > < span class = "mfrac" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:1.3603em;" > < span style = "top:-2.314em;" > < span class = "pstrut" style = "height:3em;" > < / span > < span class = "mord" > < span class = "mord mathnormal" style = "margin-right:0.03588em;" > ω< / span > < / span > < / span > < span style = "top:-3.23em;" > < span class = "pstrut" style = "height:3em;" > < / span > < span class = "frac-line" style = "border-bottom-width:0.04em;" > < / span > < / span > < span style = "top:-3.677em;" > < span class = "pstrut" style = "height:3em;" > < / span > < span class = "mord" > < span class = "mord" > < span class = "mord mathnormal" style = "margin-right:0.22222em;" > V< / span > < span class = "msupsub" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:0.3283em;" > < span style = "top:-2.55em;margin-left:-0.2222em;margin-right:0.05em;" > < span class = "pstrut" style = "height:2.7em;" > < / span > < span class = "sizing reset-size6 size3 mtight" > < span class = "mord mathnormal mtight" style = "margin-right:0.13889em;" > T< / span > < / span > < / span > < / span > < span class = "vlist-s" > < / span > < / span > < span class = "vlist-r" > < span class = "vlist" style = "height:0.15em;" > < span > < / span > < / span > < / span > < / span > < / span > < / span > < span class = "mspace" style = "margin-right:0.2222em;" > < / span > < span class = "mbin" > − < / span > < span class = "mspace" style = "margin-right:0.2222em;" > < / span > < span class = "mord" > < span class = "mord mathnormal" style = "margin-right:0.00773em;" > R< / span > < span class = "msupsub" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:0.3283em;" > < span style = "top:-2.55em;margin-left:-0.0077em;margin-right:0.05em;" > < span class = "pstrut" style = "height:2.7em;" > < / span > < span class = "sizing reset-size6 size3 mtight" > < span class = "mord mathnormal mtight" > A< / span > < / span > < / span > < / span > < span class = "vlist-s" > < / span > < / span > < span class = "vlist-r" > < span class = "vlist" style = "height:0.15em;" > < span > < / span > < / span > < / span > < / span > < / span > < / span > < span class = "mord" > < span class = "mord mathnormal" style = "margin-right:0.07847em;" > I< / span > < span class = "msupsub" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:0.3283em;" > < span style = "top:-2.55em;margin-left:-0.0785em;margin-right:0.05em;" > < span class = "pstrut" style = "height:2.7em;" > < / span > < span class = "sizing reset-size6 size3 mtight" > < span class = "mord mathnormal mtight" > A< / span > < / span > < / span > < / span > < span class = "vlist-s" > < / span > < / span > < span class = "vlist-r" > < span class = "vlist" style = "height:0.15em;" > < span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < span class = "vlist-s" > < / span > < / span > < span class = "vlist-r" > < span class = "vlist" style = "height:0.686em;" > < span > < / span > < / span > < / span > < / span > < / span > < span class = "mclose nulldelimiter" > < / span > < / span > < / span > < / span > < / span > < / span > < / p >
< / math >
< p > < span class = "katex-display" > < span class = "katex" > < span class = "katex-mathml" > < math xmlns = "http://www.w3.org/1998/Math/MathML" display = "block" > < semantics > < mrow > < mi > τ< / mi > < mo > =< / mo > < mi > K< / mi > < mi mathvariant = "normal" > Φ< / mi > < msub > < mi > I< / mi > < mi > A< / mi > < / msub > < mo > =< / mo > < mfrac > < mrow > < msub > < mi > V< / mi > < mi > T< / mi > < / msub > < mo > − < / mo > < msub > < mi > R< / mi > < mi > A< / mi > < / msub > < msub > < mi > I< / mi > < mi > A< / mi > < / msub > < / mrow > < mi > ω< / mi > < / mfrac > < msub > < mi > I< / mi > < mi > A< / mi > < / msub > < / mrow > < annotation encoding = "application/x-tex" > \tau=K\Phi I_A=\frac{V_T-R_AI_A}{\omega}I_A< / annotation > < / semantics > < / math > < / span > < span class = "katex-html" aria-hidden = "true" > < span class = "base" > < span class = "strut" style = "height:0.4306em;" > < / span > < span class = "mord mathnormal" style = "margin-right:0.1132em;" > τ< / span > < span class = "mspace" style = "margin-right:0.2778em;" > < / span > < span class = "mrel" > =< / span > < span class = "mspace" style = "margin-right:0.2778em;" > < / span > < / span > < span class = "base" > < span class = "strut" style = "height:0.8333em;vertical-align:-0.15em;" > < / span > < span class = "mord mathnormal" style = "margin-right:0.07153em;" > K< / span > < span class = "mord" > Φ< / span > < span class = "mord" > < span class = "mord mathnormal" style = "margin-right:0.07847em;" > I< / span > < span class = "msupsub" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:0.3283em;" > < span style = "top:-2.55em;margin-left:-0.0785em;margin-right:0.05em;" > < span class = "pstrut" style = "height:2.7em;" > < / span > < span class = "sizing reset-size6 size3 mtight" > < span class = "mord mathnormal mtight" > A< / span > < / span > < / span > < / span > < span class = "vlist-s" > < / span > < / span > < span class = "vlist-r" > < span class = "vlist" style = "height:0.15em;" > < span > < / span > < / span > < / span > < / span > < / span > < / span > < span class = "mspace" style = "margin-right:0.2778em;" > < / span > < span class = "mrel" > =< / span > < span class = "mspace" style = "margin-right:0.2778em;" > < / span > < / span > < span class = "base" > < span class = "strut" style = "height:2.0463em;vertical-align:-0.686em;" > < / span > < span class = "mord" > < span class = "mopen nulldelimiter" > < / span > < span class = "mfrac" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:1.3603em;" > < span style = "top:-2.314em;" > < span class = "pstrut" style = "height:3em;" > < / span > < span class = "mord" > < span class = "mord mathnormal" style = "margin-right:0.03588em;" > ω< / span > < / span > < / span > < span style = "top:-3.23em;" > < span class = "pstrut" style = "height:3em;" > < / span > < span class = "frac-line" style = "border-bottom-width:0.04em;" > < / span > < / span > < span style = "top:-3.677em;" > < span class = "pstrut" style = "height:3em;" > < / span > < span class = "mord" > < span class = "mord" > < span class = "mord mathnormal" style = "margin-right:0.22222em;" > V< / span > < span class = "msupsub" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:0.3283em;" > < span style = "top:-2.55em;margin-left:-0.2222em;margin-right:0.05em;" > < span class = "pstrut" style = "height:2.7em;" > < / span > < span class = "sizing reset-size6 size3 mtight" > < span class = "mord mathnormal mtight" style = "margin-right:0.13889em;" > T< / span > < / span > < / span > < / span > < span class = "vlist-s" > < / span > < / span > < span class = "vlist-r" > < span class = "vlist" style = "height:0.15em;" > < span > < / span > < / span > < / span > < / span > < / span > < / span > < span class = "mspace" style = "margin-right:0.2222em;" > < / span > < span class = "mbin" > − < / span > < span class = "mspace" style = "margin-right:0.2222em;" > < / span > < span class = "mord" > < span class = "mord mathnormal" style = "margin-right:0.00773em;" > R< / span > < span class = "msupsub" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:0.3283em;" > < span style = "top:-2.55em;margin-left:-0.0077em;margin-right:0.05em;" > < span class = "pstrut" style = "height:2.7em;" > < / span > < span class = "sizing reset-size6 size3 mtight" > < span class = "mord mathnormal mtight" > A< / span > < / span > < / span > < / span > < span class = "vlist-s" > < / span > < / span > < span class = "vlist-r" > < span class = "vlist" style = "height:0.15em;" > < span > < / span > < / span > < / span > < / span > < / span > < / span > < span class = "mord" > < span class = "mord mathnormal" style = "margin-right:0.07847em;" > I< / span > < span class = "msupsub" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist"
< / math >
< p dir = "auto" > Assume no saturation, speed locked(?):< / p >
< p dir = "auto" > This doesn't seem right. We are meant to use the machine constant and the proportionality of current to magnetic flux.< / p >
< p > < span class = "katex-display" > < span class = "katex" > < span class = "katex-mathml" > < math xmlns = "http://www.w3.org/1998/Math/MathML" display = "block" > < semantics > < mrow > < mfrac > < msub > < mi > E< / mi > < mrow > < mi > A< / mi > < mn > 2< / mn > < / mrow > < / msub > < msub > < mi > E< / mi > < mrow > < mi > A< / mi > < mn > 1< / mn > < / mrow > < / msub > < / mfrac > < mo > =< / mo > < mfrac > < msub > < mi > I< / mi > < mrow > < mi > f< / mi > < mn > 2< / mn > < / mrow > < / msub > < msub > < mi > I< / mi > < mrow > < mi > f< / mi > < mn > 1< / mn > < / mrow > < / msub > < / mfrac > < / mrow > < annotation encoding = "application/x-tex" > \frac{E_{A2}}{E_{A1}}=\frac{I_{f2}}{I_{f1}}< / annotation > < / semantics > < / math > < / span > < span class = "katex-html" aria-hidden = "true" > < span class = "base" > < span class = "strut" style = "height:2.1963em;vertical-align:-0.836em;" > < / span > < span class = "mord" > < span class = "mopen nulldelimiter" > < / span > < span class = "mfrac" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:1.3603em;" > < span style = "top:-2.314em;" > < span class = "pstrut" style = "height:3em;" > < / span > < span class = "mord" > < span class = "mord" > < span class = "mord mathnormal" style = "margin-right:0.05764em;" > E< / span > < span class = "msupsub" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:0.3283em;" > < span style = "top:-2.55em;margin-left:-0.0576em;margin-right:0.05em;" > < span class = "pstrut" style = "height:2.7em;" > < / span > < span class = "sizing reset-size6 size3 mtight" > < span class = "mord mtight" > < span class = "mord mathnormal mtight" > A< / span > < span class = "mord mtight" > 1< / span > < / span > < / span > < / span > < / span > < span class = "vlist-s" > < / span > < / span > < span class = "vlist-r" > < span class = "vlist" style = "height:0.15em;" > < span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < span style = "top:-3.23em;" > < span class = "pstrut" style = "height:3em;" > < / span > < span class = "frac-line" style = "border-bottom-width:0.04em;" > < / span > < / span > < span style = "top:-3.677em;" > < span class = "pstrut" style = "height:3em;" > < / span > < span class = "mord" > < span class = "mord" > < span class = "mord mathnormal" style = "margin-right:0.05764em;" > E< / span > < span class = "msupsub" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:0.3283em;" > < span style = "top:-2.55em;margin-left:-0.0576em;margin-right:0.05em;" > < span class = "pstrut" style = "height:2.7em;" > < / span > < span class = "sizing reset-size6 size3 mtight" > < span class = "mord mtight" > < span class = "mord mathnormal mtight" > A< / span > < span class = "mord mtight" > 2< / span > < / span > < / span > < / span > < / span > < span class = "vlist-s" > < / span > < / span > < span class = "vlist-r" > < span class = "vlist" style = "height:0.15em;" > < span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < span class = "vlist-s" > < / span > < / span > < span class = "vlist-r" > < span class = "vlist" style = "height:0.836em;" > < span > < / span > < / span > < / span > < / span > < / span > < span class = "mclose nulldelimiter" > < / span > < / span > < span class = "mspace" style = "margin-right:0.2778em;" > < / span > < span class = "mrel" > =< / span > < span class = "mspace" style = "margin-right:0.2778em;" > < / span > < / span > < span class = "base" > < span class = "strut" style = "height:2.3324em;vertical-align:-0.9721em;" > < / span > < span class = "mord" > < span class = "mopen nulldelimiter" > < / span > < span class = "mfrac" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:1.3603em;" > < span style = "top:-2.314em;" > < span class = "pstrut" style = "height:3em;" > < / span > < span class = "mord" > < span class = "mord" > < span class = "mord mathnormal" style = "margin-right:0.07847em;" > I< / span > < span class = "msupsub" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:0.3361em;" > < span style = "top:-2.55em;margin-left:-0.0785em;margin-right:0.05em;" > < span class = "pstrut" style = "height:2.7em;" > < / span > < span class = "sizing reset-size6 size3 mtight" > < span class = "mord mtight" > < span class = "mord mathnormal mtight" style = "margin-right:0.10764em;" > f< / span > < span class = "mord mtight" > 1< / span > < / span > < / span > < / span > < / span > < span class = "vlist-s" > < / span > < / span > < span class = "vlist-r" > < span class = "vlist" style = "height:0.2861em;" > < span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < span style = "top:-3.23em;" > < span class = "pstrut" style = "height:3em;" > < / span > < span class = "frac-line" style = "bor
< / math >
< / body >
< / html >
