From 9417b0a466fe081f5d060edfb3df24ccce97846e Mon Sep 17 00:00:00 2001 From: Peter Date: Fri, 28 Oct 2022 22:16:04 +0800 Subject: [PATCH] some DC machine stuff, pdf script to concatenate solutions --- .gitignore | 2 +- 2022-10-28-15-52-14.png | Bin 0 -> 74241 bytes 2022-10-28-15-52-44.png | Bin 0 -> 34802 bytes 2022-10-28-15-52-58.png | Bin 0 -> 29069 bytes 2022-10-28-15-53-29.png | Bin 0 -> 23175 bytes 2022-10-28-16-30-51.png | Bin 0 -> 67270 bytes 2022-10-28-18-21-53.png | Bin 0 -> 65139 bytes 2022-10-28-18-22-17.png | Bin 0 -> 48781 bytes 2022-10-28-18-28-51.png | Bin 0 -> 39194 bytes README.md | 85 ++++++++++++++++++++++++++++++++++++++++ etc/pdf.ps1 | 9 +++++ 11 files changed, 95 insertions(+), 1 deletion(-) create mode 100644 2022-10-28-15-52-14.png create mode 100644 2022-10-28-15-52-44.png create mode 100644 2022-10-28-15-52-58.png create mode 100644 2022-10-28-15-53-29.png create mode 100644 2022-10-28-16-30-51.png create mode 100644 2022-10-28-18-21-53.png create mode 100644 2022-10-28-18-22-17.png create mode 100644 2022-10-28-18-28-51.png create mode 100644 etc/pdf.ps1 diff --git a/.gitignore b/.gitignore index 8f73941..f08278d 100644 --- a/.gitignore +++ b/.gitignore @@ -1 +1 @@ -etc/ \ No newline at end of file +*.pdf \ No newline at end of file diff --git a/2022-10-28-15-52-14.png b/2022-10-28-15-52-14.png new file mode 100644 index 0000000000000000000000000000000000000000..ca40e9f5dfc63079f4e569a1e7bff5f0a26e8776 GIT binary patch literal 74241 zcmYg&by$?q_O*a?H%K=~NrNCrhlGN_&@dpONGn4t-5}j4A>AzqD^_dV}Ed#|F@h#9LL<)e|;h>?BrZ&Ys~GMUdeN91g_})5V4qxy~z)m4UNXq zBNg8BHmz~|2}<(OFYqmRgC#fqX^nlcgxm535@ucfUm016|p>>6FWSN@4qr z2k?I0?=B2i9M4`P@NRu_C6GBz>D!sAs$lky-uZAOe{evGpGfEFdid%=T2>-=Oy`pM z5l7jC31bBx|0Nm8OzRu77UTN;!HqvrA{o~Yr>gap*=|jR8xNi=&Z79(`fF-NAa@c! z{nH=h<<2#Kx3*DZ@9DMT<^YFAP75DgFTUT%!5u!oOm}^4Z2|2JZ8+E2iK5{ZNxwWk zFrv6__{UsswA;kWx+xla@rXdcdw0x-$0JCdMTUxm)@S>T(!M3?g$E|XWdu(Hlm99O zMoLTj=&R6QvR_iz6OHoG~*R9#(@+X_CoXdD|bz+VV} z4j~GcIFs(XNvGcc2rG^yu zJLugDA8q_GO!2EXQ1|J0{46Qi<(j=f$8Gz@3xjSFk^*IUXp%@{C1uWZG{yUf6PHW; zTv-16Ss$m?BrWIv-H9}`LW|X|8K?U(o9Dj>%Ruw6)ruwTR)Wpw+B6$?Z;sZZ)?t*y z+03RT%4@ybVFQUmB;Ho*b7GoA|K=~RzRiw93J#9V&s)Mo3rob<#GQ*pmqzr-!!kWF zdO~A0;G6Aa8ob3M){+A2f7dbK9D+`=Go(Tyxf3cfILJ5o#4=8SRq1Z~nGdyuiHWq5 z4p(*_R#0#zGwxA@aSuEshXu%eXA-r0dO^s^ls&iJ;&~d?u29mv-s+O!hJAZ2adkRK z4y%1|AvCzXq&};9CP%_1E>JA`?F%Nv20gg2;?Q?2el#F1e6Hi7tt!g*80T%`hgSmF z$%mty$ehWVsJoV@+$a?k9x}l#_kri*IVFSi1y|YBUNB$2_b_v%PCsG)RK)>1GY+y& zqM>WSj))|d`{8^xmZ5UU&Hiyynp*c1JH+7IlWxOSUrwFJ&x2L>sqqyJ+N~WO{6E5% zMNFm$XJb%z$~DVZaKv9r6nl-dD(VjHc6mn?5Is(L#=kz{M6>-D9!LOvfPfgM@MI2g zDh3_~RL%(bF6PLKE9H2G^`+r|KJ%8ax5bHc;*kbiyx*4|<)&T8?ENH;;IVt5Vu{|$ zD}mFdBII2n*nlrN^3NL57~bDS%W|O~FJ2~7J{q1KVOlNvSeS!>Z_Xs3_-M%B$r4o@ zNk;A`^9e8Hj^&D_Hjcrs!t&)Ks!*aUz0_Zv%nWFO-W!+iS**mg{8wXps z>FDOX_WFx=dC#9VOP*sa>)smbMAjye7s1LoD~;UaKK?*mhTtHb{aX=KaL)9B`lOn) z?OqixXQ*M}yer$AxJ(=q)3>$nG;U|575Vckx99Vn;i04p+@Q08F$H#^cTi^b?#Y>fX@G{+c{#gLotN zT-q+jHK!t?$~WxKPh!;nVUjkz8}@BM%SpeEk*}b5?$D(Ykk=tr86PUn->8dYV^CeY zg`4T+x01xt{o9!!lFY9>KYSn?;(UB_UZX*_y2( zAj7R%vnM5%@zL8oNS~ok#_11AHc2Z@=w=Z zO@=`o(a5rul-0B)s6LOS4(3VX>i=83U_0fncX2yOPKOx&pcjAbc}gp8)TkEt@v8qX zeUdq@Z%56$6d?xYqW?t8%0oEVKgWvFKLRUEf;}`?dDer$YdemkabBGuj7l3yE_g7y zxYfo?>bDT|8lNI;0>hl=9Oa;FmDf-p(ot8`y)ff^l^LbtTNM=7_< zFLR2r5`N3R)-o@OQg+0`S!dI@Dq=8k@u{F9+`O@rf)A%=sv(Wh(E9rl4CMZ(4n&^$o{F1c}cg*Y8j-WIa zTKRt&v&KZm@g&dLrIbN5(rb1DQpO&f(6+p3?HU+*bTAB0W2i1%%9xPv>*&S|;Q$CA z*JB5v%=+&Q?;NzC#ByF52?;9m z>{OuKZ=0lgr0NuHUh9PhCtV{uN;))`vYUB(5;w%Xwkz4Q*VAoYTYAuI&lU+^#-1*W z1G$9;rPHx-BrtMH{5-Pkx-jYUTploHM(u^0uXO?X3B9I(cvG7cYSo`iSjloB%i(2j za8j3;xXFnDtn4Ii`-7r!;mHjA`$}1Dy8FudRNW;{y*O;sZ{!`V#@sOu?JtYj`1qjt z_S7fIR~?-XrcaXz{O(EK+?Gr2eaXXQ)y|P+P|YnEWiaCX2d)4zg zx(!HHOLh)@90fK*{yIYXICiZ#Voniir)IB0%KWi;R~^lKs_?sXue3SZOXCmaRwUL< zJ0qtQbEL>x$-F0_R(qEbm)njn-M_QUdXfI*BGpwRbNicAh4Hc?=@<3J!iRQ&GB^ZL7n+eiXTpsrbI-`CZjU{3yClqAiO`3i=?gUTvf0fj=KKq{{Vb4GCE$X82xkrBb|j zoakWj9fPiQGu4u8m9KI3^Km5E)x#csXW=-WhmL0-dh`E8X{*%{crad0?B_Yz+a}TtWQl!2(xD8-hyX&YiG?I9e(SRx^07aE z!a*iu*8ga4AV6otu}^nYpCO6uR^Cni)iv^fHJ_4mwW#rKHB#^UR1L3=K<6_d@gwO? 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P_>a~RJ+-HYtZ)1uwZ_}| literal 0 HcmV?d00001 diff --git a/README.md b/README.md index 2a3545d..3f34483 100644 --- a/README.md +++ b/README.md @@ -8,6 +8,7 @@ I draw them with a mouse - Double check all are in the correct phase! Multiplications and divisions by $\sqrt{3}$ or $3$ where necessary must be checked! Try annotating everything that does not have an associated phase. - Check conjugate in current. $\bar{S}=\bar{V}\bar{I}^*$ +- Check transformer parameters are referred to the proper side #### Y-$\Delta$ transformation (Balanced case) @@ -200,3 +201,87 @@ P_\text{mech}&=P_\text{F\\\&W}+P_\text{misc}+P_\text{out} $$ --- + +### Magnetic circuit analogy + +| Magnetic circuit | name | | Electrical circuit | name | +| ----------------------------------- | ---------------------------- | --- | ------------------------ | ----------------------- | +| $$\mathcal F$$ | Magnetomotive force [A-turn] | | $$\mathcal E$$ | Electromotive force [V] | +| $$\mathcal R$$ | Reluctance [1/H] | | $$R$$ | Resistance [$\Omega$] | +| $$\Phi$$ | Magnetic flux [Wb] | | $$I$$ | Current [A] | +| $$\mathcal P=\frac{1}{\mathcal R}$$ | Permeance [H] | | $$G=\frac{1}{R}$$ | Conductivity [$\mho$] | +| $$\mathcal F=\Phi\mathcal R$$ | Hopkinson's law | | $$V=IR$$ | Ohm's law | +| $$\mathcal R=\frac{l}{\mu A}$$ | | | $$R=\frac{l}{\sigma A}$$ | + +--- + +### Transformers + +$$Z_P=Z_S\left(\frac{N_P}{N_S}\right)^2=Z_S n^2$$ + +#### Maximum power. + +If load is resistive ($jX_\text{load}=0$) then for maximum power transfer: + +$$R_\text{load}=|{R_\text{src}}^2+j{X_\text{src}}^2|$$ + +#### Parameter identification + +![](2022-10-28-15-52-14.png) + +| Open-circuit test | Short-circuit test | +| ---------------------------- | ---------------------------- | +| ![](2022-10-28-15-53-29.png) | ![](2022-10-28-15-52-58.png) | + +#### Voltage regulation + +$$\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}|}$$ + +Ignore shunt resistance. Refer from primary side. Use KVL to determine $V_\text{in}$. + +Voltage regulation is typically small. + +$$|V_\text{in}|=|V_\text{rated,P}+I_\text{L,P}\cdot\bar Z|$$ + +![](2022-10-28-16-30-51.png) + +### DC machine + +| Separately excited machine | Shunt excited | Series excited | +| ---------------------------------------- | ----------------------------------------------------------------- | --------------------------------------------------------------------------------- | +| ![](2022-10-28-18-21-53.png) | ![](2022-10-28-18-22-17.png) | ![](2022-10-28-18-28-51.png) | +| | Similar torque-speed characteristic to separately-excited machine | High torque per ampere. Used in high-torque applications | +| Requires two independent voltage sources | | Do not run unloaded - infinite speed at 0 torque as $\omega\propto 1/\sqrt{\tau}$ | +| Motor control using $R_f$ | Motor control using $R_F$ | Motor control using $V_T$. | + +#### Starting DC motors + +$R_A$ might need to be adjusted so it is high initially in large DC motors, as the starting current is high since there is no back-emf created by $E_A$. + +#### Magnetizating curve + +When a question specifies the field current or $R_\text{adj}$, refer to magnetization curve. Magnetizating curve is valid at a specific speed $n_{m1}$, and the curve is used to find $E_{A1}$. Using the load condition to find the armature current $I_A=\tau_\text{ind}/(K\varPhi)$, $V_A$ can be used to find a second induced EMF $E_{A2}$. Using $E_{A2}$ find the speed $n_{m2}$ by scaling $n_{m1}$ by $E_{A2}/E_{A1}$. + +#### Idk + +$$P_\text{mech}=E_AI_A$$ + +No-load separately excited machine. Assuming no mechanical losses. + +$$E_A=V_A\text{ (No load)}$$ +$$I_A=0\text{ (No load)}$$ + +Armature reaction causes increase in speed and causes instability as the core saturates near the poles. Can be reduced with compensating winding which is in series with the armature coil. + +$$K\Phi\omega=E_A$$ +$$K\Phi I_A=\tau$$ + +For shunt motor + +$$K\Phi=\frac{V_T-R_AI_A}{\omega}$$ +$$\tau=K\Phi I_A=\frac{V_T-R_AI_A}{\omega}I_A$$ + +Assume no saturation, speed locked(?): + +This doesn't seem right. We are meant to use the machine constant and the proportionality of current to magnetic flux. +$$\frac{E_{A2}}{E_{A1}}=\frac{I_{f2}}{I_{f1}}$$ diff --git a/etc/pdf.ps1 b/etc/pdf.ps1 new file mode 100644 index 0000000..3ba97f6 --- /dev/null +++ b/etc/pdf.ps1 @@ -0,0 +1,9 @@ +pdftk ` + F="ENSC3016_PS_T4_b_DC Machines_Solution[50d7a8].pdf" ` + E="ENSC3016_PS_T4_a_DC Machines_Solution[3a221a].pdf" ` + D="ENSC3016_T7_PS_Synchronous_Machines_Part3_Solutions[71c8f8].pdf" ` + C="ENSC3016_T8_PS_Induction_Machines_Part2_Solutions(2)[7cca6e].pdf" ` + B="ENSC3016_Induction_Machines_Solutions[74fb7b].pdf" ` + A="ENSC3016_PS_T6_c_Transformers_Solution[b4ede2].pdf" ` + cat A2 A3 D3-5 C6 B3-6 E F ` + output print.pdf verbose \ No newline at end of file