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 0000000..ca40e9f Binary files /dev/null and b/2022-10-28-15-52-14.png differ diff --git a/2022-10-28-15-52-44.png b/2022-10-28-15-52-44.png new file mode 100644 index 0000000..32b4a13 Binary files /dev/null and b/2022-10-28-15-52-44.png differ diff --git a/2022-10-28-15-52-58.png b/2022-10-28-15-52-58.png new file mode 100644 index 0000000..d75c976 Binary files /dev/null and b/2022-10-28-15-52-58.png differ diff --git a/2022-10-28-15-53-29.png b/2022-10-28-15-53-29.png new file mode 100644 index 0000000..00a5156 Binary files /dev/null and b/2022-10-28-15-53-29.png differ diff --git a/2022-10-28-16-30-51.png b/2022-10-28-16-30-51.png new file mode 100644 index 0000000..952e967 Binary files /dev/null and b/2022-10-28-16-30-51.png differ diff --git a/2022-10-28-18-21-53.png b/2022-10-28-18-21-53.png new file mode 100644 index 0000000..da156a3 Binary files /dev/null and b/2022-10-28-18-21-53.png differ diff --git a/2022-10-28-18-22-17.png b/2022-10-28-18-22-17.png new file mode 100644 index 0000000..9b54bc0 Binary files /dev/null and b/2022-10-28-18-22-17.png differ diff --git a/2022-10-28-18-28-51.png b/2022-10-28-18-28-51.png new file mode 100644 index 0000000..62bbf23 Binary files /dev/null and b/2022-10-28-18-28-51.png differ 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