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Why are the drawings bad?

I draw them with a mouse

Etc

FIRST-PASS CHECKS

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)

$Z_\Delta=3Z_Y$

Types of power factors (From `ENSC2003`)

Where $\bar{S}=|\bar{S}|\angle\varphi$ :

$\varphi = \arctan\left(\frac{Q}{P}\right) = \theta_v-\theta_i$

	Lagging	Leading	Unity
Voltage	Current behind	Current ahead	In phase
Load type	Inductive	Capacitive	Resistive
$Q$	$Q>0$	$Q<0$	$Q=0$
$\varphi$	$\varphi>0°$	$\varphi<0°$	$\varphi=0°$
PF [Load]	$[0,1)$	$[0,1)$	$1$
PF [Source]	$[0,-1)$	$[0,-1)$	$-1$

Power types in induction motor

Type	Description	Equivalent terms
Input power	Power into machine. $V_T=V_{3\phi}$ , $I_L=I_{3\phi}$	$P_\text{in}$ , $\sqrt{3}V_TI_L\cos(\theta)$
Output power	Mechanical output power of the machine, excludes losses	$P_\text{out}$ , $P_\text{load}$
Converted power	Total electrical power converted to mechanical power, includes useful power and mechanical losses inside machine	$P_\text{conv}$ , $P_\text{converted}$ , $P_\text{mech}$ , $P_\text{developed}$ , $\tau_\text{mech}\times\omega_m$
Airgap power	Power transmitted over airgap.	$P_\text{AG}$ , $\tau_\text{mech}\times\omega_s$
Mechanical loss	Power lost to friction and windage	$P_\text{mechanical loss}$ , $P_\text{F\\\&W}$ , $P_\text{friction and windage}$
Core loss	Power lost in machine magnetic material due to hysteresis loss and eddy currents	$P_\text{core}$
Rotor copper loss	Due to resistance of rotor windings	$P_r$ , $P_\text{RCL}$
Stator copper loss	Due to resistance of stator windings	$P_s$ , $P_\text{SCL}$
Miscellaneous loss	Add 1% to losses to account for other unmeasured losses	$P_\text{misc}$ , $P_\text{stray}$

$\begin{align} P_\text{in}&=P_\text{SCL}+P_\text{RCL}+P_\text{core}+P_\text{F\\\&W}+P_\text{misc}+P_\text{out}\\ P_\text{AG}&=P_\text{RCL}+P_\text{F\\\&W}+P_\text{misc}+P_\text{out}\\ P_\text{mech}&=P_\text{F\\\&W}+P_\text{misc}+P_\text{out} \end{align}$

Note - assume loss is 0 if not mentioned!

Type	Description	Symbols
Load torque, Shaft torque	Torque experienced by load after all losses	$\tau_\text{load}$ , $\tau_\text{shaft}$

$3\phi$ induction motor

Etc.

Slip speed $N_\text{slip}=N_{s\text{ (sync)}}-N_r=sN_{s\text{ (sync)}}$
"1/4 of rated load" != "1/4 times full load"
- Means 1/4 of full load slip as it is in the linear region. Accounts for the minimum load.
Rated power stated in machine specification refers to the output power $P_\text{out}$ , and excludes all losses.
Speed regulation using machine speed:
$\text{SR}=\frac{N_{r,\text{NL}}-N_{r,\text{FL}}}{N_{r,\text{FL}}}$

Diagram

Equivalent model

Assumptions

$x_m\approx X_m$ $x_{m} \approx X_{m}$
- $R_c\ggg X_m\Rightarrow r_c\lll x_m$
- $x_m=\frac{{R_c}^2}{{R_c}^2+{X_m}^2}X_m\approx\frac{\cancel{{R_c}^2}}{\cancel{{R_c}^2}}X_m=X_m$
$r_c\approx {X_m}^2/R_c$ $r_{c} \approx X_{m}^{2} / R_{c}$
- $R_c\ggg X_m\Rightarrow r_c\lll x_m$
- $r_c=\frac{{X_m}^2}{{R_c}^2+{X_m}^2}R_c\approx\frac{{X_m}^2}{{R_c}^2}R_c=\frac{{X_m}^2}{R_c}$

Diagram

DC test

$\Delta$ machine

$R_s=\frac{3}{2}\cdot\frac{V_{\text{DC},3\phi}}{I_{\text{DC},3\phi}}$

Y machine

$R_s=\frac{1}{2}\cdot\frac{V_{\text{DC},3\phi}}{I_{\text{DC},3\phi}}$

No-load test

Assumptions

$P_\text{out}=0$ $P_{out} = 0$
- No output power as no load.
$R_r/s=\infty$ $R_{r} / s = \infty$ and $I_r=0$ $I_{r} = 0$
- Infinite rotor resistance, ignore rotor path.

Diagram

Using assumptions, remove rotor part of circuit and only consider stator and magnetizing path.

Blocked rotor test

Assumptions

Ignore magnetizing path, $I_m=0$ $I_{m} = 0$
- $I_r\ggg I_m$ as $R_r/s\ggg Z_m$
$R_r/s=R_r$ $R_{r} / s = R_{r}$ , $s=1$ $s = 1$
- Slip is $1$ as rotor is blocked.
$x_s=x_r'$ $x_{s} = x_{r}^{'}$
- Same number of turns in stator and rotor
and $x_r=f_0/f_\text{BL} \times x_r'$ $x_{r} = f_{0} / f_{BL} \times x_{r}^{'}$
- Note: $x_r'$ is the inductance at $f_\text{BL}$ , the blocked rotor test frequency which is less than the nominal frequency $f_0$

Diagram

Ignore magnetizing path

Single-phase induction motor

Diagram

Blocked-rotor

Diagram

No-load

Diagram

Synchronous machine

Etc

$E_A=V_{1\phi}-I_A(R_A+j X_s)$

$I_A=\text{CONJUGATE}\left(\frac{|S_{3\phi}|\angle\arccos(x)}{3V_{1\phi}}\right), \begin{cases}x=+\text{PF} && \text{lagging} \\ x=-\text{PF} && \text{leading}\end{cases}$

Voltage regulation

$\text{VR}=\frac{|V_\text{NL}|-|V_\text{FL}|}{|V_\text{FL}|}=\frac{|E_A|-|V_{1\phi,\text{rated}}|}{|V_{1\phi,\text{rated}}|}$

$V_\text{FL}$ is the full-load voltage which is the full-load/maximum rated voltage at the output terminal.
Calculate $E_A$ at full load by calculating the current as shown above.
$V_\text{NL}$ is the no-load voltage, which in the no-load case will be $E_A$ .

No-load	Full-load

Power factor	Voltage regulation
Lagging	Positive
Unity	Near 0
Leading	Negative

Open and short circuit test

Note - double-check if the axis refers to per-phase or line voltage/current.

Open-circuit test	Short-circuit test

Power flow

$P_\text{out}$ is the rated power

$P_\text{out}=S_\text{rated}\times \text{PF}$

$\begin{align} P_\text{in}&=P_\text{copper}+P_\text{core}+P_\text{F\\\&W}+P_\text{misc}+P_\text{out}\\ P_\text{mech}&=P_\text{F\\\&W}+P_\text{misc}+P_\text{out} \end{align}$

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

Open-circuit test	Short-circuit test

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.

$|V_\text{in}|=|V_\text{rated,P}+I_\text{L,P}\cdot\bar Z|$

DC machine

Separately excited machine	Shunt excited	Series excited

	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.

$\frac{E_{A2}}{E_{A1}}=\frac{I_{f2}}{I_{f1}}$

Etc

FIRST-PASS CHECKS

Y-Δ\DeltaΔ transformation (Balanced case)

Types of power factors (From ENSC2003)

Power types in induction motor

3ϕ3\phi3ϕ induction motor

Etc.

Diagram

Equivalent model

Assumptions

Diagram

DC test

Δ\DeltaΔ machine

Y machine

No-load test

Assumptions

Diagram

Blocked rotor test

Assumptions

Diagram

Single-phase induction motor

Diagram

Blocked-rotor

Diagram

No-load

Diagram

Synchronous machine

Etc

Voltage regulation

Open and short circuit test

Note - double-check if the axis refers to per-phase or line voltage/current.

Power flow

Magnetic circuit analogy

Transformers

Maximum power.

Parameter identification

Voltage regulation

DC machine

Starting DC motors

Magnetizating curve

Idk

Y- $\Delta$ transformation (Balanced case)

Types of power factors (From `ENSC2003`)

$3\phi$ induction motor

$\Delta$ machine