more im diagrams

.gitignore

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+etc/

README.md

@@ -1,3 +1,22 @@
+> Why are the drawings bad?
+
+I draw them with a mouse
+
+### 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 motor
 
 | Type               | Description                                                                                                      | Equivalent terms                                                                                               |
@@ -22,33 +41,104 @@ P_\text{mech}&=P_\text{F\\\&W}+P_\text{misc}+P_\text{out}
 \end{align}
 $$
 
-## No-load test
+Note - assume loss is 0 if not mentioned!
 
-| Assumption                     | Eqn               | Reason                         |
+| Type                      | Description                                 | Symbols                                 |
-| ------------------------------ | ----------------- | ------------------------------ |
+| ------------------------- | ------------------------------------------- | --------------------------------------- |
-| rotor current is insignificant | $I_r \approx 0$   | high rotor resistance          |
+| Load torque, Shaft torque | Torque experienced by load after all losses | $\tau_\text{load}$, $\tau_\text{shaft}$ |
-| no output mechanical power     | $P_\text{out}=0$  | no load                        |
+
-| high rotor resistance          | $R_r/s\to \infty$ | $s\to 0$, high slip at no load |
+## $3\phi$ 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
+
+![](2022-10-26-22-06-19.png)
+
+### Equivalent model
+
+#### Assumptions
+
+- $x_m\approx X_m$
+  - $R_c\ggg X_m\Rightarrow r_c\lll x_m$
+  - $x_m=\frac{{R_c}^2}{{R_c}^2+{X_m}^2}X_m\approx\frac{\cancel{{R_c}^2}}{\cancel{{R_c}^2}}X_m=X_m$
+- $r_c\approx {X_m}^2/R_c$
+  - $R_c\ggg X_m\Rightarrow r_c\lll x_m$
+  - $r_c=\frac{{X_m}^2}{{R_c}^2+{X_m}^2}R_c\approx\frac{{X_m}^2}{{R_c}^2}R_c=\frac{{X_m}^2}{R_c}$
+
+### Diagram
+
+![](2022-10-26-21-53-13.png)
+
+### DC test
+
+#### $\Delta$ machine
+
+$$R_s=\frac{3}{2}\cdot\frac{V_{\text{DC},3\phi}}{I_{\text{DC},3\phi}}$$
+![](2022-10-26-22-43-25.png)
+
+#### Y machine
+
+$$R_s=\frac{1}{2}\cdot\frac{V_{\text{DC},3\phi}}{I_{\text{DC},3\phi}}$$
+![](2022-10-26-22-48-09.png)
+
+### No-load test
+
+#### Assumptions
+
+- $P_\text{out}=0$
+  - No output power as no load.
+- $R_r/s=\infty$ and $I_r=0$
+  - Infinite rotor resistance, ignore rotor path.
+
+#### Diagram
 
 Using assumptions, remove rotor part of circuit and only consider stator and magnetizing path.
 
 ![](2022-10-25-11-45-26.png)
 
-## Blocked rotor test
+### Blocked rotor test
 
-| Assumption              | Eqn                                | Reason                                                                          |
+#### Assumptions
-| ----------------------- | ---------------------------------- | ------------------------------------------------------------------------------- |
+
-| ignore magnetizing path | $I_r\ggg I_m$                      | magnetizing current is low compared to rotor current as rotor resistance is low |
+- Ignore magnetizing path, $I_m=0$
-| low rotor resistance    | $R_r/s\approx R_r$                 | $s\approx 1$, slip is $1$ when blocked                                          |
+  - $I_r\ggg I_m$ as $R_r/s\ggg Z_m$
-|                         | $X_r\approx f_0/f_{BL}\times X_r'$ | $X_r'\approx X_{BL}/2$                                                          |
+- $R_r/s=R_r$, $s=1$
-|                         | $X_r'\approx X_{BL}/2$             | $X_s\approx X_r'$                                                               |
+  - Slip is $1$ as rotor is blocked.
-|                         | $X_s\approx X_r'$                  |
+- $x_s=x_r'$
+  - Same number of turns in stator and rotor
+- and $x_r=f_0/f_\text{BL} \times x_r'$
+  - 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
 
 ![](2022-10-25-11-46-04.png)
 
-## Equivalent model
+---
 
-| Assumption | Eqn                      | Reason                               |
+## Single-phase induction motor
-| ---------- | ------------------------ | ------------------------------------ |
+
-|            | $x_m\approx X_m$         | $R_c\ggg X_m\Rightarrow r_c\lll x_m$ |
+### Diagram
-|            | $r_c\approx {X_m}^2/R_c$ | $R_c\ggg X_m\Rightarrow r_c\lll x_m$ |
+
+![](2022-10-26-21-47-29.png)
+
+### Blocked-rotor
+
+#### Diagram
+
+![](2022-10-26-21-48-00.png)
+
+### No-load
+
+#### Diagram
+
+![](2022-10-26-21-47-49.png)