diff --git a/.gitignore b/.gitignore new file mode 100644 index 0000000..8f73941 --- /dev/null +++ b/.gitignore @@ -0,0 +1 @@ +etc/ \ No newline at end of file diff --git a/2022-10-26-21-47-29.png b/2022-10-26-21-47-29.png new file mode 100644 index 0000000..ef2745e Binary files /dev/null and b/2022-10-26-21-47-29.png differ diff --git a/2022-10-26-21-47-49.png b/2022-10-26-21-47-49.png new file mode 100644 index 0000000..73bb2b7 Binary files /dev/null and b/2022-10-26-21-47-49.png differ diff --git a/2022-10-26-21-48-00.png b/2022-10-26-21-48-00.png new file mode 100644 index 0000000..862a592 Binary files /dev/null and b/2022-10-26-21-48-00.png differ diff --git a/2022-10-26-21-53-13.png b/2022-10-26-21-53-13.png new file mode 100644 index 0000000..af7f04d Binary files /dev/null and b/2022-10-26-21-53-13.png differ diff --git a/2022-10-26-22-06-19.png b/2022-10-26-22-06-19.png new file mode 100644 index 0000000..3761437 Binary files /dev/null and b/2022-10-26-22-06-19.png differ diff --git a/2022-10-26-22-43-25.png b/2022-10-26-22-43-25.png new file mode 100644 index 0000000..4fa099c Binary files /dev/null and b/2022-10-26-22-43-25.png differ diff --git a/2022-10-26-22-48-09.png b/2022-10-26-22-48-09.png new file mode 100644 index 0000000..d410889 Binary files /dev/null and b/2022-10-26-22-48-09.png differ diff --git a/README.md b/README.md index 44d11ea..ad799c7 100644 --- a/README.md +++ b/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} $$ -## No-load test +Note - assume loss is 0 if not mentioned! -| Assumption | Eqn | Reason | -| ------------------------------ | ----------------- | ------------------------------ | -| rotor current is insignificant | $I_r \approx 0$ | high rotor resistance | -| no output mechanical power | $P_\text{out}=0$ | no load | -| high rotor resistance | $R_r/s\to \infty$ | $s\to 0$, high slip at no load | +| Type | Description | Symbols | +| ------------------------- | ------------------------------------------- | --------------------------------------- | +| Load torque, Shaft torque | Torque experienced by load after all losses | $\tau_\text{load}$, $\tau_\text{shaft}$ | + +## $3\phi$ induction motor + +### Etc. + +- Slip speed $N_\text{slip}=N_{s\text{ (sync)}}-N_r=sN_{s\text{ (sync)}}$ + +- "1/4 of rated load" != "1/4 times full load" + - Means 1/4 of full load slip as it is in the linear region. Accounts for the minimum load. +- Rated power stated in machine specification refers to the output power $P_\text{out}$, and excludes all losses. +- Speed regulation using machine speed: $$\text{SR}=\frac{N_{r,\text{NL}}-N_{r,\text{FL}}}{N_{r,\text{FL}}}$$ + +### Diagram + +![](2022-10-26-22-06-19.png) + +### Equivalent model + +#### Assumptions + +- $x_m\approx X_m$ + - $R_c\ggg X_m\Rightarrow r_c\lll x_m$ + - $x_m=\frac{{R_c}^2}{{R_c}^2+{X_m}^2}X_m\approx\frac{\cancel{{R_c}^2}}{\cancel{{R_c}^2}}X_m=X_m$ +- $r_c\approx {X_m}^2/R_c$ + - $R_c\ggg X_m\Rightarrow r_c\lll x_m$ + - $r_c=\frac{{X_m}^2}{{R_c}^2+{X_m}^2}R_c\approx\frac{{X_m}^2}{{R_c}^2}R_c=\frac{{X_m}^2}{R_c}$ + +### Diagram + +![](2022-10-26-21-53-13.png) + +### DC test + +#### $\Delta$ machine + +$$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 | -| ----------------------- | ---------------------------------- | ------------------------------------------------------------------------------- | -| ignore magnetizing path | $I_r\ggg I_m$ | magnetizing current is low compared to rotor current as rotor resistance is low | -| low rotor resistance | $R_r/s\approx R_r$ | $s\approx 1$, slip is $1$ when blocked | -| | $X_r\approx f_0/f_{BL}\times X_r'$ | $X_r'\approx X_{BL}/2$ | -| | $X_r'\approx X_{BL}/2$ | $X_s\approx X_r'$ | -| | $X_s\approx X_r'$ | +#### Assumptions + +- Ignore magnetizing path, $I_m=0$ + - $I_r\ggg I_m$ as $R_r/s\ggg Z_m$ +- $R_r/s=R_r$, $s=1$ + - Slip is $1$ as rotor is blocked. +- $x_s=x_r'$ + - 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 | -| ---------- | ------------------------ | ------------------------------------ | -| | $x_m\approx X_m$ | $R_c\ggg X_m\Rightarrow r_c\lll x_m$ | -| | $r_c\approx {X_m}^2/R_c$ | $R_c\ggg X_m\Rightarrow r_c\lll x_m$ | +## Single-phase induction motor + +### Diagram + +![](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)