peter/Power-and-Machines-notes
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@ -1,3 +1,8 @@
```
!\[\]\(([^\)]*)\)
<center><img src="$1" width=400px></center>
```
> Why are the drawings bad?
I draw them with a mouse
@ -43,7 +48,7 @@ $$ \varphi = \arctan\left(\frac{Q}{P}\right) = \theta_v-\theta_i$$
| 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 | $P_\text{misc}$, $P_\text{stray}$ |
![](2022-10-25-11-33-40.png)
<center><img src="2022-10-25-11-33-40.png" width=400px></center>
$$
\begin{align}
@ -72,7 +77,7 @@ Note - assume loss is 0 if not mentioned!
### Diagram
![](2022-10-26-22-06-19.png)
<center><img src="2022-10-26-22-06-19.png" width=400px></center>
### Equivalent model
@ -87,19 +92,21 @@ Note - assume loss is 0 if not mentioned!
### Diagram
![](2022-10-26-21-53-13.png)
<center><img src="2022-10-26-21-53-13.png" width=400px></center>
### DC test
#### $\Delta$ machine
$$R_s=\frac{3}{2}\cdot\frac{V_{\text{DC},3\phi}}{I_{\text{DC},3\phi}}$$
![](2022-10-26-22-43-25.png)
<center><img src="2022-10-26-22-43-25.png" width=400px></center>
#### Y machine
$$R_s=\frac{1}{2}\cdot\frac{V_{\text{DC},3\phi}}{I_{\text{DC},3\phi}}$$
![](2022-10-26-22-48-09.png)
<center><img src="2022-10-26-22-48-09.png" width=400px></center>
### No-load test
@ -114,7 +121,7 @@ $$R_s=\frac{1}{2}\cdot\frac{V_{\text{DC},3\phi}}{I_{\text{DC},3\phi}}$$
Using assumptions, remove rotor part of circuit and only consider stator and magnetizing path.
![](2022-10-25-11-45-26.png)
<center><img src="2022-10-25-11-45-26.png" width=400px></center>
### Blocked rotor test
@ -133,7 +140,7 @@ Using assumptions, remove rotor part of circuit and only consider stator and mag
Ignore magnetizing path
![](2022-10-25-11-46-04.png)
<center><img src="2022-10-25-11-46-04.png" width=400px></center>
---
@ -141,19 +148,19 @@ Ignore magnetizing path
### Diagram
![](2022-10-26-21-47-29.png)
<center><img src="2022-10-26-21-47-29.png" width=400px></center>
### Blocked-rotor
#### Diagram
![](2022-10-26-21-48-00.png)
<center><img src="2022-10-26-21-48-00.png" width=400px></center>
### No-load
#### Diagram
![](2022-10-26-21-47-49.png)
<center><img src="2022-10-26-21-47-49.png" width=400px></center>
## Synchronous machine
@ -171,8 +178,8 @@ $$\text{VR}=\frac{|V_\text{NL}|-|V_\text{FL}|}{|V_\text{FL}|}=\frac{|E_A|-|V_{1\
- $V_\text{NL}$ is the no-load voltage, which in the no-load case will be $E_A$.
| No-load | Full-load |
| ---------------------------- | ---------------------------- |
| ![](2022-10-27-20-15-13.png) | ![](2022-10-27-20-19-47.png) |
| ---------------------------------------------------------------- | ---------------------------------------------------------------- |
| <center><img src="2022-10-27-20-15-13.png" width=300px></center> | <center><img src="2022-10-27-20-19-47.png" width=300px></center> |
| Power factor | Voltage regulation |
| ------------ | ------------------ |
@ -185,8 +192,8 @@ $$\text{VR}=\frac{|V_\text{NL}|-|V_\text{FL}|}{|V_\text{FL}|}=\frac{|E_A|-|V_{1\
#### **Note** - double-check if the axis refers to per-phase or line voltage/current.
| Open-circuit test | Short-circuit test |
| ---------------------------- | ---------------------------- |
| ![](2022-10-27-15-31-49.png) | ![](2022-10-27-15-32-07.png) |
| ----------------------------------------------------------------- | ---------------------------------------------------------------- |
| <center><img src="2022-10-27-15-31-49.png" width=300px ></center> | <center><img src="2022-10-27-15-32-07.png" width=300px></center> |
### Power flow
@ -227,11 +234,11 @@ $$R_\text{load}=|{R_\text{src}}^2+j{X_\text{src}}^2|$$
#### Parameter identification
![](2022-10-28-15-52-14.png)
<center><img src="2022-10-28-15-52-14.png" width=400px></center>
| Open-circuit test | Short-circuit test |
| ---------------------------- | ---------------------------- |
| ![](2022-10-28-15-53-29.png) | ![](2022-10-28-15-52-58.png) |
| ---------------------------------------------------------------- | ---------------------------------------------------------------- |
| <center><img src="2022-10-28-15-53-29.png" width=300px></center> | <center><img src="2022-10-28-15-52-58.png" width=300px></center> |
#### Voltage regulation
@ -243,13 +250,13 @@ Voltage regulation is typically small.
$$|V_\text{in}|=|V_\text{rated,P}+I_\text{L,P}\cdot\bar Z|$$
![](2022-10-28-16-30-51.png)
<center><img src="2022-10-28-16-30-51.png" width=400px></center>
### 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) |
| ---------------------------------------------------- | ----------------------------------------------------------------- | --------------------------------------------------------------------------------- |
| <center><img src="2022-10-28-18-21-53.png"></center> | <center><img src="2022-10-28-18-22-17.png"></center> | <center><img src="2022-10-28-18-28-51.png"></center> |
| | 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 $V_T$. |