peter/ENSC3016-ELEC3016-Power-and-Machines-notes
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## Power types in 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 | $P_\text{misc}$, $P_\text{stray}$ |
![](2022-10-25-11-33-40.png)
$$
\begin{align}
P_\text{in}&=P_\text{SCL}+P_\text{RCL}+P_\text{core}+P_\text{F\&W}+P_\text{misc}+P_\text{out}\\
P_\text{AG}&=P_\text{RCL}+P_\text{F\&W}+P_\text{misc}+P_\text{out}\\
P_\text{mech}&=P_\text{F\&W}+P_\text{misc}+P_\text{out}
\end{align}
$$
## No-load test
| 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 |
Using assumptions, remove rotor part of circuit and only consider stator and magnetizing path.
![](2022-10-24-20-04-52.png)
## 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 |
| | $X_r\approx f_0/f_{BL}\times X_r'$ | $X_r'\approx X_{BL}/2$ |
| | $X_r'\approx X_{BL}/2$ | $X_s\approx X_r'$ |
| | $X_s\approx X_r'$ |
## Equivalent model
| Assumption | Eqn | Reason |
| ---------- | ------------------------ | ------------------------------------ |
| | $x_m\approx X_m$ | $R_c\ggg X_m\Rightarrow r_c\lll x_m$ |
| | $r_c\approx {X_m}^2/R_c$ | $R_c\ggg X_m\Rightarrow r_c\lll x_m$ |