## 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.

![](2022-10-25-11-45-26.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                                          |
|                         | $X_r\approx f_0/f_{BL}\times X_r'$ | $X_r'\approx X_{BL}/2$                                                          |
|                         | $X_r'\approx X_{BL}/2$             | $X_s\approx X_r'$                                                               |
|                         | $X_s\approx X_r'$                  |

![](2022-10-25-11-46-04.png)

## Equivalent model

| Assumption | Eqn                      | Reason                               |
| ---------- | ------------------------ | ------------------------------------ |
|            | $x_m\approx X_m$         | $R_c\ggg X_m\Rightarrow r_c\lll x_m$ |
|            | $r_c\approx {X_m}^2/R_c$ | $R_c\ggg X_m\Rightarrow r_c\lll x_m$ |