No-load and blocked rotor tests of induction motor

The no-load test and the blocked rotor test of a three-phase induction motor are the counterparts of the open-circuit and short-circuit tests of a transformer. Together they give the parameters of the per-phase equivalent circuit ($R_1, X_1, R_2', X_2', R_c, X_m$) without loading the motor.

Circuit used

 3-ph       +--[A]--[W1]--+
 variable --|             |--- 3-ph
 supply  ---+--[ ]--[W2]--+--- induction
 (autotr.)  |     [V]     |--- motor
            +-------------+
 Two-wattmeter method: P = W1 + W2

An ammeter, a voltmeter and two wattmeters (two-wattmeter method) are connected between a variable three-phase supply (autotransformer) and the stator.

No-load test

Procedure: The motor runs uncoupled from any load at rated voltage and rated frequency. Readings: line voltage $V_0$, line current $I_0$ and input power $P_0 = W_1 + W_2$.

Theory: At no load the slip is very small ($s \approx 0$), so $R_2'/s$ is very large and the rotor branch is practically open. The current $I_0$ (25–40 % of rated, because of the air gap) is mainly magnetising current. Input power covers:

$$P_0 = \text{stator Cu loss} + \text{core loss} + \text{friction and windage loss}$$

Calculations (per phase, star equivalent):

$$\begin{aligned} V_{ph} &= \frac{V_0}{\sqrt{3}}, \qquad \cos\phi_0 = \frac{P_0}{\sqrt{3}\,V_0 I_0} \\ P_{rot} &= P_0 - 3 I_0^2 R_1 \quad (\text{core + mechanical loss}) \\ I_w &= I_0 \cos\phi_0, \qquad I_\mu = I_0 \sin\phi_0 \\ R_c &= \frac{V_{ph}}{I_w}, \qquad X_m = \frac{V_{ph}}{I_\mu} \end{aligned}$$

Also $Z_0 = V_{ph}/I_0 \approx X_1 + X_m$, so a more accurate value is $X_m = X_0 - X_1$ once $X_1$ is known from the blocked rotor test. Friction and windage loss can be separated from core loss by repeating the test at reduced voltages and extrapolating the $P_0$–$V^2$ curve to zero voltage.

Blocked rotor test

Procedure: The rotor is held stationary (blocked) and a reduced voltage (about 10–20 % of rated) is applied, raised until rated current flows. Readings: $V_{sc}$, $I_{sc}$, $P_{sc}$. For accurate rotor values, the test is ideally done at about 25 % of rated frequency, since the rotor normally works at slip frequency.

Theory: With the rotor at rest, $s = 1$, so $R_2'/s = R_2'$ is small. The magnetising branch has a much higher impedance and, at low voltage, draws very little current; it is neglected. Core loss is negligible at low voltage and there is no mechanical loss, so $P_{sc}$ is almost entirely the full-load copper loss of stator and rotor.

Calculations (per phase):

$$\begin{aligned} Z_{eq} &= \frac{V_{sc}/\sqrt{3}}{I_{sc}}, \qquad R_{eq} = \frac{P_{sc}}{3 I_{sc}^2} = R_1 + R_2' \\ X_{eq} &= \sqrt{Z_{eq}^2 - R_{eq}^2} = X_1 + X_2' \\ R_2' &= R_{eq} - R_1 \end{aligned}$$

$R_1$ is measured by a DC test on the stator winding (DC resistance multiplied by about 1.2 for skin effect; for a star winding, $R_1 = R_{dc,\,line}/2$).

Splitting $X_{eq}$: Usually $X_1 = X_2' = X_{eq}/2$ (IEEE gives other ratios, e.g. 0.4 : 0.6 for class B and 0.3 : 0.7 for class C designs).

Using the results: equivalent circuit

  R1    jX1          jX2'     R2'
 -^^^---mmm----+------mmm------^^^--+
               |    |               |
 V1          Rc[]  []jXm            [] R2'(1-s)/s
               |    |               |    (load)
 --------------+------+-------------+

With these values the equivalent circuit can predict current, power factor, torque, efficiency and slip at any load, and the data can also be used to draw the circle diagram.