Induction generator and excitation capacitor

Induction motor as induction generator

If a three-phase induction motor connected to the supply is driven by a prime mover above synchronous speed, the slip becomes negative ($s<0$). The rotor conductors now cut the rotating field faster than the field itself rotates, so the rotor emf and current reverse. The torque opposes the driving torque, and the machine converts mechanical power into electrical power, which it delivers to the supply. It still draws lagging reactive power from the supply (or from capacitors) for magnetisation.

For an isolated (stand-alone) system the reactive power is supplied by capacitors connected across the stator terminals. This is the self-excited induction generator.

Procedure to find the excitation capacitor

1. Run the machine as a motor at the supply frequency and no load. Measure terminal (phase) voltage $V$ against magnetising current $I_m$ to get the no-load magnetisation curve (V against $I_m$). It is linear at first and then saturates.
2. A capacitor of capacitance $C$ per phase draws a current $I_c = \frac{V}{X_c}$, with $X_c = \frac{1}{2\pi f C}$. In the V-I plane it is a straight line through the origin with slope $X_c$.
3. For stable voltage, the capacitor line must cut the magnetisation curve. The intersection point gives the generated voltage.
4. For a required voltage $V_0$: read $I_m$ at $V_0$ from the curve. Then

$$X_c = \frac{V_0}{I_m}, \qquad C = \frac{I_m}{2\pi f V_0}$$

5. Minimum (critical) capacitance: the line tangent to the linear part of the curve has slope $X_m$ (unsaturated magnetising reactance), so

$$C_{min} = \frac{1}{\omega X_m} = \frac{1}{\omega^2 L_m}, \quad \omega = 2\pi f$$

If $C < C_{min}$, the line does not meet the curve and the voltage does not build up.

 V
 |            /  Xc line (larger C: flatter)
 |        _.-*---- saturation curve
 |     .-'  /
 |   .'   /
 |  / /
 +------------------> Im
   V0 found at crossing

The generated frequency depends on speed: $f \approx \frac{P N_r}{120}$ less the small slip, so frequency is a little different from that used in the test. Use the frequency of operation in $X_c$.