Conditions for induction generator, T-S curve

An induction machine works as an induction generator when its rotor is driven by a prime mover above synchronous speed, so the slip becomes negative and the torque reverses. It then delivers active power to the supply.

Conditions for generator operation

1. Speed above synchronous speed: $N_r > N_s = \frac{120f}{P}$, so slip $s = \frac{N_s - N_r}{N_s} < 0$.
2. Source of reactive power: the machine has no separate field winding. It must take its magnetising current from the grid (grid-connected), or from a capacitor bank across the stator terminals (self-excited, stand-alone).
3. Frequency and voltage fixed by the grid: when grid-connected, the grid keeps the frequency and terminal voltage. For stand-alone use, residual magnetism and sufficient capacitance are needed for voltage build-up.
4. Prime mover with enough power: a turbine or engine must drive the rotor so that the mechanical input exceeds losses. The speed is only 2 to 5 % above $N_s$ at rated load.
5. Capacitor value must exceed a critical value so that the magnetising line is crossed (self-excited case).

Explanation with T-S curve

The torque-slip curve extends on both sides of $s = 0$.

• $0 < s < 1$: motoring region (torque positive, power flows from the supply to the shaft).
• $s < 0$: generating region. The curve is an inverted image of the motoring part, with torque negative. The maximum (pull-out) generating torque occurs at $s \approx -s_m$.
• $s > 1$: braking (plugging) region, rotor runs opposite to the field.

 T
 |        motoring
 |         _.-*-._
 |      _-'       `-._
 +-----+-------+-----------> s
 s=1       s=0   (N=Ns)
 ...  _.-'  generating  (s<0)
 |  *-'
 |

Beyond $N_s$ the slip is negative, the rotor emf and current reverse, and the electromagnetic torque opposes the prime mover. The air-gap power $P_g = \frac{P_{conv}}{1-s}$ becomes negative, meaning power is fed to the stator and then to the grid. If the driving torque exceeds the maximum generating torque, the machine runs away (loses stability), so the prime mover torque must stay below the pull-out value.