Wind and Hydropower Systems

Wind turbine generator systems

A wind turbine converts the kinetic energy of moving air into shaft work, and the generator at the end of the drivetrain converts that work into electrical power. For a grid-connected system, three ideas matter most: the operating slip of the induction generator, the power coefficient of the rotor, and the control strategies that keep the rotor near its best speed.

An induction machine works as a motor or as a generator depending on whether its rotor runs below or above the synchronous speed N_s = \frac{120f}{P} set by the stator field. The slip is defined as s = \frac{N_s - N}{N_s}, where N is the rotor speed. Motoring gives 0 < s \le 1, whereas generating requires s < 0, because the turbine drives the rotor faster than the rotating field.

• Zero slip — the rotor runs exactly at synchronous speed, so no rotor current is induced and no torque is produced. Example: a rotor that matches the field speed carries no active power.
• Slip of one — the rotor is stationary, as in a locked rotor at start-up. It is a motoring condition, not a generating one.
• Negative slip — the rotor runs above synchronous speed and the machine delivers active power to the grid. This is the generating condition.
• Slip greater than one — the rotor turns against the direction of the field, as in plugging braking. It is not normal generation.

The rotor power coefficient C_p = \frac{P_{\text{rotor}}}{\frac{1}{2}\rho A V^3} gives the fraction of the wind's kinetic power that the rotor extracts. Its theoretical upper bound is the Betz limit, C_p \le \frac{16}{27} \approx 0.593. No practical rotor exceeds this value, so a stated maximum of 0.65 is not the Betz limit.

For a given rotor, C_p depends on the tip-speed ratio \lambda = \frac{\omega R}{V}. It rises to a peak at an optimum \lambda and then falls, so it is not a monotonically increasing function of \lambda. Multi-blade, low-speed rotors reach their peak at low \lambda.