Electricity Production from Renewables Energies

3.10 Exercises

3.10.1. Fixed speed wind turbines

This exercise draws inspiration from the French Agrégation interne exam in electrical engineering from 2001. Figure 3.67 gives the characteristic of the mechanical power, which is supplied by a fixed speed wind turbine on an electrical network at 50 Hz for a wind speed of 15 m/s according to the turbine rotational speed. The nominal operating point is chosen so that the supplied power is at a maximum. An induction machine with two pole pairs is used.

Figure 3.68. Curve of the power, according to the rotational speed with constant wind speed (15 m/s) supplied by a wind turbine

A. With a speed multiplier with a 31.7 ratio, determine the optimal generator rotational speed, as well as its slip.

B. Determine the electromagnetic torque of the induction machine, given that the multiplier has an efficiency of 96%. The generator mechanical losses are worth 6 kW in this operating point.

C. At low slip values, in the machine single-phase equivalent diagram, the resistor term will be much higher than the inductive term l₂ω. By bringing back the rotor part of the single-phase diagram to the stator side, the expression of the electromagnetic torque is obtained by erasing the coefficient n. The nominal voltage between the phases is worth U1 = 326 ...