more severe for a single-phase fault than a three-phase fault. The most important quantity is the first peak current as it determines the rating of the protective circuit breaker needed to protect the generator against such faults. The short circuit current has a slowly decaying DC component, and an AC component. The latter is larger than the direct on-line starting inrush current, and may reach 10-15 times the full load rated current.

The transient current and torque, in any case, are calculated using the generalized equivalent circuit of the machine in terms of the d-axis and q-axis transient and subtransient reactance and time constants.4-6 The q-axis terms do not enter in the induction generator transient analysis, as the d-axis and the q-axis terms are identical due to the perfect circular symmetry in the electromagnetic structure.

References

1.Rahim, Y. H. A. 1997. “Controlled Power Transfer from Wind Driven Reluctance Generators,” IEEE Winter Power Meeting, Paper No. PE-230-EC-1-09, New York, 1997.

2.Say, M. G. 1983. “Alternating Current Machines,” New York, John Wiley & Sons, 1983.

3.Alger, P. L. 1965. “The Nature of Induction Machines.” New York, Gordon and Breach. 1965.

4.Adkins, B. 1964. “The General Theory of Electrical Machines,” London, Chapman and Hall. 1964.

5.Kron, G. 1967. “Equivalent Circuits of Electrical Machines,” New York, Dover Publications, 1967.

6.Yamayee, Z. A. and Bala, J. L. 1994. “Electromechanical Devices and Power Systems,” New York, John Wiley & Sons, 1994.

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7

Generator Drives

The turbine speed is generally much lower than the desired speed for the electrical generator. For this reason, the turbine speed in most wind systems is stepped up using a drive system. The system can be fixed-speed or vari- able-speed as described in this chapter.

The wind-power equation as derived in Chapter 3 is as follows:

where Cp = rotor power coefficient.

As seen earlier, the value of Cp varies with the ratio of the rotor tip-speed to the wind speed, termed as the tip-speed-ratio TSR. Figure 7-1 depicts a typical relationship between the power coefficient and the tip-to-speed ratio. As the wind speed changes, the TSR and the power coefficient will vary. The Cp characteristic has single maximum at a specific value of the TSR. Therefore, when operating the rotor at constant speed, the power coefficient will be maximum at only one wind speed.

For achieving the highest annual energy yield, the value of the rotor power coefficient must be maintained at the maximum level all the time, regardless of the wind speed. The theoretical maximum value of Cp is 0.59, but the practical limit is 0.5. Attaining Cp above 0.4 is considered good. Whatever value is attainable with a given wind turbine, it must be maintained constant at that value. Therefore, the rotor speed must change in response to the changing wind speed. To achieve this, the speed control must be incorporated in the system design to run the rotor at high speed in high wind and at low speed in low wind. This is illustrated in Figure 7-2. For given wind speeds V1 , V2, or V3 , the rotor power curves versus the turbine speed are plotted in solid lines. In order to extract the maximum possible energy over the year, the turbine must be operated at the peak power point at all wind speeds. In the figure, this happens at points P1 , P2, and P3 for the wind speed V1 , V2 , and V3 , respectively. The common factor among the peak power production points P1 , P2 , and P3 is the constant high value of TSR, close to 0.5.

Operating the machine at the constant tip-speed ratio corresponding to the peak power point means high rotor speed in gusty winds. The centrifugal

© 1999 by CRC Press LLC

FIGURE 7-1

Rotor power coefficient versus tip-speed ratio has a single maximum.

forces produced in the rotor blades under such speeds can mechanically destroy the rotor. Moreover, the generator producing power above its rated capacity may electrically destroy the generator. For these reasons, the turbine speed and the generator power output must be controlled.

7.1Speed Control Regions

The speed and the power controls in the wind power systems have three distinct regions:

•the optimum constant Cp region.

•the speed-limited region.

•the power-limited region.

These regions are shown in Figure 7-3. Typically the turbine starts operating (cut in) when the wind speed exceeds 4-5 m/s, and is shut off at speeds exceeding 25 to 30 m/s. In between, it operates in one of the above regions. At a typical site, the wind-turbine may operate about 70 to 80 percent of the time. Other times, it is off due to wind speed too low or too high.

© 1999 by CRC Press LLC

FIGURE 7-2

Turbine power versus rotor-speed characteristics at different wind speeds. The peak power point moves to the right at higher wind speed.

FIGURE 7-3

Three distinct rotor-speed control regions.

© 1999 by CRC Press LLC