WIND ENERGY SYSTEMS - Cd3wd

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Chapter 5—Electrical Network 5–14 easily be shown to be zero in the balanced case. I n = I a + I b + I c = 0 A (25) The total power supplied to the load is three times the power supplied to each phase. |S tot | = 3|E a ||I a | VA P tot = 3|E a ||I a | cos θ W (26) Q tot = 3|E a ||I a | sin θ var The total power can also be expressed in terms of the line-to-line voltage E ab . |S tot | = √ 3|E ab ||I a | VA P tot = √ 3|E ab ||I a | cos θ W (27) Q tot = √ 3|E ab ||I a | sin θ var We shall illustrate the use of these equations in the discussion on synchronous generators in the next section. 3 THE SYNCHRONOUS GENERATOR Almost all electrical power is generated by three-phase ac generators which are synchronized with the utility grid. Engine driven single-phase generators are used sometimes, primarily for emergency purposes in sizes up to about 50 kW. Single-phase generators would be used for wind turbines only when power requirements are small (less than perhaps 20 kW) and when utility service is only single-phase. A three-phase machine would normally be used whenever the wind turbine is adjacent to a three-phase transmission or distribution line. Three-phase machines tend to be smaller, less expensive, and more efficient than single-phase machines of the same power rating, which explains their use whenever possible. It is beyond the scope of this text to present a complete treatment of three-phase synchronous generators. This is done by many texts on electrical machines. A brief overview is necessary, however, before some of the important features of ac generators connected to wind turbines can be properly discussed. Wind Energy Systems by Dr. Gary L. Johnson November 21, 2001
Chapter 5—Electrical Network 5–15 A construction diagram of a three-phase ac generator is shown in Fig. 9. There is a rotor which is supplied a direct current I f through slip rings. The current I f produces a flux Φ. This flux couples into three identical coils, marked aa ′ , bb ′ ,andcc ′ , spaced 120 o apart, and produces three voltage waveforms of the same magnitude but 120 electrical degrees apart. ❦ . . . ❦ ✲ ☛ I f ✡ ❦ ✻ Φ ❦ . ❦ ✟. ✠ ∨ ✟ ω ✠ ❦ Figure 9: Three-phase generator The equivalent circuit for one phase of this ac generator is shown in Fig. 10. It is shown in electrical machinery texts that the magnitude of the generated rms electromotive force (emf) E is given by |E| = k 1 ωΦ (28) where ω =2πf is the electrical radian frequency, Φ is the flux per pole, and k 1 is a constant which includes the number of poles and the number of turns in each winding. The reactance X s is the synchronous reactance of the generator in ohms/phase. The generator reactance changes from steady-state to transient operation, and X s is the steady-state value. The resistance R s represents the resistance of the conductors in the generator windings. It is normally much smaller than X s , so is normally neglected except in efficiency calculations. The synchronous impedance of the winding is given the symbol Z s = R s + jX s . The voltage E is the open circuit voltage and is sometimes called the voltage behind synchronous reactance. It is the same as the voltage E a of Fig. 8. The three coils of the generator can be connected together in either wye or delta, although the wye connection shown in Fig. 8 is much more common. When connected in wye, E is the line to neutral voltage and one has to multiply it by √ 3 to get the magnitude of the line-to-line voltage. The frequency f of the generated emf is given by Wind Energy Systems by Dr. Gary L. Johnson November 21, 2001
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