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Chapter 5—Electrical Network 5–22 magnitude and phase. Generator action is obtained by increasing the magnitude of E with the field control. The pitch controller sets the blade pitch at the optimum point if the blades are not already at this point. The blade torque will attempt to accelerate the generator, but this is impossible because the generator and the power grid are in synchronism. The torque will advance the relative position of the generator rotor with respect to the power grid voltage, however, so E will lead V by the power angle δ. The input mechanical power to the generator is fixed for a given wind speed and blade pitch, which also fixes the output power. If |E| is changed by the generator field control, then the power angle will change automatically to maintain this fixed output power. This synchronization process may sound very difficult, but is accomplished routinely by automatic equipment. If the wind speed and blade pitch are such that the turbine and generator are slowly accelerating through synchronous speed, the relay can usually be closed just as synchronous speed is reached. The microprocessor control would then adjust the field current and the blade pitch for proper operating conditions. An observer would see a smooth operation lasting only a minute or so. The control systems necessary for synchronization and the generator field supply are not cheap. On the other hand, their costs are not strongly dependent on system size over the normal range of wind turbine sizes. This means that the control systems would form a small fraction of the total turbine cost for a 1000-kW turbine, but a substantial fraction for a 5-kW turbine. For this reason, the synchronous generator will be more common in sizes of 100 kW and up, and not so common in the smaller sizes. 4 PER UNIT CALCULATIONS Problems such as those in the previous section can always be worked using the actual circuit values. There is an alternative, however, to the use of actual circuit values which has several advantages and which is widely used in the electric power industry. This is the per unit system, in which voltages, currents, powers, and impedances are all expressed as a percent or per unit of a base or reference value. For example, if a base voltage of 120 V is chosen, voltages of 108, 120, and 126 V become 0.90, 1.00, and 1.05 per unit, or 90, 100, and 105 percent, respectively. The per unit value of any quantity is defined as the ratio of the quantity to its base value, expressed as a decimal. One advantage of the per unit system is that the product of two quantities expressed in per unit is also in per unit. Another advantage is that the per unit impedance of an ac generator is essentially a constant for a wide range of actual sizes. This means that a problem like the preceding example needs to be worked only once in per unit, with the results converted to actual values for each particular size of machine for which results are needed. We shall choose the base or reference as the per phase quantities of a three-phase system. Thebaseradianfrequencyω base = ω o is the rated radian frequency of the system, normally Wind Energy Systems by Dr. Gary L. Johnson November 21, 2001
Chapter 5—Electrical Network 5–23 2π(60) = 377 rad/s. Given the base apparent power per phase S base and base line to neutral voltage V base ,the following relationships are valid: I base = S base V base A (35) Z base = R base = X base = V base I base Ω (36) P base = Q base = S base VA (37) We may even define a base inductance and a base capacitance. L base = X base ω o (38) 1 C base = (39) X base ω o The per unit values are then the actual values divided by the base values. V pu = V V base (40) I pu = Z pu = I Ibase Z Zbase (41) (42) ω pu = L pu = C pu = ω ω base = ω ω o (43) L L base (44) C C base (45) Example Wind Energy Systems by Dr. Gary L. Johnson November 21, 2001
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