The Doubly Fed Induction Generator (DFG) is a Variable-Speed Constant-Frequency Generator operating in either subsynchronous or supersynchronous mode. In this paper the transient behavior of the Doubly Fed Induction Generator, symmetrically loaded, after a three phase short circuit is presented. Both speed and rotor excitation voltage and frequency remain unchanged during short circuit. The complete mathematical model of the transient state and experimental results are given as well as the transient state equivalent circuit.The Doubly Fed Induction -chine, is known since the beginning of the century. Its performance was investigated for either motor or generator operation, but mainly in the steady state. Transient state was investigated in [l], [a] and [3] but only for the single and double cage induction motor. In this paper the authors, following procedures similar to those of [l], [2] and [3], present a generalized analysis of the DFG in the transient state during the three phase short circuit from load condition. A detailed mathematical analysis is presented from which the transient DFG parameters, the transient equivalent circuit, as well as the DFG transient response are obtained. The theoretical results were verified by experiments. ANALYSISTo determine the DFG short circuit stator and rotor currents, the DFG is assumed to rotate at a constant speed wn = (1-s)w and is considered to be excited from the rotor dide by a frequency converter with a voltage phasor Vz. During the period of short circuit, the speed as well as the rotor excitation voltage and frequency remain unchanged.The stator of the DFG may, either be connected to the infinite bus of voltage VI, or supply an isolated passive load RotjwLo at constant voltage VI. Stator and rotor voltages, currents as well as DFG parameters are expressed in terms of d, q , y -axis' quantities, with the d,q axes rotating at synchronous speed [l] , Fig. 1 90 SM 414-3 EC the IEEE Electric Machinery Committee of the IEEE Power Engineering Society for presentation at the IE!%E/ \ W t + O Fig. 1 The 3-phase DFG and the d,q axes.The self inductance d,q components for either stator (index 1) or rotor (index 2) are considered equal due to the fact that the stator and rotor balanced windings are distributed around a smooth uniform air gap. The same applies also to the mutual inductances [l] . Thus:The stator and rotor flux linkage d, q components (4) (5) (6) (7)are :The d,q voltage components for stator ma rotor may be derived from (4) through (7).where w is the synchronous angular speed, s is the slip and p is the differential operator (d/dt).Substituting (4) through (7) in ( 8 ) through (11) appropriately, the DFG equations in the transient state are deduced: 63In the case where the stator is short circuited, the stator voltages Vld and VIg become zero. The rotor excitation voltage V2 is divided into the components VZd and VZq along the direct and quadrature axes. The short circuit equations for the DFG may be obtained by applying Laplace transformation to (12) through ...

106 82 Athens , Greece Ab_strac_f, A detailed analysis of the performance o f the Doubly-Fed Induction Generator (DFG) under synchronous operating condition in the steady state is presented. The rotor is excited by a voltage phasor the magnitude and the frequency of which can vary independently. The frequency supplied has always such a value that, if superimposed on the rotor speed a synchronous rotating field results. This produces variable-speed constantfrequency characteristics of the DFG over a wide speed range. By varying the excitation voltage magnitude the stator and rotor power factor can be controlled so that maximum efficiency tan b e achieved. By varyinq the angle a between the stator and the rotor applied voltages, DFG active power delivered can be controlled. The wide range of variable-speed constant-frequency operation and the capability o f load variation and power factor control, makes the DFG attractive for wind power conversion systems a5 well a s variable speed hydroelectric generators, 0885-8%9/89/093%0495WI .OO 0 1989 IEEE 4% angle a between the stator applied voltage 0 1 and the rmztor excitation voltage VZ referred t o the stator.In the following each one of the performance characteristics ; f the DFG i.e. stator and rotor currents I 1 and I n , active power P a and P2, reactive power Q I and Q z , copper losses Pri and P,P, mechanical power P, and electromagnetic torque T are deduced as functions of the slip 5 , the magnitude Vz and the angle a. All magnitudes except P . and T are considered per phase. All electrical quantities entering the terminals of both stator and rotor are considered positive. This also holds f o r P,. The electromagnetic torque T is considered positive i f it is motoring. a. Stator Quantities

In this paper, an electrical drive model, implementing a doubly-fed differential drive (DFDD) is presented. Two doublyfed induction machines, having the corresponding rotor phases connected, constitutes the differential wheel drive. Two inverters are supplying the machine stators with three-phase power of variable magnitude and frequency. The power required to supply the inverters may be delivered from a constant voltage dc source like a battery. Active power requirements for the machines and the inverters over the DFDD speed range may be obtained. Reactive power requirements for minimum copper loss may be derived as well. The DFDD may provide propulsion to electrical vehicles.

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