## Islanding and selfexcitation of induction generators

Fixed-speed wind turbines use induction generators to provide damping in the drive train and, as there is no direct access to the field of an induction generator, the magnetizing current drawn from the stator leads to a requirement for reactive power. In order to reduce the reactive power supplied from the network it is conventional to fit fixed-speed wind turbines with local power factor correction (PFC) capacitors. As long as the induction machine is connected to a distribution network its terminal voltage is fixed and so the PFC capacitors merely reduce the reactive power drawn from the network. However, once the induction generator is isolated from the network then there is the possibility of a resonant condition, known as self-excitation, leading to large over-voltages (Allan, 1959, Hindmarsh, 1970). When the generator is isolated from the network it will tend to accelerate as its load is removed. This increase in rotational speed, and consequently of frequency, adds to the possibility of self-excitation. There have been a number of cases reported of sections of distribution network, to which wind turbines are connected, becoming isolated and over-voltages resulting in damage to customers' equipment.

Figure 7.28 showed the conventional equivalent circuit of an induction machine with the PFC capacitors connected at the terminals (McPherson, 1981) but with no connection to the network. At normal running speed and frequency, the slip (s) is small and so the impedance of the rotor branch is high and, to a first approximation, can be considered an open circuit. As the stator impedance (Rs + jXs) is much smaller than the magnetizing reactance jXm then the equivalent circuit may be simplified to a simple parallel connection of the PFC capacitors and the magnetizing reactance. Thus the equivalent circuit of Figure 7.26 may be reduced to that of Figure 10.22. This is a conventional LC parallel circuit but in this case Xm is a nonlinear function of voltage due to magnetic saturation. Energy is added to the circuit from the wind turbine. An indication of the likely voltage which will occur as the wind-turbine rotor accelerates can be gained by considering the intersection of the capacitive and inductive voltages as the current is identical in each element of this simplified model. This is shown in Figure 10.23. Point X indicates the self-excitation voltage at frequency /1, say 50 Hz, while point Y illustrates the self-excitation voltage at an increased frequency, /2, say 55 Hz. Such simple calculations are jXc jXm

Figure 10.22 Reduced

Terminal voltage

Current in resonant circuit

Figure 10.23 Illustration of Self-excitation at Two Frequencies f and f2 (Ic - Current in Capacitors, Im - Current in Magnetizing Reactance of Induction Machine)

Equivalent Circuit to Illustrate Resonance Leading to Self-excitation

Equivalent Circuit to Illustrate Resonance Leading to Self-excitation

Terminal voltage

Current in resonant circuit

Figure 10.23 Illustration of Self-excitation at Two Frequencies f and f2 (Ic - Current in Capacitors, Im - Current in Magnetizing Reactance of Induction Machine)

indicative only as they are based on a very simple representation of the induction generator and even then it is difficult to obtain reliable data for the saturation characteristic of the machine. However, as self-excitation is a most undesirable condition for grid-connected wind turbines, precise calculations of the voltage rise are seldom required.

Self-excitation can be avoided by limiting the PFC capacitance, including any capacitance of the distribution network, to a value which will not lead to the resonant condition at any credible frequency which will be experienced during overspeed. Alternatively, the potential for this condition must be recognized and fast-acting over-voltage and over-frequency protection arranged to stop the wind turbine if islanding occurs.

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