In a system with only a single generator, or in which all generators are identical, the average system frequency is governed by the following differential equation: The same equation gives a good approximation to the solution for a more complex system if parameters derived from appropriate weighted averages of shaft kinetic energy, governor dynamics, etc., are used. Solving this equation for £(t) assuming that there is a change in the available generation capacity at t = 0 provides the following expression for the transient response:
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