An optimization algorithm is presented for an underfrequency load shedding system which is composed of several stages that are tripped at preset frequencies. The optimization of this system is considered with respect to a cost function that includes a dynamic part, which is the integral of the deviation from nominal frequency, and a static part which is the total load shedding. The optimization is constrained by the requirement of minimum allowed frequency and limitation on the total load of the shedding system. A projected gradient method is used for the solution, and analytic expressions for the partial derivatives are used to simplify the computation. Results of applying the optimization to a model of the Israeli power system are given together with a study of the cost parameters.
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