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The paper considers simultaneous placement and tuning of power system stabilizers for stabilization of power systems over a wide range of operating conditions using genetic algorithm. The power system operating at various conditions is considered as a finite set of plants. The problem of setting parameters of power system stabilizers is converted as a simple optimization problem that is solved by a genetic algorithm and an eigenvalue-based objective function. A single machine -infinite bus system and a multi-machine system are considered to test the suggested technique. The optimum placement and tuning of parameters of PSSs are done simultaneously. A PSS tuned using this procedure is robust at different operating conditions and structure changes of the system.