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A novel real-parameter quantum evolutionary algorithm is presented. The algorithm pieces together ideas from EA and quantum computing to provide a robust technique that can be utilized to optimize even highly constrained non-linear functions with real parameters. Economic Load Dispatch (ELD) and Reactive Power Dispatch (RPD) are two important problems in power systems that are modeled using nonlinear, discontinuous objective functions and constraints. The proposed method has been applied to these problems and its performance is found to be better than other methods.