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This paper presents an evolutionary algorithm based on quantum computation for bid-based optimal real and reactive power (P-Q) dispatch. The proposed quantum-inspired evolutionary algorithm (QEA) has applications in various combinatorial optimization problems in power systems and elsewhere. In this paper, the QEA determines the settings of control variables, such as generator outputs, generator voltages, transformer taps and shunt VAR compensation devices for optimal P-Q dispatch considering the bid-offered cost. The algorithm is tested on the IEEE 30-bus system, and the results obtained by the QEA are compared with those obtained by other modern heuristic techniques: ant colony system (ACS), enhanced GA and simulated annealing (SA) as well as the original QEA. Furthermore, in order to demonstrate the applicability of the proposed QEA, it is also implemented in a different problem, which is to minimize the real power losses in the IEEE 118-bus transmission system. The comparisons demonstrate an improved performance of the proposed QEA.