This paper proposes a parallel evolutionary strategy to solve a large-scale dynamic optimal reactive power flow (ORPF) problem to minimize the transmission losses while ensuring that the power system constraints are met, by varying the voltage magnitude of generators, the transformer taps and all reactive power support, installed in the power system. The existing heuristic algorithms are time-consuming due to the large number of sequential calculations that need to be carried out. This paper proposes the use of a parallel evolutionary strategy to speed up the optimization of a large-scale ORPF problem based on the orthogonal design and the Nash equilibrium. The paper proposes to apply the orthogonal crossover operator for small but good representative combination samples, and then to apply the Nash Equilibrium to refine the combinations (i.e., to achieve the optima). The proposed design is effective to strengthen both the exploration and the exploitation of the decision space to obtain the global optimum. The simulation results validate the effectiveness of the proposed algorithms for a large-scale ORPF when applied on the IEEE 30-and IEEE 118 bus systems when compared with the results from current state-of-art approaches.