Global Optimization Algorithms for Power Systems Based on Moment Theory

In order to achieve global optimization of power systems, the author proposes a method based on moment theory. In power system optimization problems, {0, 1} economic dispatch and optimal power flow problems are typical non-convex programming problems. The {0, 1} economic scheduling problem belongs to the mixed integer programming problem, which has a complex solving process and is difficult to ensure the global optimal solution, and even cannot obtain a feasible solution. The global optimal solution of the optimal power flow problem has been a goal that scholars have been striving for a long time. They have attempted to use the semi-definite programming convex relaxation method to obtain it, but it is still difficult. In the constructed model, the control center takes discrete variables and uses decimal integer encoding to improve computational efficiency. The application of mixed selection operators and adaptive adjustment of crossover/mutation rates improves convergence performance. Five hundred reactive power optimizations were conducted on an IEEE 14 node system, and the experimental results showed that the active power loss of the optimized power flow has significantly decreased compared to the initial power flow. The number of voltage out of limit buses has decreased by 5, and the voltage out of limit has also decreased. The annual expenditure has decreased by more than 1 million yuan, and the economic benefits are considerable. It has been proven that the moment value of the obtained optimal solution is equal to the global optimal solution of the original problem. Therefore, the global optimal solution of the optimal power flow problem can be directly obtained from the moment solution.