Study On Global Optimization For Power System Based On Theory Of Moment

Optimization theory has been widely applied in power system planning and operation, and it is playing an increasing significant role. This applications develop various optimization problems which solutions will affect the power system based on its merit. Over the past decades, all kinds of optimization are used with many positive results for the problems. However, power system optimization being nonconvex, it is an enormous challenge to solve the global optimum since traditional optimization methods can not assure the global optimality. Therefore, it has important theoretic and realistic meanings to study new global optimization theories and explore the global optimum for power system optimization problems.Based on moment semidefinite programming (MSDP), which is the brand-new achievement of global optimization, this thesis focuses on the theory study for the global optimization algorithm of power system. With moment theory in the field of probability, power system polynomial optimization problems can be transformed as moment expressions, and relaxed as semidefinite programming (SDP) models in the moment space through constructing semidefinite moment matrices. This kind of SDP model is called MSDP model, and its optimal value can gradually approach the original global optimum as increasing the order of moment matrix. Moreover, a judgment criterion of global optimum is introduced to guarantee the global optimality for the solution.In the power system optimization problems,{0,1}-economic dispatch (ED) and optimal power flow (OPF) are two typical nonconvex programming problems. The {0,l}-ED problem is a mixed integer program problem, its solution process is complex and is hard to get the global optimum, and even can not obtain a feasible solution. The global optimum of OPF problem is the goal of the long-term effort for the scholars, and it was attempted to be sovled by SDP convex relaxation method, but that is still difficult. This thesis employs MSDP method to solve these two problems, and obtains exact global optimum with2-order relaxation model in general. The main research achievements of this study are as follows.1) A MSDP model for {O,1}-ED problem is proposed. The integer constraints in the {O,1}-ED model are written as polynomial complementary form, and the problem is converted to moment space, then a corresponding MSDP model can be established by introducting the semidefinite constraints. The results show that, its optimal solutions can meet the criterion of global optimum, and the integer solutions of the0/1variables can be got without dividing the original problem.2) The MSDP algorithm of {0,1}-ED problem is proposed for solving multiple global optimal solutions. There may be one or more global optimal solutions for the {0,1}-ED since it belongs to the combined optimization problem. And the number of solutions of {0,1}-ED can be judged by the criterion of global optimum. When there are multiple global optimal solutions, the optimized result of MSDP is the moment of original solutions about a probability measure. And the multiple global optimal solutions of {0,1}-ED problem can be extracted from the MSDP solution by an eigenvalue method with singular value decomposition. An illustrative example showed that the method succeeded in finding multiple meaningful global optimal solutions. This process provides a useful insight into solving combinatorial optimization problems of power system.3) A MSDP model for OPF problem is proposed. The OPF model being written as polynomial optimization problem with inequality constraints, a corresponding MSDP model can be established by the semidefinite relaxation techniques in moment space. This MSDP model can be solved with rank-1moment solution for OPF standard cases and the counterexamples of existing SDP method, and the global optimum is guaranteed. It is showed that the MSDP model overcome the problem of no rank-1solution in solving OPF by existing SDP method.4) The MSDP global optimization algorithm of OPF problem is proposed. As the moment solution of MSDP-OPF model is rank-1, it ensures that the global optimal solution of OPF is unique. The probability measure of the solution is Dirac function now, and then the moment solution is equal to the original global optimum. Consequently, the global optimal solution of OPF can be got from moment solution directly.This thesis was supported in part by the National Natural Science Foundation of China (51167001) and by The National Basic Research Program of China (2013CB228205)...