Power System Optimization Based On Complementarity Constraints

The optimization of power system makes the operation, control and programming of power system more reasonable, scientific and economic, which includes a lot of and even total aspects of power system. Two of these aspects are thoroughly studied in this thesis: reactive power optimization control (RPOC) and power flow solvability control (PFSC). The objective of reactive power optimization is to minimize the active power loss, which is achieved by adjusting system parameters, subject to equality constraints and un-equality constraints. The restoration of power flow solvability is to adjust parameters, including active power related and reactive power parameters to achieve the maximum total loads subject to security constraints. To focus on the deficits and difficulties of RPOC and PFSC, with the theory of nonlinear complementarity as tool, a thoroughly exploration and study have been done in this thesis and many satisfactory achievements are obtained. The main achievements and research contents are listed as followed.First, to overcome the difficulty in processing the discrete variables and small convergence region of the deterministic methods, a new method, complementarity constraint based smooth Newton method, has been proposed for RPOC with discrete variables. The complementarity constraints in the Karush-Kuhn-Tucker (KKT) conditions are transformed into a set of smooth nonlinear equations by smooth relaxation function, which ensures nonsingularity of the Hessian matrix, and solved by smooth Newton method. The upper and lower integer bounds of the discrete variables are constructed as complementarity constraints, and embedded into the smooth Newton method to approach its integer solution successively. Test results on sample systems demonstrate that the proposed method is featured by: first, large convergence region; second, a simple and efficient strategy of adopting the complementarity constraints conditions to address discrete variables, thus optimal solutions for both continuous and discrete variables can be obtained.Then, the optimal model of PFSC is presented to obtain maximum total loads. The power flow function and other security constraints are set to be constraint conditions. The active parameters including generator active output and active load requirements) and reactive power parameters including generator reactive output and var compensation equipment are set to be control variables. The model is solved by complementarity constraint based smooth Newton method. To increase calculating speed, a decomposition algorithm is further constructed using the weak coupling property between active power related equations and reactive power related equations.When decomposition algorithm couldn't converge, Newton method is reused. Test results on sample systems demonstrate that complementarity constraint based smooth Newton method can address large unsolvable region of power flow. Although the iteration number of the proposed decomposition algorithm is a little bigger than that of smooth Newton method, the total calculation time is less than smooth Newton method by 20% due to the significant reduction of each iteration time.Optimization technique based on complementarity constraint overcomes many deficits of traditional optimization methods. It has large convergence region and fast calculation speed, so the power system optimization algorithm and software developed based on the optimization technique in the thesis could have a strong potential to be applied for practical power system.