Power Systems Reactive Planning Based On The Extended Second-Order Cone Programming

One important task in power system planning is the reactive power planning, which is trying not only to meet the requirement of current operating, but also to adapt the future development of the power system. Generally, reactive planning optimization is to determinate the location and the capacity of Var compensation subject to both of the operational requirements and economy. The proposal thesis focuses on the research for the location and capacity of Var compensation in the reactive power planning based on the optimal theory and second-order cone programming.First of all, the nonlinear reactive planning model based on L1-norm is established. In this model, the capacitive and inductive compensation are presented separately, and the objective function is the sum using L1-norm. According to the characteristics of L1-norm and the complementary nature of capacitive and inductive compensation in the same node, the compensation sites can be determined while calculating the capacity. The simulation of four test systems and a practical system are compared with the traditional model which minimize the capacity compensation. The results show that the model based on L1-norm has the less total compensation capacity and compensation sites. Moreover, the sites are more reasonable and the voltage optimization control impact is obvious. Secondly, an extended second-order cone programming model is created extended from the L1-norm model mentioned above. In this model, the node power equations are converted into linear expressions equivalently, and the second-order partial derivatives are focused on quadratic cones and tangent trigonometric functions. It is helpful to simplify and reduce the previous derivation process. Case studies show that the model converting is completely equivalent. By using the primal-dual interior point method (IPM), the benefit of the converts are reducing the density of Hessian matrix effectively, improving the calculation efficiency, and maintaining the excellent solving characteristics of IPM. Since some new variables and constraints are introduced, a simplified method for the extended second-order cone programming is proposed in the thesis as well. In detail, the model is vectorized by node-branch matrix, which reduces the number of constraints and variables according to elementary transformation significantly and improves the computing consumption. For the large scale system, the efficiency is more obvious.Finally, the constraints of the system voltage stability margin and on-load tap-changing transformer are combined into the proposed model due to the engineering demand. The relationship between the voltage stability and load growth is analyzed by solving the normal and critical state simultaneously, and the effect of the transformation ratios fixed-or-not as well. Considering the voltage stable margin, the final planning scheme provided by the proposal model can guarantee to meet the growth of load, keep the safe electrical distance between operate and collapse point, and satisfy the future development of power system.