An Optimal Power Flow Model Based On A Transformer Model With A Virtual Node In Polar Coordinates

Optimal power flow(OPF)is a complex non-linear programming problem.It is the optimization analysis of stable running.OPF must meet the requirements of the rules of the power system operation and security constraints.By adjusting control variables of the system, it can optimize the parameters of the intended target function.With the rapid development of the power system,more and more control equipment to be used for power grids in mediating system's operation.These devices put into use in optimizing the running way of the system. But,at the same time,it makes the large optimal flow problems more complicated and an increase difficult of their analysis and calculation.Transformer is one of the most important control equipment in power system,widely used in every corner which current and voltage need to change.More than the previous model, OPF is based on the traditional transformer-type equivalent circuit∏established.This model can not be directly reflected in the surge voltage transformer's regulatory role and is complex to the analysis and calculation.Based on the virtual node transformer model,in polar coordinates system,we established a new OPF model which the objective function is to minimize operating costs.The use of the widely used polar coordinates that not only to reflect the power of the physical parameters of significance but also to make the model more concise, easy to understand,analyse and memory.The import of virtual nodes,which put the transformer voltage amplitude replace variable ratio,reduced the number of variables of expressions.At the same time,for equality constraints of the Jacobian and Hessian matrix,the reduction in the number of non-zero elements were reduced at least in the number of transformers 2 times and 6 times,thus reducing the amount of computation.Using Matlab programming,in polar coordinates system,we applied the primal-dual interior point method to solve the OPF model based on the transformer model of traditional∏type equivalent circuit and based on virtual nodes transformer model respectively.In the same circumstances,we did such as TEST4,IEEE14～300 and S-1047 nodes seven test systems simulation.Simulation results confirm the equivalence of two transformal model and the superiority of this OPF based on a transformer model with a virtual nodes.