Dynamic Reactive Power Optimization Method Based On Transformer Dummy Node Model In The Polar Coordinate

In the mathematical model of reactive power optimization problem,the transformer is usually expressed by the equivalent Π circuits model,which takes turn ratio as a variable and makes AC power flow equations contain complex polynomial such as the square of turn ratio multiplied by the square of voltage magnitude,its highly nonlinearity increases the difficulty to solve the problem.Recent years,scholars apply the transformer dummy node model,instead of the equivalent Π circuits model,to the static reactive power optimization problem.The voltage magnitude at the dummy node is added to variables,replacing turn ratio,to express the voltage change from one side of the transformer to another,this makes AC power flow equations do not contain complex polynomial about turn ratio and its square,reduces the nonlinearity of the problem,simplifies the model and improves its solving efficiency.This paper improves the transformer dummy node model in the mixed polar coordinate,expressing the transformer admittance in the polar coordinate,and obtains the transformer dummy node model in the polar coordinate,which is not only more concise,but also completely retains the advantage of the former.Then this paper proposes a dynamic reactive power optimization method based on the transformer dummy node model in the polar coordinate,considering discrete control devices have action times constraints during the optimization time,in order to prevent its frequent actions as well as consequent increasement of equipment operation cost and accident risk.Three-stage solution algorithm is employed to improve solving efficiency.In the first stage,the original mixed integer nonlinear programming model is converted into nonlinear programming model by relaxing discrete variables,and the initial solution is got by the interior-point method.Then mixed integer quadratic programming models,minimizing approximation variance of each discrete variable while satisfying the action times constraint of discrete control device,are established in the second stage to get the solution of discrete variables.In the third stage,with discrete variables are determined,the nonlinear programming model formed in the first stage is solved to get the solution of continuous variables.In this algorithm,the first stage and the third stage are nonlinear problems,and the transformer dummy node model can reduce the nonlinearity of problems and improve solving efficiency.Test results prove that the proposed method is more efficient than the method based on the transformer equivalent Π circuits model,and could optimize the reactive power flow and improve economy of power systems,on the premise of satisfying various constraints including the action times limits of discrete control devices during the optimization time,thereby possess important theoretical value and broad application prospect.