Research On An Accurate Algorithm For Transforming Mixed Integer Reactive-power Optimization Into Continuous One In Power Systems

From mathematical point of view, reactive-power optimization problem is a complicated nonlinear mixed integer programming problem with discrete and continuous variables on object function and constraints. It is difficult for traditional mathematical programming to solve this problem.This paper takes primal-dual interior-point method as basic algorithm and makes a deep research on the nonlinear mixed-integer programming model of reactive-power optimization problem. An expanded interior-point algorithm is presented, which can successfully realize discretization of discrete variables in optimization process by constructing a penalty function for them and incorporating it into the nonlinear primal-dual interior-point algorithm directly. Then presents a new algorithm for solving mixed integer reactive-power optimization problem. By means of binary encoding technology, all discrete variables are converted into linear combination of several 0-1 variables. The constraints of binary variables are converted into equivalent complementarity constraints, and these complementarity constraints can be changed into equivalent non-smooth equations further by using nonlinear complementarity function. Thus the original problem can be transformed into a differentiable nonlinear programming problem through smoothing processing, which can be solved using nonlinear primal-dual interior-point algorithm. By selecting the timing of introducing the binary encoding technology, the discretization of discrete variables can harmony coordination with the nonlinear interior-point method.Results on Ward & Hale 6, IEEE 14,30,118-bus systems demonstrate that the proposed method can handle discrete variables effectively and has good convergence. After comparison with the traditional primal-dual interior-point method and the expanded interior-point algorithm by incorporating a penalty function, it showed that the proposed method has certain advantage when discrete variables have more taps.