Piecewise Normalized Normal Constraint Method Applied to Minimization of Voltage Deviation and Active Power Loss in an AC–DC Hybrid Power System

In this paper, we establish a mathematical model of the multi-objective reactive power optimization (MORPO) problem in an ac-dc hybrid power system. To get an evenly distributed set of Pareto solutions of this MORPO problem throughout a whole day, we propose a piecewise normalized normal constraint (PNNC) method. Based on this method, the Pareto frontier is divided into four arcs so that the fluctuation of angle between the tangent line at each Pareto point and its sub-Utopia line is reduced. By doing so, the original MORPO problem is transformed into four sets of single objective optimization problems, which can be solved efficiently by a nonlinear primal-dual interior-point method. Performance of the PNNC method is tested on a real ac-dc interconnection system. The results demonstrate that it has the capability to generate a more evenly distributed set of Pareto solutions when compared with the normalized normal constraint (NNC) and weighted sum (WS) methods. In addition, a fuzzy-based membership value assignment method is employed to derive 96 optimal compromise solutions corresponding to 96 time periods in a whole day; the numerical outcomes show that a saving in active power loss and an improvement in the voltage profile can be gained simultaneously.