Solving reactive-power dispatch by a penalty function/linear programming method

Three criteria are used in this paper for the formulation of the nonlinear reactive-power dispatch problem: (1) the minimization of real-power transmission losses (RPL); (2) the feasibility enforcement of the system's violated constraints (FEC); and (3) the minimum deviation of node voltages from specified values (AVD). These problems are mathematically defined in terms of a full set of control variables: generation voltages, transformer turn ratios and switchable shunt susceptances. The solution to each of these reactive-power dispatch problems is obtained by solving a sequence of linear problems using a penalty function/linear programming (PF/LP) algorithm. Sensitivity matrices for both the inequality constraints on dependent variables and objective function coefficients are used to construct a mathematical model of the linear programming problems. Tests are conducted on the standard IEEE 30-bus power network and the Mexican 253-node longitudinal power system. Comparison is made to solutions obtained by a quadratic programming technique.