A mixed-integer programming approach for the linearized reactive power and voltage control-comparison with gradient projection approach

A mixed-integer programming approach is presented for the optimal control of reactive power in a power system, in comparison to the gradient projection approach. Although the problem is originally a nonlinear optimization problem, it can be formulated as a mixed-integer linear programming (MILP) problem without deterioration of solution accuracy to a certain extent. In order to obtain the linearized version of the problem, a new Jacobian matrix decomposition method is adopted in a unified approach of real and reactive power mismatch. The MILP code is developed by the branch and bound process search for the optimal solution. The variables for modeling transformer tap positions are handled as discrete integer ones, and other variables continuous ones. Numerical data resulting from a case study using a modified IEEE 30 bus system with contingency (line outages) show that the MILP can produce more reductions of magnitude in the operating cost, compared to the results obtained from the gradient projection programming approach based on the scheme of rounding intelligently and of weighting factor for fast convergence. The convergence characteristics of the results obtained from two optimization methods in searching for the optimal solution are also presented and discussed