Voltage stability constrained multi-objective optimal reactive power dispatch under load and wind power uncertainties: A stochastic approach

Optimal reactive power dispatch (ORPD) problem is an important problem in the operation of power systems. It is a nonlinear and mixed integer programming problem, which determines optimal values for control parameters of reactive power producers to optimize specific objective functions while satisfying several technical constraints. In this paper, stochastic multi-objective ORPD (SMO-ORPD) problem is studied in a wind integrated power system considering the loads and wind power generation uncertainties. The proposed multi objective optimization problem is solved using ε-constraint method, and fuzzy satisfying approach is employed to select the best compromise solution. Two different objective functions are considered as follow: 1) minimization of the active power losses and 2) minimization of the voltage stability index (named L-index). In this paper VAR compensation devices are modeled as discrete variables. Moreover, to evaluate the performance of the proposed method for solution of multi-objective problem, the obtained results for deterministic case (DMO-ORPD), are compared with the available methods in literature. The proposed method is examined on the IEEE-57 bus system. The proposed models are implemented in GAMS environment. The numerical results substantiate the capability of the proposed SMO-ORPD problem to deal with uncertainties and to determine the best settings of control variables.