Multi-objective optimal reactive power dispatch considering uncertainties in the wind integrated power systems

Abstract

One of the most principle optimization problems which gained the attention of power system operators around the world is optimal power flow (OPF). The OPF basically performs an intelligent power flow and optimizes the system operation condition by optimally determination of control variables. It also considers a specific set of operational constraints and technical limits for this aim, which guaranties both feasibility and optimality of the scheduled operation condition. Generally, this problem can be categorized into two main sub-problems, i.e. optimal reactive power dispatch (ORPD) and optimal real power dispatch, which are differ in their aims and control variables. This chapter deals with the first one, ORPD, which has significant impact on power system security. ORPD is modeled as an optimization problem with nonlinear functions and mixed continuous/discrete variables. Thus, it is a complicated optimization problem. The multi-objective ORPD (MO-ORPD) problem is studied, taking into account different operational constraints such as bus voltage limits, power flow limits of branches, limits of generators voltages, transformers tap ratios and the amount of available reactive power compensation at the weak buses. Three different objective functions are considered in the proposed MO-ORPD framework, which are minimizing total active power losses, minimizing voltage variations and minimizing voltage stability index (L-index). These conflicting objectives are optimized via e-constraint method. In order to model the stochastic behavior of demand and wind power generation, it is necessary to modify the MO-ORPD problem, and develop a probabilistic approach to handle the uncertainties in MO-ORPD problem. Hence, a two-stage stochastic MO-ORPD (SMO-ORPD) is suggested to handle the load and wind power uncertainties in the MO-ORPD problem. In the proposed two-stage stochastic optimization model, the decision variables are classified into two categories, namely, “here and now” and “wait and see” variables. The optimal values of “here and now” variables should be known before realization of scenarios, and therefore, their values are the same for all scenarios while the optimal values of “wait and see” variables are based on the realized scenario, and hence their values are scenario dependent. Moreover, in order to examine performance of the proposed SMO-ORPD and the impact of wind power generation on the results of SMO-ORPD, deterministic ORPD (DMO-ORPD) has also been solved in two modes: DMO-ORPD without wind farms (WFs) and any uncertainty, for the sake of comparison with the available methods in recent literature, and DMO-ORPD with WFs. In this chapter the reactive power compensation devices are modeled as discrete/continuous control variables. DMO-ORPD and SMO-ORPD are formulated as mixed integer non-linear program (MINLP) problems, and solved by General Algebraic Modeling System (GAMS). Also, the IEEE 30-bus standard system is utilized for evaluation of the proposed MO-ORPD models.