Multi‐objective stochastic optimal power flow considering voltage stability and demand response with significant wind penetration

In this study, a multi‐objective stochastic optimal power flow (SOPF) problem with the presence of uncertain wind power generations is introduced. In particular, this study has two main contributions. First, it proposes a multi‐objective SOPF which consists of the operating cost, voltage stability and emission effects as the objective functions. The wind uncertainty is formulated as a scenario‐based technique. Demand response program is considered in this study, which is one of the most efficient control ways to reduce the risk of voltage instability after a contingency occurrence or a stressed loading condition. In addition, the proposed approach uses the technique of fuzzification to normalise all objective functions and to find the optimal solution. The second contribution proposes a line voltage stability index (LVSI). The proposed LVSI can detect precisely the voltage collapse in comparison with other LVSIs, especially after the occurrence of a given contingency due to the dynamic elements of the system. The proposed multi‐objective SOPF is also carried out with different existing LVSIs as the objective functions. These approaches are tested and validated by the modified WECC test system, the IEEE 39‐bus.