Multi-Objective-Optimization-Based Optimal Sizing of Grid-Following SVG for Enhancing Transient Voltage Stability of Wind Farms Connected to Weak Grids

When large-scale wind power bases are connected to weak grids, post-fault transient voltage recovery becomes a critical constraint on stable system operation. This paper proposes a multiobjective sizing framework for a grid-following static var generator (SVG) in which a reduced-order RK4 transient model is embedded directly in the capacity decision. The three measurement objectives are post-fault voltage recovery time, SVG investment cost, and system active-power loss, subject to minimum-voltage, recovery-time, and stability constraints. The baseline Pareto set is obtained with NSGA-II, while optimizer dependence is examined against NSGA-III and SMS-EMOA under a common evaluation budget. The grid-strength study is extended to SCR = 1.5–10.0, and the optimization scenarios retain fault-voltage levels of 0.70–0.80 p.u. A separate low-voltage-ride-through (LVRT)-aware wind-turbine model is used to evaluate active-power curtailment, reactive-current priority, and coordinated SVG-wind-turbine support. Under SCR = 2.5 and a retained fault-voltage level of 0.70 p.u., the refined capacity scan shows that enabling wind-turbine reactive support reduces the SVG capacity required to meet the same 0.019 s recovery-time target from 39 to 13 Mvar in the adopted control setting. A 10-state PMSG full-converter average-value model predicts recovery time within 1–2 ms of the reduced model for SCR = 1.5–10.0, although the reduced model overestimates post-fault voltage overshoot in very weak grids. Sequence-domain studies further quantify the additional negative-sequence, DC-link, and rotor-speed stress caused by unbalanced faults. The framework is therefore intended as a planning-stage screening tool rather than a substitute for switching-level electromagnetic-transient verification.