Voltage Support Effectiveness Assessment and Differentiated Sizing of Static Var Generators in Weak Distribution Networks with Multiple Grid-Following Wind Farms

High penetration of grid-following (GFL) wind farms can aggravate voltage recovery problems in weak distribution networks. Although static var generators (SVGs) can provide rapid reactive-power support, their planning effectiveness varies significantly with installation location and network condition. This paper proposes a planning-level framework for evaluating voltage support effectiveness (VSE) and determining differentiated SVG capacities in weak distribution networks with multiple GFL wind farms. A physics-informed VSE index is constructed from AC voltage–reactive-power sensitivity together with upstream reference SCR, fault severity, and electrical distance factors. A VSE-based recovery time surrogate is then incorporated into a bi-objective SVG siting-and-sizing model that minimizes the investment cost and estimated maximum recovery time. The framework is evaluated on the IEEE 33-bus system over 270 grid strength and fault scenarios. Discrete enumeration and non-dominated solution screening yield 38 Pareto solutions. The selected differentiated configuration installs 49.9 Mvar, 31.8 Mvar, and 50.0 Mvar at buses 3, 10, and 33, respectively, achieving an aggregated VSE of 1.757, an estimated maximum recovery time of 1.092 s, and a total investment cost of RMB 2.554 million. Among the four representative schemes, this configuration is the only one that satisfies both the VSE and recovery time requirements. The results demonstrate the importance of accounting for location-dependent voltage support effectiveness in SVG planning.