Admittance‑Based Two‑Stage Optimisation of GFM‑STATCOM Parameters for Transient Voltage Support in DFIG Wind Farms

When the point of common coupling voltage of a DFIG wind farm dips due to a grid fault, conventional grid‐forming STATCOMs (GFM‑STATCOMs) typically concentrate reactive power support during the fault‑on interval, while recovery‑stage overvoltage and oscillations are often insufficiently addressed. This paper proposes a two‑stage coordinated tuning method for GFM‑STATCOMs. First, an admittance‑based aggregated model of the DFIG–STATCOM–transformer–grid system is derived, yielding closed‑form expressions for the GFM‑STATCOM q‑axis reactive‑current channel and analytical sensitivities with respect to the virtual impedance and the Q–V droop coefficient, while explicitly accounting for crowbar engagement and transformer magnetising. Second, a smooth nonlinear programming formulation is constructed over two fixed time windows, where hard limits and soft‑threshold penalties jointly shape peak values and area‑based indices. Finally, PSCAD and hardware‐in‐loop simulations under multiple short‑circuit ratios validate the method: the tuned GFM‑STATCOM improves fault‑time voltage support and significantly suppresses recovery‑stage overvoltage and oscillations.