Lyapunov-certified state-feedback virtual power compensation for transient stability of current-saturated grid-forming converters

Hard current limiting constrains fault ride-through by grid-forming (GFM) converters in low-inertia grids. Under severe voltage sags the current limit forces an abrupt transition from voltage-source to current-source operation, and existing virtual-power-compensation (VPC) schemes (fixed, ramped, or deficit-based) do not provide a formal Lyapunov decay guarantee on the quadratic swing-equation energy. Exact feedback linearisation of the saturated swing equation yields a closed-form state-feedback schedule z x ∗ ( δ , ω ) that enforces V ̇ = − ( D + k d ) ω 2 on the quadratic candidate; a companion result shows that no velocity-free schedule achieves a prescribed quadratic decay rate under the same candidate. An input-to-state-stability certificate bounds the residual under grid-parameter estimation error. An angle–velocity additive decomposition (Motion-Decoupled-Basis) separates the law into a 64-entry look-up table and a single-multiply damping accelerator, with ζ = 0.80 (nominal VSM: 0.11). The implementation executes in 11 cycles on a TMS320F28379D DSP. An eighth-order averaged model (LC filter, SVM overmodulation, anti-windup) gives pk | ω | = 3.34 rad/s under a V g = 0.4 pu symmetric sag and pk | ω | = 2.21 rad/s under a composite phase jump; among the compared schemes, only the proposed law retains synchronism in both. With reactive priority, the symmetric-sag peak falls to 0.60 rad/s; all 63 second-order estimation-error cases remain synchronised. Controller-hardware-in-the-loop tests on an EGBox FPGA real-time simulator assess the response against IEEE Std 2800-2022 and ENTSO-E fault-ride-through windows, extended to a deep V g = 0.2 pu sag.