Overcoming PLL Delay Constraints in Virtual Inertia Control: A Smith Predictor Approach

ABSTRACT

Virtual inertia (VI) effectiveness in low‐inertia microgrids is constrained by measurement delays introduced by phase‐locked loop (PLL) synchronization. This paper investigates the delay–inertia relationship in a 37‐MVA islanded microgrid and extracts an empirical, case‐specific Hopf‐boundary regression model, ( in seconds, over 19 boundary points). A Smith predictor‐based delay compensation strategy with scheduled lead augmentation is proposed; it extends the absolute critical delay from approximately 60 ms (conventional VI) to beyond 295 ms and lifts the practical ceiling from 3 to 6 s at  ms. In a head‐to‐head comparison against optimally detuned stable conventional VI, lead‐lag‐only compensation, and regression‐based adaptive inertia at  ms, the proposed method achieves comparable frequency nadir while reducing peak ESS power by 47%–54%; this peak‐power dominance is the principal practical benefit. Under high delay–inertia combinations where conventional VI is in saturated limit‐cycle operation, peak‐power reduction reaches up to 72% as a separate bifurcation‐avoidance benefit. Nonlinear analysis shows that conventional VI undergoes a supercritical Hopf bifurcation; the proposed compensation eliminates this bifurcation throughout the tested envelope and raises the stable‐cell count of a sweep from 32% to 100%. Controller hardware‐in‐the‐loop validation on a Xilinx PYNQ‐Z2 reproduces the MATLAB Smith‐predictor frequency nadir within 0.1% across four delay points and confirms sensor‐noise and inertia‐mismatch robustness on real hardware. Power‐HIL with a real inverter, full quantitative benchmarking against MPC and , and a techno‐economic study are identified as essential future work.