Fractional-order PI control with Modified Stability Locus for grid connected inverters: Stability enhancement and real-time validation

Conventional proportional–integral (PI) controllers are widely used in grid-connected and islanded inverters, but their fixed gains often yield limited transient response. Fractional-order PI (FOPI) controllers offer improvements by incorporating fractional terms, yet approximating these with first-order ODEs poses challenges, as traditional methods either inflate the system order or compromise accuracy. To overcome these limitations, this paper employs the Modified Stability Boundary Locus (M-SBL) technique, converting fractional expressions into integer-order equivalents while preserving both system order and precision. A generalized inverter model is developed, and fractional orders are optimized using a genetic algorithm, achieving a 25.36% reduction in controller error within 50 iterations. Furthermore, converting the first-order ODE model into a linearized small-signal version reduces computational complexity and accelerates simulations by five times compared to nonlinear methods. Stability is confirmed through eigenvalue analysis and the Lyapunov direct method. Real-time experiments on an OPAL-RT validate the model under dynamic load changes, low voltage ride through (LVRT), voltage sag, and parameter uncertainty conditions. • Developed M-SBL approximated fractional order controller for grid tied inverter. • Developed model preserves system order while enhancing overall system stability. • GA-optimized fractional controllers ensure matched linear and nonlinear responses. • Eigenvalue, Lyapunov theory, modal analyses confirm improved damping and stability. • OPAL-RT tests confirm resilience to load shifts, LVRT events, and uncertainties.