Fractional-Order Control for Islanded Inverters: Accurate Modeling and Improved Stability Through Modified SBL Fitting

The modeling and control of grid-connected or islanded inverters often rely on conventional proportional–integral (PI) controllers, whose fixed values of proportional (<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$K_{p}$</tex-math></inline-formula>) and integral gains (<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$K_{i}$</tex-math></inline-formula>) limit their transient response performance. This article addresses these limitations by implementing fractional-order PI controllers, enhanced through the modified-stability boundary locus technique, which approximates fractional terms as integer-order equivalents for greater control precision. A generalized model of the inverter is developed with optimized fractional orders determined using particle swarm optimization, achieving 76.45% reduction in controller error compared to conventional PI controllers within 20 iterations. A small-signal model further improves simulation speed by nearly six times over the nonlinear model. Stability is analyzed through the eigenvalue method and the Lyapunov direct method. Such analysis confirms asymptotic stability and provides insights into system damping and dynamics. Experimental validation via a real-time simulator (OPAL-RT) under dynamic conditions demonstrates the robustness and practical applicability of the proposed model, with better transient response and error minimization.