Fuzzy-adaptive MPPT and Kalman-filter SOC estimation for Lyapunov-stable predictive energy management in solar-integrated EV charging stations

This research develops a coordinated control, estimation, and dispatch framework for a solar-photovoltaic-integrated electric-vehicle charging station (EVCS) with battery storage and grid backup, and reports four contributions. First, a fuzzy-adaptive-step perturb-and-observe (P&O) maximum-power-point-tracking (MPPT) algorithm varies its perturbation step with the local power–voltage sensitivity and reaches 98.1% ± 0.1% tracking efficiency over 15 randomised irradiance scenarios with a single fixed parameter set, compared with 95.0% ± 0.6% for fixed-step P&O and 97.8% ± 0.2% for a linear-adaptive law re-tuned for each scenario (Welch’s t-test, t = 5.2, p < 0.0001, fuzzy-adaptive vs. re-tuned). Second, an extended Kalman filter (EKF) fuses Coulomb counting with a second-order Thevenin battery model to estimate state of charge (SOC), the pair is shown observable by a Popov–Belevitch–Hautus (PBH) test and, across 20 Monte Carlo trials, reduces mean SOC estimation RMSE from 2.45% to 0.118%. Third, a model-predictive-control (MPC) energy-management system (EMS) replaces static rule-based dispatch with receding-horizon optimisation, lowering operating cost by 6.8% under a perfect-forecast assumption while revealing an explicit trade-off against grid independence. Fourth, a switched-system stability analysis constructs mode-dependent Lyapunov functions and derives an average-dwell-time bound (τ_a* = 2.31 ms) that certifies exponential stability of the linearised converter dynamics for any mode-switching sequence respecting this bound. The complete simulation delivers 93.6% system efficiency, DC-bus regulation within ± 5%, and grid dependency of 14.2%. Of the four contributions, only the fuzzy-adaptive MPPT and EKF-SOC layers were implemented on an ESP8266 hardware prototype, on that subset, hardware-measured system efficiency (91.2%) agrees with simulation (93.6%) to within 2.4 percentage points. The MPC-EMS dispatch result and the Lyapunov stability proof remain simulation-level findings, and hardware validation of both is set out as a priority for future work.