A Novel Red-Billed Blue Magpie Optimizer Tuned Adaptive Fractional-Order for Hybrid PV-TEG Systems Green Energy Harvesting-Based MPPT Algorithms

Hybrid PV-TEG systems can harvest both solar electrical and thermoelectric power, but their operating point drifts with irradiance, temperature gradients, partial shading, and load changes—often yielding multi-peak P-V characteristics. Conventional MPPT (e.g., P&O) and fixed-structure integer-order PID struggle to remain fast, stable, and globally optimal in these conditions. To address fast, robust tracking in these conditions, we propose an adaptive fractional-order PID (FOPID) MPPT whose parameters (Kp, Ki, Kd, λ, μ) are auto-tuned by the red-billed blue magpie optimizer (RBBMO). RBBMO is used offline to set the controller’s search ranges and weighting; the adaptive law then refines the gains online from the measured ΔV, ΔI slope error to maximize the hybrid PV-TEG output. The method is validated in MATLAB R2024b/Simulink 2024b, on a boost-converter–interfaced PV-TEG using five testbeds: (i) start-up/search, (ii) stepwise irradiance, (iii) partial shading with multiple local peaks, (iv) load steps, and (v) field-measured irradiance/temperature from Shanxi Province for spring/summer/autumn/winter. Compared with AOS, PSO, MFO, SSA, GHO, RSA, AOA, and P&O, the proposed tracker is consistently the fastest and most energy-efficient: 0.06 s to reach 95% MPP and 0.12 s settling at start-up with 1950 W·s harvested (vs. 1910 W·s AOS, 1880 W·s PSO, 200 W·s P&O). Under stepwise irradiance, it delivers 0.95–0.98 kJ at t = 1 s and under partial shading, 1.95–2.00 kJ, both with ±1% steady ripple. Daily field energies reach 0.88 × 10−3, 2.95 × 10−3, 2.90 × 10−3, 1.55 × 10−3 kWh in spring–winter, outperforming the best baselines by 3–10% and P&O by 20–30%. Robustness tests show only 2.74% power derating across 0–40 °C and low variability (Δvmax typically ≤ 1–1.5%), confirming rapid, low-ripple tracking with superior energy yield. Finally, the RBBMO-tuned adaptive FOPID offers a superior efficiency–stability trade-off and robust GMPP tracking across all five cases, with modest computational overhead.