Exact Computer Modeling of Photovoltaic Sources with Lambert-W Explicit Solvers for Real-Time Emulation and Controller Verification
Abdulaziz Almalaq1, Ambe Harrison2,*, Ibrahim Alsaleh1, Abdullah Alassaf1, Mashari Alangari1
1 Department of Electrical Engineering, University of Hail, Hail, 55211, Saudi Arabia
2 Department of Electrical and Electronics Engineering, College of Technology (COT), University of Buea, Buea, P.O. Box 63, Cameroon
* Corresponding Author: Ambe Harrison. Email: 
Computer Modeling in Engineering & Sciences https://doi.org/10.32604/cmes.2025.074815
Received 18 October 2025; Accepted 16 December 2025; Published online 04 January 2026
Abstract
We present a computer-modeling framework for photovoltaic (PV) source emulation that preserves the exact single-diode physics while enabling iteration-free, real-time evaluation. We derive two closed-form explicit solvers based on the Lambert W function: a voltage-driven V-Lambert solver for high-fidelity I–V computation and a resistance-driven R-Lambert solver designed for seamless integration in a closed-loop PV emulator. Unlike Taylor-linearized explicit models, our proposed formulation retains the exponential nonlinearity of the PV equations. It employs a numerically stable analytical evaluation that eliminates the need for lookup tables and root-finding, all while maintaining limited computational costs and a small memory footprint. The R-Lambert model is integrated into a buck-converter emulator equipped with a discrete PI regulator, which generates current references directly from sensed operating points, thus supporting hardware-constrained implementation. Comprehensive numerical experiments conducted on six commercial modules from various technologies (mono, poly, and multicrystalline) demonstrate significant accuracy improvements under the IEC EN 50530 near-MPP criterion: the V-Lambert solver reduces the ±10% Vmpp band error by up to 61 times compared to an explicit-model baseline. Dynamic simulations under varying irradiance, temperature, and load conditions achieve millisecond-scale settling with accurate trajectory tracking. Additionally, processor-in-the-loop experimental validation on an embedded microcontroller supports the simulation results. By unifying exact analytical modeling with embedded realization, this work advances computer modeling for PV emulation, MPPT benchmarking, and controller verification in integrated renewable energy systems.
Keywords
Photovoltaic emulators (PVE); explicit PV model (EPVM); IEC EN 50530; Lambert function; maximum power point (MPP); PVE integration; processor-in-the loop
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