Original Article

Modeling the electrical mismatch caused by potential-induced degradation in crystalline silicon photovoltaic modules and strings

Department of Electrical and Photonics Engineering, Technical University of Denmark, Frederiksborgvej 399, 4000 Roskilde, Denmark

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Received: 16 September 2025
Accepted: 8 December 2025
Published online: 26 January 2026

Abstract

Potential-induced degradation (PID) can not only reduce the output power of a solar cell but also create additional power losses due to non-uniform degradation within a module, string or array, leading to mismatch in the electrical performance of the solar cells in the system. This work models the impact of PID-polarization (increases surface recombination velocity in a solar cell) and PID-shunting (increases recombination in depletion region and shunts the p-n junction of a solar cell) on the current-voltage (I-V) characteristics of a 22 × 8 photovoltaic array and estimates the array level power mismatch losses (the difference between array level power loss and the average power loss of the modules in the array). Each solar cell in the array is represented by a two-diode equivalent circuit model, and PID is introduced in a solar cell by degrading the model parameters including the light generated photocurrent, dark saturation currents, shunt resistance and ideality factor. The module level model is validated with modules that are PID degraded in the laboratory and is used as baseline for creating the array level model: the root-mean square error between simulated and measured I-V curves are within 0.2 A. To generate realistic PID affected I-V characteristics curves, the degradation in solar cells is applied non-uniformly within a module, string and array. For a PV array affected by PID-polarization and PID-shunting, the mismatch losses can increase up to 0.72% and 2.35% which is in addition to the power losses of ∼5.25% and ∼10% caused by PID itself, respectively. The annual energy losses are estimated by increasing the severity of PID in the arrays during a one-year-simulation and it resulted in 4.84% and 10% less in the annual energy production of the arrays, respectively.