MODELING THE PROCESS OF CLEANING A PHOTOVOLTAIC MODULE FROM SNOW COVER USING THE REVERSE CURRENT HEATING METHOD

Abstract

Abstract. Introduction. A mathematical model for removing snow from a silicon photovoltaic module by applying a reverse current, which switches the cells into a heating mode, is presented. The model combines the equations of the transient thermal balance of composite layers with the mechanical conditions governing the sliding of the snow layer. For the first time, the linear temperature dependence of silicon resistance and a stepwise function describing the variation in the friction coefficient (a decrease from 0.6 to 0.005 upon the formation of a meltwater film) are considered simultaneously. Based on the Biot criterion (Bi ≈ 0.052), the module is demonstrated to be isothermal through its thickness. The numerical solution of the system of transient differential equations was implemented using the Runge – Kutta - Fehlberg (RKF45) method with automatic selection of the integration step and spline approximation of nonlinear parameters. Numerical simulations determined the effectiveness limits of the method within the temperature range from −5 to −25 °C at a power of 600 W for snow layers with thicknesses of 2, 5, and 10 cm. It was established that neglecting the temperature coefficient of silicon resistance underestimates the calculated cleaning time by 1.5–2.5% due to a 2–3% reduction in heating power. The specific energy consumption of the process was determined to range from 0.020 to 0.231 kWh/m², and a critical operating condition was identified at −25 °C for a 10 cm snow layer (ts = 50.9 min, E_total = 0.463 kWh), requiring forced boosting of the power supply output.

Materials and Methods. The object of the study is an industrial silicon photovoltaic module (PV module) with an area of A, installed at an angle Q relative to the Earth's surface. A uniform layer of dry snow with a thickness of hs and an initial density of ρ₀ is present on the front surface of the module. An external direct-current power supply is connected to the module. The Joule heating power P(T) is considered as a function of the thermal state of the semiconductor structures of the PV module, determined by the temperature dependence of their internal electrical resistance.

Results. Figures 1 and 2 present the results of a numerical study of the dynamics of snow removal from a photovoltaic module (PV module) at a fixed nominal Joule heating power of P₀=600 W and varying outdoor air temperatures Ts from -5 °C to -25 °C for three characteristic snow-layer thicknesses, hs =2, 5, and 10 cm.

Conclusion. In this study, an improved mathematical model of the transient thermal balance and mechanical conditions for the initiation of snow-layer detachment from the surface of a photovoltaic module using the reverse current heating method was developed and verified. Unlike existing static approaches, the model rigorously accounts, for the first time, for the temperature dependence of the heat generation power P(T), caused by the negative temperature coefficient of resistance (TCR) of silicon semiconductor structures when powered by a direct-current source.