Mathematical modeling of solar farm performance degradation in a dynamic environment for condition-based maintenance

Abstract

This paper aims to address the challenge of modeling and optimizing condition-based maintenance policies for a degraded solar farm in varying environmental conditions. Dust accumulation and temperature increases are the two main causes of performance reduction and energy loss in the system. In this research, dust accumulation is modeled by the non-homogeneous compound Poisson process, and three different mathematical models for the efficiency reduction of photovoltaic panels due to dust accumulation are considered. The effects of wind and rain, taken as covariates, on dust accumulation and temperature are investigated by stochastic process modeling. The covariate process is considered a time-homogeneous Markov chain with finite state space. The PV surface temperature is modeled by a non-homogeneous Markov chain with finite state space and transition matrices under covariate states. Different PV panels exhibit varied degradation rates, influenced by their position and tilt angle to sunlight. In the framework of the system, we derive multiple maintenance policies aimed at achieving the minimum cost criterion. The expected long-term average maintenance costs under different covariate conditions and maintenance policies are evaluated through simulation experiments to compare the effectiveness of each policy.