Probabilistic and deterministic analysis of single diode model of a solar cell: a case study

Abstract

Abstract The paper presents a probabilistic and deterministic analysis for parameterization of solar cells to study the electrical behavior based on single diode model. Estimation of electrical parameters is important in design, control, and delivery of solar power through a solar cell. Due to non-linearity and non-convexity of the parameterization problem, the single objective function is transformed into set of sub-problems through Pascoletti–Serafini Scalarization using ε -constraint method. Thus, each sub-problem is minimized to obtain a unique set of points on Pareto front. The results are compared with multi-variable Newton Raphson (NR), Particle Swarm Optimization (PSO), and Black Widow Optimization (BWO) based on convergence accuracy, precision and ability to trace non-convex region. Solarex MSX83 (36 cells) is considered as the test case for the validation of deterministic optimization models under Standard test Conditions (STCs). Electrical characteristics are plotted under STC (1000 W/m2, 1.5 A.M. spectrum, 25 °C) which shows fair agreement with the actual experimental curves present in the datasheet. The results obtained from the proposed bi-objective minimization algorithm shows a better convergence response with an additional benefit of tracing the convexity of the problem. Moreover, the proposed technique also ensures a good fit as suggested by the statistical means. Finally, a probabilistic model is proposed for single diode model of a solar cell in the presence of parametric uncertainty. Random samples of uncertain electrical parameters are obtained using Latin hypercube and Monte Carlo sampling methods to estimate the probability of the output response. It can be concluded that the objective function shows a bi-modal distribution under parametric variations which may arise due to measurement error, shading losses, surface defects, and manufacturing issues.