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

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.</jats:p

Probabilistic screening and behavior of solar cells under Gaussian parametric uncertainty using polynomial chaos representation model

AbstractThe paper presents a hierarchical polynomial chaos expansion-based probabilistic approach to analyze the single diode solar cell model under Gaussian parametric uncertainty. It is important to analyze single diode solar cell model response under random events or factors due to uncertainty propagation. The optimal values of five electrical parameters associated with the single diode model are estimated using six deterministic optimization techniques through the root-mean-square minimization approach. Values corresponding to the best objective function response are further utilized to describe the probabilistic design space of each random electrical parameter under uncertainty. Adequate samples of each parameter corresponding Gaussian uncertain distribution are generated using Latin hypercube sampling. Furthermore, a multistage probabilistic approach is adopted to evaluate the model response using low-cost polynomial chaos series expansion and perform global sensitivity analysis under specified Gaussian distribution. Coefficients of polynomial basis functions are calculated using least square and least angle regression techniques. Unlike the highly non-linear and complex single diode representation of solar cells, the polynomial chaos expansion model provides a low computational burden and reduced complexity. To ensure reproducibility, probabilistic output response computed using proposed polynomial chaos expansion model is compared with the true model response. Finally, a multidimensional sensitivity analysis is performed through Sobol decomposition of polynomial chaos series representation to quantify the contribution of each parameter to the variance of the probabilistic response. The validation and assessment result shows that the output probabilistic response of the solar cell under Gaussian parametric uncertainty correlates to a Rayleigh probability distribution function. Output response is characterized by a mean value of 0.0060 and 0.0760 for RTC France and Solarex MSX83 solar cells, respectively. The standard deviation of $$\pm$$ ± 0.0034 and $$\pm$$ ± 0.0052 was observed in the probabilistic response for RTC France and Solarex MSX83 solar cells, respectively.</jats:p

A techno-economic analysis of the roof top off-grid solar PV system for Jamshedpur, Jharkhand, India

Abstract As the exhaust rate of the conventional sources has geared up already, this is compelling the power industries to install the power plants based on the non-conventional sources so that future demand of the energy supply can be fulfilled. Among the various sources of renewable energy like wind, hydro, tidal etc., solar energy is the most easily accessible and available renewable energy source. Ensuring the feasibility of any energy source not only technical but also the economical perspective is the most important criteria. This paper has incorporated both the perspective and has done the techno-economic analysis to determine the optimum combination of the PV array size and battery size to minimize the overall electricity generation per unit. In this paper, a standalone solar PV system has been analyzed for the location of Jamshedpur, where an effort has been done to choose the optimum combination of the solar array and battery size within the desired range of LLP so that the electricity generation cost per unit can be minimized. The overall duration of the analysis has been done for a year and the outcome of the research has been verified with the help of MATLAB software.</jats:p