Sensitivity Analysis of a Photovoltaic Cell with a Single-Diode Model at Maximum Power Point: A Derivative-Based Approach

The necessity of sensitivity analysis has rapidly increased for systems with unknown or uncertain mathematical relationships between inputs and outputs. In this regard, the single-diode model (SDM) of a photovoltaic (PV) cell can be considered an uncertain, complex, nonlinear system with a non-convex relationship between its output power and five unknown electrical parameters as inputs. In this paper, a rigorous mathematical analysis is applied to determine both the local and global sensitivities of the PV cell’s output power with respect to the five input electrical parameters at the maximum power point (MPP). The local and global sensitivity analyses are obtained through partial derivatives of the PV power with respect to all five inputs. For the global analysis, all electrical parameters are normalized between ۰ and ۱ within their feasible ranges of variation. Then, the complex partial derivative functions with normalized variables are approximated using multivariable quadratic functions via the least-squares optimization method. Finally, five separate quintuple integrals of the approximated squared partial derivative functions are numerically calculated in the unit hypercube H^۵. Precise quantitative values are reported for both local and global analyses at the MPP. It is verified that the diode ideality factor and the parallel resistance have the highest and lowest impact on SDM performance, respectively.

کلیدواژه ها:

Single-diode model ، Sensitivity analysis ، Global and local ، Numerical analysis ، Model based analysis