[Paper Review] An Accurate Analytical Approach for the Parameterization of the Single Diode Model of Photovoltaic Cell

Muhammad Saqib Ali, Syed Muhammad Raza Kazmi|arXiv (Cornell University)|May 13, 2020

Photovoltaic System Optimization Techniques51 references4 citations

TL;DR

This paper proposes a novel analytical method to derive the fifth equation for parameterizing the single diode model of photovoltaic (PV) modules, using the maximum power point (MPP) condition on the P-I characteristic curve. By eliminating iterative or approximative techniques, the method achieves superior accuracy—demonstrated by the lowest RMSE of 3.68×10⁻³ A for PWP-201 and 7.97×10⁻⁴ A for RTC France—surpassing both single and double diode model approaches in simulating real I-V and P-V curves.

ABSTRACT

A single diode model with five parameters is the simplest and robust approach for modeling a photovoltaic (PV) module in a simulated environment. These parameters need to be accurately extracted from the specifications given in the datasheet of the PV module such that the simulation model should exhibit the same characteristics as the actual measurements. A definite set of five independent equations, that should represent the characteristics of the PV module as accurately as possible, is needed to solve for these five parameters. In literature, the first four equations are easily created from the key data points on the characteristic curve given in the datasheet of the PV module. The main challenge however is the formulation of the fifth equation. The approaches found in literature have inherent inaccuracies due to some approximations or iterative techniques leading to discrepancy in the simulated model. This paper presents a unique analytical approach for the formulation of the fifth equation which yields the most accurate single diode model. As evident from the results, the proposed method is superior to not just the single diode model approaches but also to the double diode ones in simulating the characteristics of the PV module with least error.

Motivation & Objective

• To address the long-standing challenge of accurately formulating the fifth independent equation required for single diode model parameterization.
• To eliminate inaccuracies from iterative or approximative methods used in prior literature for the fifth equation.
• To develop a robust, non-iterative analytical approach that ensures the simulated I-V and P-V curves closely match experimental measurements.
• To demonstrate that the proposed method outperforms not only single diode models but also advanced double diode models in accuracy.

Proposed method

• Derives the fifth equation using the maximum power point (MPP) condition on the power-current (P-I) characteristic curve, ensuring physical consistency.
• Uses the MPP voltage and current to form a precise analytical constraint that links the five unknown parameters: Iph, Is, n, Rs, and Rsh.
• Establishes a system of five independent, non-iterative equations from key datasheet data points and the MPP condition.
• Solves the system using MATLAB’s fsolve function, ensuring convergence to a unique, accurate parameter set.
• Validates the model by simulating I-V and P-V curves and comparing them with experimental data from PWP-201 and RTC France PV modules.
• Employs RMSE as the quantitative metric to benchmark performance against existing single and double diode model techniques.

Experimental results

Research questions

• RQ1 How can the fifth equation for single diode model parameterization be derived without relying on iterative or approximate methods?
• RQ2 Can an analytical formulation based on the MPP condition yield more accurate I-V and P-V curve simulations than existing meta-heuristic or approximative approaches?
• RQ3 Does the proposed method achieve better accuracy than both single diode and double diode model parameterization techniques?
• RQ4 What is the quantitative improvement in simulation accuracy, measured by RMSE, when using the proposed method compared to state-of-the-art alternatives?

Key findings

• The proposed method achieves an RMSE of 3.68×10⁻³ A for the PWP-201 PV module, the lowest among all compared techniques.
• For the RTC France module, the method achieves an RMSE of 7.97×10⁻⁴ A, significantly lower than the next best method (8.24×10⁻⁴ A).
• The absolute error of the proposed method remains consistently lower than all benchmarked approaches across all measurement points, as shown in Fig. 6 and Fig. 8.
• The method outperforms not only single diode models but also double diode models, including those using advanced optimization like chaotic whale optimization (CWO) and adaptive WDO.
• The analytical derivation using the MPP on the P-I curve eliminates the need for iterative algorithms, reducing computational complexity while improving accuracy.
• The results confirm that the proposed method provides the most accurate simulation of the actual I-V and P-V characteristics of PV modules.