Estimation of Parameters of One-diode and Two-diode Photovoltaic Models: A Chaotic Gravitational Search Algorithm based Approach

ABSTRACT

Photovoltaic (PV) module is one of the major sources of clean energy to substantially reduce the global carbon footprint. Researchers are keen on developing an equivalent PV mathematical model to acquire insights regarding its monitoring and operations. This is a stimulating task as these modules are sensitive to operational conditions. In this work, a chaotic gravitational search algorithm (CGSA) based method is proposed for estimating the PV parameters of the one-diode and the two-diode PV models. The proposed method includes an update to confine the decision variables within the appropriate ranges. It is tested on the RTC France cell and the Photowatt-PWP-201 PV module. The suitability is highlighted considering the mean absolute error (MAE) and the root mean square error (RMSE) between the experimental and the estimated currents. For example, the errors are in the orders of ${10}^{-4}$ and ${10}^{-3}$ (one-diode model) and ${10}^{-5}$ and ${10}^{-4}$ (two-diode model), respectively, for the Photowatt-PWP-201 PV module. A comparative analysis of the proposed method with several popular algorithms (e.g. equilibrium optimizer (EO), whale optimization algorithm (WOA), Harris hawks optimization (HHO), variants of particle swarm optimization (PSO) etc.) is presented. Results and the comparative analysis confirm the effectiveness of the suggested approach.

KEYWORDS:

• One-diode model
• two-diode model
• chaotic gravitational search algorithm
• parameter estimation
• photovoltaic module

Nomenclature

Nomenclature	=	Parameters
$I_{\mathit{ph}}$	=	Photo generated current ($\mathit{A}$)
$I_o$	=	Reverse saturation current of $\mathit{D}$ ($\mathit{\mu A}$)
$I_{\mathit{o}1}$	=	Reverse saturation current of $D_1$ ($\mathit{\mu A}$)
$I_{\mathit{o}2}$	=	Reverse saturation current of $D_2$ ($\mathit{\mu A}$)
$V_{\mathit{oc}}$	=	PV open circuit voltage ($\mathit{V}$)
$I_{\mathit{sc}}$	=	PV short circuit current ($\mathit{A}$)
$V_L$	=	PV output voltage ($\mathit{V}$)
$I_L$	=	PV output current ($\mathit{A}$)
$V_m$	=	PV maximum voltage ($\mathit{V}$)
$I_m$	=	PV maximum current ($\mathit{A}$)
$P_m$	=	PV maximum power ($\mathit{W}$)
$R_s$	=	Series resistance ($\mathrm{\Omega }$)
$R_{\mathit{sh}}$	=	Shunt resistance ($\mathrm{\Omega }$)
$I_{\mathit{sh}}$	=	Current through $R_{\mathit{sh}}$ ($\mathit{A}$)
$I_d$	=	Diode $\mathit{D}$ current ($\mathit{A}$)
$I_{\mathit{d}1}$	=	Diode $D_1$ current ($\mathit{A}$)
$I_{\mathit{d}2}$	=	Diode $D_2$ current ($\mathit{A}$)
$\mathit{\eta }$	=	Ideality factor of diode $\mathit{D}$
${\eta }_1$	=	Ideality factor of diode $D_1$
${\eta }_2$	=	Ideality factor of diode $D_2$
$\mathit{k}$	=	Boltzmann’s constant ($\mathit{J}/K^{-1}$)
$V_t$	=	Thermal voltage ($\mathit{mV}$)
$\mathit{G}$	=	Irradiance ($\mathit{W}/m^2$)
$N_s$	=	Number of cells in series
$T_{\mathit{cell}}$	=	PV cell temperature ($\mathit{K}$)
$\mathit{q}$	=	Charge of an electron ($\mathit{C}$)

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Notes on contributors

Omkar Singh

Omkar Singh is a Ph.D. scholar at the Department of Electrical and Electronics Engineering, National Institute of Technology Sikkim (NIT Sikkim), India. His areas of interest include renewable energy systems and cyber-physical systems.

Arabinda Ghosh

Arabinda Ghosh received his Ph.D. degree in Electrical and Electronics Engineering from National Institute of Technology Sikkim (NIT Sikkim), India in 2022. He is currently a postdoctoral researcher at the Max Planck Institute for Software Systems, Kaiserslautern, Germany. His areas of interest include intelligent control, optimization, and cyber-physical systems.

Anjan Kumar Ray

Anjan Kumar Ray is an Associate Professor in the Department of Electrical and Electronics Engineering, National Institute of Technology Sikkim (NIT Sikkim), India. He received his PhD degree from Indian Institute of Technology Kanpur (IIT Kanpur), India. He was a research associate at Ulster University, UK and was associated with the EU FP7 project RUBICON.