Simple, fast and accurate two-diode model for photovoltaic modules Kashif Ishaque n , Zainal Salam, Hamed Taheri Faculty of Electrical Engineering, Universiti Teknologi Malaysia, UTM 81310, Skudai, Johor Bahru, Malaysia article info Article history: Received 9 April 2010 Received in revised form 23 July 2010 Accepted 20 September 2010 Available online 20 October 2010 Keywords: PV module Multi-crystalline Mono-crystalline Thin-film STC abstract This paper proposes an improved modeling approach for the two-diode model of photovoltaic (PV) module. The main contribution of this work is the simplification of the current equation, in which only four parameters are required, compared to six or more in the previously developed two-diode models. Furthermore the values of the series and parallel resistances are computed using a simple and fast iterative method. To validate the accuracy of the proposed model, six PV modules of different types (multi-crystalline, mono-crystalline and thin-film) from various manufacturers are tested. The performance of the model is evaluated against the popular single diode models. It is found that the proposed model is superior when subjected to irradiance and temperature variations. In particular the model matches very accurately for all important points of the I–V curves, i.e. the peak power, short-circuit current and open circuit voltage. The modeling method is useful for PV power converter designers and circuit simulator developers who require simple, fast yet accurate model for the PV module. & 2010 Elsevier B.V. All rights reserved. 1. Introduction Photovoltaic (PV) power system is a popular renewable energy source due to the absence of moving parts and therefore almost maintenance free. The main component of the system, i.e. the PV module utilizes standard semiconductor processes that can be fabricated with relatively minimum facilities [1]. Furthermore, the power converters (DC–DC converter and/or inverter) that interface the modules with the grid or batteries are well established technologies. However, in a PV power generation, due to the high cost of the modules, optimal use of the available solar energy has to be ensured. This necessitates an accurate simulation model of the PV system, especially the modules. PV module modeling primarily involves the estimation of the non-linear I–V curves. Previous researchers have utilized circuit topologies to model the characteristics of the module when subjected to environmental variations such as changed in irradiance and temperature. By far, the simplest approach is the single diode model i.e. a current source in parallel to a diode [2,3]. An improved version is the inclusion of one series resistance to the circuit, R s [4–8]. Although the model is still relatively simple, it exhibits serious deficiencies when subjected to high temperature variations because it does not account for the open circuit voltage coefficient, K V [5]. An extension of the single diode model which includes an additional shunt resistance, R p is suggested by numerous authors [9–12]. Including R p , the number of parameters is increased to five. Using this model, the accuracy is improved. The single diode models were based on the assumption that the recombination loss in the depletion region is absent. In a real solar cell, the recombination represents a substantial loss, which cannot be adequately modeled using a single diode. Consideration of this loss leads to a more precise model known as the two-diode model [13]. However, the inclusion of the additional diode increases the parameters to seven (new parameters: I o2 , a 2 ). The main challenge now is to estimate the values of all the model parameters while maintaining a reasonable computational effort. To determine the parameters for the above-mentioned topologies, various computational methods are proposed. The single diode with R s -model only requires four parameters, namely short-circuit current (I sc ), saturation current (I o ), diode ideality factor (a) and the series resistance, R s . In [4,7] an iterative programming method is introduced to estimate the values of R s and a. These values are further refined by interpolation technique [6]. Several numerical algorithms to model the I–V curves using single diode with R p and R s are proposed; these include resistive- companion method [9], non-linear least square optimization [10] and other iterative solutions described in [11,12]. Although significant improvement over the single diode with R s -model is obtained, this approach demands more computing effort. Recently, several authors [14–20] use artificial intelligence (AI) such as fuzzy logic [14] and artificial neural network (ANN) [15–20] to model the I–V curves. This is a logical approach if one Contents lists available at ScienceDirect journal homepage: www.elsevier.com/locate/solmat Solar Energy Materials & Solar Cells 0927-0248/$ - see front matter & 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.solmat.2010.09.023 n Corresponding author. Tel.: + 607 5536187; fax: + 607 5566272. E-mail addresses: kashif@fkegraduate.utm.my (K. Ishaque), zainals@fke.utm.my (Z. Salam). Solar Energy Materials & Solar Cells 95 (2011) 586–594