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An Approach to Mathematically Model a Photovoltaic Cell - Using the Maxwell Boltzmann Statistics

B. F. Akpiri, G. Odo


In this work, an approach to the mathematical modeling and simulation of a photovoltaic cell is presented. Previous work on the Shockley diode equation uses the Fermi – Dirac statistics. In this report, we will use the classical Maxwell Boltzmann statistics. For simplicity, the model considered is the single diode, photovoltaic cell model. The Shockley diode equation is first formulated using Maxwell Boltzmann (MB) statistics. A single diode model equation is then derived and simulated. Matlab was used to perform the simulations using the looping iterative method. Results that were obtained were identical with the typical single diode photovoltaic cell model current - voltage and power – voltage plots.

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Vivek, S. C & Sawle, Y. (2015). Single diode PV cell modeling and study of characteristics of a single and two diode equivalent circuit. Electrical and Electronics Engineering: An International Journal (ELELIJ), 4 (3), 13-24, Available at:

Jenny Nelson (2003). The Physics of Solar Cells. Imperial College Press, Imperial College, UK, ISBN-1-86094-340-384, Available at:

Yetayew, T. & Jyothsna, T.R. (2013). Improved single-diode modeling approach for photovoltaic modules using data sheet, Annual IEEE India Conference (INDICON), (pp.1-6), Mumbai, India, Available at:

Gow, J.A. & Manning, C.D. (1999). Development of a photovoltaic array model for use in power-electronics simulation studies. IEEE Proceedings- Electric Power Applications, 146 (2), 193-200, Available at:

Eduardo Lorenzo (1994). Solar Electricity: Engineering of Photovoltaic Systems. Progensa, Spain, ISBN-84-86505-55-0, Available at:

Andreea, S., Valentin, M. & Marius, P. (2017). Parameters Extraction for the One-Diode Model of a Solar Cell. American Institute of Physics Conference Proceedings, (pp.1-5), Available at:

Aurel, G., Lica, S., Bularka, S., Roland, S. & Dan, Lascu (2018). A Novel High Accuracy PV Cell Model Including Self Heating and Parameter Variation. Energies, 11 (36), 1-21, Available at: 10.3390/en11010036.

Ukoima, K. N. & Ekwe, O. A. (2019). Three diode model and simulation of photovoltaic (PV) cells. Umudike Journal of Engineering and Technology (UJET), 5 (1), 108-116, Available at:

Ekwe, O, A. & Ukoima, K. N. (2019). Resistance, temperature and irradiance parameter analysis of a single diode photovoltaic (PV) cell model. Umudike Journal of Engineering and Technology (UJET), 5 (1), 97-107, Available at:

Sambit, S. (2018). How do we get a Shockley diode equation? What is the proof for it? Quora, Available at:


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