Mathematical Analysis of Solar Photovoltaic Array Configurations with Partial Shaded Modules

V BALARAJU, Ch. Chengaiah


Solar-based photovoltaic (SPV) cells produce power from sunlight through the photovoltaic effect. The yield voltage of a single PV cell is small, so the voltage is extended by interfacing PV cells in series arrangement known as PV module or panel. Solar PV array comprises of series and parallel connections of modules in the grid structure with a few columns and rows. The various kinds of SPV array configurations or topologies are shaped by changing the number of electrical connections between module to module in an array. This paper presents the mathematical examination of 6×6 size regular SPV array configurations, including Total-Cross-Tied, Parallel, Honey-Comb, Series-Parallel, Series, Bridge-Linked types beneath un-shading case, and different proposed shading cases (primarily short narrow, short wide, long narrow, and long wide shadings). The electrical proportionate circuit of the SPV array setups was analyzed by Kirchhoff’s laws at distinctive nodes and loops in a sun powered PV array. The location of global maximum power point (GMPP) was determined hypothetically and distinguished in Matlab/simulation software at various shading conditions.

Citation: Raju, V.B., and Chengaiah, C. (2020). Mathematical Analysis of Solar Photovoltaic Array Configurations with Partial Shaded Modules. Trends in Renewable Energy, 6, 121-143. DOI: 10.17737/tre.2020.6.2.00115


Photovoltaic cell; Module; Array; Configurations; Shaded modules; Row currents; PV array power

Full Text:



Fahrenbruch, A., and Bube, R. (2012). Fundamentals of solar cells: photovoltaic solar energy conversion, Elsevier

Dirk, A., Assmann, D., Laumanns, U., and Uh, D. (2006). Renewable energy: a global review of technologies, policies and markets, Routledge

Kumar, A., Pachauri, R. K., and Chauhan, Y. K. Experimental analysis of SP/TCT PV array configurations under partial shading conditions. In: Proc., 2016 IEEE 1st International Conference on Power Electronics, Intelligent Control and Energy Systems (ICPEICES), pp: 1-6. DOI: 10.1109/icpeices.2016.7853403

Bingöl, O., and Özkaya, B. (2018). Analysis and comparison of different PV array configurations under partial shading conditions. Solar Energy, 160, 336-343. DOI: 10.1016/j.solener.2017.12.004

Pendem, S. R., and Mikkili, S. (2018). Modelling and performance assessment of PV array topologies under partial shading conditions to mitigate the mismatching power losses. Solar Energy, 160, 303-321. DOI: 10.1016/j.solener.2017.12.010

Nguyen, D., and Lehman, B. A reconfigurable solar photovoltaic array under shadow conditions. In: Proc., 2008 Twenty-Third Annual IEEE Applied Power Electronics Conference and Exposition, IEEE, pp: 980-986

Parlak, K. Åž. (2014). PV array reconfiguration method under partial shading conditions. International Journal of Electrical Power & Energy Systems, 63, 713-721. DOI: 10.1016/j.ijepes.2014.06.042

Rani, B. I., Ilango, G. S., and Nagamani, C. (2013). Enhanced power generation from PV array under partial shading conditions by shade dispersion using Su Do Ku configuration. IEEE Transactions on sustainable energy, 4(3), 594-601

Wang, Y.-J., and Hsu, P.-C. (2011). An investigation on partial shading of PV modules with different connection configurations of PV cells. Energy, 36(5), 3069-3078. DOI: 10.1016/

Tatabhatla, V. M. R., Agarwal, A., and Kanumuri, T. (2019). Improved power generation by dispersing the uniform and non-uniform partial shades in solar photovoltaic array. Energy Conversion and Management, 197, 111825. DOI: 10.1016/j.enconman.2019.111825

Krishna, G. S., and Moger, T. (2019). Enhancement of maximum power output through reconfiguration techniques under non-uniform irradiance conditions. Energy, 187, 115917. DOI: 10.1016/

Raju, V.B., and Chengaiah, Ch. (2019). Performance Analysis of Conventional, Hybrid and Optimal PV Array Configurations of Partially Shaded Modules. International Journal of Engineering and Advanced Technology, 9(1), 3061-3073. DOI: 10.35940/ijeat.A1661.109119

Chao, K.-H., Lai, P.-L., and Liao, B.-J. (2015). The optimal configuration of photovoltaic module arrays based on adaptive switching controls. Energy Conversion and Management, 100, 157-167. DOI: 10.1016/j.enconman.2015.04.080

Zhu, L., Li, Q., Chen, M., Cao, K., and Sun, Y. (2019). A simplified mathematical model for power output predicting of Building Integrated Photovoltaic under partial shading conditions. Energy Conversion and Management, 180, 831-843. DOI:

Belhachat, F., and Larbes, C. (2015). Modeling, analysis and comparison of solar photovoltaic array configurations under partial shading conditions. Solar Energy, 120, 399-418. DOI:



  • There are currently no refbacks.

Copyright (c) 2020 V. Bala Raju, Dr. Ch. Chengaiah

Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.

Creative Commons License This work is licensed under a Creative Commons Attribution 4.0 License.
Copyright @2014-2024 Trends in Renewable Energy (ISSN: 2376-2136, online ISSN: 2376-2144)