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Electrical and thermal analyses of solar PV module by considering realistic working conditions

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Abstract

Photovoltaic (PV) cells are used as clean energy technologies for generating electricity from solar irradiance. In designing and modeling of PV-based energy systems, it is crucial to consider their efficiency and the factors influencing it. Among the effective factors on the cell efficiency, temperature is very crucial. Ambient temperature, speed of wind and solar irradiance are among the most significant parameters which influence the cell temperature and its electrical output. In this regard, computation fluid dynamics is employed in the current study for determining cell temperature under different operating conditions. In order to achieve more realistic and accurate solution, the cell efficiency in the model is considered as a temperature-dependent variable. On the basis of determined temperatures by the model at high wind speed, ambient temperature impact on the cell performance becomes more remarkable. Finally, the outputs of numerical simulation are applied in an artificial neural network (GMDH type) to propose a predictive and simple-to-use model. The proposed model has reliable performance, and its maximum relative deviation does not exceed 0.04%. Employing the proposed model instead of computational fluid dynamic for predicting the PV performance will result in saving time. Moreover, using the ANN-based model is more cost-effective compared with experimental evaluation of PV efficiency.

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Acknowledgements

This work was supported by National Natural Science Foundation of China “study on water vapor transport and convergence mechanism of continuous rainstorm in western southern Xinjiang” 41965002.

Author information

Authors and Affiliations

  1. Urumqi Meteorological Satellite Earth Station, Ürümqi, 830002, Xinjiang, China

    Yong Wang

  2. Department of Renewable Energies, Faculty of New Sciences and Technologies, University of Tehran, Tehran, Iran

    Mojtaba Lak Kamari & S. Haghighat

  3. Institute of Research and Development, Duy Tan University, Da Nang, 550000, Viet Nam

    Phuong Thao Thi Ngo

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  1. Yong Wang
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  2. Mojtaba Lak Kamari
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  3. S. Haghighat
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  4. Phuong Thao Thi Ngo
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Correspondence to Phuong Thao Thi Ngo.

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Appendix

Appendix

$$\begin{aligned} {\text{PV}}\;{\text{temperature}} & = 0.0231958 - \text{``}x2,cubert \text{''} *0.0316685 \\ & \quad + \text{``}x2,cubert\text{''}^{2} *0.0106318 + N2*1.00001 \\ \end{aligned}$$

Cubert refers to cube root of the variable. The coefficients of the above relationships are determined as follows:

$$\begin{aligned} N2 & = 0.00647592 + N7*0.999046 - N7 \\ & \quad *N3*0.092254 + N3^{2} *0.0922887 \\ N3 & = 0.00261091 + N211*N4*0.000824379 \\ & \quad - N211^{2} *0.000810837 + N4*0.999622 \\ \end{aligned}$$
$$\begin{aligned} N4 & = 0.00317369 - N175*N5*0.00173443 \\ & \quad + N5*0.999537 + N5^{2} *0.00175109 \\ N5 & = -\,0.00107796 - N132*0.908563 - N132*N6 \\ & \quad *0.0658552 + N132^{2} *0.0658494 + N6*1.90872 \\ N6 & = 1.2314e - 05 - N18*0.379204 + N7*1.3792 \\ \end{aligned}$$
$$\begin{aligned} N18 & = 0.152712 - \text{``}x2, cubert\text{''} *0.209675 \\ & \quad + \text{``}x2, cubert\text{''}^{2} *0.0712132 + N33*0.999968 \\ N33 & = 0.00936582 + N135*2.49913 - N135*N50 \\ & \quad *0.206423 - N50*1.50049 + N50^{2} *0.206473 \\ N50 & = -\, 3.71406e - 05 + N72 \\ & \quad *0.420583 + N80*0.579419 \\ \end{aligned}$$
$$\begin{aligned} N72 & = - 0.00220666 + N86 \\ & \quad *0.91771 + N223*0.0824507 \\ N86 & = -\, 0.240458 + N288*0.140302 + N288 \\ & \quad *N183*0.0850968 - N288^{2} *0.0497795 \\ & \quad + N183*0.902546 - N183^{2} *0.0371009 \\ N135 & = 0.00384783 + N144*0.999371 + N144 \\ & \quad *N178*0.0147639 - N144^{2} *0.0147388 \\ \end{aligned}$$
$$\begin{aligned} N178 & = -\, 0.341559 + N222*1.05714 \\ & \quad + N222*N272*0.756685 - N222^{2} \\ & \quad *0.381096 - N272^{2} *0.377694 \\ \end{aligned}$$
$$\begin{aligned} N272 & = 1.39321 + N283*0.73278 \\ & \quad - N283*N288*0.200142 + N283^{2} \\ & \quad *0.0936019 + N288^{2} *0.118237 \\ \end{aligned}$$
$$\begin{aligned} N132 & = 0.0107129 - N279*N144*0.0889394 \\ & \quad + N279^{2} *0.0440109 + N144 \\ & \quad *0.998501 + N144^{2} *0.0449539 \\ \end{aligned}$$
$$\begin{aligned} N211 & = -\, 2.43905 + N234*N274*1.10337 \\ & \quad - N234^{2} *0.514654 + N274 \\ & \quad *1.37029 - N274^{2} *0.602303 \\ \end{aligned}$$
$$\begin{aligned} N274 & = -\, 0.743314 + N285*1.04661 \\ & \quad - N285*N288*0.196438 + N285^{2} \\ & \quad *0.08035 + N288^{2} *0.116391 \\ \end{aligned}$$
$$\begin{aligned} N234 & = 0.478429 + N247*1.65665 - N247 \\ & \quad *N270*0.806042 + N247^{2} *0.377994 \\ & \quad - N270*0.731898 + N270^{2} *0.430775 \\ \end{aligned}$$
$$\begin{aligned} N7 & = -\, 0.00446863 + N263*N8 \\ & \quad *0.0433208 - N263^{2} *0.0216105 \\ & \quad + N8*1.00096 - N8^{2} *0.0217491 \\ \end{aligned}$$
$$\begin{aligned} N8 & = 0.00172127 + N70*N10*0.0228501 \\ & \quad - N70^{2} *0.022841 + N10.999748 \\ \end{aligned}$$
$$\begin{aligned} N10 & \quad = -\, 9.03766e - 06 + N11 \\ & \quad *0.554263 + N13*0.445738 \\ \end{aligned}$$
$$\begin{aligned} N13 & = 8.91061e - 05 - N103 \\ & \quad *0.180372 + N19*1.18037 \\ \end{aligned}$$
$$\begin{aligned} N19 & = 0.152712 - \text{``}x2, cubert\text{''} *0.209675 \\ & \quad + \text{``}x2, cubert\text{''}^{2} *0.0712132 + N31*0.999968 \\ \end{aligned}$$
$$\begin{aligned} N31 & = 0.00936581 + N136*2.49912 \\ & \quad - N136*N49*0.206423 - N49 \\ & \quad *1.50049 + N49^{2} *0.206472 \\ \end{aligned}$$
$$\begin{aligned} N49 & = -\, 3.71406e - 05 + N71 \\ & \quad *0.420583 + N80*0.579419 \\ \end{aligned}$$
$$\begin{aligned} N80 & = 4.97292 - \text{``}x1, cubert\text{''} *1.02295 \\ & \quad + \text{``}x1, cubert\text{''} *N151*0.00280606 \\ & \quad + \text{``}x1, cubert\text{''}^{2} *0.0528973 + N151 \\ & \quad *0.967288 + N151^{2} *0.000218337 \\ \end{aligned}$$
$$\begin{aligned} N151 & = -\, 0.0949699 + N194*0.918072 \\ & \quad + N194*N287*0.112501 \\ & \quad - N194^{2} *0.0514051 + N287 \\ & \quad *0.103919 - N287^{2} *0.0621251 \\ \end{aligned}$$
$$\begin{aligned} N287 & = -\, 1.53933e - 11 + N289 \\ & \quad *0.505814 + N288*0.494186 \\ \end{aligned}$$
$$\begin{aligned} N223 & = 0.880811 + N239*1.97695 - N239 \\ & \quad *N268*1.0462 + N239^{2} *0.487292 \\ & \quad - N268*1.11051 + N268^{2} *0.56367 \\ \end{aligned}$$
$$\begin{aligned} N268 & = -\, 7.25972 + N285*0.951151 \\ & \quad + N290*0.576199 \\ \end{aligned}$$
$$\begin{aligned} N103 & = -\, 0.0515652 + N141*1.00751 \\ & \quad + N141*N175*0.025256 \\ & \quad - N141^{2} *0.0255262 \\ \end{aligned}$$
$$\begin{aligned} N175 & = 0.00596692 + N207*0.995909 \\ & \quad - N207*N279*0.390179 + N207^{2} \\ & \quad *0.195468 + N279^{2} *0.194852 \\ \end{aligned}$$
$$\begin{aligned} N279 & = -\, 57.7188 + N291*7.96579 - N291^{2} \\ & \quad *0.270193 + N288*0.954365 \\ \end{aligned}$$
$$\begin{aligned} N207 & = -\, 110.262 + \text{``}x3, cubert\text{''} *39.5695 \\ & \quad - \text{``}x3, cubert\text{''} *N235*1.28097 \\ & \quad - \text{``}x3, cubert\text{''}^{2} *3.57949 + N235 \\ & \quad *8.2203 - N235^{2} *0.119627 \\ \end{aligned}$$
$$\begin{aligned} N141 & = -\, 0.0954672 + N194*1.16815 - N194 \\ & \quad *N260*0.000722723 - N260*0.151148 \\ \end{aligned}$$
$$\begin{aligned} N260 & = -\, 2.20828 + N273*N280*0.68587 \\ & \quad - N273^{2} *0.323532 + N280*1.31479 \\ & \quad - N280^{2} *0.373014 \\ \end{aligned}$$
$$\begin{aligned} N280 & = -\, 57.7188 + N289*0.954365 \\ & \quad + N291*7.96579 - N291^{2} *0.270193 \\ \end{aligned}$$
$$\begin{aligned} N11 & = 0.0189442 - N261*N22*0.0317829 \\ & \quad + N261^{2} *0.0159293 + N22 \\ & \quad *0.996999 + N22^{2} *0.0159654 \\ \end{aligned}$$
$$\begin{aligned} N22 & = 0.0228881 + N235*0.0873567 - N235 \\ & \quad *N32*0.464764 + N235^{2} *0.229053 \\ & \quad + N32*0.909114 + N32^{2} *0.235838 \\ \end{aligned}$$
$$\begin{aligned} N32 & = 0.00936581 + N136*2.49912 \\ & \quad - N136*N43*0.206423 - N43 \\ & \quad *1.50049 + N43^{2} *0.206472 \\ \end{aligned}$$
$$\begin{aligned} N43 & = -\, 3.71406e - 05 + N73*0.420583 \\ & \quad + N81*0.579419 \\ \end{aligned}$$
$$\begin{aligned} N81 & = 4.97292 - \text{``}x1, cubert\text{''} *1.02295 \\ & \quad + \text{``}x1, cubert\text{''} *N152*0.00280606 \\ & \quad + \text{``}x1, cubert\text{''}^{2} *0.0528973 + N152 \\ & \quad *0.967288 + N152^{2} *0.000218337 \\ \end{aligned}$$
$$\begin{aligned} N152 & = -\, 0.0949699 + N288*0.103919 \\ & \quad + N288*N194*0.112501 - N288^{2} \\ & *0.0621251 + N194*0.918072 \\ & \quad - N194^{2} *0.0514051 \\ \end{aligned}$$
$$\begin{aligned} N194 & = -\, 0.0828595 + N214*1.00463 \\ & \quad - N214*N285*0.073721 + N214^{2} \\ & \quad *0.0346316 + N285^{2} *0.0391432 \\ \end{aligned}$$
$$N285 = 4.00183e - 12 + N286*1$$
$$N288 = -\, 1.90377e - 11 + N289*1$$
$$\begin{aligned} N136 & = 0.00384783 + N144*0.999371 + N144 \\ & \quad *N177*0.0147639 - N144^{2} *0.0147388 \\ \end{aligned}$$
$$\begin{aligned} N177 & = -\, 0.341559 + N222*1.05714 \\ & \quad + N222*N271*0.756685 - N222^{2} \\ & \quad *0.381096 - N271^{2} *0.377694 \\ \end{aligned}$$
$$\begin{aligned} N271 & = 1.39321 - N289*N283*0.200142 \\ & \quad + N289^{2} *0.118237 + N283 \\ & \quad *0.73278 + N283^{2} *0.0936019 \\ \end{aligned}$$
$$\begin{aligned} N222 & = 0.805898 + N235*2.0658 - N235 \\ & \quad *N270*0.952221 + N235^{2} *0.436849 \\ & \quad - N270*1.18723 + N270^{2} *0.519673 \\ \end{aligned}$$
$$\begin{aligned} N144 & = -\, 0.052361 - N286*N186*0.14162 \\ & \quad + N286^{2} *0.072843 + N186 \\ & \quad *0.99962 + N186^{2} *0.0689882 \\ \end{aligned}$$
$$\begin{aligned} N186 & = -\, 0.84518 + \text{``}x2, cubert\text{''} *1.06288 \\ & \quad - \text{``}x2, cubert\text{''}^{2} *0.297821 + N214*0.994919 \\ \end{aligned}$$
$$\begin{aligned} N235 & = -\, 8.3909 + \text{``}x2, cubert\text{''} *7.65986 \\ & \quad - \text{``}x2, cubert\text{''} *N289*0.041149 \\ & \quad - \text{``}x2, cubert\text{''}^{2} *1.43983 + N289*1.07564 \\ \end{aligned}$$
$$\begin{aligned} N261 & = 0.634361 - \text{``}x1, cubert\text{''}^{2} *0.0202351 \\ & \quad + N270*1.19384 - N270^{2} *0.00794511 \\ \end{aligned}$$
$$\begin{aligned} N270 & = -\, 7.25972 + N286*0.951151 \\ & \quad + N291*0.576199 \\ \end{aligned}$$
$$\begin{aligned} N70 & = 0.0002238 - N158*0.20047 \\ & \quad + N73*1.20045 \\ \end{aligned}$$
$$\begin{aligned} N73 & = -\, 0.00220666 + N85*0.91771 \\ & \quad + N224*0.0824507 \\ \end{aligned}$$
$$\begin{aligned} N224 & = 0.880811 + N239*1.97695 \\ & \quad - N239*N269*1.0462 \\ & \quad + N239^{2} *0.487292 - N269 \\ & \quad *1.11051 + N269^{2} *0.56367 \\ \end{aligned}$$
$$\begin{aligned} N269 & = -\, 7.25972 + N286*0.951151 \\ & \quad + N290*0.576199 \\ \end{aligned}$$
$$N290 = 5.1583e - 11 + N291*1$$
$$\begin{aligned} N239 & \quad = -\, 2.85763 + \text{``}x2, cubert\text{''} *3.89983 \\ & \quad - \text{``}x2, cubert\text{''}^{2} *1.31306 \\ & \quad + N247*0.999956 \\ \end{aligned}$$
$$\begin{aligned} N247 & = 3.22139 + \text{``}x1, cubert\text{''} *N286*0.0229248 \\ & \quad - \text{``}x1, cubert\text{''}^{2} *0.0639829 + N286*1.13969 \\ & \quad - N286^{2} *0.0129041 \\ \end{aligned}$$
$$\begin{aligned} N85 & = -\, 0.240458 + N289*0.140302 \\ & \quad + N289*N183*0.0850968 - N289^{2} \\ & \quad *0.0497795 + N183*0.902546 \\ & \quad - N183^{2} *0.0371009 \\ \end{aligned}$$
$$\begin{aligned} N183 & \quad = 5.94237 - \text{``}x1, cubert\text{''} *1.35722 \\ & \quad + \text{``}x1, cubert\text{''}^{2} *0.0759933 \\ & \quad + N214*1.00592 \\ \end{aligned}$$
$$\begin{aligned} N158 & = 0.354255 - N283*N196*0.146762 \\ & \quad + N283^{2} *0.0755541 + N196 \\ & \quad *0.938916 + N196^{2} *0.0736527 \\ \end{aligned}$$
$$\begin{aligned} N196 & \quad = -\, 0.338869 - N289^{2} \\ & \quad *0.0022405 + N214*1.0558 \\ \end{aligned}$$
$$\begin{aligned} N214 & = -\, 38.9389 + \text{``}x3, cubert\text{''} *5.99525 \\ & \quad - \text{``}x3, cubert\text{''} *N291*0.0790012 \\ & \quad - \text{``}x3, cubert\text{''}^{2} *1.60002 + N291 \\ & \quad *6.39682 - N291^{2} *0.185338 \\ \end{aligned}$$
$$\begin{aligned} N291 & = 14.2519 - \text{``}x1, cubert\text{''}^{2} \\ & \quad *0.0478873 + \text{``}x2, cubert\text{''} *2.4899 \\ \end{aligned}$$
$$\begin{aligned} N283 & = 2.18225 + \text{``}x3, cubert\text{''} *N286 \\ & \quad *0.101307 - \text{``}x3, cubert\text{''}^{2} \\ & \quad *0.227686 + N286*0.69054 \\ \end{aligned}$$
$$\begin{aligned} N263 & = 0.262529 + \text{``}x2, cubert\text{''} *N273 \\ & \quad *0.0965029 + N273*0.836305 \\ \end{aligned}$$
$$\begin{aligned} N273 & = -\, 0.743314 + N286*1.04661 \\ & \quad - N286*N289*0.196438 + N286^{2} \\ & \quad *0.08035 + N289^{2} *0.116391 \\ \end{aligned}$$
$$\begin{aligned} N289 & = 19.2327 - \text{``}x1, cubert\text{''}^{2} \\ & \quad *0.0466787 + \text{``}x3, cubert\text{''} *4.04301 \\ & \quad - \text{``}x3, cubert\text{''}^{2} *1.44745 \\ \end{aligned}$$
$$\begin{aligned} N286 & = 17.175 + \text{``}x2, cubert\text{''} *2.81578 \\ & \quad - \text{``}x3, cubert\text{''}^{2} *0.800226 \\ \end{aligned}$$

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Wang, Y., Kamari, M.L., Haghighat, S. et al. Electrical and thermal analyses of solar PV module by considering realistic working conditions. J Therm Anal Calorim 144, 1925–1934 (2021). https://doi.org/10.1007/s10973-020-09752-2

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  • DOI: https://doi.org/10.1007/s10973-020-09752-2

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