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Impact of government policies on photovoltaic supply chain considering quality in the power distribution system: a case study

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Abstract

Nowadays, due to the lack of energy and the harmful effects of fossil fuels on the environment, many countries seek to use renewable sources such as solar energy, a clean and free energy source. Direct conversion of solar energy into electricity is the reason for using solar cells. This paper proposes a three-echelon photovoltaic supply chain with two suppliers (domestic and foreign), two power plants (big and small), and a power distribution system with government intervention. We consider three approaches, including (1) the decentralized model, (2) the centralized model, and (3) the government’s role in the photovoltaic supply chain. In the first model, the power distribution system is a leader, and other members are followers. In the second model, we explore the whole supply chain as a centralized model, and in the third model, the government has the leading role, and the rest of the members follow. Indeed, in the last model, the role of the government as a supporter that gives subsidies and tax exemptions to keep members in a competitive market is investigated, and the decision variables of the government (tariffs) are obtained. Finally, based on real example from the power industry of Iran, sensitivity analysis and managerial insights are proposed.

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Notes

  1. http://irist.iust.ac.ir/index.php?slc_lang=en

  2. http://ie.iust.ac.ir/index.php?sid=61&slc_lang=en

  3. http://fn.iust.ac.ir/index.php?slc_lang=en&sid=94

  4. http://www.satba.gov.ir/en/home

  5. http://www.sabainfo.ir/en/home

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Authors and Affiliations

  1. School of Industrial Engineering, Iran University of Science and Technology, Tehran, Iran

    Sahar Matinfard, Saeed Yaghoubi & Maedeh Kharaji Manouchehrabadi

Authors
  1. Sahar Matinfard
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  2. Saeed Yaghoubi
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  3. Maedeh Kharaji Manouchehrabadi
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Contributions

Sahar Matinfard: software, validation, investigation, formal analysis, resources, data curation, writing — original draft preparation, writing — reviewing and editing, conceptualization, methodology, and visualization.

Saeed Yaghoubi: conceptualization, methodology, formal analysis, writing — reviewing and editing, visualization, supervision, and project administration.

Maedeh Kharaji Manouchehrabadi: software, writing — original draft preparation, data curation, methodology, formal analysis, writing — reviewing and editing.

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Correspondence to Saeed Yaghoubi.

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The authors declare no competing interests.

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Responsible Editor: Philippe Garrigues

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Appendices

Appendix 1. Model 3.1

The amount of decentralized (Stackelberg leader–follower game) decision variables is shown in this part:

$${x}_{d}^{*}=\frac{\begin{array}{c}({c}^{2}{c}_{d}\alpha {\left(-1+{\beta }_{1}\right)}^{2}+8b{c}_{\xi }\left({c}_{d}\left(-1+{\beta }_{1}\right)\left(-1+\alpha {\beta }_{1}+{\beta }_{2}-\alpha {\beta }_{2}\right)-{c}_{f}{\beta }_{1}\left(\alpha {\beta }_{1}+{\beta }_{2}-\alpha {\beta }_{2}\right)\right)\gamma \\ +{b}^{2}{c}_{\xi }{w}^{4}{\left({c}_{d}\left(-1+{\beta }_{1}\right)\left(-1+\alpha {\beta }_{1}+{\beta }_{2}-\alpha {\beta }_{2}\right)-{c}_{f}{\beta }_{1}\left(\alpha {\beta }_{1}+{\beta }_{2}-\alpha {\beta }_{2}\right)\right)}^{2}{\gamma }^{2})+({t}_{z}-w)\\ (-1+2{\beta }_{1})({-c}^{2}{c}_{d}{c}_{f}{k}^{2}(-1+\gamma )(4{c}_{d}{c}_{f}{k}^{2}+b{w}^{2}({c}_{d}\left(-1+\alpha \right)\left(-1+{\beta }_{1}\right)\left(-1+{\beta }_{2}\right)+{c}_{f}{\beta }_{1}\\ \left(\alpha {\beta }_{1}+{\beta }_{2}-\alpha {\beta }_{2}\right))\gamma )+b{c}_{\xi }\gamma (4{c}_{f}{c}_{d}{k}^{2}+b{w}^{2}({-c}_{d}\left(-1+{\beta }_{1}\right)\left(-1+\alpha {\beta }_{1}+{\beta }_{2}-\alpha {\beta }_{2}\right)+\\ {{c}_{f}{\beta }_{1}(\alpha {\beta }_{1}+{\beta }_{2}-\alpha {\beta }_{2}))\gamma )}^{2})))\end{array}}{\begin{array}{c}((4{c}_{d}{c}_{f}{k}^{2}-b{c}_{d}{w}^{2}\left(-1+{\beta }_{1}\right)\left(-1+\alpha \left({\beta }_{1}-{\beta }_{2}\right)+{\beta }_{2}\right)\gamma +b{c}_{f}{w}^{2}{\beta }_{1}\left(\alpha \left({\beta }_{1}-{\beta }_{2}\right){\beta }_{2}\right)\gamma )\\ (b{c}_{\xi }\gamma (4{c}_{d}{c}_{f}{k}^{2}+b{w}^{2}{\left({-c}_{d}\left(-1+{\beta }_{1}\right)\left(-1+\alpha {\beta }_{1}+{\beta }_{2}-\alpha {\beta }_{2}\right)+{c}_{f}{\beta }_{1}\left(\alpha {\beta }_{1}+{\beta }_{2}-\alpha {\beta }_{2}\right)\right)\gamma )}^{2}\\ -{c}^{2}{c}_{d}{c}_{f}{k}^{2}(-1+\gamma )(4{c}_{d}{c}_{f}{k}^{2}+b{w}^{2}({-c}_{d}\left(-1+{\beta }_{1}\right)\left(-2+\alpha +\alpha {\beta }_{1}+2{\beta }_{2}-2\alpha {\beta }_{2}\right)+\\ 2{c}_{f}{\beta }_{1}\left(\alpha {\beta }_{1}+{\beta }_{2}-\alpha {\beta }_{2}\right))\gamma ))))\end{array}}$$
(28)
$${x}_{f}^{*}=\frac{\begin{array}{c}-((b{c}_{d}w\left(-1+\alpha \left({\beta }_{1}-{\beta }_{2}\right)+{\beta }_{2}\right)\gamma (ak({c}_{d }^{2}{c}_{f}{k}^{2}\left(16{c}_{f}{{c}_{\xi }k}^{2}+{c}^{2}{w}^{2}\alpha {\left(-1+{\beta }_{1}\right)}^{2}\right)-{c}_{d}{c}_{f}{k}^{2}{w}^{2}({c}^{2}{c}_{d}\alpha {\left(-1+{\beta }_{1}\right)}^{2}+8b{c}_{\xi }({c}_{d}(-1+{\beta }_{1})\\ \left(-1+\alpha {\beta }_{1}+{\beta }_{2}-\alpha {\beta }_{2}\right)-{c}_{f}{\beta }_{1}(\alpha {\beta }_{1}+{\beta }_{2}-\alpha {\beta }_{2})))\gamma +{b}^{2}{c}_{\xi }{w}^{4}{\left({c}_{d}\left(-1+{\beta }_{1}\right)\left(-1+\alpha {\beta }_{1}+{\beta }_{2}-\alpha {\beta }_{2}\right)-{c}_{f}{\beta }_{1}\left(\alpha {\beta }_{1}+{\beta }_{2}-\alpha {\beta }_{2}\right)\right)}^{2}{\gamma }^{2})+\\ ({t}_{z}-w)\left(-1+2{\beta }_{1}\right)({-c}^{2}{c}_{d}{c}_{f}{k}^{2}\left(-1+\gamma \right)\left(4{c}_{d}{c}_{f}{k}^{2}+b{w}^{2}\left({c}_{d}\left(-1+\alpha \right)\left(-1+{\beta }_{1}\right)\left(-1+{\beta }_{2}\right){+c}_{f}{\beta }_{1}\left(\alpha {\beta }_{1}+{\beta }_{2}-\alpha {\beta }_{2}\right)\right)\gamma \right)+\\ b{c}_{\xi }\gamma (4{c}_{f}{c}_{d}{k}^{2}+b{w}^{2}({-c}_{d}\left(-1+{\beta }_{1}\right)\left(-1+\alpha {\beta }_{1}+{\beta }_{2}-\alpha {\beta }_{2}\right)+{{c}_{f}{\beta }_{1}(\alpha {\beta }_{1}+{\beta }_{2}-\alpha {\beta }_{2}))\gamma )}^{2})))\end{array}}{\begin{array}{c}((4{c}_{d}{c}_{f}{k}^{2}-b{c}_{d}{w}^{2}\left(-1+{\beta }_{1}\right)\left(-1+\alpha \left({\beta }_{1}-{\beta }_{2}\right)+{\beta }_{2}\right)\gamma +b{c}_{f}{w}^{2}{\beta }_{1}\left(\alpha \left({\beta }_{1}-{\beta }_{2}\right){\beta }_{2}\right)\gamma )\\ (b{c}_{\xi }\gamma (4{c}_{d}{c}_{f}{k}^{2}+b{w}^{2}{\left({-c}_{d}\left(-1+{\beta }_{1}\right)\left(-1+\alpha {\beta }_{1}+{\beta }_{2}-\alpha {\beta }_{2}\right)+{c}_{f}{\beta }_{1}\left(\alpha {\beta }_{1}+{\beta }_{2}-\alpha {\beta }_{2}\right)\right)\gamma )}^{2}-{c}^{2}{c}_{d}{c}_{f}{k}^{2}(-1+\gamma )\\ (4{c}_{d}{c}_{f}{k}^{2}+b{w}^{2}({-c}_{d}\left(-1+{\beta }_{1}\right)\left(-2+\alpha +\alpha {\beta }_{1}+2{\beta }_{2}-2\alpha {\beta }_{2}\right)+2{c}_{f}{\beta }_{1}\left(\alpha {\beta }_{1}+{\beta }_{2}-\alpha {\beta }_{2}\right))\gamma ))))\end{array}}$$
(29)
$${p}_{1}^{*}=\frac{\begin{array}{c}(a(2{c}_{d}{c}_{f}{k}^{2}+b{w}^{2}\left(-{c}_{d}\left(-1+{\beta }_{1}\right)\left(-1+\alpha {\beta }_{1}+{\beta }_{2}-\alpha {\beta }_{2}\right)+{c}_{f}{\beta }_{1}\left(\alpha {\beta }_{1}+{\beta }_{2}-\alpha {\beta }_{2}\right)\right)\gamma )\\ ({c}_{d}^{2}{c}_{f}{k}^{2}\left(16{c}_{f}{c}_{\xi }{k}^{2}+{c}^{2}{w}^{2}\alpha {\left(-1+{\beta }_{1}\right)}^{2}\right)-{c}_{d}{c}_{f}{k}^{2}{w}^{2}({c}^{2}{c}_{d}\alpha {\left(-1+{\beta }_{1}\right)}^{2}+8b{c}_{\xi }\\ ({c}_{d}\left(-1+{\beta }_{1}\right)\left(-1+\alpha {\beta }_{1}+{\beta }_{2}-\alpha {\beta }_{2}\right)-{c}_{f}{\beta }_{1}\left(\alpha {\beta }_{1}+{\beta }_{2}-\alpha {\beta }_{2}\right))\gamma )+{b}^{2}{c}_{\xi }{w}^{4}{c}_{d}\left(-1+{\beta }_{1}\right)\\ \left(-1+\alpha {\beta }_{1}+{\beta }_{2}-\alpha {\beta }_{2}\right)-{{c}_{f}{\beta }_{1}\left(\alpha {\beta }_{1}+{\beta }_{2}-\alpha {\beta }_{2}\right))}^{2}{\gamma }^{2})+{c}_{d}{c}_{f}k({t}_{z}-w)(-1+2{\beta }_{1})\\ (-2b{c}_{\xi }\gamma (4b{w}^{2}{\left(-{c}_{d}\left(-1+{\beta }_{1}\right)\left(-1+\alpha {\beta }_{1}+{\beta }_{2}-\alpha {\beta }_{2}\right)+{c}_{f}{\beta }_{1}\left(\alpha {\beta }_{1}+{\beta }_{2}-\alpha {\beta }_{2}\right))\gamma \right)}^{2}+\\ {c}^{2}(-1+\gamma )(8{c}_{d}^{2}{c}_{f}^{2}{k}^{4}+2b{c}_{d}{c}_{f}{k}^{2}{w}^{2}-{c}_{d}\left(-1+{\beta }_{1}\right)\left(-3+\alpha +2\alpha {\beta }_{1}+{3\beta }_{2}-3\alpha {\beta }_{2}\right)\\ +3{c}_{f}{\beta }_{1}\left(\alpha {\beta }_{1}+{\beta }_{2}-\alpha {\beta }_{2}\right))\gamma +{b}^{2}{w}^{4}{(c}_{d}\left(-1+{\beta }_{1}\right)\left(-1+\alpha {\beta }_{1}+{\beta }_{2}-\alpha {\beta }_{2}\right)-{c}_{f}{\beta }_{1}\\ {\left(\alpha {\beta }_{1}+{\beta }_{2}-\alpha {\beta }_{2}\right))}^{2}{\gamma }^{2})))\end{array}}{\begin{array}{c}((4{c}_{d}{c}_{f}{k}^{2}-b{c}_{d}{w}^{2}\left(-1+{\beta }_{1}\right)\left(-1+\alpha \left({\beta }_{1}-{\beta }_{2}\right)+{\beta }_{2}\right)\gamma +b{c}_{f}{w}^{2}{\beta }_{1}\left(\alpha \left({\beta }_{1}-{\beta }_{2}\right)+{\beta }_{2}\right)\gamma )\\ (b{c}_{\xi }\gamma (4{c}_{d}{c}_{f}{k}^{2}+b{w}^{2}\left(-{c}_{d}\left(-1+{\beta }_{1}\right)\left(-1+\alpha {\beta }_{1}+{\beta }_{2}-\alpha {\beta }_{2}\right)+{c}_{f}{\beta }_{1}\left(\alpha {\beta }_{1}+{\beta }_{2}-\alpha {\beta }_{2}\right)\right)\\ +{{c}_{f}{\beta }_{1}\left(\alpha {\beta }_{1}+{\beta }_{2}-\alpha {\beta }_{2}\right))\gamma )}^{2}-{c}^{2}{c}_{d}{c}_{f}{k}^{2}(-1+\gamma )(4{c}_{d}{c}_{f}{k}^{2}+b{w}^{2}(-{c}_{d}\left(-1+{\beta }_{1}\right)\\ \left(-2+\alpha +\alpha {\beta }_{1}+{2\beta }_{2}-2\alpha {\beta }_{2}\right)+2{c}_{f}{\beta }_{1}\left(\alpha {\beta }_{1}+{\beta }_{2}-\alpha {\beta }_{2}\right))\gamma )))\end{array}}$$
(30)
$${q}^{*}=\frac{\begin{array}{c}(c{c}_{d}{c}_{f}k(-1+\gamma )(4a{c}_{d}{c}_{f}{k}^{3}-2abk{w}^{2}({c}_{d}\left(-1+{\beta }_{1}\right)\left(-1+\alpha {\beta }_{1}+{\beta }_{2}-\alpha {\beta }_{2}\right)-{c}_{f}{\beta }_{1}\\ \left(\alpha {\beta }_{1}+{\beta }_{2}-\alpha {\beta }_{2}\right))\gamma -{c}_{f}{\beta }_{1}\left(\alpha {\beta }_{1}+{\beta }_{2}-\alpha {\beta }_{2}\right))\gamma -{b}^{2}({t}_{z}-w){w}^{2}\left(-1+{2\beta }_{1}\right)({c}_{d}\left(-1+{\beta }_{1}\right)\\ \left(-1+\alpha {\beta }_{1}+{\beta }_{2}-\alpha {\beta }_{2}\right)-{c}_{f}{\beta }_{1}\left(\alpha {\beta }_{1}+{\beta }_{2}-\alpha {\beta }_{2}\right)){\gamma }^{2}))\end{array}}{\begin{array}{c}b{c}_{\xi }\gamma (4{c}_{d}{c}_{f}{k}^{2}+b{w}^{2}{\left(-{c}_{d}\left(-1+{\beta }_{1}\right)\left(-1+\alpha {\beta }_{1}+{\beta }_{2}-\alpha {\beta }_{2}\right)+{c}_{f}{\beta }_{1}\left(\alpha {\beta }_{1}+{\beta }_{2}-\alpha {\beta }_{2}\right)\right)\gamma )}^{2}\\ -{c}^{2}{c}_{d}{c}_{f}{k}^{2}(-1+\gamma )(4{c}_{d}{c}_{f}{k}^{2}+b{w}^{2}(-{c}_{d}\left(-1+{\beta }_{1}\right)\left(-2+\alpha +\alpha {\beta }_{1}+{2\beta }_{2}-2\alpha {\beta }_{2}\right)+\\ 2{c}_{f}{\beta }_{1}\left(\alpha {\beta }_{1}+{\beta }_{2}-\alpha {\beta }_{2}\right))\gamma ))\end{array}}$$
(31)

Appendix 2. Model 3.2

The amount of centralized decision variables is shown in this fragment:

$${x}_{d}^{c}=\frac{\begin{array}{c}-((b{c}_{f}{c}_{\xi }w(-1+\alpha ){\beta }_{2}\gamma (b({cs}_{f}+{t}_{z}\alpha -w\left(1+\alpha \right)-\left({cs}_{f}+{cs}_{d}\left(-1+{t}_{d}\right)+2{t}_{z}-2w\right)\alpha {\beta }_{1}+\\ \left({cs}_{f}+{cs}_{d}\left(-1+{t}_{d}\right)\right)\left(-1+\alpha \right){\beta }_{2}+{c}_{c}(-1+{t}_{f})(-1+\alpha \left({\beta }_{1}-{\beta }_{2}\right)+{\beta }_{2}))\gamma -ak(-1+\alpha +\gamma )))\end{array}}{\begin{array}{c}({c}^{2}{c}_{d}{c}_{f}{k}^{2}{\left(-1+\alpha +\gamma \right)}^{2}+b{c}_{\xi }\gamma {(b{c}_{f}{w}^{2}{\left(-1+\alpha \right)}^{2}{\beta }_{2}^{2}\gamma +{c}_{d}(b{w}^{2}(1+\alpha -2\alpha {\beta }_{1}+\left(-1+\alpha \right){\beta }_{2})}^{2}\\ \gamma -4{c}_{f}{k}^{2}(-1+\alpha +\gamma )))))\end{array}}$$
(32)
$${x}_{f}^{c}=\frac{\begin{array}{c}-((b{c}_{d}{c}_{\xi }w(-1+\alpha \left(-1+2{\beta }_{1}-{\beta }_{2}\right)+{\beta }_{2})\gamma (b({cs}_{f}+{t}_{z}\alpha -w\left(1+\alpha \right)-\left({cs}_{f}+{cs}_{d}\left(-1+{t}_{d}\right)+2{t}_{z}-2w\right)\alpha {\beta }_{1}+\left({cs}_{f}+{cs}_{d}\left(-1+{t}_{d}\right)\right)\left(-1+\alpha \right){\beta }_{2}+\\ {c}_{c}(-1+{t}_{f})(-1+\alpha \left({\beta }_{1}-{\beta }_{2}\right)+{\beta }_{2}))\gamma -ak(-1+\alpha +\gamma )))\end{array}}{({c}^{2}{c}_{d}{c}_{f}{k}^{2}{\left(-1+\alpha +\gamma \right)}^{2}+b{c}_{\xi }\gamma (b{c}_{f}{w}^{2}{\left(-1+\alpha \right)}^{2}{\beta }_{2}^{2}\gamma +{c}_{d}{(b{w}^{2}(1+\alpha -2\alpha {\beta }_{1}+\left(-1+\alpha \right){\beta }_{2})}^{2}\gamma -4{c}_{f}{k}^{2}(-1+\alpha +\gamma )))))}$$
(33)
$${p}_{1}^{c}=\frac{\begin{array}{c}({c}^{2}{c}_{d}{c}_{f}k({cs}_{f}+{t}_{z}\alpha -w\left(1+\alpha \right)-\left({cs}_{f}+{cs}_{d}\left(-1+{t}_{d}\right)+2{t}_{z}-2w\right)\alpha {\beta }_{1}+\left({cs}_{f}+{cs}_{d}\left(-1+{t}_{d}\right)\right)\\ \left(-1+\alpha \right){\beta }_{2}+{c}_{c}(-1+{t}_{f})(-1+\alpha \left({\beta }_{1}-{\beta }_{2}\right)+{\beta }_{2}))(-1+\alpha +\gamma )+{c}_{\xi }(-2b{c}_{d}{c}_{f}k\\ ({cs}_{f}+{t}_{z}\alpha -w\left(1+\alpha \right)-({cs}_{f}+{t}_{z}\alpha -w\left(1+\alpha \right)-\left({cs}_{f}+{cs}_{d}\left(-1+{t}_{d}\right)+2{t}_{z}-2w\right)\alpha {\beta }_{1}+\\ \left({cs}_{f}+{cs}_{d}\left(-1+{t}_{d}\right)\right)(-1+\alpha ){\beta }_{2}+{c}_{c}(-1+{t}_{f})(-1+\alpha \left({\beta }_{1}-{\beta }_{2}\right)+{\beta }_{2}))\gamma +a(b{c}_{f}{w}^{2}\\ {\left(-1+\alpha \right)}^{2}{\beta }_{2}^{2}\gamma (b{w}^{2}(1+\alpha -2\alpha {\beta }_{1}+\left(-1+\alpha \right){{\beta }_{2})}^{2}\gamma -2{c}_{f}{k}^{2}(-1+\alpha +\gamma )))))\end{array}}{\begin{array}{c}({c}^{2}{c}_{d}{c}_{f}{k}^{2}{\left(-1+\alpha +\gamma \right)}^{2}+b{c}_{\xi }\gamma (b{c}_{f}{w}^{2}{\left(-1+\alpha \right)}^{2}{\beta }_{2}^{2}\gamma +{c}_{d}{(b{w}^{2}(1+\alpha -2\alpha {\beta }_{1}+\left(-1+\alpha \right){\beta }_{2})}^{2}\\ \gamma -4{c}_{f}{k}^{2}(-1+\alpha +\gamma )))))\end{array}}$$
(34)
$${q}^{c}=\frac{\begin{array}{c}-(({cc}_{d}{c}_{f}k(-1+\alpha +\gamma )(b(-{cs}_{f}+w-{t}_{z}\alpha +w\alpha +\left({cs}_{f}+{cs}_{d}\left(-1+{t}_{d}\right)+2{t}_{z}-2w\right)\alpha {\beta }_{1}-({cs}_{f}+\\ {cs}_{d}\left(-1+{t}_{d}\right))\left(-1+\alpha \right){\beta }_{2}-{c}_{c}(-1+{t}_{f})(-1+\alpha \left({\beta }_{1}-{\beta }_{2}\right)+{\beta }_{2}))\gamma +ak(-1+\alpha +\gamma )))\end{array}}{\begin{array}{c}({c}^{2}{c}_{d}{c}_{f}{k}^{2}{\left(-1+\alpha +\gamma \right)}^{2}+b{c}_{\xi }\gamma {(b{c}_{f}{w}^{2}{\left(-1+\alpha \right)}^{2}{\beta }_{2}^{2}\gamma +{c}_{d}(b{w}^{2}(1+\alpha -2\alpha {\beta }_{1}+\left(-1+\alpha \right){\beta }_{2})}^{2}\\ \gamma -4{c}_{f}{k}^{2}(-1+\alpha +\gamma )))))\end{array}}$$
(35)

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Matinfard, S., Yaghoubi, S. & Kharaji Manouchehrabadi, M. Impact of government policies on photovoltaic supply chain considering quality in the power distribution system: a case study. Environ Sci Pollut Res 29, 58810–58827 (2022). https://doi.org/10.1007/s11356-022-19884-7

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