Integrated resilient strategies of renewable power generation and distribution

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Integrated resilient strategies of renewable power generation and distribution

Gorbachuk V.M. Gorbachuk Vasyl Mykhajlovych, Doctor of Science in Physics and Mathematics, Senior Research Associate, Head of the Department of Intelligent Information Technologies, V.M.Glushkov Institute of Cybernetics of the National Academy of Sciences of Ukraine, Suleimanov Seit-Bekir Suleimanov Seit-Bekir, MA in Economics, MSc in Applied Physics and Nanomaterials, Junior Research Associate, V.M.Glushkov Institute of Cybernetics of the National Academy of Sciences of Ukraine, Batih L.O. Batih Liudmyla Omelianivna, MSc in Accounting and Taxation, MSc in Avionics, PhD Student, V.M.Glushkov Institute of Cybernetics of the National Academy of Sciences of Ukraine

Abstract

The interaction of the government financial system, the state banking system, and the investment system of renewable photovoltaic (PV) power generation equipment can lead to sustainable strategies of these three parties (including government subsidies and bank loans) in the distributed state PV market depending on its level of development.

However, the instability of power output, caused by the variability and changing nature of renewable energy sources, poses challenges for large-scale power dispatch. In addition, the development of the PV industry has been constrained by a long period of return on investment in solar photovoltaics and the need for large initial investments.

Household consumers, living in residential premises, are one of the main long-term buyers of electricity and therefore have the potential to become investors in small distributed solar PV installations. Compared to centralized large-scale PV power plants or industrial and commercial PV plants, small-scale residential distributed PV plants have many specific advantages: reduced upfront investment required to build a centralized power plant; reduction of losses on the line caused by the transmission of electricity over long distances; improving the balance between supply and demand for electricity due to limited geographical area. In order to facilitate the resettlement of residents in small dwellings and their transformation into energy consumers of the power system, the government should use appropriate strategic tools to encourage residents to plan investments in PV installations.

The important questions are remained: whether government subsidies and bank loans can significantly contribute to dissemination of PV installations at the different levels of PV market development; which evolutionarily stable states will be formed at different development levels of the PV market; how the volume of government subsidies, the share of bank loans, the capacity of PV installations implemented by investors will affect the evolutionary trajectories of the all PV market dimensions and the transformations of various evolutionary stable states. In order to answer those questions, numerical simulations are to be performed studying evolutionary trajectories at different development levels of the PV market.

Key words: distributed state market, photovoltaic power generating equipment, energy efficiency, government subsidies, bank loans.

Анотація

Інтегровані резильєнтні стратегії відновлюваної генерації та розподілу енергії

Горбачук Василь Михайлович, доктор фізико-математичних наук, старший науковий співробітник, завідувач відділу інтелектуальних інформаційних технологій, Інститут кібернетики імені В.М.Глушкова НАН України

Сулейманов Сеїт-Бекір, магістр з економіки, магістр з прикладної фізики та наноматеріалів, молодший науковий співробітник, Інститут кібернетики імені В.М.Глушкова

Батіг Людмила Омелянівна, магістр з обліку та оподаткування, магістр з авіоніки, аспірант, Інститут кібернетики імені В.М.Глушкова НАН України

На початку третього тисячоліття широку увагу привертають виснаження викопних джерел енергії та забруднення довкілля, спричинене швидким зростанням попиту на енергію: досліджувалися відгук попиту, планування робіт, виробництво електроенергії з відновлюваних джерел. Виробництво електроенергії з відновлюваних джерел є важливим способом сприяння енергозбереженню та поліпшення енергоефективності.

Серед відновлюваних джерел одними з найпоширеніших і найперспективніших є джерела сонячної енергії. Проте нестабільність вихідної потужності, спричинена мінливістю і змінною природою відновлюваних джерел енергії, породжує виклики для широкомасштабної диспетчеризації потужності.

Крім того, розвиток фотоелектричної галузі стримували тривалий період віддачі на інвестиції у сонячну фотоелектричну енергію та потреба у великих початкових капіталовкладеннях. Для задоволення зростаючого попиту на енергію та зменшення викидів вуглекислого газу багато держав активно підтримує поширення фотоелектричного енергогенеруючого обладнання. При цьому урядова фінансова система і державна банківська система відіграють ключову роль у сприянні відповідним інвестиціям. Взаємодія урядової фінансової системи, державної банківської системи та інвестиційної системи фотоелектричного енергогенеруючого обладнання може вести до стійких стратегій цих трьох сторін (включаючи обсяги урядових субсидій і банківських позик) на розподіленому державному ринку фотоелектричної енергії в залежності від рівня розвитку цього ринку. Оскільки ринок може перебувати на початковому, середньому і зрілому рівні свого розвитку, то немає гарантії, що будь-який рівень розвитку ринку однаково сприятиме інвестиціям у фотоелектричне енергогенеруюче обладнання. Можна припустити, що урядові субсидії та банківські позики відіграють важливішу роль на середньому рівні розвитку ринку фотоелектричної енергії. Крім того, урядова фінансова система і державна банківська система сприяють встановленню обладнання більшої фотоелектричної потужності з вищими інвестиційними витратами.

Ключові слова: розподілений державний ринок, фотоелектричне енергогенеруюче обладнання, енергоефективність, урядові субсидії, банківські позики.

Introduction

Problem statement. Exhaustion of fossil resources, climate change and other environmental and security problems caused by massive energy consumption explain the considerable attention to sustainable energy generation. Renewable energy generation has proven to be a promising solution to climate change and other environmental issues by reducing fossil fuel consumption [1].

Analysis of the recent research and publications. On February 8, 2022, the well- known Norwegian company Emergy announced the postponement of the construction of Europe's largest wind farm (power plant, PP) «Zofia» in Melitopol district of Zaporizhzhya region of Ukraine due to the following reasons: constant questions about receiving payment from the state enterprise «Guaranteed Buyer» which is the buyer of renewable energy (from the Emergy's view, the government lacks a clear vision of the auction process); difficulties in attracting large-scale foreign direct investment in Ukraine's renewable energy market (partly due to the geopolitical situation with the Russian Federation (RF)); the short period of time left for the construction and commissioning of wind turbines (according to current legislation of Ukraine, to receive incentives, all renewable energy facilities must be commissioned by the end of 2022) [2]. Emergy has built some infrastructure for the project, and in the run-up to the resumption of construction will analyze alternative electricity sales opportunities, including the sale of electricity to large consumers on the basis of bilateral agreements. The planned foreign direct investment in the «Zofia» project exceeded 1 billion euros, and the main contractor was China Electric Power Equipment and Technology Co Ltd, a subsidiary of the State Grid Corporation of China [3]. On February 12, 2022, 4 days after the publication of the above-mentioned Emergy decision, international insurance companies began to pause supporting flights to Ukraine. On February 24, 2022, 16 days after the Emergy decision, the RF launched a war against Ukraine along the border (Luhansk, Sumy, Kharkiv, Chernihiv regions), as well as on the border of Zaporizhzhya and Kherson regions with the temporarily occupied in 2014 Crimea, on the border with the temporarily occupied in 2014 Donetsk and Luhansk regions, on the border of Zhytomyr, Kyiv, Chernihiv regions with Belarus, striking cruise and ballistic missiles (including weapons transferred to the RF from Ukraine under the Budapest Memorandum of 1994) in other regions of Ukraine. The main targets of the attack are state and critical infrastructure, including energy facilities. On the same day, the RF troops captured the Kakhovka and Kyiv Hydroelectric Power Plants (HPPs), the Chornobyl Nuclear Power Plant (where the largest nuclear catastrophe in human history took place in 1986, which catalyzed the collapse of the USSR), and the «Zofia» wind farm. A system analysis of events in Ukraine in February - March 2022 was presented by Tommy Ahonen, a well-known digital technology expert [4], who in 1989 received a Master's degree in Business Administration from St. John's University (established in 1870) in 1999. From 2001 he worked as the Global Head of Nokia's 3G Business Consulting, and since 2001 he has leaded TomiAhonen Consulting. The World Bank has studied the impact of RF aggression against Ukraine on Europe and Central Asia [5], but without offering answers to current challenges to critical infrastructures, including energy [6]. The unresolved part of the overall problem is the study of integrated sustainable mechanisms for supporting energy infrastructure.

Purpose. The unprecedented armed capture of two nuclear power plants on February 24 and March 4, 2022, indicates the need to develop models and measures to support critical infrastructure, including energy, in force majeure under so-called catastrophic risks [7, 8]. References to such circumstances have led international insurance companies to suspend support for flights to Ukraine, but a feature of the energy infrastructure is the difficulty or impossibility of stopping its operation at once. The aim of the work is to show how modern alternative energy expands the arsenal of technological and organizational means of energy infrastructure.

Basic material

Prior to the Chornobyl disaster, nuclear energy was considered the novel technology, alternative to traditional energy. Since the introduction of innovative energy technologies in general has certain patterns, especially in terms of a system and integrated approach, experience of alternative energy in the recent past is useful for the efficient use of alternative energy today [9]: according to the State Agency of Ukraine on Exclusion Zone Management and the Institute for Safety Problems of Nuclear Power Plant of the National Academy of Sciences of Ukraine [10, 11], during the temporary occupation of the Chornobyl nuclear power plant in 2022, the RF destroyed the Chornobyl zone archives, which had accumulated for decades and proved useful to the Ukrainian experts (colleagues of one of the authors) eliminating the consequences of the accident on Fukushima NPP (Japan) since 2011.

On February 26, 2022, 2 days after the invasion of the RF troops in 9 regions of Ukraine from the North, East, South, the Ukrainian troops recaptured the Kyiv HPP; the staff of the Kyiv HPP was in refuge; Kyiv HPP did not work. Leaving the Crimea and passing the Kherson region, on February 26, the RF troops approached the city of Energodar (Vasylivsky district of the Zaporizhzhya region), where the Europe's largest nuclear power plant - the Zaporizhzhya nuclear power plant (NPP) - is located. Using the proximity to the Zaporizhzhya NPP for their own defense, the RF troops deployed multiple rocket launchers in the direction of the Zaporizhzhya NPP with a maximum range of 42 km. Surrounding Energodar, on February 27, the RF troops moved from the district center of Velyka Bilozerka to Dniprorudne and the district center of Vasylivka, and the RF sabotage groups began operating in Energodar. On February 28, the RF troops concentrated about 90 units of military machinery in the village of Dniprovka and reached the borders of Energodar. On March 1, the International Atomic Energy Agency (IAEA) lost contact with Zaporizhzhya NPP monitoring stations. For three days (February 28, March 1, March 2) thousands of civilians in Energodar, including employees of the Zaporizhzhya NPP, blocked the capture of the Zaporizhzhya NPP by the RF troops. The lack of a sufficient and rapid proactive response to the actions of the RF military around the besieged Ukrainian nuclear power plant was perceived by the RF as a permission to escalate. On March 2, the RF troops used grenades against civilians in the village of Vodiane near Energodar. On March 3, about 100 units of the RF armored vehicles entered Energodar, and on the night of March 4, a large-scale fire broke out on the territory of the Zaporizhzhya NPP as a result of shelling by the RF tanks; the RF troops allowed to liquidate this fire to divisions of the State Emergency Service of Ukraine only after the end of fight. In this area, in addition to the six nuclear power units, there is also a storage of spent nuclear fuel. Three soldiers of the National Guard of Ukraine, responsible for the protection of critical infrastructure by the Law of Ukraine, were killed during the defense of the Zaporizhzhya NPP.

It is obvious that the capabilities of the National Guard of the attacked country alone are not enough to protect nuclear power plants in case of force majeure or catastrophic risks [7, 12]. For example, in such circumstances, international insurance companies, other financial and economic private, national and international organizations may take timely measures, such as preventive measures to pause support for air services to Ukraine, starting from February 12, 2022, 12 days before the first missile attacks.

During the storming of the Zaporizhzhya NPP, only one of the six power units of this NPP was connected to the united power system of Ukraine. After the shelling and fire, the city of Energodar lost heat supply. On March 4, the State Nuclear Regulatory Inspectorate of Ukraine (SNRIU) informed the IAEA of the first-ever armed seizure of a working nuclear power plant. The IAEA Director General told a news conference that «shelling near a nuclear power plant violates the fundamental principle of protecting nuclear facilities». The IAEA has set up a fire response center at the Zaporizhzhya NPP. On March 6, the SNRIU informed the IAEA about the impossibility of obtaining information on the status of the nuclear facility due to the loss of communication with the Zaporizhzhya NPP by phone, fax, e-mail; the IAEA Director General has expressed deep concern over reports that RF troops are demanding coordination with them on any interaction with the nuclear facility. The state enterprise «National Nuclear Power Generating Company «Energoatom» reported that the staff of the Zaporizhzhya NPP has been held hostage for several days and has problems with regular food supplies. On March 7, the SNRIU informed the IAEA that the Zaporizhzhya NPP could not receive the necessary spare parts and medicines. The IAEA has stopped receiving data from the safeguards monitoring system of this NPP. According to the SNRIU, half of the main high-voltage power lines of this NPP were damaged, and the transformer of one of the nuclear power units was sent for emergency repairs due to damage to the cooling system during the fighting on March 4. During these battles, the reactor compartment of another nuclear power unit was damaged. On March 4, 2022, Great Britain convened an emergency meeting of the UN Security Council due to the capture of the Zaporizhzhya NPP by the RF. At this meeting, the US Permanent Representative to the UN Linda Thomas-Greenfield officially stated:

«By the grace of God, the world narrowly averted a nuclear catastrophe last night. We all waited to exhale as we watched the horrific situation unfold in real time. I applaud the ability of the Ukrainian operators to keep all six reactors in safe conditions while under attack and to report, as they were able to, to their nuclear regulator. Moreover, we appreciate the State Nuclear Regulatory Inspectorate of Ukraine for its continuous updates to the IAEA and to the international community. We are gravely concerned that the Ukrainian operators are now doing their jobs under extreme duress.

Russia's attack last night put Europe's largest nuclear power plant at grave risk. It was incredibly reckless and dangerous. And it threatened the safety of civilians across Russia, Ukraine, and Europe. As a first step, we call on Russia to withdraw its troops from the plant to permit medical treatment for injured personnel, to ensure operators have full access to the site and are able to communicate with nuclear regulators, and to allow the operators to conduct shift changes to ensure the continued safe operation of the plant. Ukrainian firefighters and nuclear engineers must have full access to the nuclear facility to assess damage, particularly to water intake piping, and mitigate a further deterioration of the situation if needed. Nuclear facilities cannot become part of this conflict. Reliable electricity is vital for the nuclear facility, as are back-up diesel generators and fuel. Safe transit corridors must be maintained. Russia must halt any further use of force th at might put at further risk all 15 operable reactors across Ukraine - or interfere with Ukraine's ability to maintain the safety and security of its 37 nuclear facilities and their surrounding populations.

The United States remains highly concerned that Russian military forces controlling the Chornobyl site have not permitted operators there to have a shift change since last week. This is highly irresponsible behavior and causes grave concerns for continued safe operations of both sites [at the Chornobyl and Zaporizhzhya NNPs] ... Russia is destroying critical infrastructure which is denying people drinking water to stay alive and gas to keep people from freezing to death in the middle of winter. The humanitarian impact of this destruction will be significant». After the assault on the territory of the Zaporizhzhya NPP were about 50 units of heavy machinery and 500 military of the RF, using the NPP as a shield in alien territory. The head of the Zaporizhzhya Regional Military Administration reported on the facts of armed marauding by the RF military in Energodar. There are problems with communication and food supply in Energodar. The RF in Energodar seized and disabled the equipment of Ukrtelecom, the largest operator of multiplex communication services in Ukraine. The mayor of Energodar planned to organize meals once a day for the city's residents. On March 9, 5 days after the storming of the NPP, under the auspices of the International Committee of the Red Cross, the evacuation of residents of Energodar and surrounding villages to the regional center of Zaporizhzhya began.

According to the UN Refugee Agency, 5 weeks after the RF's aggression against Ukraine started, the number of refugees from Ukraine to other countries exceeded 4 million (about 10% of the total population of country), half of whom were children. In other words, in 5 weeks more people left Ukraine than the population of more than 20 European countries, such as Croatia, Georgia, Bosnia and Herzegovina, Armenia, Albania, Lithuania, Moldova, Slovenia, Latvia, Northern Macedonia, Kosovo, Estonia, Cyprus, Luxembourg, Montenegro, Malta, Iceland and others. As large and widespread sources of solar radiation are increasingly considered one of the main renewable energy sources, such resources are being actively promoted by many countries. Although some countries have rich solar radiation resources and considerable potential for their use, the cost of solar energy remains high due to the backwardness of production technologies in these countries. In addition, the expected long payback period, the need for large initial investments, high risks for variable and volatile renewable energy create additional difficulties for investment in the photovoltaic (PV) market in any country. Therefore, the state of investment in the PV market of the country largely depends on the policy of its government.

Appropriately selected government instruments can help address current environmental issues by deploying small PV plants. One of the mechanisms of government incentives for residential prosumers is the Stackelberg model. The important factors influencing on decision making about investing in PV technology in a particular place (region) are regional solar radiation intensity (SRI), levelized cost of electricity (LCOE) [14] and feed-in tariffs (FITs), such as the so-called green tariffs in Ukraine. It can be shown that the economic role of government subsidies in small homogeneous PV plants is gradually declining. The role of government subsidies in the PV market has gradually changed from stimulating residents to initial investment in PV installations to stimulating higher capacity PV installations. Appropriate government subsidies can reduce the restrictions of SRI, LCOE, FIT on the development of PV installations by residents of the regions. At the same time, the results [15] show that the optimal subsidy, set according to the conditions of specific regions, is sufficient to motivate residents to implement PV installations and maximize the benefits of government and residents, whereas a single subsidy policy is less effective than a regional subsidy policy. These results can be useful for producing recommendations for decision makers about efficient and targeted strategies [16]. Some countries have specific strategies to stimulate centralized PV power plants and small distributed PV plants: centralized PV power plants are stimulated by preferential tariffs and subsidies, and distributed PV plants are stimulated by subsidies per unit of energy produced. For instance, regional preferential tariffs can be an important instrument of stimulating the introduction of PV generation. According to them, the entire territory of the state is divided into several resource zones, based on regional resources of solar radiation, implying that each region has its own level of FIT.

The study results of the study of FIT policy for centralized PV power plants can be applied to distributed PV installations, among which two groups are distinguished - industrial and commercial PV installations, as well as household (residential) PV installations. Different subsidy strategies are used for those groups. The subsidy strategy for industrial and commercial PV plants depends on the extent to which the PV plant relates to its own production, own consumption, sale of surplus or all electricity. Regardless of the adopted model of electricity sales, a single subsidy strategy is applied for residential distributed PV installations - subsidies per unit of energy produced.

There are the impact studies of state incentive policy on residential PV installations. Some estimates of the efficiency of state and municipal incentives to promote the introduction of residential solar PV installations show that each additional dollar for incentives leads to an average of an additional 500 W of installed capacity. Surveys and experiments show that subsidies are an important factor in stimulating the introduction of solar PV installations. These studies confirm the obvious impact of government subsidies on such implementations, but the circumstances and levels of this impact need better understanding for more efficient and targeted government support in developing the necessary subsidy strategies.To better understand how the state uses subsidy tools to encourage residents to implement PV installations, it is necessary to analyze the scenarios in which r esidents decide on such implementations. Due to considerable differences in regional solar radiation resources and the dynamic development of local markets, there is a high heterogeneity of investment in PV installations among different regions. As this heterogeneity creates complex and diverse challenges to the formation of the government's subsidy strategy, we will first summarize the factors influencing the implementation of PV installations by residents. The first factor is the individual characteristics of the resident, in particular the levels of income, education and environmental awareness of an individual, the effects of the social environment (peer effects). The second factor is the technological features of photovoltaic power generation, which are reflected in the costs and periods of return on investment in PV installations. The third factor is external features, including external incentives - FIT [17] and subsidies per unit of energy produced [18, 19]. The fourth factor is the features of the natural environment, which mainly relate to regional SRI indicators [17, 20]. The factors mentioned above should be taken into account when formulating public policy, which should also take into account the diverse and difficult to measure personal characteristics of residents. Since the realistic goal is to launch a general policy of financial incentives common to all regions of the state, such a policy should be based on measurable economic indicators as determinants of assessing the impact on investment behavior of residents. FIT and state subsidy are characterized by different purposes and methods of application. energy solar carbon renewable photovoltaic

With the rapid development of the sharing economy, the provision of financial support and the sharing of investment risks among investors in the PV energy have become key means of promoting the PV industry. State incentive policy was viewed an efficient approach to intense promotion of PV systems. Government subsidies reduce the need for large initial investments, and market mechanisms such as FIT and tax rebates increase return on investment and reduce payback periods. In addition, bank loans are considered another major source of external financing for the development of the PV industry. The announcement by the Brazilian Development Bank (founded in 1952) to provide loans for solar PV projects at low interest rates has had a positive effect on the proliferation of residential PV systems. Third-party financing with appropriate risksharing is considered an efficient approach to promote the use of ph otovoltaic technologies. Because government subsidies put pressure on the state budget, and bank loans require banks to take major credit risks, clear barriers to governments and banks, supporting the development of the PV industry, arise.

By 2022, the issue of computing such targeted government subsidies and bank loans with limited credit risks, which maximize incentives for the dissemination of PV technologies, need better understanding. The efficiency of government subsidies or bank loans is usually determined by a single criterion (scalar index). The Stackelberg game- theoretic model for studying the role of government strategies for stimulating PV technologies was suggested [18]. It turned out that the application of government strategies to stimulate the introduction of PV facilities is not always result-oriented: assessing the efficiency of a single renewable energy policy in different regions showed the importance of regional geographical, technical and socio-economic indicators. The World Bank has developed guidelines for providing the best loans to promote solar PV technology in developing countries [21]. A dynamic game-theoretic model for analyzing the behavior of governments and banks in the process of financing PV companies has been developed [22]. In general, the state should support banking institutions and proper interest rates to stimulate investments of PV companies. Government subsidies can reduce the risk of bank loans to support investors in PV technology, if these subsidies are received not by investors but by banks: bank risks are usually lower than those of borrowers and investors. Although in reality government subsidies and bank loans often interact to support investors in PV technology, such interactions remain unexplored.

Conclusions

The main participants in the distributed PV market are the government, banks and potential investors in PV technology. The government regulates this market by establishing acceptable incentive strategies to encourage potential investors to develop PV facilities. The main resources of external financing for investors in PV technologies are provided by banks, which get interest on their loans. Banks are supervised (by regulatory fines in case of refusal to lend to potential investors in PV technology) and motivated by the state in order to provide loans and financial assistance to such investors. Potential investors in PV technologies make final decisions on the development and implementation of PV facilities, based on their own goals and abilities to work under a variety of circumstances, government incentive strategies, bank lending strategies. In this way, the government creates incentives for potential investors in PV technology to protect the environment and increase welfare, and financial institutions and investors share risks in a competitive market environment.

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17. Monarca, U., Cassetta, E., Pozzi, C., Dileo, I. (2018). Tariff revisions and the impact of variability of solar irradiation on PV policy support: the case of Italy. Energy Policy, August, 119, 307-316.

18. Chen, W., & Wei, P. (2018). Socially optimal deployment strategy and incentive policy for solar photovoltaic community microgrid: a case of China. Energy Policy, May, 116, C, 86-94.

19. Mundaca, L., & Samahita, M. (2020). What drives home solar PV uptake? Subsidies, peer effects and visibility in Sweden. Energy Research & Social Science, February, 60, 101319.

20. Kaplani, E., & Kaplanis, S. (2012). A stochastic simulation model for reliable PV system sizing providing for solar radiation fluctuations. Applied Energy, September, 97, 970-981.

21. Miller, D., & Hope, C. (2000). Learning to lend for off-grid solar power: policy lessons from World Bank loans to India, Indonesia, and Sri Lanka. Energy Policy, February, 28, 2, 87-105.

22. Xu, L., Zhang, Q., Wang, K., Shi, X. (2020). Subsidies, loans, and companies' performance: evidence from China's photovoltaic industry, February. Applied Energy, 260, 114280.

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13. Haivoronskyy O.O., Ermoliev Yu.M., Knopov P.S., Norkin V.I. Mathematical modeling of distributed catastrophic and terrorist risks. Cybernetics and Systems Analysis. 2015. Vol. 51. № 1. P. 85-95.

14. Горбачук В., Дунаєвський М., Батіг Л. Нова енергетика й економічні зміни. Економіка. Фінанси. Бізнес. Парадигмальні зрушення в економічній теорії ХХІ ст. А.І.Ігнатюк (ред.) Київ: КНУ імені Т.Шевченка, 2021. С. 45-47.

15. Zhu X., Liao B., Yang S. An optimal incentive policy for residential prosumers in Chinese distributed photovoltaic market: a Stackelberg game approach. Journal of Cleaner Production. 2021, July. Vol. 308. 127325.

16. Zhu X., Liao B., Yang S., Pardalos P.M. Evolutionary game analysis on government subsidy policy and bank loan strategy in China's distributed photovoltaic market. Annals of Mathematics and Artificial Intelligence. 2021, May. https://doi.org/10.1007/s10472-021-09729-3.

17. Monarca U., Cassetta E., Pozzi C., Dileo I. Tariff revisions and the impact of variability of solar irradiation on PV policy support: the case of Italy. Energy Policy. 2018, August. Vol. 119. P. 307-316.

18. Chen W., Wei P. Socially optimal deployment strategy and incentive policy for solar photovoltaic community microgrid: a case of China. Energy Policy. 2018, May. Vol. 116. Issue C. P. 86-94.

19. Mundaca L., Samahita M. What drives home solar PV uptake? Subsidies, peer effects and visibility in Sweden. Energy Research & Social Science. 2020, February. Vol. 60. 101319.

20. Kaplani E., Kaplanis S. A stochastic simulation model for reliable PV system sizing providing for solar radiation fluctuations. Applied Energy. 2012, September. Vol. 97. P. 970-981.

21. Miller D., Hope C. Learning to lend for off-grid solar power: policy lessons from World Bank loans to India, Indonesia, and Sri Lanka. Energy Policy. 2000, February. Vol. 28. Issue 2. P. 87-105.

22. Xu L., Zhang Q., Wang K., Shi X. Subsidies, loans, and companies' performance: evidence from China's photovoltaic industry. 2020, February. Applied Energy. Vol. 260. 114280.

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