The Impact of Environmental Policies on Renewable Energy Storage Decisions in the Power Supply Chain

Abstract

Energy storage is a proficient means of enhancing power supply reliability and facilitating the use of renewable energy. To study the impact of policies on energy storage decisions in the power supply chain, this paper constructs an electricity supply chain and compares the equilibrium results under four scenarios based on the Stackelberg game theory. The research reveals that both discharge subsidy and investment subsidy play a beneficial role in improving the level of energy storage technology, regardless of whether power producers choose to invest in or lease energy storage equipment. Furthermore, when combined with the implementation of a renewable portfolio standard, these subsidies can have beneficial outcomes. During the early stages of development in the energy storage industry, investment subsidy proves more advantageous for enhancing both technology levels and electricity demand. Conversely, at later stages of industry development, discharge subsidies become increasingly advantageous for enhancing technological advancements and fulfilling electricity demand. Furthermore, implementing a strategy in which power generators invest in energy storage can enhance their profitability while concurrently advancing technological standards and satisfying electricity demand.

1. Introduction

Renewable energy plays a critical role in reducing emissions and addressing climate change. Ensuring a stable and efficient energy supply is essential for achieving sustainable economic growth [1]. Consequently, there has been an increasing focus on implementing policies to promote renewable energy in recent years [2]. The Renewable Portfolio Standard (RPS) has been implemented in various nations and is recognized as one of the most efficacious programs for promoting renewable energy [3]. However, with the continuous development and widespread use of renewable energy, its volatility and uncertainty have posed significant challenges to energy dispatch and balancing. In response to this issue, energy storage technology has emerged as a solution [4]. Energy storage serves the purpose of storing surplus energy and releasing it during periods of high or low demand. This addresses the necessity for a swift response from the power system to supply changes, optimizes the distribution and scheduling of electrical energy, and enhances the dependability and cost-effectiveness of energy delivery [5].

Energy storage systems are utilized in conjunction with wind and solar power generation to tackle the challenges of renewable energy consumption and to alleviate its variability [6]. According to industry statistics from the China Electricity Council, as of the end of 2023, the majority of commissioned electrochemical energy storage power stations are situated on the power generation side, accounting for 49.11% of the total. Renewable energy dominates energy storage on the power generation side, accounting for 90.63%. However, significant initial costs and uncertain profits of future returns make renewable energy power generation enterprises exceedingly prudent when it comes to investing in energy storage [7]. Consequently, many power generation enterprises also consider collaborating with energy storage enterprises.

Provincial and municipal governments in China have enacted various energy storage subsidy plans [8]. The two most commonly implemented types of subsidies are discharge subsidies and investment subsidies.

Table 1. Energy storage subsidy policies in selected regions of China in 2024.

Regions in China	Type of Subsidy	Subsidized Standards
Chengdu, Sichuan Province	Discharge Subsidy	0.3 CNY/kWh
Huangpu District, Guangzhou	Discharge Subsidy	0.2 CNY/kWh
Binhai New District, Tianjin	Discharge Subsidy	0.5 CNY/kWh
Haiyan County, Jiaxing	Discharge Subsidy	0.25 CNY/kWh
Pudong New District, Shanghai	Investment Subsidy	10%
Baiyun District, Guangzhou	Investment Subsidy	≤10%
Guangming District, Shenzhen	Investment Subsidy	20%
Beijing	Investment Subsidy	≤30%

compiles data on energy storage subsidy policies in selected regions of China for 2024. Despite ongoing efforts by the Chinese government to implement energy storage policies, there is still a lack of well-defined policy objectives and subsidy schemes. Additionally, significant variations in subsidy policies exist across different regions. In contrast, some developed countries have well-established policies regarding energy storage. For example, as early as 2009, California in the United States included energy storage in the subsidy coverage of its self-generation incentive program. In 2021, they issued more precise instructions about the subsidy amount for energy storage installation. The Australian Renewable Energy Agency was established in 2012 to offer financial support for the development and implementation of renewable energy technologies ranging from initial laboratory research to large-scale commercial deployment.

Considering RPS and energy storage subsidy, this study categorizes the types of energy storage for power generators into two modes: investing in energy storage and leasing energy storage equipment. It utilizes the Stackelberg game model to address the following issues:

RQ1: What are the optimal energy storage decisions for different entities in the power supply chain under different environmental policies?

RQ2: How does the implementation of environmental policies affect different modes of energy storage? Which energy storage model is more likely to contribute to the development of renewable energy?

RQ3: How can the appropriate adjustment of various policies promote the advancement of energy storage technology and encourage the growth of the energy storage industry and renewable energy generation, considering the impacts of the renewable energy quota obligation, subsidy amount, subsidy ratio, and lease coefficient of energy storage equipment on supply chain energy storage decisions?

2. Materials and Methods

Currently, there are already numerous studies focused on renewable energy, RPS, and energy storage.

In the field of renewable energy studies, numerous scholars have focused on the impact in mitigating carbon emissions. Bird et al. found that cap-and-trade mechanisms had a significant effect on the quantity of electricity generated from renewable energy sources, thereby influencing overall carbon emission levels [9]. Dahal et al. emphasized the importance of implementing renewable energy policies to achieve carbon neutrality [10]. Hanif et al. confirmed that the use of renewable energy effectively regulates carbon emissions, while the reliance on non-renewable energy exacerbates them [11]. Yu et al. indicated that the development of renewable energy in China has a positive impact on reducing emissions [12]. Zhang et al. utilized the STIRPAT model to explore the relationship between investment in renewable energy and carbon emissions, revealing variations in influence across different stages of investment [13]. Meng et al. examined how the consumption of renewable energy affects carbon emissions across 30 provinces in China [14]. Yang et al. found that allocating a higher percentage of investment towards wind energy leads to decreased carbon emissions, whereas directing more investment towards solar and bioenergy results in increased emissions [15]. Siddik et al. proposes that the government should actively promote the use of renewable energy sources in order to cultivate a low-carbon economy [16]. Xu et al. recommended that the Chinese government continue to expand investment in renewable energy, improve financial efficiency, and provide an efficient financial market environment for renewable energy [17].

In the realm of research on Renewable Portfolio Standards (RPS), the effects of RPS implementation and potential policy improvements have been widely discussed. García-Álvarez et al. emphasized the necessity of a more risk-free framework to bolster investor confidence in RPS [18]. Young and Bistline highlighted the significant impact of future gas pricing on the ability of RPS to reduce carbon dioxide emissions [3]. Meanwhile, Bento et al. revealed that, while the implementation of RPS can lead to either a substantial increase in available resources or significant reductions in emissions, achieving both simultaneously is challenging [19]. Zhao et al. delved into the impact of incentives on the costs and effects of RPS, offering valuable insights for government development of dynamic incentive mechanisms [20]. Zhu et al. found that increasing green certificate prices encourages greater investment in renewable energy, but only when renewable energy quota obligations are excessively high; otherwise, it diminishes motivation for power companies to invest in renewable energy [21]. Yan et al. demonstrated that a combination of cap-and-trade mechanisms and RPS is most effective for promoting renewable energy [22], while Hu et al. discovered that an increase in renewable energy quota obligations can lead to a decline in green electricity consumption and higher carbon emissions [23]. Lee analyzed and examined the long-term impact of renewable portfolio standard on electricity prices and found that it depends on changes in long-term average costs [24].

In the field of energy storage studies, many scholars have focused on the technology of energy storage rather than considering its role in decision-making within the power supply chain. Rohit et al. highlighted the benefits of energy storage in the power supply chain and conducted a comprehensive comparison of various energy storage technologies [25]. Wang et al. examined two energy infrastructures in Chongming, China, from 2016 to 2040, demonstrating that the implementation of energy storage systems can enhance the efficiency of renewable energy utilization by 2040 [26]. Arbabzadeh et al. found that implementing energy storage technology has a positive impact on reducing carbon emissions [27]. Liu and Bao explored how energy storage could improve coordination and benefits within the wind power supply chain, finding that setting appropriate prices promotes wind energy utilization and enhances overall supply chain efficiency [28]. Zhang et al. demonstrated that energy storage can enhance power system reliability and increase renewable energy penetration [29]. Sayed et al. discussed issues related to managing various renewable energy sources and storage systems as well as recent advances in green hydrogen production and fuel cells, which pave the way for a wide range of renewable energy applications [30]. Zhao et al., through numerical results, showed that integrating with an effective strategy for utilizing stored energies enhances power system flexibility and increases utilization of renewable generation [31].

We thoroughly reviewed the existing research in the aforementioned three areas. In summary, the innovative points of this study can be summarized as follows:

• The existing literature on renewable energy predominantly focuses investment, pricing, and the reduction in carbon emissions within the power supply chain. There is a greater emphasis on technical research regarding energy storage, while there is a scarcity of studies that examine the selection of energy storage models. Additionally, there is limited literature on improving energy storage technology from a supply chain perspective. This paper examines investment in energy storage equipment from a supply chain perspective and analyzes the effects of various stakeholders investing in such equipment, hence enhancing research on new power systems.
• China has implemented various environmental policies for the power industry, such as RPS and cap-and-trade mechanisms, with relatively mature research in this area. However, China’s policies on energy storage are still in an exploratory stage. While various provinces and cities in China have implemented different energy storage policies, the literature specifically focused on these policies remains scarce. The paper analyzes and contrasts two prevalent energy storage subsidy schemes in China, offering a foundation for governmental decision-making about the implementation of such policies.

3. Problem Definition

In the context of RPS, the power generator has both renewable energy generation units and traditional thermal power generation units. The electricity seller, who is responsible for RPS, is required to purchase a specified percentage of renewable energy and green certificates from the power generator. In this paper’s power supply chain, the power generator stores renewable energy and makes decisions on the energy storage model to maximize profits. The power generator decides whether to invest in energy storage directly or to lease energy storage equipment from a professional energy storage provider. In this study, we used the Stackelberg game to determine the equilibrium solution, with a focus on the impact of various incentive policies and energy storage models on power generators’ energy storage decisions. The Stackelberg game is able to reflect the structure of the electricity market well, and conforms to the decision-making sequence of the electricity supply chain. It is able to capture not only the impact of the policy on the subsidized (generators and storage service providers), but also the impact on the entire supply chain and other players in the supply chain.

In the case where the power generator invests in energy storage, this paper constructed a power supply chain with the power generator as the leader and the electricity seller as the follower, as shown in Figure 1, and the decision-making sequence of the power generator and the electricity seller is as follows: firstly, the generator decides on the wholesale electricity price and the level of energy storage technology, and secondly, the seller decides on the amount of electricity demand. In the case where the power generator leases the energy storage equipment, this paper constructed a power supply chain with the power generator and the energy storage provider as the leader and the electricity seller as the follower, as shown in Figure 2, and the decision-making sequence of the power generator, the electricity seller, and the energy storage provider is as follows: firstly, the generator decides on the wholesale electricity price, the energy storage provider decides on the level of the storage technology, and then the seller decides on the amount of electricity demand.

To facilitate the modeling and solution, the following assumptions were made in this paper:

Assumption 1.

With energy storage devices, the power generator can deliver electricity with more stability. According to Chen et al., customers’ electricity demand is determined not only by the price of power but also by its stability [32]. Consumers will prefer more stable electricity because it is safer and more reliable. This study assumed that the power demand function is connected to the level of energy storage technology, as follows: $q=a-p+bt$, where $a$ is the basic electricity demand of the market; $p$ is the market price of electricity, where the higher the $p$, the lower the electricity demand; $b (0<b<1)$ is the sensitivity coefficient of energy storage technology level, where the larger the $b$, the more importance consumers attach to the level of energy storage technology; and $t$ is the level of energy storage technology of the energy storage equipment, where the higher the $t$, the higher the electricity demand.

Assumption 2.

The electricity seller purchases thermal and renewable electricity from the power generator at the wholesale electricity price $w$ and sells it to the consumption side at the market electricity price $p$. It is further assumed that both thermal power and renewable energy production facilities already exist. The unit production cost of thermal power is $c_t$ and that of renewable energy is $c_r$, and the cost of transmission and distribution of electricity and the rate of energy loss are not taken into consideration. Currently, the cost of renewable energy is decreasing year by year, but it still lacks competitiveness relative to fossil energy sources such as coal [33]; so, in this study, it was assumed that the unit production cost of renewable energy is greater than the unit production cost of thermal power, i.e., $c_r>c_t$.

Assumption 3.

In this paper, only the storage of renewable energy was considered, and thermal power storage was not considered. In order to mitigate the problem of intermittency of renewable energy and thus improve the stability of power supply, an effective solution is to invest in energy storage technology and equipment to maximize the balance between power supply and demand [34]. It was assumed that the investment cost of energy storage is related to the level of energy storage technology. In order to pursue a higher level of energy storage technology, a higher investment cost of energy storage needs to be invested in. Therefore, it can be assumed that the energy storage investment cost function of the power generator or energy storage provider is ${\displaystyle \frac{1}{2}}\beta t^2$ [35], where $\beta$ is the cost coefficient of energy storage investment. There exists a boundary condition for it, and when it is too high, it indicates that the current energy storage industry has not yet developed to the extent that it can support large-scale investment, and it needs to wait for further technological progress. This functional form is widely used in economic and engineering modeling to represent the case of increasing marginal costs, and can effectively represent the trend of rising costs during the advancement of energy storage technology.

Assumption 4.

When a power generator leases energy storage equipment from an energy storage provider, the equipment, technology, and services are all leased together with the energy storage equipment. In this paper, it was assumed that the cost that an energy storage provider charges is correlated with the equipment’s level of energy storage technology. Therefore, it was assumed that the cost function of energy storage equipment leasing for the power generator is $ft$ [32], where $f$ is the lease coefficient of the energy storage equipment.

The lease coefficient of the energy storage equipment was impacted by market considerations in this study, rather than being used as a decision variable. In the pre-development period of the energy storage industry, due to the high cost of investing in energy storage, few companies invested in energy storage; so, few companies in the market can provide leasing services. Therefore, the cost of leasing energy storage equipment was higher at this time. When the energy storage industry develops into a mature stage, the cost of leasing energy storage equipment will be reduced.

Assumption 5.

Electricity sellers are responsible for RPS and are required to provide consumers with a certain percentage of the total electricity supplied from renewable energy sources. Assume that one green certificate is issued for each unit of renewable energy produced by the power generator, and the two are bundled and sold to the electricity seller. The price of the green certificate is $p_c$, the renewable energy quota obligation is $\theta$, the amount of renewable energy purchased by the electricity seller from the power generator is $\theta q$, and the amount of thermal power is $(1-\theta )q$ [36].

Assumption 6.

Governments can support energy storage through two key channels: investment subsidy and discharge subsidy. The discharge amount of energy storage equipment is influenced by its storage capacity, discharge efficiency, discharge depth, etc. To simplify the model and parameters, the storage capacity, discharge efficiency, and discharge depth were uniformly summarized in this paper as the level of energy storage technology. The discharge amount of the energy storage equipment is positively correlated with the level of energy storage technology, and the higher the level of energy storage technology, the higher the discharge amount [37]. To simplify the subsequent calculations, this paper introduced the discharge coefficient of energy storage equipment $\gamma$, assuming that the discharge volume is a primary function of the energy storage technology level. Under the discharge subsidy, the government provides subsidies to energy storage investment enterprises by the standard of RMB $d$/kWh, and the amount of the discharge subsidy is $d\gamma q_e$. There is a boundary condition for $d$ such that, when it is too high, the marginal benefits of additional subsidies are reduced. This is because, at very high levels of subsidies, the costs of policy implementation and administration may outweigh the benefits. Under the investment subsidy, the government grants enterprises a certain percentage of the energy storage investment amount, and the amount of the investment subsidy is ${\displaystyle \frac{1}{2}}\alpha \beta t^2$, where $\alpha$ is the subsidy ratio of energy storage investment. There exists a boundary condition for $\alpha$ that, when too high, may lead to over-investment in energy storage technologies that are not yet cost-effective, thus reducing the overall return on investment.

3.1. Problem Modeling

To investigate the impacts of different energy storage models and energy storage subsidies on the energy storage decision-making of the power supply chain under RPS, four power supply chain decision-making models were constructed in this section with two models of power generator investing in energy storage or leasing energy storage equipment, and two energy storage policies of discharge subsidy or investment subsidy. The four models are denoted by superscripts 1, 2, 3, and 4, respectively, and (*) represents the equilibrium solution. The symbols involved in this paper and their meanings are explained in

Table 2. Notation and variable definitions.

Notation	Description
$w$	Wholesale electricity price
$q$	Electricity demand
$t$	Level of energy storage technology
$a$	Basic electricity demand of the market
$b$	Sensitivity coefficient of the energy storage technology level
$p$	Market price of electricity
$c_t$	Unit production cost of thermal power
$c_r$	Unit production cost of renewable energy
$d$	Subsidy amount per unit of discharge
$\alpha$	Subsidy ratio of energy storage investment
$\beta$	Cost coefficient of energy storage investment
$f$	Lease coefficient of energy storage equipment
$\gamma$	Discharge coefficient of energy storage equipment
$\theta$	Renewable energy quota obligation
$p_c$	Green certificate transaction price
${\pi }_G$	Power generation’s profit
${\pi }_S$	Power seller’s profit
${\pi }_E$	Energy storage provider’s profit

.

3.1.1. Scenario 1: Supply Chain Decision Model for the Power Generator Investing in Energy Storage Under Discharge Subsidy

The decision functions of the power generator and seller are, respectively:

$${\pi }_G^1=\theta q\left(w+p_c-c_r\right)+(1-\theta )q(w-c_t)-{\displaystyle \frac{1}{2}}\beta t^2+d\gamma q_e$$

(1)

$${\pi }_S^1=\theta q(p-p_c-w)+(1-\theta )q(p-w)$$

(2)

According to the inverse induction method, it can be obtained:

$$q^1={\displaystyle \frac{a+bt-w-p_c\theta }{2}}$$

(3)

When $\beta -{\displaystyle \frac{b^2}{4}}>0$ is satisfied, the Hessian matrix is negative definite and there are extreme values. Let ${\displaystyle \frac{\partial {\pi }_G}{\partial t}}=0$ and ${\displaystyle \frac{\partial {\pi }_G}{\partial w}}=0$, which yields:

$$t^{1*}={\displaystyle \frac{-4d\gamma +b(-a+c_t+c_r\theta -c_t\theta )}{b^2-4\beta }}$$

(4)

$$w^{1*}={\displaystyle \frac{-2bd\gamma +b^2[c_t+c_r\theta -\left(c_t+p_c\right)\theta ]-2\beta [a+c_t+c_r\theta -\left(c_t+2p_c\right)\theta ]}{b^2-4\beta }}$$

(5)

$$q^{1*}={\displaystyle \frac{-bd\gamma +\beta (-a+c_t+c_r\theta -c_t\theta )}{b^2-4\beta }}$$

(6)

Substituting Equations (4)–(6) into Equations (1) and (2) yields the equilibrium profits of the power generation’s profit and the power seller’s profit:

$$\begin{gathered} {\pi }_G^{1*}=-{\displaystyle \frac{1}{2\left(b^2-4\beta \right)}}[a^2\beta -2a{c}_t\beta +{c_t}^2\beta +2abd\gamma -2b{c}_{t}d\gamma +4d^2{\gamma }^2+2(-c_t \\ +ct)(a\beta -c_t\beta +bd\gamma )\theta +({c_r-c_t)}^2\beta {\theta }^2] \end{gathered}$$

(7)

$${\pi }_S^{1*}={\displaystyle \frac{{\{bd\gamma +\beta \left[a+c_t\left(-1+\theta \right)-c_r\theta \right]\}}^2}{{(b^2-4\beta )}^2}}$$

(8)

Proposition 1.

The optimal energy storage technology level $t^{1*}$, the optimal wholesale electricity price $w^{1*}$, the optimal demand $q^{1*}$, as well as the generator’s profit ${\pi }_G^{1*}$ and the seller’s profit ${\pi }_S^{1*}$ for the power supply chain in Scenario 1 are shown above.

3.1.2. Scenario 2: Supply Chain Decision Model for the Power Generator Investing in Energy Storage Under Investment Subsidy

The decision functions of the power generator and seller are, respectively:

$${\pi }_G^2=\theta q\left(w+p_c-c_r\right)+(1-\theta )q(w-c_t)-{\displaystyle \frac{1}{2}}\beta t^2+{\displaystyle \frac{1}{2}}\alpha \beta t^2$$

(9)

$${\pi }_S^2=\theta q\left(p-p_c-w\right)+(1-\theta )q(p-w)$$

(10)

According to the inverse induction method, it can be obtained:

$$q^2={\displaystyle \frac{a+bt-w-p_c\theta }{2}}$$

(11)

When $(1-\alpha )\beta -{\displaystyle \frac{b^2}{4}}>0$ is satisfied, the Hessian matrix is negative definite and there are extreme values. Let ${\displaystyle \frac{\partial {\pi }_G}{\partial t}}=0$ and ${\displaystyle \frac{\partial {\pi }_G}{\partial w}}=0$, which yields:

$$t^{2*}={\displaystyle \frac{b(-a+c_t+c_r\theta -c_t\theta )}{b^2+4(-1+\alpha )\beta }}$$

(12)

$$w^{2*}={\displaystyle \frac{b^2[c_t+c_r\theta -\left(c_t+pc\right)\theta ]+2(-1+\alpha )\beta [a+c_t+c_r\theta -\left(c_t+2p_c\right)\theta ]}{b^2+4(-1+\alpha )\beta }}$$

(13)

$$q^{2*}={\displaystyle \frac{\left(-1+\alpha \right)\beta [a+c_t(-1+\theta )-c_r\theta ]}{b^2+4(-1+\alpha )\beta }}$$

(14)

Substituting Equations (12)–(14) into Equations (9) and (10) yields the equilibrium profits of the power generation’s profit and the power seller’s profit:

$${\pi }_G^{2*}={\displaystyle \frac{(-1+\alpha )\beta {[a+c_t(-1+\theta )-c_r\theta ]}^2}{2b^2+8(-1+\alpha )\beta }}$$

(15)

$${\pi }_S^{2*}={\displaystyle \frac{{(-1+\alpha )}^2{\beta }^2{[a+c_t(-1+\theta )-c_r\theta ]}^2}{{[b^2+4\left(-1+\alpha \right)\beta ]}^2}}$$

(16)

Proposition 2.

The optimal energy storage technology level $t^{2*}$, the optimal wholesale electricity price $w^{2*}$, the optimal demand $q^{2*}$, as well as the generator’s profit ${\pi }_G^{2*}$ and the seller’s profit ${\pi }_S^{2*}$ for the power supply chain in Scenario 2 are shown above.

3.1.3. Scenario 3: Supply Chain Decision Model for the Power Generator Leasing Energy Storage Equipment Under Discharge Subsidy

The decision functions of the power generator, seller, and energy storage provider are, respectively:

$${\pi }_G^3=\theta q\left(w+p_c-c_r\right)+(1-\theta )q(w-c_t)-f{q}_e$$

(17)

$${\pi }_S^3=\theta q\left(p-p_c-w\right)+(1-\theta )q(p-w)$$

(18)

$${\pi }_E^3=f{q}_e-{\displaystyle \frac{1}{2}}\beta t^2+d\gamma q_e$$

(19)

According to the inverse induction method, it can be obtained:

$$q^3={\displaystyle \frac{a+b{q}_e-w-p_c\theta }{2}}$$

(20)

Next, the power generator decides on the wholesale electricity price $w$ and the energy storage provider decides on the level of energy storage technology $t$ simultaneously. It can be obtained that the wholesale electricity price $w$ and the level of energy storage technology $t$ are, respectively:

$$t^{3*}={\displaystyle \frac{f+d\gamma }{\beta }}$$

(21)

$$w^{3*}={\displaystyle \frac{1}{2}}[a+c_t+c_r\theta +{\displaystyle \frac{b\left(f+d\gamma \right)}{\beta }}-\left(c_r+2p_c\right)\theta ]$$

(22)

$$q^{3*}={\displaystyle \frac{b(f+d\gamma )+\beta [a+c_t(-1+\theta )-c_r\theta ]}{4\beta }}$$

(23)

Substituting Equations (21)–(23) into Equations (17) and (19) yields the equilibrium profits of the power generation’s profit, the power seller’s profit, and the energy storage provider’s profit:

$$\begin{gathered} {\pi }_G^{3*}={\displaystyle \frac{1}{8{\beta }^2}}\{b^2{\left(f+d\gamma \right)}^2+2b\beta (f+d\gamma )[a+c_t(-1+\theta )-c_r\theta ]+\beta \{-8f(f+d\gamma ) \\ +\beta {[a+c_t(-1+\theta )-c_r\theta ]}^2\}\} \end{gathered}$$

(24)

$${\pi }_S^{3*}={\displaystyle \frac{{\{b\left(f+d\gamma \right)+\beta \left[a+c_t\left(-1+\theta \right)-c_r\theta \right]\}}^2}{16{\beta }^2}}$$

(25)

$${\pi }_E^{3*}={\displaystyle \frac{{(f+d\gamma )}^2}{2\beta }}$$

(26)

Proposition 3.

The optimal energy storage technology level $t^{3*}$, the optimal wholesale electricity price $w^{3*}$, the optimal demand $q^{3*}$, as well as the generator’s profit ${\pi }_G^{3*}$ and the seller’s profit ${\pi }_S^{3*}$ for the power supply chain in Scenario 1 are shown above.

3.1.4. Scenario 4: Supply Chain Decision Model for the Power Generator Leasing Energy Storage Equipment Under Investment Subsidy

The decision functions of the power generator, seller, and energy storage provider are, respectively:

$${\pi }_G^4=\theta q\left(w+p_c-c_r\right)+(1-\theta )q(w-c_t)-f{q}_e$$

(27)

$${\pi }_S^4=\theta q\left(p-p_c-w\right)+(1-\theta )q(p-w)$$

(28)

$${\pi }_E^4=f{q}_e-{\displaystyle \frac{1}{2}}\beta t^2+{\displaystyle \frac{1}{2}}\alpha \beta t^2$$

(29)

According to the inverse induction method, it can be obtained:

$$q^4={\displaystyle \frac{a+b{q}_e-w-p_c\theta }{2}}$$

(30)

Next, the power generator decides on the wholesale electricity price $w$ and the energy storage provider decides on the level of energy storage technology $t$ simultaneously. It can be obtained that the wholesale electricity price $w$ and the level of energy storage technology $t$ are, respectively:

$$t^{4*}=-{\displaystyle \frac{f}{(-1+\alpha )\beta }}$$

(31)

$$w^{4*}={\displaystyle \frac{1}{2}}[a+c_t+c_r\theta +{\displaystyle \frac{bf}{\beta -\alpha \beta }}-\left(c_t+2p_c\right)\theta ]$$

(32)

$$q^{4*}={\displaystyle \frac{1}{4}}[a+{\displaystyle \frac{bf}{\beta (1-\alpha )}}+c_t(-1+\theta )-c_r\theta ]$$

(33)

Substituting Equations (31)–(33) into Equations (27) and (29) yields the equilibrium profits of the power generation’s profit, the power seller’s profit, and the energy storage provider’s profit:

$$\begin{array}{cc}\hfill {\pi }_G^{4*}={\displaystyle \frac{1}{8{\left(1-\alpha \right)}^2{\beta }^2}}& \{f^2[b^2+8\left(-1+\alpha \right)\beta ]-2bf(-1+\alpha )\beta [a+c_t(-1+\theta )-c_r\theta ]\hfill \\ \hfill +& {(-1+\alpha )}^2{\beta }^2{[a+c_t(-1+\theta )-c_r\theta ]}^2\}\hfill \end{array}$$

(34)

$${\pi }_S^{4*}={\displaystyle \frac{{\{bf+\left(1-\alpha \right)\beta \left[a+c_t\left(-1+\theta \right)-c_r\theta \right]\}}^2}{16{\left(-1+\alpha \right)}^2{\beta }^2}}$$

(35)

$${\pi }_E^{4*}={\displaystyle \frac{f^2}{2\beta (1-\alpha )}}$$

(36)

Proposition 4.

The optimal energy storage technology level $t^{4*}$, the optimal wholesale electricity price $w^{4*}$, the optimal demand $q^{4*}$, as well as the generator’s profit ${\pi }_G^{4*}$ and the seller’s profit ${\pi }_S^{4*}$ for the power supply chain in Scenario 1 are shown above.

3.2. Model Analysis

This section analyses the impacts of renewable energy quota obligation, subsidy amount per unit of discharge, and subsidy ratio of energy storage investment on the level of energy storage technology, electricity demand, power generator profits, and electricity seller profits. The equilibrium solutions for the four scenarios are also compared.

Inference 1.

As the renewable energy quota obligation increases, there is

(1) 

${\displaystyle \frac{\partial t^{1*}}{\partial \theta }}<0, {\displaystyle \frac{\partial t^{2*}}{\partial \theta }}<0, {\displaystyle \frac{\partial t^{3*}}{\partial \theta }}=0, {\displaystyle \frac{\partial t^{4*}}{\partial \theta }}=0;$

(2) 

${\displaystyle \frac{\partial q^{1*}}{\partial \theta }}<0, {\displaystyle \frac{\partial q^{2*}}{\partial \theta }}<0, {\displaystyle \frac{\partial q^{3*}}{\partial \theta }}<0, {\displaystyle \frac{\partial q^{4*}}{\partial \theta }}<0;$

(3) 

${\displaystyle \frac{\partial {\pi }_G^{1*}}{\partial \theta }}<0, {\displaystyle \frac{\partial {\pi }_G^{2*}}{\partial \theta }}<0, {\displaystyle \frac{\partial {\pi }_G^{3*}}{\partial \theta }}<0, {\displaystyle \frac{\partial {\pi }_G^{4*}}{\partial \theta }}<0;$

(4) 

${\displaystyle \frac{\partial {\pi }_S^{1*}}{\partial \theta }}<0, {\displaystyle \frac{\partial {\pi }_S^{2*}}{\partial \theta }}<0, {\displaystyle \frac{\partial {\pi }_S^{3*}}{\partial \theta }}<0, {\displaystyle \frac{\partial {\pi }_S^{4*}}{\partial \theta }}<0.$

Inference 1(1) demonstrates that, as the renewable energy quota obligation increases, the investment of the generator in the level of energy storage technology decreases. The reason for this is that, when the renewable energy quota obligation increases, the power generator is required to create a greater amount of renewable energy. According to Zou et al., the cost of renewable energy can be competitive with fossil energy by 2030–2050 as the relevant technology matures [33]. Therefore, at present, this study continues to believe that the cost of producing renewable energy is higher than that of conventional thermal power. Due to resource constraints, the increase in the cost of power generation will cause power producers to consider reducing the cost of investing in energy storage, thus inhibiting the level of energy storage technology. Furthermore, the level of energy storage technology will remain unchanged in both generator leasing scenarios with the increase in the renewable energy quota obligation. Since the energy storage provider determines the level of energy storage technology in both scenarios, the RPS does not impose any limitations on the energy storage provider. Inference 1(2) demonstrates that the electricity demand decreases in all scenarios as the renewable energy quota obligation increases. This is because, in generator investment scenarios, a decrease in the level of energy storage technology results in a drop in the amount of electricity needed. In generator leasing scenarios, when the renewable energy quota obligation increases, the electricity seller’s profit decreases. To compensate, the seller often raises the market price of electricity to improve their profit. However, this increase in price results in a fall in the electricity demand. Inference 1(3)–(4) show that, as the renewable energy quota obligation increases, the profits of both the power generator and seller decrease. The increase in the renewable energy quota obligation leads to an increase in the cost of electricity generation for the generator and the cost of obtaining green certificates for the electricity seller. Consequently, both profits decline.

Inference 2.

As the subsidy amount per unit of discharge increases, there is

(1) 

${\displaystyle \frac{\partial t^{1*}}{\partial d}}>0, {\displaystyle \frac{\partial t^{3*}}{\partial d}}>0;$

(2) 

${\displaystyle \frac{\partial q^{1*}}{\partial d}}>0, {\displaystyle \frac{\partial q^{3*}}{\partial d}}>0;$

(3) 

${\displaystyle \frac{\partial {\pi }_G^{1*}}{\partial d}}>0, when 0<f<f_1, {\displaystyle \frac{\partial {\pi }_G^{3*}}{\partial d}}>0, when f>f_1, {\displaystyle \frac{\partial {\pi }_G^{3*}}{\partial d}}<0;$

(4) 

${\displaystyle \frac{\partial {\pi }_S^{1*}}{\partial d}}>0, {\displaystyle \frac{\partial {\pi }_S^{3*}}{\partial d}}>0.$

• $f_1={\displaystyle \frac{b\{bd\gamma +\beta \left[a+c_t\left(-1+\theta \right)-c_r\theta \right]\}}{4\beta -b^2}}$

Inference 2(1)–(2) show that, as the subsidy amount per unit of discharge increases, both the level of energy storage technology and the electricity demand rise. A larger subsidy per unit of discharge reduces the financial burden of investing in energy storage, making investors more inclined to invest more in higher technology levels. Advanced energy storage technology results in a more reliable electricity supply, hence boosting electricity demand. Inference 2(3) demonstrates that, as the subsidy for energy storage per unit of discharge increases, the power generator’s profit in the generator investment scenario increases. However, in the generator leasing scenario, the power generator’s profit first grows and subsequently decreases. In the generator investment scenario, the increase in the subsidy amount per unit of discharge will provide the generator with more financial assistance. Additionally, an increase in electricity demand will result in higher profits from the sale of electricity. In the generator leasing scenario, when the energy storage subsidy per unit of discharge exceeds a certain threshold, the energy storage provider is inclined to make substantial investments in energy storage technology. When the energy storage technology reaches a high level, the generator’s profit decreases since the cost of leasing storage equipment exceeds the revenue gained from selling additional electricity. Inference 2(4) shows that, as the subsidy amount per unit of discharge increases, the power seller’s profit rises in all cases. This is because the power seller’s profit is not affected by the energy storage factor and increases only due to the increase in electricity demand.

Inference 3.

As the subsidy ratio of energy storage investment increases, there is

(1) 

${\displaystyle \frac{\partial t^{2*}}{\partial \alpha }}>0, {\displaystyle \frac{\partial t^{4*}}{\partial \alpha }}>0;$

(2) 

${\displaystyle \frac{\partial q^{2*}}{\partial \alpha }}>0, {\displaystyle \frac{\partial q^{4*}}{\partial \alpha }}>0;$

(3) 

${\displaystyle \frac{\partial {\pi }_G^{2*}}{\partial \alpha }}>0, when 0<f<f_2, {\displaystyle \frac{\partial {\pi }_G^{4*}}{\partial \alpha }}>0, when f>f_2, {\displaystyle \frac{\partial {\pi }_G^{4*}}{\partial \alpha }}>0;$

(4) 

${\displaystyle \frac{\partial {\pi }_S^{2*}}{\partial \alpha }}>0, {\displaystyle \frac{\partial {\pi }_S^{4*}}{\partial \alpha }}>0.$

• $f_2={\displaystyle \frac{b\left(-1+\alpha \right)\beta [a+c_t(-1+\theta )-c_r\theta ]}{b^2+4(-1+\alpha )\beta }}$

Inference 3(1)–(2) show that both the level of energy storage technology and electricity demand rise as the subsidy ratio of energy storage investment increases. The reason is similar to those assigned to Inferences 2(1)–(2) and will not be repeated here. Inference 3(3) shows that, as the subsidy ratio of energy storage investment increases, the power generator’s profit in the generator investment scenario also increases, while the power generator’s profit in the generator leasing scenario first grows and subsequently decreases. The reason is similar to that for Inference 2(3). Inference 3(4) shows that the power seller’s profit increases in all scenarios as the subsidy ratio of energy storage investment increases. The reason is similar to that for Inference 2(4).

Inference 4.

Comparison of discharge subsidy and investment subsidy in the scenario where the power generator invests in energy storage

(1) 

$\mathit{When} 0<\alpha <{\alpha }_1,t^{1*}>t^{2*}; \mathit{when} {\alpha }_1<\alpha <1,t^{1*}<t^{2*}$.

(2) 

$\mathit{When} 0<\alpha <{\alpha }_1,q^{1*}>q^{2*}; \mathit{when} {\alpha }_1<\alpha <1,q^{1*}<q^{2*}$.

(3) 

$\mathit{When} 0<\alpha <{\alpha }_2,{\pi }_G^{1*}>{\pi }_G^{2*}; \mathit{when} {\alpha }_2<\alpha <1,{\pi }_G^{1*}<{\pi }_G^{2*}$.

(4) 

$\mathit{When} 0<\alpha <{\alpha }_1,{\pi }_S^{{1*}^{*}}>{\pi }_S^{2*}; \mathit{when} {\alpha }_1<\alpha <1,{\pi }_S^{1*}<{\pi }_S^{2*}$.

• ${\alpha }_1={\displaystyle \frac{d\gamma ({4\beta -b}^2)}{\beta \{4d\gamma +b\left[a+c_t\left(-1+\theta \right)-c_r\theta \right]\}}},{\alpha }_2={\displaystyle \frac{2d\left(4\beta {-b}^2\right)\gamma \{2d\gamma +b\left[a+c_t\left(-1+\theta \right)-c_r\theta \right]\}}{\beta {\{4d\gamma +b\left[a+c_t\left(-1+\theta \right)-c_r\theta \right]\}}^2}}$

Inference 4(1)–(2) demonstrate that, when the subsidy ratio of energy storage investment is above the threshold ${\alpha }_1$, the investment subsidy has a greater capacity to enhance the level of energy storage technology and stimulate electricity demand. This is because a higher subsidy ratio for energy storage investment allows the power generator to obtain more financial support through the investment subsidy. As a result, they will have more funds available to invest in energy storage, which in turn promotes the level of energy storage technology. Since electricity demand is positively correlated with the level of energy storage technology, an increase in the latter will result in a corresponding increase in the former. When the subsidy ratio of energy storage investment is low, the financial assistance received by the generator through the investment subsidy will be comparatively less than the discharge subsidy. This leads to a higher level of energy storage technology and electricity demand under the discharge subsidy. In addition, the threshold ${\alpha }_1$ is negatively correlated with the sensitivity coefficient of energy storage technology level, which is lower as the consumer prefers a more stable electricity supply. Thus, if customers exhibit a stronger preference towards the level of energy storage technology, the government can implement more investment subsidies, which will be more favorable to the level of energy storage technology and electricity demand.

Inference 4(3) demonstrates that the investment subsidy benefits the power generator’s profit more when the subsidy ratio of energy storage investment exceeds the threshold ${\alpha }_2$. This is because when the government sets a low investment subsidy ratio, the generator receives less financial support through the investment subsidy compared to the discharge subsidy. In this case, the discharge subsidy is more favorable to the power generator’s profit, and vice-versa for the investment subsidy. In addition, the threshold ${\alpha }_2$ is positively correlated with the cost coefficient of energy storage investment. As the energy storage industry develops, the cost coefficient of energy storage investment will decrease due to the learning effect and scale effect. Therefore, when the energy storage industry reaches a mature stage, the investment subsidy becomes more advantageous for the power generator’s profit. Inference 4(3) demonstrates that, when the subsidy ratio of energy storage investment is high, the investment subsidy has a more favorable impact on the power seller’s profit improvement. This is because the level of storage technology, electricity demand, and market price of electricity are higher under investment subsidy, and therefore, the power seller’s profit is higher.

Inference 5.

Comparison of discharge subsidy and investment subsidy in the scenario where the power generator leases energy storage equipment

(1) 

$\mathit{When} 0<\alpha <{\alpha }_3,t^{3*}>t^{4*}; \mathit{when} {\alpha }_3<\alpha <1,t^{{3*}^{*}}<t^{4*}$.

(2) 

$\mathit{When} 0<\alpha <{\alpha }_3,q^{3*}>q^{{IL}^{*}}; \mathit{when} {\alpha }_3<\alpha <1,q^{3*}<q^{{4*}^{*}}$.

(3) 

$\mathit{When} 0<f<f_3\mathit{or} f>f_4,{\pi }_G^{3*}>{\pi }_G^{4*}; \mathit{when} f_3<f<f_4,{\pi }_G^{3*}<{\pi }_G^{4*}$.

(4) 

$\mathit{When} 0<\alpha <{\alpha }_3,{\pi }_S^{3*}>{\pi }_S^{4*}; \mathit{when} {\alpha }_3<\alpha <1,{\pi }_S^{3*}<{\pi }_S^{4*}$.

• ${\alpha }_3={\displaystyle \frac{d\gamma }{f+d\gamma }},f_3={\displaystyle \frac{b\left(1-\alpha \right)\{bd\gamma +2\beta \left[a+c_t\left(-1+\theta \right)-c_r\theta \right]\}}{b^2(-2+\alpha )-8(-1+\alpha )\beta }}, f_4={\displaystyle \frac{d\gamma (1-\alpha )}{\alpha }}$

Inference 5(1)–(2) demonstrate that, when the subsidy ratio of energy storage investment is below the threshold ${\alpha }_3$, the discharge subsidy has a stronger positive impact on the level of energy storage technology and electricity demand. This occurs because a fall in the investment subsidy ratio results in a reduction in the financial support received by the energy storage provider, who acts as the investor in energy storage. Consequently, their motivation to invest in energy storage diminishes. Consumer preference for energy storage technology directly affects electricity demand. When energy storage technology is at a lower level, electricity demand decreases accordingly. In the pre-development period of the energy storage industry, energy storage technologies are not yet fully mature, and the initial investment costs of the equipment are relatively high. Consequently, the lease coefficient of energy storage equipment $f$ is also higher. Since the threshold ${\alpha }_3$ is negatively correlated with $f$, ${\alpha }_3$ is relatively low at this stage, and the subsidy ratio of energy storage investment is likely to exceed this threshold. It is recommended that the government implement more investment subsidies. The practical reason is that the cost of investing in energy storage technologies is relatively high at this stage, which reduces the willingness to invest. The government needs to provide a higher subsidy ratio of energy storage investment to encourage investment in energy storage technologies and thereby promote the improvement in energy storage technology levels. Therefore, in the early stages of energy storage industry development, it is recommended that the government implement more investment subsidy policies. However, as the energy storage industry gradually matures, technologies continue to advance, equipment costs gradually decrease, and the market scale expands, the lease coefficient will also decrease accordingly. Implementing discharge subsidies can more directly increase the utilization rate of energy storage equipment, increase discharge volumes, and thereby enhance energy storage technology levels and electricity demand.

Inference 5(3) demonstrates that, if the lease coefficient of energy storage equipment is either too low or too high, the discharge subsidy is more conducive to the power generator’s profit. This is because the low lease coefficient of energy storage equipment leads to a high ${\alpha }_3$, then the level of storage technology and electricity demand under the discharge subsidy is more likely to be higher than under the investment subsidy. As a result, the power generator under the discharge subsidy can generate more profit by selling electricity. When the lease coefficient of energy storage equipment is too high, the revenue generated by energy storage is insufficient to offset the cost of the lease. At this time, ${\alpha }_3$ is low, indicating that the level of energy storage technology under the discharge subsidy is lower than that under the investment subsidy, and therefore, the generator’s storage leasing cost is lower; so, the generator’s profit under the discharge subsidy will be relatively higher. Inference 5(4) demonstrates that a lower lease coefficient of energy storage equipment leads to a more advantageous discharge subsidy for the power seller’s profit. The reason is similar to that for Inference 4(4).

Inference 6.

Comparison of the scenarios where the power generator invests in energy storage or leases energy storage equipment under the discharge subsidy policy

(1) 

$\mathit{When} 0<f<f_5,t^{1*}>t^{3*}; \mathit{when} f>f_5,t^{1*}<t^{3*}$.

(2) 

$\mathit{When} 0<f<f_5,q^{1*}>q^{3*}; \mathit{when} f>f_5,q^{1*}<q^{3*}$.

(3) 

${\pi }_G^{1*}>{\pi }_G^{3*}$.

(4) 

$\mathit{When} 0<f<f_5,{\pi }_S^{1*}>{\pi }_S^{3*}; \mathit{when} f>f_5,{\pi }_S^{1*}<{\pi }_S^{3*}$.

• $f_5={\displaystyle \frac{b\{bd\gamma +\beta \left[a+c_t\left(-1+\theta \right)-c_r\theta \right]\}}{4\beta -b^2}}$

Inference 6(1)–(2) demonstrate that, when the lease coefficient of energy storage equipment is below the threshold $f_5$, it is more advantageous for the power generator to make its investment in energy storage, considering the level of energy storage technology and electricity demand. When the lease coefficient of energy storage equipment is high, it indicates that the energy storage industry is in its early stage. Encouraging power generators to lease energy storage equipment can not only reduce their initial investment risks but also accelerate the dissemination of and improvement in technology through learning effects. As the industry matures, power generators directly invest in energy storage equipment, enabling them to fully exploit economies of scale, reduce unit costs, and thereby promote the improvement in energy storage technology levels and the increase in electricity demand. In addition, the threshold $f_5$ is positively correlated with the subsidy amount per unit of discharge. Therefore, when the energy storage industry is dominated by power generators, the government can increase this threshold $f_5$ by increasing the subsidy amount per unit of discharge. Whereas when the energy storage industry is dominated by energy storage providers, the government can increase the threshold $f_5$ by decreasing the subsidy amount per unit of discharge. This will help maximize the overall level of energy storage technology and electricity demand. In addition, $f_5$ is also positively correlated with the sensitivity coefficient of energy storage technology level. Thus, when consumers have a stronger preference towards a specific level of energy storage technology, investment in energy storage by generators is more favorable to the level of storage technology and electricity demand.

Inference 6(3) demonstrates that the power generator’s profit in the generator investment scenario is higher than that in the generator leasing scenario. The discharge subsidy can efficiently alleviate the cost of the generator’s investment in energy storage. Inference 6(4) demonstrates that, when the lease coefficient of energy storage equipment is below the threshold $f_5$, the generator investment scenario is more favorable to the power seller’s profit. The reason is similar to that for Inference 4(4).

Combined with Corollary 6(1)–(4), it can be seen that, when the lease coefficient of energy storage equipment is below the threshold $f_5$, all equilibrium solutions in the generator investment scenario will exceed those in the generator leasing scenario. In turn, this threshold is positively correlated with the subsidy amount per unit of discharge. Therefore, if the government implements a discharge subsidy, it is advisable to incentivize power generators to invest in energy storage when the subsidy amount per unit of discharge is high. This will guarantee that the level of energy storage technology, electricity demand, power generators’ profits, and power sellers’ profits are all relatively better.

Inference 7.

Comparison of the scenarios where the power generator invests in energy storage or leases energy storage equipment under the investment subsidy policy

(1) 

$\mathit{When} 0<f<f_6,t^{2*}>t^{4*}; \mathit{when} f>f_6,t^{2*}<t^{4*}$.

(2) 

$\mathit{When} 0<f<f_6,q^{2*}>q^{4*}; \mathit{when} f>f_6,q^{2*}<q^{4*}$.

(3) 

${\pi }_G^{2*}>{\pi }_G^{4*}$.

(4) 

$\mathit{When} 0<f<f_6,{\pi }_S^{2*}>{\pi }_S^{4*}; \mathit{when} f>f_6,{\pi }_S^{2*}<{\pi }_S^{4*}$.

• $f_6={\displaystyle \frac{b\left(1-\alpha \right)\beta [a+c_t(-1+\theta )-c_r\theta ]}{4\beta \left(1-\alpha \right)-b^2}}$

Inference 7(1)–(2) demonstrate that, when the lease coefficient of energy storage equipment exceeds the threshold $f_6$, it is more favorable for the power generator to lease energy storage equipment to increase the level of energy storage technology and electricity demand, for the same reason as that for Inference 6. In addition, the threshold $f_6$ is negatively correlated with the sensitivity coefficient of energy storage technology level. When consumer preference for energy storage is stronger, the level of energy storage technology and electricity demand in the generator leasing scenario is more likely to be greater than in the generator investment scenario. As a result, generators are more inclined to lease energy storage equipment at this time.

Inference 7(3) demonstrates that the power generator’s profit is higher in the generator investment scenario than in the generator leasing scenario. The reason is similar to that for Inference 6(3) and will not be repeated here. Inference 7(4) demonstrates that, when the lease coefficient of energy storage equipment is below the threshold $f_6$, the generator investment scenario is more favorable to the power seller’s profit. The reason is similar to that for Inference 6(4).

Combined with Corollary 7(1)–(4), it can be seen that, when the lease coefficient of energy storage equipment is below the threshold $f_6$, all equilibrium solutions in the generator investment scenario exceed those in the generator leasing scenario. The threshold is positively correlated with the lease coefficient of energy storage equipment. Thus, when the government implements the investment subsidy, it is advisable to incentivize power generators to invest in energy storage if the subsidy ratio is large. This will guarantee that the level of energy storage technology, electricity demand, power generators’ profits, and power sellers’ profits are all relatively better.

4. Numerical Analysis

In this section, we employ numerical analysis methods to effectively show the impact of energy storage models and energy storage subsidies on the decision-making of the power supply chain under RPS. This section refers to Yan et al. and Chen et al. and energy storage subsidy policies implemented by various provinces and cities in China [22,32].

4.1. Impact of Renewable Energy Quota Obligation and Subsidy Amount per Unit of Discharge on Equilibrium Solutions

This section analyses the impact of renewable energy quota obligation and subsidy amount per unit of discharge on the equilibrium solution. The parameters were set as $a=10$, $b=0.6$, $f=0.5$, $c_t=0.3$, $c_r=0.4$, $\alpha =0.1$, $\gamma =0.8$, and $\beta =0.5$, and we took $\theta \in (\mathrm{0,1})$ and $d\in (\mathrm{0,1})$. Observing Figure 3a–d, we find:

Figure 3a shows that the level of energy storage technology in scenarios 1 and 2 decreases as the renewable energy quota obligation increases, and the level of energy storage technology in scenarios 1 and 3 increases as the subsidy amount per unit of discharge increases. Figure 3b shows that the electricity demand decreases with the increase in renewable energy quota obligation in all four scenarios, and the electricity demand increases with the increase in subsidy amount per unit of discharge in scenarios 1 and 3. Figure 3c,d shows that the power generator’s profit and power seller’s profit decreases with the increase in renewable energy quota obligation in all four scenarios, and the power generator’s profit and power seller’s profit increases with the increase in subsidy amount per unit of discharge in scenarios 1 and 3, which aligns with Inference 1. From Inference 1, it can be inferred that the renewable energy quota obligation has a negative impact on the equilibrium solution in all scenarios. However, when looking at the graph trend, it is evident that the inhibitory effect of the renewable energy quota obligation on the equilibrium solution is quite small compared to the effect of the subsidy amount per unit of discharge. Although RPS may reduce the level of energy storage technology and electricity demand, the implementation of a discharge subsidy can easily offset the suppressive effects of the RPS, even if the subsidy amount per unit of discharge is relatively small. Furthermore, RPS ensures the consumption of renewable energy; hence, the overall advantages surpass the drawbacks. In addition, the threshold of the subsidy amount per unit of discharge for each equilibrium solution in scenario 3 over scenario 4 is relatively small, between 0 and 0.1. It is worth noting that the storage subsidy policies implemented in China indicate that there is virtually no subsidy amount per unit of discharge within this range in practical terms. Consequently, the discharge subsidy in the generator leasing scenario exhibits a more favorable policy impact compared to the investment subsidy.

4.2. Impact of Renewable Energy Quota Obligation and Subsidy Ratio of Energy Storage Investment on the Equilibrium Solution

This section analyses the impact of renewable energy quota obligation and subsidy ratio of energy storage investment on the equilibrium solution. The parameters were set as $a=10$, $b=0.6$, $f=0.5$, $c_t=0.3$, $c_r=0.4$, $\gamma =0.8$, $\beta =0.5$, and $d=0.3$, and we took $\theta \in (\mathrm{0,1})$ and $\alpha \in (\mathrm{0,0.4})$. As can be seen from the implemented energy storage subsidy policies, no investment subsidy policy in practice sets the ratio at greater than 30%. The upper limit of a was set to 40% to facilitate a more intuitive comparison. Observing Figure 4a–d, we find:

Figure 4a shows that the level of energy storage technology in scenarios 2 and 4 increases as the subsidy ratio of energy storage investment increases. This effect is particularly prominent in scenario 2, where a higher subsidy ratio leads to a more significant increase in the level of energy storage technology. Figure 4b shows that the electricity demand in scenarios 2 and 4 increases with the increase in the subsidy ratio of energy storage investment. Figure 4c,d show that the power generator’s profit and the power seller’s profit in scenarios 2 and 4 increase with the increase in the subsidy ratio of energy storage investment. Similar to the findings in Section 4.1, it is evident here that the reduction in the equilibrium solution caused by the renewable energy quota obligation is minimal compared to the influence of the subsidy ratio of energy storage investment. And the implementation of investment subsidies can easily compensate for this disincentive. Considering that RPS guarantees the consumption of renewable energy, it is beneficial to simultaneously apply RPS and investment subsidies. In addition, the threshold of the subsidy ratio of energy storage investment for each equilibrium solution in scenario 4 over scenario 3 is relatively large, ranging from 0.3 to 0.4. It is worth noting that the storage subsidy policies implemented in China indicate that there is virtually no subsidy ratio of energy storage investment within this range in practical terms. Therefore, the policy impact of the discharge subsidy in the generator leasing scenario is more favorable compared to the investment subsidy. Furthermore, the magnitude of the growth in each equilibrium solution in the generator investment scenario becomes more pronounced when the subsidy ratio of energy storage investment rises. This indicates that the impact of the policy is more noteworthy when power generators invest in energy storage under the investment subsidy policy.

The implementation of RPS can increase the consumption of renewable energy and enhance environmental benefits. However, it will also increase the production cost of renewable energy and the intermittency problem will affect the stability of power supply, which will affect the profit of power producers. However, combining Figure 3c and Figure 4c, it can be observed that, under the combination of RPS and energy storage subsidy policy, the profit of power producers is enhanced. This is because, on the one hand, the electricity consumption side favors more stable electricity, and the improvement in the level of energy storage technology enhances the stability of electricity and raise the demand for electricity, thus boosting the profitability of power generators. On the other hand, the addition of the energy storage subsidy policy can very effectively reduce the pressure on power generators to invest in energy storage, thereby reducing the cost of energy storage investment.

4.3. Impact of Lease Coefficient of Energy Storage Equipment on the Equilibrium Solution

This section analyses the impact of the lease coefficient of energy storage equipment on the equilibrium solution. The parameters were set as $a=10$, $b=0.6$, $c_t=0.3$, $c_r=0.4$, $\alpha =0.1$, $\gamma =0.8$, $\beta =0.5$, $d=0.3$, and $\theta =0.3$, and we took $f\in (\mathrm{0,1})$. Observing Figure 5a–d, we find:

Scenarios 1 and 2 are both the generator investment scenarios. The equilibrium solutions for these scenarios do not depend on the lease coefficient of energy storage equipment. To facilitate observation and comparison, these two scenarios are also depicted in the image. Figure 5a,b,d show that the level of energy storage technology, the electricity demand, and the power seller’s profit in scenarios 3 and 4 all increase when the lease coefficient of energy storage equipment increases. When $f<1$, the equilibrium solutions in scenarios 3 and 4 are smaller than those in scenarios 1 and 2, and they tend to surpass the equilibrium solutions in scenarios 1 and 2. Nevertheless, the lease coefficient of energy storage equipment in practice has already surpassed the range established in this study, making it challenging to obtain such a high number. Thus, it can be inferred that, overall, the energy storage technology level, electricity demand, and power seller’s profit are higher in the generator investment scenario compared to the generator leasing scenario. It is worth noting that, in Figure 5c, the power generator’s profit grows and subsequently decreases when the lease coefficient of energy storage equipment increases in scenarios 3 and 4, and it does not surpass the power generator’s profits in scenarios 1 and 2. This is because, in our model, the profit of the electricity generator in the scenario of generator leasing is affected by both the cost of the energy storage lease and the revenue from electricity sales. The cost of leasing energy storage equipment is directly related to lease coefficient of energy storage equipment $f$. Revenue from electricity sales is affected by the level of energy storage technology, which in turn affects the stability and reliability of electricity supply. Higher levels of energy storage technology lead to a higher demand for electricity, which in turn leads to higher revenues. However, when f exceeds a certain threshold, the additional cost of leasing energy storage equipment can begin to outweigh the increased revenue from electricity sales. It is clear from Figure 5c that there exists a value of $f$ that makes the generator’s profit optimal, and the generator can flexibly adjust its storage strategy by observing the cost of storage leasing in the market.

5. Conclusions and Policy Implications

Despite the promise of energy storage to enhance the proliferation of renewable energy, there is presently insufficient research regarding the influence of various energy storage policies and models on decision-making within the power supply chain. Therefore, this article focused on the impact of different energy storage subsidy policies combined with different energy storage models under RPS, which provides a basis for energy storage decision-making in the electricity supply chain. In this article, four scenarios were presented and two types of supply chain models were developed to illustrate this point. By analyzing the equilibrium solutions, we identified the following key findings:

• In the scenario of generator investment or generator leasing, a higher subsidy ratio for energy storage investment is advantageous in increasing the level of energy storage technology and electricity demand. During the pre-development stage of the energy storage industry, stable power supply is crucial for the power consumption side. If power generators invest in energy storage, it will be more beneficial for the investment subsidy to enhance the level of energy storage technology and electricity demand. Additionally, during this time, the lease coefficient of energy storage equipment is also relatively high. Consequently, if power generators opt to lease energy storage equipment, it will be more beneficial for the investment subsidies to enhance the level of energy storage technology and electricity demand. Conversely, in the mature stage of the energy storage industry, regardless of the energy storage models, it is more beneficial for discharge subsidies to enhance both levels of technology and electricity demand.
• The model of power generators investing in energy storage becomes more advantageous for increasing their profits when the discharge subsidy or investment subsidy is implemented. When the lease coefficient of energy storage equipment is low, this model also becomes more favorable for enhancing energy storage technology and meeting electricity demand. In the early stages of development in the energy storage industry, the lease coefficient of energy storage equipment tends to be high, leading power generators to invest in energy storage equipment primarily to maximize their profits. However, this approach does not contribute significantly to improving the level of energy storage technology or meeting electricity demand. Conversely, in the mature stage of the energy storage industry, power generators choose to invest in energy storage not only to maximize their profits but also to enhance the level of energy storage technology and meet electricity demand.
• An increase in either the subsidy amount per unit of discharge or the subsidy ratio of energy storage investment has a positive impact on the level of energy storage technology, electricity demand, and the profits of electricity sellers. This policy effect is particularly significant when power generators invest in energy storage under the investment subsidy policy. In the mature stage of the energy storage industry, when the subsidy ratio of energy storage investment is low, power generators can improve their profits by relying on a higher subsidy amount per unit of discharge or a higher subsidy ratio of energy storage investment.
• The increase in the renewable energy quota obligation imposes constraints on energy storage technology, electricity demand, and the revenues of power generators and sellers. However, whether it is implemented with a discharge subsidy or an investment subsidy, its constraining effect is relatively minor. The Renewable Portfolio Standard (RPS) significantly influences the consumption of renewable energy. As the quota obligation increases, so does the consumption of renewable energy. Therefore, RPS plays a beneficial role in advancing renewable energy.

The aforementioned findings may offer valuable managerial insights and policy implications.

Firstly, when the government considers providing subsidies for energy storage or when power generators choose energy storage models, it is important to consider the level of preference that consumers have for a reliable electricity supply. If consumers strongly prefer a certain level of energy storage technology, then government investment subsidies will be more beneficial in promoting the adoption of advanced energy storage technology and meeting electricity demand. Similarly, if consumers have a strong preference for specific energy storage technology when discharge subsidies are implemented by the government, power generators may choose to invest independently in order to maximize profits and meet consumer demands. In cases where consumers strongly favor particular levels of energy storage technology while the government implements investment subsidies, additional incentives should be provided to power generators who opt to lease energy storage equipment. This approach will encourage power generators to lease energy storage equipment and ultimately promote the advancement of energy storage technology and meet electricity demand.

Secondly, when the government considers providing subsidies for energy storage or when power generators are choosing energy storage models, it is important to consider the different development stages of the energy storage industry. During the pre-development stage of the energy storage industry, it is recommended that the government implement an investment subsidy policy and encourage power generators to lease energy storage equipment. As the energy storage industry matures, it is recommended that the subsidy ratio of energy storage investment be gradually reduced. This will help prompt energy storage investment companies to stop relying on subsidies and focus on improving their technological competitiveness, which will in turn promote sustainable development of the industry. In implementing this policy, the government may also consider providing additional incentives to power generators who choose to lease energy storage equipment. This approach will restructure the energy storage industry towards a focus on power generators leasing energy storage equipment, which can promote advancements in energy storage technology and meet electricity demand. When the energy storage industry develops to a mature stage, it is advisable for the government to implement discharge subsidies and encourage power generators to invest in their own energy storage systems. By increasing the subsidy amount per unit of discharge, more power generators can be encouraged to invest in this technology. This strategy will shift focus within the industry towards power generator investment in their own energy storage systems, promoting further improvements in technology and meeting electricity demand.

Finally, it is imperative for the government to persist in enforcing RPS. As renewable energy technology advances, it is essential to gradually raise the renewable energy quota obligation to encourage the consumption of renewable energy. Moreover, the government can simultaneously implement an energy storage subsidy policy alongside RPS. On the one hand, RPS holds the authority to establish quota obligations and compel enterprises to consume renewable energy. On the other hand, the purpose of the energy storage subsidy is to enhance energy storage technology and improve the stability of renewable energy. This will ultimately enable firms to consume more renewable energy and assist them in meeting their RPS consumption objectives.