The Benefit Realization Mechanism of Pumped Storage Power Plants Based on Multi-Dimensional Regulation and Leader-Follower Decision-Making

Abstract

The roles and benefits of pumped storage are reflected in different stakeholders of the power system. The multi-dimensionality and non-linearity of pumped storage multi-stakeholder decision-making make pumped storage benefit realization a hot research topic with challenges. This paper takes pumped storage benefit sharing as the breakthrough. It adopts multiple regulation strategies and multi-level decision-making measures based on the multiple objectives of different stakeholders. A method and a framework for pumped storage benefit realization are proposed. This paper proposes the objective function system with the fairness objective at the leader level, the participation objective at the secondary leader level, and the efficiency objective at the follower level. It also constructs a three-level Leader-Follower objective model with multi-dimensional regulation and multiple values, and it develops the corresponding solution method based on Stackelberg dynamic game and interactive algorithms. The results reveal that the values of fairness, participation, and efficiency indicators of the pumped storage plant are 1.75%, 0.25%, and 9.75%, respectively, and all the indicators meet the requirements. The research results are conducive to promoting the realization of a win-win situation for different stakeholders of pumped storage, and they highlight how pumped storage plants can fulfill their functions in the power system as well as ensure its survival and development.

1. Introduction

As the world’s dominant energy storage technology, pumped storage hydropower plants accounted for 94% of the world’s total power storage projects up to the end of 2020 [1]. China has a vast territory and relatively abundant resources for building pumped storage plants. It currently has an installed capacity of 52.2 GW of pumped storage and will continue to dominate the market for new nuclear power construction in the future. According to China’s medium- and long-term development plan for pumped storage, site selection and planning for pumped storage have been comprehensively carried out nationwide, with a total installed capacity planned to exceed 62 GW by 2025, reaching about 120 GW by 2030. Pumped storage hydropower can assist in peak shaving, frequency and phase modulation, spinning reserve, and ramping, which brings significant economic benefits to the power grid, pumped storage plants, other power sources, and power users. In addition, the evolution of power system reform in China, especially the separation of power plants from the grid, has increased the number of stakeholders from one to several [2,3,4]. In this context, it is important to assess the benefit realization mechanism of pumped storage to promote its construction.

Many studies have been conducted to evaluate the benefits of pumped storage, including economic [5], technical [6], and environmental benefits [7]. However, there is a lack of research on the mechanism of distributing benefits and costs among multiple stakeholders, which is crucial for the construction and long-term development of pumped storage. To evaluate the economic benefit of pumped storage, it is not only necessary to scientifically and accurately define and quantify the total amount of economic benefits but to also objectively and reasonably allocate the benefits to different stakeholders to achieve reasonable compensation and sustainable development among different stakeholders [8,9,10]. To determine reasonable compensation, the economic benefits generated by pumped storage power plants for the power grid, pumped storage power plants, other power sources, and electricity users must be converted into reasonable financial incomes following the principle of “who benefits, who compensates” to achieve mutually beneficial cooperation between pumped storage and related stakeholders [11,12,13].

The evaluation of pumped storage should directly reflect the changes in costs and benefits of different stakeholders and should not simply be a weighted sum [9,10]. The operation of pumped storage requires the redistribution of revenues and benefits among different stakeholders through public pricing, investment allocation, and treatment of externalities [14,15]. The evaluation, from the perspective of stakeholders, is conducted by calculating costs and benefits; however, it considers the interests of different stakeholders, reflecting the goals of efficiency, participation, and fairness of multiple stakeholders in modern social development [16,17,18,19,20,21]. Therefore, the cost and benefit evaluation of pumped storage should be carried out from two perspectives: the individual interests of logically related stakeholders and a comparison of the interests of different stakeholders. The individual stakeholder evaluation mainly focuses on efficiency, and the comparison between the interests of different stakeholders focuses on participation and fairness.

In terms of solving the multi-stakeholder benefit realization mechanism of pumped storage, with the continuous development of the power system, the multi-stakeholder decision-making problem of pumped storage is becoming larger in scale and more complex in structure. Thus, a complex system with multi-dimensionality and non-linearity is formed that requires innovation in relevant research methods. This study seeks to elucidate pumped storage benefit sharing, and proposes a three-level Leader-Follower objective model and a corresponding solution method based on dynamic games and interactive algorithms to reasonably distribute the benefits and costs among stakeholders related to pumped storage projects. This provides a reference for the pumped storage power plant to collect fees from the beneficiaries so that it can reasonably recover costs and make profits in the power system.

2. Materials and Methods

2.1. Research Framework

The research framework of this paper is to adopt multi-dimensional regulation measures to achieve a reasonable distribution of pumped storage’s benefits and costs among different stakeholders, according to the requirements of multiple objectives. The participation of multiple stakeholders, i.e., decision-makers, in the decision-making process has the following characteristics: the decision-making process is divided into three different levels (leader, secondary and follower); the government at the leader level has the power to set electricity prices, and the decision-makers at the secondary leader level and the follower level include power grids, thermal power plants, electricity users, and pumped storage plants; the leader (adhering to the fairness goal) exercises some control and guidance over the secondary leader (adhering to the participation goal), and the secondary leader exerts some control and guidance over the followers (adhering to the efficiency goal) through different regulation strategies; and lower-level decision-making is based on upper-level decision variables, thus forming a Leader-Follower hierarchical decision-making process (Figure 1).

Multi-dimensional regulation mainly adopts economic policy measures to distribute the external economy of pumped storage projects. It mainly includes the following three aspects: first, the regulation objectives are clarified, and the output and services of pumped storage are fairly distributed; second, it plays the role of the regulation mechanism in a coordinated way. As the output and services of pumped storage are both direct products and commodities, the regulation mechanism must consider planning and marketing; and third, it cooperates with economic regulation means, mainly including public pricing, investment sharing, and treatment of externalities (lease payment).

(1)

Multiple value objectives

Improving the development effect of pumped storage projects begins with a clear understanding of the shared values, goals, and objectives of development. The diversified core values include fairness, participation, and efficiency, which run through the entire evaluation and decision-making process. They are related to the benefits and costs of pumped storage projects, where benefits refer to the capacity benefits and electricity benefits provided by pumped storage. The benefits provided to the power grid include black start, phase modulation, and power grid loss avoidance; the benefit provided to other power sources (coal-fired power stations) includes additional electricity, coal saving by spinning reserve, coal saving by pumped storage, dynamic tracking benefits, and coal savings from pumped storage; benefit to electricity consumers is avoided net economic losses of users; and the direct benefit of pumped storage power plant comes from power generation. Costs refer to the direct and indirect costs associated with the construction and operation of the pumped storage power station, and these costs need to be borne by all stakeholders.

①

Fairness objective. According to the viewpoint of modern economics, the purpose of pumped storage as an infrastructure project is to enhance and improve social welfare, which is reflected in the aspect of fairness. In this study, the objective of fairness is mainly the reasonable distribution of benefits and costs related to pumped storage projects among different stakeholders to achieve a win-win situation in which all stakeholders can achieve a fair and reasonable expected return rate;

②

Participation objective. Participative decision-making means that all stakeholders have the opportunity to participate in decision-making. Traditional project evaluation methods usually only care about the interests of relevant stakeholders or analyze from the perspective of the state or society. In fact, pumped storage projects will adjust the current pattern while gaining benefits. The process will have different impacts on different stakeholders, which needs to be accurately evaluated using the cost and benefit analysis method based on different stakeholders. A benefit sharing mechanism should be achieved at the project level for all participants. All those who obtain benefits should bear the costs, and those who bear the costs should also obtain benefits;

③

Efficiency objective. Through negotiation, only satisfactory benefits and target return rates that are recognized by the main stakeholders are proposed in the early stage. It is required that they be calculated based on life-cycle full-scope costs (including external costs) and full-scope benefits (including external benefits), with each stakeholder taking the maximum financial internal rate of return (FIRR) for itself as the optimization objective.

(2)

Multi-dimensional regulation strategy

Multi-dimensional regulation is mainly the use of economic policy measures to coordinate and control the conflict of interests between different stakeholders caused during project implementation. The key lies in the implementation of multi-dimensional regulation strategies, such as public pricing, investment allocation, and treatment of externalities.

①

Public pricing. The pricing principle of the output or services of pumped storage power plants should consider the following two aspects. First, public pricing should reflect the requirements of social welfare and undertake its realization. Second, it should reflect the profit requirements of investors. Reasonable public pricing standards for pumped storage products or services are as follows: abiding by and reflecting the benefit principle, taking the compensation cost as the basic limit, considering the willingness to pay, the nature of public service rights, the principle of profit and loss balance, and the principle of supply and demand balance;

②

Benefit (investment) sharing. Pumped storage projects require a reasonable sharing of benefits and investments among different stakeholders. Whether the investment cost borne by stakeholders is within the acceptable range determines their support for the project. The cooperative game method can be used to allocate the pumped storage benefits (investment). Whether the sharing is reasonable depends on whether it is “fair”. The reasonableness of the sharing fairness shall be checked;

③

Treatment of externalities (lease payments). In addition to direct costs and benefits, pumped storage also generates indirect costs and/or benefits, which are collectively referred to as externalities. Pumped storage power plants often use transfer payments to compensate for their financial benefits to improve their external economy. Lease payment is a common method for the treatment of externalities. The principle of sharing is that the treatment of externalities can be achieved by paying a certain percentage of the shared benefits to pumped storage as lease payments, as required by multiple values. In addition to the financial income from direct power generation of pumped storage power plants, other beneficiaries are required to make value compensation to pumped storage power plants at different capital return rates. The principle of compensation is that the net economic benefits (the upper limit of the lease) obtained by the grid, other power sources, and electricity users are compensated to pumped storage power plants in a certain proportion.

(3)

Leader-follower decision-making

In the power system, there are many stakeholders (decision-makers) involved in the operation of pumped storage power plants. Moreover, they are at different levels and each level has its objective function. The overall importance of higher-level objectives also increases accordingly. Therefore, the final decision often follows a coordinated process involving decision-makers at all levels. This type of problem is mainly a hierarchical decision-making problem, which has the following characteristics: (i) pumped storage plants and related multiple independent decision-makers participate in decision-making and have their objective functions and decision variables; (ii) the decision of a decision-maker will affect the interests of other decision-makers; (iii) the entire decision system has a Leader-Follower structure. In other words, multiple decision-makers are at different decision levels. The higher-level decision-makers generally have more power, and the upper- and lower-level decision-makers have a Leader-Follower relationship of mutual constraints; and (iv) the final decision made by all decision-makers should be a satisfactory decision acceptable to all decision-makers.

Decision-making problems with Leader-Follower structures should be solved by building multi-level mathematical programming models based on mathematical programming theories and methods. The multi-level mathematical programming problem is proposed in the study of a class of mathematical programming problems that include sub-optimization problems in the constraints. The general model of such problems can be divided into two levels. The upper level is a composite optimization problem containing the optimal decision variables of the lower level, while the lower level is parametric programming with the decision variables of the upper level as the parameters.

2.2. Three-Level Leader-Follower Objective Model with Multi-Dimensional Regulation and Multiple Values

2.2.1. Three-Level Leader-Follower Objective Function System

The model system refers to the criteria for judging the rationality of the project benefit calculation, which reflects the composition of multiple objectives under the synergy of multi-dimensional strategies. Among the multiple objectives, fairness is the highest objective, participation is the process objective, and efficiency is the basic objective. Decision-makers are at three different levels (leader, secondary, and follower), and the upper-level decision-makers can exercise certain control and guidance over the lower-level decision-makers. The decision-making process at the lower level takes the decision-making variables used by the upper-level decision-makers as the premise to form the leader–follower hierarchical decision-making process. The constructed model system consists of three levels with the leader–follower relationship: the leader considers the fairness among different stakeholders; the secondary leader reflects the participation of different stakeholders; and the followers insist on the efficiency of different stakeholders.

In the leader–follower decision-making process, the strategy adopted by the leader is public pricing, which includes the pricing of electricity (capacity) and power in the power system. The strategy adopted by the secondary leader level is benefit sharing, which refers to the rational measurement of the benefits generated by pumped storage to each stakeholder. The strategy at the follower level is the treatment of externalities, which refers to the study of the lease payments to pumped storage based on the rational measurement of the external effects generated by pumped storage to each stakeholder.

(1)

Fairness model at the leader level: fairness-based objective function

Fairness mainly considers that the difference in rates of return between stakeholders should be within a reasonable range. As the scale of investment contributed by different stakeholders is different, the principle of fairness judgment should take the relative economic return as the indicator. Given that the cost and benefit processes of different stakeholders in the project are different from year to year, the dynamic discounting method is used to calculate their costs and benefits. Moreover, the optimization criterion should be the minimum difference between the maximum and minimum FIRRs of different stakeholders. The objective function is as follows.

$$f=min\left\{\begin{array}{c}\underset{n=1,\dots N}{\max }\underset{FIR{R}_n}{arg}\left[{{\displaystyle \sum }}_{t=1}^T{\left[B\left(p,s,e\right)-C\left(p,s,e\right)\right]}_{n,t}\cdot {\left(1+FIR{R}_n\right)}^{-t}=0\right]\\ \underset{n=1,\dots N}{-\min }\underset{FIR{R}_n}{arg}\left[{{\displaystyle \sum }}_{t=1}^T{\left[B\left(p,s,e\right)-C\left(p,s,e\right)\right]}_{n,t}\cdot {\left(1+FIR{R}_n\right)}^{-t}=0\right]\end{array}\right.$$

(1)

where $f$ is the fairness indicator; $t$ is the timestep (year) of the calculation period; $n$ is the $n$th stakeholder in the project; $T$ and $N$ are the total number of the project calculation years and stakeholders, respectively; $p$, $s$, and $e$ are the public pricing, investment sharing, and externality of multi-dimensional regulation measures, respectively; $B\left(p,s,e\right)$ and $C\left(p,s,e\right)$ are the benefits and costs with public pricing ($p$), investment sharing ($s$), and treatment of externalities ($e$), respectively; $FIR{R}_n$ is the actual rate of return obtained by the $n$th stakeholder;

(2)

Participation model for the secondary leader level-participation-based objective function

In this study, the cost or benefit bearing in the life cycle of the pumped storage project is taken as the standard to determine the stakeholders. All stakeholders are explored, especially those who bear the losses and risks for the project. The participation criterion is the realization of a win-win situation for stakeholders during the implementation of the project. This study assumes that the minimum return rate of each stakeholder achieved by multi-dimensional regulation is greater than the minimum expected target return rate proposed by each stakeholder as the objective function. If reasonable compensation or benefit is not achieved, this indicates that the process is unreasonable. The objective function is as follows:

$$f{f}_n=\left\{\underset{FIR{R}_n}{arg}\left[{{\displaystyle \sum }}_{t=1}^T{\left[B\left(p,s,e\right)-C\left(p,s,e\right)\right]}_{n,t}\cdot {\left(1+FIR{R}_n\right)}^{-t}=0\right]-i_n\right\}\ge 0$$

(2)

where $f{f}_n$ is the participation indicator, $i_n$ is the target rate of return for the $n$th stakeholder, and the remaining parameters have the same meaning as above;

(3)

Efficiency model for the follower level-efficiency-based objective function

The maximization of the benefits of different stakeholders is used as a criterion to reflect efficiency, and the maximization of FIRR for different stakeholders is used for specific characterization. The FIRR is the discount rate when the net financial cash flow of stakeholders during the calculation period is equal to zero. The objective function is

$$ff{f}_n=\underset{n=1,\dots N}{\max }\left\{\underset{FIR{R}_n}{arg}\left[{{\displaystyle \sum }}_{t=1}^T{\left[B\left(p,s,e\right)-C\left(p,s,e\right)\right]}_{n,t}\cdot {\left(1+FIR{R}_n\right)}^{-t}=0\right]\right\}$$

(3)

where $ff{f}_n$ is the efficiency indicator; the remaining parameters have the same meaning as above.

2.2.2. Stackelberg Game-Based Decision Mechanism and Model Solving

The leader-follower decision-making problem is characterized by $p$, $s$, and $e$ as the decision variables of the decision-makers and $f$, $f{f}_n$, and $ff{f}_n$ as the objectives of the $n$th decision-maker at the leader, secondary leader, and follower levels, respectively. The decision-making mechanism of the model is such that the decision-maker at the upper level announces the decision first and then each decision-maker at the lower level chooses the optimal decision at that level under this premise. Its process also affects the constraint set and objective function of the problem at the upper level. Furthermore, the decision-maker at the upper level can then adjust his/her decision variables until the objective functions of decision-makers at each level are optimal.

Specifically, $f$ is optimized on $p$, $s$, and $e$, but only $p$ is determined by the topmost level; $f{f}_n$ is optimized on $s$ and $e$ with fixed $p$, but only $s$ is determined by the middle level; $ff{f}_n$ is optimized on $e$ with fixed $p$ and $s$, and $e$ is determined by the bottom level.

For this problem, this paper adopts a Stackelberg game-based solution method. Stackelberg game is a non-cooperative complete information dynamic game with multiple independent decision-makers [22]. The first decision maker makes a decision behavior through its own factors, and the latter decision maker obtains the decision information of the first actor and makes a decision by combining its own factors [23]. This method is widely used in dynamic pricing and energy management studies [24,25,26]. Therefore, the Stackelberg game can be used to solve the problem of this research. The three-level leader–follower game decision process is as follows: (i) public pricing of various electricity products and services provided by pumped storage is determined by the leader. Game subjects at the secondary leader level calculate the benefits of pumped storage for different stakeholders based on the above pricing, i.e., the shared benefits. Different stakeholders at the follower level pay the lease fees based on the shared benefits; (ii) the solution is evaluated by the decision-maker at the leader level and stopped if it is satisfactory. Otherwise, a new solution is used as a base point to continue the game until the decision-maker at the leader level is satisfied; (iii) constraints are then added to the problems at the leader level based on the strategy choices at the secondary leader and follower levels such that the solution obtained using the interactive algorithm is better than the strategy of the previous round of the game; (iv) constraints are then added to the problems at the secondary leader level based on the strategy choices at the leader and follower levels. The solution obtained with this strategy is better than that obtained in the previous round of the game, and the process is performed until the decision-maker at the secondary leader level is satisfied; and (v) constraints are then added to the decision-making problems at the follower level such that the solution that is obtained is better than that in the previous round of the game, and the process is stopped if the decision-maker at the follower level is satisfied. The flow chart of the decision-making mechanism and model-solving method is shown in Figure 2.

3. Case Study

The HH power grid is located in the central region of China, dominated by coal-fired power plants. According to the analysis and prediction of regional economic and social development, the maximum load of the HH power grid will be 26,200 MW by 2030, and the power demand will be 159 billion kWh. With the increasing peak-valley difference, there is a need to build a new power supply for peak shaving in the power system. The proposed BB pumped-storage power station will play an important role in helping to meet the peak shaving demand of the HH power system around 2030. The BB pumped storage power plant, which has 4 × 300 MW single-shaft mixed-flow reversible pump turbines, is designed to have an installed capacity of 1200 MW. The investment cost of the pumped storage power plant is considered as 4500 CNY/kW, the total construction period is 6 year, and the service life is 50 years. The annual operation cost of the power plant is considered as 2.5% of the investment. The daily power generation hours of the installed capacity are 5 h, and the design annual power generation is 2190 million kWh.

The economic benefit analysis of a pumped storage power station is carried out on two schemes of the HH power system, with and without the BB pumped storage power station. The first scheme is composed of the BB pumped storage power station (1200 MW), conventional hydropower, and thermal power stations; the second scheme is composed of coal-fired thermal power stations (1200 MW), conventional hydropower, and other thermal power stations. By analyzing the cost of the optimal equivalent alternative without the BB pumped storage power station, the economic benefits of the pumped storage power station to the thermal power station group and electricity users in the HH power system are calculated.

Stakeholders related to the BB pumped storage power plant are identified as the entities who bear the entire life cycle cost and benefits of the plant. They are the power grid, other power plants (coal-fired thermal power plants), electricity consumers, and the pumped storage plant itself. According to the data provided by the region, the difference between the maximum and minimum FIRRs between the various stakeholders should not be greater than 2%, as a constraint for the calculation of the fairness indicator at the leader level; the minimum expected rate of return for the power grid, coal-fired power plants, power consumers, and the pumped storage power plant is 10.00%, 9.50%, 11.00%, and 9.50%, respectively, which are the parameters for the participatory indicator calculation at the secondary leader level. Using the methodology and model established in this paper, the realization of the pumped storage value compensation mechanism was studied. It focused on the fairness, participation, and efficiency of stakeholders, as well as the application of public pricing, benefit sharing, and lease payments.

4. Results

4.1. Analysis of the Stackelberg Decision-Making Process

According to the characteristics of the research problem, a three-level leader–follower game relationship was formed between the main leader, secondary leader, and followers. The main leader acts first, and the secondary leader and the followers act later. This cycle continues until a satisfactory decision-making scheme is obtained. The main leader considers the public interests of various stakeholders and takes public pricing as its game strategy. The secondary leader takes the benefit sharing (calculation) of different stakeholders as its game strategy. The followers take the payment of pumped storage lease fees from different stakeholders as their game strategy.

Under the principle of fairness, the objective function of the leader takes a differential return rate between the pumped storage power plant and different stakeholders of not greater than 2.0% as the optimization principle and objective. The decision variable adopted is public pricing, which mainly includes the pricing of various products and services provided to different stakeholders by the pumped storage power plant.

With the given public pricing of electricity by the leader and under the principle of participation, the objective function of the secondary leader is that the minimum return rates of different stakeholders are not less than their expected minimum capital FIRRs.

The objective function at the follower level maximizes the FIRR of different stakeholders who adhere to the efficiency principle under the conditions that the leader gives a public pricing strategy, and the secondary leader takes part under the principle of a minimum expected target return rate.

4.2. Application of the Multi-Dimensional Regulation Strategy

This paper regulates the costs and benefits of pumped storage stakeholders through public pricing, benefit sharing, and lease payments sharing strategies, including the benefits and costs for power grids, thermal power plants, electricity users, and pumped storage itself. The details of the calculation of the benefits and lease payments are shown in the Supplementary Materials, and the regulation results are as follows:

(1)

Public pricing

The benefits associated with pumped storage capacity are called capacity benefits and those associated with electricity generation are called electricity benefits. In this paper, the benefits provided by the pumped storage power plant to other stakeholders are respectively calculated, according to the capacity and electricity functions.

①

Benefit pricing for the power grid. Among the benefits brought to the power grid by the 1.2 million kW capacity of pumped storage, the black start and phase modulation benefits are priced at 99.85 yuan/kW and 5.46667 yuan/kW, respectively. Among the benefits brought to the power grid by the 1095 million kWh power generation of pumped storage, the price for reducing the loss of power generation is 0.00264 yuan/kWh;

②

Benefit pricing for other power supplies. Among the benefits brought by the 1.2 million kW capacity of pumped storage to other power supplies, the increased power generation benefit of thermal power plants, the coal saving benefit of spinning reserve, and the coal saving benefit of fast tracking capacity of pumped storage are priced at 917.5 yuan/kW, 44.675 yuan/kW, and 21.75 yuan/kW, respectively. The price of coal saving benefits brought by the 1095 million kWh power generation of pumped storage to other power supplies is 0.0548 yuan/kWh;

③

Benefit pricing for electricity users. The benefits brought by the 1095 million kWh power generation of pumped storage to electricity users (avoided economic losses of users) are priced at 0.08028 yuan/kWh;

④

Pricing for the financial income of pumped storage power generation. Based on the optimized operation analysis, the annual generation capacity of BB pumped storage is 1095 million kWh. There are no peak and valley electricity prices at the power generation side of the power grid, and the power generation price of pumped storage is 0.30 yuan/kWh.

(2)

Benefit sharing calculations

①

Benefits for the power grid. Among the benefits brought to the power grid by the 1.2 million kW capacity of pumped storage, the black start and phase modulation benefits are 119.82 million yuan and 6.56 million yuan, respectively. Among the benefits brought by pumped storage to the power grid, the benefit of reducing power generation loss is 2.89 million yuan;

②

Benefits for other power supplies. Among the benefits brought by the 1.2 million kW capacity of pumped storage to other power supplies, the increased power generation benefit of thermal power plants, the coal saving benefit of spinning reserve, and the coal saving benefit of fast tracking capacity of pumped storage are 1101 million yuan, 53.61 million yuan, and 26.11 million yuan, respectively. The coal saving benefit of the 1095 million kWh power generation brought to other power supplies is 60 million yuan;

③

Benefits for electricity users. The benefits brought by the 1095 million kWh power generation of pumped storage to electricity users (avoided economic losses of users) are 87.91 million yuan;

④

Financial income of pumped storage power generation. The BB pumped storage power plant has an annual generation capacity of 1095 million kWh, which results in an income of 328.5 million yuan from pumped storage power generation.

(3)

Analysis of lease payments

①

Lease sharing analysis. The shared benefits generated by the pumped storage power plant to the grid, other power supplies, and users are 129.27 million yuan, 1240.72 million yuan, and 87.91 million yuan, respectively. When the benefits of the stakeholders are allocated to the pumped storage power plant in a certain proportion and the pumped storage capital FIRR requirement of 9.75% is met, the financial income required is 1809.63 million yuan. After deducting 328.5 million yuan of direct financial income from power generation, stakeholders need to compensate 1481.13 million yuan to the pumped storage plant. The benefits (lease fees) shared by the power grid, other power supplies, and electricity users to pumped storage are 98.48 million yuan, 993 million yuan and 61.15 million yuan, respectively. The calculation results of the lease payment are shown in

Table 1. Multi-dimensional means to realize the benefits of the BB pumped storage power plant and calculation results of multiple objective functions.

Categories	Item	Stakeholder 1	Stakeholder 2	Stakeholder 3	Pumped Storage Power Plant
		Power Grid	Other Power Supplies	Electricity Consumer
Public pricing	Black start (CNY/kW)	99.85000
	Phase modulation (CNY/kW)	5.46667
	Grid loss avoidance (CNY/kWh)	0.00264
	Additional electricity (CNY/kW)		917.50000
	Coal saving by spinning reserve (CNY/kW)		44.67500
	Coal saving by pumped storage (CNY/kW)		21.75000
	Dynamic tracking benefits (CNY/kWh)		0.05480
	Avoided user net economic losses (CNY/kWh)			0.08028
	Direct income from pumped storage generation (CNY/kWh)				0.30000
Benefit sharing	Black start benefits (Million CNY)	119.82
	Phase modulation benefits (Million CNY)	6.56
	Avoided grid loss (Million CNY)	2.89
	Additional electricity benefits (Million CNY)		1101.00
	Coal savings from spinning reserve (Million CNY)		53.61
	Dynamic tracking benefits (Million CNY)		26.11
	Coal savings from pumped storage (Million CNY)		60.00
	Avoided net economic losses of users (Million CNY)			87.91
	Direct income from pumped storage power generation (Million CNY)				328.50
	Subtotal (Million CNY)	129.27	1240.72	87.91	328.50
Lease payments	Pumped storage revenue payments (Million CNY)	98.48	993.00	61.15	328.50
Efficiency objective	FIRR of different stakeholders	10.50%	10.00%	11.50%	9.75%
Participation objective	The portion of return rate greater than the minimum expected return rate	0.50%	0.50%	0.50%	0.25%
Fairness objective	Maximum and minimum return rate differential	1.75%

;

②

Design of lease fee realization mechanism. In most cases, the power grid has no reasonable capacity price, peak, and valley price and various dynamic benefit prices. According to the current overall environment, leasing to the power grid and other power sources (coal or nuclear power) and collecting capacity price from large industrial users are better schemes according to the benefit relationship. As an intermediary and trading platform, the power grid enterprises take the power grid as the leasing hub to collect the corresponding leasing fees according to the benefits of various stakeholders to achieve a win-win situation for the pumped storage itself, the power grid, other power stations, and electricity users.

The power grid leases the BB pumped storage to distribute the pumped storage capacity to each thermal power plant. The power generation or utilization hours (excluding valley pumping) with and without pumped storage of each thermal power plant shall be respectively calculated. The increased power generation of thermal power plants with pumped storage shall be taken as the basis for compensating pumped storage. The coal-saving benefits of pumped storage are shared based on the increased valley pumping power. Based on the changes in the spinning reserve and dynamic tracking capacity undertaken by thermal power plants with and without pumped storage, the spinning reserve benefit and dynamic tracking benefit are shared. The power grid shall pay the black start benefit, phase modulation benefit, and avoided economic loss of grid to the pumped storage in an appropriate proportion. The power grid pays all the direct financial income of power generation by pumped storage as compensation for the costs of pumped storage. The power grid pays a certain proportion of the avoided user economic losses with the constructed pumped storage power plant as the compensation for its costs. The electricity user shall compensate the pumped storage expenses in a certain proportion.

4.3. Study of Multiple-Value Objective Function System

Following the above leader–follower decision-making and game strategy and the calculation method of benefits of stakeholders mentioned in the Supplementary Materials, the objective functions are obtained as follows.

(1)

Fairness objective function at the leader level

After the leader–follower game optimization, the FIRRs of power grid, other power supplies, and electricity users are 10.50%, 10.00%, and 11.50%, respectively, according to the corresponding maximum objective functions. The FIRR of the pumped storage power plant is 9.75%. The difference between the maximum and minimum FIRRs of pumped storage and different stakeholders is 1.75%, which is less than the target differential return rate of 2%. The return rates of pumped storage and stakeholders reflect the fairness after the game. Furthermore, the return rates obtained are recognized by all stakeholders. Therefore, the goal of fairness is achieved;

(2)

Participation objective function at the secondary leader level

After the leader–follower game optimization, according to the FIRRs of pumped storage and related stakeholders, it can be judged from the determination of the return rate objectives in the participation model that the FIRRs of the power grid, other power supplies, electricity users, and pumped storage are greater than the corresponding expected return rates by 0.50%, 0.50%, 0.50%, and 0.25%, respectively. Different stakeholders have obtained a reasonable rate of return, which reflects the principle of full participation;

(3)

Efficiency objective function at the follower level

The objective function at the follower level is that with the given public pricing of power by the leader and under the principle of participation, the minimum return rates of different stakeholders should not be less than their expected minimum capital FIRRs. It can be seen from the optimization results of the leader–follower game (see Table 1) that the FIRRs of the pumped storage stakeholders are greater than the corresponding expected minimum return rates.

5. Discussion

The research on the benefit realization mechanism of the pumped storage power plant highlights the following few points:

(1)

The benefit compensation mechanism of the BB pumped storage reflects the reasonable compensation principle of “benefit and cost sharing”. In reality, the cost of pumped storage is mainly shared by electricity users and the power grid, while other beneficiaries fail to reasonably share the cost. This is the main reason why pumped storage cannot thrive under the current power system. If the situation is not improved, the construction of pumped storage power plants cannot reflect the reasonable compensation and win-win principle of “benefit and cost sharing”. As long as other power sources can reasonably compensate for the leasing costs of pumped storage power plants, they can expect a reasonable return;

(2)

The compensation mechanism is determined based on the market principle of mutual benefit and reasonableness. A model is proposed based on the analysis of the benefits brought to power generation companies and power grid companies by pumped storage. Moreover, the relevant benefits are used as the basis for lease fee sharing. The corresponding lease fees are paid on the premise that all parties can benefit, which is in line with the market transaction conditions and realizes a win-win situation for all three parties. It shows that the business model has a solid theoretical basis for smooth operation;

(3)

Presently, power plants are reluctant to pay for leased pumped storage because pumped storage with limited installed capacity cannot bring about measurable benefits. The joint leasing operation model can resolve this contradiction by allocating pumped storage installed capacity to several power plants with large-scale units so that their load rate can be significantly increased. Under this operation mode, the generation side revenue can be measured accurately and effectively, which will greatly increase the leasing willingness of power plants with large-scale units. The pumped storage power plant obtains the capacity lease fee by signing the auxiliary service agreement with the power grid company. On the premise of completing the auxiliary services required by the agreement, the pumped storage units can be flexibly arranged for power generation or pumping to maximize the benefits;

(4)

When this method is adopted, the benefits of pumped storage to power generation companies and power grid companies are “visible, calculable and tangible”. In such a case, pumped storage will fulfill its functions in the power system, ensuring its survival and development. Moreover, a win-win situation can be ensured for pumped storage, other power plants, power grid and electricity users;

(5)

This study proposes criteria for judging the reasonableness of a project by multiple values and proposes the use of multi-dimensional regulation means to achieve the multiple-value objectives. Based on the establishment of this method and model system, there is a complex equilibrium solution process. The authors will discuss how to use game theory and group decision-making methods to study the game equilibrium realization mechanism in a separate article.

(6)

This research still faces some challenges. Future research needs to consider the influence of population movement, environment, electricity price, and other related factors during the operation of pumped storage, and give confidence intervals for the realization of pumped storage benefit on this basis.

6. Conclusions

This paper proposes a benefit realization mechanism of the pumped storage power plant based on multi-dimensional regulation and leader–follower decision-making method. The following conclusions can be drawn from this study:

(1)

The evaluation of pumped storage benefits should directly reflect changes in the costs and benefits of different stakeholders, such as the grid, other power sources, and electricity users, and should not be a weighted sum of these costs and benefits. The evaluation and analysis of costs and benefits should be carried out from two perspectives: the individual interests of the grid, other power sources, and electricity users that are logically related and the comparison between the interests of different stakeholders. The evaluation of individual stakeholders focuses on efficiency objectives and a comparative evaluation between different stakeholders focuses on the analysis of participation and fairness objectives;

(2)

The realization of pumped storage benefits requires the redistribution of benefits between different stakeholders, such as pumped storage, power grid, other power sources, and electricity users through public pricing, benefit sharing, and treatment of externalities (lease payment). The evaluation from the stakeholder perspective is the calculation of costs and benefits, but in essence it considers the interests of different stakeholders, reflecting the realization of efficiency, participation, and fairness of multiple stakeholders in modern social development;

(3)

The pumped storage benefits are analyzed based on the three-level leader–follower game relationship among the leader, the secondary leader, and the followers. The leader acts first and then the secondary leader and the followers act later. The leader represents the decision-makers of the public interests of all stakeholders, takes public pricing as the game strategy and uses the fairness objective function as the optimization goal. The secondary leader reflects the benefit sharing of different stakeholders and takes the participation objective function as the optimization objective. The followers take the lease fees paid by different stakeholders as their game strategy and the maximum return rate of stakeholders as the optimization objective.