A Cooperative Game Theoretical Approach for Designing Integrated Photovoltaic and Energy Storage Systems Shared Among Localized Users

Abstract

To address the increasing need for clean energy and efficient resource utilization, this paper aims to provide a cooperative framework and a fair profit allocation mechanism for integrated photovoltaic (PV) and energy storage systems that are shared among different types of users within a regional alliance, including industrial, commercial, and residential users. A cooperative game model is proposed and formulated by a two-level optimization problem: the upper level determines the optimal PV and storage capacities to maximize the alliance’s net profit, while the lower level allocates profits using an improved Nash bargaining approach based on Shapley value. The model simultaneously incorporates different real-world factors such as time-of-use electricity pricing, system life cycle cost, and load diversity. The results demonstrate that coordination between energy storage systems and PV systems can avoid 18% of solar curtailment losses. Compared to independent deployment by individual users, the cooperative sharing model increases the net present value by 8.41%, highlighting improvements in cost-effectiveness, renewable resource utilization, and operational flexibility. Users with higher demand or better load–generation matching gain greater economic returns, which can provide decision-making guidance for the government in formulating differentiated subsidy policies.

1. Introduction

1.1. Background and Significance

Energy, as a key driver of economic development, has become a focal point of global competition [1]. In response to the dual constraints of climate change and resource-related environmental pressures, China has explicitly proposed its goals of achieving “carbon peaking” and “carbon neutrality” and is actively promoting a profound transformation of energy production and consumption. The country is accelerating the construction of a new power system centered on renewable energy [2]. However, the intermittent and unstable nature of renewable energy sources such as photovoltaics (PV) poses significant challenges to the stability of the power grid [3]. To mitigate this issue, energy storage technologies have emerged as key enablers for improving the utilization of renewables and maintaining source–grid–load balance. By enabling time-shifting and power regulation, energy storage systems can smooth the output curve of variable renewable sources, reduce curtailment, and participate in auxiliary services such as frequency regulation, peak shaving, and demand response, thereby enhancing the flexibility and stability of the power system [4]. Nevertheless, high costs and long payback periods continue to limit their application potential in the renewable energy integration and power system optimization [5].

Against this backdrop, the integrated photovoltaic and energy storage system (PV-ESS) model has emerged. This approach promotes the deep integration of energy production and consumption by deploying PV systems alongside energy storage facilities. Multiple users can share energy storage resources through joint construction or leasing arrangements, facilitating renewable energy sharing and cost allocation, and thereby improving both economic performance and operational efficiency [6]. However, there is currently a lack of standardized frameworks and operational mechanisms for the coordinated development of integrated PV-ESS involving multiple users and oriented toward shared stakeholder interests. In practice, the deployment of such systems involves third-party operators, various user types and grid enterprises, each representing distinct stakeholders that face structural conflicts and engage in strategic interactions concerning cost allocation, benefit distribution, and risk sharing. At the same time, these entities are also interdependent through energy service reliance and system-level operational coordination. Therefore, it is essential to establish a unified framework for configuration optimization and collaborative operation, to ensure a fair and sustainable development path.

This paper adopts a stakeholder perspective and utilizes data-driven methods to investigate the optimal configuration of integrated PV-ESSs, as well as cooperative mechanisms among different users during system operation based on cooperative game theory. The proposed approach aims to enhance both system efficiency and stakeholder fairness. Through quantitative modeling and case-based comparisons, the study validates the effectiveness of collaborative mechanisms in enhancing economic performance and resource utilization. The findings are intended to provide an objective basis for optimization decisions by different user types and operators, contributing to the large-scale urban deployment of distributed renewable energy and new storage technologies, and supporting the optimization of the energy structure and the high-quality development of the new energy industry.

1.2. Literature Review

In recent years, academic research in the field of PV-ESS has accelerated significantly. Based on existing studies, the literature review is primarily organized around the following three aspects for systematic analysis.

Research on system capacity configuration primarily focuses on achieving an optimal balance between economic efficiency and operational stability. One stream of studies builds multi-objective optimization models under time-of-use pricing mechanisms to explore how appropriate energy storage sizing strategies can enhance overall system economic benefits [7,8]. Building upon this, some scholars have proposed bi-level optimization frameworks, in which the upper-level model addresses the energy storage capacity configuration, while the lower-level model focuses on the optimal operation of multi-microgrid systems, thereby effectively reducing user costs and improving overall system performance [9]. Other studies incorporate demand-side response and source–load interaction to develop nested bi-level optimization models that optimize storage sizing while enhancing local consumption of renewable energy [10]. To address the high uncertainty of renewable energy output, several studies introduce multi-stage stochastic programming approaches, constructing uncertainty scenarios through discrete probability distributions [11,12] and K-means clustering techniques [13], thereby improving model adaptability under complex environments. Collectively, these studies offer multi-dimensional theoretical foundations and methodological references for the efficient configuration of energy storage systems.

In the context of regional alliances, shared systems that integrate the concept of the sharing economy have emerged as an effective means to enhance both energy utilization efficiency and system-level economic performance [14]. Existing research primarily focuses on the rational design of sharing mechanisms and the optimization of operational strategies to simultaneously achieve user profit maximization and system performance enhancement. In terms of mechanism design, a substantial body of literature emphasizes the optimization of user combinations and resource allocation based on heterogeneous electricity demand patterns [15], integrating factors such as frequency regulation market price forecasts [16] to formulate leasing strategies aimed at maximizing individual economic benefits. These studies propose various static and dynamic sharing models, which not only simplify system management but also reinforce mutually beneficial relationships among users [17]. Compared with fixed allocation strategies, approaches based on bi-level optimization and game theoretic coordination frameworks [18,19] endow users with greater flexibility in capacity negotiation and resource scheduling. Furthermore, some studies couple self-owned and leasing models, incorporating stepwise cost functions to quantify economies of scale, thus overcoming the limitations of traditional single-mode configurations [20]. From the perspective of operational strategy optimization, a bi-level framework integrating shared energy storage with demand response has been proposed, quantifying the synergistic value of storage sizing and flexible load management [21]. Moreover, multi-user sharing models have been further extended to virtual power plants and demand response markets [22,23], leveraging differences in user load profiles to complement charging and discharging behaviors, thereby significantly improving the utilization and cost-effectiveness of energy storage systems.

In alliance-based shared systems, ensuring fair distribution of benefits or costs among multiple stakeholders is essential for maintaining cooperative relationships and securing the long-term stability of the alliance. A study modeled a day-ahead optimization algorithm to maximize community profits and proposed three cost-sharing schemes for peer-to-peer (P2P) trading, including equal allocation, trading participation-based allocation, and a benefit compensation mechanism. They aim to coordinate benefit distribution among members and enhance cooperation incentives and fairness. Results show that differentiated schemes can safeguard overall member benefits while mitigating cost increases caused by resource inequality [24]. Another study [25] employed improved Nucleolus methods that minimize excess costs within the coalition to achieve equitable cost-sharing and enhance the structural stability of the alliance. Additionally, Nash bargaining theory has been introduced into cooperative operation models between shared storage systems and microgrid stakeholders [26,27,28], addressing both transactional mechanisms and the dynamic nature of distribution negotiations. A Nash bargaining method has been further developed, based on the magnitude of interactive value contributions, to equitably allocate cooperation costs and benefits [29]. Alternatively, advanced cooperative game theoretic algorithms such as the A-CGT method have been developed to generate constrained strategies with greater precision [30]. These algorithms are particularly suitable for applications in large-scale regional energy systems. In recent years, some studies have further combined shared storage mechanisms with P2P energy trading markets [31,32], aiming to achieve fairness in resource allocation and economic efficiency in distributed settings. Overall, these approaches have significantly improved the fairness and practicality of benefit allocation in shared storage systems, providing robust decision-making support for multi-agent collaborative operations.

From the perspective of research trends, the optimization of energy storage configuration, as well as issues related to system stability and economic performance, has become relatively common. However, as shown in

Table 1. Summary of related literature.

Ref.	PV-ESS Integration	Multi-User Cooperation			Methodology
		Industrial	Commercial	Resident	Multi-Level Model	Game Theory	Marginal Allocation
[15]	✓	🗶	🗶	✓	✓	🗶	🗶
[16]	🗶	🗶	✓	🗶	✓	✓	🗶
[17]	🗶	🗶	🗶	✓	🗶	✓	🗶
[18]	✓	🗶	🗶	✓	✓	✓	✓
[19]	✓	🗶	🗶	✓	✓	✓	🗶
[20]	✓	🗶	🗶	✓	✓	🗶	🗶
[21]	✓	🗶	🗶	✓	✓	🗶	🗶
[22]	✓	🗶	🗶	✓	🗶	✓	✓
[23]	✓	🗶	🗶	✓	✓	✓	🗶
[24]	✓	🗶	🗶	✓	✓	🗶	✓
[25]	🗶	✓	🗶	🗶	✓	✓	✓
[26]	✓	✓	✓	✓	✓	✓	🗶
[27]	✓	✓	🗶	🗶	✓	✓	✓
[28]	✓	🗶	🗶	✓	✓	✓	✓
[29]	🗶	✓	🗶	🗶	✓	✓	✓
[30]	✓	✓	🗶	🗶	✓	✓	✓
[31]	✓	🗶	🗶	✓	🗶	✓	🗶
[32]	✓	✓	✓	🗶	✓	✓	🗶
*	✓	✓	✓	✓	✓	✓	✓

* This paper.

, studies on the integrated and complementary development of regionally integrated PV-ESS are still in their early stages. Although some shared models have been proposed in the past two to three years, many studies focus on specific user types without accounting for user diversity in real-world regional energy systems, thus failing to reflect the essential characteristics of regional sharing.

To meet the growing demand for coordinated planning and equitable cooperation in distributed energy systems, this paper proposes a framework for integrated PV-ESS. Unlike most existing studies that focus on homogeneous users or treat PV and energy storage planning in isolation, this work simultaneously considers industrial, commercial, and residential users within a regional alliance. By leveraging the heterogeneity in their electricity demand profiles, the framework enhances system synergy and value creation. A two-level optimization model is further developed to support coordinated PV-ESS planning. This study not only establishes a macro-level institutional framework for regional energy collaboration but also provides a micro-level solution for system design and operational strategies. The effectiveness of the proposed model is validated through numerical experiments, offering theoretical support and practical pathways for the scalable deployment of shared energy systems in a local area.

1.3. Paper Structure

The rest of this paper is structured as follows. Section 2 outlines the core stakeholders, vital element combinations, and subsequent mechanisms of the integrated PV-ESS. Section 3 establishes relevant models to characterize the operation of the system. Section 4 analyzes case studies in various scenarios to show the key factors impacting the system performance. Section 5 further discusses the practical significance and current limitations of developing regional integrated PV-ESSs. Finally, the conclusions and directions for future study are presented in Section 6.

2. Problem Description

This study focuses on regional alliance planning to deploy an integrated PV and new energy storage system. From a system-level perspective, it investigates the shared utilization and optimal configuration of integrated PV-ESS infrastructure. The alliance is led by a third-party operator who undertakes the investment and construction of renewable energy facilities and collaborates with industrial, commercial, and residential users interested in adopting clean energy. The alliance jointly manages the operation and benefit allocation of the integrated system, aiming to address the configuration and operational mechanisms of PV systems and energy storage systems from the perspective of both the third-party operator and various user types.

The integrated PV-ESS considered in this study includes PV generation units and energy storage facilities, as illustrated in Figure 1. Based on the actual electricity consumption profiles of users, the generation system is designed as an off-grid model, directly connected to the low-voltage distribution network on the user side, without feeding electricity into the public grid, to avoid external grid impacts. Meanwhile, to ensure users’ power demand is met when PV generation is insufficient, the residential load remains connected to the national grid. This study assumes that the power quality, such as voltage stability, harmonic distortion and fluctuation, is managed locally through appropriately configured inverters and energy management systems, in compliance with standard user-side design practices. In addition, given the system does not export electricity and operates entirely within the user-side boundary, grid-side constraints such as the feeder capacity limits or voltage drop considerations are not included in the model. Due to the inherent coupling between system components, the operator must assess two key variables—installed capacity of PV units and the scale of battery storage—when evaluating the overall construction cost. These two variables together determine the system’s capital investment.

Within the constructed operational framework of the integrated PV-ESS (as illustrated in Figure 2), a cooperative alliance is formed among the regional operator and various electricity users. The alliance’s aim is to achieve shared access and efficient utilization of PV and storage resources. To ensure coordinated interests and standardized governance, a non-profit alliance committee is established to oversee system operations and profit allocation. The committee does not participate in investment or revenue collection but sets operational rules, manages payments, and distributes profits.

Under this mechanism, the operator, as the system investor, is responsible for the development and operation of PV and energy storage equipment. Users join the alliance by signing an agreement and pay electricity fees based on national time-of-use tariffs, enjoying the right to use the electricity supplied by the PV-ESS. During system operation, PV generation is prioritized to meet the users’ real-time demands. When the output is insufficient, stored energy is discharged to compensate, while any surplus PV is stored for later use. In cases where both PV and energy storage cannot fully meet the demand, the alliance committee will purchase electricity from the national grid to supplement it.

Hence, the alliance’s overall revenue derives from the electricity cost savings achieved by substituting grid electricity with PV-ESS power. Specifically, the difference between the total payments made by users and the grid electricity procurement costs constitutes the economic benefit brought by the PV-ESS. After deducting investment and operational costs, the remaining distributable profit is allocated by the alliance committee based on each participant’s marginal contribution to the system. A cooperative game theoretical approach is applied to design a fair and sustainable benefit distribution mechanism that maintains the long-term incentive for both the operator and participating users.

In summary, the operator and various electricity consumers such as industrial, commercial, and residential users within the region jointly establish a cooperative game theoretic alliance mechanism. This mechanism takes advantage of the temporal differences in user load profiles to achieve power complementarity and improve energy utilization efficiency. The problem addressed in this study involves system-level capacity planning and user-level profit allocation, which correspond to distinct decision objectives and stakeholder roles. Integrating both aspects into a single unified model would significantly increase computational complexity and reduce the interpretability of economic behaviors among different participants. Therefore, this study proposes a two-level optimization model, aiming to maximize alliance profit and ensure fair benefit allocation. In the upper-level model, the alliance determines optimal PV and storage capacities to maximize overall net profit. In the lower-level model, based on the optimal configuration results, the profit is distributed using an improved Shapley value method and a generalized Nash bargaining framework, which consider each user’s marginal contribution in different cooperation scenarios. This approach balances the operator’s return on investment and the users’ electricity cost savings, enhancing both cooperation stability and economic viability.

3. Mathematical Models for Integrated PV-ESS

To coordinate system planning and benefit allocation in a shared PV-ESS alliance, this study constructs a two-level optimization model. The upper-level optimization model includes objective function, cost structure, and operational constraints. The lower-level is a profit allocation model based on a Nash bargaining mechanism.

3.1. Objective Function of the Upper-Level Model

In the shared operation model of an integrated PV-ESS, the core objective of optimal configuration is to maximize the total alliance profit while comprehensively considering the full life cycle investment and operational costs. The user benefits considered in this study throughout the system’s life cycle include electricity cost savings from energy consumption reduction and demand charge savings. The total investment costs of the system consist of the initial investment in the PV system, as well as the initial investment and replacement costs of the energy storage system. Accordingly, the objective function for the optimal configuration of the integrated PV-ESS can be expressed as:

$$max F=\left(\sum _{i=1}^{\left|I\right|}{B}_i^{in}+\sum _{j=1}^{\left|J\right|}{B}_j^{co}+\sum _{k=1}^{\left|K\right|}{B}_k^{re}\right)-C^{pv}-C^{ess}$$

(1)

where $F$ is the net profit of the users; $I$, $J$, $K$ denote the sets of industrial, commercial, and residential users, respectively; $\left|I\right|$, $\left|J\right|$ and $\left|K\right|$ represent the total number of users in each category; industrial users are denoted by $i\in I$, commercial users by $j\in J$ and residential users by $k\in K$; $B_i^{in}$, $B_j^{co}$, $B_k^{re}$ denote the total benefits obtained by industrial, commercial, and residential users; $C^{pv}$ and $C^{ess}$ represent the costs of the PV system and the operational and maintenance costs of the energy storage system.

3.1.1. Electricity Cost Reduction Benefits for Industrial Users

In the benefit module for industrial users, this study comprehensively considers two main sources of profit: the reduction in energy charges and the reduction in basic (demand-based) electricity charges. Both types of savings are calculated over the full life cycle of the project and adjusted by incorporating inflation and discount rates to reflect the time value of money. The electricity cost reduction benefits for industrial users can be expressed as follows:

$$B_i^{in}=B_i^{in,1}+B_i^{in,2}$$

(2)

where $B_i^{in,1}$ is the energy charge savings; $B_i^{in,2}$ is the basic (demand charge) savings for industrial user $i$.

Specifically, after deploying the integrated PV-ESS, industrial users can obtain electricity from two primary sources: (1) the electricity directly generated and supplied by the PV panels, (2) the electricity generated by the PV system, stored in the energy storage system, and later discharged to meet user demand. These two sources effectively reduce the volume of electricity purchased from the state grid.

The electricity cost savings from reduced grid consumption are calculated as the sum of the discharge power from both sources multiplied by the corresponding time-of-use electricity prices. This value is then converted into a life cycle benefit over the entire project horizon. Furthermore, the model incorporates both the inflation rate and the discount rate. Accordingly, the energy charge savings for industrial user $i$ can be expressed as:

$$B_i^{in,1}=\sum _{p=1}^P\sum _{d=1}^D{S}_{i,d}{\left({\displaystyle \frac{1+r}{1+w}}\right)}^p$$

(3)

$$S_{i,d}=\sum _{t=1}^T\left[P_{i,d}^{pv,f}\left(t\right)+P_{i,d}^{ess,f}\left(t\right)\right]\Delta t·m_i\left(t\right)$$

(4)

where $p$ is the project’s total life cycle; $D$ is the number of operational days per year for the shared energy storage system, with $D$= 365; $r$ is the annual inflation rate; $w$ is the discount rate; $S_{i,d}$ denotes the electricity cost savings obtained by industrial user $i$ on day $d$ from the integrated PV-ESS; $T$ is the number of time intervals in one day, thus T = 24; $P_{i,d}^{pv,f}\left(t\right)$ represents the power output from the PV system to industrial user $i$ during time period $t$ on day $d$; $P_{i,d}^{ess,f}$ represents the power output from the shared energy storage system to industrial $i$ during time period $t$ on day $d$; $m_i\left(t\right)$ is the time-of-use electricity price in period $t$.

For industrial users, basic electricity charges are typically calculated either by transformer capacity or by maximum monthly demand. Compared to the former, demand-based billing offers stronger price signals to encourage peak shaving and load optimization. This study adopts the maximum demand billing approach, utilizing the shared energy storage system to reduce peak loads and lower demand charges. The corresponding life cycle reduction in demand charges for industrial users is calculated as follows:

$$B_i^{in,2}=\sum _{p=1}^P\sum _{m=1}^M{S}_{i,m}{\left({\displaystyle \frac{1+r}{1+w}}\right)}^p$$

(5)

$$S_{i,m}={(P_{i,m}^{\mathrm{a}}-P}_{i,m}^{\mathrm{b}})m_b$$

(6)

where $M$ denotes the number of operational months per year, taken as $M$ = 12; $S_{i,m}$ represents the reduction in monthly demand charges for industrial user $i$ in month $m$; $P_{i,m}^{\mathrm{a}}$ is the maximum monthly demand of industrial user $i$ in month $m$ before the deployment of the integrated PV-ESS; $P_{i,m}^{\mathrm{b}}$ is the maximum monthly demand of industrial user $i$ in month $m$ after the deployment of the integrated PV-ESS; $m_b$ is the price of the demand charge.

3.1.2. Electricity Cost Reduction Benefits for Commercial and Residential Users

For commercial and residential users, electricity expenses are primarily calculated using a flat-rate pricing scheme, under which the total electricity cost is fully determined by the actual electricity consumption. The modeling approach for their electricity cost savings is consistent with that of industrial users, with the key difference being the specific time-of-use electricity price structures adopted. The corresponding electricity cost reduction can be expressed as:

$$B_j^{co}=\sum _{p=1}^P\sum _{d=1}^D{S}_{j,d}{\left({\displaystyle \frac{1+r}{1+w}}\right)}^p$$

(7)

$$B_k^{re}=\sum _{p=1}^P\sum _{d=1}^D{S}_{k,d}{\left({\displaystyle \frac{1+r}{1+w}}\right)}^p$$

(8)

$$S_{j,d}=\sum _{t=1}^T\left[P_{j,d}^{pv,f}\left(t\right)+P_{j,d}^{ess,f}\left(t\right)\right]\Delta t{·m}_j\left(t\right)$$

(9)

$$S_{k,d}=\sum _{t=1}^T\left[P_{k,d}^{pv,f}\left(t\right)+P_{k,d}^{ess,f}\left(t\right)\right]\Delta t{·m}_k\left(t\right)$$

(10)

3.2. Cost Structure of the Upper-Level Model

3.2.1. Construction and Installation Cost of the PV System

The total construction cost of the integrated PV-ESS consists of two main components: the construction cost of the PV power generation system and the construction and replacement cost of the energy storage system, primarily composed of storage batteries. Among these, the cost calculation methods for different components of the PV power generation system vary depending on their type. Based on this, the construction cost of the PV power generation system can be expressed as:

$$C^{pv}=C^m+C^{inv}+C^{SE}+C^{AF}+C^{PVC}$$

(11)

$$C^m=C^s·N^{pv}$$

(12)

$$C^{SE}=N^{pv}·p^{SE}$$

(13)

$$C^{AF}=N^{pv}·p^{AF}$$

(14)

$$C^{PVC}=N^{pv}·p^{PVC}$$

(15)

where $C^{pv}$ represents the total construction cost of the PV power generation system; $C^m$ is the cost of PV modules, $C^{inv}$ is the cost of PV inverters; $C^{SE}$ is the cost of power distribution equipment; $C^{AF}$ is the cost of PV accessories (including cables, PV brackets, etc.); $C^{PVC}$ the cost of PV controllers; $C^s$ is the unit cost per area of PV modules; $N^{pv}$ is the installed capacity of the PV panels. Equation (13) represents the cost of accessories such as cables and mounting brackets; $p^{AF}$ denotes the cost of auxiliary components that are directly related to the installed PV capacity.

3.2.2. Installation Cost of the Energy Storage System

The installation cost of the energy storage system, denoted as $C^A$, is primarily determined by its rated capacity. It can be expressed as:

$$C^A=C^e{E}^{max}$$

(16)

where $C^e$ represents the unit cost per unit of storage capacity; $E^{max}$ denotes the rated capacity of the shared energy storage system.

3.2.3. Replacement Cost of the Energy Storage System

The replacement cost of the energy storage system, denoted as $C^B$, is primarily determined by the unit replacement cost per unit of power capacity. Considering the time value of money, the total replacement cost over the system’s life cycle can be expressed as:

$$C^B=\sum _{z=1}^{⌊{\displaystyle \frac{P}{5}}⌋}{C}^x{E}^{max}{\left({\displaystyle \frac{1+r}{1+w}}\right)}^{5z}$$

(17)

where $z$ is the number of replacements; $⌊{\displaystyle \frac{P}{5}}⌋$ represents the total number of replacements over the life cycle; $C^x$ denotes the unit replacement cost per unit of storage capacity.

3.3. Operational Constraints of the Upper-Level Model

3.3.1. PV Power Supply Constraint

The PV power output is determined by factors such as solar irradiance, panel area, conversion efficiency, and power loss rate. The PV-generated energy can be expressed as:

$$E_d^{pv}\left(t\right)=P_d^{pv}\left(t\right)·\Delta t=\rho \cdot {\eta }^{pv}\cdot {\displaystyle \frac{G_d\left(t\right)}{G_{\mathrm{s}\mathrm{t}\mathrm{c}}}}\cdot N^{pv}\cdot \left({\eta }_{\downarrow }\right)\cdot \Delta t$$

(18)

where $E_d^{pv}\left(t\right)$ represents the PV energy output at time $t$ on day $d$; $P_d^{pv}\left(t\right)$ denotes the PV power output at that moment; $\Delta t$ is the time interval; $\rho$ is the derating factor accounting for environmental factors such as dust accumulation and hot-spot effects; ${\eta }^{pv}$ is the inverter efficiency of the PV system; $G_d\left(t\right)$ denotes the solar irradiance at time $t$ on day $d$ under the typical meteorological year; $G_{stc}$ is the standard irradiance level under standard test conditions; $N^{pv}$ is the installed capacity of the PV panels. In addition, a degradation factor ${\eta }_{\downarrow }$ is introduced to simulate the gradual decline in PV module efficiency over time due to aging.

3.3.2. Power Allocation Constraints

To achieve rational allocation and optimized utilization of power resources, this study adopts an operation strategy that prioritizes clean energy usage. Specifically, PV generation is prioritized to meet user load demand. When PV output is insufficient, stored energy is utilized. If the combined PV and storage power still cannot meet the load, the power shortage is compensated by the public grid. Based on the relationship among PV generation, energy storage level, and user load demand, system operation is divided into three scenarios.

Scenario 1: When PV generation exceeds the total real-time load demand of all users, $P_d^{pv}\left(t\right)\cdot \Delta t\ge \sum _{u=1}^U{P}_{u,d}^{load}\left(t\right)\cdot \Delta t$. PV power is first used to satisfy all users’ real-time electricity demands. The surplus PV energy is stored in the energy storage system. In this case, the PV-supplied power to each user equals their real-time load, as expressed in Equation (19). Meanwhile, the energy stored in the energy storage system during this period is limited by three factors: the surplus PV power, the rated charging power of the storage system during the time interval, and the remaining storable capacity of the energy storage. Hence, the charging amount is defined as the minimum of these three values, as shown in Equations (20)–(22).

$$P_{u,d}^{pv}\left(t\right)\cdot \Delta t=P_{u,d}^{load}\left(t\right)\cdot \Delta t,u=\mathrm{1,2},···U$$

(19)

$$P_d^{ess,c}\left(\mathrm{t}\right)\cdot \Delta t\le {[P}_d^{pv}\left(t\right)-\sum _{u=1}^U{P}_{u,d}^{load}\left(t\right)]\cdot \Delta t\cdot {\eta }^c$$

(20)

$$P_d^{ess,c}\left(t\right)\cdot \Delta t\le P^{ess,max}\cdot \Delta t$$

(21)

$$P_d^{ess,c}\left(t\right)\cdot \Delta t\le {\displaystyle \frac{E^{max}-E_d^{ess}\left(t\right)}{{\eta }^c}}$$

(22)

where $u$ denotes the user index, $u=\mathrm{1,2},···U$, and $U$ represents the total number of users, including industrial, commercial, and residential users; $P_{u,d}^{pv}\left(t\right)$ denotes the PV power obtained by user $u$ at time $t$ on day $d$; $P_{u,d}^{load}$ denotes the actual load demand of user $u$ at time $t$ on day $d$; $P_d^{ess,c}\left(\mathrm{t}\right)$ denotes the charging power of the energy storage system at time $t$ on day $d$; ${\eta }^c$ denotes the charging efficiency of the energy storage system; $P^{ess,max}$ represents the rated charging power of the energy storage device; $E^{max}$ denotes the rated capacity of the shared energy storage system; $E_d^{ess}\left(t\right)$ denotes the energy stored in the system at time $t$ on day $d$.

Scenario 2: PV generation is insufficient, but the combined energy from PV and energy storage can meet the total user load. $P_d^{pv}\left(t\right)\cdot \Delta t\le \sum _{u=1}^U{P}_{u,d}^{load}\left(t\right)\cdot \Delta t$, $P_d^{pv}\left(t\right)\cdot \Delta t+E_d^{ess}\left(\mathrm{t}\right)\cdot {\eta }_d\ge \sum _{u=1}^U{P}_{u,d}^{load}\left(t\right)\cdot \Delta t$. Under this condition, PV power is still prioritized and allocated to users. The remaining unmet demand is then supplemented by the energy storage system. The PV energy assigned to each user is distributed proportionally according to the user’s load relative to the total system load, as shown in Equation (23). The residual load not met by PV is supplied by the energy storage system. However, this discharge is subject to constraints including: the residual load after PV allocation, the maximum rated discharging power of the energy storage system for the time interval, and the currently available releasable energy in the energy storage system. Thus, the discharging power allocated to each user from the energy storage system is the minimum of these three factors, as indicated in Equations (24)–(26). Furthermore, the total discharging power and total energy discharged to all users must not exceed the maximum discharging power and total energy capacity of the energy storage system.

$$P_{u,d}^{pv}\left(t\right)\cdot \Delta t=P_d^{pv}\left(t\right)\cdot {\displaystyle \frac{P_{u,d}^{load}\left(t\right)}{\sum _{u=1}^U{P}_{u,d}^{load}\left(t\right)}}\cdot \Delta t$$

(23)

$$P_{u,d}^{ess,f}\left(t\right)\cdot \Delta t\le {[P}_{u,d}^{load}\left(t\right)-P_{u,d}^{pv}\left(t\right)]\cdot \Delta t/{\eta }^d$$

(24)

$$0\le P_{u,d}^{ess,f}\left(t\right)\le P^{ess,max}$$

(25)

$$0\le P_{u,d}^{ess,f}\left(t\right)\cdot \Delta t\le E_d^{ess}\left(t\right)\cdot {\eta }^d$$

(26)

$$0\le \sum _{u=1}^U{P}_{u,d}^{ess,f}\left(t\right)\le P^{ess,max}$$

(27)

$$0\le \sum _{u=1}^U{P}_{u,d}^{ess,f}\left(t\right)·\Delta t\le E_d^{ess}\left(t\right)\cdot {\eta }^d$$

(28)

where $P_{u,d}^{pv}\left(t\right)\cdot \Delta t$ represents the amount of PV energy provided to user $u$ at time $t$ on day $d$; $P_d^{pv}\left(t\right)\cdot \Delta t$ represents the total PV energy generation at time $t$ on day $d$; $P_{u,d}^{ess,f}\left(t\right)\cdot \Delta t$ represents the energy supplied from the energy storage system to user $u$ at time $t$ on day $d$; ${[P}_{u,d}^{load}\left(t\right)-P_{u,d}^{pv}\left(t\right)]\cdot \Delta t$ denotes the remaining demand of user $u$ after deducting the PV power supplied; ${\eta }^d$ represents the discharging efficiency of the energy storage system; $P^{ess,max}$ is the rated power of the energy storage system; $E_d^{ess}\left(t\right)$ is the energy stored in the energy storage system at time $t$ on day $d$.

Scenario 3: The combined electricity from PV-ESS is still insufficient to meet the total user demand. $P_d^{pv}\left(t\right)\cdot \Delta t+E_d^{ess}\left(t\right)\cdot {\eta }_d<\sum _{u=1}^U{P}_{u,d}^{load}\left(t\right)$. In this case, the available PV-ESS electricity will be allocated to users in proportion to their real-time load share of the total system load. The unmet portion will be supplemented by the public power grid. The PV energy allocated to each user is proportionally distributed based on the ratio of the user’s load to the total system load, as shown in Equation (29). The remaining demand for each user is then met by the energy storage system, also proportionally distributed based on each user’s load share. However, the allocation of storage discharge must also satisfy the rated power constraints of the energy storage system, as specified in Equations (30) and (31). In addition, the total discharging power and the total discharging energy provided to all users must not exceed the maximum discharging power and energy capacity of the energy storage system.

$$P_{u,d}^{pv}\left(t\right)\cdot \Delta t=P_d^{pv}\left(t\right)\cdot {\displaystyle \frac{P_{u,d}^{load}\left(t\right)}{\sum _{u=1}^U{P}_{u,d}^{load}\left(t\right)}}\cdot \Delta t$$

(29)

$$P_{u,d}^{ess,f}\left(t\right)\cdot \Delta t\le E_d^{ess}\left(t\right)\cdot {\displaystyle \frac{P_{u,d}^{load}\left(t\right)}{\sum _{u=1}^U{P}_{u,d}^{load}\left(t\right)}}\cdot {\eta }^d$$

(30)

$$P_{u,d}^{ess,f}\left(t\right)\cdot \Delta t\le P^{ess,max}\cdot \Delta t$$

(31)

$$0\le \sum _{u=1}^U{P}_{u,d}^{ess,f}\left(t\right)\le P^{ess,max}$$

(32)

3.3.3. Capacity and Charging/Discharging State Update Constraint

The energy level of the shared energy storage system at the next time step should equal the current energy level plus the charged energy at the current time, minus the discharged energy. The specific formula is as follows:

$$E_d^{ess}\left(t+1\right)=E_d^{ess}\left(t\right)+P_d^{ess,c}\left(t\right)\cdot {\eta }^c\cdot \Delta t-{\displaystyle \frac{P_d^{ess,f}\left(t\right)\cdot \Delta t}{{\eta }^d}}$$

(33)

where $E_d^{ess}\left(t+1\right)$ is the energy level of the storage system at time $t+1$ on day $d$; $P_d^{ess,c}\left(t\right)\cdot {\eta }^c\cdot \Delta t$ is the energy charged to the storage system at time $t$; ${\displaystyle \frac{P_d^{ess,f}\left(t\right)\cdot \Delta t}{{\eta }^d}}$ is the energy discharged from the storage system at time $t$.

The energy level of the energy storage system must remain within its rated capacity:

$$E^{min}\le E_d^{ess}\left(t\right)\le E^{max}$$

(34)

where $E_d^{ess}\left(t\right)$ is the energy level of the storage system at time $t$ on day $d$; $E^{max}$ and $E^{min}$ are the maximum and minimum storage levels.

The energy storage system cannot charge and discharge simultaneously:

$$u^{ess,c}\left(t\right)+u^{ess,f}\left(t\right)\le 1$$

(35)

where $u^{ess,c}\left(t\right)$ and $u^{ess,f}\left(t\right)$ are binary variables indicating the charging and discharging states of the energy storage system at time $t$, respectively. Specifically, $u^{ess,f}\left(t\right)$= 1 and $u^{ess,c}\left(t\right)$ = 0 represent a discharging state, $u^{ess,c}\left(t\right)$ = 1 and $u^{ess,f}\left(t\right)$ = 0 represent a charging state, while $u^{ess,c}\left(t\right)$ = 0 and $u^{ess,f}\left(t\right)$ = 0 indicate that the system is neither charging nor discharging.

3.4. Profit Allocation of the Lower-Level Model

In the benefit allocation model constructed in this study, an improved Nash bargaining approach based on the Shapley value is introduced to address the multilateral cooperation characteristics stemming from the joint participation of third-party operators and various types of users in the operation of a regional integrated PV-ESS. The Shapley value is employed to distinguish the actual contributions of different users within the alliance. After quantifying these contributions, a cooperative game model based on generalized Nash bargaining theory is established, wherein each participant’s contribution is incorporated into the bargaining objective function. The model aims to derive an allocation result that balances efficiency and fairness by maximizing the product of utility improvements raised to the power of each participant’s contribution weight.

This model not only satisfies the resource coordination constraints within the feasible region of the alliance’s overall benefits but also reflects the differentiated contribution levels of various stakeholders. It thereby enhances the stability and sustainability of multi-party cooperation, offering a robust theoretical foundation and decision-making support for the collaborative utilization of regional energy resources.

3.4.1. Definition of Improved Shapley Value Based Contribution

The traditional Shapley value method is widely used in cooperative game theory for benefit allocation. Its core idea is to determine each participant’s share of the total benefit based on their marginal contribution to different coalitions. However, when the number of users is large and the system structure is complex, the traditional Shapley value approach suffers from high computational complexity and may overlook actual differences in user benefits in practice. To address this issue, this study introduces an improved Shapley value algorithm based on the marginal contribution principle, aiming to better reflect users’ actual contributions. In the improved approach, the contribution of each coalition member is defined as the ratio between the change in the coalition’s total benefit after that member joins and the overall benefit change of the coalition. Specifically, the bargaining parameter is determined by removing a user and observing the impact on the net benefit of the alliance. For each user $i$, the net benefit $F_{-i}$ of the alliance without that user is calculated and compared to the original net benefit $F$ of the full alliance. The contribution of user $i$ is then defined as:

$$\Delta F_i=F-F_{-i}$$

(36)

where $F$ is the net benefit of the alliance including all users; $F_{-i}$ is the net benefit after removing user $i$.

Based on these contribution values, the improved Shapley value weight ${\alpha }_i$ for user $i$ is given by:

$$\Delta F_i=F-F_{-i}$$

(37)

$${\alpha }_i={\displaystyle \frac{\Delta F_i}{{\sum }_{j=1}^n\Delta F_j}}$$

(38)

where $\Delta F_i$ is the benefit increase user $i$ brings to the alliance; ${\sum }_{j=1}^n\Delta F_j$ is the total increase in benefit from all participating users.

3.4.2. Generalized Nash Bargaining Model

In the operation of a regional PV-ESS, multiple types of users, including industrial, commercial, and residential users, jointly participate, forming a complex multilateral cooperative relationship. In benefit allocation problems involving multiple stakeholders, the classical Nash bargaining model is often adopted. This model provides a foundational framework for fair distribution by maximizing the product of each participant’s surplus utility. However, the traditional model assumes equal bargaining power among all parties, which makes it unsuitable for complex alliance scenarios where significant differences in contribution exist. In the context of PV-ESS, the asymmetric cooperation among industrial, commercial, and residential users arises from their differences in load characteristics, electricity consumption scales, and contribution to overall system synergy. To address this, the study adopts a Generalized Nash Bargaining Model (GNBM) that incorporates differentiated bargaining power parameters reflecting each participant’s actual contribution.

By incorporating bargaining power parameters, which are based on the contribution weights derived from the improved Shapley value, into the bargaining objective function, the model captures the real-world disparities among participants more accurately and establishes a more realistic and incentive-compatible benefit allocation mechanism. The specific form of the generalized bargaining model is as follows:

$$\left\{\begin{array}{c}\mathit{max}{\left(R^{op}-D^{op}\right)}^{{\alpha }^{op}}·{\displaystyle \prod _{i=1}^{\left|I\right|}}{\left(R_i^{in}-D_i^{in}\right)}^{{\alpha }_i^{in}}·{\displaystyle \prod _{j=1}^{\left|J\right|}}{\left(R_j^{co}-D_j^{co}\right)}^{{\alpha }_j^{co}}·{\displaystyle \prod _{k=1}^{\left|K\right|}}{\left(R_k^{re}-D_k^{re}\right)}^{{\alpha }_k^{re}}\\ s.t. R^{op}\ge D^{op}\\ R_i^{in}\ge D_i^{in} \forall i\in I\\ R_j^{co}\ge D_j^{co} \forall j\in J\\ R_k^{re}\ge D_k^{re} \forall k\in K\end{array}\right.$$

(39)

where $R^{op}$, $R_i^{in}$, $R_j^{co}$, $R_k^{re}$ represent the post-cooperation revenues of the operator, industrial, commercial, and residential user, respectively; $D^{op}$, $D_i^{in}$, $D_j^{co}$, $D_k^{re}$ denote their pre-cooperation revenues, which are also referred to as disagreement points in the bargaining process. The parameter $\alpha$ indicates the bargaining power of each participant.

Given that the post-cooperation revenues and bargaining power parameters for all users are known, the generalized Nash bargaining objective Equation (39) can be further transformed into a logarithmic form for easier computation:

$$\left\{\begin{array}{c}\mathit{max}{\alpha }^{\mathit{op}}\mathit{ln}\left(R^{op}-D^{op}\right)+{\displaystyle \sum _{i=1}^{\left|I\right|}}{\alpha }_i^{in}ln\left(R_i^{in}-D_i^{in}\right)+{\displaystyle \sum _{j=1}^{\left|J\right|}}{\alpha }_j^{co}ln\left(R_j^{co}-D_j^{co}\right)+{\displaystyle \sum _{k=1}^{\left|K\right|}}{\alpha }_k^{re}ln\left(R_k^{re}-D_k^{re}\right)\\ s.t. R^{op}\ge D^{op}\\ R_i^{in}\ge D_i^{in} \forall i\in I\\ R_j^{co}\ge D_j^{co} \forall j\in J\\ R_k^{re}\ge D_k^{re} \forall k\in K\end{array}\right.$$

(40)

By introducing the bargaining power parameter $\alpha$, the GNBM achieves a more equitable benefit allocation when participants have unequal contributions. This parameter quantitatively reflects each stakeholder’s bargaining ability, derived from the improved Shapley value method, which captures users’ actual contributions to the alliance. Unlike traditional GNBMs that rely on exogenous weights or subjective assignments, the proposed method provides an endogenous, contribution-based weighting mechanism. This enhances the model’s fairness, realism, and incentive compatibility, making it better suited for complex multi-agent cooperation in integrated PV-ESS.

4. Numerical Experiments and Case Analysis

The optimization model is solved by a genetic algorithm. All the case studies listed in Section 4 were implemented in Visual Studio Community 2022 software to conduct computational simulations.

Table 2. Parameter settings and data sources for the numerical experiments.

Parameter List	Parameter Definition	Value	Data Source
$I$	Number of industrial users	2	/
$J$	Number of commercial users	20	/
$K$	Number of residential users	200	/
$C^x$	Unit replacement cost of energy storage capacity	CNY 457.92/kWh	Report from China Photovoltaic Industry Association [33]
$p^{AF}$	Cost of PV-related accessories	CNY 2.945/W	Relevant Literature [34]
$m_b$	Maximum demand charge for industrial users	CNY 38/kW/month	Electricity tariff in Shanghai [35]
$m_i\left(t\right)$	Peak/Standard/Off-peak electricity price for industrial users	CNY 0.981/0.58/0.3/kWh	Electricity tariff in Shanghai [35]
$m_j\left(t\right)$	Peak/ Off-peak electricity price for commercial users	CNY 0.81/0.42/kWh	Electricity tariff in Shanghai [35]
$m_k\left(t\right)$	Peak/ Off-peak electricity price for resident users	CNY 0.63/0.30/kWh	Electricity tariff in Shanghai [35]
$\rho$	Derating factor of PV system	0.9	Relevant Literature [34]
${\eta }^{pv}$	Inverter efficiency	95%	Related Design Manuals [36]
${\eta }_{\downarrow }$	Annual degradation rate of PV modules	85%	Relevant Literature [34]
$G_d\left(t\right)$	Sunlight intensity	/	National Renewable Energy Lab
$G_{\mathrm{s}\mathrm{t}\mathrm{c}}$	Sunlight intensity under standard conditions	1 kW/m2

presents the key parameter and data sources used in the numerical experiments.

The mathematical model developed in Section 3 provides a comprehensive framework to describe the interactions and game dynamics among stakeholders in the integrated PV-ESS. To validate the model’s effectiveness and practical relevance, this section presents a series of numerical experiments and five representative case studies. These cases are designed to explore various configurations and compare different deployment strategies under real-world conditions, providing intuitive insights and quantitative guidance for decision-makers. In addition to evaluating technical feasibility and economic viability, the case studies also aim to test the robustness of the profit allocation mechanism under varying user structures and regional environments. This multi-scenario analysis ensures that the proposed cooperative framework can adapt to diverse urban energy systems and maintain its fairness and scalability across use cases.

4.1. Case Study 1: Application of the Integrated PV-ESS in a Mixed-Use District in Shanghai

This case study examines a typical mixed-use district in Shanghai, comprising two large-scale industrial users, 20 commercial buildings (10 shopping malls and 10 office buildings), and 200 high-rise residential buildings. User load profiles are based on 2024 submetering data from the Shanghai Electric Power Company. Industrial user 1 consumes 32 million kWh annually with a load variation ratio of 65%, while industrial user 2 consumes 18 million kWh annually with a variation ratio of 28%. Shopping malls exhibit high variability in load due to holiday traffic, while office buildings maintain stable loads during daytime working hours. Residential user data are classified into five types based on electricity consumption patterns. The aim is to optimize system configuration to meet user demands and operational constraints while maximizing the net present value (NPV) over the project’s life cycle.

The optimal configuration results are shown in

Table 3. Optimal configuration of integrated PV-ESS.

Metric	Value	Description
PV system capacity (kWp)	162,755.36	Approximately 295,818 modules
Storage system capacity (kWh)	104,421.39	Lithium iron phosphate batteries, 93.8% efficiency
Total energy supplied (MWh)	121,452.08	Sum of PV-ESS supply
Electricity demand (MWh)	194,219.13	Annual total load across all user types
PV-ESS energy share (%)	62.53	Total energy supplied by the photovoltaic storage system/Total load power consumption of users × 100%
NPV (CNY mil.)	309.64	Over 25 years, adjusted for inflation and discounting
Payback period (years)	9.00	Static, below industry average
Internal rate of return (%)	10.99	Exceeds 6.5% benchmark for infrastructure projects

. The best performing configuration includes a PV system with a capacity of 162,755.36 kWp, equivalent to approximately 295,818 standard 550W modules, and an energy storage capacity of 104,421.39 kWh. The system employs lithium iron phosphate batteries, which provide a charging and discharging efficiency of 93.8%. This setup reduces daily load volatility by 76%. The PV-ESS provides 121,452.08 MWh annually, accounting for 62.53% of the district’s total electricity demand of 194,219.13 MWh. This reduces grid dependency to 37.47% and saves approximately CNY 100.65 million in electricity costs per year. Over a 25-year period, the system achieves a total NPV of CNY 309.64 million, with a payback period of 9 years and an internal rate of return (IRR) of 10.99%, well above the 6.5% benchmark for infrastructure investments in Shanghai.

In this scenario, users’ revenues are initially used to recover capital investments. After breakeven, the remaining profits are distributed based on users’ marginal contributions via the Shapley value. As shown in

Table 4. Revenue distribution among participants.

Participant	Contribution Weight (%)	Revenue (CNY mil.)
Operator	23.53	72.85
Industrial user 1	13.31	41.20
Industrial user 2	16.42	50.85
Shopping malls (1–10)	0.42 (avg.)	1.31 (avg.)
Office buildings (11–20)	0.77 (avg.)	2.38 (avg.)
Residential buildings	0.17 (avg.)	0.52 (avg.)

, all participants benefit from the cooperative model. The operator receives the highest share, amounting to 23.53%, reflecting its responsibility for the initial investment and long-term operational risks. Industrial user 1, characterized by a 65% load variation and a 13% reduction in peak demand, achieves a Shapley marginal contribution of 13.31%. In contrast, industrial user 2, with a relatively stable load, achieves better utilization of solar output with a 20% higher PV absorption rate, resulting in a greater contribution value.

Each office building achieves a contribution rate of 0.77% and received CNY 2.38 million in returns, which is 1.8 times the amount received by shopping centers. This difference stems from their daytime load aligning better with PV output, resulting in a higher direct solar utilization rate. For residential buildings, the per-unit revenue is only CNY 0.52 million, which is about 0.8% of industrial user 1’s revenue. However, residential users benefit from scale aggregation, shared monitoring systems, and potential policy subsidies, thereby enhancing the system’s resilience and grid responsiveness.

Figure 3 illustrates the return rates of different users, calculated as the ratio between their allocated dividends and their initial electricity expenditures. Industrial user 1, with high peak–valley differences and a significant load ratio, achieved a dividend of CNY 41.20 million and a return rate of approximately 15%. Industrial user 2, with a more stable load and better alignment with PV generation hours, reached a slightly higher return rate of 16%, benefiting from greater PV self-consumption.

Shopping malls 1–10 typically concentrate their energy use in the evening, necessitating frequent reliance on storage, which leads to higher energy losses. Nonetheless, due to their large total loads and exposure to time-of-use pricing, their per-unit dividends reached CNY 1.31 million, with a return rate of 17%. Office buildings 11–20 achieved an even higher return rate of 18%, owing to high alignment between office hour loads and PV output, reducing storage dependence.

The return rate for residential users starts at approximately 13% and remains relatively stable, overall lower than that of industrial and commercial users. This is primarily attributed to the homogeneous electricity consumption patterns and the large user base, resulting in a relatively low per-unit dividend of only CNY 538,800. Nevertheless, the overall impact of residential users is significant. By replacing 200 sets of distributed devices with a unified monitoring and control system, operation and maintenance costs were reduced over the project life cycle. Furthermore, the diversified and complementary nature of residential demand profiles improved regional load balancing and enabled demand-side response aggregation.

From Figure 3, it is evident that the effectiveness of electricity cost reduction varies across user types depending on load characteristics. Industrial and commercial users enjoy greater dividends relative to their electricity cost due to peak shaving and load–PV alignment, while residential users contribute to system stability through aggregation, offering a scalable model for distributed energy coordination.

These outcomes confirm the technical and economic benefits of the integrated PV-ESS in mixed-use districts, and also demonstrate its capacity to enhance local energy self-sufficiency. The cooperative deployment leads to a 76% reduction in daily load volatility, which significantly improves grid stability and reduces peak load pressures. The PV-ESS meets more than 60% of the district’s total electricity demand and lowers dependency on the main grid to below 40%. Furthermore, the detailed profit allocation results, calculated via the marginal contribution method, further confirm the fairness of the proposed model. All user types and the operator can benefit from the scheme, which reflects the efficiency and inclusivity of the cooperative framework. This case thus serves as a scalable template for promoting regional low-carbon transitions in other urban areas.

4.2. Case Study 2: Comparative Analysis of Cooperative vs. Independent Deployment Models

To assess the economic advantages of the cooperative integrated PV-ESS sharing model, this case compares it with a scenario in which each user independently configures and operates their own PV-ESS. The analysis is conducted in two steps. First, the technical and economic indicators for independently deployed systems by industrial, commercial, and residential users are evaluated. Then, these results are compared with the cooperative model to quantify the benefits brought by load complementarity and shared infrastructure.

Table 5. Comparison of cooperative and independent deployment models.

Metric	Cooperative Model	Industrial Only	Commercial Only	Residential Only
PV capacity (kWp)	162,755.36	60,403.96	17,732.61	58,830.72
Storage capacity (kWh)	104,421.39	41,968.87	4884.17	19,209.53
Total energy supplied (MWh)	121,452.08	25,831.48	8688.22	44,691.16
User load demand (MWh)	194,219.13	57,444.37	21,719.85	115,052.49
PV-ESS coverage (%)	62.53	44.96	40.01	38.84
NPV (CNY mil.)	309.64	128.32	62.45	94.86
Payback period (years)	9.00	8.00	7.00	9.00
Internal rate of return (%)	10.99	12.45	13.28	10.86

presents a comparison of the optimal configurations and economic performance between the cooperative model and the three independent user models.

Under the cooperative model, the optimized system includes 162,755 kWp of PV capacity and 104,421 kWh of energy storage, supplying approximately 12,145 MWh of clean energy annually, which accounts for 62.5% of the total load. This configuration achieves an NPV of CNY 309.64 million, a payback period of 9 years, and an IRR of 10.99%. In contrast, when only industrial users deploy the system independently, the configuration includes 60,403 kWp of PV and 41,969 kWh of storage. Despite the large size, it supplies only 25,831 MWh, covering 44.96% of their total demand, and yields a reduced NPV of CNY 128.32 million. Commercial and residential users, in their respective independent deployments, achieve even lower energy coverage ratios of 40.01% and 38.84%, with corresponding NPVs of CNY 62.45 million and CNY 94.86 million, respectively. Although their IRRs are slightly higher, the absolute economic gains are significantly diminished due to the absence of inter-user load complementarity and economies of scale.

These results clearly demonstrate that cross-user, cross-scenario cooperation maximizes the utilization efficiency and economic value of PV-ESS, making it the optimal pathway for regional energy sharing and cost reduction.

Further analysis of revenue distribution reveals enhanced returns for all parties under the cooperative scheme. As shown in

Table 6. Dividend comparison between cooperative and independent deployment models.

Participant	Cooperative Dividend (CNY mil.)	Independent Dividend (CNY mil.)	Improvement (%)
Operator	72.85	60.45	20.52
Industrial user 1	41.20	39.26	4.94
Industrial user 2	50.85	48.05	5.84
Shopping malls (avg.)	1.31	1.25	4.09
Office buildings (avg.)	2.38	2.24	6.34
Residential buildings (avg.)	0.53	0.52	3.34

, the operator’s profit rises from CNY 60.45 million in the independent case to CNY 72.85 million, an increase of 20.5%. Industrial users 1 and 2 gain 4.94% and 5.84% more in profit, respectively, due to improved load balancing and storage optimization. Commercial users, particularly office buildings, see the largest relative increase, thanks to better PV–load alignment. Residential users also benefit modestly from shared infrastructure, with their average dividend rising from CNY 0.52 million to CNY 0.53 million.

The operator benefits the most from the cooperative model, with a 20.5% increase in returns due to system scaling and cost amortization. Industrial user 2, whose load profile aligns well with PV output, gains more than industrial user 1, who relies more heavily on storage during peak times. Office buildings outperform shopping malls due to their daytime consumption, which minimizes reliance on storage and associated losses. While residential users see the smallest per-unit gain, their aggregate contribution remains significant due to scale.

4.3. Case Study 3: Comparison Between PV-ESS Integration and PV-Only Deployment Models

This case focuses on comparing the performance of two commercial deployment models: (1) an integrated PV-ESS and (2) a PV-only system without storage. The objective is to evaluate the critical role of storage in mitigating load fluctuations and improving renewable energy utilization.

As shown in

Table 7. Comparison of optimal solutions between PV-ESS and PV-Only systems.

Metric	PV-ESS	PV-Only System
PV capacity (kWp)	162,755.36	97,365.14
Storage capacity (kWh)	104,421.39	/
Project revenue (CNY mil.)	1006.46	590.71
Project cost (CNY mil.)	696.81	321.29
NPV (CNY mil.)	309.64	269.41
PV coverage (%)	62.53	53.82
Operator profit (CNY mil.)	72.85	67.63
Industrial user profit (CNY mil.)	92.06	78.22
Commercial user profit (CNY mil.)	36.99	32.57
Residential user profit (CNY mil.)	107.75	90.99

, removing the storage component reduces the PV system size to 97,365.14 kWp and significantly impacts project economics. While total project revenue drops from CNY 1,006.46 million to CNY 590.71 million, investment costs fall from CNY 696.81 million to CNY 321.29 million. However, net user profit declines by 14.93%, decreasing from CNY 309.64 million to CNY 269.41 million. This reduction is mainly attributed to curtailed PV output and lower utilization efficiency. The share of user electricity created by PV also drops from 62.53% to 53.82%. The absence of storage forces the system to curtail surplus PV power generated during daytime hours, which cannot be stored for later use in evening peaks. This leads to increased reliance on the grid during high-tariff periods and reduces overall system profitability.

Figure 4 illustrates the typical daily load and PV generation curves. In the integrated system, excess electricity generated between 10:00 and 16:00 is stored and dispatched during peak hours (17:00 to 21:00), effectively smoothing the net load curve and reducing peak demand. This coordinated charging and discharging strategy maximizes PV self-consumption while also minimizing grid electricity purchases during high-tariff periods, thus improving overall economic performance. In contrast, the PV-only system lacks the flexibility to shift energy across time, so any surplus generation during midday hours must be curtailed. This leads to a significant waste of renewable resources, lower PV utilization efficiency, and increased reliance on the external power grid during evening peaks. Additionally, the inability to manage supply–demand mismatch may exacerbate grid volatility and reduce the system’s contribution to local energy resilience.

Figure 5 compares the equivalent net load curves under both scenarios. With storage, peak demand is flattened from 25,662 kW to approximately 15,562 kW, significantly reducing high-tariff grid purchases. Without storage, the full peak must be met by the grid, increasing energy costs and curtailment losses.

Removing the storage component reduces NPV, while also leading to unstable load balancing and higher electricity procurement from the grid during peak hours. Without storage, the system is unable to shift excess midday generation to evening demand, leading to a 22.4% increase in peak-hour grid imports. This compromises grid flexibility and undermines one of the key motivations for deploying distributed renewable systems. This case confirms that energy storage enhances PV self-consumption and demand flexibility, and improves economic viability of distributed energy systems. The absence of storage results in curtailed generation, increased grid reliance, and reduced returns for all participants.

4.4. Case Study 4: Impact Analysis of Government PV Subsidies

This case investigates a scenario where a regional PV-ESS integration project receives government subsidies based on PV electricity consumption. Except for the subsidy mechanism, all model settings remain consistent with those in Case 1. According to Shanghai’s local subsidy policy, during the first five years of operation, users are eligible for a subsidy of CNY 0.3/kWh for PV electricity actually consumed from the integrated system. Unlike generation-based subsidies, the approach is consumption-based, aiming to promote active utilization.

After optimization, the results are summarized in

Table 8. Comparison of key metrics with and without subsidy.

Metric	With Subsidy	Without Subsidy
PV capacity (kWp)	169,379.49	162,755.36
Storage capacity (kWh)	115,207.70	104,421.39
Project cost (CNY mil.)	735.17	696.81
NPV (CNY mil.)	450.08	309.64
Operator profit (CNY mil.)	123.87	72.85
Industrial user profit (CNY mil.)	124.44	92.06
Commercial user profit (CNY mil.)	49.67	36.99
Residential user profit (CNY mil.)	152.11	107.75
Operator profit margin (%)	16.85	10.45
Payback period (years)	8.00	9.00

. The optimal PV capacity increases to 169,379.49 kWp, and storage capacity grows to 115,207.70 kWh. Under this configuration, the operator invests CNY 735.17 million and earns a profit of CNY 123.87 million, corresponding to a profit margin of 16.85%. On the user side, the total profit for industrial users reached CNY 124.44 million, with an average of CNY 62.22 million per user. Commercial users achieved a total profit of CNY 49.67 million, averaging CNY 2.48 million per user. Residential users obtained the highest total profit of CNY 152.11 million, with an average of CNY 0.76 million per user. These results verify the economic viability of the proposed integrated model under government support.

The introduction of consumption-based subsidies significantly improves the attractiveness of cooperative models. Industrial and residential users show a 35–40% profit increase, which improves their return on investment and lowers the payback period by 2.7 years on average. These results suggest that performance-based subsidies are more effective than static ones, especially in motivating user behavioral change and ensuring system-level synergy.

Therefore, policy design should transition from flat-rate subsidies to differentiated, performance-based incentives that reward stakeholder contributions and promote multi-party collaboration. These approaches stabilize investment returns while also ensuring equitable stakeholder participation.

4.5. Case Study 5: Regional Adaptability Based on Solar Irradiation Conditions

Given the significant regional differences in electricity pricing and solar subsidies across China, this case focuses solely on the impact of solar irradiation on the feasibility of PV-ESS integration. In addition to Shanghai, eight other cities were selected for analysis: Lhasa, Guangzhou, Urumqi, Beijing, Taiyuan, Jiayuguan, Shenyang, and Chengdu. These cities represent diverse solar resources and climate conditions, as illustrated in Figure 6, inspired by [34].

The optimization results for each location are summarized in

Table 9. Regional comparison of optimized PV-ESS configuration and profitability.

Region	PV Capacity (kWp)	Storage Capacity (kWh)	Project Cost (CNY mil.)	NPV (CNY mil.)	Operator Profit (CNY mil.)
Shanghai	162,755.36	104,421.39	696.81	309.64	72.85
Taiyuan	146,371.92	98,498.98	633.69	377.51	102.62
Beijing	143,549.14	99,605.24	626.06	445.33	130.76
Guangzhou	139,678.72	104,083.97	620.14	405.47	114.88
Shenyang	136,846.42	76,610.36	568.77	370.67	104.87
Jiayuguan	122,828.31	74,227.22	518.87	392.95	118.34
Urumqi	114,849.69	46,164.14	449.62	330.67	98.42
Lhasa	95,064.12	82,180.07	440.26	439.41	149.97
Chengdu	83,818.39	0.00	276.60	132.34	32.36

. Except for Chengdu, where solar conditions are poor, the proposed mode proves to be economically viable in all other regions, with net present values ranging from CNY 300 million to CNY 500 million. Among them, Beijing, Lhasa, and Jiayuguan show particularly strong performance, benefiting from high solar irradiance and favorable climate conditions.

In contrast, although cities like Taiyuan, Guangzhou, and Shenyang require larger system capacities, their relatively higher installation costs result in lower operator profit margins compared to Beijing. Overall, the PV-ESS scale, storage capacity, and project profitability show strong positive correlations, while profit structures differ across regions.

Figure 7 shows the profit distribution by user type across regions. Lhasa demonstrates the strongest economic outcome, with operator profits reaching CNY 149.97 million and both industrial and residential user profits ranking among the highest. This success is largely attributed to its abundant solar resources and high storage utilization. In contrast, Chengdu exhibits the weakest performance: without storage and with limited solar irradiance, the system struggles to reach economic viability, with operator profit only CNY 32.36 million. Cities such as Beijing, Guangzhou, and Jiayuguan achieve balanced profits across all user types. Beijing stands out, with residential users receiving over CNY 144.19 million in total, the highest nationwide, demonstrating that moderate yet stable solar resources, combined with optimized system design, can achieve win–win outcomes for all stakeholders.

This variation in performance underscores the importance of regional adaptation in PV-ESS deployment. Locations with favorable solar radiation levels and demand diversity benefit more from cooperative deployment models. In contrast, areas with lower irradiance such as Chengdu require tailored system sizing or enhanced policy incentives to achieve similar returns. These case-based insights confirm the scalability and flexibility of the proposed model and emphasize the necessity of localized planning to maximize system efficiency and stakeholder engagement.

5. Discussion

5.1. Practical Implications of the Regional Shared PV-ESS Model

The results of the numerical experiments and case studies confirm that the regional shared PV-ESS model offers clear advantages over independent deployment approaches. Cooperative deployment enables better load complementarity, improves local PV utilization, enhances system flexibility, and significantly increases economic returns. The inclusion of energy storage further strengthens system performance by reducing curtailment and enabling time-shifting of electricity supply. Well-designed, consumption-based subsidies also play a critical role in boosting stakeholder participation and improving financial viability. Moreover, regional variations in solar resources significantly affect project outcomes, emphasizing the need for site-specific system design.

To accelerate the deployment of shared PV-ESS systems, policymakers should establish region-specific subsidy frameworks that reward actual renewable energy consumption, simplify grid access for shared infrastructure, and support the role of neutral third-party operators. Government agencies may also launch pilot programs in urban communities to demonstrate cooperative energy governance and test adaptive pricing and benefit-sharing models. These efforts will help lower financing barriers, promote equitable participation, and create replicable models for broader implementation in other regions.

In the long term, energy authorities should integrate shared PV-ESS development into broader urban energy transition strategies, aligning it with national carbon neutrality goals and distributed grid modernization. Incentive mechanisms should be designed with long-term sustainability in mind, ensuring that cost-effectiveness, energy justice, and public engagements are simultaneously addressed. Furthermore, regional energy planning could benefit from cross-sector collaboration between energy regulators, municipal governments, and private investors to jointly build resilient, low-carbon energy communities tailored to local demand profiles and solar potential.

5.2. Contributions and Limitations

This study makes several contributions. It proposes a quantifiable and operationally feasible cooperative PV-ESS model and designs a marginal contribution-based profit allocation mechanism that ensures fairness and efficiency. By applying an improved Shapley value method, user returns are directly linked to load profiles, participation time windows, and marginal benefits. This approach mitigates the traditional “free rider” problem and enhances user engagement within the cooperative framework.

Furthermore, the model integrates stakeholder diversity, load heterogeneity, real-world electricity pricing, and government subsidies into a unified optimization and benefit-sharing structure. Through multi-scenario validation, the study demonstrates clear scalability and adaptability, providing a replicable framework for other energy coordination scenarios such as source–grid–load–storage integration.

Despite these strengths, the model has several limitations. The PV generation model simplifies the physical environment by considering only solar irradiance as the key input, while omitting factors such as ambient temperature, panel orientation, and weather variability, which may influence actual power output. Secondly, the model presumes a stable environment across several key dimensions, including consistent user participation, fixed electricity pricing, and secure grid accessibility throughout the project lifecycle. However, in practice, these elements are often dynamic and politically influenced.

Future research should aim to incorporate real-time data streams to support adaptive pricing, load forecasting, and real-time dispatch. In addition, emerging technologies such as blockchain-based P2P energy trading and AI-powered system coordination offer promising avenues to enhance transparency, trust, and system intelligence in multi-agent energy systems. These innovations could further expand the relevance and resilience of the proposed model in more complex, data-rich, and decentralized energy environments.

6. Conclusions

This paper proposes a cooperative development framework for integrated PV-ESS from a regional and multi-stakeholder perspective. A two-level optimization model is designed to configure the shared PV-ESS capacity, and an improved Shapley value method along with a generalized Nash bargaining model is adopted to establish a fair and reasonable benefit allocation mechanism. Under the optimal configuration, PV-ESS can supply up to 62.53% of the region’s electricity demand through clean energy, with a total NPV of CNY 309.64 million over its lifecycle. Compared to scenarios in which users deploy systems independently, the cooperative operation model generates approximately CNY 24 million in additional value and significantly enhances the economic viability and resource efficiency of the system. In contrast, the absence of energy storage leads to a 14.93% reduction in NPV and an 8.71% decline in the clean energy supply ratio, further confirming the irreplaceable role of energy storage in improving renewable energy utilization and overall system performance.

The proposed mechanism not only ensures fairness among heterogeneous users but also reflects their differentiated contributions in terms of load demand and PV generation matching. The study offers a replicable decision-making framework that integrates optimal system design with equitable stakeholder cooperation. These insights can help guide energy planners, investors, and policymakers seeking scalable and inclusive low-carbon solutions. Future research could explore real-time demand response, behavioral heterogeneity, and blockchain-based P2P trading mechanisms to further refine the model and enhance its practical applicability.