INTRODUCTION
With the rapid development of renewable energy (RE) technologies and the large-scale integration of flexible resources on the demand side, the power grid is transforming into the Energy Internet, which has accelerated the construction of the electricity market. As an important feature of the smart grid, the demand-side response can effectively improve system operation efficiency and reduce energy cost by integrating flexible resources, which has been widely used in the promotion of electricity power marketisation. However, flexible resources with small capacity and scattered distribution generally do not meet the grid connection conditions and cannot participate in market transactions, which further restrict the participation of demand-side response in the market [1, 2]. Virtual power plants (VPPs) provide energy balance, frequency regulation, and new energy consumption services for the power grid by integrating multiple types of flexible resources, such as energy storage and flexible load, which develop rapidly on the distribution side and show certain economic values [3, 4].
Recently, China has successively issued the pilot rules with the deepening research on the electricity market [5–9]. Virtual power plant not only can aggregate ‘source-network-load’ resources to participate in the electricity market to deal with the uncertainty of RE but also tap flexible peak shaving resources to participate in peak-shaving auxiliary services in the spot market [10]. As an independent market entity, VPP aggregates distributed energy resources to participate in the electricity market in the form of price takers, which can transact electricity, to maximise profits [10, 11] and formulate bidding strategies according to each member. According to the mechanism in North China, the bidding model for VPP to participate in the peak shaving market is determined, and the benefits are distributed among members through Shapely [12]. By participating in peak shaving for interruptible loads and energy storage, a peak shaving bidding model aiming at the lowest cost of VPP peak shaving was established [13]. Virtual power plants influence and restrict one another when participating in the energy market and providing peak shaving auxiliary services. Therefore, considering the multimarket bidding problem of VPP participating in the electricity market and the peak shaving market simultaneously is necessary. The business operation mode and the organization method of VPP participating in the energy market and auxiliary service market on the distribution side were discussed in [14]. To address this problem, the optimal bidding strategy and the model for VPP were proposed and established in [15]. However, when the distributed energy resources within the VPP belong to different property rights owners, the direct management of the internal members by the VPP is no longer suitable, and studying the coordinated operation and bidding of multiple subjects within the VPP are necessary.
In a multi-agent VPP, the VPP operator (VPPO) and each distributed energy source are multiple stakeholders, and a conflict of interest or association exists [16–18]. Internal multi-agent collaboration is the key to bidding decisions and coordinated operations. Through the double-layer optimization model, a VPP double-layer bidding strategy considering the purchase and sale risk is proposed to complete the bidding of VPP and demand-side resources [8]. In addition, the master-slave game theory is an important means to deal with the multi-agent coordination optimization problem within the VPP [19–21]. By constructing a master-slave game model between VPP and electric vehicles, the electricity sales price is used to guide electric vehicles to charge in an orderly manner [20]. For VPP with multiple stakeholders, a two-tier bidding model of the master-slave game between VPP and each member was established to determine the transaction price and dispatching plan of each member within the VPP [21].
For each independent agent in the Energy Internet, the construction of energy storage equipment cannot achieve energy complementation among agents, which has high investments and construction costs. Considering the dual needs of user comfort and electricity, a model was established to realize active operation and improve the utilization rate of distribution network assets, which can improve the operation strategy of the active distribution network [22]. The sharing economy has made great contributions to the commercialisation of industrial models in terms of saving economic costs and improving resource utilization [23]. Thus, the shared energy storage service mechanism of multiple photovoltaic producers and consumers under the Community Energy Internet; a master-slave sharing model between the shared energy storage system (SESS) and multiple producers was applied to achieve win-win benefits for shared energy storage and consumers [24]. Moreover, the organic combination of energy storage technology and shared ideas has promoted the development of shared energy storage. The definition of cloud energy storage is proposed, and the optimization and prospect of cloud energy storage in the future were summarised and prospected [25]. Aiming at the community integrated energy system, a day-ahead scheduling model for residential users based on shared energy storage was proposed, which verifies that shared energy storage can effectively benefit the overall income of residential users while creating profit space for shared energy storage operators (SESSO) [26]. According to the characteristics of different industrial users' load differences, a collaborative operation model of shared energy storage and multiple different types of industrial users is established, and the construction costs were effectively reduced compared with the energy storage equipment independently built by each industrial user [27].
Shared energy storage system involves the optimal scheduling of multiple different stakeholders, and the disorderly competition between them will reduce the efficiency of the electricity market. Non-cooperative game and cooperative game theories are used to solve the problem of interest distribution between multiple subjects [28]. The Nash bargaining theory is applicable to solve the problem of balanced distribution of interests among multiple subjects, belonging to the category of cooperative game. By alternating a direction method of multipliers, a Nash bargaining cooperative optimization model for wind-solar hydrogen multi-agent energy system is proposed and solved [29]. Considering the uncertainty of market price, RE, and integrated demand response, an integrated energy trading model based on Nash negotiation is proposed [30].
According to the analysis above, the main contributions are summarised as follows:
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This paper innovatively introduces the sharing mechanism into the distribution network to explore whether the SESS can improve the operation characteristics and economic revenues. Different from previous studies, the proposed dynamic capacity model of shared energy storage overcomes the user power interaction phenomenon caused by traditional modelling methods and reveals the essence of shared energy storage of improving efficiency.
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Based on the Nash transaction theory, the proposed multiple VPPs-SESS transaction bargaining models can achieve a fair distribution of benefits after cooperation. VPPs with higher RE power also reap higher benefits in energy sharing, which can stimulate the enthusiasm of VPPs to participate in energy cooperation effectively.
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A multi-VPP interactive model based on the bargaining game theoretic is proposed. The multiplayer game theory is used to simulate the bidding behaviour of multiple VPPs participating in the electricity market so that the dynamic multi-VPP control and operation system are more suitable for the future electricity market.
The remainder of this paper is organised as follows. The operation architecture of multiple virtual power plants (MVPPs) with a SESS (MVPPs-SESS) is formulated in Section 2. The mathematical models of SESS and MVPPs are presented in Sections 3 and 4, respectively. Based on the mathematical model, a bargaining game-theoretic solution method for the MVPPs-SESS trading problem is proposed in Section 5. Case studies are conducted in Section 6. Finally, conclusions are drawn in Section 7.
ARCHITECTURE OF MULTI VPPs-SESS
The VPPO monitors the changes in smart load (SL) in real time and formulates the power dispatching strategy for the interconnection of MVPPs-SESS in the next 24 h. Each VPP is equipped with distributed generators (DG), RE, and energy storage system. However, a single VPP's dispatching capacity is limited, and it may cause a waste of resources, such as power abandonment. Multiple virtual power plants can realize energy interaction between VPPs and optimise energy resource allocation with the cooperation of VPPO. The MVPPs-SESS interconnection system constructed in this paper is shown in Figure 1.
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Figure 1 shows that the demand-side load can be divided into the fixed load (FL) and SL. Fixed load refers to the load whose use state has a great effect on users and cannot be adjusted at will. By contrast, SL is the load that can work intermittently, which is mainly manifested in the characteristics of shift, transfer, and reduction, and is an important part of participating in demand response [31, 32].
In addition, the RE (photovoltaic and wind) generation of each VPP provides priority to meeting the daily load usage of users. When the power generation of RE is sufficient, it can be shared with other VPPs through VPPO. Thus, renewable resources can be allocated reasonably and electricity costs can be reduced.
In the interconnected system of multiple VPPs, VPPO can use price, incentive mechanisms, and other methods to guide the energy demand of users to coordinate the energy load and energy supply in time and space among VPPs. To guarantee its power load demand and the energy security of the distribution network, the interconnection system can reduce the power consumption through other forms of energy and complementation among VPPs when the distribution network's electricity consumption reaches its peak. When the power consumption of the distribution network is at a low point, the supply and demand of multiple VPPs can be coordinated by improving the overall power consumption capacity of the interconnected system.
ESS BASED ON THE SHARING MECHANISM
The SESS gains profits by providing capacity leasing services to VPPs, and VPPs reduce their operating costs by using energy storage services. Taking 1 day and 1 h as the research period and duration, the economic model of the SESS is as follows:
The dynamic capacity model of SESS was established based on the charging and discharging power through a grid structure between multiple users and SESS, which is shown in Equation (10) in most previous studies. When the left side of Equation (10) (the capacity of SESSO) is 0 kW, the power interaction may not be 0 kW (i.e, +5, −3, −2 kW), which indicates that the power inter transmission has formed in VPPs. The traditional modelling method potentially introduces power transmission among multiple users, which is unfavourable to SESSO.
ECONOMIC SCHEDULING MODEL OF VPPs
The VPP is mainly composed of DG, RE, and other resources, which have functions of load shedding, power outsourcing, and use of energy storage services. Specifically, the economic cost of the internal resources of VPP is modelled.
Distributed generators operation cost
With the construction of a new power system, despite many RE sources in the operation of VPP, the controllable distributed generator still plays a certain position on a short time scale. When the controllable distributed generator units participate in the operation of the power system, the economic model is as follows:
Renewable power generation
The output of RE running in the VPP should be within the corresponding rated range. This paper mainly considers photovoltaic generators and wind turbines, the output constraints are as follows:
Smart loads
The adjustable characteristics of smart loads determine their applicability to participate in the absorption of RE, which are of great importance to the coordination and optimization of SESS. To make this model universal, the participation of various smart loads in power grid operation under the guidance of power grid regulation and the electricity price is considered.
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Shiftable load. This type of load has low requirements for the real-time performance of the service. Within its allowable time range, the load can be allocated to other time periods if the execution is completed within the time allowed by the delay to achieve flexible allocation within the allocated time period. The economic model of the response characteristics is as follows:
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Transferable load. Within the allowable time range, this type of load can allocate part of the load to other time periods and realize the flexible transfer of operating time and operating power within its assignable time period. Its operating time and operating power can be adjusted to minimise its cost. The economic model of the response characteristics is as follows:
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Reducible load. Under the incentive of actual operating cost or real-time electricity price, this type of load can be reduced to a certain amount according to the regulation of the power grid or the active participation of users, and its power can be artificially adjusted to play a role of peak shaving during peak electricity consumption. The economic model of the response characteristics is as follows:
Therefore, after VPP participates in the demand response in time period , the new power demand is as follows:
Power exchange with external units
When the output of the internal resources of the VPP cannot meet the balance between supply and demand of the system, it can ensure stable operation by exchanging power with the external grid. This scenario only allows VPP to purchase power from the grid to prevent the VPP from reselling power for price arbitrage.
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VPP is short of power. The VPP is in a power shortage state when the output of VPP cannot meet the internal load demand. At this time, the economic model of interaction with external power is as follows:
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VPP is surplus power. When the internal load of a VPP is low and the unit output has more surplus in a time period , the VPP is in a surplus power state. At this time, the economic model of interaction with external power is as follows:
After the VPP responds to the TOU price, it needs to maintain the balance of the system supply and demand:
MULTI VPPs-SESS TRANSACTION MODEL
Considering that the internal purchase and sell prices of electricity set by the VPPO are not attractive enough, this paper proposes a collaborative operation mode of SESS and MVPPs to minimise the economical operating costs of both parties through the game of electricity price. The energy trading problem of multiple VPPs is formulated as follows:
Although the cooperation among VPPs can effectively decrease the total operation cost of the co-optimization system, an unfair allocation of payoffs might lower the willingness of VPPs to cooperate and restrict the sustainable development of SESS transactive energy trading. Given that Nash bargaining could offer a fair Pareto optimal solution, it is adopted to solve the proposed SESS transactive energy trading model [33]. It is specifically expressed as follows:
Based on the above content, the solution procedures are shown as follows (in parallel):
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Set the iteration parameter , cost coefficients and , and penalty cost parameters of SL. Initialise the output of RE. Input the initial data and related operation constraints. Define convergence threshold .
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Construct game strategy sets including the output of DG, the operation state and power of SL, the charging and discharging plan of SESS, the buy and sell power, and the internal electricity price.
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Give the initial point of each VPP iteration and upload the state to the VPPO.
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VPPO receives the electricity price for VPPs, uses the CPLEX solver to solve the distribution of SL participating in demand response and the electric energy participating in the SESS, and then calculates and retains .
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Calculate and retain the current costs based on the game strategy within a day.
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Calculate and retain the current revenue based on energy storage trading by SESS within a day.
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Update .
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If the terminal condition is satisfied, that is, , end the iteration; otherwise, go back to Step D.
CASE STUDY
Case description
A total of 4 VPPs and 1 SESS are adopted to analyse the energy-reserve co-optimization. The output of RE and smart loads parameters in VPPs is shown in Figure 2 and Table 1. The SESS parameters can be found in [25], where the ratio of rated capacity to power limit is 0.2, the charge and discharge cost per unit is 0.3¥/(kWh), and the costs of capacity and power are 1100 and 1000 ¥/kWh, respectively. The life and daily maintenance cost of the energy storage device are 8 years and 0.20¥, respectively. The initial capacity of each VPP is assumed half of its rented capacity from SESS at the initial moment. TOU price is shown in Table 2.
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TABLE 1 Smart load (SL) parameters in each virtual power plant (VPP)
Project | Parameters | ||||
Shiftable load | (¥/kWh) | 0.4 | |||
(kW) | 144.5 | ||||
(h) | 7 | 4 | |||
Transferable load | (¥/kWh) | 0.1 | |||
(¥/kWh) | 0.2 | ||||
(h) | 12 | 9 | |||
(kW) | 700 | 600 | |||
Reducible load | (¥/kWh) | 2 | 2.2 | ||
Fixed load | (kW) | 1400 | 1200 |
TABLE 2 Time-of-use tariff division and price
Type | Peak time | Normal time | Valley time |
Time division (h) | 7–10, 19–22 | 11–18 | 1–6, 23–24 |
Electricity price (¥/kW·h) | 1.2567 | 0.8406 | 0.4263 |
All case studies are simulated on MATLAB, solved by the Yalmip tool with CPLEX and Interior Point Optimizer solver. Two cases are designed to demonstrate the effectiveness of the proposed co-optimization mode.
Case
All VPPs are equipped with energy storage equipment individually and operate independently.
Case
MVPPs-SESS use shared energy storage services and operate cooperatively.
Results and discussion
Economic benefit analysis
Shared energy storage operator needs to design reasonable capacity to maximise their profits. Virtual power plant operator also divides the required capacity and charging and discharging power of each VPP, according to the rated capacity given by the SESS, and adjusts the output of the internal equipment. The profits of SESS and the total operating costs of VPPO in different cases are shown in Table 3.
TABLE 3 SESS profitability and virtual power plant operator (VPPO) total operating costs
Case | SESS/¥ | VPPO/¥ | Total cost/¥ |
Case 1 | −279620.4 | 6.313473334 × 108 | 6.316269538 × 108 |
Case 2 | 7055.68 | 4.957311 × 108 | 4.957240443 × 108 |
Table 3 shows that the collaborative operation cost is reduced by 21.52% in two ways. The SESS has 7055.68 ¥ revenue in Case 2, whereas SESS has 279,620.4 ¥ loss in Case 1, which changes from the loss state to the profitable state. Moreover, the operation cost of VPPO in Case 2 is reduced from 6.313,473,334 × 108 ¥ to 4.957,311 × 108 ¥ compared with Case 1. On the one hand, the dynamic capacity leasing mechanism can effectively improve the overall utilization rate of RE and energy storage devices to satisfy energy consumption. On the other hand, due to the demand response of the SL, the user side has more flexible adjustment capabilities, that is, the VPP's ‘local absorption’ ability is stronger.
To explore the cost reduction further, based on the solution method and the objective function constructed in Section 5, the operation costs of the four VPPs can be obtained in Case 2. The comparison in Figure 3 shows that the operation costs of VPP1, VPP2, VPP3, and VPP4 are 1.1851 × 108 ¥, 1.51,111 × 108 ¥, 1.12 × 108 ¥, and 1.141,111 × 108 ¥ by Nash bargaining, respectively, which have been reduced to varying degrees after 20 iterations (shown in Figure 4). VPP1 is equipped with DG, wind power, and photovoltaics, whose operation cost is reduced by 25.67%. Although the uncertainty of RE is relatively large, it is also complementary and intermittent to some extent. The SESS is used to alleviate the contradiction between renewable generation and load power consumption, thus reducing the energy consumption cost. VPP2 is equipped with DG only, which has a weak regulation ability to follow loads. Shared energy storage system provides flexible adjustment capabilities during load peaks and valleys to reduce the cost of curtailment and reduces the operation cost by 25.91%. In addition to DG, VPP3 is only equipped with photovoltaics, whereas VPP4 is only equipped with wind turbines. Compared with VPP1, it has less uncertainty. Compared with VPP2, certain adjustment capabilities are observed. Using SESS can enhance the system's flexibility to reduce the cost of abandoning wind and light. Thus, the operation cost of the two is reduced by 14.57% and 16.61%. For VPPs equipped with RE (VPP1, VPP3, and VPP4), their bargaining benefits are proportional to the amount of RE, and higher revenues are obtained in energy sharing.
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In VPP1, Figure 5 shows the internal equipment output of the two cases and Figure 6 shows the comparison between internal power price and TOU price. During the period of 7:00–14:00 and 18:00–24:00, Case 2 buys a large amount of power external compared with Case 1, which can be explained in two aspects. On the one hand, due to high energy consumption during this period, the SESS cannot meet the load demand even though it is used. On the other hand, as shown in Figure 6, the price of buying power from VPP is lower than the TOU price. Although the total power bought in Case 2 is more than that in Case 1, the cost of buying power is lower, and the economy of buying power from VPP is better than that from the grid.
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Operating result analysis
When the VPP operates independently, it can only rely on its existing equipment to arrange energy production and conversion. However, after using SESS, the energy demand can be met through the coordinated operation of equipment. Based on one operating day, the change in the overall utilization rate of energy storage is determined by analysing the changes in the energy storage capacity in Cases 1 and 2. The charge-discharge curve is shown in Figure 7 (positive means charging and negative means discharging).
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The figure shows that the maximum charging and discharge capacity of Case 1 are 956.43,253 and 1170 kW, respectively. The maximum charging capacity of Case 2 is the same as that of Case 1, and the maximum discharge capacity is 970 kW. Given that the load is low and the power is abundant in resources during 1:00–7:00, all the energy storage devices are charged and stored. However, a large difference is observed between 14:00 and 18:00. Case 2 is in the discharging state, but Case 1 is in the charging state, which is the reason for the different charging and discharging frequency of energy storage devices in the two cases. Specifically, Case 1 performs 18 charges and 5 discharges, whereas Case 2 carries out 13 charges and 5 discharges. The utilization frequency of energy storage in energy dispatch of Case 1 is remarkably higher than that of Case 2 because of the SESS, which does well in rationally utilising resources and reducing the charging frequency of energy storage devices. Moreover, the sum of self-discharge and actual power consumption in Case 1 is 4994.76 kW, which is much higher than 280.5648 kW of Case 2.
The internal resources output of VPP4 in the two cases are shown in Figure 8. In Case 1, the maximum output and minimum output of the DG are 3741.94 and 240.54 kW, respectively, the average output is 1945.738,701 kW, and the maximum offset relative to the mean is 1796.2013 kW; all of the above-related quantities in Case 2 are 3556.7, 496.9, 1878.120,833, and 1668.57,917 kW, respectively. The average generating capacity, the relative mean value, and the peak value of DG in Case 2 are less than those in Case 1. On one hand, the average generating capacity of the generator sets in Case 2 is less than that in Case 1. By rationally utilising energy storage services and adjusting the smart loads' operation plan, the distributed resources within the VPP are more fully utilised, effectively reducing the load state of the DG. On the other hand, the relative mean value of the generator output in case 2 is smaller than that in Case 1, and its peak value is also lower than that in Case 1. The dispatch plan of the DG under the operation mode proposed in this paper is better than that of Case 1.
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Figure 9 shows the optimization output of internal resources in VPP2 and VPP3. Combined with Figures 5 and 8b, all loads of SL that can be cut off are cutoff: 210 kW is cut off in each period of the first four dispatch periods of VPP1, and 70 kW is cut off in the fifth period. In the first four scheduling periods of VPP2–VPP4, 180 kW is cut off in each period, and 60 kW is cut off in the fifth period. All of the first four periods reach the maximum cutting load limitation of each period. Thus, for VPPs, the operating cost of the reducible load is greater than the cost of cutting load. In dispatching operations, the cost of load cutting is preferential, and this part of the electricity is transferred to other smart loads.
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CONCLUSION
With the development of sharing economy, this paper proposes an economic operation model of shared energy storage trading mechanism applied to multi-VPP interconnection systems to explore the advantage of SESS in saving economic costs and improving the utilization of RE. The key findings are summarised as follows:
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The energy trading model of energy storage based on the sharing mechanism proposes an economic resource utilization solution for VPP to participate in the competitive electricity market. Compared with traditional studies, the dynamic capacity model of the SESS in this paper not only increases the SESS revenue by 102.52% but also reduces the collaborative operation cost by 21.52%, which has overcome the phenomenon of user power interaction.
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After the benefits of VPPO are distributed fairly, all VPPs achieve Pareto optimality. The VPP with higher RE power can obtain higher benefits in the energy sharing system according to the operation costs reduced by 25.67%, 25.91%, 14.57%, and 16.61%. Thus, the MVPPs-SESS transaction model stimulates the enthusiasm of each VPP to participate in energy cooperation and encourages distributed entities to increase RE power generation construction effectively.
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The internal resources and external market coordination strategy realize the effective management within the VPPO through the dynamic game of electricity price among VPPs, which make the distributed resources fully utilised and DG output optimised. Moreover, the demand side has more flexible adjustment capabilities, and the ‘local consumption’ is stronger due to the addition of demand response and SESS, realizing effective load management and higher renewable DG utilization.
ACKNOWLEDGEMENT
This work was supported by the National Natural Science Foundation of China (52177103, U2166211).
CONFLICT OF INTEREST
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
DATA AVAILABILITY STATEMENT
Data are available on request from the authors.
Cruz, M.R.M., et al.: A comprehensive survey of flexibility options for supporting the low‐carbon energy future. Renew. Sustain. Energy Rev. 97, 338–353 (2018). [DOI: https://dx.doi.org/10.1016/j.rser.2018.08.028]
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Abstract
The emergence of the shared energy storage mode provides a solution for promoting renewable energy utilization. However, how establishing a multi‐agent optimal operation model in dealing with benefit distribution under the shared energy storage is still a challenge. Considering the multi‐agent integrated virtual power plant (VPP) taking part in the electricity market, an energy trading model based on the sharing mechanism is proposed to explore the effect of the shared energy storage on multiple virtual power plants (MVPPs). To analyse the relationship among MVPPs in the shared energy storage system (SESS), a game‐theoretic method is introduced to simulate the bidding behaviour of VPP. Furthermore, the benefit distribution problem of the virtual power plant operator (VPPO) is formulated based on the Nash bargaining theory. In the case study, the proposed method is conducted in four VPPs with different resource endowments in terms of techno‐economic and operation efficiency. Results verify that the multiple virtual power plants with a shared energy storage system interconnection system based on the sharing mechanism not only can achieve a win‐win situation between the VPPO and the SESS on an operation cost but also obtain the optimal allocation scheme and improves the operation efficiency of the VPPs.
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