Multi-type aggregator non-cooperative game electric energy transaction method

By establishing a non-cooperative game power trading method for multi-type aggregators, the transaction threshold problem of distributed wind power and photovoltaic power supply in the new power market is solved, and the multi-participant power trading architecture and Nash equilibrium solution are realized, and the market strategy and transaction results are optimized. .

CN119205342APending Publication Date: 2024-12-27ANHUI ELECTRIC POWER TRADING CENT CO LTD +3
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Patent Information

Application Number
CN202411385014.X
Authority / Receiving Office
CN · China
Patent Type
Applications(China)
Current Assignee / Owner
Filing Date
2024-09-30
Publication Date
2024-12-27

AI Technical Summary

Technical Problem

In the new power market, distributed wind power and photovoltaic power supply are difficult to meet the market transaction threshold due to low capacity. In the non-cooperational game relationship between aggregators, it is difficult to consider the influence of multiple participants in the optimization of market strategy, resulting in the market outage The results of the clearance were not ideal.

Method used

A multi-type aggregator non-cooperative game power trading method is proposed, a multi-participant power trading structure is established, a non-cooperative game model is established based on the transaction structure and model, and its Nash equilibrium solution is found, and a distribution network is supported to formulate reasonable trading models and Trading rules.

Benefits of technology

The coordinated participation of multiple types of distributed energy aggregators and distribution network operators has been achieved, the power trading model has been optimized, the rational decision-making of market strategies has been ensured, and the efficiency and economicality of market clearance results have been improved.

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Abstract

The invention discloses a multi-type aggregator non-cooperative game electric energy transaction method, and belongs to the technical field of electric power system operation and planning, and the method comprises the steps: S1, building a multi-participant electric energy transaction architecture in consideration of the common participation of a multi-type distributed energy aggregator and a power distribution network operator; s2, on the basis of the electric energy transaction architecture, establishing an electric energy transaction mode; and S3, based on the electric energy transaction architecture and the transaction mode, establishing a non-cooperative game model and solving a Nash equilibrium solution of the non-cooperative game model. The technology can be used for energy main body operation and transaction work in a distributed energy high-permeability power distribution network, and provides support for establishing an electric energy transaction mechanism between a power distribution network operator and a multi-type distributed energy aggregator.
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Description

Technical Field

[0001] The present invention belongs to the technical field of power system operation and planning, and specifically relates to a non-cooperative game power trading method for multiple types of aggregators. Background Art

[0002] Renewable energy trading plays an important role in promoting the clean and low-carbon transformation of energy production and consumption. At present, with the continuous promotion of renewable energy, the potential of wind and solar power generation to participate in energy trading is increasing. In the context of the new power market, the rational use of these renewable power resources can significantly improve the operating efficiency of the distribution network. However, the capacity of distributed wind power and photovoltaic power is generally low, and it is difficult for the units to meet the market transaction capacity threshold. Therefore, they often form a variety of different types of aggregators independently or together with load resources, and conduct electricity trading with other market participants in the form of aggregators. With the goal of economic optimization, aggregators can act as operators of electric energy resources, minimize electricity costs by optimizing their power purchase and sales plans, and maximize their economic benefits. When there are multiple aggregators in the market, when formulating market strategies, they need to consider not only the internal resource output and market prices, but also the impact of the strategies of other market participants. Competition will also form between aggregators, and they will affect the market clearing results by adjusting their own market strategies. Through the continuous iteration of aggregator strategy optimization and market clearing, convergence to the Nash equilibrium of the market.

[0003] In summary, a non-cooperative game relationship can be formed between aggregators and distribution network operators. In a non-cooperative game relationship, the goal of the participants is personal rationality and optimal decision-making. In a non-cooperative market environment, multiple market participants are in a competitive relationship and only consider their own optimal economic benefits. In this case, the strategy optimization of aggregators and distribution network operators needs to consider the market strategies of other participants. And this influence is usually manifested in the impact of the market strategies of aggregators and distribution network operators on the market clearing results. Summary of the invention

[0004] Taking into account the development needs of the prior art, the purpose of the present invention is to provide a non-cooperative game electricity trading method for multiple types of aggregators. This method takes into account the situation where multiple types of distributed energy aggregators and distribution network operators participate together, establishes a multi-party electricity trading architecture, and on the basis of the trading architecture, establishes an electricity trading model. Based on the trading architecture and the trading model, a non-cooperative game model is established and its Nash equilibrium solution is sought. The method has strong practical application significance and provides support for the distribution network to formulate reasonable trading models and trading rules.

[0005] The purpose of the present invention can be achieved by the following technical solutions: A non-cooperative game power trading method for multiple types of aggregators, comprising the following steps: S1, considering the participation of multiple types of distributed energy aggregators (AGs) and distribution network operators (DGOs), establish a multi-party electricity trading architecture; S2, based on the power trading framework, establish a power trading model; S3, based on the electricity trading architecture and electricity trading model, establish a non-cooperative game model and find its Nash equilibrium solution.

[0006] Beneficial effects of the present invention: A trading framework that considers the participation of multiple aggregators and distribution network operators of distributed energy is proposed; a specific trading model is given based on the trading framework; a non-cooperative game model is established based on the framework and trading model, and the Nash equilibrium solution is sought. BRIEF DESCRIPTION OF THE DRAWINGS

[0007] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, for ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0008] Figure 1 It is an overall implementation flow chart of the non-cooperative game power trading method of multiple types of aggregators of the present invention; Figure 2 This is a diagram of the electric energy transaction architecture in which the S1 multi-type distributed energy aggregator and the distribution network jointly participate, provided by the present invention. The arrows in the diagram indicate the flow of electric energy transactions; DETAILED DESCRIPTION

[0009] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0010] like Figure 1 As shown, a multi-type aggregator non-cooperative game power trading method includes the following steps: S1, considering the participation of multiple types of distributed energy aggregators (AGs) and distribution network operators (DGOs), establish a multi-party electricity trading architecture.

[0011] In response to the current demand for distributed power aggregation transactions, the present invention proposes an energy transaction architecture involving multiple types of distributed energy aggregators and distribution network operators; Figure 2 As shown, the architecture is specifically described as follows: The distributed energy mentioned in the transaction structure mainly includes distributed wind power, distributed photovoltaic power, etc. Due to the small capacity of a single unit, this type of distributed energy does not meet the threshold for participating in market transactions. Based on interests or geographical location factors, it is aggregated into aggregators, and the aggregators participate in the energy market as the trading subjects. The aggregators may also include loads, which mainly include various types of industrial, commercial and residential user loads.

[0012] The above-mentioned aggregators are divided into three types according to the power resources they aggregate: first aggregators, second aggregators, and third aggregators. Figure 2 They are marked as AG-1, AG-2 and AG-3 respectively. The second aggregator is divided into the second power purchase aggregator (AG-2 (power purchase)), the second power sales aggregator (AG-2 (power sales)) and the second balancing aggregator (AG-2 (balancing)).

[0013] Among them, AG-1 is formed by the aggregation of distributed energy, and only aggregates distributed energy including distributed photovoltaic and distributed wind power. All the electricity generated by AG-1 at all times will be sold to DGO or other types of aggregators AG-2 (power purchase) and AG-3.

[0014] The aggregation scope of AG-2 includes distributed energy and loads, and the power generated by distributed energy within its aggregation scope will first meet the load demand within its aggregation scope. If there is surplus distributed energy power, it will be sold to other aggregators or DGOs, which is AG-2 (power sales); if distributed energy is not enough to support the load demand within the aggregation scope, it will purchase power from other aggregators or DGOs, which is AG-2 (power purchase); if its distributed energy generation just meets the load demand within its own aggregation scope, it is AG-2 (balance).

[0015] AG-3 only aggregates loads, and all the electricity it needs will be purchased from DGO or AG-1 and AG-2 (electricity sales).

[0016] As an important market participant under the transaction structure, the regional distribution network operator DGO's main functions are to purchase electricity sold by aggregators AG-1 and AG-2 (electricity sales) when necessary; to sell electricity to aggregators AG-2 (electricity purchase) and AG-3; and to provide support services for electricity transactions between aggregators AG-1, AG-2 and AG-3, and to charge corresponding transaction service fees.

[0017] S2, execute the power trading mode based on the above power trading architecture. Before describing the trading steps of the power trading mode, first describe the setting of step execution: the trading steps are executed in a complete trading time period. The unit price of electricity purchased by DGO from aggregators AG-1 and AG-2 (electricity sales) and the unit price of electricity sold to aggregators AG-2 (electricity purchase) and AG-3 is a fixed value, < , unit: yuan / (kW·h). DGO provides support services for transactions between aggregators AG-1, AG-2, and AG-3, and charges service fees to both parties according to the transaction volume. The transaction process meets the following requirements: time period Within the transaction, the power generation of AG-1, the power sales / purchase of AG-2 and the power purchase of AG-3 are all fixed values, and each aggregator and DGO are aware of the above parameters of each aggregator participating in the transaction, the power purchase price and power sales price of DGO.

[0018] The transaction steps include: S21, during trading hours At the initial moment, AG-1, AG-2 (power sales) and DGO independently quote prices. AG-1 and AG-2 (power sales) quote the prices they sell to AG-2 (power purchase) and AG-3. Quote, transaction service fee provided by DGO Quote; S22, AG-2 (power purchase) and AG-3 trade electricity with AG-1, AG-2 (power sales) or DGO in turn according to the power sales prices of AG-1 and AG-2 (power sales) and the service prices of DGO, in accordance with the principle of minimizing transaction costs, until their own power shortage is met. In order to facilitate the actual power purchase operation, the transaction order is set as follows: ①AG-2 (power purchase) and AG-3 purchase electricity in order from large to small power shortage; ②When the power shortages of AG-2 (power purchase) and AG-3 are the same, the aggregator with a smaller initial aggregator number purchases electricity first; ③When the power purchase unit costs from AG-1, AG-2 (power sales) and DGO are the same, AG-2 (power purchase) and AG-3 purchase electricity from AG-1 and AG-2 (power sales) first; ④When the power sales prices of AG-1 and AG-2 (power sales) are the same, AG-2 (power purchase) and AG-3 purchase electricity from the aggregator with a larger initial number first; S23: If there is still surplus electricity in AG-1 and AG-2 (electricity sales) after step S22, they will sell all the surplus electricity to DGO and obtain the income from electricity sales to DGO. At the initial moment, the power vector of all aggregators selling or purchasing electricity is P, with dimension 1×N. The i-th component Pi represents the power of aggregator i selling electricity to the outside, which can be negative, indicating that it purchases electricity from the outside. Suppose the number of AG-1 and AG-2 (selling electricity), AG-2 (purchasing electricity) and AG-3, AG-2 (balance) in the system are Nb, Ns and N0, respectively, corresponding to the number of positive, negative and zero elements in P, then Nb + Ns + N0 = N. When Nb = 0, it means that all aggregators in the area are AG-2 (purchasing electricity) / AG-3 type aggregators, and all aggregators purchase electricity directly from DGO; when Ns = 0, it means that all aggregators in the area are AG-1 / AG-2 (selling electricity) type aggregators, and all aggregators sell electricity directly to DGO; in both cases, the aggregators do not need to bargain with DGO or other aggregators to complete the transaction. Therefore, at this time, "the game exists" and "Ns and Nb are not 0" are equivalent.

[0019] S3, based on the power trading architecture and power trading mode, establish a non-cooperative game model and find its Nash equilibrium solution. The specific solution is as follows: S31, in the non-cooperative game model, the game participants mainly include AG-1, AG-2 (electricity sales) and DGO; S32, in the non-cooperative game model, the game strategies of AG-1 and AG-2 (electricity sales) are their electricity prices, and their strategy set is [0, max], where max is the upper limit of the electricity price that can be set by the aggregator in the trading market; DGO’s game strategy is to charge the support service fee for the electricity exchange between aggregators, and its strategy set is [0, max], where max is the upper limit of the service fee for power trading between aggregators stipulated by the trading market; S33, in the non-cooperative game model, the game profit of DGO is calculated as follows: DGO income It mainly consists of the following three parts: The generation cost of the electricity sold by DGO to the aggregator ; Revenue from trading electricity between DGO and aggregators ; The service fee income collected by DGO for electricity trading between aggregators .

[0020] , DGO power generation cost: The power sold by DGO to aggregators or users comes from the grid supply or purchase from power generators. There are many sources. This application uses the comprehensive unit power generation cost. To represent the unit cost of this electricity price. It should be noted that when DGO sells electricity, if it also purchases electricity from some aggregators, the purchased electricity will be sold directly without having to be obtained from power generation equipment or the main grid. Therefore, the cost of DGO electricity generation can be expressed as: , In the formula, is the total amount of electricity sold by DGO to all aggregators, For DGO The power sold by aggregators (AG-2 (power purchase), AG-3 types), , They are power sales, aggregators ; It is the total number of AG-2 (power purchase) and AG-3 type aggregators; ; is the total amount of electricity purchased by DGO from all aggregators. For DGO The power purchased by aggregators (AG-1, AG-2 (electricity sales) types), is the total number of AG-1 and AG-2 (electricity sales) type aggregators, is the purchased power, Is an aggregator .

[0021] Revenue from electricity trading with aggregators: DGO can obtain electricity sales revenue by selling electricity directly to AG-2 (electricity purchase) and AG-3. At the same time, DGO will pay the corresponding electricity purchase cost when purchasing electricity from AG-1 and AG-2 (electricity sales). In summary, the revenue generated by DGO's direct electricity trading with aggregators can be expressed as: , In the formula, Revenue generated by direct trading of electricity between DGO and aggregators; The revenue that DGO gets from selling electricity to aggregators. ; The cost of DGO purchasing electricity from aggregators, . and The calculation method is: , , In the formula, during the trading time Within the range, The unit price at which DGO sells electricity to aggregators; The unit price for DGO to purchase electricity from aggregators; For DGO The power sold by aggregators (AG-2 (power purchase), AG-3 types); For DGO The power purchased by each aggregator (AG-1, AG-2 (electricity sales) type); It is the total number of AG-2 (power purchase) and AG-3 type aggregators; It is the total number of AG-1 and AG-2 (electricity sales) type aggregators.

[0022] Transaction service fee income between aggregators: When power transactions occur between aggregators, DGO provides support services to both parties. Therefore, DGO will charge the same transaction service fee to both parties. . This income It is also included in the income of DGO, and the calculation method is: , in, For Aggregators With aggregators Trading power between; S34, in the non-cooperative game model, the game benefits of AG-1 and AG-2 (electricity sales) are calculated as follows: The revenue of aggregators AG-1 and AG-2 (electricity sales) mainly consists of the following three parts: ; The generation cost of the electricity sold by the aggregator ; Transaction service fee paid to DGO when selling electricity to AG-2 (power purchase) and AG-3 type aggregators .Right now: , It consists of two parts, namely, the income from AG-1 and AG-2 (electricity sales) sold to DGO Revenue from electricity sales to AG-2 (power purchase) and AG-3 type aggregators .

[0023] , , , in, The number of aggregators of type AG-2 (power purchase) and AG-3; The price of electricity sold by aggregators to DGO, ; The power sold to DGO; The price of electricity sold to AG-2 (power purchase) and AG-3 type aggregators; To the The electricity sales capacity of an aggregator.

[0024] The generation cost of the electricity sold by the aggregator is calculated as: , in, is the unit power generation cost of the aggregator.

[0025] The transaction service fee paid to DGO when selling electricity to AG-2 (power purchase) and AG-3 type aggregators is calculated as follows: , in, Aggregators The electricity sold.

[0026] S35, according to the Nash equilibrium existence theorem, discretize the game strategy, search the entire game strategy space according to the Nash equilibrium definition, and find the Nash equilibrium solution. The game strategy space refers to the sum of the game strategies set in the above steps.

[0027] In the description of this specification, the description with reference to the terms "one embodiment", "example", "specific example", etc. means that the specific features, structures, materials or characteristics described in conjunction with the embodiment or example are included in at least one embodiment or example of the present invention. In this specification, the schematic representation of the above terms does not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described can be combined in any one or more embodiments or examples in a suitable manner.

[0028] The above shows and describes the basic principles, main features and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments, and the above embodiments and descriptions are only for explaining the principles of the present invention. Without departing from the spirit and scope of the present invention, the present invention may have various changes and improvements, and these changes and improvements all fall within the scope of the present invention to be protected.

Claims

1. A non-cooperative game power trading method for multiple types of aggregators, characterized in that: The following steps are involved: S1, considering the joint participation of multiple types of distributed energy aggregators and distribution network operators DGO, establish a multi-party electricity trading architecture; S2, based on the power trading framework, establish a power trading model; S3, based on the electricity trading architecture and electricity trading model, establish a non-cooperative game model and find its Nash equilibrium solution.

2. A non-cooperative game power trading method for multiple types of aggregators according to claim 1, characterized in that: In S1, the established multi-party electric energy trading architecture includes: The distributed energy aggregators are divided into three types according to the electric energy resources they aggregate: first aggregators, second aggregators, and third aggregators. The second aggregators are divided into second power purchase aggregators, second power sales aggregators, and second balancing aggregators. The first aggregator is formed by the aggregation of distributed energy resources and only aggregates distributed energy resources including distributed photovoltaic and distributed wind power. All electricity generated by the first aggregator at all times will be sold to DGO or the second power purchasing aggregator / third aggregator; The aggregation scope of the second aggregator includes distributed energy and loads. The power generated by the distributed energy within its aggregation scope will first meet the load demand within its aggregation scope. If there is surplus distributed energy power, it will be sold to other aggregators or DGOs. At this time, it behaves as the second power sales aggregator; if the distributed energy is not enough to support the load demand within the aggregation scope, it will purchase electricity from other aggregators or DGOs. At this time, it behaves as the second power purchase aggregator; if its distributed energy generation just meets the load demand within its own aggregation scope, it behaves as the second balancing aggregator; The third aggregator only aggregates loads, and all the electricity it needs will be purchased from DGO or the first aggregator or the second electricity sales aggregator; The three-dimensional functions of the regional distribution network operator DGO under the electricity trading framework are to purchase electricity sold by the first aggregator and the second electricity sales aggregator when necessary; sell electricity to the second electricity purchasing aggregator and the third aggregator; and provide support services for electricity transactions between the first aggregator, the second aggregator and the third aggregator, and charge corresponding transaction service fees.

3. A non-cooperative game power trading method for multiple types of aggregators according to claim 1, characterized in that: In S2, the transaction steps of the electric energy transaction mode are in a complete transaction time period. The unit price of electricity purchased by DGO from the first aggregator and the second electricity sales aggregator is and the unit price of electricity sold to the second electricity purchasing aggregator and the third electricity aggregator is a fixed value, < , the unit is yuan / (kW·h). DGO provides support services for transactions between the first aggregator, the second aggregator, and the third aggregator, and charges service fees to both parties according to the transaction volume. The transaction process meets the following requirements: time period The power generation of the first aggregator, the power sales or purchase of the second aggregator, and the power purchase of the third aggregator are all fixed values, and each aggregator and DGO are aware of the above parameters of each aggregator participating in the transaction, the power purchase price and power sales price of DGO; The transaction steps of the power trading model based on the power trading framework established by S1 include: S21, during trading hours At the initial moment, the first aggregator, the second electricity sales aggregator and DGO independently quote prices, and the first aggregator and the second electricity sales aggregator sell electricity to the second electricity purchase aggregator and the third aggregator at the price Quote, transaction service fee provided by DGO Quote; S22, the second electricity purchasing aggregator and the third electricity aggregator conduct electricity transactions with the first aggregator, the second electricity selling aggregator or DGO in turn according to the electricity selling prices of the first aggregator and the second electricity selling aggregator and the service price of DGO, in accordance with the principle of minimizing their transaction costs, until their own electricity shortage is met; S23: If after step S22, the first aggregator and the second electricity sales aggregator still have surplus electricity, they will sell all the remaining electricity to DGO and obtain the income from selling electricity to DGO.

4. A non-cooperative game power trading method for multiple types of aggregators according to claim 3, characterized in that: The transaction sequence of the electricity transaction in step S22 is as follows: The second electricity purchasing aggregator and the third electricity purchasing aggregator purchase electricity in the order of the largest electricity deficit to the smallest one; When the power shortage of the second and third power purchasing aggregators is the same, the aggregator with the smaller initial aggregator number will purchase power first; When the unit cost of electricity purchased from the first aggregator, the second electricity sales aggregator and the DGO is the same, the second electricity purchase aggregator and the third aggregator shall give priority to purchasing electricity from the first aggregator and the second electricity sales aggregator; When the electricity selling prices of the first aggregator and the second electricity selling aggregator are the same, the second electricity purchasing aggregator and the third electricity purchasing aggregator shall give priority to purchasing electricity from the aggregator with a larger initial number.

5. A non-cooperative game power trading method for multiple types of aggregators according to claim 1, characterized in that: In S3, based on the power trading architecture and power trading mode, a non-cooperative game model is established and its Nash equilibrium solution is sought, including: S31, in the non-cooperative game model, the game participants mainly include the first aggregator, the second electricity sales aggregator and the DGO; S32, in the non-cooperative game model, the game strategies of the first aggregator and the second electricity sales aggregator are their electricity prices, and their strategy set is [0, max], where max is the upper limit of the electricity price that can be set by the aggregator in the trading market; DGO’s game strategy is to charge the support service fee for the electricity exchange between aggregators, and its strategy set is [0, max], where max is the upper limit of the service fee for power trading between aggregators stipulated by the trading market; S33, in the non-cooperative game model, the game profit calculation method of DGO is as follows: DGO income It mainly consists of the following three parts: The generation cost of the electricity sold by DGO to the aggregator ; Revenue from trading electricity between DGO and aggregators ; The service fee income collected by DGO for electricity trading between aggregators ; , The DGO power generation cost is expressed as: , In the formula, is the total amount of electricity sold by DGO to all aggregators, Represents a complete trading period. is the unit cost of electricity purchased by DGO from the grid or power generators, For DGO The power sold by each aggregator, , They are electricity sales power, aggregators ; is the number of second electricity purchasing aggregators and third electricity purchasing aggregators; ; is the total amount of electricity purchased by DGO from all aggregators. For DGO The power purchased by each aggregator, is the number of first aggregators and second electricity sales aggregators, is the purchased power, Is an aggregator ; The revenue generated by direct electricity trading between DGO and the first aggregator, the second electricity sales aggregator, the second electricity purchase aggregator, and the third aggregator is expressed as: , In the formula, Revenue generated by direct trading of electricity between DGO and aggregators; The revenue that DGO gets from selling electricity to aggregators. ; The cost of DGO purchasing electricity from aggregators, , and The calculation method is: , , In the formula, during the trading time Within the range, The unit price at which DGO sells electricity to aggregators; The unit price for DGO to purchase electricity from aggregators; For DGO The power sold by each aggregator; For DGO The power purchased by each aggregator; is the total number of second electricity purchasing aggregators and third electricity purchasing aggregators; is the total number of first aggregators and second electricity sales aggregators; DGO collects transaction service fees from both parties of the transaction Service fee income The calculation method is: , in, For Aggregators With aggregators Trading power between; S34, in the non-cooperative game model, the game benefits of the first aggregator and the second electricity sales aggregator are calculated as follows: The income of the first aggregator and the second electricity sales aggregator consists of the following three parts: ; The generation cost of the electricity sold by the aggregator ; Transaction service fees paid to DGO when selling electricity to the second electricity purchasing aggregator and the third electricity purchasing aggregator : , It consists of two parts: the income from the first aggregator and the second electricity sales aggregator selling electricity to DGO. , and the income from selling electricity to the second electricity purchasing aggregator and the third electricity aggregator : , , , in, is the total number of second electricity purchasing aggregators and third electricity purchasing aggregators; The price of electricity sold by aggregators to DGO, ; The power sold to DGO; The price of electricity sold to the second power aggregator and the third power aggregator; To the The power sold by each aggregator; The generation cost of the electricity sold by the aggregator is calculated as: , in, is the unit power generation cost of the aggregator; The transaction service fee paid to DGO for selling electricity to the second electricity purchasing aggregator and the third electricity purchasing aggregator is calculated as follows: , S35, according to the Nash equilibrium existence theorem, the game strategy is discretized, and the entire game strategy space is searched according to the Nash equilibrium definition to obtain the Nash equilibrium solution.