Operation method for providing leasing service based on limited rationality shared energy storage

Abstract

The invention discloses an operation method for providing a leasing service based on limited rationality shared energy storage, the operation method for providing the leasing service based on the shared energy storage is oriented to a multi-microgrid power distribution system, and the shared energy storage provides an energy storage leasing service for a plurality of microgrids as required. And efficient sharing and utilization of energy storage resources are realized through time and space differences of energy storage used by different microgrids. A shared energy storage operator is taken as a main body, and a shared energy storage operation strategy for depicting irrational behaviors of a microgrid cluster based on a master-slave game is provided for the influence of limited rational response behaviors of the microgrid operator on a shared energy storage pricing strategy when the shared energy storage rental price is uncertain. A double-layer optimization framework is constructed based on a master-slave game, and the balance of the interests of the two parties is finally realized through the iterative game of the micro-grid operator and the shared energy storage operator. The method is a data driving method, detailed physical parameters are not needed, the energy storage requirement of the microgrid is simplified, computing resources are saved, and the computing efficiency is improved.

Description

Technical Field

[0001] The present invention relates to the field of electrical engineering technology, and in particular to an operating method for providing leasing services for shared energy storage based on bounded rationality. Background Art

[0002] In the study of shared energy storage leasing service operational strategies, developing a reasonable pricing mechanism and analyzing the leasing decisions of multiple stakeholders are crucial. The current market comprises diverse participants, including microgrid operators and shared energy storage operators. Analyzing the leasing behavior of these stakeholders and establishing a reasonable pricing system are key issues in promoting the development of energy storage sharing models. Different types of energy storage users have varying degrees of price sensitivity, and changes in leasing prices directly impact their leasing demand. Therefore, when providing leasing services to multiple microgrids, shared energy storage should develop a reasonable and fair pricing mechanism to ensure economic efficiency and fairness for both parties involved. This is crucial for increasing the absorption of new energy and the commercialization and scale-up of shared energy storage.

[0003] To address this issue, a two-stage operation method is needed to improve the utilization and revenue of shared energy storage. The corresponding research work on the two-stage operation method for providing leasing services for shared energy storage has important theoretical and engineering value. Summary of the Invention

[0004] In response to the problems existing in the existing technology, the present invention proposes a two-stage operation method for providing leasing services for shared energy storage based on bounded rationality, based on the different preferences of operators for leasing electricity prices and combined with the ideas of prospect theory. This method accurately characterizes the impact of the bounded rationality characteristics of microgrid operators on shared energy storage pricing, estimates more practical leasing strategies, avoids the risk of suboptimal economic benefits caused by decision mismatch, and designs more practical shared energy storage operation strategies.

[0005] To achieve the above object, the present invention adopts the following technical solutions:

[0006] An operating method for providing a leasing service for shared energy storage based on bounded rationality includes the following steps:

[0007] (1) Using a community detection algorithm to cluster microgrids; selecting the output characteristics of microgrids and the preference for using energy storage as comprehensive similarity measurement indicators, where the output characteristics include the output size and the shape trend of the output curve; based on the comprehensive similarity measurement indicators, the similarity matrix between microgrids in the multi-microgrid distribution system is calculated, and the microgrids are clustered using a community detection algorithm;

[0008] (2) After clustering the microgrid using the community detection algorithm, the rationality coefficients of each cluster taking into account the differences in rationality are solved based on the endowment effect, so as to accurately characterize the different reactions of different types of renters when facing uncertain electricity prices, and then simulate the rational behavior of various types of energy storage renters; according to the characteristics of different microgrid clusters and their satisfaction with the rental electricity price of shared energy storage, different rationality coefficients are set to represent their rationality;

[0009] (3) The Stackelberg game framework is used for modeling optimization to solve the decision-making of shared energy storage operators and microgrid clusters to determine the time-sharing leasing price through game interaction; the upper-level shared energy storage operators are related to the leasing demand of the lower-level microgrid operators through leasing pricing strategies, and the demand of microgrid operators is in turn related to the profit optimization of shared energy storage operators. The upper-level shared energy storage leasing service pricing model and the lower-level microgrid operator leasing demand model are established; the dynamic interaction between the upper and lower levels is used through continuous iteration to eventually reach a market equilibrium.

[0010] Furthermore, in step (1), the community detection algorithm is used to cluster the microgrid, specifically: the Fast Unfolding algorithm in the community detection algorithm is used to select the characteristic value index and combine it with the similarity between microgrids, and the nodes with high similarity are clustered, that is, the distributed microgrid is clustered into clusters with different rationality levels, and the final multi-microgrid clustering is achieved by optimizing the modularity function, and the finite rationality coefficients [γ1, γ2, ..., γ k ], which is used to subsequently solve different rationality coefficients for microgrid clusters with different rationality levels.

[0011] Furthermore, in the step (1), the similarity matrix between the microgrids of the multi-microgrid distribution system is obtained based on the comprehensive similarity measurement index, specifically: the similarity matrix between the microgrids of the multi-microgrid distribution system is obtained based on the comprehensive similarity measurement index by determining the comprehensive similarity index. Since in the community network, the similarity index is used to measure the intimacy between nodes and reflect the similarity between nodes; when clustering multiple microgrids, the output characteristics of the microgrid and the preference for using energy storage are selected as the comprehensive similarity measurement index; the comprehensive similarity index includes: the similarity measurement of the residual power size, the similarity measurement of the residual power curve shape trend and the similarity measurement of the preference for using energy storage.

[0012] Furthermore, the comprehensive similarity index is specifically:

[0013] (a) Residual power similarity measurement

[0014] The power difference represents the shaded area between the two residual power curves and the coordinate axis. If the two microgrid residual power curves are similar, the power sizes of the two must be similar. Therefore, the residual power similarity s1(i, j) of i and j is defined as:

[0015]

[0016] in, Respectively represent the residual power of microgrids i and j at time t; the larger the value of s1, the more similar the residual power of the two is; T = 24, the time step is 1h;

[0017] (b) Similarity measurement of residual power curve morphology trend

[0018] The morphological trend indicates the power output in different microgrids. Under the same weather conditions and in the same area, the morphological trends of two residual power curves are similar. The cosine similarity algorithm is used to calculate the output waveform similarity between microgrids i and j.

[0019] Assuming that the wind and solar power output of the microgrid has a surplus beyond meeting its own load demand, that is, the residual power of the microgrid is positive, the cosine similarity of the residual power of the microgrid ranges from [0, 1]. The larger the similarity value, the higher the cosine similarity. The waveform similarity of the two residual power curves is positively correlated with the size of the similarity value. Therefore, the similarity s2(i, j) of the residual power curve shape trend of microgrid i and j is defined as:

[0020]

[0021] (c) Similarity measure using energy storage preference

[0022] Based on historical deviation data and historical energy storage usage, the subjective preference of microgrid operators for energy storage usage is characterized; assuming that the historical energy storage usage data of energy storage users in the area is known Where 1 means that energy storage is used and 0 means that it is not used; then define an indicator p to quantify the energy storage preference i , to express the microgrid's preference for energy storage use. The preference index is defined as:

[0023]

[0024] in, Indicates the usage of energy storage; represents the actual output of microgrid i at time t; represents the output plan submitted by microgrid i at time t, i.e., the predicted output in the day-ahead phase. A higher value of the energy storage preference index indicates that the microgrid is more inclined to use energy storage when the output deviation is large, i.e., the higher the preference level.

[0025] Therefore, the similarity between microgrids i and j regarding energy storage usage preferences is expressed as:

[0026] s3(i,j)=1-|p i -p j |;

[0027] Among them, p i represents the preference of microgrid i for using energy storage; p j represents the preference degree of microgrid j to use energy storage;

[0028] The calculated similarity value s3(i,j) is used as the similarity between microgrids i and j regarding the preference for leasing energy storage. The similarity metric is positively correlated with the similarity of the energy storage preferences of the two microgrids.

[0029] The three similarities mentioned above, namely, the similarity measure of the remaining power size, the similarity measure of the remaining power curve shape trend, and the similarity measure of the energy storage preference, are normalized to obtain the comprehensive similarity measure distance S. The larger the comprehensive measure distance, the higher the similarity of the two curves. The expression is as follows:

[0030] s ij =s1(i,j)·s2(i,j)·s3'(i,j);

[0031] Among them, s3'(i,j) represents the normalized similarity;

[0032] Therefore, the similarity matrix S is expressed as:

[0033]

[0034] After obtaining the comprehensive similarity index, a modularity function is established based on the Fast Unfolding algorithm in the community detection algorithm to evaluate the strength of the community structure. The value of the modularity function Q is positively correlated with the tightness of the connection within the community. The modularity function expression is defined as:

[0035]

[0036] Where,

[0037]

[0038] Among them, the weight of the connection line between nodes i and j is expressed as A ij Indicates; k i represents the sum of the edge weights of node i; the sum of all edge weights of the network is represented by h; if two nodes i and j are classified into the same partition, then the function on the contrary The relationship between nodes is described by node similarity. Therefore, the weight of the edge between nodes needs to be replaced by the calculated value of node similarity. The improved modularity function is:

[0039]

[0040] Where,

[0041]

[0042] Among them, the similarity between nodes i and j is s ij 'Measurement; the sum of similarities between node i and other nodes is s i The cumulative value of similarity between nodes in the entire network is represented by s, and the similarity is obtained by S. Furthermore, after the microgrid is clustered using the community detection algorithm in step (2), the rationality coefficient of each type of cluster taking into account the difference in rationality is solved based on the endowment effect, specifically:

[0043] To characterize the operating habits of microgrid operators, a utility function is constructed with two dimensions. The utility function represents the trade-off between price satisfaction and operational comfort when leasing shared energy storage.

[0044] The price satisfaction is determined by the rental electricity price, and the total cost saved by the microgrid through leasing shared energy storage is positively correlated with the satisfaction with the rental electricity price. The utility function is used as an indicator to measure the microgrid's satisfaction with the rental price and is normalized. Referring to the historical average deviation of the microgrid under peak and valley time-of-use electricity prices, the price satisfaction of the microgrid cluster m is expressed as:

[0045]

[0046] in, Indicates that cluster m does not rent energy storage to pay the deviation assessment fee, and the expression is:

[0047]

[0048] The total cost of leasing some energy storage for cluster m is expressed as:

[0049]

[0050] Where, Δt = 1h; represents the rental cost of cluster m; N m represents the number of microgrids in the mth cluster; represents the initial deviation of microgrid i in cluster m at time t; represents the energy storage rental amount of microgrid i in cluster m at time t;

[0051] The operational comfort level is determined by the degree to which the leasing strategy changes the microgrid operator's initial operating behavior. Therefore, the absolute value of the difference in microgrid output deviation before and after leasing energy storage is normalized to quantify the microgrid operator's satisfaction with the leasing method. The difference in leasing volume is negatively correlated with user satisfaction with the operating method, indicating that the microgrid operator needs to adjust its grid-connected output task. Conversely, if the difference is negative, it indicates that the microgrid operator's leasing strategy is consistent with its most suitable leasing behavior, and the microgrid operator does not need to adjust its grid-connected output task. Assuming that the microgrid operator's initial energy storage leasing demand curve is the maximum comfort curve, the operational comfort level of the mth cluster is expressed as:

[0052]

[0053] Therefore, the expression of the rental energy storage satisfaction of microgrid cluster m is:

[0054]

[0055] Among them, ω 1,m ,ω 2,m They represent the weight coefficients of price satisfaction and operation comfort of cluster m respectively;

[0056] Introducing parameter μ m It represents the degree of distortion of the endowment effect on cluster m’s response to changes in the rental price of electricity and its leasing strategy. The distorted satisfaction expression is modified to:

[0057]

[0058] Therefore, the bounded rationality coefficient of cluster m in responding to shared energy storage leasing is expressed as:

[0059]

[0060] Furthermore, the Stackelberg game framework is used in step (3) to model and optimize the decision-making process of the shared energy storage operator and the microgrid cluster to determine the time-sharing rental price through game interaction. This is based on the accurate description of the different reactions of different types of lessees when facing uncertain electricity prices in step (2), and then the simulation of the rational behavior of various types of energy storage lessees. The prospect theory in behavioral economics is used to analyze the uncertain electricity prices of energy storage operators. Specifically,

[0061] In the pricing model for leasing services, electricity prices are represented in the form of probability distributions. Using prospect theory from behavioral economics, the objective probability components corresponding to electricity price components are modified to probability components reflecting the microgrid's subjective response to electricity price changes. This captures the influence of non-completely rational psychological factors on decision-making behavior, thereby reflecting the bounded rationality of microgrid operators. Prospect theory captures the influence of participants' bounded rationality on their decision-making behavior, and further explores how participants make the most reasonable choices based on risk and return when making decisions. Starting from the consumer's perspective, this theory introduces a probability weighting function to convert the decision-maker's objective probability into a subjective probability. According to prospect theory, decision-makers use their subjective probability w(p) rather than the objective probability p to measure the value of the outcome, and thus understand how subjective evaluations distort the objective probability p.

[0062] The improved prospect theory uses the cumulative probability form to describe uncertainty factors, and uses a low-complexity expression form to characterize the decision maker's risk-averse behavior when there is a high probability of gain and risk-seeking behavior when there is a high probability of loss:

[0063]

[0064] Among them, p(X n ) represents the uncertain event X n The objective probability of occurrence; ω(p(X n ),γ n ) represents the probability value of the decision maker’s subjective preference obtained using prospect theory; γ n is the rationality coefficient, which is used to quantify the rationality of the decision maker, 0≤γ n ≤1;

[0065] When traditional expected utility theory guides decision-making behavior, it considers the objective probability of the decision:

[0066]

[0067] Among them, U(X n ) represents the selection of uncertain event X n The utility value of E EUT represents the expected utility value;

[0068] The response behavior of microgrid operators to electricity prices considering the improved prospect theory is expressed as:

[0069]

[0070] Therefore, the framework of improved prospect theory is introduced to characterize the response of microgrid operators to dynamic leasing electricity prices.

[0071] In the pricing model of leasing services, in order to reflect the uncertainty of electricity prices, the electricity prices are expressed in the form of probability distribution; and They represent the rental price vectors purchased / sold by the lower-level microgrid to the upper-level shared energy storage, respectively, and are expressed as:

[0072]

[0073] Where J represents the price vector dimension, that is, each period has J electricity price components; each electricity price component corresponds to a probability value, and the corresponding probability distribution is described in vector form:

[0074]

[0075] Similarly, the electricity selling price set by shared energy storage at time t is expressed as:

[0076]

[0077] The corresponding probability distribution vector is expressed as:

[0078]

[0079] Among them, the dimension J of the price vector is related to the degree of system uncertainty. The stronger the randomness, the larger the J value;

[0080] Since the lower-level clusters have different subjective preferences for different electricity prices, the prospect theory is introduced to improve the objective probability distribution of electricity prices to and

[0081] Electricity purchase price The subjective probability is changed to:

[0082]

[0083] Electricity sales price The subjective probability is changed to:

[0084]

[0085] The purchase and sale electricity prices of the lower-level microgrid during leasing are rewritten as:

[0086]

[0087] Furthermore, the operation process of the upper-layer shared energy storage leasing service pricing model in step (3) is as follows:

[0088] The upper-level shared energy storage leasing service pricing model serves as the upper layer of the two-layer game model. It optimizes the pricing strategy with the goal of maximizing the overall benefits of leasing income and operation and maintenance loss costs, and formulates energy storage leasing electricity prices and sends them to the lower-level microgrid operators, where the leasing demand of the microgrid cluster is the input parameter. The shared energy storage operator chooses to charge service fees based on the actual energy storage charge and discharge volume used by the microgrid cluster. The objective function for establishing shared energy storage is:

[0089] maxR SES =R lea -C G -C om -C dg ;

[0090] Among them, R lea Indicates the rental income within a cycle; C G represents the interaction cost between shared energy storage and distribution network; C om represents the operation and maintenance cost; C dg represents the loss cost;

[0091] (a) Rental income R lea

[0092]

[0093] Where M represents the number of microgrid clusters; represents the charging and discharging power of the i-th microgrid in cluster m;

[0094] (b) Interaction cost C between shared energy storage and distribution network G

[0095]

[0096] Among them, P t G represents the interactive power between the shared energy storage and the distribution network; Indicates the price of electricity purchased by shared energy storage from the distribution network; represents the price of electricity sold by shared energy storage to the distribution network;

[0097] (c) Operation and maintenance cost C om

[0098]

[0099] Where δ represents the unit operation and maintenance cost of energy storage; P t c represents the total charging power of energy storage at time t; P t d represents the total discharge power of energy storage at time t;

[0100] (d) Loss cost Cdg

[0101] By analyzing the operating characteristics and attenuation laws of electrochemical energy storage systems, an economic cost calculation model for energy loss during the cycle is established. The loss cost is expressed as:

[0102]

[0103] Among them, the battery loss cost coefficient λ dg , which is closely related to the construction cost of the energy storage unit, the maximum number of cycles, and the upper and lower limits of the state of charge, and can be expressed as:

[0104]

[0105] Among them, s inv represents the initial construction cost; N cycle Indicates the maximum number of cycles with a discharge depth of 1; E max Indicates the rated capacity of energy storage;

[0106] The initial construction cost is expressed as:

[0107] s inv =m con ·E max ;

[0108] Among them, m con is the unit construction cost;

[0109] The constraints mainly consider electricity price constraints, energy storage charging and discharging power constraints, and power balance constraints;

[0110] To prevent microgrids from directly participating in distribution network interactions, the following electricity price constraints are introduced:

[0111]

[0112] in, represents the average price of electricity purchased by the microgrid from the shared energy storage at time t; represents the average price of electricity sold by the microgrid to the shared energy storage at time t;

[0113] The electricity price probability as the upper-level decision variable has the following constraints:

[0114]

[0115] Energy storage constraints must take into account both charge and discharge power constraints and state of charge (SOC) constraints:

[0116]

[0117] Among them, P maxIndicates the upper limit of the charging and discharging power of the energy storage. The energy storage cannot be charged and discharged at the same time:

[0118] SOC min ·E max ≤E t ≤SOC max ·E max ;

[0119] Among them, SOC represents the state of charge of energy storage; E t Indicates the energy state of energy storage at time t; E max The energy upper limit of energy storage is a key design parameter of the energy storage system and determines the energy storage scale of the system;

[0120] The energy state of the stored energy at time t depends on the state at time t-1:

[0121]

[0122] Among them, η ch and η dis Respectively represent the charging and discharging power of energy storage;

[0123] During the optimization process, the initial energy state and the final energy state are equal:

[0124] E0=E T ;

[0125] Finally, the power balance constraints need to be considered:

[0126]

[0127] Furthermore, the operation process of the lower-layer microgrid operator leasing demand model is as follows:

[0128] The lower-level model receives upper-level electricity price information as input parameters, and adjusts its own leasing demand and operation plan in response to leasing prices to minimize electricity costs. With the goal of minimizing the overall operating cost of the cluster, it optimizes the leasing power of each cluster, thereby formulating the optimal leasing energy storage scheduling plan for the next day and transmitting the energy storage demand to the upper-level shared energy storage operator.

[0129] The operating cost C of microgrid cluster m m It mainly includes the cost of leasing energy storage, transaction service fees and power fluctuation assessment costs:

[0130]

[0131] (a) Rental cost of cluster m

[0132]

[0133] in represents the response of the mth cluster to the electricity price after considering its own subjective preferences;

[0134] (b) Transaction service fees of cluster m

[0135]

[0136] where ρ t represents the unit transaction service cost of cluster m at time t;

[0137] (c) Deviation assessment cost of cluster m

[0138]

[0139] in, represents the output plan submitted by microgrid i in cluster m at time t; t represents the unit assessment cost at time t; π represents the power fluctuation assessment coefficient;

[0140] Lease power constraints:

[0141]

[0142] in, Indicates the maximum charging power of the energy storage station; Indicates the maximum discharge power of the energy storage power station.

[0143] Compared with the prior art, the present invention has the following beneficial effects:

[0144] The paper pioneered the introduction of prospect theory into the decision-making modeling of microgrid operators, effectively characterizing their differentiated preferences for leasing prices, narrowing the deviation between actual leasing behavior and rationally simulated behavior, accurately estimating more realistic leasing strategies, and accurately characterizing the impact of bounded rationality on shared energy storage pricing. Combining community detection algorithms with endowment effect theory, the paper achieves precise clustering and rationality characterization of distributed microgrids. It can quickly and dynamically divide microgrid clusters according to characteristics, accurately identify the rationality coefficients of different types of microgrids, and better understand the actual response behavior of microgrid operators to uncertain leasing prices. A two-layer optimization framework is constructed based on the master-slave game. Through iterative games between microgrid operators and shared energy storage operators, a balance of interests is achieved between the two parties, effectively avoiding the risk of suboptimal economic benefits due to decision mismatches. The paper demonstrates correctness and feasibility in the design of shared energy storage pricing mechanisms. BRIEF DESCRIPTION OF THE DRAWINGS

[0145] Figure 1 This is the operational strategy architecture diagram for leasing shared energy storage according to the present invention;

[0146] Figure 2 This is a flow chart for realizing the cooperative operation of new energy and energy storage in the present invention. DETAILED DESCRIPTION

[0147] The present invention will be further described in detail below with reference to the accompanying drawings and specific implementation examples.

[0148] like Figure 1 The two-stage operation method for providing shared energy storage leasing services based on bounded rationality in this invention provides an operational strategy framework for leasing shared energy storage. The game participants are the shared energy storage operator and the microgrid operator. Both parties aim to maximize their own interests, and their decisions are influenced by each other and follow a certain order. Therefore, this can be considered a master-slave game model. The shared energy storage operator is the leader, with a strategy of "shared energy storage leasing pricing." The microgrid operator is the follower, with a strategy of "energy storage leasing service usage."

[0149] like Figure 2 This is the game implementation process of the second stage of the two-stage operation method for providing leasing services for shared energy storage based on bounded rationality of the present invention. The two-stage operation method includes the following steps:

[0150] (1) Phase 1: Multi-microgrid clustering based on community detection algorithm. Using the community detection algorithm, by selecting appropriate eigenvalue indicators and combining the similarity between microgrids, the distributed microgrids are clustered into clusters with different rationality levels. The output characteristics of the microgrid and the preference for using energy storage are selected as comprehensive similarity measurement indicators, where the output characteristics include the output size and the morphological trend of the output curve. Based on the comprehensive similarity measurement indicators, the similarity matrix between the microgrids of the multi-microgrid distribution system can be calculated. Then, the Fast Unfolding algorithm in the community detection algorithm is used to cluster the nodes with high similarity and optimize the modularity function to achieve the final multi-microgrid clustering.

[0151] After clustering microgrids using a community detection algorithm, we then calculated rationality coefficients for each cluster based on the endowment effect, taking into account differences in rationality. This accurately captures the varying responses of different types of renters to uncertain electricity prices, enabling a more comprehensive simulation of the rational behavior of various energy storage renters. Different microgrid clusters, depending on their characteristics, have varying levels of satisfaction with shared energy storage rental prices. Therefore, based on the endowment effect and the actual preferences of each cluster, we set different rationality coefficients to characterize their rationality.

[0152] In step (1), the microgrid is clustered using a community detection algorithm, the clustering of the microgrid is achieved based on the Fast Unfolding algorithm in the community detection algorithm, and the bounded rational coefficients [γ1, γ2, ..., γ k], laying the foundation for solving different rationality coefficients for microgrid clusters with different rationality levels in the second phase. Microgrids are clustered using a community detection algorithm. First, a comprehensive similarity metric is determined: In a community network, the similarity metric is used to measure the closeness between nodes and reflect the similarity between them. When clustering multiple microgrids, the output characteristics of the microgrids and the preference for using energy storage can be selected as comprehensive similarity metrics. Output characteristics include output size and the morphological trend of the output curve. Based on this comprehensive similarity metric, a similarity matrix between microgrids in a multi-microgrid distribution system can be calculated.

[0153] 1) Residual power similarity measurement

[0154] The power difference represents the shaded area between the two residual power curves and the coordinate axis. If the two microgrid residual power curves are similar, the power sizes of the two microgrids must be similar. Therefore, the residual power similarity s1(i, j) of i and j is defined as:

[0155]

[0156] in, They represent the residual power of microgrids i and j at time t respectively; the larger the value of s1, the more similar the residual power of the two is; T = 24, the time step is 1h.

[0157] 2) Similarity measurement of residual power curve shape trend

[0158] The morphological trend represents the power output of different microgrids. Under the same weather conditions and in the same region, the morphological trends of two residual power curves should be similar. The cosine similarity algorithm is used to calculate the output waveform similarity between microgrids i and j.

[0159] Assuming that the wind and solar power output of the microgrid has a surplus after meeting its own load demand, that is, the residual power of the microgrid is positive, the cosine similarity of the residual power of the microgrid ranges from [0,1]. The larger the similarity metric value, the higher the waveform similarity of the two residual power curves. Therefore, the similarity s2(i,j) of the residual power curve shape trend of microgrid i and j is defined as:

[0160]

[0161] 3) Using similarity metrics of energy storage preferences

[0162] Different microgrids have different preferences for using energy storage. The subjective preference of microgrid operators for energy storage use can be characterized based on historical deviation data and historical energy storage usage. Since the user's historical energy storage usage is subject to privacy protection, actual data is difficult to obtain. To simplify the model, this section makes reasonable assumptions about the energy storage usage behavior of different microgrids. It is known that the historical energy storage usage data of energy storage users in the area (1 means energy storage is used, 0 means it is not used). Then define an indicator p to quantify energy storage preference i , to express the microgrid's preference for energy storage use. The preference index is defined as:

[0163]

[0164] in, Indicates the usage of energy storage; represents the actual output of microgrid i at time t; It represents the output plan submitted by microgrid i at time t, that is, the predicted output in the day-ahead stage.

[0165] Therefore, the similarity between microgrids i and j regarding energy storage usage preferences can be expressed as:

[0166]

[0167] Among them, p i represents the preference of microgrid i for using energy storage; p j Indicates the preference of microgrid j for using energy storage.

[0168] The calculated similarity value s3(i, j) can be used as the similarity between microgrids i and j regarding the preference for leasing energy storage. The higher the value, the more similar the energy storage preferences of the two microgrids are.

[0169] 4) Comprehensive similarity index

[0170] After normalizing the above three similarities, we get the comprehensive similarity metric distance S. The larger the comprehensive metric distance, the higher the similarity between the two curves. The expression is:

[0171] s ij =s1(i,j)·s2(i,j)·s3'(i,j);

[0172] Among them, s3'(i,j) represents the normalized similarity.

[0173] Therefore, the similarity matrix S can be expressed as:

[0174]

[0175] After obtaining the comprehensive similarity index, we then establish a modularity function based on the Fast Unfolding algorithm in the community detection algorithm to evaluate the strength of the community structure. The modularity function Q can reflect the tightness of the internal connection of the community. The higher its value, the closer the connection between the nodes in the same community is, which means that the cluster structure obtained by the division is more stable, and also means that the classification result is more reasonable. The modularity function expression is defined as:

[0176]

[0177] Where,

[0178]

[0179] Among them, the weight of the connection line between nodes i and j is expressed as A ij Indicates; k i represents the sum of the edge weights of node i; the sum of all edge weights of the network is represented by h. If two nodes i and j are classified into the same partition, the function on the contrary The relationship between nodes is described by node similarity. Therefore, the weight of the edge between nodes needs to be replaced by the calculated value of node similarity. The improved modularity function is:

[0180]

[0181] Where,

[0182]

[0183] Among them, the similarity between nodes i and j is s ij 'Measurement; the sum of similarities between node i and other nodes is s i Indicates; the cumulative value of the similarity between nodes in the entire network is represented by s, and the similarity is obtained by S.

[0184] Then, after clustering the microgrid system, the rationality coefficient of each cluster was calculated based on the endowment effect. To characterize the operating habits of microgrid operators, a utility function was constructed with two dimensions. The utility function represents the trade-off between the reduced power fluctuations when leasing shared energy storage and the dissatisfaction caused by the operational inconvenience caused to the microgrid itself by leasing energy storage. The former is defined as price satisfaction, reflecting the microgrid operator's price preference; the latter is defined as operational comfort, reflecting the microgrid operator's leasing behavior preferences.

[0185] Price satisfaction is determined by the rental electricity price, which is the most important factor influencing microgrid leasing decisions. The higher the total cost a microgrid saves by leasing shared energy storage, the higher the satisfaction with the rental electricity price and the greater the propensity to choose leasing. Using the utility function as an indicator to measure microgrid satisfaction with rental prices and normalizing it, referring to the historical average deviation of microgrids under peak and valley time-of-use electricity prices, cluster m, price satisfaction is expressed as:

[0186]

[0187] in, Indicates that cluster m does not rent energy storage to pay the deviation assessment fee, and the expression is:

[0188]

[0189] The total cost of leasing some energy storage for cluster m is expressed as:

[0190]

[0191] in, represents the rental cost of cluster m; N m represents the number of microgrids in the mth cluster; represents the initial deviation of microgrid i in cluster m at time t; represents the energy storage rental amount of microgrid i in cluster m at time t; Δt = 1h.

[0192] Operational comfort is a subjective feeling of the microgrid operator in the process of leasing energy storage, which is determined by the degree of change in the initial operating behavior of the microgrid operator itself due to the leasing strategy. Therefore, the absolute value of the difference in microgrid output deviation before and after leasing energy storage is normalized to quantify the microgrid operator's satisfaction with the leasing method. The higher the difference in leasing volume, the lower the user's satisfaction with the operating method, which means that the microgrid operator needs to adjust its operating tasks as much as possible to cope with changes in the electricity price of leasing energy storage. Conversely, the smaller the difference in leasing volume, the more consistent the microgrid operator's leasing strategy is with its most suitable leasing behavior, and the microgrid operator does not need to adjust the grid-connected output task. At this time, the microgrid operator is more satisfied with the leasing method. Assuming that the microgrid operator's initial energy storage leasing demand curve is the maximum comfort curve, the operational comfort of the mth cluster is expressed as:

[0193]

[0194] Therefore, the expression of the rental energy storage satisfaction of microgrid cluster m is:

[0195]

[0196] Among them, ω1,m ,ω 2,m are the weight coefficients of price satisfaction and operation comfort of cluster m respectively.

[0197] Introducing parameter μ m It represents the degree of distortion of the endowment effect on cluster m’s response to changes in the rental price of electricity and its leasing strategy. The distorted satisfaction expression is modified to:

[0198]

[0199] Therefore, the bounded rationality coefficient of cluster m in responding to shared energy storage leasing can be expressed as:

[0200]

[0201] (2) Phase II: Shared energy storage operation model based on prospect theory. Shared energy storage operators and microgrid clusters determine the time-sharing leasing price through game interaction. This decision-making process reflects the hierarchy and profit-seeking nature of multiple parties and can be modeled and optimized using the Stackelberg game framework. The upper-level shared energy storage operators influence the leasing demand of the lower-level microgrid operators through leasing pricing strategies, and the demand of the microgrid operators in turn affects the profit optimization of the shared energy storage operators. This dynamic interaction between the upper and lower levels will eventually reach a market equilibrium through continuous iteration.

[0202] In the leasing service pricing model, a probability distribution is used to represent electricity prices to reflect uncertainty. Using prospect theory from behavioral economics, the objective probability component corresponding to the electricity price is modified to reflect the microgrid's subjective response to price changes. This captures the influence of non-fully rational psychological factors on decision-making, thereby reflecting the bounded rationality of microgrid operators.

[0203] In step (2), the uncertain electricity price of the energy storage operator is first analyzed based on prospect theory:

[0204] In the pricing model for rental services, a probability distribution is used to represent electricity prices to reflect the uncertainty of electricity prices. Leveraging prospect theory from behavioral economics, the objective probability component corresponding to the electricity price is modified to reflect the microgrid's subjective response to price changes. This captures the influence of non-fully rational psychological factors on decision-making behavior, thereby demonstrating the bounded rationality of microgrid operators. Prospect theory explores how participants make the most reasonable choices based on risk and reward by capturing the influence of psychological factors of bounded rationality on their decision-making behavior. Starting from the consumer's perspective, this theory introduces a probability weighting function to convert the decision-maker's objective probabilities into subjective probabilities, providing a new approach to solving this problem. According to prospect theory, decision-makers use their subjective probability w(p) rather than the objective probability p to weigh the value of possible outcomes, revealing how subjective evaluations distort the objective probability p.

[0205] Prelec developed an improved prospect theory that uses cumulative probability to describe uncertainty. This method uses a low-complexity expression to characterize the behavior of decision makers who avoid risks when there is a high probability of gain and seek risks when there is a high probability of loss:

[0206]

[0207] Among them, p(X n ) represents the uncertain event X n The objective probability of occurrence; ω(p(X n ),γ n ) represents the probability value of the decision maker’s subjective preference obtained using prospect theory; γ n is the rational coefficient, 0≤γ n ≤1.

[0208] Prospect theory explains the fact that people tend to overestimate low-probability outcomes and underestimate medium- to high-probability outcomes, which is something that the commonly used traditional expected utility theory cannot explain. When guiding decision-making behavior, traditional expected utility theory considers the objective probability of the decision:

[0209]

[0210] Among them, U(X n ) represents the selection of uncertain event X n The utility value of E EUT Represents the expected utility value.

[0211] The response behavior of microgrid operators to electricity prices considering the improved prospect theory can be expressed as:

[0212]

[0213] Therefore, we introduce the framework of improved prospect theory to characterize the response of microgrid operators to dynamic leasing electricity prices. Different microgrid operators have different preferences for energy storage leasing, and their preferences may be irrational, especially when electricity prices are uncertain. Some operators are more willing to take risks, and their rationality coefficient γ n The higher the value, the more conservative some may be. n The lower the value.

[0214] In the pricing model of leasing services, in order to reflect the uncertainty of electricity prices, the electricity prices are expressed in the form of probability distribution. and They represent the rental price vectors purchased / sold by the lower-level microgrid to the upper-level shared energy storage, respectively, and are expressed as:

[0215]

[0216] Where J represents the price vector dimension, that is, each period has J electricity price components. Each electricity price component corresponds to a probability value, and the corresponding probability distribution can be described in vector form:

[0217]

[0218] Similarly, the electricity selling price set by shared energy storage at time t is expressed as:

[0219]

[0220] The corresponding probability distribution vector is expressed as:

[0221]

[0222] Among them, the dimension J of the price vector is related to the degree of system uncertainty. The stronger the randomness, the larger the J value.

[0223] Considering that the lower-level clusters have different subjective preferences for different electricity prices, the prospect theory is introduced to improve the objective probability distribution of electricity prices to and

[0224] Electricity purchase price The subjective probability is changed to:

[0225]

[0226] Electricity sales price The subjective probability is changed to:

[0227]

[0228] The purchase and sale electricity prices of the lower-level microgrid during leasing can be rewritten as:

[0229]

[0230] Shared energy storage operators and microgrid clusters determine time-of-use rental prices through interactive game theory. This decision-making process reflects the hierarchical and profit-seeking nature of multiple stakeholders and can be modeled and optimized using the Stackelberg game framework. The upper-level shared energy storage operator influences the rental demand of the lower-level microgrid operator through its leasing pricing strategy, and the microgrid operator's demand, in turn, influences the shared energy storage operator's revenue optimization. This dynamic interaction between the upper and lower levels, through continuous iteration, ultimately leads to market equilibrium.

[0231] 1. Upper layer - shared energy storage leasing service pricing model

[0232] The upper-level shared energy storage leasing service pricing model, as the upper level of the two-level game model, optimizes the pricing strategy with the goal of maximizing overall benefits such as leasing income and operation and maintenance loss costs, and formulates energy storage leasing electricity prices and sends them to the lower-level microgrid operators, with the leasing demand of the microgrid cluster as the input parameter. Considering the characteristics of microgrid cluster energy storage service usage periods being relatively few and dispersed, and the large differences in charging and discharging demand peaks and valleys, the shared energy storage operator chooses to charge service fees based on the actual energy storage charging and discharging volume used by the microgrid cluster. The objective function for establishing shared energy storage is:

[0233] maxR SES =R lea -C G -C om -C dg ;

[0234] Among them, R lea Indicates the rental income within a cycle; C G represents the interaction cost between shared energy storage and distribution network; C om represents the operation and maintenance cost; C dg Indicates loss cost.

[0235] (a) Rental income R lea

[0236]

[0237] Where M represents the number of microgrid clusters; represents the charging and discharging power of the i-th microgrid in cluster m.

[0238] (b) Interaction cost C between shared energy storage and distribution network G

[0239]

[0240] Among them, P t Grepresents the interactive power between the shared energy storage and the distribution network; Indicates the price of electricity purchased by shared energy storage from the distribution network; Indicates the price of electricity sold by shared energy storage to the distribution network.

[0241] (c) Operation and maintenance cost C om

[0242]

[0243] Where δ represents the unit operation and maintenance cost of energy storage; P t c represents the total charging power of energy storage at time t; P t d Represents the total discharge power of energy storage at time t.

[0244] (d) Loss cost C dg

[0245] Frequent charging and discharging operations will cause loss of energy storage batteries, so it is necessary to consider the battery loss cost taking into account the energy storage life. The loss cost is expressed as:

[0246]

[0247] Among them, the battery loss cost coefficient λ dg , which is closely related to the construction cost of the energy storage unit, the maximum number of cycles, and the upper and lower limits of the state of charge, and can be expressed as:

[0248]

[0249] Among them, s inv represents the initial construction cost; N cycle Indicates the maximum number of cycles with a discharge depth of 1; E max Indicates the rated capacity of energy storage.

[0250] The initial construction cost is expressed as:

[0251] s inv =m con ·E max ;

[0252] Among them, m con Unit construction cost.

[0253] The constraints mainly consider electricity price constraints, energy storage charging and discharging power constraints, and power balance constraints.

[0254] To prevent microgrids from directly participating in distribution network interactions, the following electricity price constraints are introduced:

[0255]

[0256] in, represents the average price of electricity purchased by the microgrid from the shared energy storage at time t; It represents the average price of electricity sold by the microgrid to the shared energy storage at time t.

[0257] The electricity price probability as the upper-level decision variable has the following constraints:

[0258]

[0259] The energy storage's own constraints need to consider the charging and discharging power constraints and the state of charge (SOC) constraints.

[0260]

[0261] Among them, P max Indicates the upper limit of the charging and discharging power of the energy storage. The energy storage cannot be charged and discharged simultaneously.

[0262] SOC min ·E max ≤E t ≤SOC max ·E max ;

[0263] Among them, SOC represents the state of charge of energy storage; E t Indicates the energy state of energy storage at time t; E max The energy upper limit of energy storage is a key design parameter of the energy storage system and determines the energy storage scale of the system.

[0264] The energy state of the stored energy at time t depends on the state at time t-1:

[0265]

[0266] Among them, η ch and η dis Represent the charging and discharging power of energy storage respectively.

[0267] During the optimization process, the initial energy state and the final energy state are equal:

[0268] E0=E T ;

[0269] Finally, the power balance constraints need to be considered:

[0270]

[0271] 2. Lower Layer - Microgrid Operator Leasing Demand Model

[0272] The lower-level model receives upper-level electricity price information as input and adjusts its own rental requirements and operating plans in response to rental prices to minimize electricity costs. With the goal of minimizing the overall operating cost of the cluster, it optimizes the rental power of each cluster. This allows it to develop an optimal rental storage scheduling plan for the next day and transmit the storage demand to the upper-level shared energy storage operator.

[0273] The operating cost C of microgrid cluster m m It mainly includes the cost of leasing energy storage, transaction service fees and power fluctuation assessment costs:

[0274]

[0275] 1) The rental cost of cluster m

[0276]

[0277] in It represents the response of cluster m to electricity price after considering its own subjective preference.

[0278] 2) Transaction service fees for cluster m

[0279]

[0280] where ρ t It represents the unit transaction service cost of cluster m at time t.

[0281] 3) Deviation assessment cost of cluster m

[0282]

[0283] in, represents the output plan submitted by microgrid i in cluster m at time t; t represents the unit assessment cost at time t; π represents the power fluctuation assessment coefficient.

[0284] Lease power constraints:

[0285]

[0286] in, Indicates the maximum charging power of the energy storage station; Indicates the maximum discharge power of the energy storage power station.

[0287] In summary, under this operating strategy, the actual response behavior of microgrid operators to uncertain leasing prices can be better characterized, the differentiated preferences of microgrid operators for leasing prices can be effectively represented, the deviation between their actual leasing behavior and the simulated behavior under rational assumptions can be narrowed, a more realistic leasing strategy can be estimated, and the risk of suboptimal economic benefits caused by decision mismatch can be avoided. This can more accurately characterize the impact of the limited rationality of microgrid operators on shared energy storage pricing, and is correct and feasible in the design of shared energy storage operation mechanisms.

[0288] The preferred embodiments of the present invention are described in detail above. However, the present invention is not limited to the specific details in the above embodiments. Within the technical concept of the present invention, various equivalent transformations can be made to the technical solutions of the present invention, and these equivalent transformations all fall within the scope of protection of the present invention.

Claims

1. An operating method for providing leasing services for shared energy storage based on bounded rationality, characterized in that: The steps include: (1) Using a community detection algorithm to cluster microgrids; selecting the output characteristics of microgrids and the preference for using energy storage as comprehensive similarity measurement indicators, where the output characteristics include the output size and the shape trend of the output curve; based on the comprehensive similarity measurement indicators, the similarity matrix between microgrids in the multi-microgrid distribution system is calculated, and the microgrids are clustered using a community detection algorithm; (2) After clustering the microgrid using the community detection algorithm, the rationality coefficients of each cluster taking into account the differences in rationality are solved based on the endowment effect, so as to accurately characterize the different reactions of different types of renters when facing uncertain electricity prices, and then simulate the rational behavior of various types of energy storage renters; according to the characteristics of different microgrid clusters and their satisfaction with the rental electricity price of shared energy storage, different rationality coefficients are set to represent their rationality; (3) The Stackelberg game framework is used for modeling optimization to solve the decision-making of shared energy storage operators and microgrid clusters to determine the time-sharing leasing price through game interaction; the upper-level shared energy storage operators are related to the leasing demand of the lower-level microgrid operators through leasing pricing strategies, and the demand of microgrid operators is in turn related to the profit optimization of shared energy storage operators. The upper-level shared energy storage leasing service pricing model and the lower-level microgrid operator leasing demand model are established; the dynamic interaction between the upper and lower levels is used through continuous iteration to eventually reach a market equilibrium.

2. The operating method for providing leasing services based on bounded rationality of shared energy storage according to claim 1, characterized in that: In step (1), the microgrid is clustered using the community detection algorithm, specifically: the Fast Unfolding algorithm in the community detection algorithm is used to select the characteristic value index and combine it with the similarity between microgrids, and the nodes with high similarity are clustered, that is, the distributed microgrid is clustered into clusters with different rationality levels, and the final multi-microgrid clustering is achieved by optimizing the modularity function, and the finite rationality coefficients [γ1, γ2, ..., γ k ], which is used to subsequently solve different rationality coefficients for microgrid clusters with different rationality levels.

3. The operating method for providing leasing services based on bounded rationality of shared energy storage according to claim 2, characterized in that: In the step (1), the similarity matrix between the microgrids of the multi-microgrid distribution system is obtained based on the comprehensive similarity measurement index, specifically: the similarity matrix between the microgrids of the multi-microgrid distribution system is obtained based on the comprehensive similarity measurement index by determining the comprehensive similarity index. Since in the community network, the similarity index is used to measure the intimacy between nodes and reflects the similarity between nodes; When clustering multiple microgrids, the output characteristics of the microgrids and the preference for using energy storage are selected as comprehensive similarity measurement indicators; the comprehensive similarity indicators include: similarity measurement of residual power size, similarity measurement of residual power curve shape trend, and similarity measurement of preference for using energy storage.

4. The operating method for providing leasing services based on bounded rationality of shared energy storage according to claim 3, characterized in that: The comprehensive similarity index is specifically: (a) Residual power similarity measurement The power difference represents the shaded area between the two residual power curves and the coordinate axis. If the two microgrid residual power curves are similar, the power sizes of the two must be similar. Therefore, the residual power similarity s1(i, j) of i and j is defined as: in, Respectively represent the residual power of microgrids i and j at time t; the larger the value of s1, the more similar the residual power of the two is; T = 24, the time step is 1h; (b) Similarity measurement of residual power curve morphology trend The morphological trend indicates the power output in different microgrids. Under the same weather conditions and in the same area, the morphological trends of two residual power curves are similar. The cosine similarity algorithm is used to calculate the output waveform similarity between microgrids i and j. Assuming that the wind and solar power output of the microgrid has a surplus beyond meeting its own load demand, that is, the residual power of the microgrid is positive, the cosine similarity of the residual power of the microgrid ranges from [0, 1]. The larger the similarity value, the higher the cosine similarity. The waveform similarity of the two residual power curves is positively correlated with the size of the similarity value. Therefore, the similarity s2(i, j) of the residual power curve shape trend of microgrid i and j is defined as: (c) Similarity measure using energy storage preference Based on the historical deviation data and the historical use of energy storage, the subjective preference of the microgrid operator for the use of energy storage is characterized; assuming that the historical energy storage use data U of the energy storage users in the area is known t s , where 1 means energy storage is used and 0 means it is not used; then define an index p to quantify energy storage preference i , to express the microgrid's preference for energy storage use. The preference index is defined as: in, Indicates the usage of energy storage; represents the actual output of microgrid i at time t; represents the output plan submitted by microgrid i at time t, i.e., the predicted output in the day-ahead phase. A higher value of the energy storage preference index indicates that the microgrid is more inclined to use energy storage when the output deviation is large, i.e., the higher the preference level. Therefore, the similarity between microgrids i and j regarding energy storage usage preferences is expressed as: s3(i,j)=1-|p i -p j |; Among them, p i represents the preference of microgrid i for using energy storage; p j represents the preference degree of microgrid j to use energy storage; The calculated similarity value s3(i,j) is used as the similarity between microgrids i and j regarding the preference for leasing energy storage. The similarity metric is positively correlated with the similarity of the energy storage preferences of the two microgrids. The three similarities mentioned above, namely, the similarity measure of the remaining power size, the similarity measure of the remaining power curve shape trend, and the similarity measure of the energy storage preference, are normalized to obtain the comprehensive similarity measure distance S. The larger the comprehensive measure distance, the higher the similarity of the two curves. The expression is as follows: s ij =s1(i,j)·s2(i,j)·s3'(i,j); Among them, s3'(i,j) represents the normalized similarity; Therefore, the similarity matrix S is expressed as: After obtaining the comprehensive similarity index, a modularity function is established based on the Fast Unfolding algorithm in the community detection algorithm to evaluate the strength of the community structure. The value of the modularity function Q is positively correlated with the tightness of the connection within the community. The modularity function expression is defined as: Where, Among them, the weight of the connection line between nodes i and j is expressed as A ij Indicates; k i represents the sum of the edge weights of node i; the sum of all edge weights of the network is represented by h; if two nodes i and j are classified into the same partition, then the function on the contrary The relationship between nodes is described by node similarity. Therefore, the weight of the edge between nodes needs to be replaced by the calculated value of node similarity. The improved modularity function is: Where, Among them, the similarity between nodes i and j is s ij 'Measurement; the sum of similarities between node i and other nodes is s i Indicates; the cumulative value of the similarity between nodes in the entire network is represented by s, and the similarity is obtained by S.

5. The operating method for providing leasing services based on bounded rationality of shared energy storage according to claim 1, characterized in that: After the microgrid is divided into clusters using the community detection algorithm in step (2), the rationality coefficients of various clusters taking into account the differences in rationality are calculated based on the endowment effect. Specifically, To characterize the operating habits of microgrid operators, a utility function is constructed with two dimensions. The utility function represents the trade-off between price satisfaction and operational comfort when leasing shared energy storage. The price satisfaction is determined by the rental electricity price, and the total cost saved by the microgrid through leasing shared energy storage is positively correlated with the satisfaction with the rental electricity price. The utility function is used as an indicator to measure the microgrid's satisfaction with the rental price and is normalized. Referring to the historical average deviation of the microgrid under peak and valley time-of-use electricity prices, the price satisfaction of the microgrid cluster m is expressed as: in, Indicates that cluster m does not rent energy storage to pay the deviation assessment fee, and the expression is: The total cost of leasing some energy storage for cluster m is expressed as: Where, Δt = 1h; represents the rental cost of cluster m; N m represents the number of microgrids in the mth cluster; represents the initial deviation of microgrid i in cluster m at time t; represents the energy storage rental amount of microgrid i in cluster m at time t; The operational comfort level is determined by the degree to which the leasing strategy changes the microgrid operator's initial operating behavior. Therefore, the absolute value of the difference in microgrid output deviation before and after leasing energy storage is normalized to quantify the microgrid operator's satisfaction with the leasing method. The difference in leasing volume is negatively correlated with user satisfaction with the operating method, indicating that the microgrid operator needs to adjust its grid-connected output task. Conversely, if the difference is negative, it indicates that the microgrid operator's leasing strategy is consistent with its most suitable leasing behavior, and the microgrid operator does not need to adjust its grid-connected output task. Assuming that the microgrid operator's initial energy storage leasing demand curve is the maximum comfort curve, the operational comfort level of the mth cluster is expressed as: Therefore, the expression of the rental energy storage satisfaction of microgrid cluster m is: Among them, ω 1,m ,ω 2,m They represent the weight coefficients of price satisfaction and operation comfort of cluster m respectively; Introducing parameter μ m It represents the degree of distortion of the endowment effect on cluster m’s response to the change of rental electricity price and its leasing strategy. The distorted satisfaction expression is modified to: Therefore, the bounded rationality coefficient of cluster m in responding to shared energy storage leasing is expressed as:

6. The operating method for providing leasing services based on bounded rationality of shared energy storage according to claim 1, characterized in that: In step (3), the Stackelberg game framework is used to model and optimize the decision-making process of the shared energy storage operator and the microgrid cluster to determine the time-sharing rental price through game interaction. This is based on the accurate description of the different reactions of different types of lessees when facing uncertain electricity prices in step (2), and then the simulation of the rational behavior of various types of energy storage lessees. The prospect theory in behavioral economics is used to analyze the uncertain electricity prices of energy storage operators. Specifically, In the pricing model for leasing services, electricity prices are represented in the form of probability distributions. Using prospect theory from behavioral economics, the objective probability components corresponding to electricity price components are modified to probability components reflecting the microgrid's subjective response to electricity price changes. This captures the influence of non-completely rational psychological factors on decision-making behavior, thereby reflecting the bounded rationality of microgrid operators. Prospect theory captures the influence of participants' bounded rationality on their decision-making behavior, and further explores how participants make the most reasonable choices based on risk and return when making decisions. Starting from the consumer's perspective, this theory introduces a probability weighting function to convert the decision-maker's objective probability into a subjective probability. According to prospect theory, decision-makers use their subjective probability w(p) rather than the objective probability p to measure the value of the outcome, and thus understand how subjective evaluations distort the objective probability p. The improved prospect theory uses the cumulative probability form to describe uncertainty factors, and uses a low-complexity expression form to characterize the decision maker's risk-averse behavior when there is a high probability of gain and risk-seeking behavior when there is a high probability of loss: Among them, p(X n ) represents the uncertain event X n The objective probability of occurrence; ω(p(X n ),γ n ) represents the probability value of the decision maker’s subjective preference obtained using prospect theory; γ n is the rationality coefficient, which is used to quantify the rationality of the decision maker, 0≤γ n ≤1; When traditional expected utility theory guides decision-making behavior, it considers the objective probability of the decision: Among them, U(X n ) represents the selection of uncertain event X n The utility value of E EUT represents the expected utility value; The response behavior of microgrid operators to electricity prices considering the improved prospect theory is expressed as: Therefore, the framework of improved prospect theory is introduced to characterize the response of microgrid operators to dynamic leasing electricity prices. In the pricing model of leasing services, the electricity price is expressed in the form of probability distribution to reflect the uncertainty of electricity price. and They represent the rental price vectors purchased / sold by the lower-level microgrid to the upper-level shared energy storage, respectively, and are expressed as: Where J represents the price vector dimension, that is, each period has J electricity price components; each electricity price component corresponds to a probability value, and the corresponding probability distribution is described in vector form: Similarly, the electricity selling price set by shared energy storage at time t is expressed as: The corresponding probability distribution vector is expressed as: Among them, the dimension J of the price vector is related to the degree of system uncertainty. The stronger the randomness, the larger the J value; Since the lower-level clusters have different subjective preferences for different electricity prices, the prospect theory is introduced to improve the objective probability distribution of electricity prices to and Electricity purchase price The subjective probability is changed to: Electricity sales price The subjective probability is changed to: The purchase and sale electricity prices of the lower-level microgrid during leasing are rewritten as:

7. The operating method for providing leasing services based on shared energy storage based on bounded rationality according to claim 1, characterized in that: The operation process of the upper-layer shared energy storage leasing service pricing model in step (3) is as follows: The upper-level shared energy storage leasing service pricing model serves as the upper layer of the two-layer game model. It optimizes the pricing strategy with the goal of maximizing the overall benefits of leasing income and operation and maintenance loss costs, and formulates energy storage leasing electricity prices and sends them to the lower-level microgrid operators, where the leasing demand of the microgrid cluster is the input parameter. The shared energy storage operator chooses to charge service fees based on the actual energy storage charge and discharge volume used by the microgrid cluster. The objective function for establishing shared energy storage is: maxR SES =R lea -C G -C om -C dg ; Among them, R lea Indicates the rental income within a cycle; C G represents the interaction cost between shared energy storage and distribution network; C om represents the operation and maintenance cost; C dg represents the loss cost; (a) Rental income R lea Where M represents the number of microgrid clusters; represents the charging and discharging power of the i-th microgrid in cluster m; (b) Interaction cost C between shared energy storage and distribution network G Among them, P t G represents the interactive power between the shared energy storage and the distribution network; Indicates the price of electricity purchased by shared energy storage from the distribution network; represents the price of electricity sold by shared energy storage to the distribution network; (c) Operation and maintenance cost C om Where δ represents the unit operation and maintenance cost of energy storage; P t c represents the total charging power of energy storage at time t; P t d represents the total discharge power of energy storage at time t; (d) Loss cost C dg By analyzing the operating characteristics and attenuation laws of electrochemical energy storage systems, an economic cost calculation model for energy loss during the cycle is established. The loss cost is expressed as: Among them, the battery loss cost coefficient λ dg , which is closely related to the construction cost of the energy storage unit, the maximum number of cycles, and the upper and lower limits of the state of charge, and can be expressed as: Among them, s inv represents the initial construction cost; N cycle Indicates the maximum number of cycles with a discharge depth of 1; E max Indicates the rated capacity of energy storage; The initial construction cost is expressed as: s inv =m con ·E max ; Among them, m con is the unit construction cost; The constraints mainly consider electricity price constraints, energy storage charging and discharging power constraints, and power balance constraints; To prevent microgrids from directly participating in distribution network interactions, the following electricity price constraints are introduced: in, represents the average price of electricity purchased by the microgrid from the shared energy storage at time t; represents the average price of electricity sold by the microgrid to the shared energy storage at time t; The electricity price probability as the upper-level decision variable has the following constraints: Energy storage constraints must take into account both charge and discharge power constraints and state of charge (SOC) constraints: Among them, P max Indicates the upper limit of the charging and discharging power of the energy storage. The energy storage cannot be charged and discharged at the same time: SOC min ·IN max ≤E t ≤SOC max ·IN max ; Among them, SOC represents the state of charge of energy storage; E t Indicates the energy state of energy storage at time t; E max The energy upper limit of energy storage is a key design parameter of the energy storage system and determines the energy storage scale of the system; The energy state of the stored energy at time t depends on the state at time t-1: Among them, η ch and η dis Respectively represent the charging and discharging power of energy storage; During the optimization process, the initial energy state and the final energy state are equal: E0=E T ; Finally, the power balance constraints need to be considered:

8. The operating method for providing leasing services based on shared energy storage based on bounded rationality according to claim 1, characterized in that: The operation process of the lower-level microgrid operator leasing demand model is as follows: The lower-level model receives upper-level electricity price information as input parameters, and adjusts its own leasing demand and operation plan in response to leasing prices to minimize electricity costs. With the goal of minimizing the overall operating cost of the cluster, it optimizes the leasing power of each cluster, thereby formulating the optimal leasing energy storage scheduling plan for the next day and transmitting the energy storage demand to the upper-level shared energy storage operator. The operating cost C of microgrid cluster m m It mainly includes the cost of leasing energy storage, transaction service fees and power fluctuation assessment costs: (a) Rental cost of cluster m in represents the response of the mth cluster to the electricity price after considering its own subjective preferences; (b) Transaction service fees of cluster m where ρ t represents the unit transaction service cost of cluster m at time t; (c) Deviation assessment cost of cluster m in, represents the output plan submitted by microgrid i in cluster m at time t; t represents the unit assessment cost at time t; π represents the power fluctuation assessment coefficient; Lease power constraints: in, Indicates the maximum charging power of the energy storage station; Indicates the maximum discharge power of the energy storage power station.

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