Virtual power plant multi-form flexible resource equivalent aggregation method considering response characteristics

By defining peak-shaving and frequency regulation performance indicators for flexible resources, and using cloud models and spectral clustering algorithms to perform hierarchical aggregation of flexible resources, the problem of large differences in equipment regulation characteristics within a multi-energy virtual power plant is solved, enabling efficient operation and emergency power response of the virtual power plant.

CN115879715BActive Publication Date: 2026-04-28POWER SUPPLY SERVICE & MANAGEMENT CENT STATE GRID JIANGXI ELECTRIC POWER CO LTD +2
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Patent Information

Authority / Receiving Office
CN · China
Patent Type
Patents(China)
Current Assignee / Owner
POWER SUPPLY SERVICE & MANAGEMENT CENT STATE GRID JIANGXI ELECTRIC POWER CO LTD
Filing Date
2022-12-07
Publication Date
2026-04-28

AI Technical Summary

Technical Problem

In the context of the energy internet, how to accurately obtain the aggregation model of multi-energy virtual power plants in order to fully leverage the flexibility of distributed resources, especially when there are many types of equipment and large differences in regulation characteristics within the multi-energy virtual power plant, to achieve coordination and aggregation among the various devices.

Method used

By defining peak-shaving and frequency-regulating performance indicators for flexible resources, selecting typical response characteristics using cloud models, and combining entropy methods and spectral clustering algorithms, flexible resources are hierarchically aggregated to form a multi-layered virtual power plant model, enabling mutual cooperation among various flexible resources.

Benefits of technology

It improves the overall operating efficiency of virtual power plants, enabling full utilization of the response potential of flexible resources in emergency situations, reducing power transmission losses in the power grid, and enhancing the safety and economy of power grid operation.

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Abstract

The application discloses a kind of virtual power plant polymorphic flexible resource equivalent aggregation methods considering response characteristics, which comprises the following steps: step 1) based on cloud model, the response characteristics of flexible resource is analyzed to select typical response characteristics, and the peak shaving, frequency modulation performance index according to the response time, response capacity, daily load fluctuation rate response performance of virtual power plant polymorphic flexible resource is established;Step 2) combined with subjective and objective comprehensive weighting method and NJW spectrum clustering, flexible resource is classified and aggregated into frequency modulation resource and peak shaving resource;Step 3) according to the design of electrical distance aggregation rule, from different scenarios, hierarchical structure of hierarchical aggregation, static equivalence and aggregation are carried out to polymorphic flexible resource.The method can effectively aggregate the flexible resource in virtual power plant, so as to fully tap the response potential of virtual power plant flexible resource when emergency power shortage occurs in power grid.
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Description

Technical Field

[0001] This invention relates to the field of flexible resource aggregation research in virtual power plants, and particularly to methods for resource characteristic classification and resource aggregation. Background Technology

[0002] In the context of the energy internet, the randomness and volatility of a large number of distributed resources, represented by new energy power generation, pose significant challenges to the power system and even the energy system, and have a major impact on the safe, reliable, and economical operation of the power grid. Virtual power plants, as an important form of effective management of distributed energy access to the power grid, aggregate a large number of distributed energy sources, controllable loads, and energy storage devices into a virtual whole, thereby participating in the operation and dispatch of the power grid, improving the safety and economy of power grid operation, and reducing power grid investment costs. To fully leverage the flexibility of multi-energy distributed resources, distributed multi-energy systems are aggregated into multi-energy virtual power plants to respond to power system dispatch. The multi-energy virtual power plant aggregation model is the foundation for power system dispatch. Because multi-energy virtual power plants contain a wide variety of equipment, with significant differences in adjustment speed, adjustment range, and adjustment duration, and exhibiting dynamic characteristics of time coupling, accurately obtaining the aggregation model of multi-energy virtual power plants is the technical foundation for fully leveraging the flexibility of multi-energy distributed resources. Summary of the Invention

[0003] The purpose of this invention is to provide a method for equivalent aggregation of multi-form flexible resources in a virtual power plant that considers response characteristics. By aggregation, the method enables mutual cooperation among various multi-form flexible resources, driving the overall evolution towards energy conservation and consumption reduction, and improving the overall operating efficiency of the virtual power plant.

[0004] To achieve the above objectives, the present invention provides the following technical solution: a method for equivalent aggregation of multi-form flexible resources in a virtual power plant considering response characteristics, comprising the following steps:

[0005] Step 1: Define the peak shaving and frequency modulation performance indicators for multi-form flexible resources;

[0006] Taking wind power plants, photovoltaic power plants, energy storage, and electric vehicles as examples, the definitions are as follows:

[0007] The cloud model is used to select the most certain response characteristics as typical response characteristics, such as response time, response capacity, and daily load volatility, and these characteristics are evaluated using the characteristic indicators established below.

[0008] Flexible resource frequency modulation performance index Y AGC τ represents the response time of flexible resources. respon d The shorter the period, the lower the daily load volatility f respondThe lower the value, the better the fit with frequency regulation services. Peak shaving services generally have lower requirements for response speed, but longer duration requirements compared to frequency regulation, typically around 15 minutes. However, peak shaving services are generally called at a lower frequency, and flexible resources can usually meet the requirements. Based on this, the controllable load peak shaving performance index Y is defined. reg To make the indicators more targeted, the above indicator definition process has eliminated features that are not of interest to the market products, and the indicator values ​​are between 0 and 1, with higher values ​​indicating a higher degree of fit.

[0009]

[0010]

[0011] Step 2: Consider the hierarchical aggregation of flexible resources' response capacity and response speed;

[0012] Based on step one, assuming the entire region is divided into m grids and the number of characteristic indicators is n, then the entropy method yields the frequency modulation objective weight w. AGC and peak-shaving objective weight w AGC / reg The steps are as follows:

[0013]

[0014]

[0015]

[0016] d AGC / reg =1-e AGC / reg (6)

[0017]

[0018] In the formula, p i AGC p i reg e represents the proportion of frequency regulation and peak shaving indicators for the i-th resource, respectively. AGC / reg d represents the entropy value of frequency modulation and peak shaving resources. AGC / reg w represents the information utility value for frequency modulation and peak shaving. AGC / reg The weights for frequency modulation and peak shaving indicators.

[0019] Spectral clustering algorithms represent several sets of load data as points V in an undirected weighted graph. An adjacency matrix is ​​used to represent the weight of the connections between each vertex. The algorithm seeks an optimal segmentation method to form multiple subgraphs, ensuring that each subgraph is as similar as possible internally, while maximizing the distance between different subgraphs. Taking a set K as an example, this paper details how to cluster flexible resources into peak-shaving resources and frequency-shaving resources. Let N be the number of flexible resource samples in set K. The detailed algorithm flow is as follows:

[0020] 1) Calculate the similarity matrix.

[0021] The similarity matrix D is a symmetric matrix, and its elements are called feature parameters. The selection of similarity feature parameters is crucial to the clustering effect. Flexible resources with similar feature parameters will be grouped together.

[0022] c i =(w i AGC Y i AGC ,w i reg Y i reg ) T (8)

[0023] C = (c1, c2, c3, ... c N (9)

[0024] c i Let w be the set of frequency modulation and peak shaving indices for the i-th grid. i AGC w represents the frequency modulation index weights for the i-th grid. i reg Let be the peak-shaving index weight for the i-th grid.

[0025] Euclidean distance is often used as a feature parameter for flexible resources w. AGC and w reg The Euclidean distance D(i,k) is calculated by the following formula.

[0026] D(i,k)=||x i -x k ||2 (10)

[0027] In the formula, i,k=1,2,3...,N; x i x k These are the objective weights corresponding to flexible resource i and flexible resource k, respectively.

[0028] 2) Construct the adjacency matrix M. The adjacency matrix is ​​constructed using a Gaussian kernel function. The construction method is as follows:

[0029]

[0030] In the formula, ξ represents the bandwidth parameter of the Gaussian kernel function, which affects the clustering effect.

[0031] 3) Calculate the normalized Laplace matrix Rstd.

[0032] First, the degree matrix H is calculated. The degree matrix is ​​a diagonal matrix that represents the sum of the weights of the edges connected to each vertex. Then, the normalized Laplacian matrix Rstd is calculated.

[0033]

[0034] R = HD (13)

[0035] R std =H -1 / 2 RH 1 / 2 (14)

[0036] Construct a new clustering matrix B. Calculate the eigenvalues ​​eigValues ​​and eigenvectors eigVectors of the Laplacian matrix Rstd, and take the eigenvectors u1, u2, ..., uk corresponding to the k largest eigenvalues ​​as row vectors to form a new matrix B with dimension N*k.

[0037] Each row is used as a new clustering element. The traditional K-means method is used to cluster matrix B, forming multiple cluster centers.

[0038] The above clustering process resulted in flexible resources being clustered into frequency-modulating resources and peak-modulating resources.

[0039] Step 3: Perform hierarchical aggregation on the clustered resources. Assuming the virtual power plant is a hierarchical structure formed by the aggregation of multi-form flexible resources, with peak shaving as the first layer and frequency regulation as the second layer, then:

[0040] L(vpp) =<L(1),L(2)> (15)

[0041] In the formula, L(i) represents the i-th layer structure, which is mathematically represented by the power required by the virtual power plant. It is an aggregate formed by the adaptive entities of the next level L(i-1) according to certain rules.

[0042]

[0043] In the formula, Let be the photovoltaic power of the peak-shaving resources in the i-th region; Let be the wind power output of the peak-shaving resources in the i-th region; Let be the energy storage capacity of the peak-shaving resources in the i-th region; X represents the flexible load power of peak-shaving resources in the i-th region; i pv To indicate whether photovoltaic resources exist in region i, assign 1 if yes, and 0 otherwise; X i w To indicate whether wind power resources exist in region i, use 1 if yes, 0 otherwise; X i esTo indicate whether energy storage resources exist in region i, use 1 if yes, and 0 otherwise; X i DR The value is 1 if there are flexible load resources in region i, and 0 otherwise.

[0044]

[0045] In the formula, Let be the photovoltaic power of the frequency regulation resources in the i-th region; Let be the wind power of the frequency regulation resources in the i-th region; Let be the energy storage capacity of the frequency regulation resources in the i-th region; Let be the flexible load power of the frequency regulation resources in the i-th region.

[0046] Based on the above, the equivalent aggregation model of the virtual power plant is as follows:

[0047]

[0048] In the formula, X i X j d(i,j) represents whether resources in regions i and j are involved in the construction of the virtual power plant; d(i,j) represents the fusion spatial distance between regions i and j.

[0049] The beneficial effects of this invention are:

[0050] This invention achieves collaboration among various flexible resources of different forms through aggregation, driving the overall evolution towards energy conservation, consumption reduction, and improved overall operating efficiency of the virtual power plant. This invention can effectively aggregate flexible resources within the virtual power plant, thereby fully tapping the response potential of the virtual power plant's flexible resources when the power grid experiences an emergency power shortage. Attached Figure Description

[0051] Figure 1 This is a flowchart of the virtual power plant multi-form flexible resource equivalent aggregation method considering response characteristics, as described in this invention. Detailed Implementation

[0052] The present invention will be further described below with reference to the accompanying drawings and specific embodiments. These embodiments are exemplary and intended to explain the present invention, and should not be construed as limiting the invention.

[0053] A method for equivalent aggregation of multi-form flexible resources in virtual power plants considering response characteristics, such as... Figure 1 As shown.

[0054] First, the cloud model is used to select the most certain response characteristics as typical response characteristics, and the characteristic indicators established below are used to evaluate them. Based on the characteristics of virtual power plants participating in demand response, response characteristic indicators are established. Referring to the response performance requirements of peak shaving and frequency regulation services for bidding resources in domestic and foreign power markets, frequency regulation performance indicators and peak shaving performance indicators that are common to each flexible resource are established respectively.

[0055]

[0056] in, This represents the response characteristics of photovoltaics at time t. This represents the response characteristics of wind power at time t. This represents the response characteristics of energy storage at time t. This represents the response characteristics of the flexible load at time t.

[0057] The flexible resource response characteristic matrix is ​​used as the raw data and input into the cloud model. A forward cloud generator is then used to select the characteristic with the highest certainty as the typical response characteristic. The calculation methods for the three numerical characteristics of the standard cloud, Ex, En, and He, are as follows:

[0058]

[0059]

[0060]

[0061] 1) Response time τ respon d This refers to the time from when the flexible resource receives a real-time or pre-set instruction from the power grid dispatch center until the actual output of the flexible resource enters within the allowable deviation range of the control target.

[0062] 2) Response capacity S respond This refers to the capacity that can participate in the response after receiving a system command.

[0063] 3) Daily load fluctuation rate f respond This reflects the stability of the response to flexible resources; the greater the load fluctuation rate, the more unstable the response.

[0064] Flexible resource frequency modulation performance index Y AGC τ represents the response time of flexible resources. respon d The shorter the period, the lower the daily load volatility f respond The lower the value, the better the fit with frequency regulation services. Peak shaving services generally have lower requirements for response speed, but longer duration requirements compared to frequency regulation, typically around 15 minutes. However, peak shaving services are generally called at a lower frequency, and flexible resources can usually meet the requirements. Based on this, the controllable load peak shaving performance index Y is defined.reg To make the indicators more targeted, the above indicator definition process has eliminated features that are not of interest to the market products, and the indicator values ​​are between 0 and 1, with higher values ​​indicating a higher degree of fit.

[0065]

[0066]

[0067] Where, τ N respond For typical response time, S N respond For typical response capacity, f N respond This represents the typical daily load fluctuation rate.

[0068] Suppose there are n resources in total, and the number of characteristic indicators is 2. Then, the entropy method yields the frequency modulation objective weight w. AGC and peak-shaving objective weight w AGC / reg The steps are as follows:

[0069]

[0070]

[0071]

[0072] d AGC / reg =1-e AGC / reg (10)

[0073]

[0074] In the formula, e represents the proportion of frequency regulation and peak shaving indicators for the i-th resource, respectively. AGC / reg d represents the entropy value of frequency modulation and peak shaving resources. AGC / reg w represents the information utility value for frequency modulation and peak shaving. AGC / reg The weights for frequency modulation and peak shaving indicators.

[0075] Spectral clustering algorithms represent several sets of load data as points V in an undirected weighted graph. An adjacency matrix is ​​used to represent the weight of the connections between each vertex. The algorithm seeks an optimal segmentation method to form multiple subgraphs, ensuring that each subgraph is as similar as possible internally, while maximizing the distance between different subgraphs. Taking a set K as an example, this paper details how to cluster flexible resources into peak-shaving resources and frequency-shaving resources. Let N be the number of flexible resource samples in set K. The detailed algorithm flow is as follows:

[0076] 1) Calculate the similarity matrix.

[0077] The similarity matrix D is a symmetric matrix, and its elements are called feature parameters. The selection of similarity feature parameters is crucial to the clustering effect. Flexible resources with similar feature parameters will be grouped together.

[0078] c i =(w i AGC Y i AGC ,w i reg Y i reg ) T (12)

[0079] C = (c1, c2, c3, ... c N (13)

[0080] c i Let w be the set of frequency modulation and peak shaving indices for the i-th grid. i AGC w represents the frequency modulation index weights for the i-th grid. i reg Let be the peak-shaving index weight for the i-th grid.

[0081] Euclidean distance is often used as a feature parameter for flexible resources w. AGC and w reg The Euclidean distance D(i,k) is calculated by the following formula.

[0082] D(i,k)=||x i -x k ||2 (14)

[0083] In the formula, i,k=1,2,3...,N; x i x k These are the objective weights corresponding to flexible resource i and flexible resource k, respectively.

[0084] 2) Construct the adjacency matrix M. The adjacency matrix is ​​constructed using a Gaussian kernel function. The construction method is as follows:

[0085]

[0086] In the formula, ξ represents the bandwidth parameter of the Gaussian kernel function, which affects the clustering effect.

[0087] 3) Calculate the normalized Laplace matrix Rstd.

[0088] First, the degree matrix H is calculated. The degree matrix is ​​a diagonal matrix that represents the sum of the weights of the edges connected to each vertex. Then, the normalized Laplacian matrix Rstd is calculated.

[0089]

[0090] R = HD (17)

[0091] R std =H -1 / 2 RH 1 / 2 (18)

[0092] Construct a new clustering matrix B. Calculate the eigenvalues ​​eigValues ​​and eigenvectors eigVectors of the Laplacian matrix Rstd, and take the eigenvectors u1, u2, ..., uk corresponding to the k largest eigenvalues ​​as row vectors to form a new matrix B with dimension N*k.

[0093] Each row is used as a new clustering element. The traditional K-means method is used to cluster matrix B, forming multiple cluster centers.

[0094] The above clustering process resulted in flexible resources being clustered into frequency-modulating resources and peak-modulating resources.

[0095] Based on the principle of local balancing, power transmission and loss on grid interconnection lines are reduced. Aggregation rules are designed based on electrical distance, and constraints are applied to the electrical distances between flexible resources to allow virtual power plants to continue aggregating into larger entities. This results in a hierarchical aggregation structure that emerges from different scenarios. The steps for designing aggregation rules are as follows:

[0096] In the i-th region (i = 1, 2, ..., m), the decision variables representing whether there are distributed power sources, energy storage devices, and flexible loads are denoted by a vector X, which consists of 0 and 1 elements.

[0097]

[0098] The set of decision variables for the entire region is:

[0099]

[0100] When modeling the optimization aggregation of virtual power plants, the traditional method sets each resource in the entire large area as a decision variable. However, the method of determining decision variables by dividing decision areas greatly reduces the number of decision variables and the computational difficulty compared to the former.

[0101] Assuming the virtual power plant is a hierarchical structure formed by the aggregation of multiple flexible resources, with peak shaving as the first layer and frequency regulation as the second layer, then:

[0102] L(vpp) =<L(1),L(2)> (20)

[0103] In the formula, L(i) represents the i-th layer structure, which is mathematically represented by the power required by the virtual power plant. It is an aggregate formed by the adaptive entities of the next level L(i-1) according to certain rules.

[0104]

[0105] It is a virtual power plant with equivalent peak-shaving capacity; Let be the energy storage capacity of the peak-shaving resources in the i-th region; Let be the flexible load power of the peak-shaving resources in the i-th region; Let be the photovoltaic power of the peak-shaving resources in the i-th region; Let be the wind power output of the peak-shaving resources in the i-th region.

[0106]

[0107] This is an equivalent virtual power plant power source type virtual power plant; Let be the photovoltaic power of the frequency regulation resources in the i-th region; Let be the wind power of the frequency regulation resources in the i-th region; Let be the energy storage capacity of the frequency regulation resources in the i-th region; Let be the flexible load power of the frequency regulation resources in the i-th region.

[0108] Based on the above, the equivalent aggregation model of the virtual power plant is as follows:

[0109]

[0110] In the formula, X i X j d(i,j) represents whether resources in regions i and j are involved in the construction of the virtual power plant; d(i,j) represents the fusion spatial distance between regions i and j.

[0111] The above examples are only used to illustrate the effects of the present invention, and the described embodiments are only a part of the embodiments of this application, not all of the embodiments. Finally, it should be noted that all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

Claims

1. A method for equivalent aggregation of multi-form flexible resources in a virtual power plant considering response characteristics, characterized in that: Includes the following steps: S1: Establish peak-shaving and frequency-modulation performance indicators for flexible resources; Based on the three response characteristics of flexible resources—response time, response capacity, and daily load fluctuation rate—and starting from the response characteristics of virtual power plants in peak shaving and frequency regulation, peak shaving and frequency regulation performance indicators of flexible resources are established. S2: Combining the objective comprehensive weighting method and NJW spectrum clustering, flexible resources are classified and aggregated into frequency modulation resources and peak modulation resources; Based on S1, after establishing the peak-shaving and frequency-modulation performance indicators of flexible resources, the objective comprehensive weighting method is used to assign weights to them, and combined with NJW spectrum clustering, the flexible resources are divided into peak-shaving resources and frequency-modulation resources. S3: Based on the classification results, design aggregation rules so that virtual power plants can continue to aggregate to form larger entities, resulting in a hierarchical structure that aggregates step by step in different scenarios.

2. The method for equivalent aggregation of multi-form flexible resources in a virtual power plant considering response characteristics as described in claim 1, characterized in that: In S1, multi-form flexible resource peak-shaving and frequency regulation performance indicators are defined, taking wind power plants, photovoltaic power plants, energy storage, and electric vehicles as examples, the definitions are as follows: Flexible resource frequency modulation performance indicators The calculation is shown in equation (1), indicating that the shorter the response time of flexible resources, the lower the daily load fluctuation rate. The lower the value, the better it matches the frequency regulation service; define the controllable load peak-shaving performance index. See equation (2); the values ​​of peak-shaving and frequency-modulation performance indicators are between 0 and 1. The larger the value, the higher the degree of fit. (1) (2) in, Typical response time Typical response capacity, Typical daily load fluctuation rate, For response capacity.

3. The method for multi-form flexible resource equalization aggregation of virtual power plants considering response characteristics according to claim 2, characterized in that: In S2, flexible resources are clustered into peak-shaving resources and frequency-shaving resources, and the steps are as follows; Assuming the entire region is divided into m grids and the number of characteristic indices is 2, the entropy method is used to obtain the frequency modulation index weights. and peak shaving index weights The steps are as follows: (3) (4) (5) (6) (7) In the formula, , and represent the proportions of the frequency regulation and peak regulation indicators for the i-th resource, respectively. The entropy value of frequency modulation and peak shaving resources. This represents the utility value of frequency modulation and peak shaving information. For frequency modulation and peak shaving index weights; NJW spectral clustering represents several sets of load data as points V in an undirected weighted graph. It uses an adjacency matrix to represent the weight of the connections between each vertex, seeking an optimal segmentation method to form multiple subgraphs, such that each subgraph is as similar as possible internally, while the distance between different subgraphs is as far as possible. Taking a set K as an example, assuming that set K contains N flexible resource samples, the detailed algorithm flow is as follows: 1) Calculate the similarity matrix; The similarity matrix D is a symmetric matrix, and the elements therein are called feature parameters. Flexible resources with similar feature parameters will be grouped together. (8) (9) Let i be the set of frequency modulation and peak shaving indices for the i-th grid. Let be the frequency modulation index weight for the i-th grid; Let be the peak-shaving index weight for the i-th grid; The Euclidean distance is used as a feature parameter for flexible resources. Calculated by the following formula; (10) In the formula, i,k=1,2,3...,N; , Flexible resources i And the objective weight corresponding to flexible resource k; 2) Construct the adjacency matrix M; use the Gaussian kernel function to construct the adjacency matrix; the construction method is as follows: (11) In the formula, The bandwidth parameter of the Gaussian kernel function affects the clustering results; 3) Calculate the normalized Laplacian matrix Rstd; First, calculate the degree matrix H, which is a diagonal matrix representing the sum of the weights of the edges connected to each vertex; then calculate the normalized Laplacian matrix Rstd. (12) (13) (14) Construct a new clustering matrix B; calculate the eigenvalues ​​eigValues ​​and eigenvectors eigVectors of the Laplacian matrix Rstd, and take the eigenvectors u1, u2, ..., uk corresponding to the largest k eigenvalues ​​as row vectors to form a new matrix B with dimension N*k. Each row is used as a new clustering element. The traditional K-means method is used to cluster matrix B to form multiple cluster centers. The clustering process resulted in flexible resources being clustered into frequency-modulating resources and peak-modulating resources.

4. The method for multi-form flexible resource equalization aggregation of virtual power plants considering response characteristics according to claim 3, characterized in that: In S3, the steps for designing aggregation rules are as follows; Assuming the virtual power plant is a hierarchical structure formed by the aggregation of multiple flexible resources, with peak shaving as the first layer and frequency regulation as the second layer, then: (15) In the formula, L(i) represents the i-th layer structure, which is mathematically represented by the power required by the virtual power plant. It is an aggregate formed by the adaptive entities of the next level L(i-1) according to certain rules. (16) In the formula, Let be the photovoltaic power of the peak-shaving resources in the i-th region; Let be the wind power output of the peak-shaving resources in the i-th region; Let be the energy storage capacity of the peak-shaving resources in the i-th region; Let be the flexible load power of the peak-shaving resources in the i-th region; The value indicates whether photovoltaic resources exist in region i; 1 indicates yes, and 0 indicates no. To indicate whether wind power resources exist in region i, 1 indicates yes, and 0 indicates no. The value indicates whether energy storage resources exist in region i; 1 indicates yes, and 0 indicates no. The value is 1 if flexible load resources exist in region i, and 0 otherwise. (17) In the formula, Let be the photovoltaic power of the frequency regulation resources in the i-th region; Let be the wind power of the frequency regulation resources in the i-th region; Let be the energy storage capacity of the frequency regulation resources in the i-th region; Let be the flexible load power of the frequency regulation resources in the i-th region; Based on the above, the equivalent aggregation model of the virtual power plant is as follows: (18) In the formula, , To represent whether resources in regions i and j are involved in the construction of the virtual power plant, 1 indicates yes, and 0 indicates no. This represents the spatial distance between region i and region j.

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