Method for modeling clusterable capacity of electric vehicles based on secondary clustering

Abstract

The application discloses a kind of electric vehicle cluster schedulable capacity modeling method based on secondary clustering, applied to large-scale electric vehicle participates in different auxiliary service scenarios of power system, and the space-time distribution of schedulable capacity is evaluated in view of the problem.Schedulable capacity of electric vehicle individual single charging process is modeled based on charging pile charging historical operation data, and the schedulable capacity index of chargeable capacity, chargeable power, dischargeable capacity and dischargeable power is obtained;Charging operation data is clustered into several charging images using K-means method;According to the scene of power system auxiliary service, the original parameters of secondary clustering are selected, and the charging pile is further clustered into several charging pile aggregates by combining the results of primary clustering using the method combining principal component analysis and self-organizing mapping;Finally, the aggregated schedulable capacity of each aggregate is obtained.The method of the application can obtain a schedulable capacity aggregation model with different space-time distribution characteristics, so as to adapt to scheduling of various types of scenarios.

Description

Technical Field

[0001] This invention relates to a method for modeling the schedulable capacity of electric vehicle (EV) clusters based on quadratic clustering. More specifically, it applies to a method for evaluating the spatiotemporal distribution of schedulable capacity of large-scale EVs participating in different ancillary services of the power grid in environments where EVs are extensively integrated into the grid. Therefore, it presents an aggregation method that integrates EV behavior habits and charging pile characteristics, as well as a modeling method for the schedulable capacity of an EV single charging process and the schedulable capacity of the cluster, thereby obtaining the spatiotemporal distribution of schedulable capacity of the EV cluster that meets the requirements of ancillary services. Background Technology

[0002] The randomness of the unstable electricity demand from massive electric vehicles (EVs) coupled with the volatility of renewable energy sources exacerbates the spatial and temporal mismatch between power system supply and demand, leading to problems such as voltage fluctuations and increased grid losses. However, the application of smart interaction technologies between EVs and the grid, such as orderly charging and Vehicle-to-Grid (V2G) technologies, along with artificial intelligence, can aggregate EVs into dispatchable resources, enabling them to participate in power system balance ancillary services such as frequency regulation, voltage regulation, and peak shaving, thereby improving the overall operating efficiency of the power system.

[0003] Because the capacity and power of a single electric vehicle are very small, while provincial and municipal ancillary services require an adjustable range of at least hundreds of kilowatts to hundreds of megawatts, existing regulations (such as the "Implementation Rules for Virtual Power Plants in Guangzhou" and the "Operation Rules for the Anhui Power Peak-Shaving Ancillary Service Market (Trial)") generally impose capacity requirements on participants in power system ancillary services. Therefore, research on the spatiotemporal characteristics of the aggregated dispatchable capacity of large-scale electric vehicles is of significant theoretical and practical importance. The aggregated dispatchable capacity of electric vehicles (EVs) refers to the ability of an EV cluster (EVA) to participate in grid ancillary services as a dispatchable resource. It represents the upper and lower limits of bidirectional energy exchange between EVs as energy storage systems and the grid, as well as the corresponding upper and lower limits of charging and discharging power, provided that user electricity demand is met.

[0004] However, existing models primarily rely on empirical methods for clustering electric vehicles (EVs) and fail to adapt cluster composition to charging infrastructure or scenario requirements. For example, they might treat one or several charging stations as a single cluster, or divide all EVs within a region into multiple clusters based on quantity. Clusters formed by these methods often lack spatiotemporal consistency among EVs within the same cluster, and different clusters lack clear characteristic differences, making it difficult to create adaptive clusters for different scenarios. Based on this, some research has proposed using intelligent clustering algorithms to form different clusters based on EV behavior data or charging station attribute data. However, current clustering algorithms generally only cluster individual EVs or charging stations, failing to comprehensively consider the impact of both. Furthermore, they do not adjust the clustering criteria according to scheduling scenario requirements, potentially reducing scheduling effectiveness. Summary of the Invention

[0005] To overcome the shortcomings of the existing technology, this invention provides a method for modeling the schedulable capacity of electric vehicles based on quadratic clustering. This method is applied to the reporting of schedulable capacity when electric vehicles participate in grid ancillary services. The aim is to obtain a schedulable capacity aggregation model with different spatiotemporal distribution characteristics through this invention, making it adaptable to various types of scheduling scenarios.

[0006] The present invention adopts the following technical solution to solve the technical problem:

[0007] The present invention features a method for modeling the schedulable capacity of electric vehicle clusters based on secondary clustering. First, it models the schedulable capacity of individual electric vehicles during a single charging process based on historical charging operation data of charging piles, obtaining four indicators describing schedulable capacity: rechargeable capacity, rechargeable power, discharging capacity, and discharging power. Second, it clusters the charging operation data into several charging profiles using the K-means method. Then, based on the scenario of power system ancillary services, it selects the original parameters for secondary clustering and combines them with the results of primary clustering, using a combination of principal component analysis and self-organizing mapping to further cluster the charging piles into several charging pile aggregates. Finally, it obtains the aggregated schedulable capacity of each aggregate.

[0008] The schedulable capacity modeling method for electric vehicle clusters based on quadratic clustering in this invention is characterized by including the following steps:

[0009] Step 1: Model the schedulable capacity for a single charging process based on individual electric vehicle charging operation data.

[0010] The individual charging operation data for electric vehicles includes: charging start time, charging end time, total charging capacity, rated charging power of the charging pile, and rated discharging power of the charging pile.

[0011] The dispatchable capacity of a single charging process refers to the upper and lower limits of the energy and power exchanged between an individual electric vehicle and the power grid, provided that the power demand of electric vehicle users is met; using rechargeable capacity SCC Rechargeable power SCP Discharge capacity SDC and discharge power SDP Four metrics are used to describe schedulable capacity;

[0012] The rechargeable capacity SCC Characterized by equation (1):

[0013] (1);

[0014] In formula (1):

[0015] by d The number representing the charging record. d =1,…, D , D This represents the total number of charging records. For charging efficiency;

[0016] SCC d,t It is numbered d Charging records in t The rechargeable capacity at any given time. P c Rated charging power;

[0017] t s For scheduling time intervals, t d,0 For the number d The charging record shows the start time of charging;

[0018] E d,c It is numbered d The total amount of electricity charged is recorded in the charging log.

[0019] E d,t It is numbered d Charging records in t The charge at time t is calculated using equation (2):

[0020] (2);

[0021] The rechargeable power SCP As represented by equation (3):

[0022] (3);

[0023] In formula (3):

[0024] SCP d,t It is numbered d Charging records in t The rechargeable power at any given time;

[0025] Dischargeable capacity SDC As represented by equation (4):

[0026] (4);

[0027] In equation (4):

[0028] SDC d,t It is numbered d Charging records in t Dischargeable capacity at any given time;

[0029] t d,end It is numbered d The charging record shows the end time of charging.

[0030] The dischargeable power SDP Characterized by equation (5):

[0031] (5);

[0032] In formula (5):

[0033] SDP d,t It is numbered d Charging records in t Dischargeable power at any given time;

[0034] P d Rated discharge power, For discharge efficiency;

[0035] Step 2: Selection of clustering parameters and data normalization:

[0036] Four parameters are selected for a single clustering operation: the proportion of idle time. ftr d , as well as charging start time, charging end time and total charging capacity obtained by reading historical data;

[0037] The percentage of idle time ftr d Characterized by equation (6):

[0038] (6);

[0039] The percentage of idle time ftr d This refers to the proportion of idle time to the total charging time, with a value of 0-1.

[0040] Then, the parameter vector of a first clustering Characterized by equation (7):

[0041] (7);

[0042] The four parameters selected for the first clustering are normalized according to equation (8):

[0043] (8);

[0044] In equation (8):

[0045] It is numbered d The normalized parameter vector of the charging record;

[0046] The vector of minimum parameter values. The vector of maximum parameter values;

[0047] Step 3: First clustering of charging behavior based on k-means algorithm:

[0048] Step 3.1: Initialize the number of clusters K The value is 2, which sets the maximum number of clusters. K max and maximum number of iterations iter max ;

[0049] Step 3.2: Based on the number of clusters K The value is randomly selected. K The first 1 data points are used as the initial cluster centers, and the initial iteration number iter is set to 1.

[0050] Step 3.3: Calculate the distance between each data object and the cluster center according to formula (9), and group the data with the nearest cluster center into one class:

[0051] (9);

[0052] In equation (9):

[0053] It is the distance between vectors a and b;

[0054] For vector a, the first... i One dimension, b iFor vector b, the first i One dimension, I Let a be the total dimension of vectors a and b;

[0055] Step 3.4: Based on the classification results of Step 3.3, calculate the result according to formula (10). k Class center coordinates R ( k This updates the center of each category.

[0056] (10);

[0057] In formula (10):

[0058] by k The number representing each category, k= 1,…, K ;

[0059] by j k Characterizing the first k The parameter vector number of the class, N k For the first k The number of parameter vectors of the class. j k = 1,…, N K ;

[0060] For the first j k A parameter vector;

[0061] Step 3.5: Increment the iteration count `iter` by 1. If the iteration count `iter` after incrementing by 1 is less than `iter`... max If yes, return to step 3.3; otherwise, proceed to step 3.6.

[0062] Step 3.6: Calculate the number of clusters according to formula (11). K Davies-Bouldin index value at time DBI ( K ):

[0063] (11);

[0064] In equation (11):

[0065] by h Characterization needs and the first k The class number of other classes that calculate distance;

[0066] For the first kThe mean distance between data objects in a class and the cluster centers;

[0067] For the first h The mean distance between data objects in a class and the cluster centers;

[0068] For the first h Class and First k Distance between cluster centers;

[0069] Step 3.7, K The value of is increased by 1. If the value after adding 1 is... K Assignment greater than K max If so, return to step 3.2; otherwise, select the one with the smallest DBI value. K Output the corresponding clustering results. Step 3 ends, completing one clustering cycle. Thus, all charging behaviors are clustered into [the following categories]. K This type, referred to as a charging portrait, has K A charging image;

[0070] Step 4: Data preparation for secondary clustering:

[0071] The objects of the secondary clustering are charging piles, and the proportion of each type of charging profile in the charging pile is called the charging profile vector, which is represented by equation (12):

[0072] (12);

[0073] In equation (12):

[0074] by s The number representing the charging station is used to identify the charging station. n S Represents the total number of charging stations. s =1,…, n S ;

[0075] For charging piles s Charging image vector; For charging piles s The k The number of charging-related images;

[0076] Based on the scenario of electric vehicles participating in auxiliary services, corresponding selection parameters are set, and the selection parameters are added to the end of the charging profile vector to form a charging pile parameter vector with multi-dimensional parameters represented by equation (13). :

[0077] (13);

[0078] In equation (13):

[0079] by M 0 The dimension of the parameter vector representing the charging pile; m 0 The dimension number representing the parameter vector of the charging pile. m 0 =1,…, M 0 ;

[0080] Charging pile parameter vector The m 0 One dimension;

[0081] total S A matrix formed by the parameter vectors of each charging pile As the raw data for secondary clustering;

[0082] The matrix Characterized by equation (14):

[0083] (14);

[0084] Step 5: Dimensionality reduction based on principal component analysis:

[0085] Step 5.1: Calculate the matrix The covariance matrix;

[0086] Step 5.2: Calculate the eigenvalues ​​of the covariance matrix. and the corresponding feature vector ;

[0087] Step 5.3: Sort the eigenvalues ​​from largest to smallest, and select the eigenvectors corresponding to the eigenvalues ​​whose sum accounts for more than 95% of the total eigenvalues, and merge them into a dimensionality-reduced matrix. ,by m The column number of the dimension-reduced matrix is ​​denoted as . The total number of columns in the dimension-reduced matrix is ​​denoted as . M ;

[0088] The dimensionality reduction matrix Characterized by equation (15):

[0089] (15);

[0090] In equation (15), This is the dimensionality-reduced parameter vector of the charging pile.

[0091] Step 6: Secondary clustering based on self-organizing map neural network:

[0092] After secondary clustering using a self-organizing map neural network (SOM), the input dimension reduction matrix is... In S vectors Clustered as L Each category forms L A collection of charging stations;

[0093] Step 7: Obtain the schedulable capacity aggregation model for each aggregate:

[0094] The L The schedulable capacity of each charging pile aggregate is the sum of the schedulable capacities of all charging records in that aggregate, as represented by equation (16):

[0095] (16);

[0096] In equation (16):

[0097] by l The number representing the charging pile assembly. l= 1,…, L ; N l Charging pile aggregate l The number of charging records in the middle;

[0098] SCC l,t The time t is numbered as l The charging capacity of the charging pile aggregate;

[0099] SCP l,t The time t is numbered as l The charging power of the charging pile aggregate;

[0100] SDC l,t The time t is numbered as l The discharge capacity of the charging pile aggregate;

[0101] SDP l,t The time t is numbered as l The charging pile aggregate can discharge power.

[0102] Complete the schedulable capacity modeling of the aggregate.

[0103] The characteristic of the electric vehicle cluster schedulable capacity modeling method based on quadratic clustering in this invention is that: in step 6, quadratic clustering is performed as follows:

[0104] The input layer of the self-organizing map neural network (SOM) is... The output layer consists of neurons arranged in two dimensions;

[0105] The neuron is related to the dimensionality reduction matrix. Number of columns M Vectors of the same length This is represented by equation (17):

[0106] (17);

[0107] In equation (17):

[0108] by j The numbering that represents neurons, in order to J Characterizes the number of neurons;

[0109] For neurons j The m Each weight corresponds to a dimension reduction matrix. The m List;

[0110] Step 6.1, Input matrix The number of input SOM neurons L Input the maximum number of iterations for the second-order clustering. ti max Initialize all neurons Initialize the number of quadratic clustering iterations. ti The value is 1;

[0111] Step 6.2: Normalize the matrix using equation (8). vectors in ;

[0112] Step 6.3: Randomly select one The distance between the neuron and all neuron vectors is calculated using equation (9), and the neuron vector with the smallest distance is selected as the winning neuron. ;

[0113] Step 6.4: Target the winning neuron The weights of neurons adjacent to the winning neuron are updated according to equation (18):

[0114] (18);

[0115] In formula (18):

[0116] For the first ti The vector of the neuron at the next iteration;

[0117] For the first ti The neuron's vector at +1 iteration;

[0118] For the first ti The learning rate at the next iteration decreases as the number of iterations increases;

[0119] For neurons and neurons The neighborhood function is characterized by equation (19):

[0120] (19);

[0121] In equation (19):

[0122] Z j For neurons j The coordinates; Z c For neurons c The coordinates;

[0123] For the first ti In the next iteration, the neighborhood radius decreases as the number of iterations increases;

[0124] Step 6.5, ti The value is incremented by 1, and it is checked whether the result after the increment is greater than 1. ti max ;

[0125] If not greater than ti max If so, return to step 6.3;

[0126] Otherwise, the secondary clustering process ends, completing the secondary clustering process based on the SOM method.

[0127] The characteristic of the electric vehicle cluster schedulable capacity modeling method based on quadratic clustering in this invention is that: in step 4, setting the corresponding selection parameters according to the scenario of electric vehicles participating in auxiliary services means: if it is used for voltage regulation, the corresponding selection parameters are set as: longitude, latitude and rated charging power of the charging pile; if it is used for peak shaving and frequency regulation, the corresponding selection parameter is set as: rated charging power.

[0128] Compared with existing technologies, the beneficial effects of this invention are reflected in:

[0129] 1. This invention models the schedulable capacity of a single EV charging process and the entire charging aggregate based on charging pile operation data. The modeling process considers the impact of ancillary service technology requirements in different scenarios on the schedulable capacity model. Compared to traditional charging process modeling methods, this invention reduces the amount of data required for modeling, thereby improving communication and computation efficiency. Furthermore, it better matches the needs of power system ancillary service scenarios.

[0130] 2. This invention comprehensively considers the behavioral characteristics of electric vehicles and the inherent characteristics of charging piles through intelligent secondary clustering, while traditional clustering methods can only consider one of the characteristics of electric vehicles and charging piles. Therefore, the clustering method of this invention can better reflect the spatiotemporal distribution of the actual schedulable capacity of electric vehicle aggregates.

[0131] 3. This invention uses a combination of k-means and SOM. Compared with using either k-means or SOM for clustering, it can take into account the advantages of k-means in terms of fast clustering speed for large-scale data and the advantages of SOM in terms of good clustering accuracy, thereby improving clustering efficiency and clustering effect. Attached Figure Description

[0132] Figure 1 and Figure 2 These represent the dispatchable capacity and dispatchable power on December 1, 2021, under frequency and voltage regulation conditions, respectively.

[0133] Figure 3 and Figure 4 These represent the dispatchable capacity and dispatchable power on December 1, 2021, under peak-shaving conditions.

[0134] Figure 5 and Figure 6 These represent the schedulable capacity and schedulable power of EVA1 on December 1, 2021, under frequency modulation conditions.

[0135] Figure 7 and Figure 8 These represent the dispatchable capacity and dispatchable power of EVA1 on December 1, 2021, under peak-shaving conditions.

[0136] Figure 9 and Figure 10 These represent the dispatchable capacity and dispatchable power of EVA1 on December 1, 2021, under voltage regulation conditions.

[0137] Figure 11 Charging power that provides a profile for "evening-time" charging. ftr =0.55.

[0138] Figure 12 Charging power to characterize "early morning" charging. ftr =0.66. Detailed Implementation

[0139] This embodiment uses a method based on secondary clustering to model the schedulable capacity of electric vehicle clusters. First, based on historical charging operation data of charging piles, the schedulable capacity of individual electric vehicles during a single charging process is modeled to obtain four indicators describing the schedulable capacity: rechargeable capacity, rechargeable power, discharging capacity, and discharging power. Second, the charging operation data is clustered into several charging profiles using the K-means method. Then, based on the scenario of power system ancillary services, the original parameters of the secondary clustering are selected and combined with the results of the primary clustering. A method combining principal component analysis and self-organizing mapping is used to further cluster the charging piles into several charging pile aggregates. Finally, the aggregated schedulable capacity of each aggregate is obtained.

[0140] The method for modeling the schedulable capacity of electric vehicle clusters based on quadratic clustering in this embodiment includes the following steps:

[0141] Step 1: Model the schedulable capacity of a single charging process based on electric vehicle charging operation data.

[0142] Electric vehicle charging operation data includes: charging start time, charging end time, total charging capacity, rated charging power of charging pile, and rated discharging power of charging pile;

[0143] Dispatchable capacity refers to the upper and lower limits of the bidirectional energy exchange between electric vehicles as energy storage systems and the power grid, provided that the power demand of electric vehicle users is met; and the corresponding upper and lower limits of charging and discharging power. (The term "dispatchable capacity" is used in this context.) SCC Rechargeable power SCP Discharge capacity SDC and discharge power SDP Four metrics are used to describe schedulable capacity; these four metrics are calculated based on two assumptions: that electric vehicles charge at a constant maximum power and that electric vehicles begin charging as soon as they are connected to a charging station.

[0144] Rechargeable capacity SCC Characterized by equation (1):

[0145] (1);

[0146] In formula (1):

[0147] by d The number representing the charging record. D This represents the total number of charging records. d =1,…, D , For charging efficiency;

[0148] SCC d,t It is numbered d Charging records in tThe rechargeable capacity at any given time. P c Rated charging power;

[0149] t s For scheduling time intervals, t d,0 For the number d The charging record shows the start time of charging;

[0150] E d,c It is numbered d The total amount of electricity charged is recorded in the charging log.

[0151] E d,t It is numbered d Charging records in t The charge at time t is calculated using equation (2):

[0152] (2);

[0153] Rechargeable power SCP As represented by equation (3):

[0154] (3);

[0155] In formula (3):

[0156] SCP d,t It is numbered d Charging records in t The rechargeable power at any given time;

[0157] Discharge capacity SDC As represented by equation (4):

[0158] (4);

[0159] In equation (4):

[0160] SDC d,t It is numbered d Charging records in t Dischargeable capacity at any given time;

[0161] t d,end It is numbered d The charging record shows the end time of charging.

[0162] Dischargeable power SDP Characterized by equation (5):

[0163] (5);

[0164] In formula (5):

[0165] SDP d,t It is numbered d Charging records in t Dischargeable power at any given time

[0166] P d Rated discharge power, For discharge efficiency;

[0167] Steps 2 through 6 below describe the main process of secondary clustering. The first clustering uses electric vehicle charging records as raw data, obtaining various charging profiles through K-means clustering. Then, the proportions of each type of charging profile in the charging piles, along with the characteristics of the charging piles determined by the scheduling scenario, are used as raw data to further cluster the charging piles. This ultimately forms EVAs with different characteristics for prediction, thus enabling quantitative assessment of ancillary service capabilities in various power system scheduling scenarios such as frequency regulation, peak shaving, and voltage regulation.

[0168] Step 2: Selection of clustering parameters and data normalization:

[0169] The purpose of primary clustering is to cluster charging records, thereby grouping a large number of charging records into several charging profiles that differ in habits such as time and amount of charge. These profiles could include those who tend to charge in the morning, those who tend to charge at night, and those who can charge all day. Primary clustering uses four parameters: the proportion of idle time. ftr d , as well as charging start time, charging end time and total charging capacity obtained by reading historical data;

[0170] Percentage of free time ftr d Characterized by equation (6):

[0171] (6);

[0172] Percentage of free time ftr d This refers to the proportion of idle time to the total charging time, with a value of 0-1.

[0173] Then, the parameter vector of a first clustering Characterized by equation (7):

[0174] (7);

[0175] The four parameters selected for the first clustering are normalized according to equation (8):

[0176] (8);

[0177] In equation (8):

[0178] It is numbered d The normalized parameter vector of the charging record;

[0179] The vector of minimum parameter values. The vector of maximum parameter values;

[0180] The parameter vectors to be normalized cannot be completely equal, therefore, It is impossible for them to be completely equal. Then, equation (8) will not have a denominator of 0.

[0181] Step 3: First clustering of charging behavior based on k-means algorithm:

[0182] Step 3.1: Initialize the number of clusters K The value is 2, which sets the maximum number of clusters. K max and maximum number of iterations iter max ;

[0183] Step 3.2: Based on the number of clusters K The value is randomly selected. K The first data point is used as the initial cluster center, and the initial iteration number iter is set to 1.

[0184] Step 3.3: Calculate the distance between each data object and the cluster center according to formula (9), and group the data with the nearest cluster center into one class:

[0185] (9);

[0186] In equation (9):

[0187] It is the distance between vectors a and b;

[0188] For vector a, the first... i One dimension, b i For vector b, the first i One dimension, I Let a be the total dimension of vectors a and b;

[0189] Step 3.4: Based on the classification results of Step 3.3, calculate the result according to formula (10). kClass center coordinates R ( k This updates the center of each category.

[0190] (10);

[0191] In formula (10):

[0192] by k The number representing each category, k= 1,…, K ;

[0193] by j k Characterizing the first k The parameter vector number of the class, N k For the first k The number of parameter vectors of the class, j k = 1,…, N K ;

[0194] For the first j k A parameter vector;

[0195] Step 3.5: Increment the iteration count `iter` by 1. If the iteration count `iter` after incrementing by 1 is less than `iter`... max If yes, return to step 3.3; otherwise, proceed to step 3.6.

[0196] Step 3.6: Calculate the number of clusters according to formula (11). K Davies-Bouldin index value at time DBI ( K ):

[0197] (11);

[0198] In equation (11):

[0199] by h Characterization needs and the first k The class number of other classes used to calculate distance;

[0200] For the first k The mean distance between data objects in a class and the cluster centers;

[0201] For the first h The mean distance between data objects in a class and the cluster centers;

[0202] For the first h Class and First k Distance between cluster centers;

[0203] The Davies-Bouldin index is a common metric for evaluating clustering quality. Its core idea is to calculate the similarity between each cluster and its most similar cluster, and then measure the overall clustering result by averaging all similarities. Higher similarity between clusters (higher Davies-Bouldin scores) indicates smaller distances between clusters, suggesting a poorer clustering result, and vice versa.

[0204] Step 3.7, K The value of is increased by 1. If the value after adding 1 is... K Assignment greater than K max If so, return to step 3.2; otherwise, select the one with the smallest DBI value. K Output the corresponding clustering results. Step 3 ends, completing one clustering cycle. Thus, all charging behaviors are clustered into [the following categories]. K This type, referred to as a charging portrait, has K A charging image;

[0205] Step 4: Data preparation for secondary clustering:

[0206] Secondary clustering is based on the results of primary clustering, further clustering according to the location information of charging piles, thus ultimately obtaining multiple EVAs; the object of secondary clustering is the charging pile, and the proportion of each type of charging image in the charging pile is called the charging image vector, which is represented by equation (12):

[0207] (12);

[0208] In equation (12):

[0209] by s The number representing the charging station is used to identify the charging station. n S Represents the total number of charging stations. s =1,…, n S ;

[0210] For charging piles s Charging image vector; For charging piles s The k The number of charging-related images;

[0211] The selection parameters are set according to the scenarios in which electric vehicles participate in auxiliary services, including:

[0212] If used for voltage regulation, set the corresponding selection parameters as follows: longitude, latitude, and rated charging power of the charging pile;

[0213] If used for peak shaving and frequency regulation, set the corresponding selection parameter as: rated charging power.

[0214] The selected parameters are added to the end of the charging profile vector to form a charging pile parameter vector with multidimensional parameters, as represented by equation (13). :

[0215] (13);

[0216] In equation (13):

[0217] by M 0 The dimension of the parameter vector representing the charging pile; m 0 The dimension number representing the parameter vector of the charging pile. m 0 =1,…, M 0 ;

[0218] Charging pile parameter vector The m 0 One dimension;

[0219] total S A matrix formed by the parameter vectors of each charging pile As the raw data for secondary clustering;

[0220] matrix Characterized by equation (14):

[0221] (14);

[0222] Step 5: Dimensionality reduction based on principal component analysis:

[0223] Step 5.1: Calculate the matrix The covariance matrix;

[0224] Step 5.2: Calculate the eigenvalues ​​of the covariance matrix. and the corresponding feature vector ;

[0225] Step 5.3: Sort the eigenvalues ​​from largest to smallest, and select the eigenvectors corresponding to the eigenvalues ​​whose sum accounts for more than 95% of the total eigenvalues, and merge them into a dimensionality-reduced matrix. ,by m The column number of the dimension-reduced matrix is ​​denoted as . The total number of columns in the dimension-reduced matrix is ​​denoted as .M ;

[0226] Dimensionality reduction matrix Characterized by equation (15):

[0227] (15);

[0228] In equation (15), This is the dimensionality-reduced parameter vector of the charging pile.

[0229] Step 6: Secondary clustering based on self-organizing map neural network:

[0230] SOM (Symptom Organization for Mesh) is an unsupervised, competitive learning neural network that maps high-dimensional data to a low-dimensional space. This low-dimensional space is typically designed as a two-dimensional grid, with each grid containing one neuron adjacent to neurons in other grids. Compared to K-means, it has two key differences: First, K-means requires pre-determining the number of classes, while SOM does not; some nodes in the hidden layer may not have any input data belonging to them. Therefore, K-means is more affected by initialization. Second, after finding the most similar class for each input data point, K-means only updates the parameters of that class, while SOM updates neighboring nodes. Therefore, SOM may be more accurate than K-means. However, on the other hand, SOM's time complexity is significantly higher than K-means. This makes SOM significantly slower than K-means, thus unsuitable for single-pass clustering with large datasets.

[0231] After secondary clustering using a self-organizing map neural network (SOM), the input dimension reduction matrix is... In S vectors Clustered as L Each category forms L A collection of charging stations;

[0232] In practice, secondary clustering is performed using the following method:

[0233] The input layer of the self-organizing map neural network (SOM) is... The output layer consists of neurons arranged in two dimensions;

[0234] Neurons are related to dimensionality reduction matrices Number of columns M Vectors of the same length This is represented by equation (17):

[0235] (17);

[0236] In equation (17):

[0237] byj The numbering that represents neurons, in order to J Characterizes the number of neurons;

[0238] For neurons j The m Each weight corresponds to a dimension reduction matrix. The m List;

[0239] Step 6.1, Input matrix The number of input SOM neurons L Input the maximum number of iterations for the second-order clustering. ti max Initialize all neurons Initialize the number of quadratic clustering iterations. ti The value is 1;

[0240] Step 6.2: Normalize the matrix using equation (8). vectors in ;

[0241] Step 6.3: Randomly select one The distance between the neuron and all neuron vectors is calculated using equation (9), and the neuron vector with the smallest distance is selected as the winning neuron. ;

[0242] Step 6.4: Target the winning neuron The weights of neurons adjacent to the winning neuron are updated according to equation (18):

[0243] (18);

[0244] In equation (18):

[0245] For the first ti The vector of the neuron at the next iteration;

[0246] For the first ti The neuron's vector at +1 iteration;

[0247] For the first ti The learning rate at the next iteration decreases as the number of iterations increases;

[0248] For neurons and neurons The neighborhood function is characterized by equation (19):

[0249] (19);

[0250] In equation (19):

[0251] Z j For neurons j The coordinates; Z c For neurons c The coordinates;

[0252] For the first ti In the next iteration, the neighborhood radius decreases as the number of iterations increases;

[0253] Step 6.5, ti The value is incremented by 1, and it is checked whether the result after the increment is greater than 1. ti max ;

[0254] If not greater than ti max If so, it returns 6.3;

[0255] Otherwise, the secondary clustering process ends, thus completing the secondary clustering process based on the SOM method.

[0256] Step 7: Obtain the schedulable capacity aggregation model:

[0257] L The schedulable capacity of each charging pile aggregate is the sum of the schedulable capacities of all charging records in that aggregate, as represented by equation (16):

[0258] (16);

[0259] In equation (16):

[0260] by l The number representing the charging pile assembly. l= 1,…, L ; N l Charging pile aggregate l The number of charging records in the middle;

[0261] SCC l,t The time t is numbered as l The charging capacity of the charging pile aggregate; SCP l,t The time t is numbered as l The charging power of the charging pile aggregate; SDC l,t The time t is numbered as l The discharge capacity of the charging pile aggregate; SDPl,t The time t is numbered as l The charging pile aggregate can discharge power.

[0262] Complete the schedulable capacity modeling of the aggregate.

[0263] This embodiment uses approximately 1.8 million charging data points generated annually from over 4,000 charging piles in a selected area as the raw data to illustrate this method. Each charging data point includes: charging start time, end time, charging amount, rated charging power, longitude, latitude, and charging pile number. Calculations show that all data in the selected area... ftr The mean is 0.62. Considering different ancillary service technical indicators, the distribution of the daily schedulable capacity of the selected area over time is calculated as follows: Figure 1 and Figure 2 as well as Figure 3 and Figure 4 As shown; Figure 1 Curve a1 in the figure represents the rechargeable capacity, and curve b1 represents the dischargeable capacity. Figure 2 Curve a2 in the figure represents the rechargeable power, and curve b2 represents the dischargeable power. Figure 3 Curve a3 represents the rechargeable capacity, and curve b3 represents the dischargeable capacity. Figure 4 Curve a4 represents the rechargeable power, and curve b4 represents the dischargeable power.

[0264] Clustering was performed on 1.78 million charging data points based on four parameters: charging start time, charging end time, charging capacity, and idle time percentage. The choice of K was iteratively evaluated using the CH parameter, and the best clustering result was achieved when K=8, with a CH value of 490640. Ultimately, 623,000 charging data points were divided into 8 charging profiles, and the results of the first clustering are shown in Table 1.

[0265] Table 1

[0266]

[0267] The charging power distribution curves of the two types with the largest number of charges are shown below. Figure 11 and Figure 12 As shown.

[0268] The selection of raw data for primary clustering is independent of the scenario, while the selection of raw data for secondary clustering depends on the scenario requirements. For the three scenarios of peak shaving, frequency regulation, and voltage regulation, peak shaving and frequency regulation do not require location parameters to participate in clustering, while voltage regulation does require location variables.

[0269] Location-independent quadratic clustering:

[0270] In frequency regulation and peak shaving scenarios, electric vehicle charging piles in a selected area are taken as the target. Based on a first clustering, a charging profile vector is formed for 4181 charging piles, which is combined with the rated charging power of the charging piles to generate a 7-dimensional vector.

[0271] PCA dimensionality reduction was employed, selecting dimensions that influenced the clustering set by more than 95%. The results showed that the dimensionality was reduced to 4 dimensions, significantly reducing the computational load. SOM clustering was then used, resulting in the secondary clustering of two classes of charging piles without considering location, as shown in Table 2.

[0272] Table 2

[0273]

[0274] Further analysis of the schedulability of EVA1 is needed, such as... Figure 5 and Figure 6 ,as well as Figure 7 and Figure 8 As shown, Figure 5 Curve a5 in the figure represents the rechargeable capacity, and curve b5 represents the dischargeable capacity. Figure 6 Curve a6 in the figure represents the rechargeable power, and curve b6 represents the dischargeable power. Figure 7 Curve a7 in the figure represents the rechargeable capacity, and curve b7 represents the dischargeable capacity. Figure 8 Curve a8 represents the rechargeable power, and curve b8 represents the dischargeable power. It can be seen that EVA1 exhibits a bimodal characteristic in both its schedulable capacity and power under peak shaving and frequency regulation scenarios. Furthermore, comparing the rechargeable and dischargeable capacities reveals that EVA1's rechargeable capacity peaks around 5:00 PM, then rapidly decreases, while its dischargeable capacity remains stable from 5:00 PM until the early morning. This indicates that a large number of electric vehicles connect to the power grid in the evening and charge rapidly until after midnight. This suggests that EVA1 has significant potential for adjusting charging power at night, and that EVA1's… ftr The value of 0.68 also indicates its great scheduling potential.

[0275] Quadratic clustering with location:

[0276] The ancillary service voltage regulation scenario refers to electric vehicles participating in distribution network voltage regulation, rather than transmission network voltage regulation within a selected area. Therefore, the region A with the most charging records in the selected area is selected as the scenario for electric vehicles participating in distribution network voltage regulation. In the voltage regulation scenario, considering the location variable, data belonging to a portion of region A from the results of a first clustering are selected. Based on this, a charging profile vector is formed for the 2122 charging piles in region A, and combined with the longitude, latitude, and rated charging power of the charging piles to generate a 6+3=9 dimensional vector.

[0277] PCA dimensionality reduction was employed, selecting dimensions that accounted for more than 95% of the clustering outcome. The results showed that the dimensionality was reduced to 5, significantly decreasing the computational load of clustering.

[0278] SOM clustering was adopted, and the final secondary clustering results including the location were shown in Table 3, which resulted in 6 classes; that is, 2122 charging piles were clustered into 6 EVAs.

[0279] Table 3

[0280]

[0281] Further analysis of the schedulability of EVA1 is needed, such as... Figure 9 and Figure 10 As shown; Figure 9 Curve a9 in the figure represents the rechargeable capacity, and curve b9 represents the dischargeable capacity. Figure 10 Curve a10 in the figure represents the rechargeable power, and curve b10 represents the dischargeable power.

[0282] As can be seen, EVA1 has more available resources at night, because EVA1's charging stations mainly operate at night. SCC, on the other hand, enters its lowest point before 6 a.m., while SDC only enters its lowest point around 9 a.m., indicating that a large number of EVs are fully charged but have not yet left the charging station at this time.

Claims

1. A method for modeling the schedulable capacity of electric vehicle clusters based on quadratic clustering, characterized by: First, based on historical charging operation data of charging piles, the schedulable capacity of individual electric vehicles during a single charging process is modeled to obtain four indicators describing schedulable capacity: rechargeable capacity, rechargeable power, discharging capacity, and discharging power. Second, the charging operation data is clustered into several charging profiles using the K-means method. Then, based on the scenario of power system ancillary services, the original parameters for secondary clustering are selected and combined with the results of primary clustering. A combination of principal component analysis and self-organizing mapping is used to further cluster the charging piles into several charging pile aggregates. Finally, the aggregated schedulable capacity of each aggregate is obtained. The method for modeling the schedulable capacity of electric vehicle clusters includes the following steps: Step 1: Model the schedulable capacity for a single charging process based on individual electric vehicle charging operation data. This data includes: charging start time, charging end time, total charging capacity, rated charging power of the charging pile, and rated discharging power of the charging pile. The schedulable capacity for a single charging process refers to the upper and lower limits of the energy and power exchanged between an individual electric vehicle and the power grid, provided that the electric vehicle user's energy demand is met. The model uses rechargeable capacity... SCC Rechargeable power SCP Discharge capacity SDC and discharge power SDP Four metrics are used to describe schedulable capacity; Step 2, Selection of clustering parameters and data normalization: Four parameters are selected for each clustering operation, namely the proportion of idle time. ftr d , as well as charging start time, charging end time and total charging capacity obtained by reading historical data; Step 3: First clustering of charging behavior based on k-means algorithm; Step 4: Data preparation for secondary clustering: The object of secondary clustering is the charging pile, and the proportion of each type of charging profile in the charging pile is called the charging profile vector; according to the scenario of electric vehicles participating in auxiliary services, the corresponding selection parameters are set and the selection parameters are added to the end of the charging profile vector; Step 5: Perform dimensionality reduction based on principal component analysis to obtain the dimensionality-reduced charging pile parameter vector; Step 6: Secondary clustering based on self-organizing map neural network: After secondary clustering through self-organizing map neural network (SOM), charging pile aggregates are formed; Step 7: Obtain the schedulable capacity aggregation model for each aggregate, and complete the schedulable capacity modeling of the aggregate.

2. The method for modeling the schedulable capacity of electric vehicle clusters based on quadratic clustering according to claim 1, characterized in that: In step 1: the rechargeable capacity SCC Characterized by equation (1): （1）； In formula (1): d The number representing the charging record. d =1,…, D , D This represents the total number of charging records. For charging efficiency; SCC d,t It is numbered d Charging records in t The rechargeable capacity at any given time. P c Rated charging power; t s For scheduling time intervals, t d,0 For the number d The charging record shows the start time of charging; E d,c It is numbered d The total amount of electricity charged is recorded in the charging log. E d,t It is numbered d Charging records in t The charge at time t is calculated using equation (2): （2）； The rechargeable power SCP As represented by equation (3): （3）； In formula (3): SCP d,t It is numbered d Charging records in t The rechargeable power at any given time; Dischargeable capacity SDC As represented by equation (4): （4）； In equation (4): SDC d,t It is numbered d Charging records in t Dischargeable capacity at any given time; t d,end It is numbered d The charging record shows the end time of charging. The dischargeable power SDP Characterized by equation (5): （5）； In formula (5): SDP d,t It is numbered d Charging records in t Dischargeable power at any given time P d Rated discharge power, For discharge efficiency; In step 2: the percentage of idle time ftr d Characterized by equation (6): （6）； The percentage of idle time ftr d This refers to the proportion of idle time to total charging time, with a value between 0 and 1; therefore, the parameter vector for a single clustering is... Characterized by equation (7): （7）； The four parameters selected for the first clustering are normalized according to equation (8): （8）； In equation (8): It is numbered d The normalized parameter vector of the charging record; The vector of minimum parameter values. The vector of maximum parameter values; The first clustering in step 3 is performed as follows: Step 3.1: Initialize the number of clusters K The value is 2, which sets the maximum number of clusters. K max and maximum number of iterations iter max ; Step 3.2: Based on the number of clusters K The value is randomly selected. K The first data point is used as the initial cluster center, and the initial iteration number iter is set to 1. Step 3.3: Calculate the distance between each data object and the cluster center according to formula (9), and group the data with the nearest cluster center into one class: （9）； In equation (9): It is the distance between vectors a and b; For vector a, the first... i One dimension, b i For vector b, the first i One dimension, I Let a be the total dimension of vectors a and b; Step 3.4: Based on the classification results of Step 3.3, calculate the result according to formula (10). k Class center coordinates R ( k This updates the center of each category. （10）； In formula (10): k The number representing each category, k= 1,…, K ; by j k Characterizing the first k The parameter vector number of the class, N k For the first k The number of parameter vectors of the class. j k = 1,…, N K ; For the first j k A parameter vector; Step 3.5: Increment the iteration count `iter` by 1. If the iteration count `iter` after incrementing by 1 is less than `iter`... max If yes, return to step 3.3; otherwise, proceed to step 3.

6. Step 3.6: Calculate the number of clusters according to formula (11). K Davies-Bouldin index value at time DBI ( K ): （11）； In formula (11): h Characterization needs and the first k The class number of other classes that calculate distance; For the first k The mean distance between data objects in a class and the cluster centers; For the first h The mean distance between data objects in a class and the cluster centers; For the first h Class and First k Distance between cluster centers; Step 3.7, K The value of is increased by 1. If the value after adding 1 is... K Assignment greater than K max If so, return to step 3.2; otherwise, select the one with the smallest DBI value. K Output the corresponding clustering results. Step 3 ends, completing one clustering cycle. Thus, all charging behaviors are clustered into [the following categories]. K This type, referred to as a charging portrait, has K A charging image; In step 4: the charging profile vector is represented by equation (12): （12）； In formula (12): s The number representing the charging station is used to identify the charging station. n S Represents the total number of charging stations. s =1,…, n S ; For charging piles s Charging image vector; For charging piles s The k The number of charging-related images; The selected parameters are added to the tail of the charging profile vector to form a charging pile parameter vector with multidimensional parameters, as represented by equation (13). : （13）； In formula (13): M 0 The dimension of the parameter vector representing the charging pile; by m 0 The dimension number representing the parameter vector of the charging pile. m 0 =1,…, M 0 ; Charging pile parameter vector The m 0 One dimension; total S A matrix formed by the parameter vectors of each charging pile As the raw data for secondary clustering; The matrix Characterized by equation (14): （14）； In step 5, the dimensionality-reduced charging pile parameter vector is obtained according to the following process: Step 5.1: Calculate the matrix The covariance matrix; Step 5.2: Calculate the eigenvalues ​​of the covariance matrix. and the corresponding feature vector ; Step 5.3: Sort the eigenvalues ​​from largest to smallest, and select the eigenvectors corresponding to the eigenvalues ​​whose sum accounts for more than 95% of the total eigenvalues, and merge them into a dimensionality-reduced matrix. ,by m The column number of the dimension-reduced matrix is ​​denoted as . The total number of columns in the dimension-reduced matrix is ​​denoted as . M ; The dimensionality reduction matrix Characterized by equation (15): （15）； In equation (15), This is the dimensionality-reduced parameter vector of the charging pile. In step 6: after secondary clustering by the self-organizing map neural network (SOM), the input dimensionality reduction matrix is... In S vectors Clustered as L Each category forms L A collection of charging stations; In step 7, the L The schedulable capacity of each charging pile aggregate is the sum of the schedulable capacities of all charging records in that aggregate, as represented by equation (16): （16）； In formula (16): l The number representing the charging pile assembly. l= 1,…, L ; N l Charging pile aggregate l The number of charging records in the middle; SCC l,t The time t is numbered as l The charging capacity of the charging pile aggregate; SCP l,t The time t is numbered as l The charging power of the charging pile aggregate; SDC l,t The time t is numbered as l The discharge capacity of the charging pile aggregate; SDP l,t The time t is numbered as l The charging pile aggregate can discharge power.

3. The method for modeling the schedulable capacity of electric vehicle clusters based on quadratic clustering according to claim 2, characterized in that: Step 6 involves secondary clustering as follows: The input layer of the self-organizing map neural network (SOM) is... The output layer consists of neurons arranged in two dimensions; The neuron is related to the dimensionality reduction matrix. Number of columns M Vectors of the same length This is represented by equation (17): （17）； In formula (17): j The numbering that represents neurons, in order to J Characterizes the number of neurons; For neurons j The m Each weight corresponds to a dimension reduction matrix. The m List; Step 6.1, Input matrix The number of input SOM neurons L Input the maximum number of iterations for the second-order clustering. ti max Initialize all neurons Initialize the number of quadratic clustering iterations. ti The value is 1; Step 6.2: Normalize the matrix using equation (8). vectors in ; Step 6.3: Randomly select one The distance between the neuron and all neuron vectors is calculated using equation (9), and the neuron vector with the smallest distance is selected as the winning neuron. ; Step 6.4: Target the winning neuron The weights of neurons adjacent to the winning neuron are updated according to equation (18): （18）； In equation (18): For the first ti The vector of the neuron at the next iteration; For the first ti The neuron's vector at +1 iteration; For the first ti The learning rate at the next iteration decreases as the number of iterations increases; For neurons and neurons The neighborhood function is characterized by equation (19): （19）； In equation (19): Z j For neurons j The coordinates; Z c For neurons c The coordinates; For the first ti In the next iteration, the neighborhood radius decreases as the number of iterations increases; Step 6.5, ti The value is incremented by 1, and it is checked whether the result after the increment is greater than 1. ti max ; If not greater than ti max If the result is positive, return to step 6.3; otherwise, end the secondary clustering process and complete the secondary clustering process based on the SOM method.

4. The method for modeling the schedulable capacity of electric vehicle clusters based on quadratic clustering according to claim 1, characterized in that: In step 4, setting the corresponding selection parameters according to the scenario of electric vehicles participating in auxiliary services means: if it is used for voltage regulation, the corresponding selection parameters are: longitude, latitude and rated charging power of the charging pile; if it is used for peak shaving and frequency regulation, the corresponding selection parameter is: rated charging power.

Images