A method for dividing distributed photovoltaic clusters in regional power distribution networks

Abstract

This invention belongs to the field of photovoltaic power generation control technology and discloses a method for partitioning distributed photovoltaic clusters in a regional distribution network. It calculates the electrical distance between nodes based on a frequency-active power sensitivity matrix and obtains the electrical distance matrix. An optimized initial centroid is obtained using the PSO algorithm. Based on the initial centroid, the K-means algorithm is applied to perform cluster analysis on the nodes of the distribution network, completing the cluster partitioning of energy storage nodes. Using energy storage nodes as centroids, the remaining photovoltaic nodes without energy storage and load nodes are further partitioned into clusters. A comprehensive performance index is obtained by weighting three indicators: active power balance, energy storage balance, and modularity. The partitioning scheme with the highest comprehensive performance index is considered the optimal cluster partitioning. This invention uses the energy storage area as the center to partition distribution areas containing distributed photovoltaics into clusters, providing necessary inertia and frequency support for the power grid.

Description

Technical Field

[0001] This invention belongs to the field of photovoltaic power generation control technology and relates to a method for dividing distributed photovoltaic clusters in a regional power distribution network. Background Technology

[0002] With the continuous development of distributed photovoltaic (PV) power, distribution areas with a high proportion of distributed PV in the power grid generally choose to configure distributed energy storage. The integration of distributed energy storage in these areas increases their renewable energy absorption capacity, while also enabling rapid adjustment of system inertia and frequency, improving system power flow, and reducing grid losses. However, large-scale application of distributed PV also presents some technical challenges, such as the need to construct a distribution network-side energy management system, and the high requirements for secondary equipment and communication systems.

[0003] When the penetration rate of massive distributed photovoltaic (PV) power in regional distribution networks reaches a certain proportion and is widely integrated, the distributed power sources and their associated energy storage within the distribution areas need to provide more support to the grid, including inertia and frequency support, and voltage support. Simultaneously, to facilitate the dispatch and management of massive distributed power sources by the distribution network, distribution areas containing distributed PV power are clustered around energy storage within the distribution network. This aims to achieve a balance between the grid, power sources, loads, and storage within the clusters, and to provide the necessary inertia and frequency support to the grid. Summary of the Invention

[0004] To improve inertia-frequency support capability, this invention provides a method for dividing distributed photovoltaic clusters in regional power distribution networks.

[0005] The technical solution adopted in this invention is: a method for dividing distributed photovoltaic clusters in a regional distribution network, comprising the following processes:

[0006] Step 1: Calculate the electrical distance between nodes based on the frequency-active power sensitivity matrix, and obtain the electrical distance matrix;

[0007] Step 2: Obtain the optimized initial centroids using the PSO algorithm. Based on the initial centroids, apply the K-means algorithm to perform cluster analysis on the nodes of the distribution network and divide the energy storage nodes into clusters.

[0008] Step 3: Use the energy storage node as the centroid to divide the remaining photovoltaic nodes and load nodes without energy storage into clusters;

[0009] Step 4: Weighted calculations are performed using three indicators: active power balance, energy storage balance, and modularity, to obtain a comprehensive performance index. The comprehensive performance index is then used to evaluate the cluster partitioning results.

[0010] Step 5: Repeat steps 2-4 to complete the traversal of different numbers of cluster partitions; the partition scheme with the highest comprehensive performance index is taken as the optimal cluster partition.

[0011] Further optimization involves defining the distance between two nodes in step one based on the frequency-active power sensitivity matrix:

[0012]

[0013] In the formula, S δP Let be the frequency-active power sensitivity matrix between node j and node i; It is the largest element in the j-th column of the frequency-active sensitivity matrix between node j and node i; d ij Let j be the distance between node j and node i;

[0014] The electrical distance between node i and node j is defined using Euclidean distance:

[0015]

[0016] In the formula, d i1 ,d i2 …d in Let represent the distances between node i and nodes 1, 2, ..., n, respectively; d j1 ,d j2 …d jn Let represent the distances between node j and nodes 1, 2, ..., n, respectively, where n is the number of nodes;

[0017] The edge weight A connecting node i and node j ij for:

[0018]

[0019] In the formula: e is the electrical distance matrix composed of the electrical distances between any two nodes in the distribution network.

[0020] Further optimization occurs in step two, where the PSO algorithm generates z particles based on z energy storage nodes, assigns an initial position and velocity to each particle, and then begins iteration. While the particles continuously update their velocity and position, the individual extreme value P of each particle is recorded. best and the global extremum G of the population best The particle's velocity and position updates are influenced by two extreme values, and the optimal solution is sought through continuous iteration. The formula is:

[0021]

[0022]

[0023] In the formula: k is the number of iterations; V represents the position of node i in the k-th iteration; i kLet ω be the velocity of node i in the k-th iteration; ω be the inertia weight; c1 and c2 be the first and second learning factors, respectively; and r1 and r2 be parameters randomly generated between 0 and 1.

[0024] Based on the PSO algorithm to optimize the K-means clustering algorithm, the bias function F of the particles is defined as:

[0025]

[0026] In the formula: K is the number of clusters; a i C is the data vector for node i; q k is the centroid of cluster q; q d is a subset of cluster q; d is the distance from the node to the centroid.

[0027] Further optimization is achieved in step two, where modularity is used as the fitness function for particle optimization, and the PSO algorithm is applied to optimize and improve the K-means clustering algorithm to divide the energy storage clusters.

[0028] Further optimization, the specific process of step two is as follows:

[0029] S11: Input the node parameters of the distribution network and the PSO algorithm parameters;

[0030] S12: Initialize the particle's velocity and position based on the electrical distance matrix between nodes;

[0031] S13: Calculate the cluster to which each node belongs, select the node with the smallest total electrical distance to the other energy storage nodes in the cluster as the centroid of the new cluster, re-divide the cluster, and calculate the fitness and extreme value of the particles.

[0032] S14: Based on the extreme values ​​of all particles, update the local optimal solution, the global optimal solution, and the position corresponding to the optimal solution;

[0033] S15: Recalculate the particle's velocity, and then determine the particle's position using the formula relating position and velocity;

[0034] S16: Determine whether the iteration termination condition is met. If yes, obtain the position of the optimal particle; otherwise, continue iterating. The obtained optimal particle is the initial centroid.

[0035] S17: Based on the optimized initial centroids obtained from PSO, the K-means algorithm is applied to cluster the energy storage nodes, thus completing the cluster partitioning of the energy storage nodes.

[0036] Further optimization, the specific process of step three is as follows:

[0037] S21: Among all n nodes, there are z energy storage nodes, and the set of energy storage nodes is:

[0038] B={ξ s}

[0039] B represents the set of all energy storage nodes, ξ s Let s represent the s-th energy storage node, where s = 1, 2, ..., z;

[0040] S22: Based on the energy storage nodes, determine the set of remaining nodes without energy storage as follows:

[0041] H={ξ s′}

[0042] H represents the set of remaining nodes without energy storage, ξ s′ This represents the s′-th node without energy storage, where s′ = 1, 2, ..., nz;

[0043] Calculate the electrical distance between nodes without energy storage and nodes with energy storage respectively:

[0044] D(ξ s ,ξ s′ )=||ξ s -ξ s′ ||2

[0045] D(ξ s ,ξ s′ ) represents the electrical distance from the s′-th node without energy storage to the s-th node with energy storage;

[0046] S23: The electrical distance matrix D of the nodes without energy storage is formed by the electrical distances from the nodes without energy storage to the energy storage nodes. The remaining nodes without energy storage are then classified into the clusters containing the nearest energy storage nodes. The final clustering result is represented by a set as follows:

[0047] C = {C x}

[0048] Where C represents the set of all clusters, i.e., the final cluster partitioning result; C x This represents the x-th cluster, which includes energy storage nodes and nodes without energy storage. After partitioning, the number of clusters remains N. c where x = 1, 2, ..., N c ;

[0049] S24: Centroid Calculation Method: The x-th Cluster C x There are m nodes in total, of which g are energy storage nodes and mg are non-energy storage nodes. Calculate the sum D of the electrical distances between the r-th energy storage node and all other nodes in the cluster. Tr :

[0050]

[0051] ξ r Let ξ represent the r-th energy storage node. r′This represents the r′-th node without energy storage, where r ≤ g; r′ = 1, 2, ..., mg;

[0052] Select the node whose sum of electrical distances to other nodes is the minimum, D. Tk =min(D Tr ) node ξ k To determine the new centroid, repeat steps S22 and S23 until the iteration ends.

[0053] Further optimization involves calculating the energy storage balance as follows:

[0054] The x-th cluster C x There are m nodes in total, of which g nodes are configured with energy storage systems. The x-th cluster C x The total discharge power of the energy storage devices in the g energy storage nodes is:

[0055]

[0056] in, This represents the rated discharge power of the energy storage device on the r-th energy storage node in the x-th cluster;

[0057] The x-th cluster C x The net power for time period h is:

[0058]

[0059] Among them, P r_load,h P r_pv,h Represent the load or instantaneous power of the photovoltaic system at the r-th node during the h-th time period, respectively.

[0060] The x-th cluster C x The average net power is:

[0061]

[0062] T represents the duration of the selected typical scenario;

[0063] Obtain the energy storage configuration coefficient y in the x-th cluster x ;

[0064]

[0065]

[0066]

[0067] Where: N c This indicates the number of cluster partitions. Based on the number of cluster partitions, Let S be the predicted value of the overall energy storage configuration coefficient, and S be the standard deviation of the overall energy storage configuration of the distribution network. This indicates the energy storage balance of the energy storage configuration.

[0068] Further optimization yields the following method for calculating active power balance:

[0069]

[0070]

[0071] Where: N c C represents the number of cluster partitions; C represents the set of all clusters. Represents the x-th cluster C x The active power balance; P x_TTL,h Represents the x-th cluster C x Net power in time period h; T is the duration of the selected typical scenario; This represents the active power balance when all clusters are viewed as a whole.

[0072] Further optimization, modularity of all clusters The definition of is:

[0073]

[0074]

[0075]

[0076] Of all n nodes, A ij This represents the edge weight connecting node i and node j, where k is 1 when node i and node j are directly connected and 0 when they are not connected. i k represents the sum of the weights of all edges connected to node i. j δ represents the sum of the weights of all edges connected to node j; W represents the sum of the weights of the entire network; δ is a 0-1 matrix, where δ(i,j) = 1 if node i and node j are in the same cluster, and δ(i,j) = 0 if they are not in the same cluster.

[0077] Further optimization yields the following comprehensive performance index ρ:

[0078]

[0079] In the formula: w1, w2 and w3 are the weights of modularity, active power balance and energy storage balance, respectively; the weights of modularity, active power balance and energy storage balance are determined by the analytic hierarchy process.

[0080] This invention addresses the electrical distance between nodes based on sensitivity definition. Compared to the commonly used impedance method for calculating electrical distance, the sensitivity method better reflects the dynamic characteristics of the network. The PSO algorithm is used to obtain optimized initial cluster centroids, avoiding the pitfalls of the K-means algorithm which is prone to getting trapped in local optima, thus improving the globality and accuracy of the clustering process. Using energy storage nodes as centroids to partition the remaining non-storage photovoltaic nodes and load nodes into clusters increases the balance between the grid, source, load, and storage within the cluster, improves inertia-frequency support, and increases energy storage utilization. Evaluating the cluster partitioning results using energy storage balance, active power balance, and modularity indices provides a more comprehensive consideration of the requirements for cluster network configuration and dynamic response, leading to the optimal partitioning results.

[0081] The proposed method for dividing distributed photovoltaic (PV) clusters in regional distribution networks facilitates the scheduling and management of massive distributed power sources in the distribution network. It divides the distribution network into clusters centered on the energy storage of the distribution area, aiming to achieve a balance between the grid, power source, load, and storage within the cluster, and to provide the grid with the necessary inertia and frequency support.

[0082] This invention considers that distribution areas with a high proportion of distributed photovoltaic power in the distribution network may choose to configure distributed energy storage. The nodes configured with energy storage are first clustered to ensure that each cluster has a certain inertia and frequency support capability for the power grid.

[0083] This invention is versatile and applicable to distribution networks with varying proportions of distributed photovoltaic power.

[0084] This invention provides a practical and effective reference for the method of dividing distributed photovoltaic clusters in regional power distribution networks. Attached Figure Description

[0085] Figure 1 This is a flowchart of the overall scheme of the present invention.

[0086] Figure 2 This is a schematic diagram of the cluster partitioning of nodes. Detailed Implementation

[0087] The present invention will be further explained in detail below with reference to the accompanying drawings and embodiments.

[0088] like Figure 1 and Figure 2 As shown, a method for partitioning distributed photovoltaic clusters in a regional power distribution network includes the following processes:

[0089] Step 1: Calculate the electrical distance between nodes based on the frequency-active power sensitivity matrix, and obtain the electrical distance matrix;

[0090] Step 2: Obtain the optimized initial centroids using the PSO algorithm. Based on the initial centroids, apply the K-means algorithm to perform cluster analysis on the nodes of the distribution network and divide the energy storage nodes into clusters.

[0091] Step 3: Use the energy storage node as the centroid to divide the remaining photovoltaic nodes and load nodes without energy storage into clusters;

[0092] Step 4: Weighted calculations are performed using three indicators: active power balance, energy storage balance, and modularity, to obtain a comprehensive performance index. The comprehensive performance index is then used to evaluate the cluster partitioning results.

[0093] Step 5: Repeat steps 2-4 to complete the traversal of different numbers of cluster partitions; the partition scheme with the highest comprehensive performance index is taken as the optimal cluster partition. When the number of clusters is different, it will affect the clustering results. By comparing the differences in comprehensive performance index when the number of clusters is different, the optimal cluster partition can be obtained.

[0094] In step one of this embodiment, the principle and process of calculating the electrical distance between nodes based on the frequency-active power sensitivity matrix and obtaining the electrical distance matrix are as follows;

[0095] In power flow calculations, the polar coordinate form of the power flow equations is:

[0096]

[0097] Where: ΔP i Let P be the change in active power at node i. i Let ΔQ be the active power at node i. i Let Q be the change in reactive power at node i. i Let δ be the reactive power of node i. j The angle of attack at node j; Δδ i U represents the change in the work angle of node i; j U is the voltage at node j; i The voltage at node i; ΔU i Let be the voltage change at node i.

[0098] The elements of the Jacobian matrix represent the frequency-power sensitivity relationship of any injected power node. In the grid-connected operation of distributed photovoltaic (PV) power generation in distribution networks, the current grid connection for accepting new energy sources often adopts a power factor of 1. Therefore, the impact of active power injected by distributed PV on node frequencies is a major influencing factor in power system analysis. The power flow equations can be expressed in Jacobian matrix form as follows:

[0099]

[0100] The Jacobian matrix can be represented by a block matrix as follows:

[0101]

[0102] In the formula, |U|=ΔU j / ΔU i J is the Jacobian matrix, J Pδ J is a block matrix representing the partial derivatives of active power with respect to the power angle. Qδ J is a block matrix representing the partial derivative of reactive power with respect to the power angle. PV J is a block matrix representing the partial derivative of active power with respect to voltage. QV Let be the block matrix of the partial derivative of reactive power with respect to voltage, where ΔP is the change in active power and ΔQ is the change in reactive power.

[0103] For a distribution system with massive distributed photovoltaic (PV) grid connection, the study focuses on the frequency change of grid-connected nodes after the injection of active power from PV power generation. The injected active power is used as the control variable, and the grid-connected node frequency is used as the controlled variable. The frequency-active power sensitivity matrix needs to be obtained through quantitative calculation of the active and reactive power of feeder branches based on the node frequency change after power flow calculation. The Jacobian matrix is ​​obtained through iterative power flow calculation using Newton-Raphson. Since the power angle has a high coupling degree with reactive power but a low coupling degree with active power, setting ΔQ = 0 yields...

[0104]

[0105] Δδ=(J Pδ -J PV J QV -1 J Qδ ) -1 ΔP

[0106] The obtained frequency-active sensitivity matrix is:

[0107] S δP =(J Pδ -J PV J QV -1 J Qδ ) -1

[0108] In the formula: Δδ is the change in work angle; J QV -1 S is the inverse matrix of the block matrix of the partial derivatives of reactive power with respect to voltage; δP This is the frequency-active power sensitivity matrix;

[0109] The frequency-active power sensitivity matrix describes the relationship between changes in injected active power and changes in node frequency; its value indicates the close relationship between the active power frequencies of the nodes. Based on the frequency-active power sensitivity matrix, the distance between two nodes is defined as follows:

[0110]

[0111] In the formula, S δP Let be the frequency-active power sensitivity matrix between node j and node i; It is the largest element in the j-th column of the frequency-active sensitivity matrix between node j and node i; d ij Let be the distance between node j and node i, representing the ratio of the change in frequency of node j to that of node i when the active power of node j changes in the frequency-active power sensitivity matrix. The smaller the ratio, the greater the influence of node j on node i, i.e., the closer the distance.

[0112] In practice, the relationships between nodes in a distribution network are related to all nodes in the network. Assuming there are n nodes in the distribution network, the electrical distance between node i and node j is defined using Euclidean distance:

[0113]

[0114] In the formula, d i1 ,d i2 …d in Let represent the distances between node i and nodes 1, 2, ..., n, respectively; d j1 ,d j2 …d jn Let represent the distances between node j and nodes 1, 2, ..., n, respectively.

[0115] Therefore, the edge weight A connecting node i and node j is... ij for:

[0116]

[0117] In the formula: e is the electrical distance matrix composed of the electrical distances between any two nodes in the distribution network.

[0118] In distribution networks, energy storage devices can store peak electricity generated by photovoltaics to offset peak loads, reduce curtailment rates, and increase asset utilization. Distributed energy storage in distribution areas also has the characteristics of rapidly adjusting power system inertia and frequency, improving system power flow, and reducing network losses, especially when distributed power sources account for a certain proportion of the distribution network capacity. Therefore, based on the role of energy storage in inertia and frequency support, nodes are divided into two categories according to whether they have energy storage devices: energy storage nodes (nodes containing distributed photovoltaics and energy storage) and nodes without energy storage (nodes containing distributed photovoltaics and load nodes, with a small proportion of photovoltaics). Energy storage nodes are then clustered using a clustering method.

[0119] The K-means algorithm is simple to implement and converges quickly, but if an inappropriate initial cluster centroid is chosen, it can lead to getting trapped in local optima. In this embodiment, step two uses an improved K-means algorithm. First, the initial centroids are optimized using the Particle Swarm Optimization (PSO) algorithm. Based on the optimized initial centroids, clusters are created, and the K-means algorithm is applied to cluster the nodes of the distribution network and to divide the energy storage nodes into clusters, thus improving the accuracy of the traditional K-means algorithm.

[0120] The PSO algorithm first generates z particles from z energy storage nodes, assigning each particle an initial position and velocity, and then begins iterative processing. While the particles continuously update their velocities and positions, the individual extreme value P of each particle is recorded. best and the global extremum G of the population best On the other hand, the particle's velocity and position updates are influenced by two extreme values. The optimal solution is found through this iterative process, as shown in the formula:

[0121]

[0122]

[0123] In the formula: k is the number of iterations; V represents the position of node i in the k-th iteration; i k Let ω be the velocity of node i in the k-th iteration; ω be the inertia weight; c1 and c2 be the first and second learning factors, respectively; and r1 and r2 be parameters randomly generated between 0 and 1.

[0124] Based on the PSO algorithm to optimize the K-means clustering algorithm, the bias function F of the particles is defined as:

[0125]

[0126] In the formula: K is the number of clusters; a i C is the data vector for node i; q k is the centroid of cluster q; q d is a subset of cluster q; d is the distance from a node to its centroid. Modularity is used as the fitness function for particle optimization, and the PSO algorithm is applied to optimize and improve the K-means clustering algorithm for energy storage cluster partitioning.

[0127] The optimized initial cluster centroids are obtained through the PSO algorithm. Based on the initial centroids, the K-means algorithm is applied to perform node clustering analysis on the distribution network. The specific process of dividing the network into clusters is as follows:

[0128] S11: Input the node parameters of the distribution network and the PSO algorithm parameters.

[0129] S12: Initialize the particle's velocity and position based on the electrical distance matrix between nodes.

[0130] S13: Calculate the cluster to which each node belongs, select the node with the smallest total electrical distance to the other energy storage nodes in the cluster as the centroid of the new cluster, re-divide the cluster, and calculate the fitness and extreme values ​​of the particles.

[0131] S14: Based on the extreme values ​​of all particles, update the local optimal solution, the global optimal solution, and the position corresponding to the optimal solution.

[0132] S15: Recalculate the particle's velocity (it cannot be less than the minimum particle velocity V). min And it cannot exceed the maximum velocity V of the particle. max Then, the position of the particle is determined by the formula relating position and velocity (the position cannot exceed the upper and lower limits of the particle's position).

[0133] S16: Determine whether the iteration termination condition is met. If so, obtain the position of the optimal particle; otherwise, continue iterating. The obtained optimal particle is the initial centroid.

[0134] S17: Based on the optimized initial centroids obtained from PSO, the K-means algorithm is applied to cluster the energy storage nodes, completing the cluster partitioning of the energy storage nodes. The cluster partitioning results of the energy storage nodes are represented by the following set:

[0135] B = {B x}

[0136] In the formula, B represents the set of all energy storage nodes. x Let x represent the x-th energy storage cluster, where x = 1, 2, ..., N. c N c The number of partitions for the cluster.

[0137] In step three of this embodiment, the specific process of dividing the remaining nodes without energy storage into clusters using the energy storage nodes as centroids is as follows:

[0138] S21: Among all n nodes, there are z energy storage nodes, and the set of energy storage nodes is:

[0139] B={ξ s}

[0140] B represents the set of all energy storage nodes, ξ s Let s represent the s-th energy storage node, where s = 1, 2, ..., z;

[0141] S22: Based on the energy storage nodes, the set of remaining nodes without energy storage can be determined as follows:

[0142] H={ξ s′}

[0143] H represents the set of remaining nodes without energy storage, ξ s′ This represents the s′-th node without energy storage, where s′ = 1, 2, ..., nz;

[0144] Calculate the electrical distance between nodes without energy storage and nodes with energy storage respectively:

[0145] D(ξ s ,ξ s′ )=||ξ s -ξ s′ ||2

[0146] D(ξ s ,ξ s′ ) represents the sth ′ The electrical distance from the s-th node without energy storage to the s-th energy storage node;

[0147] S23: The electrical distance matrix D of the nodes without energy storage is formed by the electrical distances from the nodes without energy storage to the energy storage nodes. The remaining nodes without energy storage are then classified into the clusters containing the nearest energy storage nodes. The final clustering result is represented by a set as follows:

[0148] C = {C x}

[0149] Where C represents the set of all clusters, i.e., the final cluster partitioning result; C x This represents the x-th cluster, which includes energy storage nodes and nodes without energy storage. After partitioning, the number of clusters remains N. c where x = 1, 2, ..., N c .

[0150] S24: Centroid Calculation Method:

[0151] Assume the x-th cluster C x There are m nodes in total, of which g are energy storage nodes and mg are non-energy storage nodes. Calculate the sum D of the electrical distances between the r-th energy storage node and all other nodes in the cluster. Tr :

[0152]

[0153] ξ r Let ξ represent the r-th energy storage node. r′ This represents the r′-th node without energy storage, where r ≤ g; r′ = 1, 2, ..., mg;

[0154] Select the node whose sum of electrical distances to other nodes is the minimum, D. Tk =min(D Tr ) node ξ kTo determine the new centroid, repeat steps S22 and S23 until the iteration ends.

[0155] This embodiment also evaluates the cluster partitioning results using three indicators: energy storage balance, active power balance, and modularity, to obtain the optimal cluster partitioning method.

[0156] (1) Energy storage balance

[0157] Assume the x-th cluster C x There are m nodes in total, of which g nodes are configured with energy storage systems (ESS). The energy storage of this cluster can be represented as follows:

[0158]

[0159] In the formula, P1 ESS P2 ESS , Let represent the rated power of the 1st, 2nd, and gth energy storage nodes in the xth cluster, respectively; the power of the energy storage converter during actual operation can be expressed as follows: (The original text appears to be incomplete and contains several grammatical errors. A more accurate translation would require the full context.)

[0160]

[0161]

[0162] In the formula: These represent the charging and discharging power of the r-th energy storage node in the x-th cluster during the h-th time period, respectively. These represent the charging and discharging reference powers of the r-th energy storage node in the x-th cluster during the h-th time period, respectively. These are the charging and discharging efficiencies of the energy storage system, respectively.

[0163] Considering the energy storage device's ability to support grid frequency, the power requirement for the energy storage device is as follows:

[0164]

[0165] In the formula: P represents the rated charging and discharging power of the energy storage device on the r-th energy storage node in the x-th cluster, respectively. r_load,h P r_pv,h These represent the load or instantaneous power of the photovoltaic system at the r-th node during the h-th time period, respectively.

[0166] Then the x-th cluster C x The total discharge power of the energy storage devices in the g energy storage nodes is:

[0167]

[0168] In reality, the load and photovoltaic power characteristics of all nodes in a cluster often exhibit the external characteristics of the load. For example, the x-th cluster C containing m nodes... x The net power for time period h is:

[0169]

[0170] The x-th cluster C x The average net power is:

[0171]

[0172] T represents the duration of the selected typical scenario;

[0173] Therefore, the energy storage configuration coefficient y in the x-th cluster can be obtained. x ;

[0174]

[0175]

[0176]

[0177] Where: N c This indicates the number of cluster partitions. Based on the number of cluster partitions, Let S be the predicted value of the overall energy storage configuration coefficient, and S be the standard deviation of the overall energy storage configuration of the distribution network. The energy storage balance is measured by the standard deviation rate of the energy storage configuration, which indicates the overall energy storage balance of the network. The higher the value, the higher the overall energy storage balance.

[0178] (2) Active power balance

[0179] In terms of grid-source-load-storage balance, to reduce active power transmission between clusters and maximize the cluster's self-absorption capacity, thereby reducing the curtailment rate, active power balance is used as an indicator for cluster classification. A high active power balance indicates a high degree of grid-source-load-storage matching within the cluster, which can effectively alleviate the uncertainty and volatility of photovoltaic output. The active power balance of the xth cluster is defined as follows:

[0180]

[0181]

[0182] Where: N c C represents the number of cluster partitions; C represents the set of all clusters. Indicates cluster C x The active power balance; P x_TTL,h Represents the x-th cluster C xNet power in time period h; T is the duration of the selected typical scenario; This represents the active power balance when all clusters are viewed as a whole.

[0183] (3) Modularity

[0184] Modularity, proposed by Mark Newman, is a method to measure the structural strength of a network community. Its value can be used to assess the quality of the network community partitioning results; a higher value indicates relatively tight connections between nodes within each community and relatively sparse connections between communities, while a lower value indicates the opposite. Distribution networks with massive distributed photovoltaic (PV) grids have a similar structure to network communities. Therefore, clustering nodes in the distribution network and structurally analyzing network communities share similar goals. Thus, modularity can be used to measure the reasonableness of the cluster partitioning results for distributed PV in the distribution network. The modularity of all clusters... The definition of is:

[0185]

[0186]

[0187]

[0188] Of all n nodes, A ij k represents the edge weight connecting node i and node j. The edge weight is 1 when node i and node j are directly connected, and 0 when they are not connected. The edge weight reflects the strength of the connection between the nodes. i k represents the sum of the weights of all edges connected to node i. j δ represents the sum of the weights of all edges connected to node j; W represents the sum of the weights of the entire network; δ is a 0-1 matrix, where δ(i,j) = 1 if node i and node j are in the same cluster, and δ(i,j) = 0 if they are not in the same cluster.

[0189] In summary, the three indicators set for evaluating the cluster partitioning results are as follows:

[0190] (1) Energy storage balance: It represents the relative magnitude of the maximum power that energy storage can provide and the maximum difference between the instantaneous power of the equivalent source-load, ensuring that each cluster has a certain inertia-frequency support capability during short periods of power balance exceeding or falling short.

[0191] (2) Active power balance: It reflects the grid-source-load-storage balance within the cluster, that is, to minimize the transmission of active power between clusters and maximize the local consumption of distributed photovoltaic energy.

[0192] (3) Modularity: This measures the degree of connection between the centroid and the nodes within the cluster. Both modularity and active power balance are no greater than 1. For a cluster, the higher the internal connectivity, the closer the modularity is to 1. Similarly, the smaller the net external power and the stronger the self-absorption capacity of the cluster, the closer the active power balance is to 1. Since the three indicators are of the same order of magnitude, the comprehensive performance index ρ is set as:

[0193]

[0194] In the formula: w1, w2 and w3 are the weights of modularity, active power balance and energy storage balance, respectively.

[0195] The Analytic Hierarchy Process (AHP) is a multi-objective comprehensive evaluation method, suitable for problems where the objective values ​​are difficult to quantify. Here, it is used to determine the weights of the three indicators that evaluate the merits of cluster partitioning results from different perspectives. The basic steps for determining the weights of each indicator are as follows:

[0196] (1) Use natural numbers between 1 and 9 as a scale to represent the relative importance between pairs of indicators.

[0197] Scale meaning 1 Both indicators are equally important. 3 One metric is slightly more important than another. 5 One metric is significantly more important than another. 7 One indicator is significantly more important than another. 9 One indicator is far more important than another. 2，4，6，8 The median of the two adjacent judgments above reciprocal If the scale of A to B is 3, then the scale of B to A is 1 / 3.

[0198] (2) Obtain a 3*3 matrix showing the pairwise relative importance of the three indicators.

[0199] Energy storage balance Active power balance Modularity Energy storage balance 1 Active power balance 1 Modularity 1

[0200] (3) Calculate the weight of each indicator.

[0201] Normalize each column of the above matrix to obtain the judgment matrix, then sum each row to obtain a 3*1 vector, and normalize it again. The eigenvector of the judgment matrix is ​​the weight vector of the three indicators.

[0202] (4) Perform a consistency check on the above results.

[0203] a. Calculate the maximum value of the eigenvalues ​​of the judgment matrix. max ;

[0204] b. Calculate the consistency index CR:

[0205]

[0206] In the formula, p is the number of indicators, which is taken as 3 here, and RI is the average random consistency, the value of which is related to the matrix order n. p Related. Generally, the larger the matrix order, the greater the probability of random deviations from consistency, as shown in the table below:

[0207]

[0208]

[0209] Looking up the table, we find that 0.58 is used here. Generally, if CR is less than 0.1, the judgment matrix can be considered to have passed the consistency test, and the weights of each indicator are finally determined.

[0210] The above description merely illustrates preferred embodiments of the present invention and is not intended to limit the invention in any other way. Any person skilled in the art may make modifications or alterations to the above-disclosed content to create equivalent embodiments. However, any simple modifications, equivalent changes, and alterations made to the above embodiments based on the technical essence of the present invention, without departing from the scope of the present invention, shall still fall within the protection scope of the present invention.

Claims

1. A method for dividing distributed photovoltaic clusters in a regional power distribution network, characterized in that, Includes the following processes: Step 1: Calculate the electrical distance between nodes based on the frequency-active power sensitivity matrix, and obtain the electrical distance matrix; Step 2: Obtain the optimized initial centroids using the PSO algorithm. Based on the initial centroids, apply the K-means algorithm to perform cluster analysis on the nodes of the distribution network and divide the energy storage nodes into clusters. Step 3: Use the energy storage node as the centroid to divide the remaining photovoltaic nodes and load nodes without energy storage into clusters; Step 4: Weighted calculations are performed using three indicators: active power balance, energy storage balance, and modularity, to obtain a comprehensive performance index. The comprehensive performance index is then used to evaluate the cluster partitioning results. Step 5: Repeat steps 2-4 to complete the traversal of different numbers of cluster partitions; the partition scheme with the highest comprehensive performance index is taken as the optimal cluster partition. The specific process of step three is as follows: S21: Among all n nodes, there are z energy storage nodes, and the set of energy storage nodes is: ； B represents the set of all energy storage nodes. Let s represent the s-th energy storage node, where s = 1, 2, ..., z; S22: Based on the energy storage nodes, determine the set of remaining nodes without energy storage as follows: ； H represents the set of remaining nodes without energy storage. Indicates the first A node without energy storage, ; Calculate the electrical distance between nodes without energy storage and nodes with energy storage respectively: ； Indicates the first The electrical distance from the s-th node without energy storage to the s-th energy storage node; S23: The electrical distance matrix D of the nodes without energy storage is formed by the electrical distances from the nodes without energy storage to the energy storage nodes. The remaining nodes without energy storage are then classified into the clusters containing the nearest energy storage nodes. The final clustering result is represented by a set as follows: ； Where C represents the set of all clusters, i.e., the final cluster partitioning result; C x This represents the x-th cluster, which includes energy storage nodes and nodes without energy storage. After partitioning, the number of clusters remains N. c where x = 1, 2, ..., N c ; S24: Centroid Calculation Method: The x-th Cluster C x There are m nodes in total, of which g are energy storage nodes and mg are non-energy storage nodes. Calculate the sum of the electrical distances D between the r-th energy storage node and all other nodes in the cluster. Tr : ； This represents the r-th energy storage node. Indicates the first A node without energy storage, ; ; Select the node whose sum of electrical distances to other nodes is the minimum, D. Tk =min(D Tr ) nodes To determine the new centroid, repeat steps S22 and S23 until the iteration ends.

2. The method for dividing regional distribution network distributed photovoltaic clusters according to claim 1, characterized in that, In step one, the distance between two nodes is defined based on the frequency-active power sensitivity matrix: ； In the formula, S δP This is the frequency-active power sensitivity matrix between node j and node i; It is the largest element in the j-th column of the frequency-active sensitivity matrix between node j and node i; d ij Let j be the distance between node j and node i; The electrical distance between node i and node j is defined using Euclidean distance: ； In the formula, d i1 , d i2 … d in Let represent the distances between node i and nodes 1, 2, ..., n, respectively; d j1 , d j2 … d jn Let represent the distances between node j and nodes 1, 2, ..., n, respectively, where n is the number of nodes; The edge weight A connecting node i and node j ij for: ； In the formula: e is the electrical distance matrix composed of the electrical distances between any two nodes in the distribution network.

3. The method for dividing regional distribution network distributed photovoltaic clusters according to claim 1, characterized in that, In step two, the PSO algorithm generates z particles based on z energy storage nodes, assigns an initial position and velocity to each particle, and then begins iterative processing. While the particles continuously update their velocities and positions, the algorithm records the individual extreme value P for each particle. best and the global extremum G of the population best The particle's velocity and position updates are influenced by two extreme values, and the optimal solution is sought through continuous iteration. The formula is: ； ； In the formula: k is the number of iterations; Let i be the position of node i in the k-th iteration; Let be the velocity of node i in the k-th iteration; Inertial weight; , These are the first and second learning factors, respectively. , The parameters are randomly generated between 0 and 1; Based on the PSO algorithm to optimize the K-means clustering algorithm, the bias function F of the particles is defined as: ； In the formula: K is the number of clusters; a i C is the data vector for node i; q k is the centroid of cluster q; q d is a subset of cluster q; d is the distance from the node to the centroid.

4. The method for dividing regional distribution network distributed photovoltaic clusters according to claim 3, characterized in that, In step two, modularity is used as the fitness function for particle optimization, and the PSO algorithm is applied to optimize and improve the K-means clustering algorithm to divide the energy storage cluster.

5. The method for dividing regional distribution network distributed photovoltaic clusters according to claim 1, characterized in that, The specific process of step two is as follows: S11: Input the node parameters of the distribution network and the PSO algorithm parameters; S12: Initialize the particle's velocity and position based on the electrical distance matrix between nodes; S13: Calculate the cluster to which each node belongs, select the node with the smallest total electrical distance to the other energy storage nodes in the cluster as the centroid of the new cluster, re-divide the cluster, and calculate the fitness and extreme value of the particles. S14: Based on the extreme values ​​of all particles, update the local optimal solution, the global optimal solution, and the position corresponding to the optimal solution; S15: Recalculate the particle's velocity, and then determine the particle's position using the formula relating position and velocity; S16: Determine whether the iteration termination condition is met. If yes, obtain the position of the optimal particle; otherwise, continue iterating. The obtained optimal particle is the initial centroid. S17: Based on the optimized initial centroids obtained from PSO, the K-means algorithm is applied to cluster the energy storage nodes, thus completing the cluster partitioning of the energy storage nodes.

6. The method for dividing distributed photovoltaic clusters in a regional power distribution network according to claim 1, characterized in that, The calculation process for energy storage balance is as follows: The x-th cluster C x There are m nodes in total, of which g nodes are configured with energy storage systems. The x-th cluster C x The total discharge power of the energy storage devices in the g energy storage nodes is: ； in, This represents the rated discharge power of the energy storage device on the r-th energy storage node in the x-th cluster; The x-th cluster C x The net power for time period h is: ； in, , Represent the load or instantaneous power of the photovoltaic system at the r-th node during the h-th time period, respectively. The x-th cluster C x The average net power is: ； T represents the duration of the selected typical scenario; Obtain the energy storage configuration coefficient in the x-th cluster. ; ； ； ； In the formula: This indicates the number of cluster partitions. Based on the number of cluster partitions, Let S be the predicted value of the overall energy storage configuration coefficient, and S be the standard deviation of the overall energy storage configuration of the distribution network. This indicates the energy storage balance of the energy storage configuration.

7. The method for dividing regional distribution network distributed photovoltaic clusters according to claim 6, characterized in that, active power... The balance is calculated as follows: ； ； In the formula: C represents the number of cluster partitions; C represents the set of all clusters. Represents the x-th cluster C x The active power balance; Represents the x-th cluster C x Net power in time period h; T is the duration of the selected typical scenario; This represents the active power balance when all clusters are viewed as a whole.

8. The method for dividing regional distribution network distributed photovoltaic clusters according to claim 7, characterized in that, Modularity of all clusters The definition of is: ； ； ； Of all n nodes, A ij This represents the edge weight connecting node i and node j. and nodes The value is 1 when the two are directly connected, and 0 when they are not connected; k i k represents the sum of the weights of all edges connected to node i. j W represents the sum of the weights of all edges connected to node j; W represents the sum of the weights of the entire network. Given a 0-1 matrix, if the nodes and nodes If they are located in the same cluster, then If they are not in the same cluster, then .

9. The method for dividing regional distribution network distributed photovoltaic clusters according to claim 8, characterized in that, comprehensively... The performance index ρ is: ； In the formula: , and The weights are respectively for modularity, active power balance, and energy storage balance; The weights of modularity, active power balance, and energy storage balance are determined using the analytic hierarchy process (AHP).

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