Distributed photovoltaic cluster coordination control method for voltage regulation of power distribution network

Abstract

The invention discloses a distributed photovoltaic cluster coordination control method for voltage regulation of a power distribution network, which relates to the field of distributed photovoltaic power generation and comprises the following steps: S1, dividing each cluster of the power distribution network by taking an electrical distance and a physical distance between nodes as cluster division indexes; evaluating a cluster division result by taking a cluster internal correlation index and an electrical modularity index as evaluation indexes, and selecting an optimal cluster division result; s2, calculating voltage sensitivity and reactive voltage sensitivity between the nodes, combining the voltage sensitivity and the reactive voltage sensitivity according to a certain weight to form comprehensive sensitivity, and selecting a dominant node in a cluster based on the comprehensive sensitivity; designing a cluster voltage deviation degree to reflect a voltage level in the cluster, and dividing the cluster into a safe cluster and a dangerous cluster; and S3, when the dangerous cluster appears, selecting an optimal safety cluster from the safety clusters according to the magnitude of the voltage deviation degree, adding reactive power to nodes containing the distributed photovoltaic modules in the optimal safety cluster, and distributing the added reactive power to the nodes of the dangerous cluster according to the capacity. It can be ensured that the power distribution network supplies power to users safely and stably, and resource waste is avoided.

Description

Technical Field

[0001] The present invention relates to the technical field of distributed photovoltaic power generation, and more specifically to a distributed photovoltaic cluster coordination control method for voltage regulation of a distribution network. Background Art

[0002] As a representative of clean energy, distributed photovoltaic power generation has the characteristics of small scale, dispersion, independence, and environmental friendliness. However, after a high proportion of distributed photovoltaic power generation is connected to the distribution network, distributed photovoltaic power generation is affected by the environment and other photovoltaic power generation, and the flow in the distribution network may change, which may cause the voltage at some load nodes in the distribution network to exceed the limit. This will not only affect the power quality on the user side, but also cause the protection device of the power grid to be activated, seriously affecting and threatening the safe operation of the distribution network.

[0003] The centralized control architecture optimizes the dispatch of distributed resources at multiple nodes based on a control center (global control center), and is the main dispatch architecture currently used in distribution networks. Due to the randomness and volatility of distributed photovoltaic power generation, as the proportion of distributed photovoltaic access to the distribution network continues to increase, the phenomenon of voltage exceeding the limit of the distribution network is becoming increasingly significant. In order to ensure that the distribution network can safely and stably supply power to users, many distributed photovoltaics have not been connected to the distribution network, resulting in a waste of resources.

[0004] Hamad et al. pointed out that it is a challenging task to use distributed photovoltaic power generation for voltage regulation in distribution networks because the intermittent nature of solar power generation may cause voltage to exceed the limit. Haghdadi et al. investigated the characteristics of photovoltaic systems contributed to the Live Map database to evaluate their accuracy and applicability, and provide a total estimate of distributed photovoltaic power generation for power system planning and operation purposes. Islam et al. developed an optimal reactive power dispatch scheme to provide voltage support in the distribution network by minimizing the total dispatch cost. Baran et al. further constrained the optimization problem to include a minimum threshold to retain the reactive power reserve of distributed photovoltaics, and used a genetic algorithm to find the optimal dispatch instruction. Elkhatib et al. proposed an algorithm that enables regional regulators to dynamically adjust their operating areas after a voltage collapse occurs, ensuring that each area has sufficient reactive power support from distributed photovoltaics to prevent further collapse. Zhou et al. proposed an algorithm that considers the P / Q modulation price with minimal system loss to maximize benefits. Kekatos et al. proposed a random voltage regulation scheme to generate reactive power modulation incentives to stabilize highly intermittent solar output. Ndiaye et al. used PSCAD to simulate and evaluate the impact of distributed solar photovoltaic (PV) systems on the performance of suburban distribution network systems. They pointed out that when PV microinverters do not provide reactive power support, the performance of the distribution network (especially the power factor at the head of the distribution network) will deteriorate, and adjusting the microinverter power factor according to the power generation level can significantly improve the performance of the distribution network.

[0005] The above research status abroad mainly focuses on finding an optimal reactive power dispatching scheme and minimizing the total dispatching cost. However, there are still some shortcomings in the current research. For example, Haghdadi et al. did not propose measures on how to use distributed photovoltaic power generation data to regulate the voltage of the distribution network, and Ndiaye et al. did not propose a specific solution for adjusting the power factor of the microinverter.

[0006] Liu Cheng et al. adopted the IEEE 33-node distribution network model and established a distributed photovoltaic and wind power generation model based on the model. Starting from the size of the access capacity of distributed power sources and the different access locations in the distribution network, they studied how the voltage level of the distribution network would fluctuate when different numbers of distributed power sources output electricity to the distribution network. Diao Shoubin et al. analyzed the principles of distributed photovoltaic power generation, the principles and structure of the grid-connected system, and the impact of grid-connected distributed photovoltaic power generation on the power grid system. Based on the measured data of single-household distributed photovoltaic power generation, they studied the output and operation characteristics of distributed photovoltaic power generation. Xu Tao et al. proposed a distributed voltage control strategy, which is based on the MAS system and improves the response speed of the system. It can not only constrain the voltage of the node, but also adjust the distributed power source so that it can fully realize the maximization of active power access. Xiao Hao et al. proposed a voltage optimization control scheme. They first comprehensively analyzed the reasons why distributed power sources were connected to the distribution network, which caused voltage fluctuations and voltage over-limit. Then, based on the idea of ​​model predictive control (MPC), they used voltage sensitivity to predict the trend of node voltage changes. By adding a feedback control module, the voltage over-limit problem caused by the distributed power sources connected to the distribution network was greatly reduced, and the operation was very flexible. You Dingjun first explained the voltage regulation method of the active distribution network, and then compared the effect of decentralized voltage control with the effect of active distribution network voltage regulation. It was concluded that the combination of centralized regulation and distributed regulation would improve the effect of voltage regulation, and the influence of control scale and environmental factors was considered. Wang Xiaoxue et al. proposed to control the distribution system based on MAS, and proposed a distributed coordinated control algorithm. Through repeated iterations, global voltage control was achieved, the algorithm was optimized, and the system response speed was greatly improved. Liu Rui et al. proposed a partition coordinated optimization control method. Based on the community partition theory, they established two partition functions to partition the active and reactive power. After iterative calculation, the problem of excessive variable dimensions was reduced, the calculation process was simplified, and the calculation time was optimized. Luo Yanyu et al. fully considered the characteristics of the distribution network and the maximum regulation capacity of distributed power sources, designed a two-layer control strategy model based on a multi-agent system, and proved the advantages of the proposed strategy in distribution network control through multiple sets of examples. Jiang Tao et al. proposed a voltage distributed optimization control strategy. By adjusting the weight factor of the objective function, the voltage of the distribution network node can be effectively regulated by distributed control, which has a certain reference value for the voltage regulation of the power grid with a high proportion of distributed power sources. Li Zheng et al. first studied the acceptance of the distribution network under the background of high-proportion access of distributed photovoltaics, and then established multiple indicators such as deviation to reflect the changes in the distribution network caused by photovoltaic access. Then, based on the weather change model, various weather conditions were simulated, and the impact of different numbers of distributed photovoltaics connected to the distribution network under various environmental conditions was analyzed in detail.Fang Guocheng et al. quantified the voltage level in the distribution network by establishing an evaluation system, and constructed various weather scenarios to evaluate and verify the effectiveness of voltage regulation strategies from multiple perspectives. Zhao Dongmei et al. first studied the regulation functions of controllable devices in transformers and distribution networks on the voltage over-limit problems caused by the access of distributed photovoltaics, and then studied the impact of the access of distributed photovoltaics at the end of the feeder on the voltage of the main grid, and obtained the relationship between the transformer tap and the acceptance capacity of distributed photovoltaics.

[0007] The above domestic research status mainly focuses on making full use of the reactive power output capacity of photovoltaics to achieve voltage stability control and the balanced distribution of its reactive power output according to its capacity. For example, an active distribution network distributed voltage control strategy based on a multi-agent system proposed by Xu Tao, a voltage distributed optimization control strategy proposed by Jiang Tao, etc.

[0008] Therefore, how to study a more optimized distributed photovoltaic control strategy and optimize the comprehensive sensitivity of the cluster is a technical problem that needs to be solved urgently by those skilled in the art. Summary of the Invention

[0009] In view of this, the present invention provides a coordinated control method for a distributed photovoltaic cluster for voltage regulation in a distribution network, which solves the problems existing in the background technology.

[0010] To achieve the above object, the present invention provides the following technical solutions:

[0011] A coordinated control method for a distributed photovoltaic cluster for voltage regulation in a distribution network includes the following steps:

[0012] S1. Taking the electrical distance and physical distance between nodes as cluster division indicators, dividing each cluster in the distribution network; using the internal correlation index and electrical modularity index of the cluster as evaluation indicators to evaluate the cluster division results, and selecting the optimal cluster division result;

[0013] S2: Calculating the voltage sensitivity and reactive power-voltage sensitivity between nodes and forming a comprehensive sensitivity with a certain weight combination, and selecting the leading node in the cluster based on the magnitude of the comprehensive sensitivity; designing the cluster voltage deviation degree to reflect the voltage level inside the cluster, and dividing the cluster into a safe cluster and a dangerous cluster;

[0014] S3: When a dangerous cluster appears, selecting the optimal safe cluster in the safe cluster according to the magnitude of the voltage deviation degree, increasing the reactive power of the nodes containing distributed photovoltaic modules in the optimal safe cluster, and distributing the increased reactive power to the nodes of the dangerous cluster according to the capacity.

[0015] Optionally, in S1, the K-means algorithm is used to divide each cluster in the distribution network, and the acquisition method of the clustering index of the K-means algorithm is specifically as follows:

[0016] Taking the node impedance matrix as the original parameter for calculating the electrical distance, the known equation (1) is:

[0017] V = ZI (1);

[0018] Expand equation (1) into equation (2):

[0019]

[0020] Where: V is the voltage matrix, Z is the impedance matrix, and I is the current matrix;

[0021] Inject a unit current at node i, while all other nodes are open-circuited, and the current only flows out from node j, that is, I i = 1, I j = 0, where j = 1, 2,..., n, j ≠ i;

[0022] According to equation (2), equation (3) can be obtained:

[0023] V ij = Z ij (3);

[0024] Where, the mutual impedance Z ij between node i and node j is equal to the voltage difference V ij between node i and node j. The electrical distance only focuses on the electrical connection between node i and node j, ignoring the influence of other nodes;

[0025] Use the input impedance of the two-port network to characterize the electrical distance between nodes, that is, the calculation formula of the equivalent impedance Z eq,ij is:

[0026] Z eq,ij = Z ii + Z jj - 2Z ij (4);

[0027] Where: Z ii is the self-impedance of node i in the impedance matrix, Z jj is the self-impedance of node j in the impedance matrix, Z ij is the mutual impedance between node i and node j;

[0028] The relationship expression between the node edge weight e ij and the electrical distance is:

[0029] e ij = 1 - Z eq,ij / max(L) (5);

[0030] Where: L is the electrical distance matrix;

[0031] Calculate the sum of the edge weights E between node i and all other nodes j i , as shown in formula (6):

[0032]

[0033] E i As a parameter of the quantized node, that is, the clustering index of the K-means algorithm.

[0034] Optionally, in S1, the evaluation indicators for dividing the clusters are the internal correlation index of the cluster and the electrical modularity index;

[0035] Cluster internal correlation index Indicates the degree of association between nodes within the cluster. The expression is:

[0036]

[0037] Where: i, j are node numbers, n is the total number of nodes, M k is the kth cluster, e ij is the edge weight of nodes i and j, is the sum of the edge weights between a node in the cluster and all nodes in the cluster, e total is the sum of the edge weights of all nodes in the distribution network;

[0038] The electrical modularity index ρ is used to judge the structural strength of the cluster, and the calculation formula is:

[0039]

[0040] Where: k i , k j are the sum of the edge weights of nodes i and j and all nodes in the distribution network respectively; when nodes i and j are assigned to the same cluster, the value of δ(i, j) is 1, otherwise the value of δ(i, j) is 0;

[0041] Taking into account the internal correlation index and electrical modularity index of the cluster, the comprehensive evaluation index ZH is defined, and the calculation formula is:

[0042]

[0043] Wherein: the comprehensive evaluation index ZH is equal to the product of the exponential value with the electrical modularity index as the power and the sum of the products of the internal correlation index of all clusters.

[0044] Optionally, in S1, in the optimal cluster division result, all nodes in the cluster meet the physical connection requirements, there are no isolated nodes in the cluster and all are distributed in the same area.

[0045] Optionally, in S2, the calculation of the comprehensive sensitivity and the selection of the dominant node specifically include the following steps:

[0046] Voltage sensitivity between nodes V i Expressed by the electrical distance between nodes, the simplified calculation formula is:

[0047]

[0048] Where: Z eq,ij is the electrical distance between points i and j in the cluster;

[0049] Based on the Jacobian matrix, the reactive voltage sensitivity C is obtained i ;

[0050] The voltage sensitivity and reactive voltage sensitivity between nodes are combined according to certain weights to form a comprehensive sensitivity S, which is expressed as:

[0051]

[0052] Where: V i is the voltage sensitivity of the node, which represents the observability of the node; C i is the reactive voltage sensitivity of the node, indicating the controllability between nodes; a is the weight factor coefficient; i∈N, N is the node included in the cluster; ΔU j is the voltage change at node j, ΔU i is the voltage change at node i, ΔQ i is the reactive power change of node j;

[0053] The node with the highest comprehensive sensitivity S in each cluster is selected as the dominant node.

[0054] Optionally, in S2, the calculation of the voltage deviation and the selection of the dangerous cluster specifically include the following steps:

[0055] According to the relationship between the reactive voltage sensitivity between nodes and the real-time voltage value of each node in the distribution network and the cluster division, the voltage deviation index of the cluster is obtained to reflect whether the voltage of the nodes inside the cluster exceeds the limit. The calculation formula is:

[0056]

[0057] Where: is the voltage deviation of the kth cluster, N is the total number of nodes in the cluster, τ is the standardization coefficient, is the reactive voltage sensitivity, U max , U min They are the highest and lowest voltages allowed for grid operation; U i is the real-time voltage value of the i-th node in the cluster, Cθθ is the reference value related to reactive voltage sensitivity;

[0058] The cluster voltage deviation exceeds 2×10 -2 The cluster is classified as a dangerous cluster, and the cluster voltage deviation is less than 2×10 -2 The cluster is divided into a security cluster.

[0059] Optionally, in S3, the control strategy when a dangerous cluster appears is as follows:

[0060] For dangerous clusters, the PV inverters inside the cluster are controlled to supply energy to the internal energy storage system and no longer output power to the distribution network, that is, the connection between the distributed PV power source and the distribution network is cut off; at the same time, the inverters of the PV nodes inside the cluster are switched to the reactive voltage regulation control mode to accept the reactive power generated by the safe cluster to regulate its voltage;

[0061] For the safe cluster, the cluster with the smallest voltage deviation is selected from all safe clusters to increase the reactive power of its internal distributed photovoltaic inverters, so as to regulate the voltage of the dangerous cluster.

[0062] The calculation formula for additional reactive power is:

[0063]

[0064] Where: ΔQ i is the reactive power received by dangerous cluster i, ξ is the correction factor, Z eq,ij is the electrical distance between the leading nodes of safe cluster j and dangerous cluster i, U max The maximum voltage allowed for grid operation, U min The lowest voltage allowed for grid operation, U θ i is the voltage value of the leading node of the dangerous cluster;

[0065] After the optimal safety cluster generates additional reactive power, the reactive power transmitted to the dangerous cluster is distributed according to the capacity of each node within the cluster to avoid overloading the grid-connected inverter of the node.

[0066] It can be seen from the above technical solutions that, compared with the prior art, the present invention discloses a distributed photovoltaic cluster coordinated control method for distribution network voltage regulation, which has the following beneficial effects:

[0067] (1) The electrical distance and physical distance between nodes are used as constraints to divide the distribution network into clusters; the cluster internal correlation index and electrical modularity index are used as evaluation indicators to evaluate the cluster division results and find the optimal cluster division to ensure that the voltage levels between nodes in the cluster are similar and the cluster division is reasonable, which is convenient for the subsequent voltage regulation work within the cluster;

[0068] (2) The selection of the dominant node based on comprehensive sensitivity can ensure that it is both controllable and observable. The dominant node can represent the cluster to make corresponding adjustments, which can ensure the stability and reliability of the system. The cluster voltage deviation meter and the voltage level of all nodes in the cluster can effectively quantify the voltage quality of each cluster and determine whether the voltage of the nodes within the cluster exceeds the limit.

[0069] (3) The voltage over-limit problem caused by dangerous clusters can be solved by using reactive power control, which can avoid the problem of reactive power transmission over long distances in the power grid. The reactive power balance of the whole system can be achieved through local reactive power balance within each cluster, thus realizing cluster-level voltage regulation. BRIEF DESCRIPTION OF THE DRAWINGS

[0070] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on the provided drawings without paying creative work.

[0071] Figure 1 A flow chart of the inter-cluster voltage collaborative control strategy provided by the present invention;

[0072] Figure 2 The node edge weight and distribution graph provided by the present invention;

[0073] Figure 3 A diagram of physical constraints provided by the present invention;

[0074] Figure 4 A schematic diagram of a three-dimensional K-means clustering sample partition provided by the present invention;

[0075] Figure 5 A schematic diagram of multiple calculation results of the comprehensive evaluation index provided by the present invention;

[0076] Figure 6 A schematic diagram of the result of the optimal clustering division of the IEEE 33-node distribution network provided by the present invention;

[0077] Figure 7 Another schematic diagram of the optimal clustering division of the IEEE 33-node distribution network provided by the present invention;

[0078] Figure 8 The voltage sensitivity between the cluster nodes provided by the present invention;

[0079] Fig. 9 A schematic diagram of reactive voltage sensitivity distribution between nodes provided by the present invention;

[0080] Fig.10 Another schematic diagram of reactive voltage sensitivity distribution between nodes provided by the present invention;

[0081] Fig.11 A distribution diagram of the comprehensive sensitivity S of each node in the cluster provided by the present invention;

[0082] Fig.12 The IEEE 33-node power distribution network provided by the present invention;

[0083] Fig.13 A voltage distribution diagram of a node not connected to distributed photovoltaic provided by the present invention;

[0084] Fig.14 A voltage distribution diagram of nodes connected to distributed photovoltaics provided by the present invention;

[0085] Fig.15 A node voltage distribution diagram after the distributed photovoltaic fluctuation provided by the present invention;

[0086] Fig.16 A schematic diagram of multi-cluster voltage coordinated control provided by the present invention;

[0087] Fig.17 The IEEE 33-node distribution network with a high proportion of distributed photovoltaic modules provided by the present invention;

[0088] Fig.18 The node voltage distribution before and after the distributed photovoltaic access provided by the present invention;

[0089] Fig.19 The node voltage distribution before and after the distributed photovoltaic fluctuation provided by the present invention;

[0090] Fig. 20 A distribution diagram of cluster voltage deviation provided by the present invention;

[0091] Fig.21 The node voltage distribution diagram before and after the dangerous cluster distributed photovoltaic removal provided by the present invention;

[0092] Fig. 22 This is a comparison diagram of voltage distribution before and after voltage regulation provided by the present invention. DETAILED DESCRIPTION

[0093] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0094] The embodiment of the present invention discloses a distributed photovoltaic cluster coordinated control method for distribution network voltage regulation, comprising the following steps:

[0095] S1. Use the electrical distance and physical distance between nodes as cluster division indicators to divide the distribution network into clusters; use the cluster internal correlation index and electrical modularity index as evaluation indicators to evaluate the cluster division results and select the optimal cluster division result;

[0096] S2: Calculate the voltage sensitivity and reactive voltage sensitivity between nodes and combine them with certain weights to form a comprehensive sensitivity. Select the leading node in the cluster based on the size of the comprehensive sensitivity. Design the cluster voltage deviation to reflect the voltage level inside the cluster and divide the cluster into a safe cluster and a dangerous cluster.

[0097] S3: When a dangerous cluster appears, the optimal safe cluster is selected from the safe clusters according to the voltage deviation, so that the nodes of the distributed photovoltaic modules in the optimal safe cluster increase reactive power, and the increased reactive power is allocated to the nodes of the dangerous cluster according to capacity.

[0098] Next, refer to Figure 1 , the specific process of the coordinated control method of distributed photovoltaic clusters is elaborated in detail.

[0099] 1. Distribution network cluster division based on electrical distance

[0100] 1.1 Calculation of clustering index

[0101] The K-means algorithm is used to divide the distribution network clusters. The clustering index of the K-means algorithm is obtained as follows:

[0102] The node impedance matrix is ​​used as the original parameter for calculating the electrical distance, and formula (1) is known:

[0103] V = ZI(1);

[0104] Expand equation (1) into equation (2):

[0105]

[0106] Where: V is the voltage matrix, Z is the impedance matrix, and I is the current matrix;

[0107] A unit current is injected into node i, and all other nodes are open, so the current only flows out from node j, that is, I i =1,I j =0, where j=1,2,...,n,j≠i;

[0108] According to formula (2), we can get formula (3):

[0109] V ij =Z ij (3);

[0110] Where, the mutual impedance Z between node i and node j is ij Equal to the voltage difference V between node i and node j ij , electrical distance only focuses on the electrical connection between node i and node j, ignoring the influence of other nodes;

[0111] Since this embodiment focuses on the voltage regulation problem of the distribution network, the spatial distance between nodes is not required, but the electrical distance between them is focused on. In order to simplify the calculation of the electrical distance between nodes and improve the efficiency of the calculation, the input impedance of the two-port network is used to characterize the electrical distance between nodes, that is, the equivalent impedance Z eq,ij The calculation formula is:

[0112] Z eq,ij =Z ii +Z jj -2Z ij (4);

[0113] Where: Z ii is the self-impedance of node i in the impedance matrix, Z jj is the self-impedance of node j in the impedance matrix, Z ij is the mutual impedance between node i and node j; equivalent impedance Z eq,ij The value of represents the electrical distance between nodes i and j. The larger the value, the greater the electrical distance between nodes.

[0114] Node edge weight e ij The relationship expression with electrical distance is:

[0115] e ij =1-Z eq,ij / max(L)(5);

[0116] Where: L is the electrical distance matrix;

[0117] Calculate the sum of the edge weights E between node i and all other nodes j i , as shown in formula (6):

[0118]

[0119] E i As a parameter of the quantized node, that is, the clustering index of the K-means algorithm.

[0120] After calculating the node impedance matrix, electrical distance conversion and node edge weight sum of the IEEE 33-node distribution network, the node edge weight sum distribution is obtained as follows: Figure 2 shown.

[0121] 1.2 Evaluation indicators for clustering

[0122] Under certain convergence conditions, the same set of data can be divided into multiple groups of different clusters. Therefore, it is necessary to find the best cluster from these different clusters as the only division result. One of the purposes of clustering in this embodiment is to ensure that the voltage levels between the nodes in the cluster are similar. Therefore, the electrical distances between the nodes in the cluster should be kept as small as possible. Therefore, the electrical distances within the cluster can be used as the evaluation index of the cluster. By designing corresponding evaluation indicators, the best cluster division result can be found, so that the electrical distances between the nodes in the same cluster are small, while the electrical distances between the nodes in different clusters are large, that is, the best target cluster division result is obtained.

[0123] In order to reasonably measure the clustering results, this embodiment uses two clustering evaluation indicators, namely, the cluster internal correlation indicator and the electrical modularity indicator.

[0124] 1.2.1 Cluster Internal Correlation Index

[0125] Cluster internal correlation index Indicates the degree of association between nodes within the cluster. The expression is:

[0126]

[0127] Where: i, j are node numbers, n is the total number of nodes, M k is the kth cluster, e ij is the edge weight of nodes i and j, is the sum of the edge weights between a node in the cluster and all nodes in the cluster, e total is the sum of the edge weights of all nodes in the distribution network;

[0128] The more reasonable the cluster division is, the greater the electrical distance between the nodes inside the cluster and the nodes in the distribution network, the smaller the edge weight, the better the internal correlation of the cluster, and the greater the ECI value of the cluster.

[0129] 1.2.2 Electrical modularity index

[0130] The electrical modularity index can accurately judge the structural strength of the cluster. The modularity index can be used to make a relatively accurate assessment of the structural strength of the cluster that is difficult to quantify. The voltage levels within the cluster with a better electrical modularity index will be closer, which is conducive to the quantification of the cluster voltage level. In the subsequent process of adjusting the cluster voltage, this method can greatly reduce the reactive power flow between clusters, thereby greatly reducing the loss caused by reactive power transmission in the distribution network, and also provides convenience for voltage regulation based on the cluster as the dispatching unit. The larger the electrical modularity index, the higher the degree of coupling within the cluster; the smaller the electrical modularity index, the lower the degree of coupling between clusters.

[0131] The calculation formula of the electrical modularity index ρ is:

[0132]

[0133] Where: k i , k j are the sum of the edge weights of nodes i and j and all nodes in the distribution network respectively; when nodes i and j are assigned to the same cluster, the value of δ(i, j) is 1, otherwise the value of δ(i, j) is 0;

[0134] Since the larger the value of the internal correlation index and the electrical modularity index of the cluster, the better the degree of cluster division, therefore, considering the internal correlation index and the electrical modularity index of the cluster comprehensively, the comprehensive evaluation index ZH is defined, and the calculation formula is:

[0135]

[0136] Wherein: the comprehensive evaluation index ZH is equal to the product of the exponential value with the electrical modularity index as the power and the sum of the products of the internal correlation indexes of all clusters. The larger the comprehensive evaluation index, the better the degree of cluster division.

[0137] 1.3 Cluster division results

[0138] Before clustering, it is necessary to ensure that the voltage levels between nodes in the cluster are similar. At the same time, in order to facilitate the subsequent voltage regulation work in the cluster, there must be no isolated nodes in the cluster, that is, the nodes clustered into the same cluster must be connected as a whole without any disconnections in the middle. Therefore, it is necessary to consider the physical connection relationship in the actual distribution network.

[0139] Design physical constraints such as Figure 3 As shown in Figure 1, physical constraints are used as another clustering indicator of the K-means algorithm, and participate in cluster division together with the node edge weight and the node edge weight. The cluster division sample of K-means in three-dimensional space is shown in Figure 1. Figure 4As shown in the figure, the divided clusters are evaluated using comprehensive evaluation indicators, and finally the optimal cluster division is obtained.

[0140] According to the number of actual nodes in the distribution network and the optimal number of cluster divisions, this embodiment chooses to divide the distribution network into six clusters. After multiple calculations, the clustering result with the largest comprehensive evaluation index is taken as the cluster division result. The results of multiple calculations of the comprehensive evaluation index are as follows: Figure 5 As shown, the cluster division results are as follows Figure 6 , Figure 7 shown.

[0141] It can be seen from the optimal clustering results that in the optimal clustering results calculated by the algorithm designed in this embodiment, all nodes in the cluster meet the requirements of physical connection, there are no isolated nodes in the cluster and they are all distributed in the same area, meeting the requirement of close voltage levels between nodes. At the same time, the number of nodes in each cluster is close, and the nodes have strong connectivity, so the clustering is more reasonable.

[0142] 2 Calculation of cluster performance indicators

[0143] 2.1 Calculation of comprehensive sensitivity and selection of dominant nodes

[0144] In order to achieve mutual coordination between clusters, it is necessary to find the dominant node of each cluster, through which the cluster can be regulated accordingly. At the same time, the dominant node of the cluster can reflect the voltage level of other nodes in the cluster, thus providing a reference for the amount of reactive power generated by the safety cluster.

[0145] When selecting the cluster leading node, it must be ensured that it is both controllable and observable to ensure the stability and reliability of the system. Based on this feature, this embodiment designs a comprehensive sensitivity S, which is composed of the voltage sensitivity between nodes and the reactive voltage sensitivity between nodes according to a certain weight combination.

[0146] Since the voltage sensitivity between nodes in the distribution network mainly depends on the electrical distance between the nodes, the voltage sensitivity V between the nodes i It can be represented by the electrical distance between nodes, and the simplified calculation formula is:

[0147]

[0148] Where: Z eq,ij is the electrical distance between points i and j in the cluster; according to the electrical distance matrix obtained above, after simulation calculation, the voltage sensitivity between each node in each cluster is as follows Figure 8 shown.

[0149] Based on the Jacobian matrix, the reactive voltage sensitivity C is obtained i ; After simulation calculation, it can be concluded that the reactive voltage sensitivity distribution between nodes is as follows: Fig. 9 , Fig.10 shown.

[0150] The voltage sensitivity and reactive voltage sensitivity between nodes are combined according to certain weights to form a comprehensive sensitivity S, which can quantify the controllability and observability of the nodes in the cluster. The node with the highest comprehensive sensitivity S in each cluster is selected as the dominant node. The expression of comprehensive sensitivity S is:

[0151]

[0152] Where: V i is the voltage sensitivity of the node, which represents the observability of the node; C i is the reactive voltage sensitivity of the node, indicating the controllability between nodes; a is the weight factor coefficient; i∈N, N is the node included in the cluster; ΔU j is the voltage change at node j, ΔU i is the voltage change at node i, ΔQ i is the reactive power change of node j;

[0153] Taking the weight factor a = 0.2, the calculated voltage sensitivity and reactive voltage sensitivity can be used to obtain the comprehensive sensitivity S of each node in each cluster, and its size distribution is as follows: Fig.11 shown.

[0154] Depend on Fig.11 It can be seen that the nodes with the highest comprehensive sensitivity in the six clusters are node 20, node 24, node 6, node 9, node 16, and node 30. Therefore, the above six nodes are selected as the leading nodes in the six clusters, and their specific comprehensive sensitivity values ​​are shown in Table 1.

[0155] Table 1 Comprehensive sensitivity of dominant nodes

[0156]

[0157]

[0158] 2.2 Calculation of voltage deviation and selection of dangerous clusters

[0159] Since this embodiment mainly studies the problem of voltage over-limit, it is necessary to evaluate the voltage level of the cluster. According to the relationship between the reactive voltage sensitivity between nodes and the real-time voltage value of each node in the distribution network and the cluster division, the voltage deviation index of the cluster is obtained to reflect whether the voltage of the nodes inside the cluster is over-limit. According to whether the voltage deviation of the cluster exceeds a certain set value, the cluster can be judged as a safe cluster or a dangerous cluster. Based on the above analysis, the calculation formula of the cluster voltage deviation is defined as:

[0160]

[0161] Where: is the voltage deviation of the kth cluster, N is the total number of nodes in the cluster, τ is the standardization coefficient (used to unify the voltage deviation of the cluster), is the reactive voltage sensitivity, U max , U min are the highest and lowest voltages allowed by the power grid operation respectively; Ui is the real-time voltage value of the i-th node in the cluster, C θθ is the reference value related to reactive voltage sensitivity;

[0162] The cluster voltage deviation exceeds 2×10 -2 The cluster is classified as a dangerous cluster, and the cluster voltage deviation is less than 2×10 -2 The cluster is divided into a security cluster.

[0163] The cluster voltage deviation index takes into account the voltage levels of all nodes in the cluster and can effectively quantify the voltage quality of each cluster. When dividing the cluster, the electrical distance between each node is the main reference. Therefore, the voltage levels between nodes in the cluster after the division are not much different. There will not be a situation where the voltage of a node in the cluster exceeds the limit while the voltage of most nodes is still at a safe level. That is, when the voltage of a node in the cluster exceeds the limit, the cluster voltage will not be at a safe level, which also explains the rationality of the cluster voltage deviation index from the perspective of the cluster.

[0164] 3. Inter-cluster voltage regulation with distributed photovoltaics

[0165] When large-scale distributed photovoltaics are connected to the distribution network, the load nodes that originally absorbed power may become power sources that emit power, thus turning the distribution network into a multi-source network, changing the originally fixed power flow direction. Since the power output of the new power source is unknown, it will cause serious voltage over-limit problems. This solution uses reactive power to control the voltage over-limit problems caused by dangerous clusters. By combining the above-mentioned optimal clustering division of the nodes in the distribution network, the problem of reactive power transmission over long distances in the power grid can be avoided. The reactive power balance of the entire system is achieved through the local reactive power balance in each cluster, and the voltage regulation at the cluster level is achieved.

[0166] 3.1 Cluster Control Strategy

[0167] like Fig.12 As shown in the figure, taking the IEEE 33-node distribution network model as an analysis example, when distributed photovoltaics are not connected, the node voltage distribution is calculated through power flow. Fig.13 shown.

[0168] In the absence of an external power supply, the voltage of multiple nodes is lower than the allowable deviation range of the distribution network voltage (-5% to 5%). In this model, the access and fluctuation of distributed photovoltaics are represented by changing the active and reactive values ​​of the nodes. Therefore, after connecting to distributed photovoltaics at nodes 4, 9, 15, 24, 28, and 32, the capacity of distributed photovoltaic output is appropriately adjusted, and the model is calculated again to obtain the node voltage distribution as follows: Fig.14 shown.

[0169] It can be seen that after the access to distributed photovoltaics, the voltage of most nodes has been significantly improved. The access to distributed photovoltaics has a significant effect on the improvement of node voltage values. However, due to the volatility of distributed photovoltaics, its output power is random. At a certain moment, the output of distributed photovoltaics reaches the maximum value. At this time, when the output of distributed photovoltaics is transmitted to the distribution network, the distribution network model is subjected to flow calculation, and its node voltage distribution is obtained as follows: Fig.15 shown.

[0170] Obviously, after the distributed photovoltaic fluctuation, the node voltage value exceeds the rated allowable voltage deviation range, that is, the node voltage exceeds the limit. The node voltage exceeding the limit will cause the insulation medium to be broken down, causing the electrical appliances to burn out, and will also accelerate the aging of electrical equipment, reducing its rated life, which is not conducive to the safe operation of the distribution network. Therefore, how to control distributed photovoltaics so that the node voltage operates within a safe and stable voltage range is a key research issue.

[0171] In this embodiment, the IEEE 33-node distribution network model has been divided into clusters, and the performance index of each cluster has been calculated. Based on the voltage deviation of each cluster, it is determined that the cluster voltage deviation exceeds 2×10 -2 The cluster is a dangerous cluster, and the cluster voltage deviation is less than 2×10 -2 The cluster is a safe cluster. The schematic diagram of multi-cluster voltage coordinated control is shown in Fig.16 shown.

[0172] For dangerous clusters: Control the PV inverters inside the cluster so that they supply energy to the internal energy storage system and no longer output power to the distribution network, which is equivalent to cutting off the connection between the distributed PV power source and the distribution network; at the same time, the inverters of the PV nodes inside the cluster are switched to the reactive voltage regulation control mode to accept the voltage regulation of the reactive power generated by the safe cluster;

[0173] For safe clusters: select the cluster with the smallest voltage deviation from all safe clusters to increase the reactive power generation of its internal distributed photovoltaic inverters, so as to regulate the voltage of dangerous clusters;

[0174] The calculation formula for additional reactive power is:

[0175]

[0176] Where: ΔQ i is the reactive power received by dangerous cluster i, ξ is the correction factor, Z eq,ij is the electrical distance between the leading nodes of safe cluster j and dangerous cluster i, U max The maximum voltage allowed for grid operation, U min The lowest voltage allowed for grid operation, U θ i is the voltage value of the leading node of the dangerous cluster;

[0177] For the dangerous cluster after the internal inverter mode is changed to Q(U) control, after the optimal safety cluster increases the reactive power, the reactive power transmitted to the dangerous cluster is distributed according to the capacity of each node within the cluster. If it is not distributed according to the capacity, the node's grid-connected inverter may be damaged due to overload, thereby further increasing the node voltage.

[0178] 3.2 Simulation voltage regulation of high-proportion distributed photovoltaic distribution network

[0179] This embodiment takes the IEEE 33-node distribution network as the research object, in which a high proportion of distributed photovoltaic modules are connected. Combined with the above cluster division, the distribution of distributed photovoltaics in the distribution network is as follows: Fig.17 shown.

[0180] The distributed photovoltaic power generation is disconnected and connected to the distribution network, and the power flow calculation is performed on the distribution network data before and after the connection, and the voltage distribution results of each node are obtained as follows: Fig.18 As shown in the figure. From the voltage distribution diagram, it can be seen that when the distributed photovoltaic has no output power, the power flow direction in the distribution network is fixed, and the voltage of the node decreases as the distance from the transformer increases. The voltage of most nodes far away from the transformer is lower than the minimum rated voltage of the distribution network, which is not conducive to the normal operation of the node load. When the distributed photovoltaic nodes in the distribution network output at rated power, the nodes that originally absorbed power become power sources that emit power, raising the voltage of the nodes in the distribution network to the normal voltage range.

[0181] At a certain moment, the sunlight condition increases or the power required by the load suddenly decreases, the power output of the distributed photovoltaic system fluctuates, and the power output of most distributed photovoltaic modules increases, which will cause the voltage level of the nodes in the distribution network to increase. When the distributed photovoltaic modules fluctuate, the data in the distribution network is subjected to flow calculation, and the voltage distribution results of all nodes are obtained as follows: Fig.19 shown.

[0182] After the distributed photovoltaic fluctuations, the voltage of most nodes in the distribution network has been greatly increased. The voltage of seven nodes exceeds the maximum voltage allowed by the distribution network, 1.05pu, which poses a threat to the safe operation of the distribution network. Therefore, it is necessary to adjust its voltage. Based on the previous division of clusters and selection of dominant nodes, the voltage deviation of each cluster is calculated separately, and the voltage deviation distribution diagram is obtained as shown in the figure. Fig. 20 shown.

[0183] Depend on Fig. 20 It can be seen that the voltage deviation of cluster 5 and cluster 6 exceeds 2×10 -2 , that is, the voltage of the nodes in the cluster exceeds the limit. Therefore, clusters 5 and 6 are judged as dangerous clusters, and the connection between the distributed photovoltaic modules in these two dangerous clusters and the distribution network is immediately cut off. The node voltage distribution diagram after the cut-off is shown in Fig.21 shown.

[0184] It can be seen that due to the high power output of the distributed photovoltaic modules of the dangerous cluster, when the distributed photovoltaic is removed, the voltage of the distribution network drops significantly, and the voltage of some nodes is even lower than the minimum allowable operating voltage of the grid 0.95pu. Therefore, it is urgent to increase the reactive power of the safe cluster to adjust the voltage of the dangerous cluster. At this time, the cluster with the largest voltage deviation from the dangerous cluster is selected to increase the reactive power. Fig. 20It can be seen that the voltage deviation of cluster 1 is the largest compared to that of the dangerous cluster. Therefore, cluster 1 is selected as the safe cluster for reactive power generation. The reactive power generated can be obtained by formula (13). The reactive power generated is allocated to the nodes containing distributed photovoltaic modules in the dangerous cluster according to capacity. After the allocation is completed, the voltage distribution diagram of the node after reactive power regulation can be obtained through power flow calculation, as shown in Fig. 22 shown.

[0185] Depend on Fig. 22 It can be seen that after the safety cluster increased reactive power and allocated it to the nodes in the dangerous cluster, the voltage of the nodes in the dangerous cluster was significantly improved compared to before the distributed photovoltaic removal, and the voltage level of all nodes in the distribution network was maintained between 0.98pu and 1.02pu. The voltage level was good and met the standard for safe operation of the power grid at rated voltage.

[0186] In order to achieve the purpose of the present invention, the above scheme can be further improved in the following ways:

[0187] 1) Cluster division based on different sensitivity indicators: The present invention uses electrical distance as the main basis for cluster division, and can further consider using other sensitivity indicators such as voltage deviation sensitivity and node load sensitivity for cluster division to more comprehensively reflect the correlation between nodes. This can improve the adaptability of cluster division under different operating conditions and enhance the control effect of voltage fluctuations.

[0188] 2) Multi-level optimized control strategy: In addition to the control within the cluster, a hierarchical control strategy can be further adopted to divide the distribution network into multiple levels (such as regions, clusters, sub-clusters, etc.), and coordinate control between different levels. This can better balance the global and local control needs, reduce the reactive power flow of the system, and improve the overall stability.

[0189] 3) Joint regulation based on distributed energy storage: In order to address the randomness of distributed photovoltaic power generation, in addition to using photovoltaic inverters for regulation, a distributed energy storage system can be further introduced into each cluster. Through the joint regulation of photovoltaic power generation and energy storage systems, flexible scheduling of active and reactive power can be achieved, thereby reducing the problem of voltage exceeding the limit.

[0190] 4) Dynamic adjustment method of electrical distance matrix: In the current technical solution, the electrical distance matrix is ​​calculated based on static network conditions. It is possible to further consider introducing a dynamic adjustment mechanism to update the electrical distance matrix in real time to reflect changes in the grid operation status, especially in the case of frequent fluctuations in distributed energy. Dynamic adjustment can better reflect the electrical connection between nodes.

[0191] 5) Improved reactive power compensation method: In the reactive power compensation process of dangerous clusters, in addition to using reactive power from safe clusters, we can further consider introducing local reactive power compensation equipment, such as static reactive power compensation devices (SVC) or dynamic reactive power compensation devices (STATCOM), to directly regulate reactive power within the dangerous cluster and reduce dependence on external reactive power transmission.

[0192] These improved solutions do not deviate from the technical content of this embodiment, and can provide more flexible and effective solutions for voltage regulation requirements in different scenarios, and can improve the application breadth and adaptability of the present invention.

[0193] The various embodiments in this specification are described in a progressive manner, and each embodiment focuses on the differences from other embodiments. The same or similar parts between the various embodiments can be referenced to each other.

[0194] The above description of the disclosed embodiments enables one skilled in the art to implement or use the present invention. Various modifications to these embodiments will be apparent to one skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the present invention. Therefore, the present invention will not be limited to the embodiments shown herein, but rather to the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A distributed photovoltaic cluster coordinated control method for distribution network voltage regulation, characterized in that: The following steps are involved: S1. Use the electrical distance and physical distance between nodes as cluster division indicators to divide the distribution network into clusters; use the cluster internal correlation index and electrical modularity index as evaluation indicators to evaluate the cluster division results and select the optimal cluster division result; S2: Calculate the voltage sensitivity and reactive voltage sensitivity between nodes and combine them with certain weights to form a comprehensive sensitivity. Select the leading node in the cluster based on the size of the comprehensive sensitivity. The cluster voltage deviation is designed to reflect the voltage level inside the cluster, and the cluster is divided into a safe cluster and a dangerous cluster; S3: When a dangerous cluster appears, the optimal safe cluster is selected from the safe clusters according to the voltage deviation, so that the nodes of the distributed photovoltaic modules in the optimal safe cluster increase reactive power, and the increased reactive power is allocated to the nodes of the dangerous cluster according to capacity.

2. A distributed photovoltaic cluster coordinated control method for distribution network voltage regulation according to claim 1, characterized in that: In S1, the K-means algorithm is used to divide the distribution network clusters. The clustering index of the K-means algorithm is obtained as follows: The node impedance matrix is ​​used as the original parameter for calculating the electrical distance, and formula (1) is known: V = ZI (1); Expand equation (1) into equation (2): Where: V is the voltage matrix, Z is the impedance matrix, and I is the current matrix; A unit current is injected into node i, and all other nodes are open, so the current only flows out from node j, that is, I i =1,I j =0, where j=1,2,…,n,j≠i; According to formula (2), we can get formula (3): In ij =Z ij (3); Where, the mutual impedance Z between node i and node j is ij Equal to the voltage difference V between node i and node j ij , electrical distance only focuses on the electrical connection between node i and node j, ignoring the influence of other nodes; The input impedance of the two-port network is used to characterize the electrical distance between nodes, that is, the equivalent impedance Z eq,ij The calculation formula is: WITH eq,ij =Z ii +Z jj -2Z ij (4); Where: Z ii is the self-impedance of node i in the impedance matrix, Z jj is the self-impedance of node j in the impedance matrix, Z ij is the mutual impedance between node i and node j; Node edge weight e ij The relationship expression with electrical distance is: e ij =1-Z eq,ij / max(L) (5); Where: L is the electrical distance matrix; Calculate the sum of the edge weights E between node i and all other nodes j i , as shown in formula (6): E i As a parameter of the quantized node, that is, the clustering index of the K-means algorithm.

3. A distributed photovoltaic cluster coordinated control method for distribution network voltage regulation according to claim 1, characterized in that: In S1, the evaluation indicators for cluster division are the internal correlation index and the electrical modularity index of the cluster; Cluster internal correlation index Indicates the degree of association between nodes within the cluster. The expression is: Where: i, j are node numbers, n is the total number of nodes, M k is the kth cluster, e ij is the edge weight of nodes i and j, is the sum of the edge weights between a node in the cluster and all nodes in the cluster, e total is the sum of the edge weights of all nodes in the distribution network; The electrical modularity index ρ is used to judge the structural strength of the cluster, and the calculation formula is: Where: k i , k j are the sum of the edge weights between nodes i, j and all nodes in the distribution network; When node i and node j are assigned to the same cluster, the value of δ(i,j) is 1, otherwise the value of δ(i,j) is 0; Taking into account the internal correlation index and electrical modularity index of the cluster, the comprehensive evaluation index ZH is defined, and the calculation formula is: Wherein: the comprehensive evaluation index ZH is equal to the product of the exponential value with the electrical modularity index as the power and the sum of the products of the internal correlation index of all clusters.

4. A distributed photovoltaic cluster coordinated control method for distribution network voltage regulation according to claim 1, characterized in that: In S1, in the optimal cluster division result, all nodes in the cluster meet the requirements of physical connection, there are no isolated nodes in the cluster and they are all distributed in the same area.

5. A distributed photovoltaic cluster coordinated control method for distribution network voltage regulation according to claim 1, characterized in that: In S2, the calculation of comprehensive sensitivity and the selection of dominant nodes specifically include the following steps: Voltage sensitivity between nodes V i Expressed by the electrical distance between nodes, the simplified calculation formula is: Where: Z eq,ij is the electrical distance between points i and j in the cluster; Based on the Jacobian matrix, the reactive voltage sensitivity C is obtained i ; The voltage sensitivity and reactive voltage sensitivity between nodes are combined according to certain weights to form a comprehensive sensitivity S, which is expressed as: Where: V i is the voltage sensitivity of the node, which represents the observability of the node; C i is the reactive voltage sensitivity of the node, indicating the controllability between nodes; a is the weight factor coefficient; i∈N, N is the node included in the cluster; ΔUj is the voltage change of the j node, ΔUi is the voltage change of the i node, and ΔQi is the reactive power change of the j node; The node with the highest comprehensive sensitivity S in each cluster is selected as the dominant node.

6. A distributed photovoltaic cluster coordinated control method for distribution network voltage regulation according to claim 1, characterized in that: In S2, the calculation of voltage deviation and the selection of dangerous clusters specifically include the following steps: According to the relationship between the reactive voltage sensitivity between nodes and the real-time voltage value of each node in the distribution network and the cluster division, the voltage deviation index of the cluster is obtained to reflect whether the voltage of the nodes inside the cluster exceeds the limit. The calculation formula is: Where: is the voltage deviation of the kth cluster, N is the total number of nodes in the cluster, τ is the standardization coefficient, is the reactive voltage sensitivity, Umax and Umin are the maximum and minimum voltages allowed by the grid operation respectively; Ui is the real-time voltage value of the i-th node in the cluster, C θθ is the reference value related to reactive voltage sensitivity; The cluster voltage deviation exceeds 2×10- 2 The cluster is classified as a dangerous cluster, and the cluster voltage deviation is less than 2×10- 2 The cluster is divided into a security cluster.

7. A distributed photovoltaic cluster coordinated control method for distribution network voltage regulation according to claim 1, characterized in that: In S3, the control strategy when a dangerous cluster appears is as follows: For dangerous clusters, the PV inverters inside the cluster are controlled to supply energy to the internal energy storage system and no longer output power to the distribution network, that is, the connection between the distributed PV power source and the distribution network is cut off; at the same time, the inverters of the PV nodes inside the cluster are switched to the reactive voltage regulation control mode to accept the reactive power generated by the safe cluster to regulate its voltage; For the safe cluster, the cluster with the smallest voltage deviation is selected from all safe clusters to increase the reactive power of its internal distributed photovoltaic inverters, so as to regulate the voltage of the dangerous cluster. The calculation formula for additional reactive power is: Where: ΔQi is the reactive power received by dangerous cluster i, ξ is the correction factor, Zeq,ij is the electrical distance between the leading node of safe cluster j and dangerous cluster i, Umax is the maximum voltage allowed for grid operation, Umin is the minimum voltage allowed for grid operation, and U θ i is the voltage value of the leading node of the dangerous cluster; After the optimal safety cluster generates additional reactive power, the reactive power transmitted to the dangerous cluster is distributed according to the capacity of each node within the cluster to avoid overloading the grid-connected inverter of the node.

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