Cluster division-based voltage control method for power distribution network containing high-proportion household photovoltaic

Abstract

The invention relates to the technical field of photovoltaic power distribution network voltage control, in particular to a power distribution network voltage control method containing high-proportion household photovoltaics based on cluster division, which comprises the following steps: step 1, cluster division and key control node selection, specifically comprising cluster comprehensive division indexes, cluster division steps and key control node selection; 2, a voltage control model based on cluster division specifically comprises an objective function, constraint conditions and model solution; and step 3, a voltage control method based on cluster division. According to the voltage control method based on cluster division provided by the invention, the power distribution network is divided into a plurality of independent clusters by using the comprehensive division index, and voltage control is realized through the energy storage priority action at the key control node of each cluster, so that the complexity of the overall voltage control of the power distribution network system is reduced, and the problems of voltage out-of-limit and the like can be quickly solved.

Description

Technical Field

[0001] The present invention relates to the technical field of photovoltaic distribution network voltage control, and in particular to a cluster-based distribution network voltage control method containing a high proportion of household photovoltaics. Background Art

[0002] With the increase in subsidies for photovoltaic power generation and the reduction in construction costs, rural distribution networks are facing a significant change: a large number of small-capacity household photovoltaic systems with dispersed layouts are connected to the power grid. This phenomenon has formed a high proportion in some areas, indicating a new trend in the transformation of rural energy structure. However, due to the randomness and intermittent nature of household photovoltaic output, and the difference from the user's usage pattern, it cannot be absorbed on the spot in time, resulting in a large number of high / low voltage coexistence problems in the distribution network, and even causing voltage over-limit, seriously affecting the safe and stable operation of the distribution network. At present, on the basis of not changing the grid structure of the distribution network, in order to solve the overvoltage problem of the distribution network, domestic and foreign research mainly focuses on traditional local control and centralized control. However, with the high proportion of decentralized distributed photovoltaic systems connected to the rural distribution network, traditional local control is difficult to solve the resulting complex distribution network overvoltage problem. Centralized control relies heavily on the system communication level, and there are problems such as high management difficulty and slow response speed. Clustering the distribution network provides a reference for solving the above problems by improving the overall cluster control technology of distributed power sources.

[0003] In a distribution network with a high proportion of household photovoltaics, cluster control and optimization divides complex centralized problems into multiple simplified sub-problems through cluster division for solution, which accelerates the solution process and optimizes the overall control strategy. Cluster control technology mainly involves the selection of cluster division indicators and voltage control. Regarding the selection of indicators, the existing technology starts from a structural perspective and establishes a modularity function by calculating the Euclidean distance between nodes to characterize the electrical distance to divide the number of clusters. The existing technology considers the electrical coupling relationship between nodes and characterizes the electrical distance for cluster division by node voltage sensitivity. The existing technology defines the spatial electrical distance based on the reactive-voltage relationship between all nodes and divides the clusters according to the spatial electrical distance. The above cluster division is mainly based on the establishment of electrical distance based on the system grid structure and network parameters, focusing on the scale of cluster division, and lacks consideration for the adjustable power within the cluster. If the photovoltaic output and load in the system are greatly different, it is easy to have insufficient or excessive adjustable power. To this end, some scholars construct cluster indicators from the perspective of power supply and demand. The prior art proposes a cluster control of "reactive power first, active power later" for distribution networks with a high proportion of distributed photovoltaics, and divides clusters based on active / reactive balance indicators. The prior art proposes to divide clusters by comprehensively considering the structural and power supply and demand relationship, including modularity function and active / reactive balance indicators. However, there are certain limitations to the division of clusters only from a structural or functional perspective. The accuracy after cluster division cannot be guaranteed, which easily causes mutual influence between clusters, resulting in poor voltage control effect of the entire distribution network. For the control of voltage after cluster division, the control means generally include reactive power compensation, reduction of active power output and active-reactive comprehensive regulation. The prior art proposes a cluster voltage coordination control strategy, which can effectively reduce the power generation loss between clusters in an environment with incomplete measurement data. The prior art realizes precise control of the voltage of the distribution network by clustering the distribution network and optimizing reactive power output by Newton method. The prior art aims to minimize photovoltaic power loss and network loss, and designs a double-layer voltage control strategy to effectively adjust the voltage level. However, the current mainstream voltage control methods face challenges in adaptability and resource utilization efficiency. They are highly dependent on the reactive power regulation capability of the system, which may not only lead to unnecessary waste of photovoltaic power generation, but also make it difficult for conventional voltage regulation resources to meet the needs of rapid response when the system encounters disturbances. Energy storage is an important means to solve the problem of new energy consumption in the future. Considering using energy storage as a voltage regulation method, and realizing the voltage, active and reactive power control of the power grid through managing energy storage, it provides a new idea for voltage control after cluster division. Summary of the invention

[0004] In view of the defects and shortcomings of the prior art, the present invention provides a voltage control method for a distribution network containing a high proportion of household photovoltaics based on cluster division.

[0005] In order to achieve the above purpose, the technical solutions provided are as follows:

[0006] A method for controlling voltage of a distribution network containing a high proportion of household photovoltaics based on cluster division is characterized by comprising the following steps:

[0007] Step 1: Cluster division and selection of key control nodes, including cluster comprehensive division indicators, cluster division steps and key control node selection;

[0008] Step 2: voltage control model based on cluster division, including objective function, constraint conditions and model solution;

[0009] Step 3: Voltage control method based on cluster division.

[0010] Preferably, in step 1, the cluster comprehensive division index includes an electrical modularity index, a coupling index, a power balance index and a comprehensive division index;

[0011] The electrical modularity index is defined as follows:

[0012] First, in order to solve the problem of complex network cluster division, the modularity function method is introduced for the scale and structure of the network; the modularity function definition method is as follows:

[0013]

[0014] Where: A ij represents the weight of the edge connecting node i and node j in the network; if node i and node j are connected, then A ij =1; if not connected, then A ij =0; represents the sum of the weights of all edges connected to node i in the network, that is, the degree weighting of node i; Represents the sum of the weights of all edges in the network; δ(i,j) is an indicator function. When nodes i and j in the network belong to the same cluster, δ(i,j) = 1; otherwise, δ(i,j) = 0;

[0015] Then, the electrical distance between nodes in the distribution network is introduced to construct the modularity index. Since the energy storage system is used for voltage regulation, the voltage control is achieved by adjusting the active power of the distribution network. Therefore, when constructing this index, its specific expression is:

[0016] ΔV=S VP ΔP (2)

[0017]

[0018] Where ΔP represents the change in active power injected between nodes, S VP,ijrepresents the sensitivity of the active power injected into node j to the voltage amplitude change of node i, ΔV is the voltage change, d ij is the related term of the ratio of the voltage change at node j to the change at node i when the active power at node j changes;

[0019] Considering that the electrical distance between nodes depends not only on the directly connected nodes but also on all other nodes in the distribution network, assuming that there are n nodes in the distribution network, the electrical distance between node i and node j in the network can be calculated by considering the above factors. The specific expression is as follows:

[0020]

[0021] Where: L ij Represents the electrical distance between node i and node j. The larger its value, the weaker the electrical connection between the two nodes, that is, the greater the electrical distance. When constructing the modularity function, this electrical distance is used as a basis for measuring the closeness between nodes. The larger its value, the smaller the corresponding edge weight in the modularity function.

[0022] Based on this, in order to quantify the degree of coupling between two nodes, the electrical distance is used as the basis to define the partition weight A V,ij ; This weight reflects the strength of the electrical connection between nodes, and its expression is as follows:

[0023]

[0024] Where: L is the electrical distance matrix, from which the modularity index based on electrical distance is obtained;

[0025] The coupling index is defined as:

[0026] The coupling index is an important parameter to measure the degree of electrical connection between nodes in clusters and within clusters. It can further improve the accuracy and precision of cluster division on the basis of traditional modularity function. The larger the index value, the higher the degree of electrical coupling between nodes within the cluster. In order to facilitate cluster operation and regulation, it should be ensured that the coupling between clusters after cluster division is small and the coupling within the cluster is large. In the distribution network, the electrical distance between nodes can represent the degree of electrical coupling between nodes. The electrical distance is used to represent the partition weight, so the partition weight can be used to represent the coupling index. Its expression is as follows:

[0027]

[0028] Where: avg() represents the mean function;

[0029] The power balance index is defined as:

[0030] In the distribution network, with the access of a high proportion of household photovoltaics, the power flow pattern becomes complicated, and significant power reverse flow may occur, accompanied by voltage limit and other problems. In order to ensure the stable operation of the power grid, the power balance problem within each cluster must be considered during the cluster division process, and efforts should be made to reduce unnecessary power reverse flow. To this end, the power balance index is introduced to reflect the state of power balance within the cluster. The larger the value, the higher the degree of power balance within the cluster. Its expression formula is as follows:

[0031] β=(β P +β Q ) / 2 (7)

[0032] Where: β represents the power balance index of the distribution network; β P Represents the total active power balance index in the distribution network system; β Q It indicates the total reactive power balance index of the distribution network system;

[0033] In the power system, active power balance is the key to ensure the stable operation of the system and the quality of power. The active power balance index intuitively reflects the balance between the active power demand and the load in the cluster. Its calculation expression is as follows:

[0034]

[0035] Where: P clu (t) i is the net power characteristic of cluster i, T is the duration of the typical time-varying scenario, and c represents the number of cluster divisions;

[0036] Reactive power balance is crucial to maintaining system voltage stability, reducing line losses, and improving power quality. The reactive power balance index reveals the balance between reactive power demand and load within the cluster, and its expression formula is as follows:

[0037]

[0038] Where: Q s,i With Q n,i represents the maximum reactive power output of the ith cluster and the reactive power demand value within the cluster, Q i is the reactive balance degree of cluster i;

[0039] The comprehensive division index is defined as:

[0040] In the case of high-proportion household photovoltaic access distribution network, a comprehensive division index is proposed by combining the electrical modularity index, coupling index and power balance index. This index takes into account the structure and functionality of the cluster on the basis of ensuring the reasonable size of the cluster and the accuracy of cluster division, and realizes structural flexibility and functional synergy. The comprehensive division index is shown in the following formula:

[0041]

[0042] Where: c represents the number of cluster divisions.

[0043] Preferably, in step 1, the cluster division step is:

[0044] Step 1: Initialize a distribution network cluster containing a high proportion of household photovoltaics and obtain various data of the target distribution network;

[0045] Step 2: Take each node in the distribution network as an independent initial cluster and use formula (11) to calculate the initial comprehensive partition index ρ of node i: im ;

[0046] Step 3: For each node i, select neighboring node j to form a new cluster (i, j), and then recalculate the comprehensive partition index ρ' of the cluster im , by traversing all possible node combinations, calculate Δρ=ρ′ for each combination im -ρ im ,When Δρ reaches the maximum positive value, it indicates that the combination between nodes i and j is optimal and they are divided into the same cluster. Based on this, the cluster division status of the distribution network and the corresponding comprehensive division index are updated;

[0047] Step 4: Treat the newly formed cluster as an independent node and repeat the cluster division process in step 3;

[0048] Step 5: Repeat steps 3 and 4 until there is no node combination in the distribution network that can improve the comprehensive partition index value by merging. At this time, the comprehensive partition index ρ′ im When the maximum value is reached, the clustering process ends.

[0049] Preferably, in step 1, the key control node is selected as a node configured with an energy storage system within each cluster. The energy storage system on a certain node can respond to system changes in the best way to achieve voltage control under the premise of meeting the overall operation requirements of the cluster. The node is defined as a key control node; the key control node mainly adjusts the active power of the distribution network node to achieve distribution network voltage control, reflecting the relationship between active power and voltage, and the voltage-power sensitivity characterizes the change of the voltage of the node at the current location with power injection. Therefore, the key control node within each cluster can be selected according to the voltage-power sensitivity;

[0050] The calculation method of voltage-power sensitivity is mainly to inverse the power flow calculation. In a distribution network with n nodes, based on the equality constraint of the power flow equation, the corresponding voltage-power sensitivity matrix is ​​obtained by inverting the Jacobian matrix. Its expression is as follows:

[0051]

[0052] Where: θ and V are the node voltage phase angle and voltage amplitude respectively; P and Q are the active power and reactive power injected into the node respectively; S en , J are the voltage-power sensitivity matrix and Jacobian matrix respectively; S VP , S VQ , S θP , S θQ They are voltage-active power, voltage-reactive power, phase angle-active power, and phase angle-reactive power sensitivity sub-matrices respectively;

[0053] In a distribution network with a high proportion of household photovoltaics, if a voltage-over-limit cluster contains N nodes after cluster division, of which m (m≤N) nodes are equipped with energy storage systems; the voltage-active sensitivity of each energy storage node in the cluster is calculated according to formula (12), denoted as {S VP,1 ,S VP,2 ,…,S VP,m}, and sort the voltage-active power sensitivity of all energy storage nodes from large to small; at this time, the node with the largest voltage-active power sensitivity is determined as the key control node of the over-limit cluster; in the subsequent cluster voltage control, the energy storage system at the key control node is preferentially selected for charging and discharging.

[0054] Preferably, in step 2, the objective function is to minimize the node voltage deviation and network loss in the entire distribution network, and the objective function can be expressed as:

[0055]

[0056] Where: U i and U jrepresents the voltage at nodes i and j; U0 represents the node voltage reference value, which is expressed in per-unit value for the convenience of calculation in the present invention, U0=1p.u.; G ij and θ ij are the conductance and phase difference angle between nodes i and j respectively;

[0057] The two objective functions are weighted and combined to construct the comprehensive objective function as follows:

[0058] f=αf1+βf2(15)

[0059] Wherein: α and β represent the weights represented by the two objective functions respectively. The present invention stipulates that α=0.7 and β=0.3 respectively according to the importance of the two objective functions.

[0060] Preferably, in step 2, the constraints on the objective function are as follows:

[0061] (1) Power flow constraints

[0062]

[0063] Where: P i and Q i Respectively represent the active power and reactive power at node i; G ij and B ij denote the conductance and susceptance between node i and node j, respectively, θ ij represents the phase difference angle between node i and node j;

[0064] (2) Node voltage upper and lower limit constraints

[0065] U min ≤U≤U max (17)

[0066] Where: U max and U min are the maximum and minimum voltages allowed in the system, U max =1.07pu and U min =0.93pu;

[0067] (3) Branch current constraints

[0068]

[0069] Where: Indicates the maximum value of the branch current connecting node n and node l;

[0070] (4) Energy storage charging and discharging power operation constraints

[0071]

[0072] Where: P max and P min are the maximum and minimum values ​​of energy storage output respectively; SOC t is the state of charge of the energy storage at time t, η is the charging and discharging efficiency of the energy storage, E ESS is the upper limit of energy storage, Δt is the time interval; SOC max and SOC min They are respectively the maximum and minimum values ​​of the energy storage charge state under the guarantee of energy storage service life.

[0073] Preferably, in step 2, a particle swarm optimization algorithm PSO is used to solve the voltage control model based on cluster division, to obtain the optimal action power of each cluster energy storage node, and to realize the voltage control of the distribution network; the steps of solving the model are:

[0074] Step 1: Set the initial position and speed of the particle;

[0075] Step 2: Cluster division is performed according to the comprehensive cluster division index, and the key control nodes in each cluster are selected according to the active voltage sensitivity, thereby setting various parameters in PSO;

[0076] Step 3: Set the particle search range and constraints in the system;

[0077] Step 4, calculate the fitness function f = αf1 + βf2, and determine whether the fitness changes after 15 consecutive iterations. If it changes, jump to step 5, otherwise, jump to step 8;

[0078] Step 5: Find the individual and group fitness values ​​according to the constraints and fitness respectively;

[0079] Step 6: Update the position and velocity of the particles, and update the individual and group fitness values;

[0080] Step 7: Determine the number of iterations. If the maximum number of iterations has not been reached, return to step 4.

[0081] Step 8: Obtain the power of the optimal energy storage action in the cluster to meet the needs of the distribution network.

[0082] Preferably, in step three, the voltage control method based on cluster division is mainly divided into the following two parts:

[0083] (1) Distribution network cluster division: Based on the above comprehensive division indicators and division methods, the distribution network with a high proportion of household photovoltaics is divided into clusters. In addition, the voltage over-limit boundary value is set to 0.93pu~1.07pu, and the real-time load and photovoltaic output data are input into the distribution network after cluster division. The voltage value of each node is obtained through power flow calculation; if there is a node whose voltage exceeds the limit, the cluster to which the node with the voltage over-limit belongs is found and recorded as an adjustable cluster. The results of this part serve as the basis for voltage control based on cluster division;

[0084] (2) Voltage control part: For clusters with voltage exceeding the limit in the distribution network, the voltage-active sensitivity of the energy storage nodes in each cluster is calculated, and the key control nodes of each cluster are selected; the minimum necessary power requirement for the voltage of all nodes in the cluster to be restored to the normal range is solved based on the particle swarm algorithm. After obtaining the power required by each cluster, according to the above-mentioned voltage control model based on cluster division, the charge state of the energy storage system at the key control node is taken into account. When the energy storage in the cluster needs to be charged or discharged, the energy storage system at the key control node in the cluster takes priority; if the capacity of the energy storage system at the key control node in the cluster is insufficient, the energy storage system at other control nodes in the cluster will bear the remaining required power;

[0085] If both positive and negative voltage limits occur within a single cluster, the net charging and discharging demand of the cluster as a whole is determined through power flow calculation. First, power balance is achieved through the coordinated scheduling of the energy storage system within the cluster. If the internal energy storage capacity is insufficient to meet the demand, the remaining power demand is coordinated by adjacent and closely coupled clusters. After each energy storage action, the power flow calculation must be re-performed to verify whether the node voltage has returned to the allowable range.

[0086] The beneficial effects of the present invention are:

[0087] 1. The voltage control method based on cluster division proposed in the present invention divides the distribution network into multiple independent clusters by using comprehensive division indicators, and realizes voltage control by giving priority to energy storage at the key control nodes of each cluster, thereby reducing the complexity of the overall voltage control of the distribution network system and being able to quickly solve problems such as voltage exceeding the limit.

[0088] 2. Aiming at the problem of dividing distribution network clusters with a high proportion of household photovoltaics, the present invention proposes a comprehensive division index. Compared with a single modularity index, the comprehensive index improves the division effect by 22.2%, the intra-cluster coupling index by 12.66%, and the power balance index by 26.56%. After using this comprehensive division index to divide the distribution network clusters, the resulting cluster size is reasonable, and the power distribution within the cluster tends to be balanced.

[0089] 3. By comparing the voltage control method without cluster division, the proposed method has obvious effects in terms of overall voltage deviation, system network loss and system optimization and control time. Specifically, the overall voltage deviation is reduced by 41.47%, the system network loss is reduced by 13.76%, and the system optimization and control time is increased by 42.22%, which verifies the effectiveness of the proposed method. BRIEF DESCRIPTION OF THE DRAWINGS

[0090] Figure 1 It is a flow chart of cluster partitioning;

[0091] Figure 2 It is the PSO algorithm flow chart;

[0092] Figure 3 It is a voltage control method based on cluster division;

[0093] Figure 4 It is the IEEE33 node photovoltaic and energy storage access topology diagram;

[0094] Figure 5 It is a comparison chart of various indicators of cluster division results;

[0095] Figure 6 This is the result diagram of IEEE33 node clustering based on comprehensive indicators;

[0096] Figure 7 This is a comparison chart of voltage control effects at 13:00;

[0097] Figure 8 It is the energy storage action status at the key control nodes of each cluster;

[0098] Fig. 9 It is the network loss situation throughout the day after voltage control. DETAILED DESCRIPTION

[0099] 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.

[0100] Example 1 Cluster division and selection of key control nodes

[0101] 1.1 Cluster comprehensive division indicators

[0102] In this paper, the selection of cluster division indicators in the distribution network with a high proportion of household photovoltaic access is mainly considered, and the electrical modularity index, coupling index and power balance index are considered. The electrical modularity index mainly measures the structural strength of the distribution network to ensure the rationality of the cluster division scale, and avoids the difficulty of voltage control after the cluster division scale is unbalanced. However, in the distribution network with a high proportion of household photovoltaic access, it is extremely unreasonable to only consider the structural structure of the distribution network for cluster division. The accuracy after cluster division should also be considered to achieve a larger coupling degree within the cluster and a smaller coupling degree between clusters. For this purpose, the coupling index is introduced. At the same time, the present invention mainly uses the charging and discharging of energy storage for voltage control, increases the power balance index, characterizes the power balance ability within each cluster, and prevents insufficient or excessive adjustable power and power return within the cluster. Combining the above indicators, a cluster comprehensive division index is constructed to cluster the distribution network containing a high proportion of household photovoltaics.

[0103] 1.1.1 Electrical modularity index

[0104] In order to solve the problem of cluster division in complex networks, Girvan and Newman introduced a modularity function method for the size and structure of the network.

[23] The modularity function is defined as follows:

[0105]

[0106] Where: A ij represents the weight of the edge connecting node i and node j in the network. If node i and node j are connected, then A ij =1; if not connected, then A ij =0; represents the sum of the weights of all edges connected to node i in the network, that is, the degree weighting of node i; It represents the sum of the weights of all edges in the network. δ(i,j) is an indicator function. When nodes i and j in the network belong to the same cluster, δ(i,j)=1; otherwise, δ(i,j)=0.

[0107] However, relying solely on the topological relationship of the distribution network to evaluate the structural performance of the cluster has limitations because it ignores the key electrical connections between cluster nodes.

[24] To this end, the present invention proposes to introduce the electrical distance between nodes in the distribution network to construct a modularity index. Since the present invention uses an energy storage system for voltage regulation and realizes voltage control by adjusting the active power of the distribution network, the specific expression when constructing this index is:

[0108] ΔV=S VP ΔP(2)

[0109]

[0110] Where ΔP represents the change in active power injected between nodes, S VP,ij represents the sensitivity of the active power injected into node j to the voltage amplitude change of node i, ΔV is the voltage change, d ij It is the related term of the ratio of the voltage change of node j to the change of node i when the active power of node j changes.

[0111] Given that the electrical distance between nodes is not only determined by the directly connected nodes, but also by all other nodes in the distribution network

[25] Assuming that there are n nodes in the distribution network, the electrical distance between node i and node j in the network can be calculated considering the above factors. The specific expression is as follows:

[0112]

[0113] Where: L ij Represents the electrical distance between node i and node j. The larger its value, the weaker the electrical connection between the two nodes, that is, the greater the electrical distance. When constructing the modularity function, this electrical distance is used as a basis for measuring the closeness between nodes. The larger its value, the smaller the corresponding edge weight in the modularity function.

[0114] Based on this, in order to quantify the degree of coupling between two nodes, we use the electrical distance as the basis to define the partition weight A V,ij This weight reflects the strength of the electrical connection between nodes, and its expression is as follows:

[0115]

[0116] Where: L is the electrical distance matrix, from which the modularity index based on electrical distance is obtained.

[0117] 1.1.2 Coupling index

[0118] The coupling index is an important parameter to measure the degree of electrical connection between nodes in clusters and within clusters. It can further improve the accuracy and precision of cluster division based on the traditional modularity function.

[15] . The larger the index value, the higher the electrical coupling degree between nodes within the cluster. To facilitate cluster operation and regulation, it should be ensured that the coupling degree between clusters is small after cluster division, and the coupling degree within the cluster is large. In the distribution network, the electrical distance between nodes can represent the electrical coupling degree between nodes. In the above text, the electrical distance is used to represent the partition weight, so the partition weight can be used to represent the coupling index. The expression is as follows:

[0119]

[0120] Where: avg() represents the average function

[0121] 1.1.3 Power balance index

[0122] In the distribution network, with the access of a high proportion of household photovoltaics, the power flow pattern becomes complicated, and significant power reverse flow may occur, accompanied by voltage limit and other problems. In order to ensure the stable operation of the power grid, the power balance problem within each cluster must be considered during the cluster division process, and efforts should be made to reduce unnecessary power reverse flow. To this end, the power balance index is introduced to reflect the state of power balance within the cluster. The larger the value, the higher the degree of power balance within the cluster.

[14] The expression formula is as follows:

[0123] β=(β P +β Q ) / 2(7)

[0124] Where: β represents the power balance index of the distribution network; β P Represents the total active power balance index in the distribution network system; β Q It indicates the total reactive power balance index of the distribution network system;

[0125] In the power system, active power balance is the key to ensure the stable operation of the system and the quality of power. The active power balance index intuitively reflects the balance between the active power demand and the load in the cluster. Its calculation expression is as follows:

[0126]

[0127] Where: P clu (t) i is the net power characteristic of cluster i, T is the duration of a typical time-varying scenario, and c is the number of cluster divisions

[0128] Reactive power balance is crucial to maintaining system voltage stability, reducing line losses, and improving power quality. The reactive power balance index reveals the balance between reactive power demand and load within the cluster, and its expression formula is as follows:

[0129]

[0130] Where: Q s,i With Q n,i represents the maximum reactive power output of the ith cluster and the reactive power demand value within the cluster, Q i is the reactive balance degree of cluster i.

[0131] 1.1.4 Comprehensive classification indicators

[0132] In the case of high-proportion household photovoltaic access distribution network, the present invention proposes a comprehensive division index by combining the electrical modularity index, coupling index and power balance index. This index takes into account the structure and functionality of the cluster on the basis of ensuring the reasonable cluster scale and cluster division accuracy, and realizes structural flexibility and functional synergy. The comprehensive division index is shown in the following formula:

[0133]

[0134] Where: c represents the number of cluster divisions

[0135] 1.2 Clustering steps

[0136] The above comprehensive classification indicators are used to cluster the distribution network with a high proportion of household photovoltaic access. The cluster division process is as follows: Figure 1 As shown:

[0137] Step 1: Initialize the distribution network cluster with a high proportion of household photovoltaics and obtain various data of the target distribution network.

[0138] Step 2: Treat each node in the distribution network as an independent initial cluster and use formula (11) to calculate the initial comprehensive partition index ρ of node i: im .

[0139] Step 3: For each node i, select neighboring node j and combine them into a new cluster (i, j), and then recalculate the comprehensive partition index ρ' of the cluster. im By traversing all possible node combinations, we calculate Δρ=ρ′ for each combination. im -ρ im When Δρ reaches the maximum positive value, it indicates that the combination between nodes i and j is optimal and they are divided into the same cluster. Based on this, the cluster division status of the distribution network and the corresponding comprehensive division index are updated.

[0140] Step 4: Treat the newly formed cluster as an independent node and repeat the cluster division process in step 3.

[0141] Step 5: Repeat steps 3 and 4 until there is no node combination in the distribution network that can improve the comprehensive partition index value by merging. At this time, the comprehensive partition index ρ′ im When the maximum value is reached, the clustering process ends.

[0142] 1.3 Selection of key control nodes

[0143] In the present invention, the voltage control of a distribution network containing a high proportion of household photovoltaic power is mainly achieved by regulating the charging and discharging of the internal energy storage of each cluster. However, after the clusters are divided in the actual distribution network, the positions of the energy storage systems configured in each cluster are different and the number is not unique. The response speeds of regulating the energy storage systems in different positions to the voltage control of the distribution network are different. Therefore, selecting the most appropriate energy storage system action in the nodes containing the energy storage system can control the voltage more quickly and ensure the power quality of the entire distribution network. In the present invention, for each node configured with an energy storage system in each cluster, the energy storage system on a certain node can respond to system changes in the best way to achieve voltage control while meeting the overall operation requirements of the cluster. This node is defined as a key control node. The key control node mainly adjusts the active power of the distribution network node to achieve voltage control of the distribution network, reflecting the relationship between active power and voltage. The voltage-power sensitivity characterizes the change of the voltage of the node at the current position with power injection.

[26] ,Therefore, the key control nodes within each cluster can be selected according to the voltage-power sensitivity.

[0144] The calculation method of voltage-power sensitivity is mainly to inverse the power flow calculation. In a distribution network with n nodes, based on the equality constraint of the power flow equation, the corresponding voltage-power sensitivity matrix is ​​obtained by inverting the Jacobian matrix, and its expression is as follows:

[0145]

[0146] Where: θ and V are the node voltage phase angle and voltage amplitude respectively; P and Q are the active power and reactive power injected into the node respectively; S en , J are the voltage-power sensitivity matrix and Jacobian matrix respectively; S VP , S VQ , S θP , S θQ They are voltage-active power, voltage-reactive power, phase angle-active power, and phase angle-reactive power sensitivity sub-matrices respectively.

[0147] In a distribution network with a high proportion of household photovoltaics, if a voltage-limited cluster contains N nodes after cluster division, of which m (m≤N) nodes are equipped with energy storage systems. The voltage-active sensitivity of each energy storage node in the cluster is calculated according to formula (12), denoted as {S VP,1 ,S VP,2 ,…,S VP,m}, and sort the voltage-active sensitivity of all energy storage nodes from large to small. At this time, the node with the maximum voltage-active sensitivity is determined as the key control node of the over-limit cluster. In the subsequent cluster voltage control, the energy storage system at the key control node is preferentially selected for charging and discharging.

[0148] Example 2 Voltage control model based on cluster division

[0149] In order to solve the voltage over-limit problem caused by high proportion of household photovoltaic access to the distribution network, a voltage control model based on cluster division is constructed based on the results of cluster division. The model takes the voltage deviation and network loss in the distribution network system as the objective function, and considers the power flow, node voltage upper and lower limits, branch current and energy storage charging and discharging power operation constraints to achieve distribution network voltage control.

[0150] 2.1 Objective Function

[0151] The objective function of the present invention is to minimize the node voltage deviation and network loss in the entire distribution network, and the objective function can be expressed as:

[0152]

[0153] Where: U i and U j represents the voltage at nodes i and j; U0 represents the node voltage reference value, which is expressed in per-unit value for the convenience of calculation in the present invention, U0=1p.u.; G ij and θ ij are the conductance and phase difference angle between nodes i and j respectively.

[0154] The two objective functions are weighted and combined to construct the comprehensive objective function as follows:

[0155] f=αf1+βf2(14)

[0156] Wherein: α and β represent the weights represented by the two objective functions respectively. The present invention stipulates that α=0.7 and β=0.3 respectively according to the importance of the two objective functions.

[0157] 2.2 Constraints

[0158] According to the actual operation of the system, the constraints of the objective function of the present invention are as follows:

[0159] (1) Power flow constraints

[0160]

[0161] Where: P i and Q i Respectively represent the active power and reactive power at node i; G ij and B ij denote the conductance and susceptance between node i and node j, respectively, θ ij Represents the phase difference angle between node i and node j.

[0162] (2) Node voltage upper and lower limit constraints

[0163] U min ≤U≤U max (16)

[0164] Where: U max and U min are the maximum and minimum voltages allowed in the system, respectively. In the present invention, U max =1.07pu and

[0165] U min =0.93pu

[0166] (3) Branch current constraints

[0167]

[0168] Where: Indicates the maximum value of the branch current connecting node n and node l.

[0169] (4) Energy storage charging and discharging power operation constraints

[0170]

[0171] Where: P max and P min are the maximum and minimum values ​​of energy storage output respectively; SOC t is the state of charge of the energy storage at time t, η is the charging and discharging efficiency of the energy storage, E ESS is the upper limit of energy storage, Δt is the time interval; SOC max and SOC min They are respectively the maximum and minimum values ​​of the energy storage charge state under the guarantee of energy storage service life.

[0172] 2.3 Model solution

[0173] The particle swarm optimization algorithm (PSO) is used to solve the voltage control model based on cluster division, and the optimal action power of each cluster energy storage node is obtained to achieve voltage control of the distribution network. Figure 2 As shown:

[0174] Step 1: Set the initial position and speed of the particle;

[0175] Step 2: Cluster division is performed according to the comprehensive cluster division index, and the key control nodes in each cluster are selected according to the active voltage sensitivity, thereby setting various parameters in PSO;

[0176] Step 3: Set the particle search range and constraints in the system;

[0177] Step 4: Calculate the fitness function f = αf1 + βf2, and determine whether the fitness changes after 15 consecutive iterations. If it changes, jump to step 5, otherwise, jump to step 8;

[0178] Step 5: Find the individual and group fitness values ​​according to the constraints and fitness respectively;

[0179] Step 6: Update the position and velocity of the particles, and update the individual and group fitness values;

[0180] Step 7: Determine the number of iterations. If the maximum number of iterations has not been reached, return to step 4.

[0181] Step 8: Obtain the power of the optimal energy storage action in the cluster to meet the distribution network requirements.

[0182] Example 3 Voltage control method based on cluster division

[0183] In the present invention, after cluster division, the energy storage system at the key control node is preferentially selected for charging and discharging, so as to realize voltage control. The voltage control method is as follows: Figure 3 As shown:

[0184] The voltage control method based on cluster division is mainly divided into the following two parts:

[0185] (1) Distribution network cluster division: Based on the above comprehensive division indicators and division methods, the distribution network with a high proportion of household photovoltaics is divided into clusters. In addition, the voltage over-limit boundary value is set to 0.93pu~1.07pu, and the real-time load and photovoltaic output data are input into the distribution network after cluster division. The voltage value of each node is obtained through power flow calculation. If there is a node whose voltage exceeds the limit, find the cluster to which the node with the voltage over-limit belongs and record it as an adjustable cluster. The results of this part serve as the basis for voltage control based on cluster division.

[0186] (2) Voltage control part: For clusters with voltage exceeding the limit in the distribution network, the voltage-active sensitivity of the energy storage nodes in each cluster is calculated, and the key control nodes of each cluster are selected. The minimum necessary power requirement for the voltage of all nodes in the cluster to return to the normal range is solved based on the particle swarm algorithm. After obtaining the power required by each cluster, according to the above-mentioned voltage control model based on cluster division, taking into account the charge state of the energy storage system at the key control node, when the energy storage in the cluster needs to be charged and discharged, the energy storage system at the key control node in the cluster takes priority. If the capacity of the energy storage system at the key control node in the cluster is insufficient, the energy storage system at other control nodes in the cluster will bear the remaining required power.

[0187] If both positive and negative voltage limits coexist within a single cluster, the net value of the cluster's overall charging and discharging demand is determined through power flow calculation. First, power balance is achieved through the coordinated scheduling of the energy storage system within the cluster; if the internal energy storage capacity is insufficient to meet the demand, the remaining power demand is coordinated by adjacent and closely coupled clusters. After each energy storage action, the power flow calculation must be re-performed to verify whether the node voltage has returned to the allowable range.

[0188] Example 4 Analysis

[0189] Take the distribution network of IEEE33 nodes connected to household photovoltaic (DPV) and energy storage system (ESS) as an example. Figure 4 As shown. Among them, bus 0 is the reference node, the number of load nodes is 32, the number of DPVs is 15, and the number of ESSs is 11. All nodes in the system are considered to be connected to time-varying loads, the system reference voltage is 10kV, and the reference capacity is 10MV.A. The energy storage configuration capacity is 400kW, the charge state range of the energy storage is 0.2~0.9, and the initial energy storage setting value is 0.5. The data of household photovoltaics comes from the corresponding photovoltaic output data on sunny days in a certain area in the summer of a certain year.

[0190] In this network, the household photovoltaic installation capacity is shown in Table 1:

[0191] Table 1 Household photovoltaic installation capacity

[0192]

[0193]

[0194] 4.1 Analysis of cluster division results

[0195] In order to illustrate the effectiveness of the comprehensive cluster division index proposed by the present invention that considers the electrical modularity index, coupling index and power balance index, two methods are used for cluster division, and the division results are compared and analyzed. Method 1 is used as a benchmark. Its cluster division index only focuses on electrical modularity, ignoring the degree of coupling between clusters and the balance of power supply and demand; while Method 2 adopts the comprehensive division index proposed by the present invention, comprehensively considering the three dimensions of electrical characteristics, system coupling and power balance. The results are shown in Table 2. In order to facilitate a more intuitive observation and comparison of the data, the data of each indicator obtained by the two schemes are plotted for comparison, as shown in Table 2. Figure 4 As shown:

[0196] Table 2 Impact of indicator type on cluster division

[0197]

[0198] Depend on Figure 5It can be seen that the number of clusters obtained by considering only a single electrical modularity index is 7, while the number of clusters obtained by using the comprehensive partitioning index proposed by the present invention is 6. Although the modularity obtained under the comprehensive partitioning index decreases by 1.39%, the ρ obtained by the partitioning is im ,γ,β indicators have all been greatly improved. Among them, the comprehensive division index ρ im The clustering index γ increased by 22.2%, the intra-cluster coupling index γ increased by 12.66%, and the power balance index β increased by 26.56%. It can be seen that the comprehensive division index proposed in the present invention can ensure that the intra-cluster coupling is stronger, the inter-cluster coupling is weaker, and the power distribution of each cluster is more balanced while taking into account the cluster scale. This shows that the present invention has a good clustering effect. The cluster division results are shown in Figure 2. Figure 6 As shown:

[0199] At the same time, after cluster division, the key control nodes within each cluster need to be selected to facilitate subsequent voltage control. The key control nodes within each cluster are selected based on the active-voltage sensitivity. The calculation results of the active-voltage sensitivity of the energy storage nodes within each cluster are shown in Table 3:

[0200] Table 3 Calculation results of active power-voltage sensitivity of energy storage nodes within each cluster

[0201]

[0202] According to the above calculation results, the energy storage nodes in each cluster are ranked, and nodes 2, 20, 7, 28, 9, and 14 are selected as key control nodes and are given priority for charging and discharging.

[0203] 4.2 Voltage control effect analysis

[0204] After the cluster division results are determined, the method proposed in the present invention is used to control the voltage of the distribution network. Among them, the acceleration constants c1 and c2 in the basic parameters of PSO are both set to 2, the number of individual scales N is set to 20, and the number of iterations M is set to 50.

[0205] In the case of the same access of photovoltaic and energy storage, in order to verify the effectiveness of the method proposed in the present invention, the present invention adopts: 1) without dividing the distribution network clusters in advance, the particle swarm algorithm is used to determine the energy storage and power that need to be activated in the distribution network, and the over-limit voltage of the distribution network is adjusted on the spot through the energy storage action; 2) the voltage control method proposed in the article, first cluster the distribution network according to the comprehensive index of cluster division, and then determine the key control nodes in each cluster, and determine the optimal action power of the energy storage that minimizes the voltage deviation and network loss in the distribution network through the particle swarm algorithm. In order to show the optimization effect of voltage over-limit risk, both schemes select the typical scene at 13:00 when the DPV output is the largest for analysis.

[0206] First, when there is no active voltage regulation equipment involved in the distribution network, the power flow calculation is performed according to the distribution network topology related parameters to obtain the voltage curve without optimization in the IEEE33 node, that is, without any voltage regulation. Secondly, the voltage curves of each node without cluster division and cluster division are calculated respectively, such as Figure 7 shown.

[0207] By comparing and analyzing the three curves, it can be seen that when the photovoltaic output is the largest at 13:00, the distribution network seriously exceeds the upper limit under the unregulated voltage, and the overall voltage of each node in the middle has a large deviation from the reference voltage, with a maximum of 0.1128pu. After optimizing and regulating the voltage through the particle swarm optimization algorithm, both the non-cluster division and the cluster division method proposed in the present invention can ensure that the voltage does not exceed the limit. However, the maximum overall deviation between each node and the reference voltage under the non-cluster division is 0.0258pu, while the maximum overall deviation between each node and the reference voltage in the cluster division method proposed in the present invention is 0.0151pu. This is because Scheme 1 cannot accurately allocate voltage regulation tasks, which may affect the voltage of other nodes when the energy storage system is in action. The voltage control method based on cluster division proposed in the present invention first performs reasonable cluster division on the distribution network and divides the distribution network into several independent control units. When the voltage exceeds the limit, the power required by the distribution network is locally consumed by the key control nodes and other control nodes within each cluster, reducing the power flow and mutual influence across clusters. After each cluster energy storage action, the flow calculation will be re-performed to determine the impact of this energy storage action on the voltage of other nodes inside and outside the cluster, avoiding unnecessary interference to the voltage stability of other clusters, thereby effectively preventing the occurrence of secondary voltage over-limit phenomenon. In addition, when cluster division is not performed, the calculation time for the distribution network voltage optimization control is 23.1396s, while the voltage control time using the method of the present invention is 13.3687s, and the calculation time is increased by 42.22%, which greatly reduces the system optimization time.

[0208] At the same time, in order to better observe the voltage control process of the method proposed in the present invention, the energy storage action at the key control nodes of each cluster after cluster division is as follows: Figure 8 In the figure, negative values ​​represent charging of the energy storage system, and positive values ​​represent discharging of the energy storage system.

[0209] Figure 8It can be seen that during the daytime peak period from 11:00 to 17:00, due to sufficient sunlight, household photovoltaics are in an efficient power generation state. In order to balance the node overvoltage phenomenon caused by household photovoltaic output, after the cluster division, the key control nodes play an important role in regulating the grid voltage and balancing supply and demand. During this period, the energy storage system at the key control node is flexibly charged according to the power required by each cluster. In particular, at 13:00, the photovoltaic output reaches its peak, and the energy storage at the key control node is adjusted to the maximum charging power accordingly, efficiently absorbing excess electricity and balancing the supply and demand of the grid.

[0210] During the late night period from 23:00 to 6:00, when the grid load is low and the nighttime electricity price is favorable, the energy storage at the key control nodes is charged. This not only reduces the reverse flow of the power grid at night, but also improves the economic benefits of the energy storage system, and prepares energy reserves for the subsequent morning peak electricity consumption. In the two periods from 7:00 to 10:00 and from 18:00 to 22:00, household photovoltaics are in a period of low or no output. At this time, the energy storage at each key control node is discharged according to the power required by each cluster to meet the electricity demand during the peak load period, and reduce dependence on the main grid power, enhancing the self-sufficiency and resilience of the local power grid. This flexible energy storage scheduling strategy not only ensures the reliability and stability of power supply, but also effectively promotes the comprehensive utilization and optimal allocation of energy.

[0211] 4.3 Network loss results analysis

[0212] Controlling the energy storage action can reduce the network loss of the distribution network system. By comparing the network loss without cluster division and the cluster division method proposed by the present invention, the network loss situation for 24 hours a day is obtained as follows: Fig. 9 shown.

[0213] It can be seen from the figure that during the whole day, the network loss without cluster division is 3.5343MW, while the network loss of the system after cluster division of the present invention is 3.048MW, and the network loss is reduced by 13.76%. At the same time, at 13:00, the network loss under the method proposed by the present invention is significantly reduced than that without cluster division. The network loss of the two schemes is not much different in some time periods, but the network loss is quite different during the peak period of household photovoltaic output or the period of large load. This is because when the two schemes have basically the same energy storage voltage regulation principle, the effects shown in the scenario of small voltage regulation pressure are often not much different. The basic function of the energy storage system, that is, charging and discharging to adjust the voltage according to the needs of the power grid, can be effectively exerted, and can better maintain the stable operation of the power grid. When household photovoltaics are at the peak of output or the load is large, Scheme 2, on the basis of cluster division, controls the power flow in the distribution network more finely and effectively. Through cluster division, the distribution network is divided into several relatively independent areas, and each cluster can achieve power balance and absorption, reducing unnecessary power transmission between clusters and further reducing network losses. The above conclusions all confirm that when the method of the present invention is used for voltage control, the operating economy of the system can be maintained at a good level while solving the voltage over-limit problem.

[0214] In order to solve the problem of voltage over-limit in the distribution network with high proportion of household photovoltaic access, the present invention proposes a voltage control method based on cluster division. After simulation verification, the following conclusions are obtained:

[0215] 1. The voltage control method based on cluster division proposed in the present invention divides the distribution network into multiple independent clusters by using comprehensive division indicators, and realizes voltage control by giving priority to energy storage at the key control nodes of each cluster, thereby reducing the complexity of the overall voltage control of the distribution network system and being able to quickly solve problems such as voltage exceeding the limit.

[0216] 2. Aiming at the problem of dividing distribution network clusters with a high proportion of household photovoltaics, the present invention proposes a comprehensive division index. Compared with a single modularity index, the comprehensive index improves the division effect by 22.2%, the intra-cluster coupling index by 12.66%, and the power balance index by 26.56%. After using this comprehensive division index to divide the distribution network clusters, the resulting cluster size is reasonable, and the power distribution within the cluster tends to be balanced.

[0217] 3. By comparing the voltage control method without cluster division, the proposed method has obvious effects in terms of overall voltage deviation, system network loss and system optimization and control time. Specifically, the overall voltage deviation is reduced by 41.47%, the system network loss is reduced by 13.76%, and the system optimization and control time is increased by 42.22%, which verifies the effectiveness of the proposed method.

[0218] It will be apparent to those skilled in the art that the invention is not limited to the details of the exemplary embodiments described above and that the invention can be implemented in other specific forms without departing from the spirit or essential features of the invention. Therefore, the embodiments should be considered exemplary and non-limiting in all respects, and the scope of the invention is defined by the appended claims rather than the foregoing description, and it is intended that all variations falling within the meaning and scope of the equivalent elements of the claims be included in the invention. Any reference numeral in a claim should not be considered as limiting the claim to which it relates.

Claims

1. A voltage control method for a distribution network containing a high proportion of household photovoltaics based on cluster division, characterized in that: The steps include: Step 1: Cluster division and selection of key control nodes, including cluster comprehensive division indicators, cluster division steps and key control node selection; Step 2: voltage control model based on cluster division, including objective function, constraint conditions and model solution; Step 3: Voltage control method based on cluster division.

2. The method for controlling voltage of a distribution network containing a high proportion of household photovoltaic power generation based on cluster division according to claim 1 is characterized in that: In step 1, the cluster comprehensive division index includes an electrical modularity index, a coupling index, a power balance index and a comprehensive division index; The electrical modularity index is defined as follows: First, in order to solve the problem of complex network cluster division, the modularity function method is introduced for the scale and structure of the network; the modularity function definition method is as follows: Where: A ij Represents the weight of the edge connecting node i and node j in the network; If node i is connected to node j, then A ij =1; if not connected, then A ij =0; represents the sum of the weights of all edges connected to node i in the network, that is, the degree weighting of node i; Represents the sum of the weights of all edges in the network; δ(i,j) is the indicator function. When nodes i and j in the network belong to the same cluster, δ(i,j)=1; Otherwise, δ(i,j)=0; Then, the electrical distance between nodes in the distribution network is introduced to construct the modularity index. Since the energy storage system is used for voltage regulation, the voltage control is achieved by adjusting the active power of the distribution network. Therefore, when constructing this index, its specific expression is: ΔV=S VP ΔP (2) Where ΔP represents the change in active power injected between nodes, S VP,ij represents the sensitivity of the active power injected into node j to the voltage amplitude change of node i, ΔV is the voltage change, d ij is the related term of the ratio of the voltage change at node j to the change at node i when the active power at node j changes; Considering that the electrical distance between nodes depends not only on the directly connected nodes but also on all other nodes in the distribution network, assuming that there are n nodes in the distribution network, the electrical distance between node i and node j in the network can be calculated by considering the above factors. The specific expression is as follows: Where: L ij Represents the electrical distance between node i and node j. The larger its value, the weaker the electrical connection between the two nodes, that is, the greater the electrical distance. When constructing the modularity function, this electrical distance is used as a basis for measuring the closeness between nodes. The larger its value is, the smaller the corresponding edge weight is in the modularity function; Based on this, in order to quantify the degree of coupling between two nodes, the electrical distance is used as the basis to define the partition weight A V,ij ; This weight reflects the strength of the electrical connection between nodes, and its expression is as follows: Where: L is the electrical distance matrix, from which the modularity index based on electrical distance is obtained; The coupling index is defined as: The coupling index is an important parameter to measure the degree of electrical connection between nodes in clusters and within clusters. It can further improve the accuracy and precision of cluster division on the basis of traditional modularity function. The larger the index value, the higher the degree of electrical coupling between nodes within the cluster. In order to facilitate cluster operation and regulation, it should be ensured that the coupling between clusters after cluster division is small and the coupling within the cluster is large. In the distribution network, the electrical distance between nodes can represent the degree of electrical coupling between nodes. The electrical distance is used to represent the partition weight, so the partition weight can be used to represent the coupling index. Its expression is as follows: Where: avg() represents the mean function; The power balance index is defined as: In the distribution network, with the access of a high proportion of household photovoltaics, the power flow pattern becomes complicated, and significant power reverse flow may occur, accompanied by problems such as voltage exceeding the limit. In order to ensure the stable operation of the power grid, the power balance problem within each cluster must be considered during the cluster division process, and efforts should be made to reduce unnecessary power reverse flow. To this end, the power balance index is introduced to reflect the state of power balance within the cluster. The larger the value, the higher the degree of power balance within the cluster. Its expression formula is as follows: β＝(β P +β Q ) / 2 (7) Where: β represents the power balance index of the distribution network; β P Represents the total active power balance index in the distribution network system; β Q It indicates the total reactive power balance index of the distribution network system; In the power system, active power balance is the key to ensure the stable operation of the system and the quality of power. The active power balance index intuitively reflects the balance between the active power demand and the load in the cluster. Its calculation expression is as follows: Where: P clu (t) i is the net power characteristic of cluster i, T is the duration of the typical time-varying scenario, and c represents the number of cluster divisions; Reactive power balance is crucial to maintaining system voltage stability, reducing line losses, and improving power quality. The reactive power balance index reveals the balance between reactive power demand and load within the cluster. Its expression formula is as follows: Where: Q s,i With Q n,i represents the maximum reactive power output of the ith cluster and the reactive power demand value within the cluster, Q i is the reactive balance degree of cluster i; The comprehensive division index is defined as: In the case of high-proportion household photovoltaic access distribution network, a comprehensive division index is proposed by combining the electrical modularity index, coupling index and power balance index. This index takes into account the structure and functionality of the cluster on the basis of ensuring the reasonable size of the cluster and the accuracy of cluster division, and realizes structural flexibility and functional synergy. The comprehensive division index is shown in the following formula: Where: c represents the number of cluster divisions.

3. The method for controlling voltage of a distribution network containing a high proportion of household photovoltaic power generation based on cluster division according to claim 1 is characterized in that: In step 1, the cluster division step is: Step 1: Initialize a distribution network cluster containing a high proportion of household photovoltaics and obtain various data of the target distribution network; Step 2: Take each node in the distribution network as an independent initial cluster and use formula (11) to calculate the initial comprehensive partition index ρ of node i: im ; Step 3: For each node i, select neighboring node j to form a new cluster (i, j), and then recalculate the comprehensive partition index ρ' of the cluster im , by traversing all possible node combinations, calculating Δρ = ρ for each combination i ' m -ρ im ,When Δρ reaches the maximum positive value, it indicates that the combination between nodes i and j is optimal and they are divided into the same cluster. Based on this, the cluster division status of the distribution network and the corresponding comprehensive division index are updated; Step 4: Treat the newly formed cluster as an independent node and repeat the cluster division process in step 3; Step 5: Repeat steps 3 and 4 until there is no node combination in the distribution network that can improve the comprehensive partition index value by merging. At this time, the comprehensive partition index ρ i ' m When the maximum value is reached, the clustering process ends.

4. The method for controlling voltage of a distribution network containing a high proportion of household photovoltaic power generation based on cluster division according to claim 1 is characterized in that: In step 1, the key control node is selected as a node configured with an energy storage system in each cluster. The energy storage system on a node can respond to system changes in an optimal way and realize voltage control under the premise of meeting the overall operation requirements of the cluster. This node is defined as a key control node; The key control nodes are mainly used to adjust the active power of the distribution network nodes to achieve voltage control of the distribution network, reflecting the relationship between active power and voltage. The voltage-power sensitivity characterizes the change of the voltage of the current node with power injection. Therefore, the key control nodes within each cluster can be selected according to the voltage-power sensitivity. The calculation method of voltage-power sensitivity is mainly to inverse the power flow calculation. In a distribution network with n nodes, based on the equality constraint of the power flow equation, the corresponding voltage-power sensitivity matrix is ​​obtained by inverting the Jacobian matrix. Its expression is as follows: Where: θ and V are the node voltage phase angle and voltage amplitude respectively; P and Q are the active power and reactive power injected into the node respectively; S en , J are the voltage-power sensitivity matrix and Jacobian matrix respectively; S VP , S VQ , S θP , S θQ They are voltage-active power, voltage-reactive power, phase angle-active power, and phase angle-reactive power sensitivity sub-matrices respectively; In a distribution network with a high proportion of household photovoltaics, if a voltage-over-limit cluster contains N nodes after cluster division, of which m (m≤N) nodes are equipped with energy storage systems; the voltage-active sensitivity of each energy storage node in the cluster is calculated according to formula (12), denoted as {S VP,1 ,S VP,2 ,…,S VP,m }, and sort the voltage-active power sensitivity of all energy storage nodes from large to small; at this time, the node with the largest voltage-active power sensitivity is determined as the key control node of the over-limit cluster; in the subsequent cluster voltage control, the energy storage system at the key control node is preferentially selected for charging and discharging.

5. The method for controlling voltage of a distribution network containing a high proportion of household photovoltaic power generation based on cluster division according to claim 1, characterized in that: In step 2, the objective function is to minimize the node voltage deviation and network loss in the entire distribution network. The objective function can be expressed as: Where: U i and U j represents the voltage at nodes i and j; U0 represents the node voltage reference value, which is expressed in per-unit value for the convenience of calculation in the present invention, U0=1p.u.; G ij and θ ij are the conductance and phase difference angle between nodes i and j respectively; The two objective functions are weighted and combined to construct the comprehensive objective function as follows: f=αf1+βf2 (15) Wherein: α and β represent the weights represented by the two objective functions respectively. The present invention stipulates that α=0.7 and β=0.3 respectively according to the importance of the two objective functions.

6. The method for controlling voltage of a distribution network containing a high proportion of household photovoltaic power generation based on cluster division according to claim 1, characterized in that: In step 2, the constraints on the objective function are as follows: (1) Power flow constraints Where: P i and Q i Respectively represent the active power and reactive power at node i; G ij and B ij denote the conductance and susceptance between node i and node j, respectively, θ ij represents the phase difference angle between node i and node j; (2) Node voltage upper and lower limit constraints IN min ≤U≤U max (17) Where: U max and U min are the maximum and minimum voltages allowed in the system, U max =1.07pu and U min =0.93pu; (3) Branch current constraints Where: Indicates the maximum value of the branch current connecting node n and node l; (4) Energy storage charging and discharging power operation constraints Where: P max and P min are the maximum and minimum values ​​of energy storage output respectively; SOC t is the state of charge of the energy storage at time t, η is the charging and discharging efficiency of the energy storage, E ESS is the upper limit of energy storage, Δt is the time interval; SOC max and SOC min They are respectively the maximum and minimum values ​​of the energy storage charge state under the guarantee of energy storage service life.

7. The method for controlling voltage of a distribution network containing a high proportion of household photovoltaic power generation based on cluster division according to claim 1, characterized in that: In step 2, the particle swarm optimization algorithm PSO is used to solve the voltage control model based on cluster division, and the optimal action power of each cluster energy storage node is obtained to realize the voltage control of the distribution network; the steps of solving the model are: Step 1: Set the initial position and speed of the particle; Step 2: Cluster division is performed according to the comprehensive cluster division index, and the key control nodes in each cluster are selected according to the active voltage sensitivity, thereby setting various parameters in PSO; Step 3: Set the particle search range and constraints in the system; Step 4, calculate the fitness function f = αf1 + βf2, and determine whether the fitness changes after 15 consecutive iterations. If it changes, jump to step 5, otherwise, jump to step 8; Step 5: Find the individual and group fitness values ​​according to the constraints and fitness respectively; Step 6: Update the position and velocity of the particles, and update the individual and group fitness values; Step 7: Determine the number of iterations. If the maximum number of iterations has not been reached, return to step 4. Step 8: Obtain the power of the optimal energy storage action in the cluster to meet the needs of the distribution network.

8. The method for controlling voltage of a distribution network containing a high proportion of household photovoltaic power generation based on cluster division according to claim 1, characterized in that: In step 3, the voltage control method based on cluster division is mainly divided into the following two parts: (1) Distribution network cluster division: Based on the above comprehensive division indicators and division methods, the distribution network with a high proportion of household photovoltaics is divided into clusters. In addition, the voltage over-limit boundary value is set to 0.93pu~1.07pu, and the real-time load and photovoltaic output data are input into the distribution network after cluster division. The voltage value of each node is obtained through power flow calculation; If there is a node whose voltage exceeds the limit, find the cluster to which the node with the voltage exceeding the limit belongs and record it as the adjustable cluster. This part of the result serves as the basis for voltage control based on cluster division. (2) Voltage control part: For clusters with voltage exceeding the limit in the distribution network, the voltage-active sensitivity of the energy storage nodes in each cluster is calculated, and the key control nodes of each cluster are selected; the minimum necessary power requirement for the voltage of all nodes in the cluster to return to the normal range is solved based on the particle swarm algorithm. After obtaining the power required by each cluster, according to the voltage control model based on cluster division, the charge state of the energy storage system at the key control node is taken into account. When the energy storage in the cluster needs to be charged or discharged, the energy storage system at the key control node in the cluster takes priority; if the capacity of the energy storage system at the key control node in the cluster is insufficient, the energy storage system at other control nodes in the cluster will bear the remaining required power; If both positive and negative voltage limits occur within a single cluster, the net charging and discharging demand of the cluster as a whole is determined through power flow calculation. First, power balance is achieved through the coordinated scheduling of the energy storage system within the cluster. If the internal energy storage capacity is insufficient to meet the demand, the remaining power demand is coordinated by adjacent and closely coupled clusters. After each energy storage action, the power flow calculation must be re-performed to verify whether the node voltage has returned to the allowable range.

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