Active power distribution network voltage optimization method considering distributed photovoltaic cluster characteristics

Abstract

The invention discloses an active power distribution network voltage optimization method considering distributed photovoltaic cluster characteristics, and the method comprises the steps: giving the initial operation data of a power distribution network, and carrying out the cluster division according to the initial operation data; according to a cluster division result, determining a self-discipline optimization objective function of each cluster according to the characteristics of each cluster, and if no reactive power regulation equipment and energy storage exist in the cluster, selecting the minimum voltage deviation as the self-discipline optimization objective function of the cluster; if reactive power regulation equipment or energy storage exists in the cluster, selecting the lowest network loss as a cluster self-discipline optimization objective function; and independently carrying out cluster self-discipline optimization on each cluster according to the respective objective function. According to the method, through two links of cluster self-discipline optimization and inter-cluster coordination optimization, different objective functions are adopted for optimization according to different cluster characteristics, and the safety, economy and flexibility of the whole network are improved.

Description

Technical Field

[0001] The present invention relates to the technical field of distribution networks, and in particular to an active distribution network voltage optimization method considering characteristics of distributed photovoltaic clusters. Background Art

[0002] The penetration rate of renewable energy in power systems continues to increase. These resources are connected to the end of the distribution network, driving the transformation of distribution networks from traditional single-terminal models to multi-terminal, controllable, and active distribution networks (ADNs). However, the intermittent and volatile nature of distributed resources makes grid-connected nodes susceptible to voltage fluctuations, overshooting, three-phase imbalance, increased network losses, and power backflow. This increases the complexity of system power flow calculations, threatens the stable operation of the power system, and can cause significant economic losses. Therefore, improving voltage control strategies to increase the utilization of distributed generation and reduce distribution network losses while ensuring system voltage stability has become a key research direction.

[0003] Traditional distribution network voltage control architectures primarily fall into three categories: local control, centralized control, and distributed control. Local control offers the advantages of fast response and low investment costs, but its voltage regulation capabilities are limited and it fails to fully utilize the system's controllable resources. Centralized control achieves global optimization through the unified allocation of voltage regulation resources, but it faces challenges such as large data volumes, heavy communication burdens, and high investment costs. In contrast, distributed control offers excellent autonomy and adaptability, low investment costs, and minimal communication data volumes. It fully leverages the autonomy of distributed photovoltaic systems and exhibits strong robustness.

[0004] Distributed control divides the distribution network into multiple clusters by dividing them into clusters. Each cluster performs self-regulation and takes coordinated optimization between clusters at the same time, solving the voltage over-limit problem caused by the high proportion of distributed photovoltaic access, reducing network losses, and making full use of the reactive compensation resources of each cluster. Currently, the commonly used cluster partitioning algorithms mainly include the following three categories, each with its own characteristics and suitable for different application scenarios: (1) Complex network community discovery algorithm: This method abstracts the distribution network into a complex network and identifies closely connected subnetworks by maximizing the modularity principle. (2) Dynamic partitioning algorithm based on cluster analysis: This algorithm realizes cluster partitioning by mining the electrical correlation characteristics between nodes. (3) Multi-objective intelligent optimization algorithm: For the multi-constraint optimization problem in cluster partitioning, intelligent algorithms show unique advantages. Various cluster partitioning algorithms for power systems often form a complementary relationship in practical applications: cluster analysis is suitable for rapid initial screening, community discovery is good at extracting structural features, and intelligent optimization is used for refined decision-making. In the construction of cluster division criteria and indicator systems, the mainstream division criteria are centered on electrical coupling, emphasizing strong electrical connections between nodes within a cluster (such as voltage sensitivity and power interaction) and weak coupling characteristics between clusters. At the same time, a comprehensive indicator system is constructed by combining indicators such as source-load-storage matching, power reserve, and communication load. However, there is a lack of assessment of the voltage regulation potential of reactive compensation devices and energy storage within the cluster.

[0005] In traditional distributed control optimization strategies, the objective functions for the intraday control phase typically fall into two categories. The first involves considering a single safety or economic objective function. The safety objective function is often primarily based on voltage offset, while the economic objective is primarily based on network losses. However, adopting a single safety objective function may increase reactive power output to improve voltage levels, leading to increased network losses. Similarly, adopting a single economic objective function to reduce network losses may exacerbate the risk of voltage overshoot. The second approach involves selecting a multi-objective optimization objective function, which prioritizes safety and economic indicators. However, the weighting of safety and economic indicators in a multi-objective optimization objective function is difficult to determine, and the optimized values for both require normalization. Furthermore, existing distribution network voltage optimization methods fail to select differentiated objective functions based on the characteristics of different distribution networks, which can lead to underutilization of reactive compensation resources and energy storage equipment, making precise optimization difficult. Summary of the Invention

[0006] In view of the above-mentioned problems that the high proportion of distributed photovoltaic access to the distribution network causes voltage over-limit, the existing cluster division indicators lack consideration of the voltage regulation potential indicator, and the distributed control optimization and control method does not select differentiated objective functions based on cluster characteristics, the present invention provides an active distribution network voltage optimization method that considers the characteristics of distributed photovoltaic clusters. It can reduce network losses in the distribution network, ensure that the voltage does not exceed the limit and is within a reasonable range, and make full use of reactive compensation resources, energy storage and other equipment. By considering the electrical distance and voltage regulation potential indicators that approximate voltage sensitivity to form a comprehensive cluster division indicator, and selecting differentiated objective functions for different cluster characteristics to achieve precise optimization, it can fully utilize various reactive compensation resources in the distribution network and improve the safety and economy of the power grid.

[0007] The present invention provides the following technical solution: a method for actively optimizing the voltage of a distribution network taking into account the characteristics of a distributed photovoltaic cluster, comprising the following steps:

[0008] Step 1: Given the initial operation data of the distribution network, cluster division is performed based on the K-means algorithm according to the comprehensive cluster division index;

[0009] Step 2: Based on the cluster division results and the characteristics of each cluster, the self-regulation optimization objective function of each cluster is determined. If there is no reactive power regulation equipment or energy storage within the cluster, the minimum voltage deviation is selected as the self-regulation optimization objective function of the cluster. If there is reactive power regulation equipment or energy storage within the cluster, the minimum network loss is selected as the self-regulation optimization objective function of the cluster. This achieves precise optimization and ensures that reactive power regulation resources within the cluster are not wasted.

[0010] Step 3: Introduce virtual edge nodes between clusters, build virtual power transmission lines to establish relationships between clusters, and decouple clusters to facilitate inter-cluster coordination and optimization;

[0011] Step 4: Initialize the Lagrangian penalty term to zero and determine the active power, reactive power, and voltage of the cluster edge nodes based on the initial operation data of the distribution network;

[0012] Step 5: Each cluster independently performs cluster self-discipline optimization based on its own objective function to obtain the optimal solution for the current cluster;

[0013] Step 6: Calculate the Lagrangian penalty term of the cluster edge nodes to facilitate the update of the objective function of inter-cluster coordination optimization;

[0014] Step 7: Add a Lagrangian penalty term to the autonomous optimization objective function of each cluster, use the alternating direction multiplier method to perform inter-cluster coordinated optimization scheduling, and construct a global distribution network solution by integrating the solutions of each cluster;

[0015] Step 8: Determine whether the result has converged based on the cluster edge node data. If so, end the process. If not, update the active power, reactive power, and voltage values of the cluster edge nodes and continue with step 5 until the optimal solution is obtained.

[0016] As a preferred embodiment of the present invention's active distribution network voltage optimization method that considers the characteristics of distributed photovoltaic clusters, the cluster division index used in step 1 is composed of an electrical distance that considers approximate voltage sensitivity and a cluster voltage regulation potential index. The electrical distance is calculated based on the approximate voltage sensitivity, linking node voltage changes with changes in active and reactive power at each node through a function.

[0017] ΔU=(HJ -1 LN) -1 ΔP+(JH -1 NL) -1 ΔQ

[0018] Where: ΔU is the node voltage change matrix, ΔP and ΔQ are the node injected active and reactive power change matrices, respectively, and H, N, J, and L are the elements of the Jacobian matrix. When ΔP and ΔQ are both 0, that is, the node injected active or reactive power remains unchanged, we can obtain:

[0019]

[0020] Where: S VP 、S VQ They are the approximate active voltage sensitivity matrix and the approximate reactive voltage sensitivity matrix respectively. The electrical distance l between node i and node j based on the approximate voltage sensitivity is ij The expression is:

[0021]

[0022] Where: d ij Indicates the degree of influence of the power change of node j on node i, d ij The smaller the value, the smaller the electrical distance between the two nodes, indicating that the power change of node j has a greater impact on node i, n s Indicates the total number of nodes in the network, They represent the active voltage sensitivity of node i, the active voltage sensitivity of node j to node i, the reactive voltage sensitivity of node i, and the reactive voltage sensitivity of node j to node i respectively.

[0023] The cluster voltage regulation potential is the ability of the reactive compensation devices and energy storage within a cluster to regulate the voltage limit of the nodes within the cluster. The voltage regulation potential indicator expression of cluster K is:

[0024]

[0025] Where: They represent the over-limit control capabilities of the reactive compensation device and energy storage within cluster K for node voltage, respectively. α3 and β3 represent the weight coefficients of the reactive compensation device and energy storage, respectively. The sum of the two is 1, and both are set to 0.5 to ensure that the voltage over-limit control capabilities of the reactive compensation device and energy storage have the same weight. The voltage over-limit control capabilities of the reactive compensation device and energy storage can be expressed as:

[0026]

[0027] Where: ΔU K,max The voltage of the node with the highest voltage in cluster K exceeds the limit. If the voltage does not exceed the limit, then ΔU K,max =0; are the active margin of energy storage and the reactive margin of reactive compensation device at node j respectively.

[0028] The comprehensive cluster division index considers the electrical distance of the approximate voltage sensitivity and the cluster voltage regulation potential index, and its expression is:

[0029]

[0030] Where: γ is the comprehensive index of cluster division, the larger its value is, the better the performance of cluster division is; ij,max for l ij The maximum value in n c The number of clusters after the network is divided.

[0031] The specific steps for cluster division are as follows:

[0032] (1) For any node i in the network, calculate its electrical distance to other nodes in the network to form a set L, that is,

[0033]

[0034] (2) Arrange all elements in the set L in ascending order and randomly select an element as the index d of node i i , node index d i Used to describe the node density around node i, that is, the number of nodes around node i or the connection density, d i The larger the value, the more nodes there are near the node.

[0035] (3) For the indicators of all nodes in the network, we sort them in ascending order and randomly select an element as the threshold. Nodes with a value smaller than the threshold have a large number of surrounding nodes and can be considered as cluster centers. Therefore, we select nodes with a value smaller than the threshold to form a set E, and select the cluster center from within this set.

[0036] (4) Select the node with the highest index in set E as the first cluster node e1.

[0037] (5) Select the node farthest from the existing cluster center from the remaining elements in set E as the next cluster center.

[0038] (6) If the division result changes, repeat steps (2)-(5) and randomly select cluster centers until the result does not change.

[0039] (7) Calculate the quantitative evaluation index SSE of cluster partitioning.

[0040] (8) After selecting the number of clusters in the elbow interval according to the elbow rule, calculate the comprehensive cluster division index respectively, and select the cluster division number and division result with the highest index value.

[0041] As a preferred solution of the active distribution network voltage optimization method considering the characteristics of distributed photovoltaic clusters described in the present invention, the objective function of minimizing voltage deviation and minimizing network loss in step 2 are respectively:

[0042]

[0043] Where: f s represents the objective function of minimizing voltage deviation, f e represents the objective function of minimizing network loss; U ref Indicates the voltage reference value; n K is the number of nodes in the cluster; r ij is the resistance of circuit ij; P ij,t , Q ij,t They represent the active power and reactive power of line ij at time t respectively; U i,t is the voltage of node i at time t.

[0044] As a preferred embodiment of the present invention's method for active distribution network voltage optimization that considers the characteristics of distributed photovoltaic clusters, step three includes: during inter-cluster collaborative optimization and control, upstream cluster I, cluster K, and downstream cluster J achieve cluster decoupling by adding virtual edge nodes and virtual power transmission lines between the three clusters. The virtual edge nodes are artificially added virtual nodes to facilitate inter-cluster decoupling. Clusters I and K are connected via line ab, and clusters K and J are connected via line cl. The edge nodes are node a of cluster I and node c of cluster K. Correspondingly, a virtual edge node a1 is added to line ab of cluster K, and a virtual edge node c1 is added to line cl of cluster J. Virtual edge node a1 belongs to cluster K, and virtual edge node c1 belongs to cluster J. First, the edge node a of the upstream cluster I and the virtual edge node a1 of cluster K exchange information and perform the next round of cluster internal self-discipline optimization. Cluster K receives the accurate voltage of the edge node a of the upstream cluster I, the active power and reactive power transmitted by the virtual power transmission line a1b, the voltage of the virtual edge node c1 of the downstream cluster J, and the real active power and reactive power transmitted by the line cl. At the same time, it sends the node voltage of the virtual edge node a1 and the accurate active power and reactive power transmitted by the line ab to the upstream cluster I, and sends the real voltage of the node c and the active power and reactive power transmitted by the virtual power transmission line c1l to the downstream cluster J.

[0045] As a preferred solution of the active distribution network voltage optimization method considering the characteristics of distributed photovoltaic clusters described in the present invention, the autonomous optimization in step five is: each cluster adopts a different objective function according to its own cluster characteristics, and independently optimizes considering line flow constraints, node voltage constraints, continuous reactive power compensation equipment constraints, distributed energy storage constraints, and interruptible load constraints.

[0046] As a preferred solution of the active distribution network voltage optimization method considering the characteristics of distributed photovoltaic clusters described in the present invention, the Lagrangian penalty term calculation formula in step 6 is:

[0047]

[0048] Where: L1 represents the Lagrangian penalty term; τ represents the penalty coefficient to ensure data consistency; λ U ,λ P ,λ Q Represent the Lagrange multipliers of voltage, active power, and reactive power respectively; the superscript n represents the number of iterations; P ab , Q ab Indicates the active power and reactive power of line ab, They represent the virtual active power and reactive power transmitted by the downstream virtual line a1b respectively; U a and are the voltages of the upstream edge node a and the downstream virtual edge node a1 respectively.

[0049] As a preferred solution of the active distribution network voltage optimization method considering the characteristics of distributed photovoltaic clusters described in the present invention, the objective function of adding the Lagrangian penalty term in step 7 is:

[0050]

[0051] As a preferred solution of the active distribution network voltage optimization method considering the characteristics of distributed photovoltaic clusters described in the present invention, the inter-cluster coordination optimization step according to the alternating direction multiplier method in step seven is:

[0052] (1) Virtual edge node voltage obtained based on cluster self-discipline optimization and virtual line power Each cluster accurately calculates the active power P transmitted by the inter-cluster line ab through the Newton-Layer method. ab,p and reactive power Q ab,p , the accurate voltage U of the edge node a in the cluster a,p , and the highest voltage inside the cluster U max and minimum voltage U min , and update the voltage compensation parameter ΔU max and ΔU min :

[0053]

[0054] (2) Adjacent clusters exchange inter-cluster edge data and its deviations, and update edge data locally based on the interactive information:

[0055]

[0056]

[0057] Where: x a is the updated value of the edge node voltage of the cluster to the upstream cluster, y ab 、z ab They are respectively the updated active power value and reactive power value transmitted between the cluster and the upstream cluster, and x c is the updated value of the edge node voltage of the cluster for the downstream cluster, y cl 、z cl They are respectively the updated active power value and reactive power value of the line transmission between the cluster and the downstream cluster, U c 、 are the voltages of the upstream edge node c and the downstream virtual edge node c1, U c,p is the exact voltage of edge node c, P cl,p and Qcl,p are respectively the active power and reactive power transmitted by the inter-cluster line cl accurately calculated by the Newton-Ray method, and They represent the virtual active power and reactive power transmitted by the downstream virtual line c1l respectively.

[0058] (3) Based on the received inter-cluster edge data, each cluster updates the Lagrange multiplier of the edge data locally:

[0059]

[0060] Where: U is the updated value of the Lagrange multiplier of the edge node voltage of the cluster to the upstream cluster, λ P ,λ Q are the updated values of the Lagrange multiplier for active power and reactive power transmitted between the cluster and the upstream cluster, respectively. c,U is the updated value of the Lagrange multiplier of the edge node voltage of the cluster to the downstream cluster, They are the updated values of the Lagrange multiplier for active power and reactive power transmitted between the cluster and the downstream cluster, respectively.

[0061] As a preferred solution of the active distribution network voltage optimization method considering the characteristics of distributed photovoltaic clusters described in the present invention, wherein: in step eight, whether the result converges is determined based on the cluster edge node data, and the convergence criterion is: the cluster edge data deviation for three consecutive times and are all less than the threshold σ d . Marginal data bias It is the sum of the absolute values of the edge node voltage deviation and inter-cluster line power deviation between cluster K and its adjacent clusters in the nth iteration.

[0062] The present invention has the following beneficial effects:

[0063] 1. The present invention effectively reduces network losses in the distribution network and improves the voltage quality of the distribution network: through the optimization adjustment scheme generated by the algorithm, the adjustable devices in the distribution network can flexibly adjust their output according to the actual load conditions, thereby improving the stability of the power grid;

[0064] 2. The present invention improves the utilization efficiency of various reactive compensation equipment, energy storage and other adjustable resources in the network: differentiated objective functions are adopted according to different cluster characteristics to achieve full utilization of reactive compensation equipment, energy storage and other adjustable resources, thereby improving overall operating efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0065] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the following briefly introduces the drawings required for describing the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. Those skilled in the art can also derive other drawings based on these drawings without inventive effort. Among them:

[0066] Figure 1 Schematic diagram of the process of the present invention,

[0067] Figure 2 This is a schematic diagram of cluster decoupling of the present invention.

[0068] Figure 3 This is a diagram of the network topology and cluster partitioning of the embodiment.

[0069] Figure 4 This is a comparison diagram of the voltage of each node at 12 noon before and after the voltage optimization of the embodiment. DETAILED DESCRIPTION

[0070] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, the specific embodiments of the present invention are described in detail below with reference to the accompanying drawings.

[0071] In the following description, many specific details are set forth to facilitate a full understanding of the present invention. However, the present invention may also be implemented in other ways different from those described herein. Those skilled in the art may make similar generalizations without violating the connotation of the present invention. Therefore, the present invention is not limited to the specific embodiments disclosed below.

[0072] Reference Figures 1-4 , provides an active distribution network voltage optimization method considering the characteristics of distributed photovoltaic clusters, including the following steps:

[0073] Step 1: Given the initial operation data of the distribution network, cluster division is performed based on the K-means algorithm according to the comprehensive cluster division index;

[0074] The present invention first adopts a cluster comprehensive division index consisting of electrical distance and voltage regulation potential that considers approximate voltage sensitivity in cluster division, and uses an improved K-means algorithm to solve the local optimal problem caused by the randomness of the initial center of the traditional algorithm, and determines the optimal number of clusters through the elbow rule and cluster comprehensive division index.

[0075] Secondly, the objective function adopted for each cluster is a differentiated objective function that takes into account the characteristics of each cluster, so as to make full use of reactive regulation resources and energy storage to achieve precise optimization.

[0076] Step 2: Based on the cluster division results and the characteristics of each cluster, the self-regulation optimization objective function of each cluster is determined. If there is no reactive power regulation equipment or energy storage within the cluster, the minimum voltage deviation is selected as the self-regulation optimization objective function of the cluster. If there is reactive power regulation equipment or energy storage within the cluster, the minimum network loss is selected as the self-regulation optimization objective function of the cluster. This achieves precise optimization and ensures that reactive power regulation resources within the cluster are not wasted.

[0077] Step 3: Introduce virtual edge nodes between clusters, build virtual power transmission lines to establish relationships between clusters, and decouple clusters to facilitate inter-cluster coordination and optimization;

[0078] Step 4: Initialize the Lagrangian penalty term to zero and determine the active power, reactive power, and voltage of the cluster edge nodes based on the initial operation data of the distribution network;

[0079] Step 5: Each cluster independently performs cluster self-discipline optimization based on its own objective function to obtain the optimal solution for the current cluster;

[0080] Step 6: Calculate the Lagrangian penalty term of the cluster edge nodes to facilitate the update of the objective function of inter-cluster coordination optimization;

[0081] Step 7: Add a Lagrangian penalty term to the autonomous optimization objective function of each cluster, use the alternating direction multiplier method to perform inter-cluster coordinated optimization scheduling, and construct a global distribution network solution by integrating the solutions of each cluster;

[0082] Step 8: Determine whether the result has converged based on the cluster edge node data. If so, end the process. If not, update the active power, reactive power, and voltage values of the cluster edge nodes and continue with step 5 until the optimal solution is obtained.

[0083] As a preferred embodiment of the present invention's method for active distribution network voltage optimization that considers the characteristics of distributed photovoltaic clusters, the cluster division in step 1 utilizes a comprehensive cluster division index consisting of an electrical distance and voltage regulation potential index that considers approximate voltage sensitivity, and an improved K-means algorithm is used to divide the clusters. The required initial distribution network operating data includes distributed photovoltaic output, load output, capacitor bank call volume, and on-load tap-changing transformer gear. The divided clusters include edge nodes and virtual edge nodes, each of which has a certain load. Some nodes are connected to distributed photovoltaics, continuous reactive power compensation devices, discrete reactive power compensation devices, energy storage, and demand-side response.

[0084] The calculation of electrical distance is based on the approximate voltage sensitivity, which links the node voltage change with the active and reactive power changes of each node in the form of a function.

[0085] ΔU=(HJ -1 LN) -1ΔP+(JH -1 NL) -1 ΔQ

[0086] Where: ΔU is the node voltage change matrix, ΔP and ΔQ are the node injected active and reactive power change matrices, respectively, and H, N, J, and L are the elements of the Jacobian matrix. When ΔP and ΔQ are both 0, that is, the node injected active or reactive power remains unchanged, we can obtain:

[0087]

[0088] Where: S VP 、S VQ They are the approximate active voltage sensitivity matrix and the approximate reactive voltage sensitivity matrix respectively. The electrical distance l between node i and node j based on the approximate voltage sensitivity is ij The expression is:

[0089]

[0090] Where: d ij Indicates the degree of influence of the power change of node j on node i, d ij The smaller the value, the smaller the electrical distance between the two nodes, indicating that the power change of node j has a greater impact on node i, n s Indicates the total number of nodes in the network, They represent the active voltage sensitivity of node i, the active voltage sensitivity of node j to node i, the reactive voltage sensitivity of node i, and the reactive voltage sensitivity of node j to node i respectively.

[0091] Cluster voltage regulation potential refers to the ability of reactive power compensation devices and energy storage within a cluster to regulate voltage violations at nodes within the cluster. Taking cluster K as an example, the cluster voltage regulation potential is expressed as:

[0092]

[0093] Where: They represent the over-limit control capabilities of the reactive compensation device and energy storage within cluster K for node voltage, respectively. α3 and β3 represent the weight coefficients of the reactive compensation device and energy storage, respectively. The sum of the two is 1, and both are set to 0.5 to ensure that the voltage over-limit control capabilities of the reactive compensation device and energy storage have the same weight. The voltage over-limit control capabilities of the reactive compensation device and energy storage can be expressed as:

[0094]

[0095] Where: ΔU K,max The voltage of the node with the highest voltage in cluster K exceeds the limit. If the voltage does not exceed the limit, then ΔU K,max =0; They are respectively the active margin of energy storage and the reactive margin of reactive compensation device at node j.

[0096] The comprehensive cluster division index considers the electrical distance of the approximate voltage sensitivity and the cluster voltage regulation potential index, and its expression is:

[0097]

[0098] Where: γ is the comprehensive index of cluster division, the larger its value is, the better the performance of cluster division is; ij,max for l ij The maximum value in n c The number of clusters after the network is divided.

[0099] The improved K-means algorithm uses the sum of square errors as a quantitative evaluation indicator, and its mathematical expression is:

[0100]

[0101] Where: Represents the distance between node j and cluster center ε K Electrical distance, n K Represents the number of nodes in cluster K. This indicator evaluates the clustering effect by calculating the sum of the squares of the distances between samples within each cluster and the cluster center. The smaller the value, the better the clustering result. Based on the classic K-means clustering algorithm, it is improved to minimize the sum of the squares of the electrical distances between nodes within the cluster and the cluster center. The objective function for voltage-optimized distributed photovoltaic cluster partitioning is:

[0102]

[0103] The specific steps are as follows:

[0104] (1) For any node i in the network, the electrical distance between it and other nodes in the network is calculated according to the above formula to form a set L, that is,

[0105]

[0106] (2) Arrange all elements in the set L in ascending order and randomly select an element as the index d of node i i , node index d i Used to describe the node density around node i, that is, the number of nodes around node i or the connection density, d i The larger the value, the more nodes there are near the node.

[0107] (3) For the indicators of all nodes in the network, we sort them in ascending order and randomly select an element as the threshold. Nodes with a value smaller than the threshold have a large number of surrounding nodes and can be considered as cluster centers. Therefore, we select nodes with a value smaller than the threshold to form a set E, and select the cluster center from within this set.

[0108] (4) Select the node with the highest index in set E as the first cluster node e1.

[0109] (5) Select the node farthest from the existing cluster center from the remaining elements in set E as the next cluster center.

[0110] (6) If the division result changes, repeat steps (2)-(5) and randomly select cluster centers until the result does not change.

[0111] (7) Calculate the quantitative evaluation index SSE of cluster partitioning.

[0112] (8) After selecting the number of clusters in the elbow interval according to the elbow rule, calculate the comprehensive cluster division index respectively, and select the cluster division number and division result with the highest index value.

[0113] By introducing approximate voltage sensitivity and cluster voltage regulation potential as comprehensive cluster division indicators, combined with an improved K-means clustering algorithm to achieve cluster division, and determining the optimal number of clusters through the elbow rule and cluster comprehensive division indicators, the local optimal problem caused by the randomness of the initial center of the traditional algorithm is solved.

[0114] In cluster division, the present invention adopts a cluster comprehensive division index composed of electrical distance and voltage regulation potential that considers approximate voltage sensitivity, and uses an improved K-means algorithm to solve the local optimal problem caused by the randomness of the initial center of the traditional algorithm, and determines the optimal number of clusters through the elbow rule and cluster comprehensive division index.

[0115] As a preferred solution of the active distribution network voltage optimization method considering the characteristics of distributed photovoltaic clusters described in the present invention, the objective function of minimizing voltage deviation and minimizing network loss in step 2 are respectively:

[0116]

[0117]

[0118] Where: f s represents the objective function of minimizing voltage deviation, f e represents the objective function of minimizing network loss; U ref Indicates the voltage reference value; n K is the number of nodes in the cluster; r ij is the resistance of circuit ij; Pij,t , Q ij,t They represent the active power and reactive power of line ij at time t respectively; U i,t is the voltage of node i at time t.

[0119] As a preferred solution of the active distribution network voltage optimization method considering the characteristics of distributed photovoltaic clusters described in the present invention, step three includes: Figure 2 As shown in the figure, during inter-cluster collaborative optimization and control, upstream cluster I, cluster K, and downstream cluster J achieve cluster decoupling by adding virtual edge nodes and virtual power transmission lines between the three clusters. Virtual edge nodes are artificially added virtual nodes to facilitate inter-cluster decoupling. Clusters I and K are connected by line ab, and clusters K and J are connected by line cl. The edge nodes are node a in cluster I and node c in cluster K. Correspondingly, virtual edge node a1 is added to line ab in cluster K, and virtual edge node c1 is added to line cl in cluster J. Virtual edge node a1 belongs to cluster K, and virtual edge node c1 belongs to cluster J. First, the edge node a of the upstream cluster I and the virtual edge node a1 of cluster K exchange information and perform the next round of cluster internal self-discipline optimization. Cluster K receives the accurate voltage of the edge node a of the upstream cluster I, the active power and reactive power transmitted by the virtual power transmission line a1b, the voltage of the virtual edge node c1 of the downstream cluster J, and the real active power and reactive power transmitted by the line cl. At the same time, it sends the node voltage of the virtual edge node a1 and the accurate active power and reactive power transmitted by the line ab to the upstream cluster I, and sends the real voltage of the node c and the active power and reactive power transmitted by the virtual power transmission line c1l to the downstream cluster J.

[0120] As a preferred solution of the active distribution network voltage optimization method considering the characteristics of distributed photovoltaic clusters described in the present invention, the autonomous optimization in step five is: each cluster adopts a different objective function according to its own cluster characteristics, and independently optimizes considering line flow constraints, node voltage constraints, continuous reactive power compensation equipment constraints, distributed energy storage constraints, and interruptible load constraints.

[0121] The objective function adopted by the present invention for each cluster is a differentiated objective function taking into account the characteristics of each cluster, so as to make full use of reactive regulation resources and energy storage and achieve accurate optimization.

[0122] As a preferred solution of the active distribution network voltage optimization method considering the characteristics of distributed photovoltaic clusters described in the present invention, the Lagrangian penalty term calculation formula in step 6 is:

[0123]

[0124] Where: L1 represents the Lagrangian penalty term; τ represents the penalty coefficient to ensure data consistency; λ U ,λ P ,λ Q Represent the Lagrange multipliers of voltage, active power, and reactive power respectively; the superscript n represents the number of iterations; P ab , Q ab Indicates the active power and reactive power of line ab, They represent the virtual active power and reactive power transmitted by the downstream virtual line a1b respectively; U a and are the voltages of the upstream edge node a and the downstream virtual edge node a1 respectively.

[0125] As a preferred solution of the active distribution network voltage optimization method considering the characteristics of distributed photovoltaic clusters described in the present invention, the objective function of adding the Lagrangian penalty term in step 7 is:

[0126]

[0127] As a preferred solution of the active distribution network voltage optimization method considering the characteristics of distributed photovoltaic clusters described in the present invention, the inter-cluster coordination optimization step according to the alternating direction multiplier method in step seven is:

[0128] (1) Virtual edge node voltage obtained based on cluster self-discipline optimization and virtual line power Each cluster accurately calculates the active power P transmitted by the inter-cluster line ab through the Newton-Layer method. ab,p and reactive power Q ab,p , the accurate voltage U of the edge node a in the cluster a,p , and the highest voltage inside the cluster U max and minimum voltage U min , and update the voltage compensation parameter ΔU max and ΔU min :

[0129]

[0130] (2) Adjacent clusters exchange inter-cluster edge data and its deviations, and update edge data locally based on the interactive information:

[0131]

[0132]

[0133] Where: x a is the updated value of the edge node voltage of the cluster to the upstream cluster, y ab 、z abThey are respectively the updated active power value and reactive power value transmitted between the cluster and the upstream cluster, and x c is the updated value of the edge node voltage of the cluster for the downstream cluster, y cl 、z cl They are respectively the updated active power value and reactive power value of the line transmission between the cluster and the downstream cluster, U c 、 are the voltages of the upstream edge node c and the downstream virtual edge node c1, U c,p is the exact voltage of edge node c, P cl,p and Q cl,p are respectively the active power and reactive power transmitted by the inter-cluster line cl accurately calculated by the Newton-Ray method, and They represent the virtual active power and reactive power transmitted by the downstream virtual line c1l respectively.

[0134] (3) Based on the received inter-cluster edge data, each cluster updates the Lagrange multiplier of the edge data locally:

[0135]

[0136] Where: U is the updated value of the Lagrange multiplier of the edge node voltage of the cluster to the upstream cluster, λ P ,λ Q are the updated values of the Lagrange multiplier for active power and reactive power transmitted between the cluster and the upstream cluster, respectively. c,U is the updated value of the Lagrange multiplier of the edge node voltage of the cluster to the downstream cluster, They are the updated values of the Lagrange multiplier for active power and reactive power transmitted between the cluster and the downstream cluster, respectively.

[0137] As a preferred solution of the active distribution network voltage optimization method considering the characteristics of distributed photovoltaic clusters described in the present invention, wherein: in step eight, whether the result converges is determined based on the cluster edge node data, and the convergence criterion is: the cluster edge data deviation for three consecutive times and are all less than the threshold σ d . Marginal data bias It is the sum of the absolute values of the edge node voltage deviation and inter-cluster line power deviation between cluster K and its adjacent clusters in the nth iteration.

[0138] The optimization process needs to meet the following constraints to ensure operational feasibility and grid security:

[0139] (1) Line flow constraints

[0140] Perform second-order cone relaxation on the power flow constraints of the distribution network. First, consider introducing:

[0141]

[0142] Where: U i,t represents the voltage of node i at time t, I ij,t represents the current of line ij at time t, α i,t represents the square of the voltage at node i at time t, β ij,t represents the square of the current of line ij at time t. The constraints that the branch flow should satisfy are:

[0143]

[0144] in

[0145]

[0146] Where: r ij 、x ij Represent the resistance and reactance of line ij respectively, P ij,t , Q ij,t They represent the active and reactive power of line ij at time t, k:j→k represents the set of branch end nodes with node j as the head node, i:i→j represents the set of branch head nodes with node j as the end node, P j,t , Q j,t are the active and reactive power injected into node j at time t, are the active and reactive power of the load at node j at time t, is the active and reactive power output of photovoltaic node j at time t, are the charging and discharging power of energy storage at node j at time t, are the load that can be shifted and the load that can be interrupted at node j at time t, is the output of the continuous reactive power compensation device SVC at node j at time t, is the output of discrete reactive power compensation device CB at node j at time t.

[0147] (2) Node voltage constraints

[0148] The node voltage constraints should satisfy:

[0149] U i,min ≤U i,t ≤U i,max

[0150] Where: U i,max 、U i,min Represent the upper and lower limits of the voltage at node i respectively.

[0151] (3) Discrete reactive power compensation equipment constraints

[0152] The capacitor CB is a discrete reactive power compensation device that uses group switching. To increase the service life of the CB, there is a certain limit on the number of switching operations. The constraints are:

[0153]

[0154] Where: represents the output of the CB connected to node i at time t, Indicates the power of a single group of CBs connected to node i, Indicates the number of CB groups that node i accesses at time t, and the value is an integer. represents the maximum number of CB switching groups connected to node i, Z represents an integer set, It is the maximum number of actions in one scheduling cycle of CB.

[0155] (4) Continuous reactive power compensation equipment constraints

[0156] The static VAR compensator SVC is a continuous VAR compensation device, and its constraints can be expressed as:

[0157]

[0158] Where: represents the output of the SVC connected to node i at time t, Indicates the upper and lower limits of the output of the SVC connected to node i.

[0159] (5) Constraints on on-load tap-changing transformers

[0160] The on-load tap-changing transformer (OLTC) is regulated in gears, which is the same as the CB. There are also certain restrictions on the number of times the OLTC can operate in a dispatch cycle. The constraints are:

[0161]

[0162] Where: represents the transformation ratio of the OLTC connected between nodes i and j at time t, Indicates the OLTC gear that nodes i and j access at time t, and the value is an integer. To adjust the step size, Indicates the upper and lower limits of the OLTC access gear, K0 is the initial gear, set to 0.95, The maximum number of actions in one OLTC scheduling cycle.

[0163] (6) Distributed energy storage constraints

[0164] The distributed energy storage ESS constraints can be expressed as:

[0165]

[0166] Where: They represent the charging and discharging power of the energy storage connected to node i at time t, Represent the minimum and maximum energy storage charging power at node i, respectively. They represent the minimum and maximum values of the energy storage discharge power at node i, denote the energy storage charging and discharging efficiency at node i, represents the energy storage charge connected to node i at time t, Δt represents the time granularity of scheduling, They represent the minimum and maximum energy storage charge of node i, They represent the energy storage charging and discharging flags at node i at time t, respectively. 0 and 1 indicate stop and start, respectively, and the two satisfy the mutually exclusive constraint:

[0167]

[0168] (7) Demand-side response constraints

[0169] Demand-side response considers shiftable loads and interruptible loads, which should meet the following requirements:

[0170]

[0171] Where: and They represent the shiftable load call amount and interruptible load call amount at node i at time t, They represent the upper and lower limits of the load transfer capacity connected to node i, They represent the upper and lower limits of the interruptible load call amount connected to node i.

[0172] The improved IEEE33 node network is used to simulate the example and verify the voltage optimization control algorithm. The topology diagram of the example is as follows Figure 3 As shown. PV represents the distributed photovoltaic access node. Node 33 is where the system is connected to the upper network through the OLTC. The OLTC ratio range is 0.95-1.05, and its tap adjustment gear has a total of 11 gears. Network nodes 3 and 8 are connected to two groups of CBs, each with 6 gears and an output range of 0-3MVar. Network nodes 19 and 25 are connected to SVCs with rated capacities of 0.5MVar and 1MVar respectively. Network nodes 24 and 29 are connected to ESSs with a maximum charge and discharge power of 0.2MW and a capacity of 3MWh respectively. Network node 12 is connected to an interruptible load, and network node 19 is connected to a shiftable load. Set parameters Both are 5, is 0.5MVar, There are 6 groups of distributed energy storage. and The upper and lower limits of network voltage are set to 1.07 pu and 0.93 pu respectively.

[0173] In order to verify the proposed voltage optimization scheduling strategy, voltage optimization is performed according to the above strategy. The cluster division results are as follows: Figure 3 As shown. At 12 noon, the voltage data of each node after regulation is obtained and compared with the voltage distribution without optimization strategy. Figure 4 shown.

[0174] Without the voltage optimization strategy, 18 nodes exceeded the upper limit, with node 17 having the highest voltage, reaching 1.12 pu. After implementing the voltage optimization scheduling strategy, the voltage offsets at each node were further improved, with the maximum voltage offset within the cluster exceeding 3%. This demonstrates that the proposed voltage optimization strategy significantly improves the overall voltage level and quality of the active distribution network.

[0175] While embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions, and alterations may be made to these embodiments without departing from the principles of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. An active distribution network voltage optimization method considering the characteristics of distributed photovoltaic clusters, characterized in that: The following steps are involved: Step 1: Given the initial operation data of the distribution network, cluster division is performed based on the K-means algorithm according to the comprehensive cluster division index; Step 2: Based on the cluster division results and the characteristics of each cluster, determine the self-regulation optimization objective function for each cluster. If there is no reactive power regulation equipment or energy storage within the cluster, the minimum voltage deviation is selected as the self-regulation optimization objective function for the cluster. If there is reactive power regulation equipment or energy storage within the cluster, the minimum network loss is selected as the self-regulation optimization objective function for the cluster. Step 3: Introduce virtual edge nodes between clusters, build virtual power transmission lines to establish relationships between clusters, and decouple clusters; Step 4: Initialize the Lagrangian penalty term to zero and determine the active power, reactive power, and voltage of the cluster edge nodes based on the initial operation data of the distribution network; Step 5: Each cluster independently performs cluster self-discipline optimization based on its own objective function to obtain the optimal solution for the current cluster; Step 6: Calculate the Lagrangian penalty term of the cluster edge nodes to update the objective function of inter-cluster coordination optimization; Step 7: Add a Lagrangian penalty term to the autonomous optimization objective function of each cluster, use the alternating direction multiplier method to perform inter-cluster coordinated optimization scheduling, and construct a global distribution network solution by integrating the solutions of each cluster; Step 8: Determine whether the result has converged based on the cluster edge node data. If so, end the process. If not, update the active power, reactive power, and voltage values of the cluster edge nodes and continue with step 5 until the optimal solution is obtained.

2. The method for active distribution network voltage optimization considering the characteristics of distributed photovoltaic clusters according to claim 1, characterized in that: In step 1, the cluster division adopts the comprehensive cluster division index including the electrical distance considering the approximate voltage sensitivity and the cluster voltage regulation potential index; Specifically: Where: γ is the comprehensive index of cluster division, l ij is the electrical distance between node i and node j, l ij,max for l ij The maximum value in ρ K is the cluster voltage regulation potential, n c The number of clusters after the network is divided.

3. The method for active distribution network voltage optimization considering the characteristics of distributed photovoltaic clusters according to claim 1, characterized in that: In step 1, cluster division includes: (1) For any node i in the network, calculate its electrical distance to other nodes in the network to form a set L, that is, (2) Arrange all elements in the set L in ascending order and randomly select an element as the index d of node i i , node index d i Used to describe the node density around node i; (3) For the indicators of all nodes in the network, arrange them in ascending order and randomly select an element as the threshold. Select the nodes smaller than the threshold to form a set E, and select the cluster center from within the set; (4) Select the node with the highest index in set E as the first cluster node e1; (5) Select the node farthest from the existing cluster center from the remaining elements in set E as the next cluster center; (6) If the division result changes, repeat steps (2)-(5) and randomly select cluster centers until the result does not change; (7) Calculate the cluster partition quantitative evaluation index SSE, specifically: Where: Represents the distance between node j and cluster center ε K Electrical distance, n K represents the number of nodes in cluster K; (8) After selecting the number of clusters in the elbow interval according to the elbow rule, calculate the comprehensive cluster division index respectively, and select the cluster division number and division result with the highest index value.

4. The method for active distribution network voltage optimization considering the characteristics of distributed photovoltaic clusters according to claim 1, characterized in that: In step 2, the objective functions of minimizing voltage deviation and minimizing network loss are: Where: f s represents the objective function of minimizing voltage deviation, f e represents the objective function of minimizing network loss; U ref Indicates the voltage reference value; n K is the number of nodes in the cluster; r ij is the resistance of circuit ij; P ij,t , Q ij,t They represent the active power and reactive power of line ij at time t respectively; U i,t is the voltage of node i at time t.

5. The method for active distribution network voltage optimization considering the characteristics of distributed photovoltaic clusters according to claim 1, characterized in that: Step three includes: During inter-cluster collaborative optimization and control, the upstream cluster I, cluster K, and downstream cluster J complete cluster decoupling by adding virtual edge nodes and virtual power transmission lines between clusters; Clusters I and K are connected via line ab, and clusters K and J are connected via line cl. The edge nodes are node a of cluster I and node c of cluster K. Accordingly, a virtual edge node a1 is added to line ab in cluster K, and a virtual edge node c1 is added to line cl in cluster J. Virtual edge node a1 belongs to cluster K, and virtual edge node c1 belongs to cluster J; First, the edge node a of the upstream cluster I and the virtual edge node a1 of cluster K exchange information and perform the next round of cluster internal self-discipline optimization. Cluster K receives the accurate voltage of the edge node a of the upstream cluster I, the active power and reactive power transmitted by the virtual power transmission line a1b, the voltage of the virtual edge node c1 of the downstream cluster J, and the real active power and reactive power transmitted by the line cl. At the same time, it sends the node voltage of the virtual edge node a1 and the accurate active power and reactive power transmitted by the line ab to the upstream cluster I, and sends the real voltage of the node c and the active power and reactive power transmitted by the virtual power transmission line c1l to the downstream cluster J.

6. The method for active distribution network voltage optimization considering the characteristics of distributed photovoltaic clusters according to claim 1, characterized in that: Step five includes: each cluster adopts different objective functions according to its own cluster characteristics, and performs independent optimization considering line flow constraints, node voltage constraints, continuous reactive power compensation equipment constraints, distributed energy storage constraints, and interruptible load constraints.

7. The method for active distribution network voltage optimization considering the characteristics of distributed photovoltaic clusters according to claim 1, characterized in that: In step 6, the Lagrangian penalty term is calculated as: Where: L1 represents the Lagrangian penalty term; τ represents the penalty coefficient to ensure data consistency; λ U ,λ P ,λ Q Represent the Lagrange multipliers of voltage, active power and reactive power respectively; P ab , Q ab Indicates the active power and reactive power of line ab, They represent the virtual active power and reactive power transmitted by the downstream virtual line a1b respectively; U a and are the voltages of the upstream edge node a and the downstream virtual edge node a1, respectively; the superscript n represents the number of iterations.

8. The method for active distribution network voltage optimization considering the characteristics of distributed photovoltaic clusters according to claim 1, characterized in that: In step 7, the objective function with the Lagrangian penalty term added is:

9. The method for active distribution network voltage optimization considering the characteristics of distributed photovoltaic clusters according to claim 1, characterized in that: In step 7, the steps for inter-group coordination optimization based on the alternating direction multiplier method are as follows: (1) Virtual edge node voltage obtained based on cluster self-discipline optimization and virtual line power Each cluster accurately calculates the active power P transmitted by the inter-cluster line ab through the Newton-Layer method. ab,p and reactive power Q ab,p , the accurate voltage U of the edge node a in the cluster a,p , and the highest voltage inside the cluster U max and minimum voltage U min , and update the voltage compensation parameter ΔU max and ΔU min : (2) Adjacent clusters exchange inter-cluster edge data and its deviations, and update edge data locally based on the interactive information: Where: x a is the updated value of the edge node voltage of the cluster to the upstream cluster, y ab 、z ab They are respectively the updated active power value and reactive power value transmitted between the cluster and the upstream cluster, and x c is the updated value of the edge node voltage of the cluster for the downstream cluster, y cl 、z cl They are respectively the updated active power value and reactive power value of the line transmission between the cluster and the downstream cluster, U c 、 are the voltages of the upstream edge node c and the downstream virtual edge node c1, U c,p is the exact voltage of edge node c, P cl,p and Q cl,p are respectively the active power and reactive power transmitted by the inter-cluster line cl accurately calculated by the Newton-Ray method, and They represent the virtual active and reactive power transmitted by the downstream virtual line c1l respectively; (3) Based on the received inter-cluster edge data, each cluster updates the Lagrange multiplier of the edge data locally: Where: U is the updated value of the Lagrange multiplier of the edge node voltage of the cluster to the upstream cluster, λ P ,λ Q are the updated values of the Lagrange multiplier for active power and reactive power transmitted between the cluster and the upstream cluster, respectively. c,U is the updated value of the Lagrange multiplier of the edge node voltage of the cluster to the downstream cluster, They are the updated values of the Lagrange multiplier for active power and reactive power transmitted between the cluster and the downstream cluster, respectively.

10. The method for active distribution network voltage optimization considering the characteristics of distributed photovoltaic clusters according to claim 1, characterized in that: In step eight, the results are judged to be convergent based on the cluster edge node data. The convergence criterion is: the cluster edge data deviation for three consecutive times and are all less than the threshold σ d ; Edge data deviation It is the sum of the absolute values of the edge node voltage deviation and inter-cluster line power deviation between cluster K and its adjacent clusters in the nth iteration.

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