An active power distribution network voltage optimization method considering characteristics of distributed photovoltaic clusters

Abstract

The application discloses an active power distribution network voltage optimization method considering distributed photovoltaic cluster characteristics, and the method comprises the following steps: given initial operation data of a power distribution network, performing cluster division according to the initial operation data; according to the cluster division result, determining a self-optimization objective function of each cluster according to the characteristics of the clusters, if there is no reactive power regulation equipment and energy storage in the cluster, selecting the minimum voltage deviation as the self-optimization objective function of the cluster; if there is reactive power regulation equipment or energy storage in the cluster, selecting the minimum network loss as the self-optimization objective function of the cluster; each cluster independently performs self-optimization according to the self-optimization objective function. Through the two links of cluster self-optimization and inter-cluster coordinated optimization, different objective functions are adopted for optimization according to different cluster characteristics, so that the safety, economy and flexibility of the overall network are improved.

Description

Technical Field

[0001] This invention relates to the field of power distribution network technology, and in particular to an active power distribution network voltage optimization method that takes into account the characteristics of distributed photovoltaic clusters. Background Technology

[0002] The penetration rate of renewable energy in power systems continues to increase. These resources, connected to the end of the distribution network, are driving the transformation of the distribution network from a traditional single-end model to a multi-end controllable active distribution network (ADN). However, the intermittency and volatility of distributed resources lead to problems such as voltage fluctuations, exceeding limits, three-phase imbalance, increased network losses, and power backflow at grid-connected nodes. This increases the complexity of system power flow calculations, threatens the stable operation of the power system, and may cause significant economic losses. Therefore, improving voltage control strategies to increase the utilization rate of distributed sources and reduce distribution network losses while ensuring system voltage stability has become an important research direction.

[0003] Traditional voltage control architectures for power distribution networks mainly include three types: local control, centralized control, and distributed control. Local control has the advantages of fast response and low investment cost, but its voltage regulation capability is limited and it cannot fully utilize the system's controllable resources. Centralized control achieves global optimization by uniformly allocating voltage regulation resources, but it faces problems such as large data volume, heavy communication burden, and high investment cost. In contrast, distributed control has good autonomy and adaptability, low investment cost, small communication data volume, can fully leverage the autonomy of distributed photovoltaic systems, and has strong robustness.

[0004] Distributed control divides the power distribution network into multiple clusters by partitioning them into clusters. Each cluster performs autonomous control and simultaneously adopts inter-cluster coordination optimization to solve the voltage over-limit problem caused by the high proportion of distributed photovoltaic access, reduce network losses, and make full use of the reactive power compensation resources of each cluster. Currently, the commonly used cluster partitioning algorithms mainly include the following three categories, each with its own characteristics and applicable to different application scenarios: (1) Complex network community detection algorithm: This type of method abstracts the power distribution network into a complex network and identifies closely connected sub-networks through the principle of maximizing modularity. (2) Dynamic partitioning algorithm based on cluster analysis: This type of algorithm realizes cluster partitioning by mining the electrical correlation characteristics between nodes. (3) Multi-objective intelligent optimization algorithm: Intelligent algorithms show unique advantages for multi-constraint optimization problems in cluster partitioning. Various cluster partitioning algorithms in power systems often form a complementary relationship in practical applications: cluster analysis is suitable for rapid initial screening, community detection is good at extracting structural features, and intelligent optimization is used for refined decision-making. In the construction of cluster division criteria and indicator system, the mainstream division criteria take electrical coupling as the core, emphasizing the strong electrical connection between nodes in the cluster (such as voltage sensitivity and power interaction) and the weak coupling characteristics between clusters. At the same time, it combines indicators such as source-load-storage matching degree, power reserve degree, and communication load to build a comprehensive indicator system. However, it lacks the assessment of the voltage regulation potential of reactive power compensation devices and energy storage in the cluster.

[0005] In traditional distributed control optimization strategies, the objective function during intraday regulation typically falls into two categories. One is a single safety or economic objective function. The safety objective function often focuses on voltage deviation, while the economic objective function focuses on network losses. However, adopting a single safety objective function might increase reactive power output to raise voltage levels, leading to increased network losses. Similarly, adopting a single economic objective function to reduce network losses might exacerbate the risk of voltage exceeding limits. The second approach involves a multi-objective optimization function, selecting different weights for safety and economic indicators. However, the weights of safety and economic in multi-objective optimization functions are difficult to determine, and the optimized values ​​require normalization. Furthermore, existing distribution network voltage optimization methods do not differentiate objective functions based on the characteristics of different clusters, easily leading to underutilization of reactive power compensation resources and energy storage devices, hindering precise optimization. Summary of the Invention

[0006] In view of the problems mentioned above, such as voltage exceeding limits caused by the high proportion of distributed photovoltaic (PV) grid integration, the lack of consideration for voltage regulation potential in existing cluster classification indicators, and the failure to select differentiated objective functions based on cluster characteristics in distributed control optimization methods, this invention provides an active distribution network voltage optimization method that considers the characteristics of distributed PV clusters. This method can reduce network losses in the distribution network, ensure that the voltage does not exceed limits and remains within a reasonable range, and fully utilize reactive power compensation resources and energy storage equipment. By considering electrical distance and voltage regulation potential indicators that approximate voltage sensitivity to form a comprehensive cluster classification index, and selecting differentiated objective functions for different cluster characteristics to achieve precise optimization, this method can fully utilize various reactive power compensation resources in the distribution network and improve the safety and economy of the power grid.

[0007] This invention provides the following technical solution: an active distribution network voltage optimization method considering the characteristics of distributed photovoltaic clusters, comprising the following steps:

[0008] Step 1: Given the initial operating data of the distribution network, perform cluster partitioning based on the K-means algorithm according to the comprehensive cluster partitioning index;

[0009] Step 2: Based on the cluster division results, determine the self-regulating optimization objective function for each cluster according to its characteristics. If there is no reactive power regulation equipment or energy storage in the cluster, select the minimum voltage deviation as the self-regulating optimization objective function for that cluster. If there is reactive power regulation equipment or energy storage in the cluster, select the minimum network loss as the self-regulating optimization objective function for that cluster, so as to achieve accurate optimization and ensure that reactive power regulation resources within the cluster are not wasted.

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

[0011] Step 4: Initialize the Lagrange 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-regulation optimization based on its own objective function to obtain the current optimal solution for each cluster;

[0013] Step 6: Calculate the Lagrange penalty term for the cluster edge nodes to facilitate updating the objective function of inter-group coordination optimization;

[0014] Step 7: Add a Lagrange penalty term to the autonomous optimization objective function of each cluster, use the alternating direction multiplier method for 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 results have converged based on the data from the cluster edge nodes. If yes, end the process; otherwise, update the active power, reactive power, and voltage values ​​of the cluster edge nodes and return to Step 5 to continue until the optimal solution is obtained.

[0016] As a preferred embodiment of the active distribution network voltage optimization method considering the characteristics of distributed photovoltaic clusters described in this invention, the cluster division in step one uses a comprehensive cluster division index composed of an electrical distance index considering approximate voltage sensitivity and a cluster voltage regulation potential index. The electrical distance is calculated based on approximate voltage sensitivity, linking the node voltage change with the active and reactive power changes of each node in a functional form.

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

[0018] In the formula: ΔU is the node voltage change matrix, ΔP and ΔQ are the changes in active and reactive power injected into the node, respectively, and H, N, J, and L are elements in the Jacobian matrix. When ΔP and ΔQ are both 0, i.e., when the active or reactive power injected into the node remains constant, we can obtain:

[0019]

[0020] In the formula: S VP S VQ These 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 is based on the approximate voltage sensitivity. ij The expression is:

[0021]

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

[0023] Cluster voltage regulation potential refers to the ability of reactive power compensation devices and energy storage within a cluster to regulate voltage exceedances at nodes within the cluster. The expression for the voltage regulation potential index of cluster K is:

[0024]

[0025] In the formula: Let α3 and β3 represent the over-limit regulation capabilities of the reactive power compensation device and energy storage within cluster K, respectively. α3 and β3 represent the weighting coefficients of the reactive power compensation device and energy storage, respectively, with a sum of 1 and both set to 0.5 to ensure equal weighting for their voltage over-limit regulation capabilities. The voltage over-limit regulation capabilities of the reactive power compensation device and energy storage can be expressed as follows:

[0026]

[0027] In the formula: ΔU K,max The voltage limit is exceeded by the node with the highest voltage in cluster K. If the voltage does not exceed the limit, then ΔU K,max =0; These represent the active power margin of the energy storage at node j and the reactive power margin of the reactive power compensation device, respectively.

[0028] The comprehensive cluster classification index considers both the electrical distance (approximate voltage sensitivity) and the cluster voltage regulation potential index, and its expression is:

[0029]

[0030] In the formula: γ is a comprehensive index for cluster partitioning; the larger the value, the better the performance of cluster partitioning; l ij,max For l ij The maximum value in n; c This represents the number of clusters after the network is partitioned.

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

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

[0033]

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

[0035] (3) For all the indicators of the nodes in the network, sort them in ascending order and randomly select an element as the threshold. Nodes with indicators less than the threshold have a large number of surrounding nodes and can be regarded as cluster centers. Therefore, select nodes with indicators less 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 that is farthest from the existing cluster center from the remaining elements in set E as the next cluster center.

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

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

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

[0041] As a preferred embodiment of the active distribution network voltage optimization method considering the characteristics of distributed photovoltaic clusters described in this invention, wherein: the objective functions for minimizing voltage deviation and minimizing network loss in step two are respectively:

[0042]

[0043] In the formula: f s The objective function f represents the function that minimizes voltage deviation. e The objective function representing the minimum network loss; U ref Indicates the voltage reference value; n K r is the number of nodes within the cluster. ij P is the resistance of line ij; ij,t Q ij,t U represents the active power and reactive power of line ij at time t, respectively; i,t Let be the voltage at node i at time t.

[0044] As a preferred embodiment of the active distribution network voltage optimization method considering the characteristics of distributed photovoltaic clusters described in this invention, 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 the clusters. The virtual edge nodes are artificially added virtual nodes to facilitate inter-cluster decoupling. Cluster I and cluster K are connected by line ab, and cluster K and cluster J are connected by line c1. 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 in cluster K, and a virtual edge node c1 is added to line c1 in cluster J. Virtual edge node a1 belongs to cluster K, and virtual edge node c1 belongs to cluster J. First, information is exchanged between edge node a of upstream cluster I and virtual edge node a1 of cluster K, and the next round of cluster internal self-regulation optimization is carried out. Cluster K receives the accurate voltage of edge node a of upstream cluster I, the active and reactive power transmitted by virtual power transmission line a1b, the voltage of virtual edge node c1 of downstream cluster J, and the actual active and reactive power transmitted by line cl. At the same time, it sends the node voltage of virtual edge node a1 and the accurate active and reactive power transmitted by line ab to upstream cluster I, and sends the actual voltage of node c and the active and reactive power transmitted by virtual power transmission line c1l to downstream cluster J.

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

[0046] As a preferred embodiment of the active distribution network voltage optimization method considering the characteristics of distributed photovoltaic clusters described in this invention, wherein: the calculation formula for the Lagrange penalty term in step six is:

[0047]

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

[0049] As a preferred embodiment of the active distribution network voltage optimization method considering the characteristics of distributed photovoltaic clusters described in this invention, wherein: the objective function for adding the Lagrange penalty term in step seven is:

[0050]

[0051] As a preferred embodiment of the active distribution network voltage optimization method considering the characteristics of distributed photovoltaic clusters described in this invention, the step of inter-cluster coordination optimization based on the alternating direction multiplier method in step seven is as follows:

[0052] (1) The virtual edge node voltage obtained from cluster self-regulation optimization and virtual line power Each cluster accurately calculates the active power P transmitted through the inter-cluster lines ab using the Newton-Lambert method. ab,p and reactive power Q ab,p The accurate voltage U of edge node a within the group a,p And the highest voltage U inside the cluster max and lowest voltage U min And update the voltage compensation parameter ΔU max and ΔU min :

[0053]

[0054] (2) Neighboring clusters exchange inter-cluster edge data and their deviations, and update the edge data locally based on the information exchanged:

[0055]

[0056]

[0057] In the formula: x a y represents the voltage update value of the edge nodes of the upstream cluster relative to the cluster. ab z ab These represent the updated active power and reactive power values ​​transmitted between this cluster and the upstream cluster, respectively. c y represents the voltage update value of the edge nodes of the downstream cluster for the cluster. cl z cl These are the active power update values ​​and reactive power update values ​​transmitted between this cluster and the downstream cluster, respectively. c , The voltages of upstream edge node c and downstream virtual edge node c1 are U, respectively. c,p For the accurate voltage of edge node c, P cl,p and Qcl,p These are the active and reactive power transmitted via the inter-group line cl, accurately calculated using the Newton-Lambert method. and These represent the virtual active 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 multipliers of the edge data locally:

[0059]

[0060] In the formula: λ U Let λ be the updated value of the Lagrange multiplier of the edge node voltage of the upstream cluster. P , λ Q These represent the updated values ​​of the active power Lagrange multipliers and reactive power Lagrange multipliers transmitted between this cluster and the upstream cluster, respectively. c,U This is the update value of the Lagrange multiplier for the voltage of the edge nodes of the downstream cluster. These are the updated values ​​of the active power Lagrange multipliers and reactive power Lagrange multipliers, respectively, for the transmission between this cluster and the downstream cluster.

[0061] As a preferred embodiment of the active distribution network voltage optimization method considering the characteristics of distributed photovoltaic clusters described in this invention, in step eight, the convergence criterion for determining whether the results converge based on the cluster edge node data is: the deviation of cluster edge data in three consecutive steps. and All are less than the threshold σ d Marginal data bias It is the sum of the absolute values ​​of the edge node voltage deviation and the inter-cluster line power deviation between cluster K and its neighboring clusters in the nth iteration.

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

[0063] 1. This invention effectively reduces network losses and improves voltage quality in the distribution network: Through the optimized adjustment scheme generated by the algorithm, the adjustable equipment in the distribution network can flexibly adjust its output according to the actual load, thereby improving the stability of the power grid;

[0064] 2. This invention improves the utilization efficiency of various adjustable resources such as reactive power compensation devices and energy storage in the network: Different objective functions are adopted for different cluster characteristics to achieve full utilization of adjustable resources such as reactive power compensation devices and energy storage, thereby improving the overall operating efficiency. Attached Figure Description

[0065] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort. Wherein:

[0066] Figure 1 This is a schematic diagram of the method flow of the present invention.

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

[0068] Figure 3 This is a network topology and cluster partitioning diagram for an example.

[0069] Figure 4 This is a comparison chart of the voltage at various nodes before and after voltage optimization at 12 noon, as shown in the example. Detailed Implementation

[0070] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings.

[0071] Many specific details are set forth in the following description in order to provide a full understanding of the invention. However, the invention may also be practiced in other ways different from those described herein, and those skilled in the art can make similar extensions without departing from the spirit of the invention. Therefore, the invention is not limited to the specific embodiments disclosed below.

[0072] Reference Figures 1-4 This paper presents an active distribution network voltage optimization method that considers the characteristics of distributed photovoltaic clusters, including the following steps:

[0073] Step 1: Given the initial operating data of the distribution network, perform cluster partitioning based on the K-means algorithm according to the comprehensive cluster partitioning index;

[0074] This invention first adopts a comprehensive cluster partitioning index that considers electrical distance and voltage regulation potential, which are based on approximate voltage sensitivity, in the cluster partitioning process. It also uses an improved K-means algorithm to solve the local optimum problem caused by the randomness of the initial center in the traditional algorithm, and determines the optimal number of clusters through the elbow rule and the comprehensive cluster partitioning index.

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

[0076] Step 2: Based on the cluster division results, determine the self-regulating optimization objective function for each cluster according to its characteristics. If there is no reactive power regulation equipment or energy storage in the cluster, select the minimum voltage deviation as the self-regulating optimization objective function for that cluster. If there is reactive power regulation equipment or energy storage in the cluster, select the minimum network loss as the self-regulating optimization objective function for that cluster, so as to achieve accurate optimization and ensure that reactive power regulation resources within the cluster are not wasted.

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

[0078] Step 4: Initialize the Lagrange 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-regulation optimization based on its own objective function to obtain the current optimal solution for each cluster;

[0080] Step 6: Calculate the Lagrange penalty term for the cluster edge nodes to facilitate updating the objective function of inter-group coordination optimization;

[0081] Step 7: Add a Lagrange penalty term to the autonomous optimization objective function of each cluster, use the alternating direction multiplier method for 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 results have converged based on the data from the cluster edge nodes. If yes, end the process; otherwise, update the active power, reactive power, and voltage values ​​of the cluster edge nodes and return to Step 5 to continue until the optimal solution is obtained.

[0083] As a preferred embodiment of the active distribution network voltage optimization method considering the characteristics of distributed photovoltaic clusters described in this invention, in step one, cluster division adopts a comprehensive cluster division index composed of electrical distance and voltage regulation potential indicators that consider approximate voltage sensitivity, and an improved K-means algorithm is used to divide the clusters. The required initial operating data of the distribution network includes distributed photovoltaic output, load output, capacitor bank call volume, and on-load tap-changing transformer tap position. The divided clusters include edge nodes and virtual edge nodes. Each node has a certain load, and some nodes are connected to distributed photovoltaic, 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 approximate voltage sensitivity, which links the changes in node voltage with the changes in active and reactive power at each node in the form of a function.

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

[0086] In the formula: ΔU is the node voltage change matrix, ΔP and ΔQ are the changes in active and reactive power injected into the node, respectively, and H, N, J, and L are elements in the Jacobian matrix. When ΔP and ΔQ are both 0, i.e., when the active or reactive power injected into the node remains constant, we can obtain:

[0087]

[0088] In the formula: S VP S VQ These 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 is based on the approximate voltage sensitivity. ij The expression is:

[0089]

[0090] In the formula: d ij d represents the degree of influence of the power change at node j on node i. ij The smaller the value, the smaller the electrical distance between the two nodes, indicating that the power change at node j has a greater impact on node i. s This represents the total number of nodes in the network. These represent the active voltage sensitivity of node i, the active voltage sensitivity of node j relative to node i, the reactive voltage sensitivity of node i, and the reactive voltage sensitivity of node j relative 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 exceedances at nodes within the cluster. Taking cluster K as an example, the expression for cluster voltage regulation potential is:

[0092]

[0093] In the formula: Let α3 and β3 represent the over-limit regulation capabilities of the reactive power compensation device and energy storage within cluster K, respectively. α3 and β3 represent the weighting coefficients of the reactive power compensation device and energy storage, respectively, with a sum of 1 and both set to 0.5 to ensure equal weighting for their voltage over-limit regulation capabilities. The voltage over-limit regulation capabilities of the reactive power compensation device and energy storage can be expressed as follows:

[0094]

[0095] In the formula: ΔU K,max The voltage limit is exceeded by the node with the highest voltage in cluster K. If the voltage does not exceed the limit, then ΔU K,max =0; These represent the active power margin of the energy storage at node j and the reactive power margin of the reactive power compensation device, respectively.

[0096] The comprehensive cluster classification index considers both the electrical distance (approximate voltage sensitivity) and the cluster voltage regulation potential index, and its expression is:

[0097]

[0098] In the formula: γ is a comprehensive index for cluster partitioning; the larger the value, the better the performance of cluster partitioning; l ij,max For l ij The maximum value in n; c This represents the number of clusters after the network is partitioned.

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

[0100]

[0101] In the formula: This indicates that node j is related to the cluster center ε. K electrical distance, n K This represents the number of nodes in cluster K. This metric evaluates the clustering effect by calculating the sum of squared distances between samples within each cluster and the cluster center; a smaller value indicates a better clustering result. An improvement on the classic K-means clustering algorithm is made to minimize the sum of squared electrical distances between nodes within a 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, calculate its electrical distance to other nodes in the network according to the above formula, and form a set L, i.e.

[0105]

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

[0107] (3) For all the indicators of the nodes in the network, sort them in ascending order and randomly select an element as the threshold. Nodes with indicators less than the threshold have a large number of surrounding nodes and can be regarded as cluster centers. Therefore, select nodes with indicators less 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 that is farthest from the existing cluster center from the remaining elements in set E as the next cluster center.

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

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

[0112] (8) After selecting the number of clusters in the elbow interval according to the elbow rule, calculate the comprehensive cluster division index for each interval, 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 partitioning indicators, and combining them with an improved K-means clustering algorithm to achieve cluster partitioning, the optimal number of clusters is determined by the elbow rule and the comprehensive cluster partitioning indicators, thus solving the local optimum problem caused by the randomness of the initial center in the traditional algorithm.

[0114] This invention adopts a comprehensive cluster partitioning index that considers electrical distance and voltage regulation potential, which are based on approximate voltage sensitivity, and uses an improved K-means algorithm to solve the local optimum problem caused by the randomness of the initial center in the traditional algorithm. Furthermore, it determines the optimal number of clusters through the elbow rule and the comprehensive cluster partitioning index.

[0115] As a preferred embodiment of the active distribution network voltage optimization method considering the characteristics of distributed photovoltaic clusters described in this invention, wherein: the objective functions for minimizing voltage deviation and minimizing network loss in step two are respectively:

[0116]

[0117]

[0118] In the formula: f s The objective function f represents the function that minimizes voltage deviation. e The objective function representing the minimum network loss; U ref Indicates the voltage reference value; n K r is the number of nodes within the cluster. ij P is the resistance of line ij;ij,t Q ij,t U represents the active power and reactive power of line ij at time t, respectively; i,t Let be the voltage at node i at time t.

[0119] As a preferred embodiment of the active distribution network voltage optimization method considering the characteristics of distributed photovoltaic clusters described in this invention, step three includes: as follows Figure 2 As shown, during inter-cluster collaborative optimization and control, the upstream cluster I, cluster K, and downstream cluster J achieve cluster decoupling by adding virtual edge nodes and virtual power transmission lines between the clusters. The virtual edge nodes are artificially added virtual nodes to facilitate inter-cluster decoupling. Cluster I and cluster K are connected via line ab, and cluster K and cluster 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 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, information is exchanged between edge node a of upstream cluster I and virtual edge node a1 of cluster K, and the next round of cluster internal self-regulation optimization is carried out. Cluster K receives the accurate voltage of edge node a of upstream cluster I, the active and reactive power transmitted by virtual power transmission line a1b, the voltage of virtual edge node c1 of downstream cluster J, and the actual active and reactive power transmitted by line cl. At the same time, it sends the node voltage of virtual edge node a1 and the accurate active and reactive power transmitted by line ab to upstream cluster I, and sends the actual voltage of node c and the active and reactive power transmitted by virtual power transmission line c1l to downstream cluster J.

[0120] As a preferred embodiment of the active distribution network voltage optimization method considering the characteristics of distributed photovoltaic clusters described in this invention, the self-regulatory optimization in step five is as follows: each cluster adopts different objective functions according to its own cluster characteristics, and independently optimizes considering line power 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 this invention for each cluster is differentiated to take into account the characteristics of each cluster, so as to make full use of reactive power regulation resources and energy storage and achieve precise optimization.

[0122] As a preferred embodiment of the active distribution network voltage optimization method considering the characteristics of distributed photovoltaic clusters described in this invention, wherein: the calculation formula for the Lagrange penalty term in step six is:

[0123]

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

[0125] As a preferred embodiment of the active distribution network voltage optimization method considering the characteristics of distributed photovoltaic clusters described in this invention, wherein: the objective function for adding the Lagrange penalty term in step seven is:

[0126]

[0127] As a preferred embodiment of the active distribution network voltage optimization method considering the characteristics of distributed photovoltaic clusters described in this invention, the step of inter-cluster coordination optimization based on the alternating direction multiplier method in step seven is as follows:

[0128] (1) The virtual edge node voltage obtained from cluster self-regulation optimization and virtual line power Each cluster accurately calculates the active power P transmitted through the inter-cluster lines ab using the Newton-Lambert method. ab,p and reactive power Q ab,p The accurate voltage U of edge node a within the group a,p And the highest voltage U inside the cluster max and lowest voltage U min And update the voltage compensation parameter ΔU max and ΔU min :

[0129]

[0130] (2) Neighboring clusters exchange inter-cluster edge data and their deviations, and update the edge data locally based on the information exchanged:

[0131]

[0132]

[0133] In the formula: x a y represents the voltage update value of the edge nodes of the upstream cluster relative to the cluster. ab z abThese represent the updated active power and reactive power values ​​transmitted between this cluster and the upstream cluster, respectively. c y represents the voltage update value of the edge nodes of the downstream cluster for the cluster. cl z cl These are the active power update values ​​and reactive power update values ​​transmitted between this cluster and the downstream cluster, respectively. c , The voltages of upstream edge node c and downstream virtual edge node c1 are U, respectively. c,p For the accurate voltage of edge node c, P cl,p and Q cl,p These are the active and reactive power transmitted via the inter-group line cl, accurately calculated using the Newton-Lambert method. and These represent the virtual active 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 multipliers of the edge data locally:

[0135]

[0136] In the formula: λ U Let λ be the updated value of the Lagrange multiplier of the edge node voltage of the upstream cluster. P , λ Q These represent the updated values ​​of the active power Lagrange multipliers and reactive power Lagrange multipliers transmitted between this cluster and the upstream cluster, respectively. c,U This is the update value of the Lagrange multiplier for the voltage of the edge nodes of the downstream cluster. These are the updated values ​​of the active power Lagrange multipliers and reactive power Lagrange multipliers, respectively, for the transmission between this cluster and the downstream cluster.

[0137] As a preferred embodiment of the active distribution network voltage optimization method considering the characteristics of distributed photovoltaic clusters described in this invention, in step eight, the convergence criterion for determining whether the results converge based on the cluster edge node data is: the deviation of cluster edge data in three consecutive steps. and All are less than the threshold σ d Marginal data bias It is the sum of the absolute values ​​of the edge node voltage deviation and the inter-cluster line power deviation between cluster K and its neighboring 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 power flow constraints

[0140] A second-order cone relaxation is applied to the power flow constraints of the distribution network. First, consider introducing:

[0141]

[0142] In the formula: U i,t I represents the voltage at node i at time t. ij,t Let α represent the current in line ij at time t. i,t β represents the square of the voltage at node i at time t. ij,t Let represent the square of the current in line ij at time t. The constraints that the branch power flow must satisfy are:

[0143]

[0144] in

[0145]

[0146] In the formula: r ij x ij P represents the resistance and reactance of line ij, respectively. ij,t Q ij,t Let P represent the active and reactive power of line ij at time t, respectively; k:j→k represents the set of terminal nodes of the branch with node j as the first terminal node; i:i→j represents the set of first terminal nodes of the branch with node j as the last terminal node; P j,t Q j,t These represent the active and reactive power injected into node j at time t. Let be the active and reactive power of the load at node j at time t, respectively. Let t be the active and reactive power output of the photovoltaic system at node j. Let be the charging and discharging power of the energy stored at node j at time t, respectively. Let be the movable load and the interruptible load at node j at time t, respectively. Let SVC be the output of the continuous reactive power compensation device at node j at time t. Let be the output of the discrete reactive power compensation device CB at node j at time t.

[0147] (2) Node voltage constraints

[0148] Node voltage constraints should satisfy:

[0149] U i,min ≤U i,t ≤U i,max

[0150] In the formula: U i,max U i,min These represent the upper and lower limits of the voltage at node i, respectively.

[0151] (3) Constraints of Discrete Reactive Power Compensation Equipment

[0152] The capacitor CB is a discrete reactive power compensation device, which adopts a group switching method. In order to increase the service life of the CB, there is a certain limit to the number of switching operations. The constraint conditions are as follows:

[0153]

[0154] In the formula: This represents the output of the CB connected at node i at time t. This indicates the power of a single CB connected to node i. This represents the number of CB groups accessed by node i at time t, and this value is an integer. Z represents the maximum number of CB switching groups connected to node i, and Z represents the set of integers. This represents the maximum number of actions within a single scheduling cycle of the CB.

[0155] (4) Constraints of continuous reactive power compensation equipment

[0156] The static var compensator (SVC) is a continuous reactive power compensation device, and its constraints can be expressed as follows:

[0157]

[0158] In the formula: This represents the output of the SVC connected to node i at time t. This indicates the upper and lower limits of the output of the SVC connected to node i.

[0159] (5) On-load tap-changing transformer constraints

[0160] On-load tap-changing transformers (OLTCs) regulate using tap positions, similar to CBs. There are also certain limitations on the number of times an OLTC can operate within a single dispatching cycle, the constraints of which are:

[0161]

[0162] In the formula: This represents the ratio of the OLTC connected between nodes i and j at time t. This represents the OLTC gear position accessed by nodes i and j at time t, and this value is an integer. To adjust the step size, This indicates the upper and lower limits of the gear position for OLTC connection, with K0 being the initial gear position, set to 0.95. This represents the maximum number of actions within one scheduling cycle of OLTC.

[0163] (6) Distributed energy storage constraints

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

[0165]

[0166] In the formula: Let represent the charging and discharging power of the energy storage connected to node i at time t, respectively. Let represent the minimum and maximum values ​​of the energy storage charging power at node i, respectively. Let represent the minimum and maximum values ​​of the energy storage discharge power at node i, respectively. Let represent the energy storage charging and discharging efficiency at node i, respectively. Δt represents the energy storage charge connected to node i at time t, and Δt represents the time granularity of the scheduling. These represent the minimum and maximum energy storage charge of node i, respectively. These represent the energy storage charging and discharging flags at node i at time t, respectively. A value of 0 and a value of 1 indicate stop and start, respectively, and they satisfy a mutual exclusion constraint:

[0167]

[0168] (7) Demand-side response constraints

[0169] Demand-side response considers both shiftable and interruptible loads, which should respectively satisfy:

[0170]

[0171] In the formula: and These represent the amount of load that can be moved and the amount of load that can be interrupted at node i at time t, respectively. These represent the upper and lower limits of the movable load that node i can access, respectively. These represent the upper and lower limits of the interruptible load call amount connected to node i, respectively.

[0172] A simulation study was conducted using an improved IEEE 33-node network to verify the voltage optimization control algorithm. The topology diagram of the simulation study is shown below. Figure 3 As shown. PV represents distributed photovoltaic (PV) access nodes. Node 33 is the connection point between the system and the upstream network via an OLTC. The OLTC's transformation ratio ranges from 0.95 to 1.05, and its tap has 11 adjustment positions. Network nodes 3 and 8 are connected to two CBs, each with 6 taps and an output range of 0-3 MVar. Network nodes 19 and 25 are connected to SVCs with rated capacities of 0.5 MVar and 1 MVar, respectively. Network nodes 24 and 29 are connected to ESSs with a maximum charging / discharging power of 0.2 MW and a capacity of 3 MWh, respectively. Network node 12 is connected to interruptible loads, and network node 19 is connected to shiftable loads. Parameter settings Both are 5. It is 0.5MVar. There are 6 groups. Distributed energy storage and Use 0.3MWh and 3MWh respectively. Set the upper and lower limits of the network voltage to 1.07pu and 0.93pu respectively.

[0173] To verify the proposed voltage-optimized scheduling strategy, voltage optimization was performed according to the strategy described above. The cluster partitioning results are as follows: Figure 3 As shown in the figure. At noon, the voltage data of each node after adjustment was obtained and compared with the voltage distribution without the optimization strategy. The voltage distribution diagram is shown below. Figure 4 As shown.

[0174] Without the voltage optimization strategy, 18 nodes exceeded their voltage limits, with node 17 having the highest voltage at 1.12 pu. After implementing the voltage optimization scheduling strategy, the voltage deviation of each node was further improved, with the maximum voltage deviation of any node within the cluster not exceeding 3%. This demonstrates that the proposed voltage optimization strategy can significantly improve the overall voltage level of the active distribution network and enhance voltage quality.

[0175] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can 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, Includes the following steps: Step 1: Given the initial operating data of the distribution network, perform cluster partitioning based on the K-means algorithm according to the comprehensive cluster partitioning index; Step 2: Based on the cluster division results, determine the self-regulating optimization objective function for each cluster according to its characteristics. If there is no reactive power regulation equipment or energy storage in the cluster, select the minimum voltage deviation as the self-regulating optimization objective function for that cluster; if there is reactive power regulation equipment or energy storage in the cluster, select the minimum network loss as the self-regulating optimization objective function for that cluster. Step 3: Introduce virtual edge nodes between clusters, construct virtual power transmission lines to establish relationships between clusters, and decouple the clusters; Step 4: Initialize the Lagrange 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-regulation optimization based on its own objective function to obtain the current optimal solution for each cluster; Step 6: Calculate the Lagrange penalty term for the cluster edge nodes to update the objective function for inter-group coordination optimization; Step 7: Add a Lagrange penalty term to the autonomous optimization objective function of each cluster, use the alternating direction multiplier method for inter-cluster coordinated optimization scheduling, and construct a global distribution network solution by integrating the solutions of each cluster. Step 8: Determine whether the results have converged based on the data from the cluster edge nodes. If so, the process ends. If not, update the active power, reactive power, and voltage values ​​of the cluster edge nodes, and proceed to step five until the optimal solution is obtained. Step three includes: During inter-cluster collaborative optimization and control, the upstream cluster I Cluster K Downstream clusters J The three clusters are decoupled by adding virtual edge nodes and virtual power transmission lines between them; Among them, cluster I and cluster K via line ab Connected, cluster K and cluster J via line cl Connected, edge nodes form a cluster I nodes a and cluster K nodes c Correspondingly in the cluster K Central route ab Add virtual edge nodes a 1. In the cluster J Central route cl Add virtual edge nodes c 1; Virtual edge node a 1 belongs to the cluster K Virtual edge nodes c 1 belongs to the cluster J ; First, through the upstream cluster I edge nodes a and cluster K Virtual edge nodes a 1. Exchange information and perform the next round of cluster internal self-regulation optimization. K Receive upstream cluster I edge nodes a Accurate voltage, virtual power transmission lines a 1 b Transmitted active and reactive power, downstream trunking J Virtual edge node c 1. Voltage, circuit cl The actual active and reactive power transmitted simultaneously to the upstream cluster I Send virtual edge nodes a Node voltage, line ab The accurate active and reactive power transmitted to the downstream cluster J issue c Node real voltage and virtual power transmission lines c 1 l The transmitted active power and reactive power.

2. The active distribution network voltage optimization method considering the characteristics of distributed photovoltaic clusters according to claim 1, characterized in that: In step one, the cluster partitioning uses comprehensive cluster partitioning indicators, including electrical distance considering approximate voltage sensitivity and cluster voltage regulation potential indicators. Specifically: In the formula: γ To define comprehensive indicators for the cluster, l ij For nodes i and nodes j Electrical distance between them l ij,max for l ij The maximum value in; ρ K Potential for cluster voltage regulation n c This represents the number of clusters after the network is partitioned.

3. The active distribution network voltage optimization method considering the characteristics of distributed photovoltaic clusters according to claim 1, characterized in that: In step one, cluster partitioning includes: (1) For any node in the network i Calculate its electrical distance to other nodes in the network and form a set. L ,Right now (2) For sets L Sort all elements in the array in ascending order, and randomly select one element as a node. i Indicators d i Node indicators d i Used to describe nodes i Surrounding node density; (3) For all the indicators of all nodes in the network, sort them in ascending order and randomly select an element as the threshold. Select the nodes with values ​​less than the threshold to form a set. E And select a cluster center from within that set; (4) Select a set E The node with the highest index will be the first cluster node. e 1; (5) In the set E Select the node furthest from the existing cluster center from the remaining elements as the next cluster center; (6) If the partitioning result changes, repeat steps (2)-(5) to randomly select the cluster center until the result does not change; (7) Calculate the cluster partitioning quantitative evaluation index SSE, specifically: In the formula: l jεK Represents a node j With cluster center ε K electrical distance, n K Represents a cluster K The number of nodes in; (8) After selecting the number of clusters in the elbow interval according to the elbow rule, calculate the comprehensive cluster division index for each interval, and select the cluster division number and division result with the highest index value.

4. The active distribution network voltage optimization method considering the characteristics of distributed photovoltaic clusters according to claim 1, characterized in that: In step two, the objective functions for minimizing voltage deviation and minimizing network loss are respectively: In the formula: f s The objective function representing the minimum voltage deviation. f e The objective function representing the minimum network loss; U ref Indicates the voltage reference value; n K This represents the number of nodes within the cluster. r ij For the line ij The resistance; P ij,t , Q ij,t They represent t Timetable ij Active power and reactive power; U i,t for t Time Node i The voltage.

5. The active distribution network voltage optimization method considering the characteristics of distributed photovoltaic clusters according to claim 1, characterized in that: Step five includes: Each cluster adopts a different objective function based on its own cluster characteristics, and independently optimizes the process by considering line power flow constraints, node voltage constraints, continuous reactive power compensation equipment constraints, distributed energy storage constraints, and interruptible load constraints.

6. The active distribution network voltage optimization method considering the characteristics of distributed photovoltaic clusters according to claim 1, characterized in that: In step six, the formula for calculating the Lagrange penalty term is: In the formula: L 1 represents the Lagrange penalty term; τλ This represents the penalty coefficient for ensuring data consistency; λ U , λ P , λ Q These represent the Lagrange multipliers for voltage, active power, and reactive power, respectively. P ab , Q ab Indicates the line ab Active power and reactive power, , Representing downstream virtual lines a 1 b The virtual active and reactive power transmitted; U a and They are the upstream edge nodes. a and downstream virtual edge nodes a 1. Voltage; superscript n Indicates the number of iterations.

7. The active distribution network voltage optimization method considering the characteristics of distributed photovoltaic clusters according to claim 1, characterized in that: In step seven, the objective function for adding the Lagrange penalty term is: 。 8. The active distribution network voltage optimization method considering the characteristics of distributed photovoltaic clusters according to claim 1, characterized in that: In step seven, the steps for inter-group coordination optimization based on the alternating direction multiplier method are as follows: (1) The voltage of the virtual edge node obtained from the cluster's self-regulatory optimization and virtual line power , Each cluster accurately calculated the inter-cluster routes using the Newton-Lambert method. ab Transmitted active power P ab，p and reactive power Q ab，p Intra-group edge nodes a accurate voltage U a,p and the highest voltage within the cluster U max and minimum voltage U min And update the voltage compensation parameter Δ U max and Δ U min : (2) Neighboring clusters exchange edge data and its deviations, and update the edge data locally based on the information exchanged: In the formula: x a This represents the voltage update value of the edge nodes of the upstream cluster relative to the cluster. y ab , z ab These are the updated active power and reactive power values ​​transmitted between this cluster and the upstream cluster, respectively. x c This represents the voltage update value of the edge nodes of the downstream cluster. y cl , z cl These are the updated active power and reactive power values ​​transmitted between this cluster and the downstream cluster, respectively. U c , They are the upstream edge nodes. c and downstream virtual edge nodes c 1 voltage, U c,p For edge nodes c The accurate voltage, P cl,p and Q cl,p These are the inter-group routes accurately calculated using the Newton-Lambert method. cl Transmitted active and reactive power, and Representing downstream virtual lines c 1 l The virtual active and reactive power transmitted; (3) Based on the received inter-cluster edge data, each cluster updates the Lagrange multipliers of the edge data locally: In the formula: λ u This is the update value of the Lagrange multiplier for the edge node voltage of the upstream cluster. λ p , λ Q These represent the updated values ​​of the active power Lagrange multipliers and reactive power Lagrange multipliers transmitted between this cluster and the upstream cluster, respectively. λ c,u This is the update value of the Lagrange multiplier for the voltage of the edge nodes of the downstream cluster. , These are the updated values ​​of the active power Lagrange multipliers and reactive power Lagrange multipliers transmitted between this cluster and the downstream cluster, respectively. τ Indicates the penalty coefficient for ensuring data consistency; superscript n Indicates the number of iterations.

9. The active distribution network voltage optimization method considering the characteristics of distributed photovoltaic clusters according to claim 1, characterized in that: In step eight, the convergence of the results is determined based on the data from the cluster edge nodes. The convergence criterion is the deviation of the cluster edge data in three consecutive steps. , and All less than the threshold σ d Marginal data deviation For clusters K The first cluster between it and its neighboring clusters n The sum of the absolute values ​​of the edge node voltage deviation and the inter-group line power deviation in the next iteration.

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