Improved louvain-based voltage sensitivity method for clustering of distribution network

Abstract

The improved Louvain-based voltage sensitivity power distribution network cluster division method belongs to the field of power system operation and planning. In view of the problems that after high penetration rate distributed photovoltaic is accessed, the traditional partition only depends on the topological structure, ignores the voltage autonomous ability of the cluster and the calculation load balance, and voltage out-of-limit and low collaborative calculation efficiency are easily caused, the improved Louvain-based voltage sensitivity power distribution network cluster division method first obtains a voltage sensitivity matrix through a power flow Jacobian matrix transformation, defines a node electrical distance and constructs a partition weight matrix; secondly, a comprehensive performance index system including electrical modularity, voltage support ability and cluster uniformity is established; finally, an improved Louvain algorithm is adopted to maximize the comprehensive index as the target to iteratively combine adjacent clusters, and the optimal partition result is selected. The improved Louvain-based voltage sensitivity power distribution network cluster division method realizes the collaborative optimization of the cohesion, functional autonomy and uniform scale of the cluster structure, improves the voltage self-regulation ability of the power distribution network, avoids the calculation load imbalance, and is suitable for the partition operation and collaborative control of large-scale distributed photovoltaic power distribution networks.

Description

Technical Field

[0001] This invention relates to the field of power system operation and planning technology, and in particular to a voltage sensitivity distribution network cluster partitioning method based on an improved Louvain method. Background Technology

[0002] Distributed photovoltaic (PV) power, as a clean and renewable energy source, is rapidly gaining penetration in distribution networks due to its flexible installation and abundant resources. This trend has transformed traditional distribution networks from passive, unidirectional power flow networks to active, bidirectional power flow networks, profoundly changing their operating characteristics and placing higher demands on their management and control. To address the complexities brought about by large-scale distributed PV integration, dividing the distribution network into several functionally independent and structurally cohesive clusters for zoned management has become an important means of improving system operating efficiency and reducing management risks.

[0003] In existing technologies, cluster partitioning methods mostly focus on cluster analysis of electrical topology. For example, the distributed generation cluster partitioning method based on binary sparrow search algorithm disclosed in CN118263846A achieves rapid cluster partitioning through algorithm optimization and focuses on power balance and flexible supply capabilities within the cluster. However, this method mainly relies on structural indicators and does not fully consider the independence of clusters in functions such as voltage regulation and resource matching. This may result in clusters lacking self-regulation capabilities in actual operation and requiring heavy reliance on external support, which violates the original intention of cluster autonomy. In addition, the distributed generation cluster partitioning method based on electrical distance matrix labels disclosed in CN118232400A constructs active and reactive power electrical distance matrices and uses label propagation algorithm to achieve distribution network partitioning, which can reflect the degree of electrical coupling between nodes well. However, this method also focuses on topology, neglecting the actual regulation capabilities and resource matching degree of the cluster under voltage over-limit scenarios, and does not effectively constrain the uniformity of cluster size, which can easily lead to the emergence of giant clusters or barren clusters, thereby causing computational load imbalance and reducing the overall system operating efficiency.

[0004] Further analysis reveals three main limitations of existing technologies: First, they neglect the functional independence of clusters, relying solely on structural indicators for partitioning, making it difficult for clusters to achieve self-regulation in actual operation. Second, they lack consideration for the uniformity of scale distribution, failing to effectively constrain cluster size, leading to uneven distribution of nodes or photovoltaic units and causing computational load imbalance. Third, the evaluation system is simplistic, often relying on a single indicator to assess the merits of cluster partitioning, making it difficult to comprehensively reflect the overall performance of the cluster in terms of structure, function, and scale. These problems make existing methods unsuitable for the management needs of high-penetration distributed photovoltaic power distribution networks, necessitating the development of a cluster partitioning method that balances electrical structure, functional independence, and cluster uniformity.

[0005] To address the aforementioned issues, this invention proposes a voltage sensitivity distribution network cluster partitioning method based on an improved Louvain method. By constructing a comprehensive performance index system that includes electrical modularity, voltage support capability, and cluster uniformity, it achieves an optimal partitioning scheme that balances structural cohesion, functional autonomy, and scale uniformity, providing solid support for the subsequent control, operation, and management of the distribution network. Summary of the Invention

[0006] The technical problem to be solved by this invention is to provide a voltage sensitivity distribution network cluster partitioning method based on an improved Louvain method. This method addresses the prominent problem that traditional distribution network cluster partitioning relies solely on electrical topology and neglects the autonomous voltage regulation capability and load balancing of the clusters under high-penetration distributed photovoltaic access conditions. It achieves synergistic optimization of cluster partitioning in terms of structural cohesion, functional independence, and scale uniformity, providing reliable technical support for the coordinated control and efficient operation management of distribution network zones.

[0007] To achieve the above technical objectives, the present invention adopts the following technical solution: This invention provides a voltage sensitivity distribution network cluster partitioning method based on an improved Louvain method. First, a Jacobian matrix is ​​constructed through distribution network power flow calculation. A voltage sensitivity matrix is ​​obtained through matrix transformation. The response components of node voltage amplitude to active and reactive power injections are extracted. The voltage sensitivity correlation between nodes is defined based on active and reactive voltage sensitivity. Then, the electrical distance between nodes is calculated using Euclidean distance. After normalization, a partition weight matrix is ​​formed that accurately reflects the tightness of electrical coupling between nodes, overcoming the shortcomings of traditional methods that rely solely on topological connections and cannot quantify the actual strength of electrical connections. Based on this, a comprehensive performance index system is constructed, including electrical modularity, voltage support capability, and cluster uniformity. The electrical modularity index quantifies the structural characteristics of high cohesion within the cluster and low coupling between clusters. The voltage support capability index evaluates the cluster's ability to autonomously solve voltage exceedance problems using internal photovoltaic reactive resources under extreme photovoltaic power generation conditions. The cluster uniformity index is obtained by weighted averaging of node quantity uniformity and photovoltaic resource uniformity, used to constrain cluster size and photovoltaic distribution balance. The three indices are summed according to their weights to obtain the comprehensive performance index used for optimization objectives.

[0008] This invention employs an improved Louvain algorithm for cluster partitioning, aiming to maximize the overall performance index. First, each node is initialized as an independent cluster, and an initial overall performance index is calculated. Then, an iterative process begins: traversing the topologically adjacent clusters of each cluster, performing temporary merges and calculating the resulting increase in overall performance index, selecting the adjacent cluster with the largest increase for formal merge, and repeating the iteration until convergence is met. Throughout the entire iteration process, all historical partition states are recorded, and the partition scheme that achieves the maximum overall performance index is selected as the final optimal cluster partitioning result. This improved algorithm no longer solely focuses on modularity but drives the merging process with a comprehensive index that considers structure, function, and uniformity. It can automatically lock the optimal number of clusters, avoiding giant clusters or resource-poor clusters, and ensuring the partitioning result has stable convergence and global optimality.

[0009] Compared with existing technologies, this invention accurately quantifies electrical coupling relationships through a voltage sensitivity matrix, making cluster partitioning more closely aligned with the actual physical characteristics of the distribution network. The constructed multi-dimensional index system simultaneously ensures the rationality of the cluster structure, the autonomy of voltage regulation, and the balance of computational load, effectively solving the problems of functional deficiencies and load imbalance in traditional partitioning methods. The improved Louvain algorithm boasts high computational efficiency and strong adaptability, quickly obtaining the optimal partitioning scheme, enabling each cluster to independently cope with voltage exceedances and significantly reducing the computational pressure of regional collaborative control, thereby improving the operational efficiency and safety stability of high-penetration distributed photovoltaic distribution networks.

[0010] The present invention provides a voltage sensitivity distribution network cluster partitioning method based on an improved Louvain method, which has the following advantages: 1. This invention effectively solves the problem that existing distribution network zoning strategies only focus on electrical topology while neglecting cluster functionality and uniformity of scale distribution. By optimizing the zoning structure, it avoids load imbalance caused by excessive differences in cluster size, and significantly improves the regional management efficiency of distribution networks with high penetration rates of distributed photovoltaic power.

[0011] 2. This invention constructs an electrical distance model based on voltage sensitivity, derives the voltage sensitivity matrix using the Jacobian matrix transformation for power flow calculation in distribution networks, and defines a partition weight matrix based on the voltage sensitivity matrix to reflect the tightness of electrical connections between nodes. This enables more accurate quantification of the electrical coupling strength between nodes in the distribution network, overcoming the limitations of traditional methods that rely solely on topology, and providing quantitative support for cluster partitioning that aligns with the physical characteristics of the power grid.

[0012] 3. This invention constructs a multi-dimensional comprehensive performance evaluation system that includes electrical modularity index, voltage support capability index, and cluster uniformity index, ensuring that the cluster achieves high cohesion and low coupling in structure. At the same time, for high-penetration photovoltaic scenarios, it ensures that each cluster has the functional independence to use internal photovoltaic reactive power resources to cope with voltage over-limit.

[0013] 4. This invention proposes a cluster partitioning strategy based on an improved Louvain algorithm. With the goal of maximizing the comprehensive performance index, it can efficiently find the optimal solution in complex network structures. By iteratively calculating and merging increments, it obtains the optimal cluster partitioning scheme that takes into account structure, functionality and uniformity, laying a solid foundation for subsequent distribution network management.

[0014] 5. This invention achieves a balanced distribution of cluster size and photovoltaic resources by constraining the cluster uniformity index, effectively avoiding problems such as unbalanced computational load and decreased iteration efficiency in the subsequent collaborative control process.

[0015] 6. This invention, through the design of voltage support capability indicators, enables each cluster to have autonomous voltage regulation capability under extreme conditions of large-scale photovoltaic power generation, and can independently handle internal voltage over-limit problems, reducing dependence on external control resources.

[0016] 7. This invention quantifies electrical coupling relationships based on voltage sensitivity, making the cluster partitioning results more consistent with the actual operating characteristics of the distribution network, with clear partition boundaries and explicit physical meaning, facilitating the implementation of regional decoupling control.

[0017] 8. The improved Louvain algorithm used in this invention has a fast convergence speed and strong global optimization ability. It can automatically lock the optimal number of clusters without the need for manual preset of the number of partitions, thereby improving the level of automation and intelligence of partitioning.

[0018] 9. This invention can effectively suppress voltage fluctuations caused by high-penetration distributed photovoltaic access, and improve the voltage stability and power supply quality of the distribution network.

[0019] 10. This invention achieves balanced distribution of computing load among clusters, significantly improving the computing speed and overall operating efficiency of partitioned collaborative control, and adapting to the real-time control needs of large-scale power distribution networks.

[0020] 11. This invention optimizes the matching relationship between reactive power resources and voltage regulation requirements within the cluster, improves the utilization rate of reactive power regulation capacity of distributed photovoltaic systems, reduces investment in reactive power compensation equipment, and lowers the construction and operation costs of the power distribution network.

[0021] 12. The method of this invention has strong versatility and adaptability, and can be applied to typical test systems such as IEEE 33-node and various actual engineering distribution networks, and has good engineering implementation and promotion application value.

[0022] 13. This invention can automatically complete the entire process of cluster partitioning without the need for complex parameter tuning and manual intervention, thereby reducing the workload and operational difficulty for power grid planning and operation personnel.

[0023] 14. This invention has been verified by the IEEE 33-node distribution network example. It has shown excellent performance in three dimensions: electrical modularity, voltage support capability and cluster uniformity. Its comprehensive performance indicators are outstanding, and its effectiveness and superiority have been fully verified.

[0024] 15. This invention provides a scientific and reliable zoning basis for the coordinated scheduling, voltage control, operation and maintenance of high-penetration distributed photovoltaic power distribution networks, supporting the efficient, safe and stable operation of the power distribution network.

[0025] 16. This invention achieves triple optimization of cluster structure cohesion, functional autonomy, and scale uniformity, comprehensively improving the operation management and adaptive adjustment capabilities of the distribution network in response to large-scale distributed photovoltaic access. Attached Figure Description

[0026] The present invention will be further described below with reference to the accompanying drawings and embodiments: Figure 1 This is a flowchart of the overall optimization method of the present invention; Figure 2 This is a diagram showing the comprehensive performance indicators of the IEEE 33-node distribution network after the implementation of cluster partitioning in this invention. Figure 3 This is a performance evaluation chart showing the cluster partitioning implemented in this invention. Figure 4 This is a schematic diagram of the IEEE 33-node distribution network structure after the implementation of the cluster partitioning in this invention. Detailed Implementation

[0027] The technical solutions of the present invention will be further described below with reference to the embodiments and accompanying drawings: Example 1 like Figure 1 As shown, this embodiment describes in detail the specific implementation steps of the present invention's voltage sensitivity distribution network cluster partitioning method based on the improved Louvain method, specifically including the following steps: Step 1: Obtain the distribution network topology and operating parameters, construct the Jacobian matrix through power flow calculation, and transform it to obtain the voltage sensitivity matrix. Based on the voltage sensitivity matrix, define a partition weight matrix reflecting the tightness of electrical connections between nodes: First, a Jacobian matrix is ​​constructed based on power flow calculation in the distribution network. The power flow calculation of the distribution network satisfies the following equation: (3); In the formula, and These represent the changes in active and reactive power injected into the nodes, respectively. and These represent the changes in node phase angle and voltage magnitude, respectively. Jacobian matrix calculated for power flow; 、 、 and These are the submatrices corresponding to the Jacobian matrix. Performing a matrix transformation on equation (3) yields the voltage sensitivity matrix: (4); In the formula, and These are used to quantify the response of the node voltage phase angle to active and reactive power injection, respectively. and These are used to quantify the response of node voltage magnitude to active and reactive power injection.

[0028] From equation (4), it can be seen that, in the case of In a distribution network with individual nodes, the voltage amplitude variation Simultaneously affected by changes in the active power of other nodes in the network. and reactive power change The impact is expressed as: (5); To comprehensively consider the combined effects of active and reactive disturbances on voltage coupling characteristics, a method based on active voltage sensitivity is adopted. and reactive voltage sensitivity Define the electrical relationships between nodes in this way Represented as: (6); In the formula, and Represented as nodes Sensitivity to reactive and active voltage at its own nodes; and Represented as nodes and nodes The reactive and active voltage sensitivity between them. For nodes and nodes The voltage sensitivity correlation between nodes. A partition weight matrix reflecting the tightness of electrical connection between nodes is defined using the voltage sensitivity matrix: (1); (7); In the formula: For nodes and nodes Electrical distance between them; The total number of nodes; , Representing nodes respectively and nodes Between, nodes and nodes The electrical relationship between them; This is the partition weight matrix defined by electrical distance.

[0029] Step 2: Construct a comprehensive performance index system for the distribution network cluster division scheme. The system includes an electrical modularity index that reflects the cohesion of the cluster structure, a voltage support capability index that reflects the voltage regulation capability within the cluster, and a cluster uniformity index that reflects the balance between cluster size and resource distribution. The comprehensive performance index is defined as the weighted sum of the three.

[0030] The formula for calculating the electrical modularity index, which reflects the cohesion of the cluster structure, is as follows: (8); In the formula, For nodes and nodes The weight of the connecting edges between them. If the two nodes are directly connected, then... Conversely, ; For nodes The sum of the weights of all connected edges. ; This is the sum of the weights of all edges in the network. ; For indicator functions, nodes and nodes The value is 1 when they belong to the same cluster, and 0 when they belong to different clusters.

[0031] The voltage support capability index aims to measure the ability of each solar cluster to resolve its internal maximum voltage problem using its internal regulation resources under extreme solar power generation scenarios. The calculation formula is as follows: (9); (10); In the formula, This provides voltage support capability for the entire partitioning scheme. This represents the total number of clusters. For the first The ability of photovoltaic reactive power regulation within a cluster to support voltage; For the first A set of nodes in a cluster; This represents the set of all photovoltaic inverter nodes; For nodes The actual voltage; The reference voltage is set to 1.05 pu; For nodes reactive power at nodes Voltage reactive power sensitivity; For photovoltaic nodes Adjustable reactive power margin.

[0032] The cluster uniformity index is composed of the average sum of node uniformity and photovoltaic uniformity, specifically expressed as: (11); (12); (13); In the formula, For cluster uniformity; For node uniformity; For photovoltaic uniformity; For the first The actual number of nodes contained in a cluster; This represents the total number of nodes in the entire distribution network. Total number of clusters; This represents the total number of photovoltaic (PV) systems in the distribution network. For the first The actual number of photovoltaic cells contained in each cluster;

[0033] The overall performance index is defined as the weighted sum of the three indices: (2); In the formula, For comprehensive performance indicators; , and These are the weighting coefficients corresponding to the electrical modularity index, voltage support capability, and cluster uniformity index, respectively, satisfying... .

[0034] Step 3: Propose a cluster partitioning strategy based on the improved Louvain algorithm. With maximizing the comprehensive performance index as the optimization objective, the optimal cluster partitioning scheme is obtained by iteratively calculating the index increment brought about by merging adjacent clusters.

[0035] The specific process includes: (1) First, collecting and organizing the network parameters, photovoltaic power sources and load data of the distribution network. Then, initialization processing is performed, treating each node in the distribution network as an independent initial cluster, and calculating the initial comprehensive performance index of each cluster under the current state based on the collected data. .

[0036] (2) Enter the iteration loop. For each cluster in the current network... Iterate through all its topologically adjacent neighbor clusters. For clusters Perform temporary merges. For each temporary merge operation, calculate the resulting increase in overall performance metrics, denoted as . .

[0037] (3) After completing the traversal and calculation of all adjacent clusters, identify the largest increment among the calculated increments. and its corresponding cluster Then, the two clusters are formally merged into a new cluster. After the merge is complete, a convergence check is performed to check whether all nodes in the distribution network have been merged. If not, return to step 2 and continue the next iteration based on the current updated cluster state; if yes, the loop ends.

[0038] (4) Once all nodes have been merged, retrieve all historical partition states recorded throughout the entire iteration process to find the optimal overall performance index. I c When the historical maximum value is reached, the cluster partitioning scheme corresponding to that moment is output as the final optimal result.

[0039] Figure 2 This is a graph showing the overall performance index of the IEEE 33-node distribution network after implementing cluster partitioning according to the present invention. As can be seen from the graph, as the number of clusters increases from 1, the overall performance index exhibits a significant single-peak characteristic of first rising and then falling. In the early stages of iteration, with the refinement of partitions, the structural cohesion of the clusters increases, and the index rises rapidly. When the number of clusters reaches 3, the overall performance index reaches its global peak, at which point the system achieves the best balance in terms of electrical modularity, voltage support capability, and cluster uniformity. Subsequently, as the number of clusters continues to increase, although the electrical distance may further shorten, it leads to excessive resource dispersion, resulting in a decrease in voltage support capability and scale imbalance, causing the overall performance index to show a monotonically decreasing trend. The improved Louvain algorithm proposed in this invention is based on this characteristic. By iteratively calculating and merging the increment, it automatically locks the highest point of the curve, thereby determining the optimal number of cluster partitions as 3, verifying the effectiveness and convergence of the algorithm in globally searching for the optimal partitioning scheme.

[0040] Figure 3This is a performance evaluation chart showing the implementation of the cluster partitioning method of this invention. As shown in the figure, to verify the effectiveness of the comprehensive partitioning strategy proposed in this invention, the partitioning results were quantitatively evaluated from three dimensions: electrical modularity, voltage support capability, and cluster uniformity. The bar chart data shows that the method of this invention performs excellently in all individual indicators: the electrical modularity reaches 0.606, indicating that the electrical connections between nodes within the partition are close while the inter-regional coupling is weak, which is conducive to achieving regional decoupling control; the voltage support capability index reaches 0.777, reflecting the high sensitivity of reactive power sources within the partition to control nodes exceeding limits, achieving a good match between reactive power resources and voltage regulation requirements; the cluster uniformity is as high as 0.877, indicating that the scale of each sub-region is relatively balanced, which is conducive to the balanced distribution of distributed computing load. Finally, the comprehensive performance index of this method reaches 0.739, fully demonstrating that the partitioning strategy can take into account both the physical topology of the distribution network and the voltage regulation requirements, laying a solid physical foundation for subsequent distribution network control.

[0041] Figure 4 This is a schematic diagram of the IEEE 33-node distribution network structure after implementing cluster partitioning according to the present invention. Taking the improved IEEE 33-node distribution system as an example, the partitioning result after applying the improved Louvain algorithm proposed in this invention is shown. In the figure, the entire distribution network is divided into several regions with different color markings, each region representing an independent control cluster.

[0042] It can be seen that, after applying the improved Louvain algorithm proposed in this invention, the partitioning results of the IEEE 33-node system deeply reflect the optimization orientation of comprehensive performance indicators. At the level of electrical modularity, each cluster strictly follows the physical topology extension law of the distribution network branches, forming a highly cohesive structure with tight internal electrical connections and weak inter-cluster coupling, and possessing clear physical boundaries. Regarding voltage support capability, this scheme ensures that each partition is equipped with sufficient adjustable reactive power resources by intelligently distributing distributed photovoltaic power sources within each cluster rather than through simple geographical separation, thus possessing independent self-regulation capabilities to cope with local voltage exceedances. Simultaneously, the partitioning results fully reflect the advantages of cluster uniformity, with the node size and resource distribution of each partition maintaining a high degree of balance, effectively avoiding the emergence of giant or barren clusters, and fundamentally eliminating the computational load imbalance and iteration efficiency shortcomings that may be faced in subsequent control and collaborative computing.

[0043] Example 2 In another preferred embodiment, based on implementation 1, such as Figure 1 As shown, this embodiment uses an improved IEEE 33-node distribution network system to verify the voltage sensitivity distribution network cluster partitioning method of the present invention based on the improved Louvain method in detail. The specific implementation steps are as follows: Step 1: Obtain the distribution network topology, line parameters, load data, and distributed photovoltaic access parameters. Construct a power flow Jacobian matrix through power flow calculation, and obtain a voltage sensitivity matrix through matrix transformation. Extract the sensitivity components of node voltage amplitude to active power and reactive power injection respectively. Define the voltage sensitivity correlation between nodes based on the sensitivity components. Further calculate and normalize the electrical distance between nodes to obtain a partition weight matrix that can accurately characterize the degree of electrical coupling between nodes, providing a quantitative basis for subsequent cluster partitioning.

[0044] Step 2: Construct a comprehensive performance index system for distribution network cluster division, calculate the electrical modularity index, voltage support capability index, and cluster uniformity index respectively, and sum the three indices according to the preset weight coefficients to obtain the comprehensive performance objective function for cluster division optimization, so as to realize the unified evaluation of cluster structure cohesion, voltage regulation autonomy, and scale distribution uniformity.

[0045] Step 3: Execute the cluster partitioning process based on the improved Louvain algorithm, initialize each node as an independent cluster, and calculate the initial comprehensive performance index; traverse the adjacent clusters of each cluster, perform temporary merging and calculate the incremental comprehensive performance index, and merge the cluster with the largest incremental index; repeat the iterative merging operation until the convergence condition is met, record the partitioning state throughout the iteration process, and select the state where the comprehensive performance index reaches the maximum value as the optimal cluster partitioning scheme.

[0046] like Figure 2 As shown, as the number of clusters gradually increases from 1, the comprehensive performance index exhibits a single-peak change characteristic of first rising and then falling. When the number of clusters is 3, the comprehensive performance index reaches the global optimum, indicating that the method of the present invention can automatically lock the optimal number of partitions and achieve the best balance between structure, function and uniformity.

[0047] like Figure 3 As shown, the optimal partitioning scheme was quantitatively verified. The results show that the three indicators of electrical modularity, voltage support capability, and cluster uniformity are all at a high level, and the overall performance is excellent, proving that the present invention has outstanding advantages in cluster structure, voltage regulation capability and load balancing.

[0048] like Figure 4 As shown, after being divided by the method of this invention, the IEEE 33-node distribution network forms multiple clusters with clear boundaries, close electrical connections, and balanced photovoltaic resource allocation. Each cluster has independent voltage regulation capabilities, low coupling between clusters, and balanced computational load, which can directly support the regional collaborative control and efficient operation management of the distribution network.

[0049] Example 3 In another preferred embodiment, this embodiment is based on embodiment 1, such as... Figure 1As shown, this embodiment uses an improved IEEE 33-node distribution network as the test object, connecting a high-penetration distributed photovoltaic system. Cluster partitioning and effect verification are completed according to the method of this invention. The specific implementation process is as follows: Step 1: Collect IEEE 33-node distribution network topology, line parameters, load and photovoltaic operation data, construct Jacobian matrix through power flow calculation and transform to obtain voltage sensitivity matrix, define node electrical distance based on voltage sensitivity, generate partition weight matrix, and accurately quantify the strength of electrical coupling between nodes.

[0050] Step 2: Construct a comprehensive performance index system that includes electrical modularity, voltage support capability, and cluster uniformity, with the weighted sum of the three as the optimization objective.

[0051] Step 3: The improved Louvain algorithm is used to iteratively optimize the process, merging adjacent clusters with the goal of maximizing the overall performance index, and automatically searching for the optimal number of partitions and partitioning scheme.

[0052] like Figure 2 As shown, with the increase of the number of clusters, the comprehensive performance index shows a single-peak distribution of first rising and then falling, reaching its peak when the number of clusters is 3. This verifies that the present invention can automatically locate the optimal partition and avoid the deviation caused by manually setting the number.

[0053] like Figure 3 As shown, after being divided according to the present invention, the electrical modularity reaches 0.606, the cluster cohesion is strong and the interval coupling is weak; the voltage support capability index reaches 0.777, each cluster can independently handle voltage over-limit by relying on internal photovoltaic reactive power; the cluster uniformity index reaches 0.877, the nodes and photovoltaic distribution are balanced, and there are no giant / barren clusters.

[0054] like Figure 4 As shown, the IEEE 33-node system is divided into three clusters with clear boundaries, close electrical connections, and balanced resource allocation. The partitioning structure is highly matched with the physical topology of the power grid.

[0055] Through implementation and verification, the beneficial effects of the present invention are as follows: 1. This invention can automatically determine the optimal number of clusters, and compared with the traditional fixed partitioning method, the overall performance index is improved by more than 15%; 2. The cluster electrical modules of this invention have a higher degree of modularity, a significant decoupling effect, and a reduction of more than 30% in the computational load for collaborative control; 3. This invention ensures sufficient voltage support for each cluster, reducing the number of voltage-over-limit nodes under high-power photovoltaic conditions by more than 70%. 4. This invention achieves uniform distribution of cluster size and photovoltaic resources, with a computational load deviation of less than 10% and a 40% improvement in collaborative computing efficiency; 5. This invention can complete the entire process partitioning without manual intervention, improving implementation efficiency by more than 50% compared to traditional methods; 6. The overall performance index of this invention in the IEEE 33-node system reaches 0.739, which is far higher than that of a single topology partitioning method, and its effectiveness has been fully verified.

[0056] In the preferred scheme, the process of defining the partition weight matrix based on the voltage sensitivity matrix in step 1 is as follows: first calculate the node... With nodes voltage sensitivity correlation Then calculate the electrical distance using the formula. Finally, the partition weight matrix is ​​obtained by normalizing the electrical distance. The above settings, through precise calculation of voltage sensitivity correlation and electrical distance, can accurately reflect the tightness of electrical coupling between nodes. The normalized partition weight matrix provides a scientific and reasonable quantitative basis for subsequent cluster partitioning, making the partitioning results more in line with the actual operating characteristics of the power grid, and effectively improving the accuracy and reliability of cluster partitioning.

[0057] In the preferred embodiment, step 1 defines a partition weight matrix that reflects the electrical connection between nodes based on the voltage sensitivity matrix, and quantifies the response of node voltage amplitude to active and reactive power injection through Jacobian matrix transformation. The above settings can more accurately reflect the physical electrical coupling strength between nodes in the distribution network than the traditional method based solely on topological distance, providing a quantitative basis that fits the actual physical characteristics of the power grid for subsequent cluster partitioning, and ensuring the scientific nature of the partitioning results.

[0058] In the preferred embodiment, the voltage sensitivity correlation From the active voltage sensitivity between nodes With reactive voltage sensitivity By defining logarithmic operations, the combined impact of active and reactive disturbances on node voltage coupling characteristics is comprehensively characterized. The above settings, by comprehensively considering active and reactive disturbances through logarithmic operations, can more comprehensively and accurately reflect the voltage coupling characteristics between nodes, avoiding the deviation caused by considering a single factor. This provides strong support for accurately quantifying the electrical connections between nodes and helps improve the adaptability of cluster partitioning to the actual operation of the power grid.

[0059] In the preferred embodiment, the comprehensive performance index system of the distribution network cluster partitioning scheme constructed in step 2 includes electrical modularity index, voltage support capability index, and cluster uniformity index, and the comprehensive performance index is defined as the weighted sum of the three. The above settings enable the partitioning strategy to not only focus on the cohesion of the topology, but also emphasize the functional independence of the cluster under the conditions of large-scale photovoltaic power generation, as well as the balance between cluster size and resource distribution, thereby avoiding the cluster calculation lag problem caused by unreasonable partitioning.

[0060] In the preferred embodiment, the electrical modularity index mentioned in step 2 is used to measure the cohesion of the cluster structure. It is calculated based on the partition weight matrix and reflects the topological characteristics of high cohesion within the cluster and low coupling between clusters. The above settings, based on the calculation of the electrical modularity index using the partition weight matrix, can scientifically quantify the cohesion of the cluster structure, making the divided clusters more structurally reasonable, with close internal node connections and loose external node connections, which is conducive to improving the stability and management efficiency of the power distribution network.

[0061] In the preferred embodiment, the voltage support capability index mentioned in step 2 is used to quantify the autonomous adjustment capability of photovoltaic reactive resources within the cluster to voltage-limit-exceeding nodes under high photovoltaic power generation conditions. It is calculated as the ratio of the photovoltaic reactive power adjustment amount within the cluster to the maximum voltage limit exceedance amount. The above setting, which quantifies the voltage support capability index in the form of a ratio, can intuitively reflect the adjustment capability of photovoltaic reactive resources within the cluster to voltage-limit-exceeding nodes, and helps to ensure that the cluster has the ability to autonomously adjust voltage during high photovoltaic power generation, thus ensuring the stable operation of the distribution network voltage.

[0062] In the preferred embodiment, the cluster uniformity index mentioned in step 2 is obtained by averaging the node uniformity and photovoltaic uniformity, which respectively characterize the balance of the distribution of the number of cluster nodes and the number of photovoltaics. The above setting, by averaging to obtain the cluster uniformity index, comprehensively considers the distribution balance of the number of nodes and photovoltaics, which can avoid the situation of excessive differences in cluster size or uneven distribution of resources, which is conducive to the load balancing calculation in the subsequent calculation and improves the overall efficiency of distribution network management.

[0063] In the preferred embodiment, the cluster partitioning strategy in step 3 adopts the improved Louvain algorithm, with the optimization objective of maximizing the comprehensive performance index. The optimal solution is obtained by iteratively calculating the index increment brought about by merging adjacent clusters. The above settings utilize the efficiency of the Louvain algorithm in complex network community detection and combine it with the unique comprehensive index of the power system for improvement. It can achieve rapid convergence while ensuring partitioning quality and adapt to the computing needs of large-scale distribution networks.

[0064] In the preferred embodiment, the improved Louvain algorithm automatically locks the number of clusters corresponding to the peak value of the comprehensive performance index during iteration, thereby achieving a globally optimal partition search. With the above settings, the improved Louvain algorithm automatically locks the number of clusters corresponding to the peak value during iteration, without the need for manual preset. It can efficiently search for the globally optimal partition in complex networks, ensuring that the partitioning scheme achieves optimal comprehensive performance and providing a reliable basis for the optimization management of the distribution network.

[0065] In the preferred scheme, the cluster partitioning scheme described in step 3 takes into account the cohesion of the distribution network electrical structure, the autonomy of voltage regulation function, and the uniformity of cluster size, so as to avoid load imbalance in collaborative calculation. With the above settings, this scheme considers multiple key dimensions to make the partitioning results more in line with the actual operation needs of the distribution network. While ensuring a reasonable electrical structure and autonomous voltage regulation, it avoids load imbalance in calculation and effectively improves the efficiency and stability of distribution network area management.

[0066] In summary, this invention proposes a voltage sensitivity distribution network cluster partitioning method based on an improved Louvain method, effectively solving specific problems in the partitioning of high-penetration distributed photovoltaic distribution network clusters in the field of power system operation and planning technology. Existing technologies mostly focus on cluster analysis of electrical topology, neglecting the functional independence and uniformity of cluster size distribution. This leads to a lack of self-regulation capability in actual operation and easily causes computational load imbalance. This invention successfully overcomes the limitations of existing technologies that rely solely on structural indicators for partitioning and neglect cluster voltage self-regulation capability and computational load balance.

[0067] This invention combines a voltage sensitivity matrix, a comprehensive performance index system, and an improved Louvain algorithm to achieve efficient and stable partitioning of distribution networks. A comprehensive performance index system is constructed, including electrical modularity, voltage support capability, and cluster uniformity indices. This system comprehensively reflects the overall performance of clusters in terms of structure, function, and scale, providing multi-dimensional quantitative support for cluster partitioning. A partition weight matrix definition method based on the voltage sensitivity matrix is ​​proposed, which can accurately quantify the electrical coupling strength between nodes, providing a quantitative basis for cluster partitioning that aligns with the physical characteristics of the power grid.

[0068] By introducing voltage support capability indicators, this approach overcomes the limitations of relying solely on structural indicators for cluster partitioning and neglecting the self-regulation capability of cluster voltage, significantly improving the self-regulation capability of clusters in actual operation. During cluster partitioning, the structural cohesion, functional autonomy, and scale uniformity of the clusters are considered simultaneously. Through optimization of the comprehensive performance indicator system, multi-dimensional cluster partitioning is achieved, effectively avoiding load imbalance in subsequent calculations. The proposed cluster partitioning strategy based on the improved Louvain algorithm, through iterative calculation of the incremental comprehensive performance indicators of merging adjacent clusters, can efficiently find the optimal solution in complex network structures, obtaining the optimal cluster partitioning scheme that balances structure, functionality, and uniformity, providing new ideas and methods for distribution network management.

Claims

1. A distribution network cluster partitioning method based on improved Louvain's voltage sensitivity method, characterized in that, Includes the following steps: Step 1: Obtain the distribution network topology and operating parameters, construct the Jacobian matrix through power flow calculation and transform it to obtain the voltage sensitivity matrix, and define a partition weight matrix based on the voltage sensitivity matrix to reflect the tightness of electrical connection between nodes; Step 2: Construct a comprehensive performance index system for distribution network cluster division. The comprehensive performance index system includes electrical modularity index, voltage support capability index, and cluster uniformity index. The comprehensive performance index is obtained by weighted summation of the three. Step 3: Using the improved Louvain algorithm, with the goal of maximizing the overall performance index, iteratively calculate the index increment of merging adjacent clusters to obtain the optimal cluster partitioning scheme.

2. The voltage sensitivity distribution network cluster partitioning method based on the improved Louvain method according to claim 1, characterized in that, The process of defining the partition weight matrix based on the voltage sensitivity matrix in step 1 is as follows: first calculate the node... and nodes The voltage sensitivity correlation is then used to calculate the electrical distance using formula (1), and finally the partition weight matrix is ​​obtained by normalizing the electrical distance: （1）； In the formula: For nodes and nodes Electrical distance between them; The total number of nodes; , Representing nodes respectively and nodes Between, nodes and nodes The electrical relationship between them.

3. The voltage sensitivity distribution network cluster partitioning method based on the improved Louvain method according to claim 2, characterized in that: The voltage sensitivity correlation is defined by logarithmic operations on the active and reactive voltage sensitivities between nodes, comprehensively characterizing the combined impact of active and reactive disturbances on the node voltage coupling characteristics.

4. The voltage sensitivity distribution network cluster partitioning method based on the improved Louvain method according to claim 1, characterized in that: The electrical modularity index mentioned in step 2 is used to measure the cohesion of the cluster structure. It is calculated based on the partition weight matrix and reflects the topological characteristics of high cohesion within the cluster and low coupling between clusters.

5. The voltage sensitivity distribution network cluster partitioning method based on the improved Louvain method according to claim 1, characterized in that: The voltage support capability index mentioned in step 2 is used to quantify the autonomous adjustment capability of photovoltaic reactive resources within the cluster to voltage over-limit nodes under high photovoltaic power generation conditions. It is calculated as the ratio of photovoltaic reactive power adjustment within the cluster to the maximum voltage over-limit.

6. The voltage sensitivity distribution network cluster partitioning method based on the improved Louvain method according to claim 1, characterized in that: The cluster uniformity index mentioned in step 2 is obtained by averaging the node uniformity and photovoltaic uniformity, which respectively characterizes the balance of the distribution of the number of cluster nodes and the number of photovoltaics.

7. The voltage sensitivity distribution network cluster partitioning method based on the improved Louvain method according to claim 1, characterized in that, The comprehensive performance indicators in step 2 are as follows: （2）； In the formula, For comprehensive performance indicators; , and These are the weighting coefficients corresponding to the electrical modularity index, voltage support capability, and cluster uniformity index, respectively. For electrical modularity indicators; This refers to the voltage support capability indicator. This is an index for cluster uniformity.

8. The voltage sensitivity distribution network cluster partitioning method based on the improved Louvain method according to claim 1, characterized in that, The execution flow of the improved Louvain algorithm in step 3 is as follows: Step 3.1: Initialize each node as an independent cluster and calculate the initial overall performance metrics; Step 3.2: Traverse adjacent clusters and temporarily merge them, then calculate the incremental performance metrics resulting from the merger; Step 3.3: Merge adjacent clusters with the largest increments and repeat the iteration until convergence; Step 3.4: Select the partition result with the largest comprehensive performance index during the iteration process as the optimal solution.

9. The voltage sensitivity distribution network cluster partitioning method based on the improved Louvain method according to claim 8, characterized in that: The improved Louvain algorithm automatically locks the number of clusters corresponding to the peak of the comprehensive performance index during iteration, thereby achieving a globally optimal partition search.

10. The voltage sensitivity distribution network cluster partitioning method based on the improved Louvain method according to claim 1, characterized in that: The cluster partitioning scheme described in step 3 takes into account the cohesion of the power distribution network's electrical structure, the autonomy of voltage regulation functions, and the uniformity of cluster size, thus avoiding load imbalance in collaborative calculation.

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