A distributed power source site selection method based on hierarchical clustering

Abstract

This invention provides a distributed generation (DG) location method based on hierarchical clustering. This method obtains the equivalent circuit of the distribution system and uses it to calculate the incremental rate of network loss and the static voltage stability of each node in the distribution system. The incremental rate of network loss and the static voltage stability of the distribution system are normalized. The normalized results of the incremental rate of network loss and the static voltage stability of each node are used to construct the sensitivity characteristics of each node. Clustering is performed on all nodes and their corresponding sensitivity characteristics to obtain the clustering results. Based on the clustering results, the installation location of the DG is selected. This invention introduces clustering analysis into the DG location process of microgrids, avoiding the limitations of intelligent optimization algorithms that often lead to local optima and low efficiency. The proposed method can efficiently obtain uniformly distributed and effective DG installation locations.

Description

Technical Field

[0001] This invention belongs to the field of power system technology, specifically relating to a distributed power source location method based on hierarchical clustering. Background Technology

[0002] With the transformation of the global energy structure and the growing acceptance of sustainable development concepts, distributed generation is playing an increasingly prominent role in power grid planning. Distributed generation can not only effectively alleviate the pressure on traditional large power grids and improve the stability of the power system, but also promote the utilization of renewable energy, reduce environmental pollution, and achieve the goal of green and low-carbon energy development.

[0003] Distributed generation (DG) sources are typically installed on the user side or at the end of the grid, directly supplying power to loads and reducing transmission and distribution losses. In the event of grid failures, DG sources can serve as backup power, improving power supply reliability. Furthermore, proper DG location can effectively improve power quality, reduce system active power losses, and enhance grid operation economics. DG location is a multi-objective optimization problem, requiring consideration of load distribution, geographical factors, and other considerations. By comprehensively considering these factors, optimal power system configuration can be achieved, making the layout of DG sources within the grid more rational and scientific. This not only improves the operating efficiency and stability of the power system but also reduces its overall risk. Therefore, exploring an efficient DG location method is of significant theoretical and practical importance for optimizing distribution network planning and improving energy utilization efficiency.

[0004] Existing distributed generation (DG) site selection methods largely consider factors such as load distribution and geographical environment, employing intelligent optimization algorithms—such as classical mathematical optimization algorithms like particle swarm optimization and genetic algorithms, and heuristic optimization algorithms—to determine the installation locations of DGs in distribution networks or microgrids. While intelligent optimization algorithms are widely used in DG site selection, different algorithms have their own advantages, disadvantages, and applicable scope. For example, while classical mathematical optimization methods can find exact solutions, they are computationally intensive and struggle with complex problems; heuristic optimization algorithms, while computationally efficient and capable of handling complex problems, may not yield globally optimal solutions. Furthermore, the parameter settings and initial conditions of the optimization algorithm also affect the solution results. Therefore, there is an inherent contradiction between the efficiency and accuracy of DG site selection methods based on intelligent optimization algorithms. Summary of the Invention

[0005] To address the aforementioned problems in the existing technology, this invention provides a distributed power source addressing method based on hierarchical clustering. The technical problem to be solved by this invention is achieved through the following technical solution:

[0006] A distributed power source location method based on hierarchical clustering includes:

[0007] S1, obtain the equivalent circuit of the power distribution system, and use the equivalent circuit to calculate the incremental rate of network loss at each node in the power distribution system;

[0008] S2, calculate the static voltage stability of each node in the power distribution system using the equivalent circuit;

[0009] S3, normalize the incremental rate of network loss and the static voltage stability of the power distribution system for each node to obtain the normalized results of the incremental rate of network loss and the static voltage stability of each node.

[0010] S4. The sensitivity characteristics of each node are composed of the normalized results of the incremental rate of network loss and the static voltage stability of each node.

[0011] S5 performs a clustering operation on all nodes and their corresponding sensitivity features in the power distribution system to obtain the clustering results;

[0012] S6. Based on the clustering results, select the installation location of the distributed power source.

[0013] Optionally, S1 includes:

[0014] S1-1, Obtain the topology of the power distribution system and simplify the topology into an equivalent circuit;

[0015] S1-2, calculate the total active power loss of all branches in the power distribution system using the equivalent circuit;

[0016] S1-3, calculate the incremental rate of network loss at each node using the total active power loss.

[0017] Optionally, the total active power loss of all branches in S1-2 is expressed as:

[0018]

[0019] In the formula, n is the total number of branches in the power distribution system, i represents the i-th branch or node, j represents the j-th branch or node, and δ ij U is the phase angle between the voltage of the i-th branch and the voltage of the j-th branch. i Let U be the voltage amplitude of the i-th branch. j Let g be the voltage amplitude of the j-th branch. ij Let be the admittance between the i-th node and the j-th node.

[0020] Optionally, S1-3 includes:

[0021] S1-31, taking the partial derivatives with respect to the voltage phase angle and voltage amplitude of the total active power loss, yields the expression for the partial derivative result, which is expressed as:

[0022]

[0023] In the formula, U is the voltage amplitude of the branch, Q is the reactive power, P is the active power, and δ is the voltage phase angle;

[0024] S1-32, converting the expression for the partial derivatives into matrix form, we obtain the partial derivative matrix, which is represented as follows:

[0025]

[0026] S1-33, the transformation matrix is ​​obtained by transforming the partial derivative matrix using the formula for obtaining the Jacobian matrix; the formula for obtaining the Jacobian matrix is ​​expressed as:

[0027]

[0028] The transformation matrix is ​​represented as:

[0029]

[0030] In the formula, the superscript T indicates the transpose of the matrix, and the superscript -1 indicates the inversion of the matrix;

[0031] S1-34, using the transformation matrix, calculate the incremental rates of active and reactive power losses at each node. The incremental rates of active and reactive power losses at each node are expressed as follows:

[0032]

[0033] In the formula, LSFP i LSFQ represents the incremental rate of active power loss at the i-th node. i Let Q represent the incremental rate of reactive power loss at the i-th node. i P represents the reactive power of the i-th node. i This represents the active power of the i-th node;

[0034] S1-35, for each node, calculate the incremental rate of network loss for that node using the incremental rate of active power loss and the incremental rate of reactive power loss. The incremental rate of network loss for the i-th node is expressed as:

[0035]

[0036] In the formula, This refers to the power factor of a distributed power source.

[0037] Optionally, S2 includes:

[0038] The static voltage stability of each node in the power distribution system is calculated using the circuit parameters of the equivalent circuit. The static voltage stability is expressed as:

[0039]

[0040] In the formula, VSI j,t U represents the static voltage stability at the j-th node during time period t. i Let R be the voltage amplitude at the i-th node during time period t. ij X ij Let P be the line resistance and reactance between the i-th node and the j-th node, respectively. j,t Q j,t These represent the active power and reactive power at the j-th node during time period t, respectively.

[0041] Optionally, S3 includes:

[0042] S3-1, the incremental rate of network loss at each node is normalized using the normalization formula for the incremental rate of network loss. The normalization formula for the incremental rate of network loss is expressed as follows:

[0043]

[0044] In the formula, L i,t Let represent the normalized result of the incremental network loss rate of the i-th node in time period t, min(LSF) represents the minimum incremental network loss rate among all nodes, and max(LSF) represents the maximum incremental network loss rate among all nodes.

[0045] S3-2, the static voltage stability of each node in the power distribution system is normalized using the stability normalization formula, which is expressed as:

[0046]

[0047] In the formula, V i,t Let VSI represent the normalized result of the static voltage stability of the i-th node during time period t, min(VSI) represents the minimum static voltage stability of all nodes, and max(VSI) represents the maximum static voltage stability of all nodes.

[0048] Optionally, the sensitivity feature of the i-th node in S4 is represented as:

[0049] K i =[L i V i ] = [L i,1 ,···,L i,T V i,1 ,···,V i,T (11);

[0050] In the formula, L i V is the normalized value of the incremental network loss rate of the i-th node over the entire time period.i Let L be the normalized value of the static voltage stability of the i-th node over the entire time period. i,T V is the normalized value of the incremental rate of network loss for the i-th node in time period T. i,T Let L be the normalized value of the static voltage stability of the i-th node during time period T. i,1 V is the normalized value of the incremental network loss rate of the i-th node in the first time period. i,1 This is the normalized value of the static voltage stability of the i-th node in the first time period.

[0051] Optionally, S5 includes:

[0052] S5-1: Treat each node as a separate class and calculate the first distance between any two nodes;

[0053] S5-2, merge nodes according to the first distance between each pair of nodes, so that the two closest nodes form a new class;

[0054] S5-3: Determine if the number of classes is less than or equal to the set value. If yes, execute S5-7; otherwise, execute S5-4.

[0055] S5-4: Calculate the second distance between classes;

[0056] S5-5: Merge the two closest classes according to the second distance;

[0057] S5-6: Determine if the number of classes is less than or equal to the set value. If yes, execute S5-7; otherwise, execute S5-4.

[0058] S5-7: The clustering results of each node are obtained. In the clustering results, the sensitivity features are clustered according to the corresponding nodes.

[0059] Optionally, the formula for calculating the second distance is expressed as follows:

[0060]

[0061] In the formula, S represents the total number of merged nodes in a certain class, and K... i Let be the sensitivity feature of the i-th node.

[0062] Optionally, S6 includes:

[0063] S6-1, find the target node that meets the installation conditions among the nodes of each cluster in the clustering results; the installation conditions include the farthest distance from the cluster center, the maximum network loss sensitivity, and the minimum static voltage stability;

[0064] S6-2, the location of the target node is used as the installation location.

[0065] Beneficial effects:

[0066] This invention provides a distributed generation (DG) location method based on hierarchical clustering. The method obtains the equivalent circuit of the distribution system and uses it to calculate the incremental rate of network loss at each node. It then calculates the static voltage stability of each node using the equivalent circuit. The incremental rate of network loss at each node and the static voltage stability of the distribution system are normalized. The normalized results of the incremental rate of network loss and static voltage stability at each node are used to construct the sensitivity characteristics of each node. A clustering operation is performed on all nodes in the distribution system and their corresponding sensitivity characteristics to obtain the clustering results. Based on the clustering results, the installation location of the DG is selected. This invention introduces clustering analysis into the DG location process in microgrids, avoiding the limitations of intelligent optimization algorithms that often lead to local optima and low efficiency. The proposed method efficiently obtains uniformly distributed and effective DG installation locations.

[0067] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0068] Figure 1 This is a flowchart illustrating a distributed power source addressing method based on hierarchical clustering provided by the present invention.

[0069] Figure 2 This is a simplified equivalent circuit diagram of the power distribution system provided by the present invention;

[0070] Figure 3 This is a flowchart illustrating the implementation of clustering all nodes provided by the present invention.

[0071] Figure 4 This is a structural diagram of the IEEE 33-node AC / DC hybrid system provided by the present invention;

[0072] Figure 5 This is a schematic diagram of the timing characteristic curve of a typical daily distributed power source provided by the present invention;

[0073] Figure 6 This is a schematic diagram of the characteristic curves of a typical daily load time sequence provided by the present invention;

[0074] Figures 7a-7c This is a tree diagram of the hierarchical clustering method provided by the present invention. Detailed Implementation

[0075] The present invention will be further described in detail below with reference to specific embodiments, but the implementation of the present invention is not limited thereto.

[0076] Combination Figures 1 to 3 This invention provides a distributed power source addressing method based on hierarchical clustering, comprising:

[0077] S1, obtain the equivalent circuit of the power distribution system, and use the equivalent circuit to calculate the incremental rate of network loss at each node in the power distribution system;

[0078] refer to Figure 2 , Figure 2 For a simplified equivalent circuit of the power distribution system, the incremental rate of network loss characterizes the degree of influence of the power injected at each node on the system network loss.

[0079] S2, calculate the static voltage stability of each node in the power distribution system using the equivalent circuit;

[0080] S3, normalize the incremental rate of network loss and the static voltage stability of the power distribution system for each node to obtain the normalized results of the incremental rate of network loss and the static voltage stability of each node.

[0081] S4. The sensitivity characteristics of each node are composed of the normalized results of the incremental rate of network loss and the static voltage stability of each node.

[0082] S5 performs a clustering operation on all nodes and their corresponding sensitivity features in the power distribution system to obtain the clustering results;

[0083] S6. Based on the clustering results, select the installation location of the distributed power source.

[0084] This invention provides a distributed generation (DG) location method based on hierarchical clustering. The method obtains the equivalent circuit of the distribution system and uses it to calculate the incremental rate of network loss at each node. It then calculates the static voltage stability of each node using the equivalent circuit. The incremental rate of network loss at each node and the static voltage stability of the distribution system are normalized. The normalized results of the incremental rate of network loss and static voltage stability at each node are used to construct the sensitivity characteristics of each node. A clustering operation is performed on all nodes in the distribution system and their corresponding sensitivity characteristics to obtain the clustering results. Based on the clustering results, the installation location of the DG is selected. This invention introduces clustering analysis into the DG location process in microgrids, avoiding the limitations of intelligent optimization algorithms that often lead to local optima and low efficiency. The proposed method efficiently obtains uniformly distributed and effective DG installation locations.

[0085] In one specific embodiment of the present invention, S1 includes:

[0086] S1-1, Obtain the topology of the power distribution system and simplify the topology into an equivalent circuit;

[0087] S1-2, calculate the total active power loss of all branches in the power distribution system using the equivalent circuit;

[0088] according to Figure 2 It can be seen that the total active power loss of all branches is expressed as:

[0089]

[0090] In the formula, n is the total number of branches in the power distribution system, i represents the i-th branch or node, j represents the j-th branch or node, and δ ij U is the phase angle between the voltage of the i-th branch and the voltage of the j-th branch. i Let U be the voltage amplitude of the i-th branch. j Let g be the voltage amplitude of the j-th branch. ij Let be the admittance between the i-th node and the j-th node.

[0091] S1-3, calculate the incremental rate of network loss at each node using the total active power loss.

[0092] In one specific embodiment of the present invention, S1-3 includes:

[0093] S1-31, taking the partial derivatives with respect to the voltage phase angle and voltage amplitude of the total active power loss, yields the expression for the partial derivative result, which is expressed as:

[0094]

[0095] In the formula, U is the voltage amplitude of the branch, Q is the reactive power, P is the active power, and δ is the voltage phase angle;

[0096] S1-32, converting the expression for the partial derivatives into matrix form, we obtain the partial derivative matrix, which is represented as follows:

[0097]

[0098] S1-33, the transformation matrix is ​​obtained by transforming the partial derivative matrix using the formula for obtaining the Jacobian matrix; the formula for obtaining the Jacobian matrix is ​​expressed as:

[0099]

[0100] The transformation matrix is ​​represented as:

[0101]

[0102] In the formula, the superscript T indicates the transpose of the matrix, and the superscript -1 indicates the inversion of the matrix;

[0103] S1-34, using the transformation matrix, calculate the incremental rates of active and reactive power losses at each node. The incremental rates of active and reactive power losses at each node are expressed as follows:

[0104]

[0105] In the formula, LSFP i LSFQ represents the incremental rate of active power loss at the i-th node. i Let Q represent the incremental rate of reactive power loss at the i-th node. i P represents the reactive power of the i-th node. i This represents the active power of the i-th node;

[0106] S1-35, for each node, calculate the incremental rate of network loss for that node using the incremental rate of active power loss and the incremental rate of reactive power loss. The incremental rate of network loss for the i-th node is expressed as:

[0107]

[0108] In the formula, This refers to the power factor of a distributed power source.

[0109] It is worth noting that: the incremental rate of network loss (LSF) i The value is usually negative. The higher the absolute value, the more significant the effect of the distributed power source on reducing network losses after connecting to the node.

[0110] In an optional embodiment of the present invention, S2 includes:

[0111] The static voltage stability of each node in a power distribution system is calculated using the circuit parameters of an equivalent circuit. Static voltage stability is an important indicator characterizing the voltage stability of a system. The formula for calculating static voltage stability is as follows:

[0112]

[0113] In the formula, VSI j,t U represents the static voltage stability at the j-th node during time period t. i Let R be the voltage amplitude at the i-th node during time period t. ij X ij Let P be the line resistance and reactance between the i-th node and the j-th node, respectively. j,t Q j,t These represent the active power and reactive power at the j-th node during time period t, respectively.

[0114] It is worth noting that the smaller the static voltage stability value, the more sensitive the bus is to voltage collapse, meaning that the bus needs more improvement. Therefore, the bus with a small static voltage stability value should be selected as the installation location for distributed power sources.

[0115] In an optional embodiment of the present invention, S3 includes:

[0116] S3-1, the incremental rate of network loss at each node is normalized using the normalization formula for the incremental rate of network loss. The normalization formula for the incremental rate of network loss is expressed as follows:

[0117]

[0118] In the formula, L i,t Let represent the normalized result of the incremental network loss rate of the i-th node in time period t, min(LSF) represents the minimum incremental network loss rate among all nodes, and max(LSF) represents the maximum incremental network loss rate among all nodes.

[0119] S3-2, the static voltage stability of each node in the power distribution system is normalized using the stability normalization formula, which is expressed as:

[0120]

[0121] In the formula, V i,t Let VSI represent the normalized result of the static voltage stability of the i-th node during time period t, min(VSI) represents the minimum static voltage stability of all nodes, and max(VSI) represents the maximum static voltage stability of all nodes.

[0122] In an optional embodiment of the present invention, the sensitivity characteristics of each node are taken as the annual incremental rate of network loss and the static voltage stability value. Therefore, the sensitivity characteristics of the i-th node are expressed as:

[0123] K i =[L i V i ] = [L i,1 ,···,L i,T V i,1 ,···,V i,T (11);

[0124] In the formula, L i V is the normalized value of the incremental network loss rate of the i-th node over the entire time period. i Let L be the normalized value of the static voltage stability of the i-th node over the entire time period. i,T V is the normalized value of the incremental rate of network loss for the i-th node in time period T. i,T Let L be the normalized value of the static voltage stability of the i-th node during time period T. i,1 V is the normalized value of the incremental network loss rate of the i-th node in the first time period. i,1 This is the normalized value of the static voltage stability of the i-th node in the first time period.

[0125] In an optional embodiment of the present invention, S5 includes:

[0126] S5-1: Treat each node as a separate class and calculate the first distance between any two nodes;

[0127] S5-2, merge nodes according to the first distance between each pair of nodes, so that the two closest nodes form a new class;

[0128] S5-3: Determine if the number of classes is less than or equal to the set value. If yes, execute S5-7; otherwise, execute S5-4.

[0129] S5-4: Calculate the second distance between classes; the formula for calculating the second distance is as follows:

[0130]

[0131] In the formula, S represents the total number of merged nodes in a certain class, and K... i Let be the sensitivity feature of the i-th node.

[0132] S5-5: Merge the two closest classes according to the second distance;

[0133] S5-6: Determine if the number of classes is less than or equal to the set value. If yes, execute S5-7; otherwise, execute S5-4.

[0134] S5-7: The clustering results of each node are obtained. In the clustering results, the sensitivity features are clustered according to the corresponding nodes.

[0135] In an optional embodiment of the present invention, S6 includes:

[0136] S6-1, find the target node that meets the installation conditions among the nodes of each cluster in the clustering results; the installation conditions include the farthest distance from the cluster center, the maximum network loss sensitivity, and the minimum static voltage stability;

[0137] S6-2, the location of the target node is used as the installation location.

[0138] It is worth noting that while node data within the same class shows minimal differences, node data across different classes exhibits significant variations. Therefore, nodes within each class that simultaneously meet the installation requirements should be selected as installation locations, namely: ① furthest from the class center; ② highest network loss sensitivity; ③ lowest static voltage stability.

[0139] The following examples will demonstrate the specific implementation process and effects of this invention.

[0140] Transforming the IEEE 33-node system into an AC / DC hybrid microgrid, such as Figure 4As shown, node 1 is the balancing node, nodes 14-18 form DC subgrid 1, and nodes 28-33 form DC subgrid 2. Both DC subgrids have a reference voltage of 10kV. The remaining nodes in the system form an AC subgrid with a reference voltage amplitude of 12.66kV. In the diagram, circles represent residential loads, triangles represent commercial loads, and squares represent mixed loads. The distributed power sources connected to the DC subgrids are photovoltaic cells, and the distributed power sources connected to the AC subgrids are wind turbines. The allowable voltage fluctuation range for each node in the system is 0.93-1.07 pu. The base capacity of the distributed power sources is 10kWh, the total installed capacity of distributed power sources in the system does not exceed 2000kW, and the allowable installed capacity of each node does not exceed 500kW.

[0141] Figure 4 The power distribution system shown has 10 load nodes that are mixed loads, as described in Table 1.

[0142] Table 1. Composition of Mixed Load

[0143]

[0144] The time-series characteristics of various types of loads and distributed power sources on typical days in each season are as follows: Figure 5 and Figure 6 As shown. The AC subnet and DC subnet form a clustering tree, as shown. Figures 7a-7c As shown. One node is selected from each of the DC subnets, and three nodes are selected from the AC subnets as the installation locations for distributed power sources, based on... Figure 1 The method involves selecting nodes 18 and 33 for the DC subnet and nodes 9, 13, and 25 for the AC subnet.

[0145] Although this application has been described herein in conjunction with various embodiments, those skilled in the art will understand and implement other variations of the disclosed embodiments by reviewing the accompanying drawings, the disclosure, and the appended claims in carrying out the claimed application. In the claims, the word "comprising" does not exclude other components or steps, and "a" or "an" does not exclude a plurality.

[0146] The above description, in conjunction with specific preferred embodiments, provides a further detailed explanation of the present invention. It should not be construed that the specific implementation of the present invention is limited to these descriptions. For those skilled in the art, various simple deductions or substitutions can be made without departing from the concept of the present invention, and all such modifications and substitutions should be considered within the scope of protection of the present invention.

Claims

1. A distributed power source addressing method based on hierarchical clustering, characterized in that, include: S1, obtain the equivalent circuit of the power distribution system, and use the equivalent circuit to calculate the incremental rate of network loss at each node in the power distribution system; S2, calculate the static voltage stability of each node in the power distribution system using the equivalent circuit; S3, normalize the incremental rate of network loss at each node and the static voltage stability of the power distribution system to obtain the normalized results of the incremental rate of network loss and the static voltage stability at each node. S4. The sensitivity characteristics of each node are composed of the normalized results of the incremental rate of network loss and the static voltage stability of each node. S5, perform clustering operation on all nodes and their corresponding sensitivity features in the power distribution system to obtain clustering results; S6. Based on the clustering results, select the installation location of the distributed power source; S1 includes: S1-1, Obtain the topology of the power distribution system and simplify the topology into an equivalent circuit; S1-2, Calculate the total active power loss of all branches in the power distribution system using the equivalent circuit; The total active power loss of all branches in S1-2 is expressed as: ； In the formula, This represents the total number of branches in the power distribution system. Indicates the first A branch or node, Indicates the first A branch road or node, For the first Branch voltage and the first The phase angle of the branch voltage, For the first The voltage amplitude of each branch, For the first The voltage amplitude of each branch, For the first The node and the first Admittance between nodes; S1-3, Calculate the incremental rate of network loss at each node using the total active power loss; S2 includes: The static voltage stability of each node in the power distribution system is calculated using the circuit parameters of the equivalent circuit. The static voltage stability is expressed as: ； In the formula, Indicates in t The first period Static voltage stability at each node , The first The node and the first The line resistance and reactance between nodes , They are respectively in t Time period Active power and reactive power at each node.

2. The distributed power source addressing method based on hierarchical clustering according to claim 1, characterized in that, S1-3 includes: S1-31, Taking the partial derivatives of the voltage phase angle and voltage amplitude with respect to the total active power loss, we obtain the expression for the partial derivative result, which is expressed as: ； In the formula, The voltage amplitude of the branch. Reactive power Active power This refers to the voltage phase angle; S1-32, the expression for the partial derivative result is converted into matrix form to obtain the partial derivative matrix, which is expressed as follows: ； S1-33, the partial derivative matrix is ​​transformed and calculated using the formula for obtaining the Jacobian matrix to obtain the transformation matrix; the formula for obtaining the Jacobian matrix is ​​expressed as: ； The transformation matrix is ​​represented as follows: ； In the formula, superscript T The superscript -1 indicates the transpose of the matrix; S1-34, Calculate the incremental rates of active and reactive power losses for each node using the transformation matrix. The incremental rates of active and reactive power losses for each node are expressed as follows: ； In the formula, Indicates the first The slight increase rate of active power loss at each node Indicates the first The slight increase rate of reactive power loss at each node Indicates the first The reactive power of each node, Indicates the first The active power of each node; S1-35, for each node, calculate the incremental rate of network loss for that node using the incremental rate of active power loss and the incremental rate of reactive power loss. The incremental rate of network loss for each node is expressed as: ； In the formula, This refers to the power factor of a distributed power source.

3. The distributed power source addressing method based on hierarchical clustering according to claim 2, characterized in that, S3 include: S3-1, the incremental rate of network loss for each node is normalized using the normalization formula for the incremental rate of network loss. The normalization formula for the incremental rate of network loss is expressed as follows: ； In the formula, Indicates the first Each node t Normalized results of the incremental rate of network loss over a given period. This represents the minimum incremental rate of network loss among all nodes. This represents the maximum value among all nodes' incremental network loss rates; S3-2, The static voltage stability of each node in the power distribution system is normalized using a stability normalization formula, which is expressed as: ； In the formula, Indicates the first Each node t Normalized results of static voltage stability over a given period. This represents the minimum static voltage stability among all nodes. This represents the maximum static voltage stability among all nodes.

4. The distributed power source location method based on hierarchical clustering according to claim 1, characterized in that, S4 The sensitivity characteristics of each node are represented as follows: ； In the formula, For the first The normalized value of the incremental rate of network loss for each node over the entire period. For the first The normalized value of the static voltage stability of each node over the entire time period. For the first Each node in the time period The normalized value of the incremental rate of network loss. For the first Each node in the time period The normalized value of static voltage stability, For the first Normalized value of the incremental rate of network loss for each node in the first time period For the first The normalized value of static voltage stability of each node in the first time period.

5. The distributed power source addressing method based on hierarchical clustering according to claim 1, characterized in that, S5 include: S5-1: Treat each node as a separate class and calculate the first distance between any two nodes; S5-2, merge nodes according to the first distance between each pair of nodes, so that the two closest nodes form a new class; S5-3: Determine if the number of classes is less than or equal to the set value. If yes, execute S5-7; otherwise, execute S5-4. S5-4: Calculate the second distance between classes; S5-5: Merge the two closest classes according to the second distance; S5-6: Determine if the number of classes is less than or equal to the set value. If yes, execute S5-7; otherwise, execute S5-4. S5-7: The clustering results of each node are obtained. In the clustering results, the sensitivity features are clustered according to the corresponding nodes.

6. The distributed power source addressing method based on hierarchical clustering according to claim 5, characterized in that, The formula for calculating the second distance is as follows: ； In the formula, S The total number of merged nodes in a certain category. For the first Sensitivity characteristics of each node.

7. The distributed power source addressing method based on hierarchical clustering according to claim 1, characterized in that, S6 include: S6-1, Find the target node that meets the installation conditions among the nodes of each cluster in the clustering results; the installation conditions include the farthest distance from the cluster center, the maximum network loss sensitivity, and the minimum static voltage stability; S6-2, The location of the target node is taken as the installation location.

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