Substation power supply range division method based on improved K-means clustering algorithm

Abstract

A transformer substation power supply range division method based on an improved K-means clustering algorithm aims to reasonably divide a transformer substation power supply area, and comprises the following steps: step 1, firstly, constructing an initial clustering center method based on a density method and in a mode of setting a dynamic change coefficient # imgabs0 #; 2, on the basis of the initial clustering center method in the step 1, introducing an inter-partition load translation strategy, and constructing an improved K-means method; 3, constructing a transformer substation range division model based on the clustering method provided in the step 2, and giving out an evaluation index; and 4, based on the transformer substation range division model constructed in the step 3, solving by adopting a particle swarm optimization (PSO) algorithm. The method is suitable for determining the number and the positions of the to-be-built substations according to the total load in the planning area, and can reduce overload and light load conditions.

Description

Technical Field

[0001] The present invention relates to the technical field of power systems, and in particular to a power supply range division technology for power system substations, and specifically to a substation power supply range division method based on an improved K-means clustering algorithm that can be applied in power system substation scenarios. Background Art

[0002] Existing substation range division methods, such as the existing technology "Substation Sizing and Site Selection Based on K-Means Clustering Particle Swarm Optimization," mostly first use the K-means clustering algorithm to divide the substation's power supply range and then combine it with intelligent algorithms for optimization. However, this method has the following technical problems: 1) Randomly selecting the initial cluster center affects the stability of the algorithm; According to the basic principles of the K-means clustering algorithm, K initial cluster centers are randomly determined, and then the optimal cluster center is iteratively searched until the algorithm converges and outputs the clustering results. If different initial cluster centers are selected, different clustering results may be obtained. This method of randomly selecting initial values will lead to unstable clustering results.

[0003] 2) The number of clusters K needs to be set manually; At the beginning of the algorithm, the number of clusters K needs to be set based on manual experience. However, in actual engineering applications, the final number of clusters of the data set is unknown. Therefore, the algorithm is highly subjective, resulting in inaccurate or unreasonable clustering results, which also limits its development and application to a certain extent.

[0004] 3) Ignoring the characteristics of the clustering data itself; The clustering evaluation criterion of the algorithm is to minimize the sum of squares of all data objects to the cluster center point of the class. In practical applications, the characteristic attributes of the data itself are not taken into account. For example, in the process of dividing the power supply range of substations, directly using the K-means clustering algorithm cannot reflect the impact of uneven load distribution on the division of the power supply range of substations, which may cause the substation to be overloaded or underloaded, affecting the safe and stable operation of the power grid.

[0005] In view of the shortcomings of the above-mentioned traditional K-means clustering algorithm, the present invention proposes corresponding improvement measures to more accurately and reasonably divide the power supply range of the substation Summary of the Invention The purpose of the present invention is to provide a substation power supply range division method based on an improved K-means clustering algorithm, which aims to fully take into account the impact of load distribution on range division, so that the total load of each divided power supply range is relatively close, reducing the occurrence of overload and underload conditions, and improving the stability and reliability of the power grid.

[0006] A method for dividing the power supply range of a substation based on an improved K-means clustering algorithm includes the following steps: Step 1: Based on the density method and setting the dynamic change coefficient The initial cluster center selection method is constructed in this way; Step 2: Based on the initial cluster center selection method in step 1, the load shifting strategy between partitions is introduced to construct an improved K-means method; Step 3: Based on the clustering method proposed in step 2, a substation range division model is constructed and evaluation indicators are given; Step 4: Based on the substation range division model constructed in step 3, the particle swarm optimization (PSO) algorithm is used to solve it.

[0007] In step 1, the following steps are included: Step 1.1: Assume that the load data set is: , in the entire dataset Using formula (1), we can get Load in With load Distance between : (1) Where: and There are two M Dimensional load, Refers to the load In the k The coordinate values of the dimensions, Refers to the load In the k The coordinate value of the dimension.

[0008] Step 1.2: According to formula (2), obtain the average distance between loads meandist : (2) Where, n is the total number of loads, for n The number of combinations of any two loads; Step 1.3: According to formula (3), obtain the density parameter of each load , integrating the density parameters of all loads, we can get the density parameter set D : (3) Where, p is any data object in the load data set, Indicates load and load distance; Step 1.4: Set the range of the number of substations to be built. Assume that the number of substations to be built is K According to the load distribution in the target year and the number and capacity of substations in the current year, the minimum number of substations to be built can be calculated. and the maximum number , as shown in formula (4) and formula (5): (4) (5) Where: int is the rounding function; is the total active power of the load; is the total load of existing substations; e is the substation load factor; is the substation power factor; is the maximum capacity of the substations to be selected; is the minimum capacity of the substations to be selected.

[0009] Step 1.5: Determine the load with the largest density parameter value as the first initial cluster center and select X Remove from the cluster, and accordingly delete the clusters whose distance to the cluster center is less than meandist load point; Step 1.6: If the number of substations to be built K If the range set in step 1.4 cannot be met, shorten the initial average distance meandist , , and clear all the initial cluster centers obtained previously; Step 1.7: Dynamically adjust the coefficient of variation , and repeat steps 1.5 to 1.6 until a substation with a larger density parameter is found within the number of substations to be built. K load points, which are the initial cluster centers.

[0010] In step 2, to ensure that the total load within each power supply range is as balanced as possible and to avoid overload and underload, an inter-partition load shifting strategy is introduced based on the initial cluster center selection method proposed in step 1. Specifically, Step 2.1: Select the method selected in step 1 K Cluster centers are obtained according to formula (1), and the distance between each load point and each cluster center is obtained. The minimum distance is found and the load is divided into the class with the closest distance to it. K power supply areas; Step 2.2: Obtain the total load in each power supply area and find the area with the highest total load. , compare the two adjacent areas and select the area with the lower total load (If there is only one adjacent area, select that area); Step 2.3: Find the area Middle distance area The nearest load point, move the load into the area .

[0011] Step 2.4: Repeat steps 2.2 to 2.3 to determine whether the total load in each power supply area is less than the set value. If so, proceed to the next step; otherwise, go to step 2.2 to re-obtain the total load in each power supply area; Step 2.5: Determine whether the total load in each power supply area is less than the maximum capacity of the substation. If so, proceed to the next step. Otherwise, return to step 1.6 and adjust the variation coefficient. Regenerate the initial cluster centers.

[0012] Step 2.6: Based on the newly generated cluster centers, determine whether the convergence criteria are met. If so, output the region division result; otherwise, jump to step 2.1.

[0013] Detailed substation power supply range division process is attached Figure 1 .

[0014] In step 3, based on the clustering method proposed in step 2, a substation range division model is constructed and evaluation indicators are given; specifically: Step 3.1: The costs in the substation scope division model include: substation investment and annual operating costs; secondary line investment annual costs; and secondary line network loss annual costs. Its objective function is as shown in formula (6)-formula (9): (6) (7) (8) (9) And the following constraints must be met: (10) (11) Where: The annual investment cost and annual operating cost of the substation; is the annual investment cost of the secondary side line of the substation; is the estimated annual network loss cost of the secondary side line of the substation; N is the number of newly built substations; is the fixed investment cost of the substation, For the i The investment cost per unit capacity of a substation is For the i The capacity of a substation, For the i Annual operating costs of a newly built substation; is the depreciation period of the substation, The depreciation period of the secondary side line of the substation; is the discount rate; For substations i The set of load nodes that supply power, , is the set of all load points; For substations i and load point j The length of the line between them; substation i The location coordinates of load j The location coordinates of is the active power of the load; For the i Maximum load factor of each substation; is the power factor; For the i The power supply radius of each substation; is the line investment cost per unit length; is the line network loss conversion coefficient, , is the line voltage, is the unit power loss discount coefficient, is the resistance per unit line length, is the annual line loss hours; Step 3.2: In order to quantify the impact of unbalanced load distribution on substation range division, the present invention introduces a load balance index and uses entropy value to process the load rate balance, as shown in formula (12): (12) Where: Indicates the load factor of the substation. Indicates substation i Active power of the supplied load node, Indicates substation i Rated capacity; If the load rate of a single substation The importance of a substation is represented by the size of the total load rate of all substations in the system. , then: (13) According to the entropy theory, the substation load rate entropy is constructed H : (14) From formula (14), we can see that It must be less than 1, so the substation load rate entropy index When the substation load is completely balanced, that is, the load rate of all substations is equal When the load rate entropy index reaches its maximum value ,in is the number of substations.

[0015] In step 4, based on the substation range division model constructed in step 3, the particle swarm optimization (PSO) algorithm is used to solve it.

[0016] Step 4.1: Initialize network parameters. Input relevant parameters such as load location and size, population size, and number of iterations. Step 4.2: Calculate the planned number range of substations using formula (4) and formula (5), let , At this time, the planned number of substations is , the number of substations to be built n is a loop variable, and the initial value of n is set to ; Step 4.3: Divide the planned area into n power supply ranges according to the substation power supply range division process in step 2; Step 4.4: Initialize the velocity and position of the particle; Step 4.5: Optimize the secondary side line of the substation based on the minimum spanning tree algorithm and calculate the particle fitness. Substituting each parameter into the objective function, the corresponding C On this basis, the load rate entropy index is obtained according to the substation capacity and power supply range division results In order to normalize the multi-target process, define the global variable and , we can better compare the advantages and disadvantages of different planning schemes. C and After standardization, the fitness can be obtained through formula (16): (15) Where, is the weight.

[0017] Step 4.6: Find the individual optimal value and the group optimal value, and update the speed and position of the particles; Step 4.7: Determine whether the termination condition is met. If so, save the planning result and set n= n +1, if not, continue with step 4.5-step 4.6; Step 4.8: Judgment n Is it greater than If yes, output the solution with the minimum fitness, otherwise continue with steps 4.3-4.7; Through the above steps, the substation power supply range division method based on the improved K-means clustering algorithm is completed.

[0018] Compared with the prior art, the present invention has the following technical effects: Using the same calculation example, the proposed method takes into account the impact of uneven load distribution within the range, ensuring that the load factor of each substation is generally between 0.42 and 0.51. This method significantly improves substation load balancing, reducing the occurrence of overload and underload conditions, thereby enhancing the stability and reliability of the power grid and increasing its overall power supply capacity. BRIEF DESCRIPTION OF THE DRAWINGS

[0019] The present invention will be further described below with reference to the accompanying drawings and examples: Figure 1 A distribution diagram of load points and substations in an actual power grid involved in an embodiment of the present invention; Figure 2 This is a schematic diagram of an actual power grid in an embodiment of the present invention; Figure 3 Schematic diagram of planning results of method 1 in an embodiment of the present invention; Figure 4 This is a schematic diagram of the planning results of method 2 in an embodiment of the present invention; Figure 5 Schematic diagram of substation load rate in method 1 and method 2 in the embodiments of the present invention. DETAILED DESCRIPTION

[0020] A method for dividing the power supply range of a substation based on an improved K-means clustering algorithm includes the following steps: Step 1: Based on the density method and setting the dynamic change coefficient The initial cluster center selection method is constructed in this way; Step 2: Based on the initial cluster center selection method in step 1, the load shifting strategy between partitions is introduced to construct an improved K-means method; Step 3: Based on the clustering method proposed in step 2, a substation range division model is constructed and evaluation indicators are given; Step 4: Based on the substation range division model constructed in step 3, the particle swarm optimization (PSO) algorithm is used to solve it.

[0021] In step 1, the following steps are included: Step 1.1: Assume that the load data set is: , in the entire dataset In the entire data set, using formula (1) we can get Load in With load Distance between : (1) Where: and There are two M Dimensional load, Refers to the load In the k The coordinate values of the dimensions, Refers to the load In the k The coordinate value of the dimension.

[0022] Step 1.2: According to formula (2), obtain the average distance between loads meandist : (2) Where, n is the total number of loads, for n The number of combinations of any two loads; Step 1.3: According to formula (3), obtain the density parameter of each load , integrating the density parameters of all loads, we can get the density parameter set D : (3) Where, p is any data object in the load data set, Indicates load and load distance; Step 1.4: Set the range of the number of substations to be built. Assume that the number of substations to be built is K According to the load distribution in the target year and the number and capacity of substations in the current year, the minimum number of substations to be built can be calculated. and the maximum number , as shown in formula (4) and formula (5): (4) (5) Where: int is the rounding function; is the total active power of the load; is the total load of existing substations; e is the substation load factor; is the substation power factor; is the maximum capacity of the substations to be selected; is the minimum capacity of the substations to be selected.

[0023] Step 1.5: Determine the load with the largest density parameter value as the first initial cluster center and select X Remove from the cluster, and accordingly delete the clusters whose distance to the cluster center is less than meandist load point; Step 1.6: If the number of substations to be built K If the range set in step 1.4 cannot be met, shorten the initial average distance meandist , , and clear all the initial cluster centers obtained previously; Step 1.7: Dynamically adjust the coefficient of variation , and repeat steps 1.5 to 1.6 until a substation with a larger density parameter is found within the number of substations to be built. K load points, which are the initial cluster centers.

[0024] In step 2, to ensure that the total load within each power supply range is as balanced as possible and to avoid overload and underload, an inter-partition load shifting strategy is introduced based on the initial cluster center selection method proposed in step 1. Specifically, Step 2.1: Select the method selected in step 1 K Cluster centers are obtained according to formula (1), and the distance between each load point and each cluster center is obtained. The minimum distance is found and the load is divided into the class with the closest distance to it. K power supply areas; Step 2.2: Obtain the total load in each power supply area and find the area with the highest total load. , compare the two adjacent areas and select the area with the lower total load (If there is only one adjacent area, select that area); Step 2.3: Find the area Middle distance area The nearest load point, move the load into the area .

[0025] Step 2.4: Repeat steps 2.2 to 2.3 to determine whether the total load in each power supply area is less than the set value. If so, proceed to the next step; otherwise, go to step 2.2 to re-obtain the total load in each power supply area; Step 2.5: Determine whether the total load in each power supply area is less than the maximum capacity of the substation. If so, proceed to the next step. Otherwise, return to step 1.6 and adjust the variation coefficient. Regenerate the initial cluster centers.

[0026] Step 2.6: Based on the newly generated cluster centers, determine whether the convergence criteria are met. If so, output the region division result; otherwise, jump to step 2.1.

[0027] Please see the attached for detailed substation power supply range division process Figure 1 .

[0028] In step 3, based on the clustering method proposed in step 2, a substation range division model is constructed and evaluation indicators are given; specifically: Step 3.1: The costs in the substation scope division model include: substation investment and annual operating costs; secondary line investment annual costs; and secondary line network loss annual costs. Its objective function is as shown in formula (6)-formula (9): (6) (7) (8) (9) And the following constraints must be met: (10) (11) Where: The annual investment cost and annual operating cost of the substation; is the annual investment cost of the secondary side line of the substation; is the estimated annual network loss cost of the secondary side line of the substation; N is the number of newly built substations; is the fixed investment cost of the substation, For the i The investment cost per unit capacity of a substation is For the i The capacity of a substation, For the i Annual operating costs of a newly built substation; is the depreciation period of the substation, The depreciation period of the secondary side line of the substation; is the discount rate; For substations i The set of load nodes that supply power, , is the set of all load points; For substationsi and load point j The length of the line between them; substation i The location coordinates of load j The location coordinates of is the active power of the load; For the i Maximum load factor of each substation; is the power factor; For the i The power supply radius of each substation; is the line investment cost per unit length; is the line network loss conversion coefficient, , is the line voltage, is the unit power loss discount coefficient, is the resistance per unit line length, is the annual line loss hours; Step 3.2: In order to quantify the impact of unbalanced load distribution on substation range division, the present invention introduces a load balance index and uses entropy value to process the load rate balance, as shown in formula (12): (12) Where: Indicates the load factor of the substation. Indicates substation i Active power of the supplied load node, Indicates substation i Rated capacity; If the load rate of a single substation The importance of a substation is represented by the size of the total load rate of all substations in the system. , then: (13) According to the entropy theory, the substation load rate entropy is constructed H : (14) From formula (14), we can see that It must be less than 1, so the substation load rate entropy index When the substation load is completely balanced, that is, the load rate of all substations is equal When the load rate entropy index reaches its maximum value ,in is the number of substations.

[0029] In step 4, based on the substation range division model constructed in step 3, the particle swarm optimization (PSO) algorithm is used to solve it.

[0030] Step 4.1: Initialize network parameters. Input relevant parameters such as load location and size, population size, and number of iterations. Step 4.2: Calculate the planned number range of substations using formula (4) and formula (5), let , At this time, the planned number of substations is , the number of substations to be built n is a loop variable, and the initial value of n is set to ; Step 4.3: Divide the planned area into n power supply ranges according to the substation power supply range division process in step 2; Step 4.4: Initialize the velocity and position of the particle; Step 4.5: Optimize the secondary side line of the substation based on the minimum spanning tree algorithm and calculate the particle fitness. Substituting each parameter into the objective function, the corresponding C On this basis, the load rate entropy index is obtained according to the substation capacity and power supply range division results In order to normalize the multi-target process, define the global variable and , we can better compare the advantages and disadvantages of different planning schemes. C and After standardization, the fitness can be obtained through formula (16): (15) Where, is the weight.

[0031] Step 4.6: Find the individual optimal value and the group optimal value, and update the speed and position of the particles; Step 4.7: Determine whether the termination condition is met. If so, save the planning result and set n = n +1, if not, continue with step 4.5-step 4.6; Step 4.8: Judgment n Is it greater than If yes, output the solution with the minimum fitness, otherwise continue with steps 4.3-4.7; Through the above steps, the substation power supply range division method based on the improved K-means clustering algorithm is completed.

[0032] Compared with the prior art, the present invention has the following technical effects: 1) Using the same calculation example, the proposed method accounts for the impact of uneven load distribution within the range, ensuring that the load factor of each substation is generally between 0.42 and 0.51. This method significantly improves substation load balance, reducing the occurrence of overload and underload conditions, thereby enhancing the stability and reliability of the power grid and increasing its overall power supply capacity.

[0033] Example: The present invention uses an actual area in Hunan as a simulation example. The load (next-level substation) distribution and capacity of the area are known, and the load coordinates and capacity are shown in Table 1. Before the planning began, there were 7 substations in the area, which were used as known quantities, with capacities of 3×1000MVA, 2×1000MVA, 3×1000MVA, 3×750MVA, 2×1000MVA, 3×750MVA, and 3×1000MVA. If there is an isolated load node, the load can be connected to the nearest existing substation. It is planned to build a new 500kV substation, and its scale options are 3×750MVA and 3×1000MVA. According to formulas (5)-(6), it is planned to build 6-9 substations in the area. When the substation has 3 main transformers, the maximum load rate is 87%. The actual power grid before the implementation of the plan is shown in the attached figure. Figure 2 The simulation parameters involved in the model are shown in Table 2.

[0034] Table 1 Load information parameters

[0035] Table 2 Simulation parameters

[0036] In order to verify the effectiveness and correctness of the method of the present invention in the face of actual engineering problems, the following two methods are used to verify the actual calculation examples and analyze the calculation results. The location and capacity of the substation after planning are shown in Table 3, and the optimal range division scheme is shown in the attached figure. Figure 3 , Attachment Figure 4 shown.

[0037] Method 1: Use K-means clustering algorithm to divide the power supply range of the substation; Method 2: Use the improved K-means clustering algorithm to divide the substation power supply range; Table 3 Substation location and capacity options for methods 1 and 2

[0038] From the attached Figure 3 , Attachment Figure 4,Table 3 shows that: on the one hand, the number and capacity plans of substations in Method 1 and Method 2 are exactly the same. ,Among them, Method 1 and Method 2 built 7 new substations, with ,capacities of 3×750MVA, 3×1000MVA, 3×750MVA, 3×1000MVA, 3×1000MVA, 3×1000MVA, ,and 3×750MVA respectively. The reason ,is that Methods 1 and 2 adopt the traditional range division model constructed ,with the “point-to-point” connection between substation and load.

[0039] On the other hand, the substation locations and the supplied load nodes obtained by Method 1 and Method 2 are different. Among them, Method 1 and Method 2 are both divided into 7 power supply ranges, but the substation locations and the supplied load points are different. The reason is that Method 1 uses the traditional K-means clustering algorithm to divide the power supply range, without considering the impact of the uneven load distribution in the planning area, and divides the power supply range based entirely on the Euclidean distance. Method 2 fully takes into account the attribute characteristics of the load itself and divides the power supply range with the improved K-means clustering algorithm.

[0040] Subsequently, the cost indicators of the solutions obtained by Method 1 and Method 2 were compared and analyzed, and the calculation results are shown in Table 4.

[0041] Table 4 Cost comparison results between method 1 and method 2

[0042] Table 4 shows that compared with Method 1, Method 2 increases the total substation planning cost, annual secondary line investment cost, and annual secondary line operating cost by 1.59%, 4.42%, and 5.27%, respectively. The annual substation investment and operating costs are the same. This is primarily due to the following: Method 1 uses the traditional K-means clustering algorithm to divide the power supply range. This method uses geometric principles to calculate the distance between load nodes and substations, minimizing this distance. This results in a relatively compact load distribution within the power supply range, shortening the distance between loads and substations, and lowering the annual substation secondary line investment and operating costs. Unlike Method 1, Method 2 considers the influence of load power to maintain load balance across substations. This results in a larger power supply range than Method 1, resulting in a relatively longer distance between loads and substations, increasing the annual line investment and operating costs. Since Methods 1 and 2 use the same substation number and capacity, the annual substation investment and operating costs are the same.

[0043] Further analysis of the substation load and total fitness of the schemes obtained by methods 1 and 2 shows the results in Table 5 and Appendix. Figure 5 shown.

[0044] Table 5 Load balancing index and total fitness of the schemes obtained by methods 1 and 2

[0045] From the attached Figure 5 As can be seen, the substation load factors in Method 1 are extremely unbalanced. Substation 1 has a load factor of 0.301 and Substation 7 has a load factor of 0.280, both of which are lightly loaded. The load balance index of Method 1 is 1.9053. In Method 2, the load factors of each substation are mostly between 0.42 and 0.51, and the load balance index is 1.9433, which is 0.038 higher than that of Method 1. The larger the load balance index, the more balanced the substation load. This phenomenon occurs because Method 1 uses the traditional K-means clustering algorithm to divide the power supply range. Its evaluation criterion is to minimize the sum of squares of the loads to the substations. In practice, this does not take into account the power size of the loads. This approach results in substations 1 and 7 being lightly loaded, resulting in overall load imbalance. Method 2 fully considers the impact of uneven load distribution during the power supply range division process. Through a load shifting strategy, the total load within each range is kept close, avoiding overload or underload phenomena.

[0046] The present invention calculates the total fitness of the two methods based on formula (15), =0.5, the maximum total cost =1.1 billion yuan, the maximum value of N of the substation to be built is 9, then the maximum value of the load rate entropy index is =2.1972, resulting in a total fitness of 1.0708 for Method 1 and 1.0665 for Method 2. This shows that Method 2 has a lower total fitness than Method 1. From the perspective of overall grid operation, although the total cost of substation zoning is slightly increased, substation load balancing is improved, reducing the occurrence of overload and underload conditions, thereby improving grid stability and reliability and increasing the overall grid power supply capacity.

[0047] In summary, the substation power supply range division method based on the improved K-means clustering algorithm proposed in the present invention fully considers the impact of unbalanced load distribution on substation range division, and is based on the clustering analysis idea and introduces a load shifting strategy to reasonably divide the substation power supply range. Compared with the method of using the traditional K-means clustering algorithm to divide the substation power supply range, the improved K-means clustering algorithm proposed in the present invention can fully take into account the impact of load distribution on range division, so that the total load of each divided power supply range is relatively close, reducing the occurrence of overload and underload, improving the stability and reliability of the power grid, and thereby increasing the overall power supply capacity of the power grid.

Claims

1. A method for dividing the power supply range of a substation based on an improved K-means clustering algorithm, characterized in that: The following steps are involved: Step 1: Based on the density method and setting the dynamic change coefficient The initial cluster center selection method is constructed in this way; Step 2: Based on the initial cluster center selection method in step 1, the load shifting strategy between partitions is introduced to construct an improved K-means method; Step 3: Based on the clustering method proposed in step 2, a substation range division model is constructed and evaluation indicators are given; Step 4: Based on the substation range division model constructed in step 3, the particle swarm optimization (PSO) algorithm is used to solve it.

2. The method according to claim 1, characterized in that In step 1, the following steps are included: Step 1.1: Assume that the load data set is: , in the entire dataset Using formula (1), we can get Load in With load Distance between : （1） Where: and There are two M Dimensional load, Refers to the load In the k The coordinate values of the dimensions, Refers to the load In the k The coordinate values of the dimensions; Step 1.2: According to formula (2), obtain the average distance between loads meandist : （2） Where, n is the total number of loads, for n The number of combinations of any two loads; Step 1.3: According to formula (3), obtain the density parameter of each load , integrating the density parameters of all loads, we can get the density parameter set D ; Step 1.4: Set the range of the number of substations to be built. Assume that the number of substations to be built is K According to the load distribution in the target year and the number and capacity of substations in the current year, the minimum number of substations to be built can be calculated. and the maximum number ; Step 1.5: Determine the load with the largest density parameter value as the first initial cluster center and select X Remove from the cluster, and accordingly delete the clusters whose distance to the cluster center is less than meandist load point; Step 1.6: If the number of substations to be built K If the range set in step 1.4 cannot be met, shorten the initial average distance meandist , , and clear all the initial cluster centers obtained previously; Step 1.7: Dynamically adjust the coefficient of variation , and repeat steps 1.5 to 1.6 until a substation with a larger density parameter is found within the number of substations to be built. K load points, which are the initial cluster centers.

3. The method according to claim 1, characterized in that In step 1.3, the density parameter set D for: （3） Where, p is any data object in the load data set, Indicates load and load distance.

4. The method according to claim 1, wherein In step 1.4, obtain the minimum number of substations to be built and the maximum number When , the following formula is used: （4） （5） Where: int is the rounding function; is the total active power of the load; is the total load of existing substations; e is the substation load factor; is the substation power factor; is the maximum capacity of the substations to be selected; is the minimum capacity of the substations to be selected.

5. The method according to claim 1, wherein In step 2, to ensure that the total load within each power supply range is as balanced as possible and to avoid overload and underload, an inter-partition load shifting strategy is introduced based on the initial cluster center selection method proposed in step 1. Specifically, Step 2.1: Select the method selected in step 1 K Cluster centers are obtained according to formula (1), and the distance between each load point and each cluster center is obtained. The minimum distance is found and the load is divided into the class with the closest distance to it. K power supply areas; Step 2.2: Obtain the total load in each power supply area and find the area with the highest total load. , compare the two adjacent areas and select the area with the lower total load ; If there is only one adjacent area, then select that area; Step 2.3: Find the area Middle distance area The nearest load point, move the load into the area ; Step 2.4: Repeat steps 2.2 to 2.3 to determine whether the total load in each power supply area is less than the set value. If so, proceed to the next step; otherwise, go to step 2.2 to re-obtain the total load in each power supply area; Step 2.5: Determine whether the total load in each power supply area is less than the maximum capacity of the substation. If so, proceed to the next step. Otherwise, return to step 1.6 and adjust the variation coefficient. Regenerate the initial cluster centers; Step 2.6: Based on the newly generated cluster centers, determine whether the convergence criteria are met. If so, output the region division result; otherwise, jump to step 2.

1.

6. The method according to claim 1, characterized in that In step 3, based on the clustering method proposed in step 2, a substation range division model is constructed and evaluation indicators are given; specifically: Step 3.1: The costs in the substation scoping model include: substation investment and annual operating costs; secondary line investment annual costs; secondary line network loss annual costs; Step 3.2: In order to quantify the impact of unbalanced load distribution on substation range division, the present invention introduces a load balance index and uses entropy value to process the load rate balance, as shown in formula (12): （12） Where: Indicates the load factor of the substation. Indicates substation i Active power of the supplied load node, Indicates substation i Rated capacity; If the load rate of a single substation The importance of a substation is represented by the size of the total load rate of all substations in the system. , then: （13） According to the entropy theory, the substation load rate entropy is constructed H : （14） From formula (14), we can see that It must be less than 1, so the substation load rate entropy index is a positive number; when the substation load is completely balanced, that is, the load rate of all substations is equal When the load rate entropy index reaches its maximum value ,in is the number of substations.

7. The method according to claim 6, characterized in that In step 3.1, the objective function is as shown in formula (6) to formula (9): （6） （7） （8） （9）。 8. The method according to claim 6, characterized in that In step 3.1, the constraints are: （10） （11） Where: The annual investment cost and annual operating cost of the substation; is the annual investment cost of the secondary side line of the substation; is the estimated annual network loss cost of the secondary side line of the substation; N is the number of newly built substations; is the fixed investment cost of the substation, For the i The investment cost per unit capacity of a substation is For the i The capacity of a substation, For the i Annual operating costs of a newly built substation; is the depreciation period of the substation, The depreciation period of the secondary side line of the substation; is the discount rate; For substations i The set of load nodes that supply power, , is the set of all load points; For substations i and load point j The length of the line between them; substation i The location coordinates of load j The location coordinates of is the active power of the load; For the i Maximum load factor of each substation; is the power factor; For the i The power supply radius of each substation; is the line investment cost per unit length; is the line network loss conversion coefficient, , is the line voltage, is the unit power loss discount coefficient, is the resistance per unit line length, is the annual line loss hours.

9. The method according to claim 1, characterized in that In step 4, based on the substation range division model constructed in step 3, the particle swarm optimization (PSO) algorithm is used to solve the problem: Step 4.1: Initialize network parameters; input relevant parameters such as load location and size, population size, and number of iterations; Step 4.2: Calculate the planned number range of substations using formula (4) and formula (5), let , , at this time the planned number of substations is , the number of substations to be built n is a loop variable, and the initial value of n is set to ; Step 4.3: Divide the planned area into n power supply ranges according to the substation power supply range division process in step 2; Step 4.4: Initialize the velocity and position of the particle; Step 4.5: Optimize the secondary side line of the substation based on the minimum spanning tree algorithm and calculate the particle fitness; Substitute each parameter into the objective function to obtain the corresponding C On this basis, the load rate entropy index is obtained according to the substation capacity and power supply range division results ; In order to normalize multiple targets, define global variables and , we can better compare the advantages and disadvantages of different planning schemes; C and After normalization, the fitness can be obtained through formula (16); Step 4.6: Find the individual optimal value and the group optimal value, and update the speed and position of the particles; Step 4.7: Determine whether the termination condition is met. If so, save the planning result and set n = n +1, if not, continue with step 4.5-step 4.6; Step 4.8: Judgment n Is it greater than If yes, output the solution with the minimum fitness, otherwise continue with steps 4.3-4.7; Through the above steps, the substation power supply range division method based on the improved K-means clustering algorithm is completed.

10. The method according to claim 9, characterized in that In step 4.5, the fitness is: （15） Where, is the weight.

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