A Distribution Network Power Supply Grid Partitioning Method Based on Improved Leuven Algorithm

Abstract

This invention discloses a distribution network power grid partitioning method based on an improved Leuven algorithm. The method includes the following steps: Step 1: Extract typical daily time-series scenarios based on historical wind power, photovoltaic, and load data within the distribution network power grid using an optimized extraction model; Step 2: Based on the typical time-series scenarios, and aiming for optimal comprehensive indicators, obtain the optimal power grid partitioning scheme for each typical day using an improved Leuven algorithm incorporating a tree structure pruning step; Step 3: Establish a grid partitioning scheme evaluation index system that includes generality indicators of partitioning results, rationality indicators of simulation operation, and representativeness indicators of cluster extraction, and select the optimal grid partitioning scheme in the form of a radar chart. This method can provide guidance for the partitioning of distribution network power grids into distribution network power supply units, promoting the standardized grid connection of distributed source, load, and storage resources and efficient collaboration among power supply units.

Description

Technical Field

[0001] This invention belongs to the field of power system planning and operation technology, and relates to a reasonable method for dividing the power supply grid into several power supply units in the context of a new type of power distribution system. Specifically, it relates to a new method for dividing the power supply grid of a power distribution network by using an improved Leuven algorithm that considers comprehensive division indicators and introduces a tree structure pruning step. Background Technology

[0002] With the rapid development of renewable energy and the continuous growth of electricity demand, traditional distribution networks are facing unprecedented challenges. To improve the flexibility and reliability of the power system, promoting the construction of new distribution networks has become a crucial task. Dividing the power grid of a new distribution network into new distribution network power supply units aims to achieve more efficient and intelligent power distribution and lay the foundation for the sustainable development of the future power system. A distribution network power supply unit refers to the 10kV distribution network power supply area obtained within the power grid based on factors such as plot function, development status, geographical conditions, load distribution, and the existing power grid.

[0003] With the widespread application of distributed generation and energy storage technologies, the structure of power systems has become increasingly complex, and traditional centralized power supply models can no longer meet the diverse and flexible demands of modern electricity. Therefore, rationally dividing the power supply grid helps optimize resource allocation and improve the overall efficiency of the system. This division not only effectively integrates various energy resources but also enables dynamic load allocation among different power supply units, enhancing the grid's responsiveness. Furthermore, by subdividing the power supply grid into multiple power supply units, more refined management and control can be achieved, enhancing the grid's rapid response to load fluctuations and faults. Each power supply unit can operate independently while also working collaboratively with other units, thereby improving the system's flexibility and stability and ensuring continuous power supply even in emergencies. In addition, this division promotes collaborative work among power supply units, achieving multi-source complementarity. Through intelligent scheduling and control technologies, each power supply unit can be optimally configured based on real-time load and generation conditions, achieving optimal resource utilization. The power supply units of the new distribution network can not only cope with local load changes but also improve efficiency at the overall grid level, further enhancing the resilience of the power system.

[0004] In conclusion, dividing the new power distribution network grid into new power distribution units is not only an inevitable choice to meet the needs of the times, but also a key step in realizing the intelligence and flexibility of the power system. This innovative measure will provide strong support for the sustainable development of the future power system, promote energy transition, and help achieve the goal of carbon neutrality. However, existing power grid division methods often suffer from problems such as a single division index, an inability to balance the optimization ability and computational efficiency of the division algorithm, and difficulty in objectively comparing the effects of division schemes, making it difficult to substantially guide the gridded and unitized operation of the power distribution network. Summary of the Invention

[0005] To overcome the aforementioned technical shortcomings of existing power grid partitioning methods, this invention provides a power grid partitioning method for distribution networks based on an improved Leuven algorithm. This method can guide the partitioning of power grids into power supply units, promoting the standardized grid connection of distributed source, load, and storage resources, as well as efficient collaboration among power supply units.

[0006] The objective of this invention is achieved through the following technical solution:

[0007] A distribution network power grid partitioning method based on an improved Leuven algorithm includes the following steps:

[0008] Step 1: Based on the historical data of wind power, photovoltaic power, and load within the power distribution network grid, extract typical daily time-series scenarios using an optimized extraction model. The specific steps are as follows:

[0009] Step 11: Using Principal Components Analysis (PCA), reduce the dimensionality of the 365-day-a-year multivariate time series data containing the "wind-solar-load" coupling to univariate time series data;

[0010] Step 12: Determine the number of clusters based on the elbow rule, and use the K-means algorithm to classify the principal component sequences, dividing the annual univariate time series data into several time series data clusters;

[0011] Step 13: Establish a multi-objective mixed-integer linear programming model as the typical day optimization extraction model. With the objectives of minimizing the number of typical days, minimizing the deviation of typical scenes, maximizing the surrounding number density, and maximizing the radiation radius, extract the most representative and differentiated typical day time series scenes from each cluster of time series data. Wherein:

[0012] The objective function of the multi-objective mixed-integer linear programming model is:

[0013]

[0014] in:

[0015]

[0016] In the formula, u=[u1,…,u N ] T ω=[ω1,…,ω N ] T The binary selection of decision variables and corresponding weighting coefficients for each typical day is given; A ξ b ξ f1 represents the original data matrix for each data type and the total data volume for each time period; f2 represents the number of typical days selected for the current sample set; f3 represents the sum of the relative deviations between the typical day and the original data, i.e., the deviation degree; f4 represents the number density around the typical day; f5 represents the total radiation radius of the typical day.

[0017] The constraints of a typical daily optimization extraction model are as follows:

[0018]

[0019] In the formula, constraint (a) is the consistency constraint between the typical day weight coefficient variable ω and the selected decision variable u; the purpose of constraint (b) is to ensure that the sum of all typical day weight coefficients is consistent with the sample size; constraint (c) is the total relative deviation range constraint, and α is the range relaxation coefficient; constraint (d) is the type constraint of the two types of decision variables.

[0020] Step 2: Based on typical time-series scenarios, and aiming for optimal comprehensive indicators, the improved Leuven algorithm, incorporating a tree-structure pruning step, is used to obtain the optimal power supply grid partitioning scheme for each typical day, where:

[0021] The comprehensive indicators include four aspects: active power matching degree index O1 (source-load-storage), modularity index O2 (based on electrical distance), reactive power support capacity index O3, and power supply unit scale balance index O4. The specific calculation methods are as follows:

[0022] (1) Active power matching index O1 of source-load-storage

[0023] The distributed generation power and generalized load power are optimized with the goal of minimizing net load, thereby obtaining the optimal distributed generation power and generalized load power corresponding to the solution. The objective of the optimization model is as follows:

[0024]

[0025] In the formula, H represents the number of scheduling periods; Ω k Let k be the set of nodes for the k-th power supply unit; Let h be the net load value of the k-th power supply unit after optimized source-load-storage scheduling; These are the original load power, the generalized load power considering energy storage charging and discharging power and demand-side response of the k-th power supply unit at time h, respectively; These are the load transfer power, load reduction power, energy storage charging power, energy storage discharging power, WT output, PV output, and MT output of the i-th node within the power supply unit, respectively.

[0026] Calculate the source-load-storage matching index O1 based on the optimization results:

[0027]

[0028]

[0029] In the formula, N Z The number of power supply units in the current power grid partitioning scheme; Let be the source-load-storage matching degree of the k-th power supply unit in the h-th time period, and

[0030] (2) Modularity index O2 based on electrical distance

[0031] The coupling relationship between nodes is characterized by the electrical distance based on the active / reactive power-voltage amplitude sensitivity matrix. The sensitivity matrix and electrical distance are calculated as follows:

[0032]

[0033] In the formula, n is the number of distribution network nodes; ΔP i ΔQ i ΔV i These represent the changes in active power injected into each node, reactive power injected into the node, and voltage amplitude, respectively; S PV S QV These are the active power-voltage amplitude sensitivity matrix and the reactive power-voltage amplitude sensitivity matrix, respectively. These are the ratios of the voltage changes at node j (node ​​j) and node i when the active / reactive power changes, respectively, representing the degree of influence of the active / reactive power change on the two nodes. D ij These represent the active electrical distance, reactive electrical distance, and combined electrical distance between node i and node j, respectively.

[0034] By utilizing electrical distance and distribution network connections, the distribution network is transformed into a relational network whose modularity can be directly calculated through edge weight calculation. The edge weight calculation method is as follows:

[0035]

[0036] In the formula, D is the comprehensive electrical distance matrix; A is the distribution network connection matrix, where A(i,j) = 1 when there is a direct connection between node i and node j, otherwise A(i,j) = 0; e ij The weights of the edges between node i and node j after the network is transformed into a relational network;

[0037] After converting the power distribution network into a relational network, the modularity index O2 based on electrical distance is calculated according to the definition of modularity. The calculation method is as follows:

[0038]

[0039] In the formula, k i k j δ(i,j) represents the sum of the weights of all connecting edges of nodes i and j, respectively; m is the sum of the weights of all edges in the entire relational network; δ(i,j) represents the same state of nodes i and j. If the two nodes are assigned to the same power supply unit, then δ(i,j) = 1, otherwise δ(i,j) = 0.

[0040] (3) Reactive power support capacity index O3

[0041] The evaluation process involves three steps: assessing reactive power demand, assessing reactive power supply capacity, and designing evaluation indicators within the range of [0,1].

[0042] Regarding the reactive power demand assessment for each power supply unit, under completely uncontrolled conditions, the overvoltage node voltage at the peak of renewable energy penetration and the undervoltage node voltage at the time of underestimation of penetration will be calculated separately for typical days. The reactive power demand of each power supply unit will be estimated according to the reactive power-voltage amplitude sensitivity matrix. The calculation method is as follows:

[0043]

[0044] In the formula, Ω k1 Ω k2 These represent the set of overvoltage nodes and the set of undervoltage nodes for the k-th power supply unit, respectively; ΔV i The absolute value of the voltage amplitude at overvoltage / undervoltage node i from the normal voltage range; The minimum capacitive reactive power required from the power supply side for the overvoltage node in the k-th power supply unit; The minimum inductive reactive power required from the power supply side for the undervoltage node in the k-th power supply unit;

[0045] Regarding the assessment of reactive power supply capacity of each power supply unit, the reactive power supply capacity of each power supply unit is described by considering the reactive power output of DG and SVC under constant power factor on the source side, based on the set DG power factor range and SVC reactive power capacity. The specific calculation method is as follows:

[0046]

[0047] In the formula, These represent the source-side capacitive reactive power and inductive reactive power supply capabilities of the k-th power supply unit, respectively. These represent the maximum capacitive reactive power that PV, WT, and SVC can provide, respectively. These represent the maximum inductive reactive power that PV, WT, MT, and SVC can provide, respectively.

[0048] Based on the estimated reactive power demand and reactive power supply capacity of each power supply unit, a reactive power support capacity index O3 is formed, which takes the following form:

[0049]

[0050] In the formula, These represent the capacitive reactive power balance, inductive reactive power balance, and comprehensive reactive power balance of the power supply unit, respectively, with values ​​ranging from 0 to 1.

[0051] (4) Power supply unit scale balance index O4

[0052] A power supply unit scale balance index O4 is introduced to limit the scale of power supply units, and its form is as follows:

[0053] O4=1 / [ασ(n Z )+1];

[0054] In the formula, σ(n) Z ) represents the standard deviation of the number of nodes in each power supply unit under the current power supply grid partitioning scheme; α is the adjustment coefficient;

[0055] The power grid partitioning includes four stages: initialization, tree structure pruning, node merging, and network collapse. The specific steps are as follows:

[0056] Step 21, Initialization Phase: Read the original load, wind and solar power output data, network initial weight matrix, and node voltage information at peak and off-peak times of new energy penetration for each node under each typical day. Treat each node as a power supply unit and initialize the partitioning algorithm process parameters.

[0057] Step 22, Tree structure pruning stage: Find the leaf nodes in the current distribution network, merge them with the parent root node to form a new network, and repeat this process until the upper limit of the tree structure pruning level is reached;

[0058] Step 23, Node Merging Phase: Traverse each node, adding each node sequentially to the unit containing the directly connected node. Calculate the increase in the comprehensive index after node merging, select the merging scheme with the largest increase, and merge the two nodes. Repeat the node merging phase until the comprehensive index can no longer increase.

[0059] For the active power matching index O1 and the reactive power support capability index O3, when calculating the index values ​​during the node merging phase, only the index for the part of the power supply unit composition that changes is calculated additionally, that is:

[0060]

[0061] In the formula, k old k in k out These are, respectively, the power supply unit numbers whose constituent nodes have not changed, the power supply unit numbers with nodes moving in, and the node numbers with nodes moving out; These represent the average active power matching degree of the corresponding power supply unit over the entire time period; These represent the overall reactive power balance of the corresponding power supply unit; N′ Z O1′ and O3′ represent the number of power supply units, active power matching index, and reactive power matching index after node merging, respectively.

[0062] For the modularity index O2, only the impact of the edge weights of nodes whose dependency relationships have changed on the index increment is considered, that is:

[0063]

[0064] In the formula, S in S out Let k be the sum of the internal edge weights of node i to be incorporated into the power supply unit, and k be the sum of the edge weights at the boundary of the power supply unit to be incorporated into the power supply unit. i k i,in These are the sum of the edge weights connecting node i and the sum of the edge weights connecting node i and the power supply unit to be merged, respectively; O2′ is the modularity index after node merging;

[0065] Step 24, Network Collapse Phase: Collapse the nodes contained in each unit into super nodes, calculate the edge weights between nodes in each power supply unit and the edge weights between internal nodes, i.e.:

[0066]

[0067] In the formula, Ω k Ω k′ Let E be the set of nodes for the k-th and k′-th network power supply units, respectively; kk′ Let s be the edge weight between network power supply unit k and network power supply unit k′ after network collapse; i E is the sum of the edge weights of all edges connecting node i in the network before collapse; kk The self-weight of network power supply unit k after network collapse;

[0068] Step 25: Use the node edge weights between power supply units as the edge weights between super nodes, and use the node edge weights within power supply units as the self weights of super nodes to form a new network. Repeat the node merging stage and network collapse stage until the comprehensive index no longer increases, thus obtaining the power grid division scheme of the distribution network corresponding to the current typical day.

[0069] Step 3: Establish an evaluation index system for grid partitioning schemes, including general applicability indicators of partitioning results, rationality indicators of simulation operation, and representativeness indicators extracted from clustering. Select the optimal grid partitioning scheme in the form of a radar chart, wherein:

[0070] The representative indicators extracted by clustering are in the following form:

[0071]

[0072]

[0073] In the formula, Γ i The power supply unit partitioning scheme is defined as follows: F1 and F2 represent the evaluation index of the daily surrounding number density and the evaluation index of the daily radiation radius, respectively.

[0074] The general applicability index of the segmentation results is in the following form:

[0075]

[0076] In the formula, N p Divide the power supply unit into different schemes; O1(Γ) j Data i The power supply unit division scheme is as follows: j Substituted into the power supply unit partitioning scheme Γ i The O1 index value is obtained after corresponding scenario data; F3 and F4 are the generality of functional index and the generality of structural index, respectively.

[0077] The simulation operation rationality indicators are in the following form:

[0078]

[0079] In the formula, Scheme for dividing power supply units Γ i Number of power supply units; Ω bus,k Ω line,k Let N be the set of nodes and the set of lines in the k-th power supply unit. b N l For the corresponding number of nodes and lines; S b,h , These represent the actual usage and upper limit of the distributed resource at node b during the h-th time period, respectively; σ(U bh(P) represents the standard deviation of the voltage sequence during the simulation operation cycle of node b; l <0) represents the power flow reversal time of line l; F5, F6, and F7 represent resource utilization, voltage stability, and power flow stability, respectively.

[0080] In this invention, the power distribution grid refers to a power supply area consisting of several adjacent plots (or user blocks) with the same power supply area classification level and basically consistent power consumption characteristics or power supply reliability requirements. The power supply area is typically 5–12 km². 2 .

[0081] Compared with the prior art, the present invention has the following advantages:

[0082] This invention can provide a division scheme from power grid to power supply unit for specific wind, solar, and load timing scenarios and actual power distribution network structure, thereby enhancing the system's ability to absorb new energy and improving orderly power consumption. Attached Figure Description

[0083] Figure 1 The flowchart shows the distribution network power grid partitioning method based on the improved Leuven algorithm.

[0084] Figure 2 This is a schematic diagram illustrating the specific process of the distribution network mesh partitioning method based on the improved Leuven algorithm.

[0085] Figure 3 This is the modified topology diagram of the IEEE 123 node example.

[0086] Figure 4 This is a typical daily selection decision diagram for various time series samples.

[0087] Figure 5 This is a heatmap of the electrical distance calculation results.

[0088] Figure 6 This section describes the changes in various indicators during the power supply grid division process under two different grid structures.

[0089] Figure 7 The process of dividing the power supply grid under two types of grid structures and different tree structures with different pruning layers.

[0090] Figure 8 A power grid division scheme for each typical day.

[0091] Figure 9 Radar chart showing the evaluation and selection results of each power grid partitioning scheme. Detailed Implementation

[0092] The technical solution of the present invention will be further described below with reference to the accompanying drawings, but it is not limited thereto. Any modifications or equivalent substitutions to the technical solution of the present invention that do not depart from the spirit and scope of the technical solution of the present invention should be covered within the protection scope of the present invention.

[0093] This invention provides a distribution network power grid partitioning method based on an improved Leuven algorithm. Starting from historical operation data of a new type of distribution network, the method realizes the partitioning from distribution network grid to distribution network unit under typical scenarios. In order to address the dual paradox of the partitioning algorithm's optimization capability and computational efficiency, an improved Leuven algorithm is proposed, which considers the comprehensive optimization of functional and structural indicators and introduces a tree structure pruning step to realize the partitioning of the distribution network power grid. The comparison process of partitioning schemes for each typical day is also given.

[0094] like Figure 1 As shown, the specific steps include the following:

[0095] Step 1: Extract typical daily time-series scenarios based on historical data under the combined "wind-solar-load" model.

[0096] Based on historical data of wind power, photovoltaic power, and load within the power distribution network grid, typical daily time-series scenarios are extracted using an optimized extraction model.

[0097] In this step, using the annual wind power data, annual photovoltaic data, and annual load data within the power distribution network grid as input, typical daily time-series scenarios are extracted according to the following steps:

[0098] (1) The multivariate time series data of 365 days a year and including the coupling of "wind-solar-load" was reduced to univariate time series data by using the principal component analysis (PCA) method.

[0099] (2) Determine the number of clusters according to the elbow rule, use the K-means algorithm to classify the principal component sequences, and divide the annual univariate time series data into several time series data clusters.

[0100] (3) A multi-objective mixed integer linear programming model (MOMILP) is established as the typical day optimization extraction model to extract the most representative and differentiated typical day time series scenes from each cluster of time series data. The extraction model aims to minimize the number of typical days, minimize the deviation of typical scenes, maximize the surrounding number density, and maximize the radiation radius.

[0101] The surrounding number density refers to the number of samples within a data sample cutoff distance, and the calculation formula is as follows:

[0102]

[0103] d ij =DTW d (X i ,X j (i,j∈[1,N].i≠j) (2);

[0104] In the formula, N is the number of typical daily samples, and i and j are the sample numbers of two typical daily samples; ρ i d represents the number density of the surrounding samples of the i-th sample; ε(·) is the sign-determining function, taking the value 1 when the independent variable is negative and 0 when it is non-negative; ij For sample X i With sample X j The matrix dynamic time bending distance between; d c The truncation distance of the sample set is taken as 1 / 3 of the maximum matrix dynamic time bending distance.

[0105] The radiation radius mainly reflects the differences between samples, and the calculation formula is as follows:

[0106]

[0107] In the formula, j is the sample number whose surrounding number density is greater than the surrounding number density of the current sample; φ is the empty set.

[0108] According to equations (1) to (3), if a sample has a larger surrounding number density and a larger radiation radius, then the sample is more representative and different, and is more likely to be selected as a typical day; if a sample has a larger radiation radius but a smaller surrounding number density, then the sample can be regarded as an extreme sample and should also be included.

[0109] To reduce the discrepancies in total quantity and distribution information between typical days and the original data, and to limit the number of typical days, the statistical indicators mainly consider the deviation Δe of wind, solar, and load, as well as the total number of typical days. The deviation is the relative deviation between the total quantity obtained by weighted summation of selected typical days and the total quantity of the original data, calculated using the following formula:

[0110]

[0111] In the formula, ω i ξ represents the decision weight when selecting typical day i; ξ represents the data type, S ξ,i S represents the total amount of data for a typical day i. ξ,all This represents the total amount of data in the current sample set.

[0112] Based on the above indicators, this invention establishes a multi-objective mixed-integer linear programming model (MOMILP) to achieve optimized extraction of typical days. The objective function is:

[0113]

[0114] in:

[0115]

[0116] In the formula, u=[u1,…,u N ] T ω=[ω1,…,ω N ] T The binary selection of decision variables and corresponding weighting coefficients for each typical day is given; A ξ b ξ f1 represents the original data matrix of each data type and the total amount of data for each time period; f2 represents the number of typical days selected in the current sample set; f3 represents the sum of the relative deviations between the typical day and the original data, corresponding to equation (4); f4 represents the number density around the typical day, corresponding to equation (1); f5 represents the total radiation radius of the typical day, corresponding to equation (3).

[0117] The constraints of a typical daily optimization extraction model are as follows:

[0118]

[0119] In the formula, constraint (a) is the consistency constraint between the typical day weight coefficient variable ω and the selected decision variable u; the purpose of constraint (b) is to ensure that the weight coefficients of all typical days are consistent with the sample size; constraint (c) is the total relative deviation range constraint, and α is the range relaxation coefficient; constraint (d) is the type constraint of the two types of decision variables.

[0120] The above model is a mixed-integer linear programming model, which can be solved directly by calling the solver.

[0121] Step 2: Based on the improved Leuven algorithm, the power supply grid is partitioned with the goal of achieving the optimal comprehensive index.

[0122] Based on typical time-series scenarios, with the goal of optimizing comprehensive indicators, the improved Leuven algorithm, which incorporates a tree structure pruning step, is used to obtain the optimal power supply grid partitioning scheme for each typical day.

[0123] In this step, the goal of power grid partitioning is to divide a large-scale power grid into several smaller power grid units based on typical scenarios and network topology. From a supply and demand balance perspective, each power supply unit needs to be as balanced and autonomous as possible internally, and the power exchange between power supply units needs to be as small as possible, thereby reducing the difficulty of power coordination between power supply units. From a network structure perspective, each power supply unit needs to have strong coupling between internal nodes and weak coupling between nodes of different power supply units, thereby reducing the impact of the actions of one power supply unit on other power supply units. Therefore, this invention starts from both functional and structural requirements to establish a comprehensive index for evaluating the effectiveness of power grid partitioning, covering four aspects: source-load-storage active power matching degree index O1, modularity index O2 based on electrical distance, reactive power support capacity index O3, and power supply unit scale balance index O4.

[0124] (1) Active power matching index O1 of source-load-storage

[0125] The net load sequence is a time-varying sequence of the difference between the load and the output of distributed generators (DG) within the system after energy storage coordination, reflecting the dynamic changes in the supply and demand relationship within the power supply unit. Therefore, the optimized net active load sequence can be used to characterize the external characteristics of the power demand of the power supply unit, and a source-load-storage active power matching index can be established based on this.

[0126] When optimizing the net load sequence, this invention mainly considers uncontrollable resources such as wind turbines (WT) and photovoltaics (PV), as well as controllable resources such as microturbines (MT), energy storage systems (ESS), loads that can be reduced, and loads that can be transferred. The specific optimization model objectives are as follows:

[0127]

[0128] In the formula, H represents the number of scheduling periods; Ω k Let k be the set of nodes for the k-th power supply unit; Let h be the net load value of the k-th power supply unit after optimized source-load-storage scheduling; These are the original load power, the generalized load power considering energy storage charging and discharging power and demand-side response of the k-th power supply unit at time h, respectively; These represent the transferred load power, reduced load power, energy storage charging power, energy storage discharging power, WT output, PV output, and MT output of the i-th node within the power supply unit, respectively.

[0129] Regarding the constraints for net load optimization, the source side mainly considers the output range constraints of MT, ramping constraints, and beginning-end consistency constraints. The load side mainly considers the range constraints of transferable loads and increase / decrease matching constraints, as well as the range constraints of load reduction. The energy storage side mainly considers the range constraints and state constraints of ESS charging and discharging power, the range constraints of battery state of charge (SOC), beginning-end consistency constraints, and continuity constraints.

[0130] Based on the net load power of each power supply unit, the average value over a certain time scale is used to construct the source-load-storage matching index O1:

[0131]

[0132] In the formula, N Z The number of power supply units in the current power grid partitioning scheme; Let be the source-load-storage matching degree of the k-th power supply unit in the h-th time period, and

[0133] As defined by the index, the active power matching degree index O1 of source-load-storage takes into account the power regulation capability of various resources, and its value ranges from 0 to 1. The larger the value of O1, the closer the net load of each power supply unit, ESS and DG after full coordination and optimization is to 0, and the better the supply and demand balance of the current power grid division scheme is.

[0134] (2) Modularity index O2 based on electrical distance

[0135] The coupling relationship between nodes is characterized by electrical distance based on the active / reactive power-voltage amplitude sensitivity matrix. The sensitivity matrix and electrical distance are calculated as follows:

[0136]

[0137] In the formula, n is the number of distribution network nodes; ΔP i ΔQ i ΔV i These represent the changes in active power injected into each node, reactive power injected into the node, and voltage amplitude, respectively; S PV S QV These are the active power-voltage amplitude sensitivity matrix and the reactive power-voltage amplitude sensitivity matrix, respectively. These are the ratios of the voltage changes at node j (node ​​j) and node i when the active / reactive power changes, respectively, representing the degree of influence of the active / reactive power change on the two nodes. D ij These represent the active electrical distance, reactive electrical distance, and combined electrical distance between node i and node j, respectively.

[0138] First, utilizing electrical distances and distribution network connections, the distribution network is transformed into a relational network whose modularity can be directly calculated by calculating edge weights. The edge weight calculation method is as follows:

[0139]

[0140] In the formula, D is the comprehensive electrical distance matrix; A is the distribution network connection matrix, where A(i,j) = 1 when there is a direct connection between node i and node j, otherwise A(i,j) = 0; e ij Let be the edge weights between node i and node j after the relationship network is transformed.

[0141] After converting the power distribution network into a relational network, the modularity index O2 based on electrical distance can be calculated directly according to the modularity definition. The calculation method is as follows:

[0142]

[0143]

[0144] In the formula, k i k j δ(i,j) represents the sum of the weights of all connecting edges of nodes i and j, respectively; m represents the sum of the weights of all edges in the entire relational network; δ(i,j) represents the same state of nodes i and j. If the two nodes are assigned to the same power supply unit, then δ(i,j) = 1, otherwise δ(i,j) = 0.

[0145] (3) Reactive power support capacity index O3

[0146] In terms of functionality, in addition to considering the active power matching degree of each power supply unit's source-load-storage, a reactive power support capability index O3 should be established to describe the internal voltage regulation capability of the power supply unit, addressing voltage control issues. This index will be established through three steps: assessing reactive power demand, assessing reactive power supply capability, and designing an evaluation index within the range of [0,1].

[0147] Regarding the assessment of reactive power demand for each power supply unit, this invention will calculate the overvoltage node voltage at the peak of renewable energy penetration and the undervoltage node voltage at the time of underestimation of penetration under a typical day, under completely uncontrolled conditions. The reactive power demand of each power supply unit will be estimated based on the reactive power-voltage amplitude sensitivity matrix. The calculation method is as follows:

[0148]

[0149] In the formula, Ω k1 Ω k2 These represent the set of overvoltage nodes and the set of undervoltage nodes for the k-th power supply unit, respectively; ΔV iThe absolute value of the voltage amplitude at overvoltage / undervoltage node i from the normal voltage range; The minimum capacitive reactive power required from the power supply side for the overvoltage node in the k-th power supply unit; This represents the minimum inductive reactive power that the undervoltage node in the k-th power supply unit needs to provide from the power supply side.

[0150] Regarding the assessment of the reactive power supply capacity of each power supply unit, this invention can describe the reactive power supply capacity of each power supply unit based on a predefined DG power factor range and SVC reactive power capacity, considering the reactive power output of DG and SVC under constant power factor at the source side. The specific calculation method is as follows:

[0151]

[0152] In the formula, These represent the source-side capacitive reactive power and inductive reactive power supply capabilities of the k-th power supply unit, respectively. These represent the maximum capacitive reactive power that PV, WT, and SVC can provide, respectively. These represent the maximum inductive reactive power that PV, WT, MT, and SVC can provide, respectively.

[0153] Based on the estimated reactive power demand and reactive power supply capacity of each power supply unit, a reactive power support capacity index O3 can be formed, which takes the following form:

[0154]

[0155] In the formula, These are the capacitive reactive power balance degree, inductive reactive power balance degree, and comprehensive reactive power balance degree of the power supply unit, respectively. The values ​​range from 0 to 1. The closer to 1, the better the estimated reactive power demand matches the estimated reactive power supply capacity.

[0156] (4) Power supply unit scale balance index O4

[0157] Considering that excessive differences in power supply unit size would unnecessarily impact subsequent planning difficulty and the rationality of base station configuration, a power supply unit size balance index O4 is introduced as a structural indicator to limit the size of power supply units. Its form is as follows:

[0158] O4=1 / [ασ(n Z )+1] (26);

[0159] In the formula, σ(n) Z ) represents the standard deviation of the number of nodes in each power supply unit under the current power grid partitioning scheme; α is the adjustment coefficient. The greater the difference in size between the power supply units, the closer the index O4 is to 0, and vice versa.

[0160] In summary, this invention uses a weighted sum of the above four indicators to obtain a comprehensive evaluation index for the power grid partitioning scheme.

[0161] Figure 2 This is a schematic diagram of the power grid partitioning algorithm based on the improved Leuven algorithm. The power grid partitioning method proposed in this invention includes four stages: initialization stage, tree structure pruning stage, node merging stage, and network collapse stage. The specific steps are as follows:

[0162] Step 21, Initialization Phase: Read initial data such as the original load, wind and solar power output data, initial network weight matrix, and node voltage information during peak and off-peak hours of renewable energy penetration for each node under typical days. Treat each node as a power supply unit and initialize the partitioning algorithm process parameters.

[0163] Step 22, Tree Structure Pruning Stage: Locate the leaf nodes in the current distribution network and merge them with the parent root node to form a new network. Repeat this process until the upper limit of the tree structure pruning level is reached.

[0164] Regardless of whether the main network structure of the distribution network is a ring network or a radial network, its ends often contain many small-scale tree-like lines. On the one hand, the characteristics of these terminal tree-like lines are often directly related to their root nodes, so their integrity should not be compromised; on the other hand, if the tree-like lines are divided into different power supply units, it will inevitably result in power supply units of extremely small size, which contradicts the actual needs of power supply unit division in the distribution network. In summary, this invention pre-collapses the small-scale tree-like structures at the network ends into super nodes, which can avoid the frequent calculation and comparison processes during the initial rounds of node merging. In addition, pre-collapse can also reduce the problem of isolated small-scale power supply units that may occur during node traversal and merging.

[0165] Step 23, Node Merging Phase: Traverse each node and add it sequentially to the unit containing the directly connected node. Calculate the increase in the comprehensive index after node merging, select the node merging scheme with the largest increase, and merge the two nodes. Repeat the node merging phase until the comprehensive index can no longer increase.

[0166] For the active power matching index O1 and the reactive power support capability index O3, when calculating the index values ​​during the node merging phase, only the index for the part of the power supply unit composition that changes is calculated additionally, that is:

[0167]

[0168] In the formula, k old k in k out These are, respectively, the power supply unit numbers whose constituent nodes have not changed, the power supply unit numbers with nodes moving in, and the node numbers with nodes moving out; These represent the average active power matching degree of the corresponding power supply unit over the entire time period; These represent the overall reactive power balance of the corresponding power supply unit; N′ Z O1′ and O3′ represent the number of power supply units, active power matching index, and reactive power matching index after node merging, respectively.

[0169] For the modularity index O2, only the impact of the edge weights of nodes whose dependency relationships have changed on the index increment is considered, that is:

[0170]

[0171] In the formula, S in S out Let k be the sum of the weights of the internal edges of node i to be incorporated into the power supply unit (where both ends of the connecting edge are within the power supply unit), and the sum of the weights of the edges at the boundary of the power supply unit to be incorporated into (where only one end of the connecting edge is within the power supply unit); i k i,in These are the sum of the edge weights connecting node i and the sum of the edge weights connecting node i and the power supply unit to be merged, respectively; O2′ is the modularity index after node merging.

[0172] Step 24, Network Collapse Phase: Collapse the nodes contained in each unit into super nodes, calculate the edge weights between nodes in each power supply unit and the edge weights between internal nodes, i.e.:

[0173]

[0174] In the formula, Ω k Ω k′ Let E be the set of nodes for the k-th and k′-th network power supply units, respectively; kk′ Let s be the edge weight between network power supply unit k and network power supply unit k′ after network collapse; i E is the sum of the edge weights of all edges connecting node i in the network before collapse; kk The autonomy of the network power supply unit k after network collapse.

[0175] Step 25: Use the node edge weights between power supply units as the edge weights between super nodes, and use the node edge weights within power supply units as the self-weights of super nodes to form a new network. Repeat the node merging stage and network collapse stage until the comprehensive index no longer increases, and the power distribution grid division scheme corresponding to the current typical day can be obtained.

[0176] Step 3: Establish an evaluation index system for grid partitioning schemes, which includes generality indexes of partitioning results, rationality indexes of simulation operation, and representativeness indexes extracted by clustering (ranked by importance). Select the optimal grid partitioning scheme in the form of a radar chart.

[0177] Since different typical scenarios will generate different power supply unit partitioning schemes, it is necessary to evaluate and select the best of each power supply unit partitioning scheme to determine the final power supply unit partitioning result. This invention establishes three types of evaluation and selection indicators to determine the final power supply unit partitioning scheme. Among them, the generality index of partitioning result includes the generality of the capability index and the generality of the structural index; the rationality index of simulation operation includes the distributed resource utilization rate, voltage stability, and power flow stability; the representativeness index of cluster extraction includes the evaluation index of the surrounding number density on typical days and the evaluation index of the radiation radius on typical days.

[0178] The meaning of extracting representative indicators through clustering is to use the complete year's data as the original sample, and to use the density of the number of days surrounding the typical day corresponding to each division scheme as the evaluation index. This index is only used to re-evaluate the rationality of the selection of typical days in the entire data space, and therefore is the least important in the evaluation and selection process of power supply unit division schemes. Its form is as follows:

[0179]

[0180] In the formula, Γ i The power supply unit is divided into two schemes: F1 and F2 represent the evaluation index of the number density around the day and the evaluation index of the radiation radius of the day, respectively.

[0181] The general applicability index of the partitioning results means that each power supply unit partitioning scheme is substituted into the scenarios corresponding to other partitioning schemes to obtain the values ​​of functional and structural indicators. The proportion of the new indicator value to the original indicator value is used to reflect the general applicability of each power supply unit partitioning scheme, which is the most important indicator in the evaluation and selection of the best option. The specific form of the indicator is as follows:

[0182]

[0183] In the formula, N p Divide the power supply unit into different schemes; O1(Γ) j Data i The power supply unit division scheme is as follows: j Substituted into the power supply unit partitioning scheme Γ i The O1 index value is obtained after corresponding scenario data, and the other similar parameters are obtained in the same way; F3 and F4 are the generality of functional index and the generality of structural index, respectively.

[0184] The meaning of the simulation operation rationality index is to combine typical days in chronological order into a simulated operating period, solve the optimal power flow problem with the goal of minimizing line loss, and statistically analyze the average resource utilization rate, average voltage fluctuation rate, and average power flow reversal rate of power supply units corresponding to each partitioning scheme. These are used as important evaluation and selection indicators for power supply unit partitioning. Its form is as follows:

[0185]

[0186] In the formula, Scheme for dividing power supply units Γ i Number of power supply units; Ω bus,k Ω line,k Let N be the set of nodes and the set of lines in the k-th power supply unit. b N l For the corresponding number of nodes and lines; S b,h , These represent the actual usage and upper limit of the distributed resource at node b during the h-th time period, respectively; σ(U b h(P) represents the standard deviation of the voltage sequence during the simulation operation cycle of node b; l <0) represents the power flow reversal time of line l; F5, F6, and F7 represent resource utilization, voltage stability, and power flow stability, respectively.

[0187] After initially establishing the evaluation and selection indicators for the three types of power supply unit division schemes, each indicator can be mapped to the [0.1,1] interval according to the correspondence between magnitude and quality. The power supply unit division schemes can then be grouped and optimized in the form of radar charts. The reason for not setting the minimum value of the mapped indicators to 0 is to prevent spikes in the radar charts from interfering with subjective judgment.

[0188] Example:

[0189] This embodiment uses the modified 123-node example, employing the modified IEEE 123-node system (…). Figure 3 Simulation analysis was conducted. The maximum transferable load and maximum load reduction ratio for each node were both 5%. The power factor range for wind and solar power was 0.95 leading to 0.95 lagging, the power factor range for micro gas turbines was 0.8 to 0.85 leading, the state of charge range for energy storage was 0.05 to 0.95, and the charge / discharge efficiency was 0.9. The reactive power compensation device was classified into capacitive and inductive operating conditions. The specific classification process is as follows:

[0190] (1) Six typical time-series scenarios can be obtained by clustering the principal component sequences. Based on the optimized extraction algorithm, typical days with outstanding typicality and differences are selected as time-series scenarios. See Figure 4 .

[0191] (2) Verify the electrical distance input matrix for errors using a heatmap format, see... Figure 5 .

[0192] (3) The proposed distribution network power grid partitioning method, which considers comprehensive indicators and the improved Leuven algorithm, was applied to each time-series scenario to obtain partitioning results. Example results show that the proposed method is applicable to both open-loop and closed-loop operating conditions. Parameter changes during the algorithm process are detailed in [link to algorithm details]. Figure 6 The impact of reducing the number of tree layers on the algorithm's progress is discussed in [link to relevant documentation]. Figure 7 The results of the typical day divisions are shown below. Figure 8 .

[0193] (4) Following the optimization process of the partitioning scheme proposed in this invention, the partitioning schemes are grouped and optimized in the form of a radar chart. (See radar chart below.) Figure 9 Taking all factors into consideration, we selected the partitioning scheme corresponding to Scheme 4 to guide the zoning planning and operation of the new power distribution network.

Claims

1. A method for dividing power supply grids in a distribution network based on an improved Leuven algorithm, characterized in that... The method includes the following steps: Step 1: Based on the historical data of wind power, photovoltaic power, and load within the power distribution network grid, extract typical daily time-series scenarios using an optimized extraction model; Step 2: Based on typical time-series scenarios, with the goal of optimizing comprehensive indicators, the improved Leuven algorithm, which incorporates a tree structure pruning step, is used to obtain the optimal power supply grid partitioning scheme for each typical day. Step 3: Establish an evaluation index system for grid partitioning schemes, including general applicability indicators of partitioning results, rationality indicators of simulation operation, and representativeness indicators extracted from clustering. Select the optimal grid partitioning scheme in the form of a radar chart, wherein: The representative indicators extracted by clustering are in the following form: ； ； In the formula, For the first Power supply unit division scheme; , These are the evaluation indicators for the number density around a representative day and the evaluation indicators for the radiation radius of a representative day, respectively. The general applicability index of the segmentation results is in the following form: ； ； In the formula, Divide the power supply unit into different schemes; To divide the power supply unit into schemes Substitute into the power supply unit division scheme Obtained after corresponding scene data Indicator value; , These are the generality of functional indicators and the generality of structural indicators, respectively. The simulation operation rationality indicators are in the following form: ； ； ； In the formula, Power supply unit partitioning scheme The number of power supply units; , The first The set of nodes and the set of lines in each power supply unit , This refers to the corresponding number of nodes and the number of lines; , They are nodes Distributed resources at the first Actual usage and upper limit for each time period; For nodes Standard deviation of voltage sequence during the simulation operation cycle; For the line The trend is reversed in time; , , These are resource utilization rate, voltage stability, and power flow stability, respectively.

2. The distribution network power supply grid partitioning method based on the improved Leuven algorithm according to claim 1, characterized in that... The specific steps of step 1 are as follows: Step 11: Using principal component analysis, reduce the dimensionality of the multivariate time series data for the entire year, which includes the coupling of "wind-solar-load", to univariate time series data. Step 12: Determine the number of clusters based on the elbow rule, and use the K-means algorithm to classify the principal component sequences, dividing the annual univariate time series data into several time series data clusters; Step 13: Establish a multi-objective mixed integer linear programming model as a typical day optimization extraction model. With the objectives of minimizing the number of typical days, minimizing the deviation of typical scenes, maximizing the surrounding number density, and maximizing the radiation radius, the most representative and differentiated typical day time series scenes are extracted from the time series data of each cluster.

3. The distribution network power supply grid partitioning method based on the improved Leuven algorithm according to claim 2, characterized in that... In step 13, the objective function of the multi-objective mixed-integer linear programming model is: ； in: ； In the formula, , The binary selection of decision variables and corresponding weight coefficient variables for each typical day are respectively; , These are the original data matrices for each data type and the total data volume for each time period, respectively. Select the number of typical days for the current sample set; This is the sum of the relative deviations between the typical day and the original data, i.e., the deviation degree; Typical daily number density; The typical daily total radiation radius; The constraints of a typical daily optimization extraction model are as follows: ； In the formula, constraint (a) is the typical daily weight coefficient variable. With the selection of decision variables Consistency constraints (b) aim to ensure that the weighting coefficients of all typical days are consistent with the sample size; constraint (c) is a constraint on the range of total relative deviation. is the range relaxation coefficient; constraint (d) is the type constraint for the two types of decision variables.

4. The distribution network power supply grid partitioning method based on the improved Leuven algorithm according to claim 1, characterized in that... In step 2, the comprehensive indicators include the source-load-storage active power matching degree indicator. Modularity index based on electrical distance Reactive power support capacity indicators Power supply unit scale balance index The four aspects are detailed in the following calculation methods: (1) Active power matching index of source-load-storage The distributed generation power and generalized load power are optimized with the goal of minimizing net load, thereby obtaining the optimal distributed generation power and generalized load power corresponding to the solution. The objective of the optimization model is as follows: ； In the formula, Number of scheduling periods; For the first A set of nodes for each power supply unit; for Time of the first Net load value after optimized scheduling of power supply unit's source, load, and storage; , , They are respectively Time of the first The original load power of each power supply unit, the generalized load power after considering the energy storage charging and discharging power and the demand-side response, and the DG power; , , , , , , The first in each power supply unit The load transfer power, load reduction power, energy storage charging power, energy storage discharging power, WT output, PV output, and MT output of each node; Calculate the source-load-storage matching index based on the optimization results. : ； ； In the formula, The number of power supply units in the current power grid partitioning scheme; For the first The power supply unit in the first The degree of source-load-storage matching during different time periods, and ; (2) Modularity index based on electrical distance The coupling relationship between nodes is characterized by the electrical distance based on the active / reactive power-voltage amplitude sensitivity matrix. The sensitivity matrix and electrical distance are calculated as follows: ； ； ； In the formula, This refers to the number of nodes in the distribution network. , , These represent the changes in active power injected into each node, reactive power injected into the node, and voltage amplitude, respectively. , These are the active power-voltage amplitude sensitivity matrix and the reactive power-voltage amplitude sensitivity matrix, respectively. , They are nodes When active / reactive power changes, it affects itself and the nodes. The ratio of the resulting voltage changes indicates the degree of influence of the active / reactive power changes on the two nodes; , , They are nodes With nodes The active electrical distance, reactive electrical distance, and combined electrical distance between them; By utilizing electrical distance and distribution network connections, the distribution network is transformed into a relational network whose modularity can be directly calculated through edge weight calculation. The edge weight calculation method is as follows: ； In the formula, For the integrated electrical distance matrix; For the distribution network connection relationship matrix, when the node With nodes When there are direct connecting lines ,otherwise ; After being transformed into a relational network, the nodes With nodes The edge weights between them; After transforming the power distribution network into a relational network, the modularity index based on electrical distance is calculated according to the definition of modularity. The calculation method is as follows: ； ； ； In the formula, , They are nodes ,node The sum of the weights of all connecting edges; This is the sum of the weights of all edges in the entire relational network; Represents a node With nodes In the case of two nodes belonging to the same power supply unit, then... ,otherwise ; (3) Reactive power support capacity index The evaluation process involves three steps: assessing reactive power demand, assessing reactive power supply capacity, and designing evaluation indicators within the range of [0,1]. Regarding the reactive power demand assessment for each power supply unit, under completely uncontrolled conditions, the overvoltage node voltage at the peak of renewable energy penetration and the undervoltage node voltage at the time of underestimation of penetration will be calculated separately for typical days. The reactive power demand of each power supply unit will be estimated according to the reactive power-voltage amplitude sensitivity matrix. The calculation method is as follows: ； ； In the formula, , The first The set of overvoltage nodes and the set of undervoltage nodes for each power supply unit; Overvoltage / undervoltage nodes The absolute value of the voltage amplitude from the normal voltage range; For the first The minimum capacitive reactive power required by the power supply side for overvoltage nodes in each power supply unit; For the first The minimum inductive reactive power required by the power supply side for the undervoltage node in each power supply unit; Regarding the assessment of reactive power supply capacity of each power supply unit, the reactive power supply capacity of each power supply unit is described by considering the reactive power output of DG and SVC under constant power factor on the source side, based on the set DG power factor range and SVC reactive power capacity. The specific calculation method is as follows: ； ； In the formula, , The first The source-side capacitive and inductive reactive power supply capacity of each power supply unit; , , These represent the maximum capacitive reactive power that PV, WT, and SVC can provide, respectively. , , , These represent the maximum inductive reactive power that PV, WT, MT, and SVC can provide, respectively. Based on the estimated reactive power demand and reactive power supply capacity of each power supply unit, a reactive power support capacity index is formed. Its form is as follows: ； ； ； ； In the formula, , , Power supply unit The values ​​for capacitive reactive power balance, inductive reactive power balance, and comprehensive reactive power balance are all between 0 and 1. (4) Power supply unit scale balance index Introducing a power supply unit scale balance index To limit the size of the power supply unit, it takes the following form: ； In the formula, This represents the standard deviation of the number of nodes in each power supply unit under the current power supply grid partitioning scheme. This is for adjusting the coefficient.

5. The distribution network power supply grid partitioning method based on the improved Leuven algorithm according to claim 4, characterized in that... Step 2, the power grid partitioning includes four stages: initialization, tree structure pruning, node merging, and network collapse. The specific steps are as follows: Step 21, Initialization Phase: Read the original load, wind and solar power output data, network initial weight matrix, and node voltage information at peak and off-peak times of new energy penetration for each node under each typical day. Treat each node as a power supply unit and initialize the partitioning algorithm process parameters. Step 22, Tree structure pruning stage: Find the leaf nodes in the current distribution network, merge them with the parent root node to form a new network, and repeat this process until the upper limit of the tree structure pruning level is reached; Step 23, Node Merging Phase: Traverse each node, adding each node sequentially to the unit containing the directly connected node. Calculate the increase in the comprehensive index after node merging, select the merging scheme with the largest increase, and merge the two nodes. Repeat the node merging phase until the comprehensive index can no longer increase. For the active power matching index Reactive power support capacity indicators When calculating the index values ​​during the node merging phase, only the index values ​​for the parts of the power supply unit whose composition changes are additionally calculated, i.e.: ； ； In the formula, , , These are, respectively, the power supply unit numbers whose constituent nodes have not changed, the power supply unit numbers with nodes moving in, and the node numbers with nodes moving out; , , These represent the average active power matching degree of the corresponding power supply unit over the entire time period; , , These represent the overall reactive power balance of the corresponding power supply unit; , , These are the number of power supply units after node merging, the active power matching index, and the reactive power matching index, respectively. Modularity index Only the impact of the edge weights of nodes whose subordinate relationships have changed on the index increment is considered, that is: ； In the formula, , They are nodes The sum of the internal edge weights of the power supply unit and the sum of the edge weights at the boundary of the power supply unit must be included. , They are nodes The sum of edge weights and nodes The sum of the weights of the edges connected to the power supply unit to be incorporated; The modularity index after node merging; Step 24, Network Collapse Phase: Collapse the nodes contained in each unit into super nodes, calculate the edge weights between nodes in each power supply unit and the edge weights between internal nodes, i.e.: ； ； In the formula, , The first With the A set of nodes for a network power supply unit; Network power supply unit after network collapse With network power supply unit The boundary rights between; Nodes in the network before collapse The sum of the edge weights of all connecting edges; Network power supply unit after network collapse The right to self; Step 25: Use the node edge weights between power supply units as the edge weights between super nodes, and use the node edge weights within power supply units as the self-weights of super nodes to form a new network. Repeat the node merging stage and network collapse stage until the comprehensive index no longer increases, thus obtaining the power distribution grid division scheme corresponding to the current typical day.

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