A mean value clustering-based distributed photovoltaic access capacity calculation method and system

Abstract

The application discloses a kind of based on mean value clustering's distributed photovoltaic access capacity calculation method and system, method includes according to power load, distributed photovoltaic power generation historical data curve is normalized, obtains unit capacity power load power curve and unit capacity distributed photovoltaic power curve;Respectively, two-dimensional mean value clustering is carried out to power curve, obtains power load and the time period division of distributed photovoltaic;Through elbow method and maximum average profile value method, the best clustering number of power load, distributed photovoltaic in each period is determined;Joint scenario of power load and distributed photovoltaic is constructed, clustering center, occurrence probability and joint probability are calculated;For each joint scenario, power flow calculation is carried out, and the maximum access capacity of distributed photovoltaic is obtained;By improving the maximum profile value method of mean value clustering, the combination clustering method of distributed photovoltaic and load joint scenario probability is constructed, and the installation margin of distributed photovoltaic is accurately obtained, to realize accurate planning to distribution network region.

Description

Technical Field

[0001] This invention relates to a method and system for calculating the access capacity of distributed photovoltaic (PV) power grids, and more particularly to a method and system for calculating the access capacity of distributed PV power grids based on mean clustering, which belongs to the field of distribution network planning and evaluation. Background Technology

[0002] With the construction of new power systems, a large number of new energy sources and new power loads are being connected to the distribution system. The distribution network is transforming from a traditional distribution network with deterministic single-phase energy flow to an active distribution network with bidirectional energy flow. The randomness and volatility of new energy sources, coupled with the uncertainty of loads, makes the analysis of the operational safety of the distribution network more complex. With the continuous advancement of policies such as county-wide rooftop photovoltaics, the penetration rate of new energy sources is gradually increasing. Large-scale distributed photovoltaic grid connection has brought huge challenges to some distribution networks, and some areas have even experienced a series of problems such as voltage exceeding limits, power flow exceeding limits, and power flow back to the upper-level grid. Therefore, it is essential to consider the uncertainty of distributed power sources and loads during the distribution network planning stage, and to quantitatively assess the regional distribution network's distributed photovoltaic access capacity while meeting relevant technical indicators. This will provide a technical basis for guiding the planning and transformation of regional distribution networks.

[0003] In terms of clustering methods, traditional clustering analysis methods for distribution networks include K-means clustering, density-based DBSCAN clustering, and Expectation-Maximum Clustering of Gaussian Mixture Model (GMM). Among them, K-Means clustering is widely used in power load clustering due to its simple calculation and fast calculation speed. However, its disadvantage is that it requires specifying the number of clusters in advance. It is also necessary to consider the probabilistic scenarios of distributed power sources and power loads for combined clustering analysis. It is essential to carry out quantitative assessment of the integration of distributed new energy sources into the distribution network.

[0004] Regarding the methods for calculating the access capacity of distributed photovoltaic (PV) power in distribution networks, existing methods mainly rely on power flow calculations based on extreme scenarios of load and distributed PV throughout the year to calculate the PV access capacity that meets operational constraints. However, the evaluation results are conservative, which affects the effective access of distributed PV and the economic efficiency of the distribution network. Summary of the Invention

[0005] Purpose of the invention: The purpose of this invention is to provide a method and system for calculating the access capacity of distributed photovoltaic (PV) based on mean clustering, which can more accurately obtain the installation margin of distributed PV and realize precise regional planning of distribution networks.

[0006] Technical solution: The distributed photovoltaic access capacity calculation method based on mean clustering described in this invention includes the following steps:

[0007] (1) Based on the historical data curves of electricity load and distributed photovoltaic power generation, the per-unit processing is performed to obtain the power curve of electricity load per unit capacity and the power curve of distributed photovoltaic power generation.

[0008] (2) Two-dimensional mean clustering was performed on the power curve of electricity load and the power curve of distributed photovoltaic power respectively to obtain the time period division of electricity load and distributed photovoltaic power.

[0009] (3) The optimal number of clusters for electricity load and distributed photovoltaic power generation in each time period was determined by the elbow method and the maximum average profile value method, respectively.

[0010] (4) Based on the time period division and the optimal number of clusters, construct a combined scenario of electricity load and distributed photovoltaic power generation for a single time period, and calculate the cluster center, occurrence probability and combined probability based on the mean clustering algorithm;

[0011] (5) Perform power flow calculations for each joint scenario to obtain the maximum permitted capacity of distributed photovoltaic power.

[0012] Furthermore, the steps for determining the optimal cluster number of electricity loads for each time period in step (3) are as follows:

[0013] (31a) Import the historical data curve of electricity load for a certain continuous period and perform data preprocessing;

[0014] (31b) Establish a two-dimensional matrix of daily total electricity load and statistical date, perform mean clustering, and form a two-dimensional graph of the sum of cluster deviations from the cluster center for each electricity load under different numbers of clusters;

[0015] (31c) Use the elbow method to find the number of power load clusters that are at inflection points and have small clustering deviations in the two-dimensional graph, perform mean clustering to obtain the initial power load clustering time period division, and then perform secondary segmentation based on changes in the grid structure of the transformer area, adjustments in the operating mode, and changes in important loads to obtain all power load time periods.

[0016] (31d) For each period of electricity load, initialize the initial value of the load cluster number M*=M=2, the maximum value of the load cluster number M_max=SQRT(365) and the load cluster profile value M_Silhouette*=0;

[0017] (31e) Perform mean clustering calculation to obtain M electricity load clusters and the cluster center of each cluster;

[0018] (31f) Based on the cluster center of each power load sample, calculate the Euclidean distance to other samples, and further calculate the average silhouette value M_Silhouette(M) when the number of clusters is M.

[0019] (31g) Compare M_Silhouette(M) and M_Silhouette*, update M_Silhouette* to the maximum value between the two, and update M* = M synchronously;

[0020] (31h) Repeat the iteration M=M+1 until M≥M_max. At this time, M* is the number of optimal power load clusters and M_Silhouette* is the maximum average profile value corresponding to the optimal power load cluster.

[0021] (31i) Repeat steps (31d)-(31h) to obtain the optimal cluster number M for all power load periods.

[0022] Furthermore, the steps for determining the optimal number of distributed photovoltaic clusters for each time period in step (3) are as follows:

[0023] (32a) Import the historical data curve of distributed photovoltaic power generation for a certain continuous period and perform data preprocessing;

[0024] (32b) Establish a two-dimensional matrix of daily total distributed photovoltaic power and statistical dates, perform mean clustering, and form a two-dimensional graph of the sum of daily photovoltaic power to cluster centers under different cluster numbers;

[0025] (32c) Use the elbow method to find the number of distributed photovoltaic clusters that are at inflection points and have small clustering deviations in the two-dimensional graph, perform mean clustering to obtain the initial distributed photovoltaic clustering time period division, and then perform secondary segmentation based on the grid connection time of distributed photovoltaics to obtain all distributed photovoltaic time periods.

[0026] (32d) For each distributed photovoltaic period, initialize the initial value of the number of photovoltaic clusters N*=N=2, the maximum value of the number of photovoltaic clusters N_max=SQRT(365), and the distributed photovoltaic cluster outline value N_Silhouette*=0;

[0027] (32e) Perform mean clustering calculation to obtain N distributed photovoltaic clusters and the cluster center of each cluster;

[0028] (32f) Based on the cluster center of each distributed photovoltaic sample, calculate the Euclidean distance to other samples, and further calculate the average silhouette value N_Silhouette(N) when the number of clusters is N;

[0029] (32g) Compare N_Silhouette(N) and N_Silhouette*, update N_Silhouette* to the maximum value between the two, and update N*=N synchronously;

[0030] (32h) Repeat the iteration N=N+1 until N≥N_max. At this time, N* is the optimal number of distributed photovoltaic clusters and N_Silhouette* is the maximum average contour value corresponding to the optimal cluster.

[0031] (32i) Repeat steps (32d)-(32h) to obtain the optimal number of clusters N for all distributed photovoltaic periods.

[0032] Furthermore, the expressions for the cluster centers, occurrence probabilities, and joint probabilities in step (4) are as follows:

[0033]

[0034] In the formula, T D For the time period of electricity load clustering, T PV To be with T D Distributed photovoltaic clustering periods that may overlap or occur simultaneously; For time period T D The m-th electricity load cluster center within the cluster. Indicates The probability of cluster centers appearing; For time period T PV The nth distributed photovoltaic clustering center in the inner region, Indicates The probability of cluster centers appearing; Indicates the distributed photovoltaic time period T PV With and electricity load period T D The percentage of time that overlaps with each other. This represents the joint probability of the joint scenario.

[0035] Further, the steps for the maximum permitted capacity of distributed photovoltaic power in step (5) are as follows:

[0036] (51) Under the safety constraints of node voltage, line current, transformer load, and power exchange with the upper-level power grid, power flow calculation is performed by combining the clustering center of the power load and the clustering center of the distributed photovoltaic in the joint scenario with the distribution area grid structure, load and photovoltaic capacity and the distribution and proportional coefficient of the grid connection point.

[0037] (52) Relax the constraints on the load node voltage, gradually increase the distributed photovoltaic capacity to evaluate the voltage qualification rate index of the distribution area, count the number of voltage over-limits, and calculate the over-limit probability by combining the joint scenario probability.

[0038] (53) Based on the probability of exceeding the limit, the voltage qualification rate boundary was fitted multiple times, and the maximum access quantity of distributed photovoltaic that meets the voltage qualification rate index was finally obtained.

[0039] The objective function for maximizing the access capacity of distributed photovoltaic power is shown in the following equation:

[0040]

[0041] In the formula, f obj C represents the maximum admission limit for distributed photovoltaic power during the clustering period. PV,j Let be the distributed optical admissions of node j.

[0042] Furthermore, the power flow calculation steps in step (51) are as follows:

[0043] (51a) Obtain the number of load clusters M and the number of distributed photovoltaic clusters N. Using the electricity load period as the reference period, construct a joint scenario of electricity load and distributed photovoltaic at the same time and calculate the probability of the joint scenario during this period.

[0044] (51b) Perform mean clustering with M cluster sizes to calculate the cluster centers of the M typical daily electricity loads. probability of occurrence Calculate the active power of the electrical load at each node. reactive power

[0045] (51c) Perform mean clustering with N clusters to calculate the cluster centers of N typical distributed photovoltaic days. probability of occurrence Calculate the active power of distributed photovoltaic power at each node. reactive power

[0046] (51d) Based on the given distributed photovoltaic installation capacity, combined with the power load of each node and the per-unit value of the distributed photovoltaic center, power flow calculation is performed on all joint scenarios to obtain the voltage of each node, line current and node switching power.

[0047] (51e) Determine if there are any branch current exceeding the limit, distribution transformer capacity exceeding the limit, or power exchange with the upstream exceeding the limit. If an exceedance occurs, reduce the amount of distributed photovoltaic installations or carry out distribution network upgrades. If no exceedance occurs, calculate the voltage exceedance probability of each node at all times under all joint scenarios in the current time period.

[0048] Furthermore, the constraints in step (51) include load node voltage constraints, line current carrying constraints, and power exchange constraints with the upstream power grid, as shown in the following expressions:

[0049]

[0050] In the formula, Let be the voltage at load node j at time t. These are the upper and lower limits of the load node voltage, with a default value of 93%-107% of the nominal voltage; Let be the voltage of distributed photovoltaic node j at time t. These are the upper and lower limits of the grid connection voltage for distributed photovoltaic node j, respectively, with the default value being 85%-110% of the nominal voltage; Let be the branch currents at node j and node j′ at time t. This is the maximum branch current limit; Let t be the active power at the distribution switch. These are the upper and lower limits of active power at the distribution gate; Let t be the reactive power at the distribution switch. These are the upper and lower limits of reactive power at the power distribution point;

[0051] The expressions for the active and reactive power of the electrical load at each node are as follows:

[0052]

[0053] In the formula, Let be the active power of the electrical load node j at time t. The predicted maximum electrical load for the distribution area. S represents the maximum value of the historical data curve of electricity load in the distribution area. b This is the base value of the total load power of the distribution area. Let Scale be the per-unit value of the load power at time t in the scenario of electricity load clustering. j,D Let φ be the proportion of the electrical load at node j to the total load of the area, and φ be the power factor angle of the distribution area.

[0054] The active and reactive power expressions for distributed photovoltaic systems at each node are as follows:

[0055]

[0056] In the formula, Let C be the active power of distributed photovoltaic node j at time t. PV This represents the maximum permitted capacity for distributed photovoltaic power in the distribution area. Let be the photovoltaic output coefficient at time t in a distributed photovoltaic clustering scenario. j,PV Let be the proportion of photovoltaic installations at node j to the total photovoltaic installations in the region. Let be the distributed photovoltaic power factor of node j.

[0057] Furthermore, the calculation of the probability of exceeding the limit in step (52) is as follows:

[0058]

[0059] In the formula: Rate represents the probability of node j exceeding its limit in a joint scenario where the electricity load clustering period and the distributed photovoltaic clustering period intersect. j Let be the cumulative probability of node j exceeding the limit across all time periods. x represents the probability of the joint scenario. j (t) represents the voltage over-limit status of the j-th electrical load node in time period t, x j (t) = 1 indicates that the state is out of bounds, x m (t) = 0 indicates that the voltage is in a non-limited state, and T represents the number of sampling points. Rate represents the cumulative number of times the limit is exceeded within a day when performing power flow calculations. VQR To meet the voltage compliance rate target for the distribution area to be evaluated, the voltage compliance rate for any electrical load node should be higher than the Rate. VQR λ represents the reserved margin.

[0060] Furthermore, the calculation process for the maximum access quantity of distributed photovoltaic power in step (53) is as follows:

[0061] (53a) Obtain the current distributed photovoltaic installation capacity of the distribution area to be evaluated

[0062] (53b) Determine the initial step size h0, and determine the convergence accuracy ε;

[0063] (53c) Let h = h0, maximum distributed photovoltaic multiplier K = 1;

[0064] (53d) Determine the step size h: if h > ε, continue to the next step; if h < ε, the calculation ends and returns to C. PV And K, return C PV This represents the maximum currently permitted distributed photovoltaic installation capacity within the distribution area.

[0065] (53e) Calculation

[0066] (53f) Using the electricity load clustering center in the joint scenario Photovoltaic Clustering Center Perform power flow calculations to obtain the voltage over-limit probability (Rate) for each node under all combined scenarios. j ;

[0067] (53g) Determine if the Rate is met. j ≤1-Rate VQR -λ, if not satisfied, take half the original step size h = h / 2, go to step (53d), if satisfied, update C. PV =C PV'And K = K + h, go to step (53d);

[0068] The expression for the maximum allowable quantity of distributed photovoltaic power is as follows:

[0069]

[0070] In the formula, max C PV To meet the maximum permitted capacity for distributed photovoltaic (PV) installations in accordance with the voltage compliance rate requirement, K represents the maximum distributed PV installation multiple. This indicates the remaining installed capacity of distributed photovoltaic systems.

[0071] The distributed photovoltaic access capacity calculation system based on mean clustering described in this invention includes:

[0072] The data curve acquisition and processing module is used to acquire and process electricity load and distributed photovoltaic power generation data curves;

[0073] The time period segmentation module is used to segment electricity load and distributed photovoltaics into time periods using two-dimensional mean clustering;

[0074] The calculation module is used to calculate the optimal number of clusters for electricity load and distributed photovoltaic power, as well as the cluster centers, occurrence probabilities, and joint probabilities.

[0075] The analysis module is used to analyze and judge the calculation results and obtain the maximum permitted capacity for distributed photovoltaic power.

[0076] Beneficial effects: Compared with the prior art, the present invention has the following significant advantages: (1) More accurate clustering: By using the maximum contour value of improved mean clustering based on K-means++, the optimal number of clusters for load and distributed photovoltaic is obtained. Compared with the traditional K-means clustering method, a new data point is randomly selected as the new center using a weighted probability distribution. (2) More accurate guidance for the planning and design of active distribution networks: By constructing a combined clustering method for the probability of distributed photovoltaic and load scenarios in the distribution area, the distributed photovoltaic and load are quantitatively analyzed through the construction of probabilistic scenarios. This method can more realistically reflect the distribution of load and distributed photovoltaic in the distribution area than deterministic extreme scenarios, and realize the distribution network access capability under source-load uncertainty. Quantitative assessment; (3) Accurately obtain the remaining distributed photovoltaic installation margin in the distribution area. By clustering the data of new energy power generation and load in the area to be assessed over the past 1-2 years as samples, the voltage is relaxed, and a comprehensive charge qualification rate index is introduced. A method for calculating the access capacity of distributed photovoltaic in the distribution area based on multiple combination scenarios is proposed. In addition, taking into account the safety and economy of the distribution network, under the premise of meeting the relevant safety limit exceedance probability index, the remaining distributed photovoltaic installation margin and the maximum distributed photovoltaic multiple in the distribution area are accurately obtained, so as to realize the quantitative assessment of the access capacity of distributed photovoltaic in the distribution network and the improvement of access capacity. Compared with the traditional use of extreme cases as the criterion for the access capacity of the distribution network, it can better explore the potential of the distribution network to access new energy. Attached Figure Description

[0077] Figure 1 This is a flowchart of the distributed photovoltaic access capacity calculation method based on mean clustering of the present invention;

[0078] Figure 2 This is a flowchart illustrating the optimal load cluster number calculation method of the present invention.

[0079] Figure 3 This is a flowchart illustrating the optimal distributed photovoltaic cluster number calculation method of the present invention.

[0080] Figure 4 This is a schematic diagram of the average contour values ​​corresponding to different numbers of clusters based on K-means++ clustering according to the present invention;

[0081] Figure 5 This is a schematic diagram illustrating the determination of clustering bias in a region based on the elbow method according to the present invention;

[0082] Figure 6 This is a flowchart illustrating the probability calculation process for a combined single-time load and distributed photovoltaic scenario according to the present invention.

[0083] Figure 7 This is a flowchart of the evaluation process for renewable energy access capability in distribution areas based on half-step repetitive power flow, as presented in this invention. Detailed Implementation

[0084] The technical solution of the present invention will be further described below with reference to the accompanying drawings.

[0085] like Figures 1-3 As shown, this invention provides a method for calculating the access capacity of distributed photovoltaic (PV) systems based on mean clustering. It employs a combined clustering method based on the probabilities of distributed PV and load scenarios in a distribution area to assess the distributed PV access capacity in an uncertain distribution area. The method combines the elbow method with the maximum profile coefficient method to calculate the optimal number of clusters for load and distributed PV. Through a distribution area renewable energy access capacity assessment process based on half-step repetitive power flow in a joint scenario, the remaining distributed PV installation margin and the maximum distributed PV multiplier in the distribution area are obtained. The method includes the following steps:

[0086] Step 1: Standardize the power curves of electricity load and distributed photovoltaic power generation based on the historical data curves to obtain the power curve of electricity load per unit capacity and the power curve of distributed photovoltaic power generation.

[0087] Maximum load power was calculated using historical data curves of electricity load and distributed photovoltaic power generation. and maximum distributed photovoltaic power Based on maximum load power and maximum distributed photovoltaic power Calculate the per-unit value, i.e., perform per-unit processing.

[0088] Based on the load forecast results for this region, the maximum load forecast value for the period to be evaluated is obtained. Based on the distributed installation situation in the region, the existing distributed photovoltaic installation volume is obtained.

[0089] Step 2: Perform two-dimensional mean clustering on the electricity load and distributed photovoltaic power curves respectively to obtain the time period division of electricity load and distributed photovoltaic.

[0090] Two-dimensional mean clustering is performed by combining historical total load data from several consecutive days with statistical dates to obtain the initial load clustering period division; the historical load data is further segmented for changes in transformer network structure, operation mode adjustments, and significant load changes to obtain all load periods; within a single period, the optimal number of load clusters for each period is determined by combining the elbow method and the maximum average profile value method.

[0091] By combining historical data of distributed photovoltaic (PV) power generation over several consecutive days with statistical dates, two-dimensional mean clustering is performed to obtain the initial distributed PV clustering time period division. The historical data of distributed PV is then further segmented based on the grid connection time of distributed PV to obtain all distributed PV time period divisions. Within a single time period, the optimal number of distributed PV clusters for each time period is determined by combining the elbow method and the maximum average profile value method.

[0092] Step 3: Determine the optimal number of clusters for the electricity load and distributed photovoltaic power generation in each time period using the elbow method and the maximum average profile value method, respectively.

[0093] like Figure 2 As shown, the steps for determining the optimal cluster number of electricity loads for each time period are as follows:

[0094] Step 31a: Import historical electricity load data curves for a certain continuous period and perform data preprocessing;

[0095] Step 31b: Establish a two-dimensional matrix of daily total electricity load and statistical dates, perform mean clustering, and generate a two-dimensional graph of the sum of cluster deviations from the cluster centers for each electricity load under different numbers of clusters;

[0096] Step 31c: Use the elbow method to find the number of power load clusters that are at inflection points and have small clustering deviations in the two-dimensional graph, perform mean clustering to obtain the initial power load clustering time period division, and then perform secondary segmentation based on changes in the transformer area grid structure, adjustments in operating mode, and changes in important loads to obtain all power load time periods;

[0097] Step 31d: For each period of electricity load, initialize the initial value of the load cluster number M* = M = 2, the maximum value of the load cluster number M_max = SQRT(365) and the load cluster profile value M_Silhouette* = 0;

[0098] Step 31e: Perform mean clustering calculation to obtain M electricity load clusters and the cluster center of each cluster;

[0099] Step 31f: Based on the cluster center of each electrical load sample, calculate the Euclidean distance to other samples, and further calculate the average silhouette value M_Silhouette(M) when the number of clusters is M;

[0100] Step 31g: Compare M_Silhouette(M) and M_Silhouette*, update M_Silhouette* to the maximum value between the two, and simultaneously update M* = M;

[0101] Step 31h: Repeat the iteration M = M + 1 until M ≥ M_max. At this time, M* is the number of optimal power load clusters and M_Silhouette* is the maximum average profile value corresponding to the optimal power load cluster.

[0102] Step 31i: Repeat steps 31d-31h to obtain the optimal cluster number M for all electricity load periods.

[0103] like Figure 3As shown, the steps for determining the optimal cluster number for distributed photovoltaic systems at each time period are as follows:

[0104] Step 32a: Import historical data curves of distributed photovoltaic power generation for a certain continuous period and perform data preprocessing;

[0105] Step 32b: Establish a two-dimensional matrix of daily total distributed photovoltaic power and statistical dates, perform mean clustering, and generate a two-dimensional graph of the sum of the clustering deviations from the daily photovoltaic power to the cluster centers under different numbers of clusters;

[0106] Step 32c: Use the elbow method to find the number of distributed photovoltaic clusters that are at inflection points and have small clustering deviations in the two-dimensional graph, perform mean clustering to obtain the initial distributed photovoltaic clustering time period division, and then perform secondary segmentation based on the grid connection time point of distributed photovoltaics to obtain all distributed photovoltaic time periods;

[0107] Step 32d: For each distributed photovoltaic period, initialize the initial value of the number of photovoltaic clusters N* = N = 2, the maximum value of the number of photovoltaic clusters N_max = SQRT(365), and the distributed photovoltaic cluster outline value N_Silhouette* = 0;

[0108] Step 32e: Perform mean clustering calculation to obtain N distributed photovoltaic clusters and the cluster center of each cluster;

[0109] Step 32f: Based on the cluster center of each distributed photovoltaic sample, calculate the Euclidean distance to other samples, and further calculate the average silhouette value N_Silhouette(N) when the number of clusters is N;

[0110] Step 32g: Compare N_Silhouette(N) and N_Silhouette*, update N_Silhouette* to the maximum value between the two, and simultaneously update N* = N;

[0111] Step 32h: Repeat the iteration N = N + 1 until N ≥ N_max. At this point, N* is the optimal number of distributed photovoltaic clusters and N_Silhouette* is the maximum average silhouette value corresponding to the optimal cluster.

[0112] Step 32i: Repeat steps 32d-32h to obtain the optimal number of clusters N for all distributed photovoltaic periods.

[0113] Step 4: Based on the time period division and the optimal number of clusters, construct a combined scenario of electricity load and distributed photovoltaic power generation for a single time period, and calculate the cluster centers, occurrence probabilities, and joint probabilities based on the mean clustering algorithm.

[0114] The cluster center and occurrence probability of each distributed photovoltaic clustering period are calculated one by one based on the mean clustering algorithm. Taking the load period as the reference period, one or more distributed photovoltaic clustering periods that are in the same period as the load reference period are selected to construct a set of load and distributed photovoltaic joint scenarios for each subdivided period, and the joint probability of each joint scenario in the scenario set is calculated.

[0115] The expressions for cluster centers, occurrence probabilities, and joint probabilities are shown below:

[0116]

[0117] In the formula, T D For the time period of electricity load clustering, T PV To be with T D Distributed photovoltaic clustering periods that may overlap or occur simultaneously; For time period T D The m-th electricity load cluster center within the cluster. Indicates The probability of cluster centers appearing; For time period T PV The nth distributed photovoltaic clustering center in the inner region, Indicates The probability of cluster centers appearing; Indicates the distributed photovoltaic time period T PV With and electricity load period T D The percentage of time that overlaps with each other. This represents the joint probability of the joint scenario.

[0118] Step 5: Perform power flow calculations for each joint scenario to obtain the maximum permitted capacity for distributed photovoltaic power.

[0119] Clustering centers of loads in joint scenarios Distributed photovoltaic clustering center Substituting the nodes of the distribution network, and considering the distribution area's grid structure, load, photovoltaic capacity, grid connection points, and proportional coefficients, the existing installed photovoltaic capacity is considered. As an initial value, given the current photovoltaic increment step size h = h0 and the photovoltaic installation multiple K = 1, the photovoltaic data is substituted into the power flow calculation. The amount of distributed photovoltaic access is gradually increased proportionally to calculate the maximum allowed capacity of distributed photovoltaic in the joint scenario under the safety constraints of node voltage, line current, transformer load, and power exchange with the upper-level grid.

[0120] The steps for maximizing the permitted capacity of distributed photovoltaic power are as follows:

[0121] Step 51: Under the safety constraints of node voltage, line current carrying capacity, transformer load, and power exchange with the upstream grid, power flow calculation is performed by combining the cluster centers of electricity loads and distributed photovoltaic cluster centers in the joint scenario with the distribution area grid structure, load and photovoltaic capacity, distribution of grid connection points, and proportional coefficients.

[0122] like Figure 6 As shown, the steps for power flow calculation are as follows:

[0123] Step 51a: Obtain the number of load clusters M and the number of distributed photovoltaic clusters N. Using the electricity load period as the reference period, construct a joint scenario of electricity load and distributed photovoltaic at the same time and calculate the probability of the joint scenario during this period.

[0124] Step 51b: Perform mean clustering with M cluster sizes to calculate the cluster centers for the M typical daily electricity loads. probability of occurrence Calculate the active power of the electrical load at each node. reactive power

[0125] Step 51c: Perform mean clustering with N clusters to calculate the cluster centers of N typical distributed photovoltaic days. probability of occurrence Calculate the active power of distributed photovoltaic power at each node. reactive power

[0126] Step 51d: Based on the given distributed photovoltaic installation capacity, combined with the power load of each node and the per-unit value of the distributed photovoltaic center, perform power flow calculations for all joint scenarios to obtain the voltage of each node, line current, and node switching power.

[0127] Step 51e: Determine if there are any branch current exceeding limits, transformer capacity exceeding limits, or power exchange limits with the upstream. If any limits are exceeded, reduce the amount of distributed photovoltaic installations or upgrade the distribution network. If no limits are exceeded, calculate the voltage exceedance probability of each node at all times under all joint scenarios in the current time period.

[0128] The constraints include load node voltage constraints, line current carrying constraints, and power exchange constraints with the upstream grid, as shown in the following expressions:

[0129]

[0130] In the formula, Let be the voltage at load node j at time t. These are the upper and lower limits of the load node voltage, with a default value of 93%-107% of the nominal voltage; Let be the voltage of distributed photovoltaic node j at time t. These are the upper and lower limits of the grid connection voltage for distributed photovoltaic node j, respectively, with the default value being 85%-110% of the nominal voltage; Let be the branch currents at node j and node j′ at time t. This is the maximum branch current limit; Let t be the active power at the distribution switch. These are the upper and lower limits of active power at the distribution gate; Let t be the reactive power at the distribution switch. These are the upper and lower limits of reactive power at the power distribution point;

[0131] The expressions for the active and reactive power of the electrical load at each node are as follows:

[0132]

[0133] In the formula, Let be the active power of the electrical load node j at time t. The predicted maximum electrical load for the distribution area. S represents the maximum value of the historical data curve of electricity load in the distribution area. b This is the base value of the total load power of the distribution area. Let Scale be the per-unit value of the load power at time t in the scenario of electricity load clustering. j,D Let φ be the proportion of the electrical load at node j to the total load of the area, and φ be the power factor angle of the distribution area.

[0134] The active and reactive power expressions for distributed photovoltaic systems at each node are as follows:

[0135]

[0136] In the formula, Let C be the active power of distributed photovoltaic node j at time t. PV This represents the maximum permitted capacity for distributed photovoltaic power in the distribution area. Let be the photovoltaic output coefficient at time t in a distributed photovoltaic clustering scenario. j,PV Let be the proportion of photovoltaic installations at node j to the total photovoltaic installations in the region. Let be the distributed photovoltaic power factor of node j.

[0137] Step 52: Relax the constraints on the load node voltage, gradually increase the distributed photovoltaic capacity to evaluate the voltage qualification rate index of the distribution area, count the number of voltage over-limits, and calculate the over-limit probability by combining the joint scenario probability.

[0138] The probability of exceeding the limit is calculated as follows:

[0139]

[0140] In the formula: Rate represents the probability of node j exceeding its limit in a joint scenario where the electricity load clustering period and the distributed photovoltaic clustering period intersect. j Let be the cumulative probability of node j exceeding the limit across all time periods. x represents the probability of the joint scenario. j (t) represents the voltage over-limit status of the j-th electrical load node in time period t, x j (t) = 1 indicates that the state is out of bounds, x m (t) = 0 indicates that the voltage is in a non-limited state, and T represents the number of sampling points. Rate represents the cumulative number of times the limit is exceeded within a day when performing power flow calculations. VQR To meet the voltage compliance rate target for the distribution area to be evaluated, the voltage compliance rate for any electrical load node should be higher than the Rate. VQR λ represents the reserved margin.

[0141] Step 53: Based on the probability of exceeding the limit, after fitting the voltage qualification rate boundary multiple times, the maximum access quantity of distributed photovoltaic power that meets the voltage qualification rate index is finally obtained.

[0142] The objective function for maximizing the access capacity of distributed photovoltaic power is shown in the following equation:

[0143]

[0144] In the formula, f obj C represents the maximum admission limit for distributed photovoltaic power during the clustering period. PV,j Let be the distributed optical admissions of node j.

[0145] like Figure 7 As shown, the calculation process for the maximum permitted capacity of distributed photovoltaic power generation is as follows:

[0146] Step 53a: Obtain the current distributed photovoltaic installation capacity of the distribution area to be evaluated.

[0147] Step 53b: Determine the initial step size h0 and the convergence accuracy ε;

[0148] Step 53c: Let h = h0, maximum distributed photovoltaic multiplier K = 1;

[0149] Step 53d: Determine the step size h: if h > ε, continue to the next step; if h < ε, the calculation ends and returns to C. PV And K, return C PV This represents the maximum currently permitted distributed photovoltaic installation capacity within the distribution area.

[0150] Step 53e: Calculation

[0151] Step 53f: Clustering centers of electricity load in the joint scenario Photovoltaic Clustering Center Perform power flow calculations to obtain the voltage over-limit probability (Rate) for each node under all combined scenarios. j ;

[0152] Step 53g: Determine if the Rate is satisfied. j ≤1-Rate VQR -λ, if not satisfied, take half the original step size h = h / 2, go to step 53d, if satisfied, update C. PV =C PV 'And K = K + h, go to step 53d;

[0153] The expression for the maximum allowable quantity of distributed photovoltaic power is as follows:

[0154]

[0155] In the formula, max C PV To meet the maximum permitted capacity for distributed photovoltaic (PV) installations in accordance with the voltage compliance rate requirement, K represents the maximum distributed PV installation multiple. This indicates the remaining installed capacity of distributed photovoltaic systems.

[0156] This invention provides a distributed photovoltaic access capacity calculation system based on mean clustering, comprising:

[0157] The data curve acquisition and processing module is used to acquire and process electricity load and distributed photovoltaic power generation data curves;

[0158] The time period segmentation module is used to segment electricity load and distributed photovoltaics into time periods using two-dimensional mean clustering;

[0159] The calculation module is used to calculate the optimal number of clusters for electricity load and distributed photovoltaic power, as well as the cluster centers, occurrence probabilities, and joint probabilities.

[0160] The analysis module is used to analyze and judge the calculation results and obtain the maximum permitted capacity for distributed photovoltaic power.

[0161] Taking load clustering as an example, the following methods are used: Figure 2 The steps shown are used to calculate the average profile value of different cluster numbers using load sampling data of a certain power distribution area for 24 hours a day for 365 days as sample data.

[0162] like Figure 4As shown, using load sampling data from a power distribution area for 365 days and 24 hours a day as sample data, the average profile value was calculated for different numbers of clusters using the maximum average profile value clustering method. The horizontal axis represents the number of clusters, with an initial value of 2 for M, and a maximum value of SQRT(365) = 20. The vertical axis represents the average profile value. As can be seen from the figure, as the value of M gradually increases, the average profile value undergoes a process of first decreasing, then increasing, and then gradually decreasing again, reaching its maximum value when M = 4.

[0163] Meanwhile, when using the elbow method to calculate the clustering bias corresponding to different M values ​​for load sampling data, such as Figure 5 As shown, as the number of categories M gradually increases, the sample division becomes more refined, the aggregation degree of each class gradually increases, and the sum of squared errors on the ordinate gradually decreases. At this point, the elbow method is used to select the inflection point of the image. That is, when M=4, the inflection point of the image indicates that further increasing the value of k will result in a very small change in the intra-class error, and it can no longer distinguish samples better than the current value of M. Since the initial number of clusters is 4 when using the maximum mean profile value method and the elbow method, considering both the calculation speed and the clustering effect, the initial number of clusters for the loading clustering is set to M=4.

[0164] Similarly, combining the maximum average profile value method and the elbow method, the optimal clustering number N for distributed photovoltaic power generation samples in the distribution area is also 4. Subsequently, the probability of exceeding the limit is calculated using a joint scenario of M=4 and N=4.

[0165] like Figure 6 As shown, the probabilistic power flow calculation method for a joint scenario of load and distributed photovoltaic power includes the following steps:

[0166] Step a: Obtain the number of load clusters M and the number of distributed photovoltaic clusters N; using the load period as the baseline period, construct a joint scenario of load and distributed photovoltaic occurring simultaneously, and calculate the probability of the joint scenario during this period;

[0167] Step b: Perform K-Means++ improved mean clustering on the load cluster number M, and calculate the cluster centers of M typical load days. and the probability of occurrence Perform K-Means++ improved mean clustering on N distributed photovoltaic clusters to calculate the cluster centers of N typical daily distributed photovoltaic clusters. and the probability of occurrence

[0168] Step c: Construct a joint scenario of load and photovoltaics, obtain the joint probability distribution of M×N sets of samples, and calculate the active power and reactive power of the load at each node:

[0169]

[0170] The active and reactive power of the distributed photovoltaic system at each node were calculated:

[0171]

[0172] Step d: Perform power flow calculations on the M×N groups of samples to obtain data such as node voltage, line current, and node power under all joint scenarios. Determine whether each group of samples exceeds the limit and calculate the probability of voltage exceeding the limit.

[0173]

[0174] The formula for calculating the scenario probability is:

[0175]

[0176] Step e: Accumulate the sum of probabilities of all joint scenarios that meet the operational safety requirements, and obtain the sum of probabilities (Rate) of joint scenarios that exceed the limits in the M×N sets of samples. j ;

[0177] Ultimately, Rate j This is the combined probability of exceeding the limit for the number of sample load clusters M and the number of distributed photovoltaic clusters N in the power distribution area.

[0178] use Figure 6 Example of a method: taking Rate VQR =98.5%, the State Grid Corporation of China's ten commitments to power supply services stipulate that the average voltage qualification rate of urban power grid residential customers should reach 98.5%.

[0179] As shown in Table 1, joint clusters with 5 clusters each for load and distributed photovoltaic (PV) data were constructed using sample load and sample distributed PV data. This represents the joint probability distribution of 5×5 samples. Clusters 1 to 5 represent a gradual decrease in the number of PV clusters from largest to smallest, while clusters 1 to 5 represent a gradual decrease in load from largest to smallest. The lowest probabilities in the combined clusters are: Load 5 - PV 1 (minimum load, maximum PV) at 0.34%; Load 5 - PV 4 (minimum load, second smallest PV) at 0.43%; and Load 5 - PV 2 (minimum load, second largest PV) at 0.46%, indicating that these three scenarios are extremely rare.

[0180] Table 1. Example of joint probability distribution of load clustering and distributed photovoltaic clustering

[0181] Load Clustering 1 1.95％ 2.65％ 3.83％ 2.46％ 3.36％ Load Clustering 2 6.08％ 8.27％ 11.92％ 7.66％ 10.46％ Load Clustering 3 4.69％ 6.38％ 9.19％ 5.91％ 8.07％ Load Clustering 4 0.64％ 0.87％ 1.25％ 0.80％ 1.10％ Load clustering 5 0.34％ 0.46％ 0.66％ 0.43％ 0.58％

[0182] When performing joint scenario probability calculations for various joint scenarios, Table 2 shows the distribution of the highest voltage at the end nodes of the joint scenarios based on the number of load clusters and distributed photovoltaic clusters. In the photovoltaic cluster 1 to load cluster 5 scenarios, the distribution network end nodes exceeded the limit, with a voltage per unit value of 1.0873 > 1.007, which exceeds the voltage qualification rate requirement for the 380V voltage level of the distribution network. Other situations did not exceed the limit.

[0183] Table 2 shows the voltage distribution of the end nodes in the combined scenario of load clustering number and distributed photovoltaic clustering.

[0184] Load Clustering 1 1.0261 1.0062 0.9827 0.9516 0.9176 Load Clustering 2 1.0485 1.0293 1.0068 0.9770 0.9445 Load Clustering 3 1.0609 1.0421 1.0200 0.9908 0.9592 Load Clustering 4 1.0696 1.0531 1.0314 1.0028 0.9718 Load clustering 5 1.0873 1.0692 1.0480 1.0202 0.9901

[0185] The scenario where the limit is exceeded is the scenario where the distributed photovoltaic output is at its maximum and the load is at its minimum. In this case, the sum of the probabilities of all joint scenarios where the limit is not exceeded is calculated as 1-Rate. j =1 - 0.34% = 99.66% > 98.5% of the distribution area safety over-limit probability index, according to Figure 7 The renewable energy access capacity estimation method based on the half-step repetitive power flow method shown is used to further calculate the maximum power generation C of distributed photovoltaic power. PV And the growth multiple K of distributed photovoltaic power.

Claims

1. A method for calculating the access capacity of distributed photovoltaic power generation based on mean clustering, characterized in that, Includes the following steps: (1) Based on the historical data curves of electricity load and distributed photovoltaic power generation, the per-unit processing was performed to obtain the electricity load power curve and distributed photovoltaic power curve per unit capacity; (2) Two-dimensional mean clustering was performed on the power load and distributed photovoltaic power curves respectively to obtain the time period division of power load and distributed photovoltaic; (3) The optimal number of clusters for electricity load and distributed photovoltaic power generation in each time period was determined by the elbow method and the maximum average profile value method, respectively. (4) Based on the time period division and the optimal number of clusters, construct a joint scenario of electricity load and distributed photovoltaic in a single time period. Calculate the cluster center and occurrence probability based on the mean clustering algorithm, and introduce the time ratio where the distributed photovoltaic time period and the electricity load time period overlap. Multiply the occurrence probability of the electricity load cluster center and the occurrence probability of the distributed photovoltaic cluster center with the time ratio to obtain the joint probability. (5) For each joint scene, a power flow calculation is performed, and the node voltage out-of-limit probability is calculated in combination with the joint probability; it is determined whether the node voltage out-of-limit probability meets a constraint condition, and the constraint condition is that the node voltage out-of-limit probability is less than or equal to wherein is a voltage qualification rate index required to be reached by a power distribution area to be evaluated, is a reserved margin; if the constraint condition is not met, the step size is halved; if the constraint condition is met, the maximum distributed photovoltaic access capacity and the maximum distributed photovoltaic multiple are updated; and the step size is determined; if the step size is greater than a convergence precision, the power flow calculation is continuously performed; if the step size is less than the convergence precision, the calculation is ended, and the maximum distributed photovoltaic installation capacity of the power distribution area under the current accessible condition is obtained.

2. The distributed photovoltaic access capacity calculation method based on mean clustering according to claim 1, characterized in that, The steps for determining the optimal cluster number of electricity load for each time period in step (3) are as follows: (31a) Import the historical data curve of electricity load for a certain continuous period and perform data preprocessing; (31b) Establish a two-dimensional matrix of daily total electricity load and statistical date, perform mean clustering, and form a two-dimensional graph of the sum of cluster deviations from the cluster center for each electricity load under different numbers of clusters; (31c) Use the elbow method to find the number of power load clusters that are at the inflection point and have small clustering deviation in the two-dimensional graph, perform mean clustering to obtain the initial power load clustering time period division, and then perform secondary segmentation based on changes in the grid structure of the transformer area, adjustments in the operating mode, and changes in important loads to obtain all power load time periods; (31d) For each period of electricity load, initialize the initial value of the load cluster number M*=M=2, the maximum value of the load cluster number M_max=SQRT(365) and the load cluster profile value M_Silhouette*=0; (31e) Perform mean clustering calculation to obtain M electricity load clusters and the cluster center of each cluster; (31f) Based on the cluster center of each power load sample, calculate the Euclidean distance to other samples, and further calculate the average silhouette value M_Silhouette(M) when the number of clusters is M. (31g) Compare M_Silhouette(M) and M_Silhouette*, update M_Silhouette* to the maximum value between the two, and update M*=M synchronously; (31h) Repeat the iteration M=M+1 until M≥M_max. At this time, M* is the number of optimal power load clusters and M_Silhouette* is the maximum average profile value corresponding to the optimal power load cluster. (31i) Repeat steps (31d)-(31h) to obtain the optimal cluster number M for all power load periods.

3. The distributed photovoltaic access capacity calculation method based on mean clustering according to claim 1, characterized in that, The steps for determining the optimal number of clusters for distributed photovoltaic power generation in each time period in step (3) are as follows: (32a) Import the historical data curve of distributed photovoltaic power generation for a certain continuous period and perform data preprocessing; (32b) Establish a two-dimensional matrix of daily total distributed photovoltaic power and statistical dates, perform mean clustering, and form a two-dimensional graph of the sum of daily photovoltaic power to cluster centers under different cluster numbers; (32c) Use the elbow method to find the number of distributed photovoltaic clusters that are at the inflection point and have small clustering deviation in the two-dimensional graph, perform mean clustering to obtain the initial distributed photovoltaic clustering time period division, and then perform secondary segmentation based on the grid connection time point of distributed photovoltaic to obtain all distributed photovoltaic time periods. (32d) For each distributed photovoltaic period, initialize the initial value of the number of photovoltaic clusters N*=N=2, the maximum value of the number of photovoltaic clusters N_max=SQRT(365), and the distributed photovoltaic cluster outline value N_Silhouette*=0; (32e) Perform mean clustering calculation to obtain N distributed photovoltaic clusters and the cluster center of each cluster; (32f) Based on the cluster center of each distributed photovoltaic sample, calculate the Euclidean distance to other samples, and further calculate the average silhouette value N_Silhouette(N) when the number of clusters is N. (32g) Compare N_Silhouette(N) and N_Silhouette*, update N_Silhouette* to the maximum value between the two, and update N*=N synchronously; (32h) Repeat the iteration N=N+1 until N≥N_max. At this time, N* is the optimal number of distributed photovoltaic clusters and N_Silhouette* is the maximum average contour value corresponding to the optimal cluster. (32i) Repeat steps (32d)-(32h) to obtain the optimal number of clusters N for all distributed photovoltaic periods.

4. The distributed photovoltaic access capacity calculation method based on mean clustering according to claim 1, characterized in that, The expressions for the cluster centers, occurrence probabilities, and joint probabilities in step (4) are as follows: ； In the formula, For the time period of electricity load clustering, To and Distributed photovoltaic clustering periods that may overlap or occur simultaneously; For time period The m-th electricity load cluster center within the cluster. Indicates The probability of cluster centers appearing; For time period The nth distributed photovoltaic clustering center in the inner region, Indicates The probability of cluster centers appearing; Indicates the period of distributed photovoltaic power generation and electricity load periods The percentage of time that overlaps with each other. This represents the joint probability of the joint scenario.

5. The distributed photovoltaic access capacity calculation method based on mean clustering according to claim 1, characterized in that, The objective function for the maximum access quantity of distributed photovoltaic power in step (5) is shown in the following formula: ； In the formula, This represents the maximum allowable number of distributed photovoltaic (PV) installations during the clustering period. Let be the distributed optical admissions of node j.

6. The distributed photovoltaic access capacity calculation method based on mean clustering according to claim 5, characterized in that, The power flow calculation steps in step (51) are as follows: (51a) Obtain the number of load clusters M and the number of distributed photovoltaic clusters N. Using the electricity load period as the reference period, construct a joint scenario of electricity load and distributed photovoltaic at the same time and calculate the probability of the joint scenario during this period. (51b) Perform mean clustering with M cluster numbers to calculate the cluster centers of M typical daily electricity loads. Probability of occurrence Calculate the active power of the electrical load at each node. reactive power ; (51c) Perform mean clustering with N clusters to calculate the cluster centers of N typical days of distributed photovoltaics. Probability of occurrence Calculate the active power of distributed photovoltaic power at each node. reactive power ; (51d) Based on the given distributed photovoltaic installation capacity, combined with the power load of each node and the per-unit value of the distributed photovoltaic center, power flow calculation is performed on all joint scenarios to obtain the voltage of each node, line current and node switching power. (51e) Determine whether there are branch current exceeding limits, distribution transformer capacity exceeding limits, or power exchange with the upstream exceeding limits. If exceeding limits occurs, reduce the amount of distributed photovoltaic installations or carry out distribution network upgrades. If no exceeding limits occurs, calculate the voltage exceeding probability of each node at all times under all joint scenarios in the current period. .

7. The distributed photovoltaic access capacity calculation method based on mean clustering according to claim 5, characterized in that, The constraints in step (51) include load node voltage constraints, line current carrying constraints, and power exchange constraints with the upstream power grid, as shown in the following expressions: ； In the formula, Let be the voltage at load node j at time t. , These are the upper and lower limits of the load node voltage, with a default value of 93%-107% of the nominal voltage. Let be the voltage of distributed photovoltaic node j at time t. , These are the upper and lower limits of the grid connection voltage for distributed photovoltaic node j, respectively, with a default value of 85%-110% of the nominal voltage; Let node j and node j be at time t. The branch current, This is the maximum branch current limit; Let t be the active power at the distribution switch. These are the upper and lower limits of active power at the distribution gate; Let t be the reactive power at the distribution switch. These are the upper and lower limits of reactive power at the power distribution point; The expressions for the active and reactive power of the electrical load at each node are as follows: ； In the formula, Let be the active power of the electrical load node j at time t. The predicted maximum electrical load for the distribution area. This represents the maximum value of the historical electricity load curve for the power distribution area. This is the base value of the total load power of the distribution area. Let be the per-unit value of the load power at time t in the scenario of electricity load clustering. Let j be the proportion of the electrical load of node j to the total load of the area. The power factor angle for the power distribution area; The active and reactive power expressions for distributed photovoltaic systems at each node are as follows: ； In the formula, Let be the active power of distributed photovoltaic node j at time t. This represents the maximum permitted capacity for distributed photovoltaic power in the distribution area. Let be the photovoltaic output coefficient at time t in the distributed photovoltaic clustering scenario. Let be the proportion of photovoltaic installations at node j to the total photovoltaic installations in the region. Let be the distributed photovoltaic power factor of node j.

8. The distributed photovoltaic access capacity calculation method based on mean clustering according to claim 5, characterized in that, The calculation of the probability of exceeding the limit in step (52) is as follows: ； In the formula: Let be the probability of node j exceeding the limit in a joint scenario where there is an intersection between a certain electricity load clustering period and a distributed photovoltaic clustering period. Let be the cumulative probability of node j exceeding the limit across all time periods. For the probability of a joint scenario, This refers to the voltage over-limit status of the j-th electrical load node during time period t. =1 indicates that the condition is in an over-limit state. =0 indicates that the voltage is in a non-limit-crossing state, and T represents the number of sampling points. This indicates the cumulative number of times the limit is exceeded within a day when performing power flow calculations.

9. The distributed photovoltaic access capacity calculation method based on mean clustering according to claim 5, characterized in that, The calculation process for the maximum access quantity of distributed photovoltaic power in step (53) is as follows: (53a) Obtain the current distributed photovoltaic installation capacity of the distribution area to be evaluated. ; (53b) Determine the initial step size h0 and the convergence accuracy ε; (53c) Let The maximum distributed photovoltaic multiplier K=1; (53d) Determine the step size h. If h > ε, proceed to step (53e); if h < ε, return. And K, returned This represents the maximum currently permitted distributed photovoltaic installation capacity within the distribution area. (53e) Calculation ; (53f) Using the electricity load clustering center in the joint scenario Photovoltaic Clustering Center Perform power flow calculations to obtain the voltage exceedance probability of each node under all combined scenarios. ; (53g) Determine if the condition is met. If not satisfied, then h = h / 2, and execute step (53d). If satisfied, update. and Execute step (53d); The expression for the maximum allowable quantity of distributed photovoltaic power is as follows: ； In the formula, To meet the maximum permitted capacity for distributed photovoltaic (PV) installations in accordance with the voltage compliance rate requirement, K represents the maximum distributed PV installation multiple. This indicates the remaining installed capacity of distributed photovoltaic systems.

10. A distributed photovoltaic access capacity calculation system based on mean clustering, characterized in that, include: The data curve acquisition and processing module is used to perform per-unit processing on the historical data curves of electricity load and distributed photovoltaic power generation to obtain the electricity load power curve and distributed photovoltaic power curve per unit capacity. The time period segmentation module is used to perform two-dimensional mean clustering on the electricity load and distributed photovoltaic power curves respectively to obtain the time period segmentation of electricity load and distributed photovoltaic. The calculation module is used to determine the optimal number of clusters for electricity load and distributed photovoltaic power generation in each time period using the elbow method and the maximum mean profile value method, respectively. Based on the time period division and the optimal number of clusters, it constructs a joint scenario of electricity load and distributed photovoltaic power generation in a single time period. It calculates the cluster centers and their occurrence probabilities based on the mean clustering algorithm, and introduces the time proportion where the distributed photovoltaic power generation time period and the electricity load time period overlap. The occurrence probabilities of the electricity load cluster centers and the occurrence probabilities of the distributed photovoltaic power generation cluster centers are multiplied by the time proportion to obtain the joint probability. The analysis module is used to perform power flow calculations for each joint scenario, calculate the voltage exceedance probability of each node based on the joint probability, and determine whether the node voltage exceedance probability meets the constraint condition, which is that the node voltage exceedance probability is less than or equal to... ,in The required voltage compliance rate for the power distribution area to be evaluated. The margin is reserved; if it is not met, the step size is half of the original size; if it is met, the maximum allowed capacity and the maximum distributed photovoltaic multiple are updated; and the step size is judged; if the step size is greater than the convergence accuracy, the power flow calculation continues; if the step size is less than the convergence accuracy, the calculation ends, and the maximum allowed distributed photovoltaic installation capacity in the distribution area is obtained.

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