Improved fuzzy c-means clustering based active power distribution network openable capacity evaluation method

Abstract

The application discloses an active power distribution network openable capacity evaluation method based on an improved fuzzy C-means clustering, and comprises the following steps: obtaining and preprocessing load historical data and photovoltaic output historical data of a power distribution network; selecting typical daily loads of the power distribution network by using the obtained load historical data and based on an improved fuzzy C-means clustering method; according to the obtained photovoltaic output historical data, the uncertain interval of the photovoltaic output is counted; a target function is constructed by taking the maximization of the openable capacity of the whole power distribution network and the minimization of network loss as the target, and the openable capacity of the power distribution network is obtained by solving the target function; wherein the constraint conditions of the target function comprise a node power flow constraint equation, a voltage constraint condition and a branch power and current constraint condition of the power distribution network; and the power flow constraint equation is obtained based on the typical daily loads of the power distribution network and by simultaneously considering electric vehicle loads and photovoltaic output. The application improves the accuracy of the openable capacity evaluation result and fully excavates the power supply capacity of the power distribution network.

Description

Technical Field

[0001] This invention relates to the field of distribution network planning, specifically to a method for assessing the openable capacity of active distribution networks based on improved fuzzy C-means clustering. Background Technology

[0002] The development of electric vehicles can alleviate the energy crisis and reduce carbon emissions. However, the large-scale grid connection of electric vehicles not only poses challenges to the operation and maintenance strategies of distribution networks but also affects their planning and expansion. Available capacity, as an important indicator for evaluating the load-carrying capacity of a distribution network, is often used to guide its planning. Available capacity can be considered as the maximum power supply capacity of the distribution network minus the typical daily load; therefore, the large-scale integration of electric vehicles into the distribution network has a significant impact on available capacity. Existing methods for assessing the available capacity of distribution networks can be mainly divided into four categories: proportional power flow increasing method, comprehensive evaluation method, mathematical analytical method, and static security constraint method.

[0003] Among them, the proportional power flow increasing method is prone to getting trapped in local optima, the comprehensive evaluation method is only a qualitative calculation method, and the calculation results are difficult to guide the planning of actual distribution networks, while the mathematical analytical method only considers the capacity constraints of the distribution network feeders and transformers. The static security constraint method fully considers the security constraints of the distribution network and takes the maximization of the openable capacity as the optimization objective. However, the existing research using the static security constraint method focuses on the impact of network reconfiguration and the rated parameters of distribution network equipment on the openable capacity, ignoring the impact of distributed photovoltaic uncertainty and load spatiotemporal distribution characteristics on the openable capacity of the distribution network.

[0004] Existing studies often use clustering algorithms to reduce the number of scenarios to select typical days. However, traditional clustering algorithms are prone to getting stuck in local optima, and existing methods often use the minimum available capacity on a typical day as the evaluation result. The evaluation result is too conservative and fails to fully explore the power supply capacity of the distribution network. Summary of the Invention

[0005] With the large-scale integration of electric vehicles into distribution networks, conducting capacity assessments for distribution network expansion is crucial. However, existing research fails to adequately consider the spatiotemporal correlation of load when selecting typical days, and current methods only provide single values, resulting in overly conservative assessments with low accuracy, failing to fully exploit the power supply potential of the distribution network. To address this issue, this invention provides a method for assessing the capacity of active distribution networks based on improved fuzzy C-means clustering. By considering the spatiotemporal characteristics of load when selecting typical day loads, this method improves the accuracy of capacity assessment results and the power supply capacity of the distribution network.

[0006] To achieve the above technical objectives, the present invention adopts the following technical solution:

[0007] A method for assessing the openable capacity of active distribution networks based on improved fuzzy C-means clustering includes:

[0008] S1: Obtain historical load data and historical photovoltaic output data of all nodes in the distribution network and perform preprocessing.

[0009] S2, the preprocessed historical load data is constructed into multiple samples with a time length of days, and the typical daily load of the distribution network is selected based on the improved fuzzy C-means clustering method;

[0010] S3, Based on the preprocessed historical photovoltaic power output data, calculate the uncertainty range of photovoltaic power output;

[0011] S4. With the goal of maximizing the overall open capacity of the distribution network and minimizing network losses, an objective function for the open capacity of the distribution network is constructed and solved to obtain the open capacity of the distribution network.

[0012] The constraints of the objective function include the power flow constraint equations, voltage constraints, branch power and current constraints for each node of the distribution network; and the power flow constraint equations are constructed based on the typical daily load of the distribution network and simultaneously consider the electric vehicle load and photovoltaic output.

[0013] Furthermore, the preprocessing of historical load data includes directly deleting missing values, outliers, and anomalies; the preprocessing of historical photovoltaic output data specifically employs the isolated forest method to detect anomalies and uses interpolation to replace the detected anomalies.

[0014] Furthermore, the step of constructing the preprocessed load history data into multiple samples with a time length of days is as follows: the load history data of each node is divided into subsequences with a time length of days, and then the subsequences of all nodes on the same day are concatenated into one sample, and n days correspond to n samples.

[0015] Furthermore, the selection of typical daily loads of the distribution network based on improved fuzzy C-means clustering specifically involves:

[0016] S2.1, the loss function for the fuzzy C-means clustering algorithm is constructed as follows:

[0017]

[0018] In the formula: J is the loss function value; x d The d-th sample is obtained by splicing together the historical load data of all nodes in the distribution network on day d; c k As the cluster center, u dk Membership degree represents the degree of membership for sample x. d The membership degree of belonging to the k-th class, where K is the number of clusters and n is the number of samples;

[0019] S2.2, Establish constraints:

[0020]

[0021] In the formula: m is a hyperparameter;

[0022] S2.3, Substituting the first constraint in equation (2) directly into the objective function, we obtain equation (3), where set(K) is the set of 1, 2, ..., K, and set(n) is the set of 1, 2, ..., n:

[0023]

[0024] In the above formula, sup() is a general mathematical symbol representing finding the upper bound; since the above formula is difficult to solve directly, we introduce the auxiliary variable η. d The K constraints are as follows:

[0025]

[0026] Then, by using second-order cone relaxation to linearize the problem shown in equation (3), the constraints are obtained as shown in equation (5):

[0027]

[0028] In the formula, U dk It is an auxiliary variable, and equivalence;

[0029] Finally, a commercial solver was used to solve the above model, and the cluster centers c were obtained. k As a typical daily load selected,

[0030] Furthermore, the uncertainty range of photovoltaic output is statistically analyzed as follows:

[0031] The Monte Carlo random sampling method was used to randomly sample the preprocessed historical photovoltaic power output data, and the portion of the sampled data that was above the average value was added to the set. The portion below the average is added to the set. D The sampling results are then averaged according to their relationship with the mean, and the upper and lower limits of the uncertainty interval are obtained as shown in equations (6)-(9).

[0032]

[0033]

[0034]

[0035]

[0036] In the formula: These represent the upper and lower bounds of the uncertainty interval for photovoltaics. and D This refers to the set of photovoltaic power output values ​​obtained from sampling that are higher or lower than the average value. Let m be the photovoltaic output obtained from the m-th sampling. This represents the average photovoltaic output across all samples.

[0037] Furthermore, the power flow constraint equations for any node j, constructed based on the typical daily load of the distribution network and simultaneously considering the electric vehicle load and photovoltaic output, are as follows:

[0038]

[0039]

[0040]

[0041]

[0042]

[0043] 0≤ΔP j,ac <∈#(15)

[0044] In the formula: B is the set of all bus nodes in the power distribution, i is the upstream node of node j, and the distance from node i to node j constitutes the distribution network branch ij; P ij,t and Q ij,t Let v(j) be the active and reactive power flow at time t on branch ij of the distribution network; v(j) be the set of downstream nodes of node j, and k be the downstream nodes of node j; P j,t and Q j,t Let r be the active and reactive components of the power injected into node j, respectively. Then, select the load injection power at time t of a typical daily load of the distribution network for node j. ij and x ij These are the resistance and reactance values ​​of branch ij, respectively; V0 is the reference node voltage. and These represent the conventional load, electric vehicle load, and photovoltaic output at node j, respectively. The values ​​corresponding to the cluster centers obtained in S2 at that time. The value range is the uncertain range of photovoltaic output obtained from step S3; ΔP j,ac Let be the open capacity at node j, θ be the power factor angle, and ∈ be a constant.

[0045] Furthermore, the constraint condition for the node voltage is shown in equation (16):

[0046] V j,min ≤V j ≤V j,max #(16)

[0047] In the formula: V j,min and V j,max These are the upper and lower voltage limits for node j, respectively;

[0048] The branch current and power constraints are shown in equations (17)-(18):

[0049]

[0050]

[0051] In the formula: I i,min and I i,max These are the upper and lower limits of the current in branch ij, respectively. Let E be the maximum capacity of branch ij, and E be the set of branches. Second-order cone relaxation is used to further restrict the relationship between branch current and node voltage, and the constraint relationship is shown in equation (19):

[0052]

[0053] Furthermore, the objective function for the open capacity of the distribution network is as follows:

[0054]

[0055] In the formula: α and β are cost coefficients, the first term is the overall open capacity of the distribution network, and the second term is the network loss.

[0056] Furthermore, the method for solving the objective function to obtain the exploitable capacity of the distribution network is as follows:

[0057] First, the objective function and constraints are written in a compact form as shown in equation (21):

[0058]

[0059] stG(X,Y)≤0

[0060] x∈X

[0061] y∈Y

[0062] In the formula: f(X,Y) is the objective function, X and Y are the feasible regions of decision variables x and y, respectively, and x and y are the decision variable vectors of network loss and the decision variables of available capacity, respectively, and x=[I ij ] T y=[ΔPj,ac V j ,P ij Q ij ] T , i,j∈B, G(X,Y) are constraints containing x and y;

[0063] Then, a two-stage relaxation algorithm is used to introduce dual variables to solve the model (20):

[0064] (1) Initialize the inner layer strategy as y 1 Set the number of iterations to inter = 1 and the iteration error to ε;

[0065] (2) Solve for the outer layer: Introduce an auxiliary variable λ and a relaxation variable σ into the inner layer model, and obtain an optimal point (x) for the outer layer optimization. inter ,λ inter ):

[0066]

[0067] stf(x,y inter -λG(x,y inter )≤σ

[0068]

[0069] (3) Solve the inner layer: based on the optimal point (x) given by the outer layer variables. inter ,λ inter ), optimize the inner layer problem, and obtain the optimal solution y of the inner layer optimization problem. inter :

[0070]

[0071] s.ty∈Y

[0072] (4) Determine if the iteration termination condition has been met: Calculate (x i ,y i ,λ i The maximum value h(x) corresponding to ) inter ,y inter ,λ inter )=f(x inter ,y inter )-λG(x inter ,y inter If h(x) inter ,y inter ,λ inter )≤σ inter If the value of ΔP in the decision variable y is increased by ε, the iteration terminates. j,acIf the openable capacity is obtained from the evaluation, then return to step (2) and increase the cut set f(x,y). inter )-λG(x,y inter )≤σ inter .

[0073] Beneficial effects

[0074] Based on the background of large-scale electric vehicle integration into the power distribution network, this invention proposes a method for assessing the open capacity of the power distribution network based on improved fuzzy C-means clustering. The advantages of this invention are:

[0075] (1) In view of the problem that the existing typical day selection method does not fully consider the spatiotemporal correlation of load, the present invention merges the daily load of all bus nodes into one sample in the typical day selection process. This method can fully explore the spatiotemporal correlation of load and improve the accuracy of the open capacity assessment results.

[0076] (2) In view of the problem that the traditional FCM algorithm is prone to getting trapped in local optima, the present invention improves the FCM algorithm. The improved FCM model can be solved by a convex optimization solver, which avoids the problem of getting trapped in local optima during the clustering process.

[0077] (3) In view of the problem that the traditional open capacity assessment method in the distribution network is too conservative, the present invention constructs an open capacity assessment model of the distribution network based on a typical day, realizes the assessment of the open capacity of the distribution network under a typical day, and is used to reflect the remaining capacity of the regional distribution network, thereby improving the power supply capacity of the distribution network. Attached Figure Description

[0078] Figure 1 This is a flowchart of the method described in an embodiment of the present invention;

[0079] Figure 2 This is a schematic diagram of the distribution network node relationship according to an embodiment of the present invention;

[0080] Figure 3 This is a flowchart illustrating the solution process for the objective function model described in this embodiment of the invention.

[0081] Figure 4 The present invention and conventional methods are used to obtain the trend of the available capacity of the distribution network over time.

[0082] Figure 5 The capacity that can be opened at each node of the distribution network. Detailed Implementation

[0083] The embodiments of the present invention will be described in detail below. These embodiments are based on the technical solutions of the present invention and provide detailed implementation methods and specific operation processes to further explain the technical solutions of the present invention.

[0084] like Figure 1 As shown in the figure, this embodiment provides a method for assessing the openable capacity of an active distribution network based on improved fuzzy C-means clustering, which mainly includes the following steps:

[0085] S1: Acquire data and perform preprocessing.

[0086] The load history data obtained in this embodiment comes from PJM, the photovoltaic output history data comes from DKA Solar Centre in Australia, and the electric vehicle charging load data comes from smart meter data in Hunan Province. The time span of the data is 1 year, and the time resolution is 15 minutes.

[0087] For missing values, outliers, and anomalies in historical photovoltaic power generation data, direct deletion is adopted; for historical load data, an isolated forest is used to detect outliers, and interpolation is used to replace the outliers.

[0088] S2, selected for typical load days.

[0089] S2.1, Construction of the objective function;

[0090] First, the historical load data of each node in the distribution network is divided into subsequences with a time length of one day. Then, the subsequences of all nodes on the same day are concatenated into one sample, resulting in n samples for n days. Let x be the sample corresponding to day d. d Then we have x d =[x 1d ,…,x jd ,…,x |B|d ], where x jd Indicates sample x d The subsequence corresponding to the j-th node in the distribution network, where |B| is the number of nodes in the distribution network. x jdh Represents the subsequence x jd The load value at time point h, N t The number of time points in a day.

[0091] The loss function for the fuzzy C-means clustering algorithm is then constructed as follows:

[0092]

[0093] In the formula: J is the loss function value; x d The d-th sample is obtained by splicing together the historical load data of all nodes in the distribution network on day d; c k As the cluster center, u dk Membership degree represents the degree of membership for sample x. d The membership degree of belonging to the k-th class, where c is the number of clusters and n is the number of samples.

[0094] S2.2, Establish constraints:

[0095]

[0096] In the formula: m is a hyperparameter;

[0097] S2.3, Substituting the first constraint in equation (2) directly into the objective function, we can obtain equation (3), where set(K) is the set of 1, 2, ..., K, and set(n) is the set of 1, 2, ..., n:

[0098]

[0099] The above equation is difficult to solve directly, so we introduce an auxiliary variable η. d The K constraints are as follows:

[0100]

[0101] Since the problem shown in equation (3) has a quadratic term, it is difficult to solve directly. Therefore, a second-order cone relaxation is performed on it to linearize the problem (the existing optimizer has good support for second-order cones and can speed up the solution). The resulting constraint is shown in equation (5):

[0102]

[0103] In the formula, U dk It is an auxiliary variable, and equivalence;

[0104] Finally, a commercial solver was used to solve the above model, and the cluster centers c were obtained. k As a typical daily load selected,

[0105] S3, calculate the uncertainty interval of photovoltaics.

[0106] The Monte Carlo random sampling method was used to randomly sample the preprocessed historical photovoltaic power output data, and the portion of the sampled data that was above the average value was added to the set. The portion below the average is added to the set. D The sampling results are then averaged according to their relationship with the mean, and the upper and lower limits of the uncertainty interval are obtained as shown in equations (6)-(9).

[0107]

[0108]

[0109]

[0110]

[0111] In the formula: These are the upper and lower bounds of the uncertainty interval for photovoltaics, respectively. and D This refers to the set of photovoltaic power output values ​​obtained from sampling that are higher or lower than the average value. Let m be the photovoltaic output obtained from the m-th sampling. This represents the average photovoltaic output across all samples.

[0112] S4, establish and solve the assessment of the openable capacity of the distribution network.

[0113] S4.1, Construct openable capacity constraints for the distribution network;

[0114] (1) Line power flow constraints

[0115] For any node j in the distribution network, its power flow constraint equations are shown in equations (10)-(15):

[0116]

[0117]

[0118]

[0119]

[0120]

[0121] 0≤ΔP j,ac <∈#(15)

[0122] In the formula: such as Figure 2 As shown, B is the set of all bus nodes in the power distribution network, i is the upstream node of node j, and the distance from node i to node j constitutes the distribution network branch ij; P ij,t and Q ij,t Let v(j) be the active and reactive power flow at time t on branch ij of the distribution network; v(j) be the set of downstream nodes of node j, and k be the downstream nodes of node j; P j,t and Q j,t Let r be the active and reactive components of the power injected into node j, respectively. Then, select the load injection power at time t of a typical daily load of the distribution network for node j. ij and x ij These are the resistance and reactance values ​​of branch ij, respectively; V0 is the reference node voltage. and These represent the conventional load, electric vehicle load, and photovoltaic output at node j, respectively. The cluster centers c obtained in S2 k The value at the corresponding time, The value range is the uncertain range of photovoltaic output obtained from step S3; ΔP j,ac Let be the available capacity at node j, θ be the power factor angle, and ∈ be a constant, which is taken as 1.5MW in this embodiment.

[0123] (2) Node voltage constraints

[0124] The constraint conditions for the node voltages are shown in equation (16):

[0125] V j,min ≤V j ≤V j,max #(16)

[0126] In the formula: V i,min and V i,max These are the upper and lower voltage limits for node i, respectively.

[0127] (3) Branch power and current constraints

[0128] The branch current and power constraints are shown in equations (17)-(18):

[0129]

[0130]

[0131] In the formula: I ij,min and I ij,max These are the upper and lower limits of the current in branch ij, respectively. Let be the maximum capacity of branch ij, and E be the set of branches.

[0132] The relationship between current and node voltage in the branch is further restricted by second-order cone relaxation, and the constraint relationship is shown in equation (19):

[0133]

[0134] S4.2, Establishment of the objective function for open capacity assessment;

[0135] The optimization objective of the available capacity of the distribution network aims to maximize the overall load-carrying capacity of the distribution network and minimize network losses. Based on this, the optimization objective can be obtained as shown in equation (20):

[0136]

[0137] In the formula: α and β are cost coefficients, which are 1000 and 1 respectively. The first term in the formula is the overall open capacity of the distribution network, and the second term is the network loss.

[0138] S4.3, Transform the objective function model;

[0139] The optimization objective function model can be written in a compact form as shown in equation (21):

[0140]

[0141] stG(X,Y)≤0

[0142] x∈X

[0143] y∈Y

[0144] In the formula: f(X,Y) is the objective function, X and Y are the feasible regions of decision variables x and y, respectively, and x and y are the decision variable vectors for network loss and the decision variables for available capacity, respectively. x=[I ij ] T y=[ΔP j,ac V j ,P ij Q ij ] T G(X,Y) is a constraint condition that includes both.

[0145] S4.4 employs a two-stage relaxation algorithm, introducing dual variables to solve the model. For example... Figure 3 As shown, it specifically includes:

[0146] S4.4.1, initialize the inner strategy as y 1 Set the number of iterations to inter = 1 and the iteration error to ε;

[0147] S4.4.2, Solving for the outer layer: Introduce an auxiliary variable λ and a slack variable σ into the inner layer model, and obtain an optimal point (x) for the outer layer optimization. inter ,λ inter ):

[0148]

[0149] stf(x,y inter )-λG(x,y inter )≤σ

[0150] x∈X

[0151] S4.4.3, Solve for the inner layer: Based on the optimal point (x) given by the outer layer variables. inter ,λ inter ), optimize the inner layer problem, and obtain the optimal solution y of the inner layer optimization problem. inter :

[0152]

[0153] s.ty∈Y

[0154] S4.4.4, Determine if the iteration termination condition has been met: Calculate (x i ,y i ,λ i The maximum value h(x) corresponding to ) inter ,y inter ,λ inter )=f(x inter ,y inter )-λG(x inter ,y inter If h(x) inter ,y inter ,λ inter )≤σ inter If the value is increased by ε, the iteration terminates, and the decision variable y contains ΔP. j,ac If the calculated open capacity is the one obtained from the evaluation, then return to step S4.4.2 and add a cut set f(x,y). inter )-λG(x,y inter )≤σ inter .

[0155] This embodiment uses an improved IEEE 33-node system to verify the effectiveness of the open capacity model. Nodes 14, 22, and 25 are connected to both conventional loads and electric vehicle loads, with a peak load of 48kW. Nodes 10, 25, and 26 are connected to photovoltaic systems with rated capacities of 130kW, 70kW, and 30kW, respectively. The 110kV transformer has a rated capacity of 5.6MVA, and the line's thermal limit capacity and current are set to 7MVA and 1.2kA, respectively. All simulations were performed on a PC with an Intel i7-11700 processor and 32GB of RAM.

[0156] In this embodiment, the typical daily base load per unit value obtained by the FCM clustering algorithm is shown in Table 1, the upper and lower limits of the photovoltaic uncertainty interval are shown in Table 2, and the spatiotemporal distribution of the overall available capacity of the distribution network obtained based on step S3 optimization is shown in Table 2. Figure 4 and Figure 5 As shown:

[0157] Table 1 Typical Daily Base Load (pu)

[0158] 1:00 0.7002 0.6799 13:00 0.6915 0.6705 2:00 0.6688 0.6720 14:00 0.6597 0.6618 3:00 0.6944 0.7331 15:00 0.6839 0.7219 4:00 0.7707 0.8047 16:00 0.7579 0.7909 5:00 0.8345 0.8634 17:00 0.8196 0.8481 6:00 0.8897 0.9139 18:00 0.8751 0.8996 7:00 0.9330 0.9439 19:00 0.9203 0.9351 8:00 0.9513 0.9610 20:00 0.9472 0.9605 9:00 0.9668 0.9582 21:00 0.9688 0.9616 10:00 0.9426 0.9253 22:00 0.9446 0.9257 11:00 0.8908 0.8359 23:00 0.8891 0.8305 12:00 0.7002 0.7315 24:00 0.7706 0.7220

[0159] Table 2 Uncertainty Range for Photovoltaics (pu)

[0160] 1:00 0 0 13:00 0.3889 0.7508 2:00 0 0 14:00 0.3867 0.7413 3:00 0 0 15:00 0.3796 0.7044 4:00 0 0 16:00 0.3609 0.6403 5:00 0 0 17:00 0.2951 0.5401 6:00 0 0 18:00 0.1024 0.3677 7:00 0 0 19:00 0 0 8:00 0.0107 0.2394 20:00 0 0 9:00 0.2397 0.5049 21:00 0 0 10:00 0.3600 0.6322 22:00 0 0 11:00 0.3825 0.7020 23:00 0 0 12:00 0.3880 0.7393 24:00 0 0

[0161] Depend on Figure 4 It can be seen that, compared to the typical daily load curve, the maximum available capacity on a typical day is opposite to its peak-to-valley difference time. Around 17:00 on the daily load curve is its peak load period, and the available capacity is at its maximum at this time. Similarly, around 3:00 on the daily load curve is the load trough, and the available capacity reaches its maximum value at this time. Combining the characteristics of typical day 1 and typical day 2, the minimum value of the maximum available capacity of the two typical days at the same node and the same time is taken as the maximum available capacity of the distribution network. Figure 5 It can be seen that the maximum available capacity of nodes located at the beginning of the line and with smaller numbers is always lower than that at the end of the line, and the available capacity on typical day 1 is generally higher than that on typical day 2. In addition, the access of photovoltaic capacity not only increases the available capacity of the photovoltaic access point, but also greatly increases the available capacity of the entire system. Compared with the case where no photovoltaic is connected, the available capacity of the location adjacent to the photovoltaic access point is also significantly improved.

[0162] The above embodiments are preferred embodiments of this application. Those skilled in the art can make various changes or improvements based on them. Without departing from the overall concept of this application, these changes or improvements should fall within the scope of protection claimed in this application.

Claims

1. A method for assessing the openable capacity of an active distribution network based on improved fuzzy C-means clustering, characterized in that, include: S1: Obtain historical load data and historical photovoltaic output data of all nodes in the distribution network and perform preprocessing. S2, the preprocessed historical load data is constructed into multiple samples with a time length of days, and the typical daily load of the distribution network is selected based on the improved fuzzy C-means clustering method; The selection of typical daily loads for the distribution network based on improved fuzzy C-means clustering is specifically as follows: S2.1, the loss function for the fuzzy C-means clustering algorithm is constructed as follows: ； In the formula: J is the value of the loss function; For the first Each sample is obtained by splicing together the historical load data of all nodes in the distribution network on day d. As cluster center, Membership degree represents the number of samples. The membership degree of a member to the k-th class, where K is the number of clusters. The number of samples; S2.2, Establish constraints: ； In the formula: m is a hyperparameter; S2.3, Substituting the first constraint in equation (2) directly into the objective function, we obtain equation (3), where set(K) is the set of 1, 2, ..., K, and set(n) is the set of 1, 2, ..., n: ； In the above formula, It is a general mathematical symbol used to represent finding an upper bound; the above formula is difficult to solve directly, so an auxiliary variable is introduced. The K constraints are as follows: ； Then, by using second-order cone relaxation to linearize the problem shown in equation (3), the constraints are obtained as shown in equation (5): ； In the formula, It is an auxiliary variable, and equivalence; Finally, a commercial solver was used to solve the above model, and the resulting cluster centers were obtained. Selected typical daily load ; S3, Based on the preprocessed historical photovoltaic power output data, calculate the uncertainty range of photovoltaic power output; S4. With the goal of maximizing the overall open capacity of the distribution network and minimizing network losses, an objective function for the open capacity of the distribution network is constructed and solved to obtain the open capacity of the distribution network. The constraints of the objective function include the power flow constraint equations, voltage constraints, branch power and current constraints for each node of the distribution network; and the power flow constraint equations are constructed based on the typical daily load of the distribution network and simultaneously consider the electric vehicle load and photovoltaic output.

2. The method for assessing the openable capacity of an active distribution network according to claim 1, characterized in that, The preprocessing of historical load data includes the direct deletion of missing values, outliers, and anomalies; the preprocessing of historical photovoltaic output data specifically employs the isolated forest method to detect anomalies and uses interpolation to replace the detected anomalies.

3. The method for assessing the openable capacity of an active distribution network according to claim 1, characterized in that, The process of constructing multiple samples with a time length of days from the preprocessed load history data is as follows: the load history data of each node is divided into subsequences with a time length of days, and then the subsequences of all nodes on the same day are concatenated into one sample, and n days correspond to n samples.

4. The method for assessing the openable capacity of an active distribution network according to claim 1, characterized in that, The uncertainty range of statistical photovoltaic output is as follows: The Monte Carlo random sampling method was used to randomly sample the preprocessed historical photovoltaic power output data, and the portion of the sampled data that was above the average value was added to the set. The portion below the average is added to the set. The sampling results are then averaged according to their relationship with the mean, and the upper and lower limits of the uncertainty interval are obtained as shown in equations (6)-(9). ； ； ； ； In the formula: These are the upper and lower bounds of the uncertainty interval for photovoltaics, respectively. and This refers to the set of photovoltaic power output values ​​obtained from sampling that are higher or lower than the average value. Let m be the photovoltaic output obtained from the m-th sampling. This represents the average photovoltaic output across all samples.

5. The method for assessing the openable capacity of an active distribution network according to claim 1, characterized in that, The power flow constraint equations for any node j, constructed based on the typical daily load of the distribution network and simultaneously considering electric vehicle load and photovoltaic output, are as follows: ； ； ； ； ； ； In the formula: B is the set of all bus nodes in the power distribution, i is the upstream node of node j, and the distance from node i to node j constitutes the distribution network branch ij; P ij,t and Q ij,t Let v(j) be the active and reactive power flow at time t on branch ij of the distribution network; v(j) be the set of downstream nodes of node j, and k be the downstream nodes of node j; P j,t and Q j,t Let r be the active and reactive components of the power injected into node j, respectively. Then, select the load injection power at time t of a typical daily load of the distribution network for node j. ij and x ij These are the resistance and reactance values ​​of branch ij, respectively; V0 is the reference node voltage. , and These represent the conventional load, electric vehicle load, and photovoltaic output at node j, respectively. The values ​​corresponding to the cluster centers obtained in S2 at that time. The value range is the uncertain range of photovoltaic output obtained from step S3; Let be the available open capacity at node j. The power factor angle, It is a constant.

6. The method for assessing the openable capacity of an active distribution network according to claim 5, characterized in that, The constraint conditions for the node voltages are shown in equation (16): ； In the formula: V j,min and V j,max These are the upper and lower voltage limits for node j, respectively; The branch current and power constraints are shown in equations (17)-(18): ； ； In the formula: I i,min and I i,max These are the upper and lower limits of the current in branch ij, respectively. Let E be the maximum capacity of branch ij, and E be the set of branches; The relationship between branch current and node voltage is further constrained by second-order cone relaxation, and the constraint relationship is shown in equation (19): 。 7. The method for assessing the openable capacity of an active distribution network according to claim 5, characterized in that, The objective function for the open capacity of the constructed distribution network is: ； In the formula: and The first term in the formula is the overall open capacity of the distribution network, and the second term is the network loss.

8. The method for assessing the openable capacity of an active distribution network according to claim 7, characterized in that, The method for solving the objective function to obtain the exploitable capacity of the distribution network is as follows: First, the objective function and constraints are written in a compact form as shown in equation (21): ； ； ； ； In the formula: f(X, Y) is the objective function, X and Y are the feasible regions of decision variables x and y, respectively, and x and y are the decision variable vectors for network loss and the decision variables for available capacity, respectively, and x = y= , G(X, Y) is a constraint condition containing x and y; Then, a two-stage relaxation algorithm is used to introduce dual variables to solve the model (21): (1) Initialize the inner layer strategy as y 1 Set the number of iterations to inter=1, and set the iteration error to... ; (2) Solve the outer layer: Introduce an auxiliary variable into the inner layer model. and slack variables And obtain an optimal point of the outer layer optimization ( ): ； ； ； (3) Solve for the inner layer: based on the optimal point given by the outer layer variables ( Optimize the inner layer problem to obtain the optimal solution to the inner layer optimization problem. : ； ； (4) Determine if the iteration termination condition has been met: Calculate Corresponding maximum value ,if If the iteration terminates, then the decision variable y will have [a certain value]. If the openable capacity is obtained from the evaluation, then return to step (2) and add a cut set. .

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