Method for rapidly evaluating bearing capacity of electric vehicle in power distribution network based on plane cutting method

Abstract

The invention belongs to the technical field of power distribution network planning, and particularly relates to a power distribution network electric vehicle bearing capacity rapid evaluation method based on a cutting plane method, and the method comprises the steps: constructing a power distribution network optimal power flow model comprising a basic load, photovoltaic and reactive compensation equipment and an electric vehicle charging load; iteratively generating a feasible region of the power distribution network based on a cutting plane method to replace traditional load flow calculation; adopting a Monte Carlo method to generate random charging scenes under different electric vehicle permeability, and considering the uncertainty of arrival time, charge state and access position; and quickly verifying whether each scene meets the safety constraint or not by utilizing the constructed feasible region, and taking the maximum satisfaction permeability as a bearing capacity evaluation result. The method accelerates the construction of the feasible region through the cutting plane method, replaces the repetitive load flow calculation with the feasible region, remarkably improves the calculation efficiency while guaranteeing the evaluation precision, and is suitable for the online rapid evaluation of the bearing capacity of the electric vehicle in the power distribution network.

Description

Technical Field

[0001] This invention relates to the field of power distribution network planning technology, and in particular to a rapid assessment method for the load-bearing capacity of electric vehicles in power distribution networks based on the cutting plane method. Background Technology

[0002] Currently, the assessment methods for the load-bearing capacity of electric vehicles in power distribution networks are mainly divided into three categories: deterministic methods, stochastic methods, and optimization-based methods.

[0003] Deterministic methods typically use pre-defined extreme scenarios to calculate power flow, resulting in conservative evaluations that fail to reflect uncertainty.

[0004] Stochastic methods (such as Monte Carlo simulation) describe uncertainties such as EV charging behavior and renewable energy output through probabilistic models, providing more comprehensive evaluation results. However, they require massive amounts of repetitive power flow calculations, resulting in extremely low computational efficiency and making it difficult to meet the needs of online or rapid evaluation.

[0005] Optimization-based methods describe the safety boundary of a system under various operating conditions by constructing a "feasible region." However, traditional feasible region construction methods (such as vertex enumeration and multi-point approximation methods) are usually computationally complex and time-consuming.

[0006] In summary, the main drawback of existing technologies lies in the difficulty of simultaneously achieving both assessment speed and accuracy. Efficient deterministic methods lack sufficient accuracy, while high-precision stochastic methods are impractical due to excessive computational time. Therefore, there is an urgent need for an electric vehicle load-bearing capacity assessment method that can significantly improve computational efficiency while ensuring assessment accuracy. Summary of the Invention

[0007] This invention proposes a rapid assessment method for the load-bearing capacity of electric vehicles in power distribution networks based on the cutting plane method, aiming to solve the technical problem in the prior art that it is difficult to balance the assessment speed and accuracy of the load-bearing capacity of electric vehicles in power distribution networks.

[0008] This invention provides a rapid assessment method for the load-bearing capacity of electric vehicles in power distribution networks based on the cleaving plane method, comprising: S1. Based on the active and reactive power data of the basic load of each node in the distribution network, construct the optimal power flow model of the distribution network. S2. Based on the aforementioned optimal power flow model, construct the feasible region of the distribution network based on the cutting plane method; S3. Use the Monte Carlo method to obtain charging scenarios under different electric vehicle penetration rates; S4. Use the feasible region of the distribution network to determine whether the charging scenarios under different electric vehicle penetration rates meet the safety constraints of the distribution network, and take the maximum penetration rate that meets the constraints as the electric vehicle carrying capacity assessment result.

[0009] The technical effect of the method for rapid evaluation of the carrying capacity of electric vehicles in distribution networks based on the cutting plane method disclosed in this invention is as follows: This method constructs the feasible region of the distribution network based on the cutting plane method, and uses the feasible region to replace the power flow calculation process of the traditional method. By verifying the EV charging scenario set obtained by Monte Carlo random sampling, the carrying capacity of electric vehicles can be rapidly evaluated.

[0010] Further, S1 includes: S1.1 Construct a set of distribution network operation constraints that includes power flow security constraints, power balance constraints, voltage security constraints, and reactive power compensation equipment regulation constraints; S1.2. Based on the Distflow model, the constraints are written in a compact form, and the power flow calculation optimization model of the distribution network is constructed as follows: ; In the formula, x is a discrete control variable, y is a continuous state variable excluding electric vehicle charging power, and z is a charging power scenario vector; , , , , , , as well as The coefficient matrix and vector are constraints.

[0011] Furthermore, the power flow safety constraints specifically include:

[0012]

[0013]

[0014]

[0015] In the formula: and These are the distribution network branches exist Active power injection and reactive power injection at any given time; and Photovoltaics exist Active power injection and reactive power injection at any given time; and These are the distribution network branches and photovoltaic Rated capacity; and Branch roads The rated active power and rated reactive power, and Branch roads The magnitudes of active and reactive power at time t; , , These are the line set, the photovoltaic set, and the optimized time set, respectively.

[0016] Further, S2 includes: S2.1, Define an initial relaxed feasible region. By solving an optimization problem that aims to maximize the degree to which the original constraints are not satisfied, we can find an extreme point in the initial feasible region that does not satisfy the original safety constraints. ; S2.2, with the aforementioned extreme point Using the direction as an example, solve another optimization problem: find the farthest point from the origin along this direction that intersects with the original feasible region. This point is the boundary point of the true feasible region. ; S2.3, at the boundary point At that point, solve the dual problem of the original optimal power flow model to obtain a cutting plane that supports the true feasible region, which has the form: ; S2.4, the cutting plane Add to the initial feasible region and update the constraints as follows: and ; S2.5. Repeat steps S2.1 to S2.4 until no points that do not meet the original safety constraints are found within the updated feasible region. At this point, output the feasible region parameters. and .

[0017] Furthermore, in S2.3, the cutting plane parameters and Obtained through calculation using dual variables, specifically: ; ; in and For the boundary point The optimal dual variables are obtained by solving the dual problem at the corresponding optimal solution.

[0018] Furthermore, S3 specifically includes: S3.1, Based on a preset probability distribution, randomly select the charging start time for each electric vehicle; S3.2, Based on the preset daily mileage probability distribution, randomly select the daily mileage of each electric vehicle, and calculate its state of charge at the start of charging based on battery capacity and power consumption per 100 kilometers. S3.3, Based on uniform distribution, randomly determine the distribution network node to which each electric vehicle is connected; S3.4 Calculate the required charging duration based on the state of charge, battery capacity, charging power and efficiency of each electric vehicle; S3.5 Based on the charging start time, charging duration, and access node of all electric vehicles, the total charging power of electric vehicles at each node in different time periods is aggregated to form a complete charging power scenario vector z.

[0019] Furthermore, in S3.1, the probability density function f(t) at the start of charging of the electric vehicle is a piecewise function: ;in, To achieve the mean at any given time, The variance of the arrival time, For the first The arrival time of the electric vehicle.

[0020] Furthermore, in S3.2, the daily mileage D follows a log-normal distribution, and its probability density function is: ; in, For the daily mileage of electric vehicles, This represents the average daily mileage. Variance of daily mileage.

[0021] Furthermore, in S4, the judgment process specifically involves: for a charging power scenario vector z, checking whether it satisfies all linear inequality constraints in the feasible region, i.e., whether it satisfies... H d and v d Let n be the row vector of coefficients and the constant term of the d-th constraint in the feasible region. H The total number of constraints is used to determine the scenario; if the scenario satisfies all constraints, it is considered a safe scenario.

[0022] Furthermore, in S4, the load-bearing capacity assessment process specifically involves: setting a series of increasing electric vehicle penetration rates; generating multiple random charging scenarios for each penetration rate and verifying them; and taking the highest penetration rate that can find at least one safe scenario as the electric vehicle load-bearing capacity assessment result of the power distribution network. Attached Figure Description

[0023] Figure 1This is a flowchart illustrating a rapid assessment method for the load-bearing capacity of electric vehicles in power distribution networks based on the cutting plane method, as proposed in an embodiment of the present invention. Figure 2 A schematic diagram of the load curve provided in an embodiment of the present invention; Figure 3 The diagram illustrates the feasible regions provided in this embodiment of the invention, wherein (a) is the feasible region for 1 time period, (b) is the feasible region for 7 time periods, (c) is the feasible region for 14 time periods, and (d) is the feasible region for 21 time periods. Figure 4 The diagram shows the line load rate provided in the embodiment of the present invention, wherein (a) is a voltage distribution diagram of each node and (b) is a load rate distribution diagram of each branch. Detailed Implementation

[0024] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0025] To address the slow evaluation speed mentioned in the background technology, which restricts its online application, this invention provides a rapid evaluation method for the carrying capacity of electric vehicles (EVs) in distribution networks based on the secant plane method. First, a feasible region of the distribution network is constructed using the secant plane method. Second, a large number of EV charging scenarios are generated using Mentcalo simulation. Finally, the constructed feasible region is used to verify whether the EV charging power corresponding to each scenario meets the distribution network safety constraints, thereby achieving rapid evaluation of EV carrying capacity. This method replaces traditional time-consuming repetitive power flow calculations with the construction of a high-precision linear feasible region, achieving rapid and accurate carrying capacity evaluation while fully considering the uncertainties of EV charging behavior. (Reference) Figures 1 to 4 As shown, the specific steps include: S1. Based on the basic load data of each node in the distribution network, construct an optimal power flow model for the distribution network that includes security constraints and operational constraints.

[0026] This step aims to establish a mathematical model that accurately describes the physical laws governing the operation of the power distribution network. Specifically, it includes the following steps: S1.1, Construction of distribution network constraints.

[0027] The constraints in the distribution network specifically include: power flow safety constraints (1)-(2) and (7)-(8), power balance constraints (3)-(6); voltage and phase angle safety constraints (9)-(10) and equipment regulation characteristic constraints (11)-(17).

[0028] (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14) (15) (16) (17) In the formula: N represents the number of linearized segments, which is a preset positive integer (e.g., N=12) used to approximate the convex hull constraint of the capacity circle through the polygon. and These are the distribution network branches exist Active and reactive power injection at any given moment; and Photovoltaics exist Active and reactive power injection at any given moment; and Branch roads and photovoltaic Rated capacity; and Distribution network nodes exist Active and reactive power injection at any given moment; and Distribution network nodes exist Active power of base load and EV load at any given time; , , and Distribution network nodes exist The static reactive power output of the generator, the reactive power output of the photovoltaic system, the output of the parallel capacitor, and the reactive power of the EV load at any given time. and Branch roads The rated active and reactive power values; , as well as Distribution network nodes exist The voltage amplitude and its upper and lower bounds at each moment; and Distribution network nodes exist Phase angle at time and its upper limit of drop; The power factor angle; , These are the tap positions and adjustment limits of the on-load tap-changing transformer; This is the ratio of the change in the transformer ratio caused by a single-step tap change. For the first A parallel capacitor The number of capacitor banks connected at any given time; and for The total number of parallel capacitor banks and the reactive power capacity of each capacitor bank; and Adjust the upper and lower limits for the static var generator; , , , , These are respectively the line set, photovoltaic set, optimized time set, parallel capacitor set, and static var generator set.

[0029] S1.2 Distribution network power flow calculation based on the Distflow model.

[0030] Based on the above constraints, the constraints are written in a compact form, and the power flow calculation optimization model of the distribution network is constructed as follows: (18) In the formula: the first constraint includes (1)-(2), (7)-(10), (14)-(15) and (17); the second constraint includes (3)-(6), (11)-(13) and (16). Includes , Integer variables; include ; Including other variables; and These are slack variables; , , , , , , as well as The coefficient matrix and vector are constraints.

[0031] Here, x includes two types of certificate decision variables: one is the tap position of the on-load tap-changing transformer, with a value range of [-2, -1, 0, 1, 2]; the other is the number of parallel capacitor banks connected, which is 5 in this embodiment. y includes all continuous variables except for the electric vehicle charging power, mainly: node voltage amplitude [0.95, 1.05], reactive power, and photovoltaic reactive power output, all of which can be calculated according to the specific circuit.

[0032] The coefficients of the discrete variable x (such as the OLTC tap position and capacitor bank switching). The coefficients corresponding to continuous variables y (such as voltage, branch power, photovoltaic reactive power, etc.); The coefficient corresponding to the electric vehicle charging power z (representing its position in the power balance). This refers to the constant terms on the right side (such as rated capacity, voltage limit, adjustment range, etc.). These are the coefficients corresponding to the discrete variable x (such as the linearization coefficient of the OLTC turns ratio, the relationship between the capacitor bank and reactive power output). The coefficients corresponding to the continuous variable y directly reflect the distribution network topology and Distflow equations, and its sub-blocks contain the node-branch correlation matrix; The coefficient corresponding to the electric vehicle charging power z; f is the constant vector on the right (such as known quantities such as base load, photovoltaic active power prediction value, etc.).

[0033] S2. Using the charging power of electric vehicles as the variable to be solved, the optimal power flow model is iteratively solved based on the cutting plane method to construct a feasible region describing the safe operation boundary of the distribution network. The feasible region is represented by a set of linear inequality constraints. This step is the core of the invention's speed improvement, aiming to approximate the complex nonlinear feasible region as a set of linear inequalities.

[0034] S2.1 Finding extreme points.

[0035] Assume the convex hull of the initial feasible region can be represented as Extreme point Let the extreme points be the points that do not satisfy the distribution network security constraints within the initial feasible region. The solution for these extreme points can be achieved using the following optimization model: (19) In the formula: and Let be the coefficient matrix and vector of the initial feasible region convex hull.

[0036] S2.2 Calculate the boundary points of the true feasible region based on the extreme points obtained in the previous iteration. .

[0037] Since the straight line connecting the critical point and the origin intersects the real feasible region at the boundary point. Therefore, solving the boundary point problem is equivalent to maximizing the length of the line segment from the origin along the critical point: (20) In the formula: Indicates the first k The extreme points obtained by solving model (19) in the second iteration are obtained; These are the boundary points to be determined. It is a scalar scaling factor, a standard setting.

[0038] S2.3. Generate feasible cutting planes based on boundary points.

[0039] To obtain the feasible cut at the boundary points, it is necessary to solve the dual form of the optimal power flow model. Solving model (20) yields... and Substituting into model (18), we obtain the form of its dual problem as follows: (twenty one) The optimal solution is obtained by solving problem (13). and Then, feasible cuts can be generated, and the calculation formula is as follows: (twenty two) (twenty three) (twenty four) S2.4 Initial feasible domain update.

[0040] The cutting plane parameters obtained from equations (23)-(24) and Substitute into the initial feasible region and In this process, the updated cutting plane can be obtained.

[0041] (25) (26) S2.5 Initial feasible region construction based on the cutting plane method.

[0042] Repeat steps S2.1-S2.4 until the objective function of model (19) reaches its optimal value. At this point, the feasible region parameters are output. and .in, The convergence tolerance is a preset value, such as 10. -4 .

[0043] like Figure 3 As shown, by iteratively increasing the cutting plane (linear inequality), the real nonlinear feasible region can be wrapped more and more tightly. Figure 3 (Mid-curved surface range). This method avoids traversing all vertices and typically achieves high accuracy with only a few dozen iterations. In the example, the construction was completed in just 15.76 seconds (see Table 1), with an error close to zero.

[0044] S3. Using the Monte Carlo method, randomly generate charging power scenarios under different electric vehicle penetration rates. This step aims to simulate the uncertainty of electric vehicle charging behavior and generate a large number of random scenarios. This step fully considers the randomness of user behavior, and the generated scenario set can represent the real spatiotemporal distribution of charging load, ensuring the statistical significance and reliability of subsequent evaluation results. Specifically, it includes: S3.1 Sampling of electric vehicle arrival times.

[0045] The probability density function of the arrival time of the electric vehicle for: (27) In the formula: =17.6; =3.4; For the first The arrival time of the electric vehicle.

[0046] S3.2 Sampling of the battery state of charge (SOC) at the arrival time of the electric vehicle; the arrival time of the electric vehicle... It is related to the daily mileage of a car, and it follows a log-normal distribution with a probability density function. for: (28) In the formula, =3.20; =0.88; This refers to the daily mileage of electric vehicles.

[0047] After obtaining the daily mileage, the arrival time can be calculated using the following formula.

[0048] (29) In the formula: =1; =24kWh; =13.5kWh; For the first The State of Charge (SOC) at the moment the electric vehicle arrives.

[0049] S3.3 Sampling of Electric Vehicle Charging Locations. The charging locations of electric vehicles follow a uniform distribution. Sampling of electric vehicle charging locations... Distribution network node to which it belongs: (30) In the formula: For the first q The distribution network node number where each user is located.

[0050] S3.4 Calculation of electric vehicle charging time.

[0051] Based on the probability density distribution of EV arrival time and driving mileage in step S3.1, the arrival time of the i-th EV is extracted.

[0052] Then, based on the EV's state of charge at the arrival time... Battery capacity Charging power and charging efficiency This allows us to determine the charging time for each vehicle. : (31) S3.5, Electric vehicle charging scenario generation.

[0053] Set the electric vehicle penetration rate (i.e., the number of electric vehicles in the power distribution network). For each electric vehicle ( Then, S3.1 and S3.4 are executed respectively. The sum of the electric vehicle charging power at each electric vehicle access node is then calculated using the formula shown below: (32) (33) In the formula: For the first q The charging power of an EV at time t; For the first electric vehicle connected to the distribution network i Each node.

[0054] S4. Substitute the charging power scenario generated in step S3 into the linear inequality constraints of the feasible region constructed in step S2 for verification. The maximum penetration rate satisfying all constraints is taken as the electric vehicle carrying capacity assessment result for this distribution network. This step utilizes the pre-constructed feasible region for efficient verification and decision-making. Specifically, it includes: S4.1 Charging scenario verification.

[0055] The generated scenario satisfies the safety constraints if the following conditions are met; otherwise, it does not: (34) In the formula: Tolerance level; for number of rows; for The d-th row vector; for The element in the d-th row; z is a column vector of . The charging power scenario vector is formed.

[0056] S4.2 Bearing capacity assessment.

[0057] Set penetration rate , Gradually increase Up to 350, z is calculated using S3 for each penetration rate, and each penetration rate pen is repeated 25 times to finally obtain the electric vehicle charging scenario set S. Then, S4.1 is used to verify whether each scenario z in the scenario set S meets the safety constraints. Subsequently, the penetration rate corresponding to the scenario in S that meets constraint (34) and has the largest penetration rate is taken as the electric vehicle carrying capacity of the current distribution network.

[0058] The core innovation of this invention lies in constructing a linear feasible region using the cutting plane method. Once this feasible region is constructed offline, it can be used online to quickly verify the safety of any charging scenario, replacing the process of repeatedly solving complex nonlinear power flow equations in the traditional Monte Carlo method. Examples show that the evaluation time of this method is only about 1 / 91 of that of traditional power flow calculation methods, a speed improvement of two orders of magnitude, demonstrating its potential for online applications. Furthermore, by iteratively approximating the real nonlinear safety boundary through the constructed feasible region using cutting planes, theoretically, any required accuracy can be achieved. Simultaneously, during the scenario generation stage, this invention fully considers the uncertainties of multiple sources such as electric vehicle arrival time, mileage, and access location, ensuring the statistical reliability of the evaluation results. Simulation results confirm that the evaluation results of this method are almost identical to those of traditional high-precision methods.

[0059] In a specific implementation scenario, the present invention provides a method for rapid assessment of the load-bearing capacity of electric vehicles in power distribution networks based on the cutting plane method, which mainly includes the following steps: S1. Based on the active and reactive power data of the base load at each node in the distribution network, construct an optimal power flow model for the distribution network. For example... Figure 2 As shown, the line has a rated capacity of 0.55 MVA, and the safe ranges for node voltage and phase angle difference are 0.95–1.05 pu and 0.03, respectively. The reference voltage is 10 kV. Nodes 10, 15, and 26 are connected to photovoltaic systems, each with a rated capacity of 0.4 MVA. A static var generator (SVA) is installed at node 30, with an adjustment range of -0.1 MVar to 0.3 MVar. Capacitor banks are connected at nodes 11 and 20, each with 5 capacitor banks, each providing 0.15 MVar of reactive power. The on-load tap-changing transformer has 5 taps, allowing for ±5% transformation ratio adjustment. Electric vehicles are connected at nodes 8, 14, 28, 25, 32, and 33, with a charging power factor of 0.98.

[0060] S2. Based on the optimal power flow model, construct the feasible region of the distribution network using the cutting plane method. The visualization results of the feasible region are as follows: Figure 3 As shown in the figure, the comparison results with other methods are shown in Table 1.

[0061] S3. Use the Monte Carlo method to obtain charging scenarios under different electric vehicle penetration rates.

[0062] S4. Using the feasible region constructed in step S2, determine whether the power of the charging scenarios under different penetration rates in S3 meets the distribution network safety constraints. Take the highest EV penetration rate as the electric vehicle carrying capacity assessment result. The assessment results are shown in Table 2, and the distribution network node voltage and branch power flow distribution caused by the corresponding charging load are as follows: Figure 4 As shown.

[0063] Table 1. Feasibility domain construction results of different methods

[0064] Table 2. Results of electric vehicle load-bearing capacity assessment using different methods

[0065] Based on the comprehensive simulation results, we can conclude that: (1) As shown in Table 1, compared with the proposed method (M0), methods M1 and M2 have lower accuracy but longer computation time. M0 avoids traversing all vertices by using the cutting plane method to construct the feasible region. Therefore, the proposed method only takes 15.76 seconds, which is at least 2.57 times faster than the traditional methods (M1 and M2), while the error is close to zero.

[0066] (2) Figure 3The feasible regions between nodes 8, 18, and 28 are shown for four time periods. The volumes of the four feasible regions, from largest to smallest, are: 21:00, 1:00, 7:00, and 14:00. Combined with... Figure 2 A comparison of the load curves shows that the relationship between the feasible region volume and the load is consistent across these four time periods: the higher the load, the smaller the feasible region volume. This reflects that the constructed feasible region can effectively represent the load fluctuations.

[0067] (3) As shown in Table 1, the carrying capacity assessment results of the method based on power flow calculation (traditional method) and the method based on feasible domain (proposed method) are almost the same. The proposed method takes 21.70s (including feasible domain construction time and scenario verification time), which is 91 times faster than the traditional method. Therefore, the proposed method significantly shortens the assessment time compared with the traditional method.

[0068] (4) Figure 4 This indicates that the voltage at the end nodes (i.e., buses 18, 33, and 22) is close to the lower limit; while the line load rate near bus 1 is the highest, but still far below the rated capacity. Therefore, the bottleneck limiting the carrying capacity of electric vehicles lies in the voltage at the end nodes; in other words, the voltage at the nodes has a much greater impact on the carrying capacity of electric vehicles than the line load rate.

[0069] Example embodiments have been disclosed herein, and while specific terminology has been used, it is for illustrative purposes only and should be construed as such, and is not intended to be limiting. In some instances, it will be apparent to those skilled in the art that features, characteristics, and / or elements described in conjunction with particular embodiments may be used alone, or in combination with features, characteristics, and / or elements described in conjunction with other embodiments, unless otherwise expressly indicated. Therefore, those skilled in the art will understand that various changes in form and detail may be made without departing from the scope of the invention as set forth in the appended claims.

Claims

1. A rapid assessment method for the load-bearing capacity of electric vehicles in power distribution networks based on the cleaving plane method, characterized in that, include: S1. Based on the active and reactive power data of the basic load of each node in the distribution network, construct the optimal power flow model of the distribution network. S2. Based on the aforementioned optimal power flow model, construct the feasible region of the distribution network based on the cutting plane method; S3. Use the Monte Carlo method to obtain charging scenarios under different electric vehicle penetration rates; S4. Use the feasible region of the distribution network to determine whether the charging scenarios under different electric vehicle penetration rates meet the safety constraints of the distribution network, and take the maximum penetration rate that meets the constraints as the electric vehicle carrying capacity assessment result.

2. The method according to claim 1, characterized in that, S1 includes: S1.1 Construct a set of distribution network operation constraints that includes power flow security constraints, power balance constraints, voltage security constraints, and reactive power compensation equipment regulation constraints; S1.

2. Based on the Distflow model, the constraints are written in a compact form, and the power flow calculation optimization model of the distribution network is constructed as follows: ； In the formula, and Let x be a vector of different slack variables, y be a discrete control variable, y be a continuous state variable excluding electric vehicle charging power, and z be a charging power scenario vector. , , , , , , as well as The coefficient matrix and vector are constraints.

3. The method according to claim 2, characterized in that, The power flow safety constraints specifically include: ； ； ； ； In the formula: and These are the distribution network branches exist Active power injection and reactive power injection at any given time; and Photovoltaics exist Active power injection and reactive power injection at any given time; and These are the distribution network branches and photovoltaic Rated capacity; and Branch roads The rated active power and rated reactive power, and Branch roads The magnitudes of active and reactive power at time t; , , These are the line set, the photovoltaic set, and the optimized time set, respectively.

4. The method according to claim 2, characterized in that, S2 includes: S2.1, Define an initial relaxed feasible region. By solving an optimization problem that aims to maximize the degree to which the original constraints are not satisfied, we can find an extreme point in the initial relaxed feasible region that does not satisfy the original safety constraints. ; S2.2, with the aforementioned extreme point Using the direction as an example, solve another optimization problem: find the farthest point from the origin along this direction that intersects with the original feasible region. This point is the boundary point of the true feasible region. ; S2.3, at the boundary point At that point, solve the dual problem of the original optimal power flow model to obtain a cutting plane that supports the true feasible region, which has the form: ; S2.4, the cutting plane Add to the initial feasible region and update the constraints as follows: and ; S2.

5. Repeat steps S2.1 to S2.4 until no points that do not meet the original safety constraints are found within the updated feasible region. At this point, output the feasible region parameters. and .

5. The method according to claim 4, characterized in that, In S2.3, the cutting plane parameters and Obtained through calculation using dual variables, specifically: ； ； in and For the boundary point The optimal dual variables are obtained by solving the dual problem at the corresponding optimal solution.

6. The method according to claim 1, characterized in that, S3 specifically includes: S3.1, Based on a preset probability distribution, randomly select the charging start time for each electric vehicle; S3.2, Based on the preset daily mileage probability distribution, randomly select the daily mileage of each electric vehicle, and calculate its state of charge at the start of charging based on battery capacity and power consumption per 100 kilometers. S3.3, Based on uniform distribution, randomly determine the distribution network node to which each electric vehicle is connected; S3.4 Calculate the required charging duration based on the state of charge, battery capacity, charging power and efficiency of each electric vehicle; S3.5 Based on the charging start time, charging duration, and access node of all electric vehicles, the total charging power of electric vehicles at each node in different time periods is aggregated to form a complete charging power scenario vector z.

7. The method according to claim 6, characterized in that, In step S3.1, the probability density function f(t) at the start of charging of the electric vehicle is a piecewise function: ;in, To achieve the mean at any given time, The variance of the arrival time, For the first The arrival time of the electric vehicle.

8. The method according to claim 7, characterized in that, In S3.2, the daily mileage D follows a log-normal distribution, and its probability density function is: ； in, For the daily mileage of electric vehicles, This represents the average daily mileage. Variance of daily mileage.

9. The method according to claim 1, characterized in that, In step S4, the judgment process specifically involves: for a charging power scenario vector z, checking whether it satisfies all linear inequality constraints in the feasible region, i.e., whether it satisfies... H d and v d Let n be the row vector of coefficients and the constant term of the d-th constraint in the feasible region. H The total number of constraints is used to determine the scenario; if the scenario satisfies all constraints, it is considered a safe scenario.

10. The method according to claim 9, characterized in that, In step S4, the load-bearing capacity assessment process specifically involves: setting a series of increasing electric vehicle penetration rates; generating multiple random charging scenarios for each penetration rate and verifying them; and taking the highest penetration rate that can find at least one safe scenario as the electric vehicle load-bearing capacity assessment result of the power distribution network.

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