A power distribution network electric vehicle carrying capacity optimization evaluation method based on operation envelope

Abstract

The present application belongs to the technical field of power distribution network operation and electric vehicle, and specifically relates to a power distribution network electric vehicle carrying capacity optimization evaluation method based on operation envelope, which is based on power distribution network node basic load data to construct power distribution network operation envelope; simulates electric vehicle charging load by considering battery degradation cost, charging income and user response willingness; constructs a price guide model based on marginal effect, linearizes load-price sensitivity by first-order Taylor expansion, solves optimal electricity price by iteration, and guides electric vehicle load to meet operation envelope constraints; increases electric vehicle penetration rate by iteration, and takes the maximum penetration rate that can be safely carried by the system as the evaluation result. The present application realizes node decoupling through operation envelope, supports distributed evaluation and optimization, significantly improves calculation efficiency, and effectively improves the carrying capacity of power distribution network for electric vehicles through detailed user behavior modeling and electricity price guide mechanism.

Description

Technical Field

[0001] This invention relates to the fields of power distribution network operation and electric vehicle technology, and in particular to a method for optimizing and evaluating the carrying capacity of electric vehicles in power distribution networks based on the operating envelope. Background Technology

[0002] Currently, electric vehicle (EV) capacity assessment methods are mainly divided into three categories: deterministic assessment methods, stochastic assessment methods, and optimization-based assessment methods. Deterministic assessment methods use pre-defined fixed or extreme scenarios as input, evaluating the system state through quasi-steady-state time-series simulations, scenario analysis, or deterministic power flow calculations. While computationally fast, they struggle to reflect the impact of uncertainties. Stochastic assessment methods model uncertainties such as EV charging behavior and renewable energy output as probability distributions, evaluating them through methods like Monte Carlo simulations. The results are more objective, but computation is enormous, resulting in slow assessment speeds. Optimization-based methods describe EV capacity by constructing feasible regions, but these typically involve complex optimization models, leading to time-consuming solutions and limiting their online application. A common problem with these methods is their excessively slow assessment speed, making them unsuitable for online assessment and real-time control.

[0003] Therefore, there is an urgent need for a method that can accurately simulate user behavior, conduct rapid and distributed assessments, and effectively improve the load-bearing capacity of the power distribution network for electric vehicles. Summary of the Invention

[0004] This invention proposes an optimized evaluation method for the carrying capacity of electric vehicles in power distribution networks based on the operating envelope, aiming to solve the technical problems of slow calculation speed and difficulty in online application of existing electric vehicle carrying capacity evaluation methods.

[0005] This invention provides a method for optimizing and evaluating the carrying capacity of electric vehicles in distribution networks based on operating envelopes, comprising: S1, based on the active and reactive power data of the basic load of each node in the distribution network, construct the operation envelope of the distribution network; S2, electric vehicle charging load simulation considering user preferences; S3, Distribution network operators set prices to guide EV loads to meet the distribution network operating envelope; S4, by increasing the penetration rate of EVs, takes the highest EV penetration rate as the result of the electric vehicle load capacity assessment.

[0006] The technical advantages of the electric vehicle carrying capacity optimization evaluation method for distribution networks based on operating envelope disclosed in this invention are: node decoupling is achieved through operating envelope, supporting distributed evaluation and optimization, and significantly improving computational efficiency; at the same time, by constructing a refined load model based on user willingness and a price guidance mechanism based on electricity price sensitivity, the carrying capacity of the distribution network for electric vehicles is effectively improved.

[0007] Furthermore, S1 specifically includes: S11. Construct a power flow calculation optimization model for the distribution network based on the Distflow model. The constraints include node power balance equations, voltage drop equations, branch current constraints, node voltage constraints, and branch capacity constraints. S12. Solve for the running envelope. The optimization objective is to maximize the sum of the running envelopes of all electric vehicle access nodes at all times. The constraint is the power flow calculation optimization model of the distribution network described in step S11.

[0008] Furthermore, the power flow calculation optimization model for the distribution network is as follows: ； ； ； ； ； ; ; In the formula, , and They represent the times at time 1 and 2 respectively. branch road The active power, reactive power, and current square; Represents nodes The set of adjacent downstream nodes; and Representing branch roads Resistance and reactance; Indicates at time t node j The active base load; This represents the size of the running envelope at node j at time t; Indicates at time t branch road The active power; Indicates at time t nodej reactive power base load; This represents the electric vehicle charging power factor angle; Indicates at time t branch road jl reactive power; Indicates at time t node j The square of the voltage, and They represent the times at time 1 and 2 respectively. node voltage square and node Electric vehicle load at the location; and Indicates the upper and lower limits of voltage; Indicates the maximum allowable current of the branch; Indicates a branch ij The maximum capacity.

[0009] Furthermore, S2 specifically includes: S21. Construct a total cost model for electric vehicle users that includes battery degradation costs and charging revenues, and calculate the electric vehicle charging load without considering user willingness based on energy and power constraints. S22. Based on the Weber-Fechner law, construct a user willingness model that reflects the probability of users responding to electricity prices; S23. Based on the user's intention, simulate the electric vehicle charging load in the form of expected load, wherein the expected load is the weighted average of the charging power when responding to the electricity price and the default charging mode when not responding to the electricity price, and the weight is the user's intention.

[0010] Furthermore, the total cost model for electric vehicle users, energy and power constraints, and user willingness model are specifically as follows: ; ; ; For the node The The total cost for an electric vehicle user consists of battery degradation costs. and charging revenue ; , , This is the preset battery degradation cost coefficient; For time t node i First n The charging power of an electric vehicle; , The preset charging revenue-cost coefficient; For node t i Electricity price at the location; The energy and power constraints that need to be met during charging and discharging are as follows: ; ; ; ; ; in, Indicates at node place electric vehicles at all times The state of charge; and These represent the lower and upper limits of the state of charge, respectively; This indicates the maximum charging / discharging power of the electric vehicle; and For the first n The times when an electric vehicle arrives at node i and leaves node i; For time intervals; This indicates the desired state of charge that the electric vehicle will achieve when it leaves the station. The state of charge of the electric vehicle at the time it reaches that point.

[0011] Furthermore, S3 specifically includes: S31. Construct a price function based on marginal effects, and introduce price signal constraints, marginal effect parameter constraints, and initial effect parameter constraints; construct a price update mechanism, use a first-order Taylor expansion to linearize the sensitivity function between electric vehicle load and price function parameters, and limit the range of parameter variation; S32. Introduce an over-limit power variable and apply constraints to the electric vehicle load based on the operating envelope; S33. With the objective of minimizing the sum of the over-limit power of all nodes at all times, and with the constraints of distribution network power flow constraints, electric vehicle charging load model, price function and its constraints, and revenue threshold as conditions, construct an optimization model for the distribution system operator. S34. By iteratively solving the optimization model of the power distribution system operator, the price function parameters are updated until the objective function of the power distribution system operator converges, and the optimized electricity price is output.

[0012] Furthermore, the price function, constraints, and price update mechanism are specifically as follows: ; ; ; ; ; ; in, Represents a node At any moment Electricity price; and These represent the marginal effect parameter and the initial effect parameter, respectively. Represents a node At any moment The base load; Represents a node The number of electric vehicles; For nodes The average load of electric vehicles; For price variance, and These are the upper and lower bounds for the marginal effect parameter; and These are the upper and lower bounds of the initial effect parameters; ; ; ; ; ; Represents a node Total load of electric vehicles at the location; This represents the electric vehicle load simulated in S2. For the first n Electric vehicle load; and Let be the partial derivative of the electric vehicle load with respect to the parameters of the price function; and Indicates the range of parameter variation; and The table shows the price function parameters obtained from the previous iteration.

[0013] Furthermore, S4 specifically includes: S41. Sample the arrival time, departure time and daily mileage of electric vehicles, and calculate the state of charge of electric vehicles at the arrival time based on the daily mileage. S42. For a given number of electric vehicles, execute steps S2 to S3. If the sum of the over-limit power obtained by optimization is zero, it indicates that the current number can be safely carried. S43. For any node objective function value This will increase the penetration rate of electric vehicles. Execute S41 and S42 until... This indicates that the maximum EV load capacity has been reached.

[0014] Furthermore, the power distribution system operator optimization model is specifically as follows: ; ; in, Indicates the revenue threshold; This represents the objective function value for the power distribution system operator, i.e., the total over-limit power. This represents the over-limit power at node i at time t; Represents a node The number of electric vehicles; Represents a node The number of electric vehicles; Let i be the electricity price at node i at time t; Let i be the node at time t. n The charging power of an electric vehicle.

[0015] Furthermore, the sampling in S41 specifically includes: ; ; ; ; in, and These represent the probability distributions for the arrival and departure times of the electric vehicle, respectively. To achieve the mean at any given time, The variance of the arrival time, For the first The node of the first The arrival time of the electric vehicle; The mean at the time of departure. The variance of the departure time. For the first The node of the first The moment the electric car departed; Let be the probability density function of the daily mileage of an electric vehicle; For the daily mileage of electric vehicles, This represents the average daily mileage. Variance of daily mileage; For electric vehicles Maximum constraint; This refers to the maximum battery capacity of an electric vehicle. This refers to the energy consumption per 100 kilometers of an electric vehicle. For the first The state of charge of an electric vehicle at node i. Attached Figure Description

[0016] Figure 1 This is a schematic diagram of the optimization process of an optimized evaluation method for the carrying capacity of electric vehicles in a distribution network based on the operating envelope, as proposed in an embodiment of the present invention. Figure 2 This is a schematic diagram of a power distribution network node structure provided in an embodiment of the present invention; Figure 3 The diagrams show a comparison of electric vehicle charging loads under different methods in the embodiments of the present invention, wherein (a) is a diagram of electric vehicle charging loads under the method provided in the embodiments of the present invention, (b) is a diagram of electric vehicle charging loads under the dynamic electricity price method, and (c) is a diagram of electric vehicle charging loads under the time-of-use electricity price method. Detailed Implementation

[0017] 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.

[0018] The technical problem this invention aims to solve is that traditional methods are too slow in computation, which limits their online application. This invention provides a method for optimizing and evaluating the carrying capacity of electric vehicles in power distribution networks based on operational envelopes, referencing... Figures 1 to 3 As shown, the specific steps include: 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. The photovoltaic data used comes from Ausgrid, and the load data comes from central China, such as... 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; nodes 4, 14, and 32 are connected to electric vehicles, with a charging power factor of 0.98.

[0019] S2. Simulation of electric vehicle charging load considering user preferences; S3. Distribution network operators set prices to guide EV (electric vehicle) loads to meet the distribution network operating envelope. The guided loads, such as... Figure 2 As shown; S4. Continuously increase the penetration rate of EVs, and take the highest EV penetration rate as the evaluation result of electric vehicle load capacity. The evaluation results are shown in Table 1, and the calculation efficiency is shown in Table 2. Table 1

[0020] Table 2

[0021] A further step, step S1, specifically includes: The optimization objective is constructed by solving the running envelope, based on the power flow equations and constraints of the Distflow model.

[0022] The power flow calculation optimization model for the distribution network is constructed as follows: (1a) (1b) (1c) (1d) (1e) (1f) (1g) In the formula, , and They represent the times at time 1 and 2 respectively. branch road The active power, reactive power, and current square; Represents nodes The set of adjacent downstream nodes; and Representing branch roads Resistance and reactance; and They represent the times at time 1 and 2 respectively. node voltage square and node Electric vehicle load at the location; and Indicates the upper and lower limits of voltage; This indicates the maximum allowable current for the branch.

[0023] Running envelope solution: The optimization objective of the running envelope is to satisfy the sum of the maximum loads of the EV access nodes under running constraint (1). The optimization model is shown below: (2) in, Indicates at time node The size of the running envelope at that location.

[0024] A further step, step S2, specifically includes: S21. EV load calculation considering battery degradation costs and charging benefits.

[0025] The charging costs for EV users are mainly due to battery degradation costs. and charging revenue Composition. Therefore, located at the node. The The total cost for each electric vehicle user is denoted as . , can be represented as follows: (3a) (3b) (3c) EVs need to meet energy and power constraints during charging and discharging: (3d) (3e) (3f) (3g) (3h) in, Indicates at node place A car at a time The state of charge (SOC); and These represent the lower and upper limits of the state of charge, respectively; This indicates the maximum charging / discharging power of the electric vehicle; and For the arrival and departure times of the EV; State of Charge (SOC) for electric vehicles at the moment of arrival.

[0026] Therefore, without considering user intentions, the EV load can be calculated by model (4): (4) In the formula: A set of nodes containing EVs. For nodes containing EVs .

[0027] S22. Calculation of user intentions based on the Weber-Fechner law.

[0028] According to the Weber-Fechner Law, the relationship between user willingness and external incentives can be represented by a logarithmic curve: (5) in, Indicates at node First The user's willingness. Its value ranges from 0 to 1, and is used to reflect the probability of a user responding to the pricing scheme of the power distribution system operator. and These represent the slope coefficient and the inflection point, respectively. Historical participation rate data are fitted using the least squares method, or sensitivity analysis is performed using Monte Carlo simulation.

[0029] S23. EV load simulation considering user preferences.

[0030] Based on quantified user intentions, the expected load of electric vehicles can be expressed as: (6) In the formula, and These represent the nodes respectively. The first The charging power of an electric vehicle when it does not respond to / responds to the power distribution system operator's price function.

[0031] in, The default charging mode when not responding to electricity price guidance is expressed as follows: (7) in, and This represents the coefficients used to approximate the charging power function when the SoC is higher than 0.9.

[0032] A further step, step S3, specifically includes: S31, Electricity Price Constraint Construction.

[0033] Based on marginal effects, at the node And time At that time, construct the following price function: (8a) (8b) in, Represents a node At any moment Electricity price; and These represent the marginal effect parameter and the initial effect parameter, respectively. Represents a node At any moment The base load; Indicates the runtime range; Represents a node The number of electric vehicles; For nodes The average value of the EV load.

[0034] Since distribution system operators must comply with market policy requirements, the following constraints must be met: price signaling constraints (9a)–(9b), and marginal effects. Constraints (9c) and initial effects Constraints (9d): (9a) (9b) (9c) (9d) In the formula: For price variance, and These are the upper and lower bounds for the marginal effect parameter; and These are the upper and lower bounds of the initial effect parameters.

[0035] To facilitate price adjustments, a price update mechanism is constructed, which introduces a sensitivity function to approximate the relationship between electric vehicle load and pricing function parameters. Based on this, a first-order Taylor expansion is used to linearize the sensitivity function, as shown in equation (3a). Equations (3b) and (3c) represent the total electric vehicle load equation. To ensure the effectiveness of the Taylor linear approximation, constraints (3d)–(3e) are used to limit the range of variation of the price function parameters. (9a) (9b) (9c) (9d) (9e) In the formula: Represents a node Total load of electric vehicles at the location; This represents the electric vehicle load simulated in S2; Let be the partial derivative of the electric vehicle load with respect to the parameters of the price function; and Indicates the range of parameter variation; and The table shows the price function parameters obtained from the previous iteration.

[0036] The sensitivity matrix can be approximated using a numerical difference method. Specifically, for the parameters at the current iteration point... and Apply small perturbations respectively and The load simulation model (4) in step S2 is solved again to obtain the total load after disturbance. and Then the partial derivative is approximately: ≈ Similarly, calculate the pair The partial derivative of . Where and Take 1% to 5% of the parameter range.

[0037] S32, Quantification of electric vehicle load-bearing capacity index.

[0038] Since electric vehicle loads exceeding the operating envelope may violate distribution network safety constraints, over-limit power should be reduced. This is crucial for improving the load-bearing capacity of electric vehicles. Based on the operating envelope constructed in S1, constraints are imposed on the electric vehicle load to meet the safe operation limits of the distribution network, as shown in Equation (7): (10a) (10b) S33. Price-guided EV carrying capacity enhancement model.

[0039] Based on the constraints in S31 and S32, the following optimization model for the power distribution system operator is established: (11) In the formula, This represents the revenue threshold.

[0040] S34, Solving the model for improving the load-bearing capacity of electric vehicles.

[0041] For any node Solving this model involves four steps: Step 1: Initialization and Number of iterations , Stop condition .

[0042] Step 2: and Substitute it into S2 to solve partial derivatives and and order , .

[0043] Step 3: Put and Substitute the values ​​into model (11) and solve for the parameters. and , Step 4: Determine Is it less than If true, the model solution ends and the output is given. and Otherwise, return to step 2.

[0044] The further solution, step S4, specifically includes: S41, EV parameter sampling.

[0045] For any node Any EV user From the following probability density function and Extract EV arrival and departure times: (12a) (12b) In the formula: and These represent the probability distributions for the arrival and departure times of the electric vehicle, respectively. To achieve the mean at any given time, The variance of the arrival time, For the first The node of the first The arrival time of the electric vehicle; The mean at the time of departure. The variance of the departure time. For the first The node of the first The moment the electric car departed.

[0046] For any node Any EV user From the following probability density function Mileage extracted in the form of mid-range: (13) In the formula, For the daily mileage of electric vehicles, This represents the average daily mileage (in km). Variance of daily mileage.

[0047] Based on daily mileage, the State of Charge (SOC) of the q electric vehicles at the i-th node at the arrival time can be obtained according to the following formula: (14) In the formula, For electric vehicles Maximum constraint; This refers to the maximum battery capacity of an electric vehicle. It is the energy consumption per 100 kilometers of electric vehicles (unit: kWh / 100km). For the first Electric vehicles arrive at the node i SOC at any given moment.

[0048] S42 and EV load-bearing capacity optimized.

[0049] For any node Its number of EV users is , For electric vehicles, Initial number of electric vehicles; based on sampling for each EV user using S41. 、 and Then execute S2-S3 to get ,like This indicates that the distribution network can support the current number of EVs.

[0050] S43, EV load capacity assessment.

[0051] For any node , ,make Execute S41 and S42 until... This indicates that the maximum EV load capacity has been reached.

[0052] Based on the comprehensive simulation results, we can conclude that: (1) Figure 3 The proposed method (a), dynamic pricing method (b), and time-of-use pricing method (c) are illustrated with their respective electric vehicle load conditions. Compared to other methods, the proposed method consistently keeps the electric vehicle load within its operating envelope, thereby ensuring the safe operation of the distribution network. and At the same time, the electric vehicle loads in other methods exceeded the operating envelope limits. This is because the electric vehicle loads in other methods exhibited significant load concentration. This indicates that the proposed method can effectively alleviate the EV load concentration problem, thereby improving load-bearing capacity.

[0053] (2) Figure 3 The improvement in electric vehicle (EV) carrying capacity was compared under three scenarios. The number of EVs connected to the grid was used as a metric for HC (charge capacity). The results show that the proposed method is 110.52% higher than the conventional method. Therefore, the proposed electricity price-guided method can effectively improve the EV carrying capacity.

[0054] (4) Table 2 shows the average computation time of the proposed method on the three nodes under different numbers of electric vehicles. When upgrading from version 1.0 to 2.0, the computation time for the upper-level problem increased by only 13.27%, and the computation time for the lower-level problem increased by only 19.24%. This is mainly because the number of electric vehicles exceeds the number of CPU cores, thus significantly reducing the efficiency of parallel computing. Therefore, when there are enough computing cores, the total computation time does not increase significantly, indicating that the proposed method can effectively support large-scale electric vehicle access.

[0055] The beneficial innovation of this invention lies in: 1. This invention proposes a method for optimizing and evaluating the carrying capacity of electric vehicles based on the operational envelope. Compared to traditional methods for evaluating the carrying capacity of EVs in distribution networks, which require centralized evaluation and optimization, the proposed method can decouple the EV access nodes through the operational envelope, enabling each node to perform distributed evaluation and optimization of the EV carrying capacity, thereby improving computational efficiency.

[0056] 2. This invention proposes an electricity price update mechanism based on user electricity price sensitivity. This mechanism approximates the relationship between electric vehicle load and pricing function parameters using a sensitivity function, and linearizes the sensitivity function using a first-order Taylor expansion. This allows the mechanism to guide electric vehicle users to change their charging load through electricity pricing, thereby improving the electric vehicle carrying capacity of the distribution network.

[0057] 3. This invention proposes an electric vehicle load simulation method that considers user willingness. This method quantifies the probability of electric vehicle users responding to electricity prices using an S-curve and incorporates user willingness into the electric vehicle load simulation through expected load, thereby improving the accuracy of the electric vehicle load simulation.

[0058] 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 method for optimizing and evaluating the carrying capacity of electric vehicles in a distribution network based on operational envelope, 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 operation envelope of the distribution network; S2, electric vehicle charging load simulation considering user preferences; S3, Distribution network operators set prices to guide EV loads to meet the distribution network operating envelope; S4, by increasing the penetration rate of EVs, takes the highest EV penetration rate as the result of the electric vehicle load capacity assessment.

2. The method according to claim 1, characterized in that, S1 specifically includes: S11. Construct a power flow calculation optimization model for the distribution network based on the Distflow model. The constraints include node power balance equations, voltage drop equations, branch current constraints, node voltage constraints, and branch capacity constraints. S12. Solve for the running envelope. The optimization objective is to maximize the sum of the running envelopes of all electric vehicle access nodes at all times. The constraint is the power flow calculation optimization model of the distribution network described in step S11.

3. The method according to claim 2, characterized in that, The power flow calculation optimization model for the distribution network is as follows: ； ； ； ； ； ； ； In the formula, 、 and They represent the times respectively. branch road The active power, reactive power, and current square; Represents nodes The set of adjacent downstream nodes; and Representing branches Resistance and reactance; Indicates at time t node j The active base load; This indicates the time node t. j Size of the running envelope at that location; Indicates the branch at time t The active power; Indicates at time t node j reactive power base load; This represents the electric vehicle charging power factor angle; Indicates at time t branch road jl reactive power; Indicates at time t node j The square of the voltage, and They represent the times respectively. node voltage square and node Electric vehicle load at the location; and Indicates the upper and lower limits of voltage; Indicates the maximum allowable current of the branch; Indicates a branch ij The maximum capacity.

4. The method according to claim 1, characterized in that, S2 specifically includes: S21. Construct a total cost model for electric vehicle users that includes battery degradation costs and charging revenues, and calculate the electric vehicle charging load without considering user willingness based on energy and power constraints. S22. Based on the Weber-Fechner law, construct a user willingness model that reflects the probability of users responding to electricity prices; S23. Based on the user's intention, simulate the electric vehicle charging load in the form of expected load, wherein the expected load is the weighted average of the charging power when responding to the electricity price and the default charging mode when not responding to the electricity price, and the weight is the user's intention.

5. The method according to claim 4, characterized in that, The total cost model for electric vehicle users includes a quadratic function of battery degradation cost and a quadratic function of charging revenue; the energy and power constraints include electric vehicle charging and discharging power limits, recursive relationship of state of charge, upper and lower limits of state of charge, expected state of charge at departure, and initial state of charge at arrival.

6. The method according to claim 1, characterized in that, S3 specifically includes: S31. Construct a price function based on marginal effects, and introduce price signal constraints, marginal effect parameter constraints, and initial effect parameter constraints; construct a price update mechanism, use a first-order Taylor expansion to linearize the sensitivity function between electric vehicle load and price function parameters, and limit the range of parameter variation; S32. Introduce an over-limit power variable and apply constraints to the electric vehicle load based on the operating envelope; S33. With the goal of maximizing the sum of the over-limit power of all nodes at all times, and with the constraints of distribution network power flow constraints, electric vehicle charging load model, price function and its constraints, and revenue threshold as conditions, construct an optimization model for the distribution system operator. S34. By iteratively solving the optimization model of the power distribution system operator, the price function parameters are updated until the objective function of the power distribution system operator converges, and the optimized electricity price is output.

7. The method according to claim 6, characterized in that, The price function consists of marginal effect parameters and initial effect parameters, and is constrained by upper and lower limits of electricity price, electricity price variance, and upper and lower bounds of parameters; the price update mechanism uses a first-order Taylor expansion to linearize the sensitivity of the total load of electric vehicles to the price function parameters, and limits the range of single-step changes of the parameters.

8. The method according to claim 6, characterized in that, S4 specifically includes: S41. Sample the arrival time, departure time and daily mileage of electric vehicles, and calculate the state of charge of electric vehicles at the arrival time based on the daily mileage. S42. For a given number of electric vehicles, execute steps S2 to S3. If the sum of the over-limit power obtained by optimization is zero, it indicates that the current number can be safely carried. S43. For any node objective function value This will increase the penetration rate of electric vehicles. Execute S41 and S42 until... This indicates that the maximum EV load capacity has been reached.

9. The method according to claim 8, characterized in that, The optimization model for the power distribution system operator aims to minimize the sum of over-limit power at all times for all nodes. The constraints include power flow constraints, electric vehicle charging load model, price function and its constraints, and revenue threshold constraints for the power distribution system operator.

10. The method according to claim 9, characterized in that, The specific probability distributions for sampling in S41 include: a normal distribution of the arrival time of the electric vehicle, a normal distribution of the departure time, and a log-normal distribution of the daily mileage; the state of charge at the arrival time is calculated based on the daily mileage, the power consumption per 100 kilometers, and the battery capacity.

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