Electric vehicle charging station planning and pricing method based on existing charging stations

Abstract

The invention discloses an electric vehicle charging station planning and pricing method based on an existing charging station, and the method achieves the deep fusion of a charging station extension decision and an operation strategy through the construction of a unified framework of planning and pricing collaborative optimization, solves a problem that the overall optimization effect is not good because of the disjunction of the two in an existing method, and improves the efficiency of electric vehicle charging station planning and pricing. And the economical efficiency and the practicability of the scheme are improved. According to the improved chaos non-uniform mutation artificial hummingbird algorithm provided by the method, population diversity is ensured through chaos initialization, and a search behavior is dynamically adjusted by adopting an adaptive mutation strategy, so that the problems that a traditional optimization algorithm is easy to fall into local optimum and slow in convergence speed when processing a high-dimensional, nonlinear and multi-constraint mixed integer programming problem are effectively solved. The Pareto optimal solution set finally output by the method provides rich tradeoff selection schemes for decision makers, scientific decision making according to different preferences (such as cost minimization or user satisfaction maximization) is supported, and the flexibility and applicability of the method are enhanced.

Description

Technical Field

[0001] This invention belongs to the field of electric vehicle charging infrastructure planning, specifically a method for planning and pricing electric vehicle charging stations based on existing charging stations. Background Technology

[0002] With the global energy transition and the rapid development of the electric vehicle (EV) industry, the demand for EV charging continues to grow rapidly. However, the layout and capacity of existing charging infrastructure are often insufficient to meet the increasing demand, leading to problems such as long waiting times and poor service experience for users. Meanwhile, the spatiotemporal uncertainty of charging load poses a challenge to the safe and stable operation of the power distribution network, potentially causing risks such as grid overload and voltage exceeding limits. Therefore, how to scientifically and rationally plan the expansion of the existing charging network and formulate effective pricing strategies to achieve synergistic optimization among the economic benefits of charging service providers, user satisfaction, and safe operation of the power grid has become a critical issue that urgently needs to be addressed in urban energy planning and power system operation.

[0003] Currently, research on the planning and pricing strategies for electric vehicle charging stations, both domestically and internationally, still faces the following major technical challenges: Planning and pricing are disconnected: Most existing studies treat charging station site selection and capacity planning and operational pricing strategies as two separate optimization problems, ignoring the strong coupling between them. This separate optimization method is unlikely to obtain a globally optimal solution and cannot truly reflect the interactive impact between investment decisions and operational strategies.

[0004] Oversimplification of models: Many studies have oversimplified the physical constraints of distribution networks when modeling, such as using DC power flow models or ignoring key safety constraints such as node voltage and line capacity. This may result in planning schemes that are not feasible in actual power grids and lack practical engineering value.

[0005] The algorithm suffers from low efficiency: This optimization problem is a high-dimensional, nonlinear, and multi-constrained mixed integer programming problem, resulting in extremely high solution complexity. Traditional optimization algorithms (such as linear programming and dynamic programming) struggle to directly handle discrete decisions and complex constraints, while standard metaheuristic algorithms (such as particle swarm optimization (PSO) and genetic algorithm (GA)) are prone to getting trapped in local optima and have slow convergence speeds, making it difficult to obtain high-quality solution sets within a reasonable timeframe.

[0006] Lack of multi-objective trade-offs: In practical decision-making, minimizing the total system cost and maximizing user satisfaction are often two conflicting objectives. Existing methods often transform this into a single-objective problem through weighted summation, failing to provide a rich set of Pareto optimal solutions for decision-makers to weigh and choose according to their actual preferences.

[0007] Therefore, there is an urgent need for a systematic approach that can uniformly consider the physical security constraints of the power grid, the economic efficiency of investment and operation, and the response of user behavior, and can efficiently solve complex multi-objective optimization problems to guide the scientific planning and operation of electric vehicle charging infrastructure.

[0008] Patent CN202311418895.6 (Multi-objective planning method for electric vehicle charging in power distribution networks based on chaotic firefly algorithm) establishes a multi-objective optimization mathematical model, including objectives such as minimizing total cost, minimizing network loss, and minimizing charging station evaluation indicators. It employs the chaotic firefly algorithm for optimization to find the global optimum. However, the charging station site selection decision does not consider the impact of adjustments to existing charging stations on the site selection of new charging stations, and it also ignores the strong coupling relationship between electric vehicle charging station planning and pricing strategies. Summary of the Invention

[0009] To address the shortcomings of existing technologies, the present invention aims to provide a method for the coordinated optimization of electric vehicle charging station expansion and pricing based on a hybrid optimization algorithm. This method solves the problem of poor global optimization results caused by the disconnect between planning and pricing strategies in existing methods; and addresses the problem that traditional optimization algorithms are prone to getting trapped in local optima and have slow convergence speed when dealing with high-dimensional nonlinear mixed integer programming problems.

[0010] The technical solution of this invention to solve the aforementioned technical problem is to design a method for planning and pricing electric vehicle charging stations based on existing charging stations, characterized in that the method includes the following steps: S1: Data Acquisition and Preprocessing Acquire traffic network data, power distribution network data, spatiotemporal distribution data of electric vehicle charging demand, location and capacity data of existing charging stations, and electricity price regulations for the target planning area, and perform data cleaning and preprocessing. S2: Determine decision variables Key decision variables for charging station j The planned capacity of charging stations And on the two typical days of summer and winter and spring and autumn hourly time-of-use electricity price and As a decision variable; Demolish existing charging stations; Upgrade existing charging stations, including reducing capacity, maintaining capacity, and expanding capacity; New charging stations will be built. S3: Obtain the total system cost based on the data in S1 and the decision variables in S2. With user satisfaction The extreme values; S4: Optimize decision variables using an improved artificial hummingbird algorithm. An improved chaotic non-uniform mutation artificial hummingbird algorithm is applied to optimize decision variables. This algorithm improves population diversity through chaotic initialization and introduces an adaptive non-uniform mutation strategy to balance global exploration and local exploitation capabilities, thereby obtaining an optimized solution set for decision variables. S5: Select the Pareto optimal solution set from the optimized solution set of the decision variables in S4; then, according to the decision requirements of the target planning area, select the final solution of the decision variables from the Pareto optimal solution set, which is the final electric vehicle charging station planning and pricing strategy.

[0011] Compared with the prior art, the present invention has the following beneficial effects: (1) By constructing a unified framework for the coordinated optimization of planning and pricing, the decision-making and operation strategy for the expansion of charging stations are deeply integrated, which solves the problem of poor global optimization effect caused by the disconnect between the two in the existing methods and improves the economy and practicality of the solution.

[0012] (2) The proposed improved chaotic non-uniform mutation artificial hummingbird algorithm ensures population diversity through chaotic initialization and dynamically adjusts the search behavior by adopting an adaptive mutation strategy. This effectively solves the problem that traditional optimization algorithms are prone to getting trapped in local optima and have slow convergence speed when dealing with high-dimensional, nonlinear, multi-constraint mixed integer programming problems.

[0013] (3) The final Pareto optimal solution set provides decision-makers with a rich set of trade-off options, supporting scientific decision-making based on different preferences (such as cost minimization or user satisfaction maximization), and enhancing the flexibility and applicability of the method. Attached Figure Description

[0014] Figure 1 This is a flowchart illustrating the steps of an embodiment of the electric vehicle charging station planning and pricing method based on existing charging stations according to the present invention.

[0015] Figure 2 This is a flowchart illustrating the steps of an embodiment of the electric vehicle charging station planning and pricing method based on existing charging stations, which uses an improved artificial hummingbird algorithm to optimize decision variables. Detailed Implementation

[0016] The specific embodiments of the present invention will be described in further detail below with reference to the accompanying drawings.

[0017] This invention provides a method for planning and pricing electric vehicle charging stations based on existing charging stations. The method includes the following steps: S1: Data Acquisition and Preprocessing Acquire traffic network data, power distribution network data, spatiotemporal distribution data of electric vehicle charging demand, location and capacity data of existing charging stations, and electricity price regulations for the target planning area, and perform data cleaning and preprocessing; specifically: S1.1: Traffic Network Data Acquisition Acquire road topology, traffic flow data, and key node (e.g., commercial areas, residential areas, transportation hubs) distribution information for the target planning area. Extract road network characteristic parameters, including road network density, capacity, and traffic congestion index. Establish a GIS-based traffic network model to calculate the travel distance and time cost from users to charging stations.

[0018] S1.2: Distribution Network Data Acquisition Collect distribution network topology parameters for the target planning area, including node numbers, branch connections, and line types. Obtain grid equipment parameters, including transformer capacity, line impedance (resistance R, reactance X), and node load baseline data. Extract grid operation constraint parameters, including node voltage upper and lower limits and line transmission capacity limits.

[0019] S1.3: Electric Vehicle Charging Demand Data Based on historical charging records and traffic survey data of the target planning area, a spatiotemporal distribution model of charging demand is established. Time-of-use electricity price limits for two typical days in summer / winter and spring / autumn are obtained, and user charging behavior parameters for different typical days (high-load days in summer / winter and regular days in spring / autumn) are statistically analyzed, including single charging amount, charging duration preference, and charging time window distribution.

[0020] S1.4: Existing charging station infrastructure data Collect the spatial coordinates, current capacity configuration, equipment model, and operational years of existing charging stations in the target planning area. Record the operational status data of each charging station, including utilization rate, failure rate, and service radius coverage. Assess the potential for upgrading existing sites, including expansion space and equipment upgrade needs.

[0021] S1.5: Electricity Price Regulations and Economic Parameters Collect time-of-use electricity pricing regulations (i.e., policy guidance) parameters for the target planning area, including peak-valley and off-peak periods, and upper and lower limits for electricity prices during each time period. Obtain investment economic parameters, including unit cost of charging equipment, land cost, and operation and maintenance cost coefficients. Set financial evaluation indicators, including discount rate, investment payback period requirements, and minimum rate of return threshold.

[0022] S1.6: Data Preprocessing Abnormal data in the data collected in S1.1-S1.5 are corrected, and outliers that significantly deviate from the normal range are removed. Missing data are filled using multiple imputation methods to ensure data integrity.

[0023] The above-described systematic data acquisition and preprocessing process provides a high-quality, standardized input data foundation for subsequent optimization modeling, ensuring the reliability and practicality of the optimization results.

[0024] S2: Determine decision variables Key decision variables for charging station j The planned capacity of charging stations And on the two typical days of summer and winter and spring and autumn hourly time-of-use electricity price and As a decision variable.

[0025] Based on the existing distribution of charging stations and the planning of new charging stations, the site selection planning of charging stations is divided into five cases: demolition of existing charging stations, reduction of capacity level of existing charging stations (capacity reduction), unchanged capacity of existing charging stations (capacity preservation), expansion of capacity level of existing charging stations (capacity expansion), and construction of new charging stations.

[0026] Introducing key decision variables Indicates charging station State changes: (1) In the formula: Indicates the planned charging station Does it exist? Indicates the planned charging station exist, Indicates the planned charging station It does not exist; Indicates the planned charging station Does it exist? Indicates the planned charging station exist, Indicates the planned charging station It does not exist; This represents the set of all charging stations. The range of values ​​is The specific meaning is as follows: Demolish existing charging stations; Upgrade existing charging stations, including reducing capacity, maintaining capacity, and expanding capacity; New charging stations will be built.

[0027] Simultaneously, capacity-related variables are introduced. Indicates charging station Capacity change: (2) In the formula: Indicates the plan to build a new charging station The capacity; Indicates the plan to build a new charging station The capacity.

[0028] State determination rules: (1) Demolish existing charging stations: , ,and ; (2) Reduction of existing charging station capacity: and ; (3) Existing charging station capacity guarantee: and ; (4) Expansion of existing charging stations: and ; (5) Construction of new charging stations: , and .

[0029] S3: Obtain the total system cost based on the data in S1 and the decision variables in S2. With user satisfaction The extreme value.

[0030] S3.1: Integrate time-of-use electricity prices for peak load days in summer and winter, and regular days in spring and autumn with key decision variables for charging stations. Post-planning capacity As a decision variable, to minimize the total system cost To achieve the goal, optimize the decision variables: (3) In formula (3): The total system cost, The investment cost mainly includes the investment cost of building a new charging station and the demolition cost of an existing station. The total operation and maintenance cost during the planning period. For state transition cost, Cost of network loss.

[0031] Investment costs : (4) (5) (6) In the formula: The investment cost for building new charging stations, The cost of dismantling the existing station, Fixed construction costs (land, infrastructure). Fixed construction costs, including land and infrastructure costs, This is a variable cost factor, including the cost of charging equipment. This is the scale economy index (typically 0.6-0.8). The discount rate is used to convert future costs into present value. For the planning period, This is the unit capacity demolition cost coefficient. , , As an indicator function, its specific meaning is: when the condition inside the parentheses is "true", When the condition is "false", . when conditions At the time of its establishment, ; when condition When not valid, . when conditions At the time of its establishment, ; when condition When not valid, . when conditions At the time of its establishment, ; when condition When not valid, .

[0032] Operation and maintenance costs : (7) In the formula: Fixed operation and maintenance costs refer to the fixed expenses that must be paid annually regardless of the charging station's utilization rate. The variable operation and maintenance cost coefficient refers to the unit cost directly related to the charging volume. The discount rate is used to convert future costs into present value. For the planning period, For charging stations In the The total annual charging amount (in kilowatt-hours) is calculated using user behavior simulation (Logit model) and load distribution.

[0033] State transition cost : (8) (9) (10) (11) In the formula: To cover expansion costs, For the benefit of capacity reduction, To ensure capacity and maintenance costs, , , It is an indicator function, and its specific meaning is: when the condition inside the parentheses is "true", When the condition is "false", . Cost per unit of expansion Ensure that the positive portion of the capacity change is taken, i.e., the size of the expanded capacity. The difficulty coefficient for capacity expansion (increases with the expansion ratio). For equipment residual value rate, Ensure that the negative portion of the capacity change is taken and converted to a positive number, i.e., the amount of capacity reduction. The demolition loss coefficient, Annual maintenance cost per unit capacity This refers to the equipment aging factor. This refers to the number of years the equipment has been in use.

[0034] Network loss cost Throughout the planning period The present value of the total economic cost incurred by the power distribution system due to active power losses: (12) In the formula: This represents the weighting of typical summer and winter days. It indicates the proportion of days in a year that exhibit "summer and winter" characteristics. The weighting of typical days in spring and autumn represents the proportion of days in a year that are characteristic of "spring and autumn". Typical summer and winter days on the 1st The hourly electricity purchase price (yuan / kWh) is subject to higher peak-valley electricity prices during summer and winter. The typical day of the Spring and Autumn Period is on the 1st The hourly electricity purchase price (RMB / kWh) can be adjusted, and a more moderate electricity pricing strategy can be implemented in spring and autumn. For the first Typical summer and winter days of the year The total active power loss of the distribution network in a given hour is obtained through power flow calculation. For the first Typical Day of the Spring and Autumn of the Year The total active power loss of the distribution network in a given hour is obtained through power flow calculation.

[0035] S3.2: Integrate time-of-use electricity prices for peak load days in summer and winter, and regular days in spring and autumn with key decision variables for charging stations. Post-planning capacity As a decision variable, to maximize user satisfaction The goal is to optimize the decision variables: (13) (14) (15) In the formula: For users, For user collection, Typical daily users in summer and winter The demand for charging will increase in summer due to air conditioning and in winter due to heating. Typical Daily Users in Spring and Autumn The charging needs. and Estimates are made using historical charging data, traffic flow data, and electric vehicle penetration prediction models, typically divided by region (such as residential area or business district) and time period. , These are typical days in summer and winter, and typical days in spring and autumn, for users. The overall effect. This represents the weighting of typical summer and winter days. It indicates the proportion of days in a year that exhibit "summer and winter" characteristics. The weighting of typical days in spring and autumn represents the proportion of days in a year that are characteristic of "spring and autumn". and The settings are based on local climate characteristics and load characteristics. , users respectively Select stations on typical summer and winter days and typical spring and autumn days. The probability of this is calculated using a multivariate Logit behavioral model, and its value depends on the user's comparison of the "utility" of different charging stations. , users respectively The expected queuing time at station j on typical summer / winter and spring / autumn days, in minutes (min). On peak load days (summer and winter), queuing time may be as long as 30-60 minutes; on normal days, it may be 5-15 minutes. The queuing theory model is used to calculate the service capacity of the charging station (number of charging piles, power) and the predicted arrival rate. , Charging stations are designated for different types of dates (summer / winter / spring / autumn). In the The hourly time-of-use electricity price is implemented with higher peak-valley prices on typical summer and winter days and more moderate pricing strategies on typical spring and autumn days. The unit is yuan / kWh, and the upper limit of the value range is usually limited by the prescribed guidance price, such as 2.0 yuan / kWh, while the lower limit is the cost price, such as 0.8 yuan / kWh. For users Arrival The distance needs to be calculated using a Geographic Information System (GIS) to determine the actual driving distance of the road network. , , The weighting coefficients for distance, waiting time, and electricity price represent the relative importance of the three core attributes (distance, time, and price), determined using the Analytic Hierarchy Process (AHP) combined with expert scoring. A judgment matrix is ​​constructed by comparing the relative importance of "distance," "waiting time," and "price," and the weights are then calculated. , , The sensitivity coefficients for distance, waiting time, and price are respectively, and model calibration is required using historical selection data. By collecting actual user selection data among charging stations with different distances, prices, and waiting times, the maximum likelihood estimation method is used to infer the values ​​of the corresponding coefficients. The larger the sensitivity coefficient value, the more sensitive the user is to that factor.

[0036] S3.3: Set constraints (1) State constraints State mutual exclusion constraint: (16) Ensure for any charging station In the "demolition" ,"renew" and "newly built" Of these three decisions, only one can be chosen.

[0037] State feasibility constraints: (17) Domain constraints explicitly define the decision variables. The range of values ​​for can only be a set. One of the values ​​in.

[0038] State transition constraints: (18) Capacity variation constraints: (19) In the formula: This represents the minimum allowable change in capacity (which may be negative, indicating a reduction in capacity). This represents the maximum allowable capacity change (indicating capacity expansion). This represents the change in capacity.

[0039] (2) Power grid security constraints AC power flow balance constraint: The power injected into any node must equal the power flowing out, i.e., power conservation. Active power balance constraint: (20) Reactive power balance constraints: (twenty one) In the formula: t represents the first... Hours (e.g., 24 hours in a day) It is the collection of all electrical connection points in a power distribution system. This represents the set of all branches (lines) in the power grid. In the first Hours, injected from power plants or upstream grid nodes The active power. In the first Hour, node The active power consumed by existing loads (such as residents and factories), In the first Hour, node The active power consumed at electric vehicle charging stations. It corresponds to active power in meaning, but the unit is reactive power (used to maintain grid voltage stability). For each node in the set , For nodes Connected nodes, In the first Hourly Node voltage amplitude, In the first Hours and nodes Connected nodes voltage amplitude, For connecting nodes and nodes The conductance of a circuit is a parameter that describes the resistive characteristics of the circuit. For connecting nodes and nodes The susceptance of a line is a parameter that describes the reactance characteristics of the line. In the first Hour, node With nodes The voltage phase angle difference between them ( ).

[0040] Node voltage constraints: The voltage of each node must be kept within a safe range at all times. This is a basic requirement for ensuring power quality and equipment safety.

[0041] (twenty two) In the formula: In the first Hour, node voltage amplitude, For nodes The minimum permissible voltage limit; too low a voltage will cause user equipment to malfunction. For nodes The maximum permissible voltage limit; excessive voltage can damage electrical equipment.

[0042] Line capacity constraints: (twenty three) In the formula: In the first Hours, flowing through the connection node and nodes The apparent power of the line is the vector sum of active and reactive power. Apparent power The modulus, For the line To the line The maximum apparent power that can be safely transmitted (thermal stability limit) will cause the line to overheat and risk failure if this value is exceeded. This indicates that for each connected node in the set and The route, In the first Hours, flowing through the line To the line current The conjugate of complex numbers.

[0043] (3) Charging station operation constraints: Capacity limitation constraints: If the charging station exist( If it does not exist, then its capacity must be within the allowable range; if it does not exist ( If ), then the capacity is forced to 0.

[0044] (twenty four) In the formula: , For charging stations The minimum and maximum capacity that can be configured.

[0045] Service capacity constraints: charging stations In the The total charging energy provided within one hour must not exceed its effective capacity limit: (25) In the formula: For users Choose a charging station The probability, For users The charging needs, Energy per charge, For capacity utilization, The duration is in hours.

[0046] Charging power constraints: charging stations In the The total charging power per hour is obtained by averaging the energy charged by all users at the station, directly linking users' charging choices to the actual physical load of the power grid.

[0047] (26) In the formula: For charging stations In the Total active charging power per hour For users In the The percentage of users' hourly charging needs (i.e., the percentage of users' hourly charging needs) In the The percentage of hourly charging energy demand relative to the total daily charging energy demand.

[0048] (4) User behavior constraints: Demand allocation constraint: On any given day, each user The charging demand must be fully allocated to each charging station, with a total allocation ratio of 100%.

[0049] (27) User selection probability constraint (Logit model): Defines the method for calculating the user selection probability. The probability that a user chooses a certain station is equal to the proportion of that station's utility index to the sum of the utility indices of all stations.

[0050] (28) (29) (30) (31) (32) In the formula: For users, For user collection, Typical daily users in summer and winter The demand for charging will increase in summer due to air conditioning and in winter due to heating. Typical Daily Users in Spring and Autumn The charging needs. , These are typical days in summer and winter, and typical days in spring and autumn, for users. The overall effect. The total number of charging stations (including existing stations and candidate stations). Two pairs of users at the typical day charging stations in spring and autumn. The utility; , users respectively Select stations on typical summer and winter days and typical spring and autumn days. The probability of. , users respectively Expected queuing time at station j on typical summer / winter days and typical spring / autumn days (queuing may be longer on peak load days). , Charging stations are designated for different types of dates (summer / winter / spring / autumn). In the Hourly time-of-use pricing can be implemented with higher peak-valley pricing on typical summer and winter days, and with a more moderate pricing strategy on typical spring and autumn days. For users Arrival distance, , , These are the weighting coefficients for distance, waiting time, and electricity price, respectively. , , These are the sensitivity coefficients for distance, waiting time, and price, respectively.

[0051] (5) Economic constraints: Total investment budget constraint: The total cost of planning and upgrading charging stations must not exceed the total project budget to ensure that the plan is economically affordable.

[0052] (33) In the formula: This represents the maximum allowed total investment budget for the project.

[0053] Investment payback period constraint: The present value of the net income of the project within the specified payback period must reach a certain percentage of the investment cost to ensure that the investment has reasonable profitability.

[0054] (34) In the formula: For the required investment payback period, For the project during the investment payback period Annual operating revenue (mainly from charging service fees). For the project during the investment payback period Annual operating and maintenance costs For the discount rate, The minimum return on investment coefficient requires that the project recover at least a certain percentage of the investment within the payback period.

[0055] (6) Service coverage constraints: The total service range of all charging stations must meet or exceed the prescribed minimum standards to ensure that there are no service blind spots and achieve equalization of basic public services.

[0056] (35) In the formula: the distance from any user to their nearest charging station must not exceed [a certain distance]. To ensure full coverage For users To the charging station distance, To specify the maximum allowed service distance.

[0057] (7) Variable type constraints Binary constraints on state variables: (36) State change decision constraints: (37) Non-negativity constraint on capacity: (38) Time-of-use electricity pricing upper and lower limits (typical summer / winter days, typical spring / autumn days): (39) , The upper and lower limits of time-of-use electricity pricing are determined by the regulations of the target planning area, and by default, the upper and lower limits of electricity pricing remain stable during the planning period.

[0058] S3.4: Under the constraints in S3.3, minimize the total system cost respectively. And maximize user satisfaction The time-of-use electricity prices on peak load days in summer and winter, and on regular days in spring and autumn, and the key decision variables of charging stations. Post-planning capacity To find the optimal variables, the total system cost is obtained. maximum value and minimum value and user satisfaction maximum value and minimum value The above optimization process can be iteratively calculated using optimization algorithms such as genetic algorithms. By performing two single-objective optimization processes, the maximum and minimum values ​​of the corresponding objective can be obtained.

[0059] S4: Optimize decision variables using an improved artificial hummingbird algorithm. An improved chaotic non-uniform mutation artificial hummingbird algorithm is applied to optimize decision variables. This algorithm enhances population diversity through chaotic initialization and introduces an adaptive non-uniform mutation strategy to balance global exploration and local exploitation capabilities, thus obtaining an optimized solution set for the decision variables. The specific process is as follows: S4.1: Parameter initialization settings; setting population size (Number of hummingbirds), maximum number of iterations ;Set state decision Upper and lower limits, planned capacity Upper and lower limits, charging stations On the two typical days of summer and winter and spring and autumn hourly time-of-use electricity price and The upper and lower limits.

[0060] For decision variables, the upper and lower bounds are defined as follows: for state variables... : , This range is slightly wider than the actual values ​​{-1, 0, 1} to ensure that the initial population has an equal chance of generating all three states during subsequent integerization operations. This applies to the planned capacity. : , ,in This represents the maximum permissible capacity. For typical daily electricity prices... and : , , , To define the permissible range of electricity prices.

[0061] S4.2: Chaotic Mapping Generates the Initial Population A hybrid encoding strategy is adopted, the core of which is to design a solution vector (i.e., the position of a "hummingbird") that can completely represent a specific planning scheme. Integer variables (site state variables) and continuous variables (capacity configuration, time-of-use pricing) are uniformly encoded in a single solution vector, facilitating unified processing by the algorithm. The encoding structure is as follows: Assuming the planning has... The planning period is for [number] charging stations (including existing and candidate stations). Year.

[0062] Each hummingbird individual (solution vector) encodes all decision variables, including site state variables, capacity configuration, and the time-of-use electricity price structure for two typical days in summer / winter and spring / autumn, as follows: (40) charging station for The total number of variables coded for each charging station is: (41) A solution vector Dimensions for: (42) In the formula: Population size (number of hummingbirds). State decision variables, For the planned capacity, and Charging stations On the two typical days of summer and winter and spring and autumn, on the 1st The hourly time-of-use electricity price, if the total number of charging stations is planned. Then the total dimension of the solution vector .

[0063] Use the Logistic chaotic map to generate chaotic sequences. At this point, the system is in a completely chaotic state, and the generated sequence possesses ergodicity and pseudo-randomness, providing a uniformly distributed initial point for population initialization and avoiding the population aggregation problem that may occur with traditional random initialization. The purpose of this step is to generate a uniformly distributed and highly diverse initial population. Based on the Logistic mapping formula, a chaotic sequence is generated: (43) In the formula: It is the chaotic value generated in the m-th iteration, and its value ranges between (0,1). According to The calculated next chaotic sequence value, The control parameter for the Logistic chaotic mapping (usually 4), when At that time, the system is in a completely chaotic state, and the generated sequence has good traversal and randomness.

[0064] According to formula (43), perform no less than N iterations to generate a chaotic sequence; then, extract an unused chaotic value from the generated chaotic sequence in sequence. Chaos value Mapping to individuals through linear transformation The The actual range of values ​​for each decision variable ,get : (44) In the formula: For the first The first individual (hummingbird) The values ​​of each decision variable at the initial time. For the first The lower bound of each decision variable. For the first Upper bounds of the decision variables: individual The decision variables are all initialized according to formula (44) to obtain the individual Initialization solution vector : (45) Perform on each individual in the population The initialization process yields the initial population.

[0065] S4.3: Calculate the initial population fitness First, each individual in the initial population is decoded. Then, the vector values ​​of each individual are used for simulation calculations to obtain the total system cost for each individual. (Based on Formula 3) and user satisfaction (Based on the value of Formula 13), the overall fitness of each individual is then calculated. : (46) (47) In the formula: For weighting coefficients, when When the value approaches 1, optimization focuses more on cost reduction; when... When the value is close to 0, optimization focuses more on improving satisfaction, which is the set fixed value; and These are the total system cost The maximum and minimum values, and These are user satisfaction The maximum and minimum values ​​are obtained from step S3.4. It is set to 10 6 -10 8 A positive penalty coefficient of orders of magnitude; the total system cost for charging station planning in a city area. The typical order of magnitude is likely 106 to 108 yuan (millions to hundreds of millions), and user satisfaction... It is a normalized value between 0 and 1. In this case, the typical range of the penalty coefficient is 10. 6 -10 8 This range is sufficient to ensure that, when optimizing costs on the order of millions, any minor constraint violation will lead to a significant deterioration in fitness. The total constraint violation degree is determined by the number of constraints violated by the solution. Penalty items It will drastically increase the fitness value. This guides the algorithm to abandon infeasible solutions and turn to search for feasible solutions in the region.

[0066] The formula for calculating the total constraint violation rate (CV) is as follows: (48) In the formula: This refers to the degree or magnitude of the violation of inequality constraints. This indicates that the constraint is satisfied and the violation is 0; if This indicates that the constraint has been violated; the amount of violation is... (the positive value itself); the deviation of the equality constraint. It refers to the absolute difference between the values ​​on the left and right sides of the equation constraint. and The weights of each constraint.

[0067] Decoding each individual in the population specifically refers to: decoding the state variables. Forced rounding and boundary truncation are performed, and state consistency correction is applied.

[0068] For each individual in the population Variables representing state decisions Perform forced rounding and boundary truncation: (49) In the formula: This is a rounding function that ensures the final result is an integer. It is the discrete integer state value obtained after decoding, which strictly belongs to the set {-1, 0, 1}.

[0069] Based on the discretized Modify the relevant variables to satisfy the logical rules: Rule 1: If (Demolition decision), then forced (The planned capacity is 0).

[0070] Rule 2: If (New decision) and Then set (minimum capacity).

[0071] Rule 3: If (Updated decision) but (There was no station at this location before the planning), this is an illegal operation, please correct it to: (New).

[0072] Simulation calculations are performed using the vector values ​​of each individual entity to obtain the total system cost for each individual entity. and user satisfaction The specific process of obtaining the value is as follows: Simulate a typical summer and winter day: using Electricity pricing, taking into account user needs in summer and winter. (Usually higher), performing 24-hour user behavior simulation (Logit model) and power grid flow calculation; simulating typical spring and autumn days: using This electricity pricing system takes into account the user demand of Spring and Autumn. Perform the same simulation to obtain the results for each charging station. In each time period The predicted load is substituted into the distribution network model, and the power flow is calculated to obtain the physical state of the power grid, including the voltage of each node, the power flow of each branch, and the total network loss.

[0073] Based on the simulation results, the costs (investment, operation and maintenance, network loss, user costs, etc., and user satisfaction) for two typical days in summer / winter and spring / autumn are calculated. Then, the weights of the typical days are used. and We then weight the results, scale them up to the whole year, and then extend them to each year of the planning period to finally obtain the objective function. and The value of .

[0074] Calculate performance values ​​for each typical day: After the simulation runs, calculate the total system cost and user satisfaction for each typical day.

[0075] For typical days in summer and winter:

[0076] For typical days in spring and autumn:

[0077] Weighted calculation of annual total performance value: The performance values ​​of different typical days are weighted according to their respective weights to obtain the final annual total performance value, which is then scaled up to the entire planning period.

[0078] Total system cost : .

[0079] User satisfaction : .

[0080] S4.4: Population Iterative Update Based on the fitness value of each individual obtained in step S4.3, the individual with the smallest fitness value is selected as the current global historical best solution, and the population is iteratively updated.

[0081] Each individual in the population executes guided flight and territory flight strategy updates with a certain probability. The update results are first decoded, then a temporary solution for each individual is obtained through greedy selection, and finally the final update vector for each individual is obtained through non-uniform mutation. The population achieves one iteration update.

[0082] The flight guidance strategy update process is as follows: Each hummingbird With a certain probability Follow the lead hummingbird in the population (the individual with the best fitness at present, denoted as...) Update the position using the following formula: (50) In the formula: This represents the current iteration number. , It is a random vector. and For the first Two different hummingbirds are randomly selected from the population in the next iteration. As a chaotic perturbation factor, it enhances global exploration capabilities. It is a vector in which each element represents the upper limit of the allowed values ​​of each decision variable in the optimization problem. It is also a vector, where each element represents the lower bound of the allowed values ​​for each decision variable in the optimization problem.

[0083] The process for updating the flight strategy in the aforementioned area is as follows: With probability Execution simulates a hummingbird's fine-grained search within a local area: If guided flight is not executed, the hummingbird searches locally within its own territory, simulating the behavior of guarding a food source. The position update formula is: (51) In the formula: It is a random number. This operation, which randomly selects another hummingbird from the population, enhances local exploitation capabilities and refines the neighborhood search of the current solution.

[0084] The specific process of greedy selection is as follows: For the The individual, in the iteration to the _th At that time, two alternative new schemes were generated through guided flight and domain flight strategies. and Decode these two schemes and then calculate their fitness values. And select the option with the smaller fitness value as its next generation. temporary new location : (52) In the formula: This indicates that the solution is a temporary result selected in the current iteration. It represents the algorithm for individual... Generated for use in the next generation temporary solution, This indicates that the candidate solution was generated through a guided flight strategy that tends to learn from the global optimum. This indicates that the candidate solution was generated using a domain flight strategy, which tends to perform a local search in the vicinity of the current location; , express , Corresponding to the decoded result, The fitness function is a function that measures the fitness of a given solution. The smaller the function value, the better the solution.

[0085] The specific process of obtaining the final update vector for each individual through non-uniform mutation is as follows: The mutation probability of each individual decreases exponentially with the number of iterations: (53) In the formula: In the first The mutation probability of the current iteration. The initial mutation probability ranges from 0.3 to 0.5. The decay coefficient controls the rate at which the probability decays, and its value ranges from 4 to 6.

[0086] Temporary solution for individual n For each decision variable, a probability-based decision is made regarding whether to mutate, using an adaptive step size. For non-uniform mutations of continuous variables (such as capacity and electricity price), a process is first generated... random numbers within the range ,like Then, perform mutation on that variable. Then calculate the non-uniform variable length: (54) In the formula: The current variable value to its boundary ( or The distance of ) for Random numbers within a range For shape parameters (usually) ), controlling the step size decay pattern.

[0087] Finally, based on the non-uniform variation in asynchronous length, the continuous variable of the individual is randomly selected to mutate upwards or downwards: Upward mutation: (55) Downward mutation: (56) For continuous variables, ensure that the mutated value remains within the allowable range: (57) For the discrete variables (state decision variables) of an individual, a dedicated mutation discrete state transition for integer variables is used; first, generate... random numbers within the range ,like If the variable is mutated, then a mutation is performed on it. Then, a random choice is made from two valid discrete states other than the current value. For example, if the current value is... The new value could be: or .

[0088] (58) Based on the discretized Modify relevant variables to satisfy logical rules: Rule 1: If (Demolition decision), then forced (The planned capacity is 0).

[0089] Rule 2: If (New decision) and Then set (minimum capacity).

[0090] Rule 3: If (Updated decision) but (There was no station at this location before the planning), this is an illegal operation, please correct it to: (New).

[0091] S4.5: Knowledge Transfer Flight Updates Population For each individual in the population that performs one iteration update in S4.4, calculate the fitness of each individual in the population according to the method in S4.3, and perform iterative updates of the population according to the method in S4.4, every certain number of generations (as an example, the generation interval is...). The algorithm performs knowledge transfer flights to update the population, eliminates inferior individuals, and introduces new random explorations to maintain population diversity and avoid premature convergence.

[0092] The specific process of knowledge transfer and population renewal is as follows: Setting the first The +1st iteration requires performing knowledge transfer flight to update the population, when the... When +1 iterations are completed, select individuals from all individuals in the current population whose fitness function is optimal. The individual with the smallest value is defined as the optimal elite solution for the current generation. and make the fitness function The individual with the largest value is defined as the optimal elite solution for the current generation and the worst-case global solution. : (59) (60) In the formula: In the first The globally optimal elite solution found in +1 generation (iteration number). In the first The worst-case solution found in +1 generation (number of iterations) This represents the parameter that makes the function achieve its minimum value. This represents the parameter that makes the function reach its maximum value. The fitness function is used to evaluate the quality of the solution. In the first +1 generation population The solution vector for each individual.

[0093] Then, explore and perturb the vicinity of the elite individual to generate new individuals: (61) In the formula: For random disturbance factors, To inject randomness into migration, The search space span for decision variables is determined to ensure that the perturbation scale is reasonable.

[0094] Immediately after the migration flight, the newborn individuals The integer decision variables in the population are discretized and state consistency corrections are performed to ensure the feasibility of the new solution. Then, the worst individual in the original population is replaced with the newly generated individual to complete the knowledge transfer. (62) In the formula: For the population obtained through knowledge transfer flight updates, For the process The population obtained after +1 iterations of updates. "Indicates merging into a newly generated or selected high-quality individual" “ "Indicates from the past" In the population obtained after +1 iterations, remove (representing set difference) individuals marked as inferior. .

[0095] S4.6: Iteration Termination The updated population obtained through knowledge transfer flight in S4.5 is used as the initial population for the next iteration. The process of calculating the population fitness in S4.3 is repeated, as is the process of iterative population update in S4.4. Every certain number of generations, the process of updating the population through knowledge transfer flight in S4.5 is performed, and then the processes in S4.3 and S4.4 are repeated. This process is continued until the maximum number of iterations is reached. Iterative updates stop; the population has passed... After several iterations, the final optimized population individuals are obtained, which is the optimized solution set of the decision variables.

[0096] S5: Select the Pareto optimal solution set from the optimized solution set of the decision variables in S4; then, according to the decision requirements of the target planning area, select the final solution of the decision variables from the Pareto optimal solution set, which is the final electric vehicle charging station planning and pricing strategy.

[0097] The optimal solution set of decision variables in S4 includes the final state of each site (new construction / expansion / capacity preservation / capacity reduction / demolition) and capacity configuration scheme, as well as the time-of-use electricity pricing strategy and time-of-use electricity pricing curve of all charging stations. The Pareto optimal solution set is extracted from the optimal solution set of the decision variables in S4 using the fast non-dominated sorting algorithm: ,untie Dominant Solution If and only if both of the following conditions are met: Condition one: (63) Condition two: (64) In the formula: and Decision variables Two different solution vectors. express The total system cost (minimization objective). express User satisfaction (maximization target); The statement that solution 1 dominates solution 2 means that solution 1 is superior to solution 2 in every aspect. If solution 1 is no worse than solution 2 in terms of total system cost and user satisfaction, and at least one of these two aspects is significantly better, then... This is the desired governing solution.

[0098] All dominant solutions selected from the optimal solution set of the decision variables in S4 constitute the Pareto optimal solution set. The crowding degree of each Pareto optimal solution is calculated: (65) In the formula: To solve The crowding level is the value of the solution. The larger the value, the more open the solution is. The higher the priority is during the selection process, thus ensuring the diversity of the solution set. Let be a Pareto optimal solution for the congestion degree to be calculated. Representing the The objective function is the total system cost. Or user satisfaction ; and To sort by the value of a certain objective function, the solutions are immediately adjacent. The previous and next solutions. , The objective function for the Pareto optimal solution set The maximum and minimum values.

[0099] Based on the total system cost of each Pareto optimal solution He Zhe user satisfaction The total system cost The horizontal axis represents user satisfaction. Using the y-axis as the vertical axis, plot a two-dimensional scatter plot of decision references. Simultaneously, using the congestion level of each Pareto optimal solution as the vertical axis, plot the corresponding total system cost. He Zhe user satisfaction The x-axis represents the total system cost. - Crowding curve, user satisfaction - Crowding curve.

[0100] Based on the decision-making requirements of the target planning area, select the final electric vehicle charging station planning and pricing strategy: 1) When the decision-making requirement for the target planning area is based on the total system cost To minimize it, we start from the total system cost. - Select the congestion curve that corresponds to the highest congestion level and the highest total system cost. The minimum Pareto optimal solution is the final electric vehicle charging station planning and pricing strategy.

[0101] 2) When the decision-making requirement for the target planning area is user satisfaction To maximize, consider user satisfaction. - Select the congestion level from the congestion curve that corresponds to the highest user satisfaction. The largest Pareto optimal solution is the final electric vehicle charging station planning and pricing strategy.

[0102] 3) When the decision requirement for the target planning area is to balance the total system cost With user satisfaction At that time, calculate the cost of improving marginal satisfaction. The Pareto optimal solution corresponding to the maximum value of this ratio is the final electric vehicle charging station planning and pricing strategy. The specific calculation process is as follows: First, each Pareto optimal solution is calculated according to the total system cost. Sort the solutions from smallest to largest. If there are solutions with the same total system cost, consider their impact on user satisfaction. In ascending order, calculate the increment between adjacent solutions last. The solution that maximizes the increment is the final electric vehicle charging station planning and pricing strategy.

[0103] Each solution includes all decision outcomes: the final state of each charging station (new construction / expansion / capacity preservation / capacity reduction / demolition), the capacity configuration of each charging station, and all time-of-use pricing strategies.

[0104] Any aspects not covered in this invention are applicable to existing technologies.

Claims

1. A method for planning and pricing electric vehicle charging stations based on existing charging stations, characterized in that, The method includes the following steps: S1: Data Acquisition and Preprocessing Acquire traffic network data, power distribution network data, spatiotemporal distribution data of electric vehicle charging demand, location and capacity data of existing charging stations, and electricity price regulations for the target planning area, and perform data cleaning and preprocessing. S2: Determine decision variables Key decision variables for charging station j The planned capacity of charging stations And on the two typical days of summer and winter and spring and autumn hourly time-of-use electricity price and As a decision variable; Demolish existing charging stations; Upgrade existing charging stations, including reducing capacity, maintaining capacity, and expanding capacity; New charging stations will be built. S3: Obtain the total system cost based on the data in S1 and the decision variables in S2. With user satisfaction The extreme values; S4: Optimize decision variables using an improved artificial hummingbird algorithm. An improved chaotic non-uniform mutation artificial hummingbird algorithm is applied to optimize decision variables. This algorithm improves population diversity through chaotic initialization and introduces an adaptive non-uniform mutation strategy to balance global exploration and local exploitation capabilities, thereby obtaining an optimized solution set for decision variables. S5: Select the Pareto optimal solution set from the optimized solution set of the decision variables in S4; then, according to the decision requirements of the target planning area, select the final solution of the decision variables from the Pareto optimal solution set, which is the final electric vehicle charging station planning and pricing strategy.

2. The method for planning and pricing electric vehicle charging stations based on existing charging stations according to claim 1, characterized in that, The specific process of S1 is as follows: S1.1: Traffic Network Data Acquisition Acquire road topology, traffic flow data, and key node distribution information for the target planning area; extract road network characteristic parameters, including road network density, traffic capacity, and traffic congestion index; and establish a GIS-based traffic network model to calculate the travel distance and time cost from users to charging stations. S1.2: Distribution Network Data Acquisition Collect distribution network topology parameters for the target planning area, including node number, branch connection relationship, and line type; obtain power grid equipment parameters, including transformer capacity, line impedance, and node load baseline data; extract power grid operation constraint parameters, including node voltage upper and lower limits and line transmission capacity limits; S1.3: Electric Vehicle Charging Demand Data Based on historical charging records and traffic survey data of the target planning area, a spatiotemporal distribution model of charging demand is established; the time-of-use electricity price limits for two typical days in summer and winter and spring and autumn are obtained, and user charging behavior parameters for different typical days are statistically analyzed, including single charging amount, charging duration preference, and charging time window distribution. S1.4: Existing charging station infrastructure data Collect the spatial coordinates, current capacity configuration, equipment model, and years of operation of existing charging stations in the target planning area; record the operating status data of each charging station, including utilization rate, failure rate, and service radius coverage. S1.5: Electricity Price Regulations and Economic Parameters Collect time-of-use electricity pricing parameters for the target planning area, including the division of peak, valley, and normal periods, and the upper and lower limits of electricity prices for each time period; obtain investment economic parameters, including the unit cost of charging equipment, land cost, and operation and maintenance cost coefficient; Set financial evaluation indicators, including discount rate, investment payback period requirement, and minimum rate of return threshold; S1.6: Data Preprocessing Abnormal data in the data collected in S1.1-S1.5 are corrected and outliers are removed; missing data are filled using multiple interpolation methods.

3. The method for planning and pricing electric vehicle charging stations based on existing charging stations according to claim 2, characterized in that, In S2, key decision variables Indicates charging station State changes: （1） In the formula: Indicates the planned charging station Does it exist? Indicates the planned charging station exist, Indicates the planned charging station It does not exist; Indicates the planned charging station Does it exist? Indicates the planned charging station exist, Indicates the planned charging station It does not exist; This represents the set of all charging stations; The range of values ​​is The specific meaning is as follows: Demolish existing charging stations; Upgrade existing charging stations, including reducing capacity, maintaining capacity, and expanding capacity; New charging stations will be built. Simultaneously, capacity-related variables are introduced. Indicates charging station Capacity change: （2） In the formula: Indicates the plan to build a new charging station The capacity; Indicates the plan to build a new charging station The capacity; State determination rules: (1) Demolish existing charging stations: , ,and ; (2) Reduce the capacity of existing charging stations: and ; (3) Capacity maintenance of existing charging stations: and ; (4) Expansion of existing charging stations: and ; (5) Construction of new charging stations: , and .

4. The method for planning and pricing electric vehicle charging stations based on existing charging stations according to claim 3, characterized in that, The specific process of S3 is as follows: S3.1: Integrate time-of-use electricity prices for peak load days in summer and winter, and regular days in spring and autumn with key decision variables for charging stations. Post-planning capacity As a decision variable, to minimize the total system cost To achieve the objective, optimize the decision variables: （3） In formula (3): The total system cost, The investment cost mainly includes the investment cost of building a new charging station and the demolition cost of an existing station. The total operation and maintenance cost during the planning period. For state transition cost, For network loss costs; Investment costs : （4） （5） （6） In the formula: The investment cost for building new charging stations, The cost of dismantling the existing station, To fix construction costs, Fixed construction costs, including land and infrastructure costs, This is a variable cost factor, including the cost of charging equipment; This is an economy of scale index. The discount rate is used to convert future costs into present value. For the planning period, This is the unit capacity demolition cost coefficient. , , As an indicator function, its specific meaning is: when the condition inside the parentheses is "true", When the condition is "false", ; when condition At the time of its establishment, ; when condition When not valid, ; when condition At the time of its establishment, ; when condition When not valid, ; when condition At the time of its establishment, ; when condition When not valid, ; Operation and maintenance costs : （7） In the formula: Fixed operation and maintenance costs refer to the fixed expenses that must be paid annually regardless of the charging station's utilization rate. The variable operation and maintenance cost coefficient refers to the unit cost directly related to the charging volume. The discount rate is used to convert future costs into present value. For the planning period, For charging stations In the The total annual charging amount, in kilowatt-hours, is calculated through user behavior simulation and load allocation. State transition cost : （8） （9） （10） （11） In the formula: To cover expansion costs, For the benefit of capacity reduction, To ensure capacity and maintenance costs, , , It is an indicator function, and its specific meaning is: when the condition inside the parentheses is "true", When the condition is "false", ; Cost per unit of expansion Ensure that the positive portion of the capacity change is taken, i.e., the size of the expanded capacity. To increase the difficulty of expansion, For equipment residual value rate, Ensure that the negative portion of the capacity change is taken and converted to a positive number, i.e., the amount of capacity reduction. The demolition loss coefficient, Annual maintenance cost per unit capacity The aging factor of the equipment. The equipment's service life; Network loss cost Throughout the planning period The present value of the total economic cost incurred by the power distribution system due to active power losses: （12） In the formula: The weighting of typical summer and winter days; representing the proportion of days in a year that exhibit "summer and winter" characteristics. The weighting of typical days in spring and autumn represents the proportion of days in a year that are characteristic of "spring and autumn". Typical summer and winter days on the 1st The hourly electricity purchase price, in yuan / kWh; The typical day of the Spring and Autumn Period is on the 1st The hourly electricity purchase price, in yuan / kWh; For the first Typical summer and winter days of the year The total active power loss of the distribution network in a given hour is obtained through power flow calculation; For the first Typical Day of the Spring and Autumn of the Year The total active power loss of the distribution network in a given hour is obtained through power flow calculation; S3.2: Integrate time-of-use electricity prices for peak load days in summer and winter, and regular days in spring and autumn with key decision variables for charging stations. Post-planning capacity As a decision variable, to maximize user satisfaction The goal is to optimize the decision variables: （13） （14） （15） In the formula: For users, For user collection, Typical daily users in summer and winter The charging needs, Typical Daily Users in Spring and Autumn The charging needs; and Estimates are made using historical charging data, traffic flow data, and electric vehicle penetration rate prediction models, and are divided by region and time period. , These are typical days in summer and winter, and typical days in spring and autumn, for users. The overall effect; The weighting of typical summer and winter days; representing the proportion of days in a year that exhibit "summer and winter" characteristics. The weighting of typical days in spring and autumn represents the proportion of days in a year that are characteristic of "spring and autumn". and Set according to local climate characteristics and load characteristics; , users respectively Select stations on typical summer and winter days and typical spring and autumn days. The probability of; , users respectively The expected queuing time at station j on typical summer / winter days and typical spring / autumn days, in minutes; , Charging stations are set up for different types of dates. In the Time-of-use electricity price per hour, in yuan / kWh; For users Arrival The distance; , , These are the weighting coefficients for distance, waiting time, and electricity price, respectively. , , These are the sensitivity coefficients for distance, waiting time, and price, respectively. S3.3: Set constraints (1) State constraints Mutual exclusion constraint: （16） Ensure for any charging station In "demolition" ,"renew" and "newly built" Of these three decisions, only one can be chosen; State feasibility constraints: （17） Domain constraints explicitly define the decision variables. The range of values ​​for can only be a set. A value in; State transition constraints: （18） Capacity variation constraints: （19） In the formula: The minimum allowable capacity change, The maximum allowable capacity change, This represents the change in capacity. (2) Power grid security constraints AC power flow balance constraint: The power injected into any node must equal the power flowing out, i.e., power conservation; Active power balance constraint: （20） Reactive power balance constraints: （21） In the formula: t represents the first... Hour, It is the collection of all electrical connection points in a power distribution system. Represents the set of all branches in the power grid. In the first Hours, injected from power plants or upstream grid nodes The active power; In the first Hour, node The active power consumed by the existing load. In the first Hour, node The active power consumed at electric vehicle charging stations; It corresponds in meaning to active power, but its unit is reactive power. For each node in the set , For nodes Connected nodes, In the first Hourly Node voltage amplitude, In the first Hours and nodes Connected nodes voltage amplitude, For connecting nodes and nodes The conductance of a circuit is a parameter that describes the resistive characteristics of the circuit. For connecting nodes and nodes The susceptance of a line is a parameter that describes the reactance characteristics of the line. In the first Hour, node With nodes Voltage phase angle difference between ; Node voltage constraints: The voltage of each node must be kept within a safe range at all times. This is a basic requirement for ensuring power quality and equipment safety. （22） In the formula: In the first Hour, node voltage amplitude, For nodes The minimum permissible voltage limit; too low a voltage will cause user equipment to malfunction. For nodes The maximum permissible voltage limit; excessive voltage can damage electrical equipment. Line capacity constraints: （23） In the formula: For at any time Flow through the connection node and nodes The apparent power of the line is the vector sum of active and reactive power. Apparent power The modulus, For the line To the line The maximum apparent power that can be safely transmitted; exceeding this value will cause the line to overheat and pose a risk of failure. This indicates that for each connected node in the set... and The route, In the first Hours, flowing through the line To the line current The conjugate of complex numbers; (3) Charging station operation constraints: Capacity limitation constraints: If the charging station exist, Then its capacity must be within the allowable range; if it does not exist, If so, the capacity is forced to 0; （24） In the formula: , For charging stations The minimum and maximum capacities that can be configured; Service capacity constraints: charging stations In the The total charging energy provided within one hour must not exceed its effective capacity limit: （25） In the formula: For users Choose a charging station The probability, For users The charging needs, Energy per charge, For capacity utilization, The duration is expressed in hours. Charging power constraints: charging stations In the The total charging power per hour is obtained by averaging the energy charged by all users at the station, directly linking users’ charging choices to the actual physical load of the power grid. （26） In the formula: For charging stations In the Total active charging power per hour For users In the The percentage of charging demand per hour, i.e., the user's charging demand per hour. In the The proportion of hourly charging energy demand to the total charging energy demand for each typical day; (4) User behavior constraints: Demand allocation constraint: On any given day, each user The charging demand must be fully allocated to each charging station, with a total allocation ratio of 100%. （27） The user selection probability constraint is based on the Logit model: it defines the calculation method for the user selection probability. The probability that a user chooses a certain station is equal to the proportion of that station's utility index to the sum of the utility indices of all stations. （28） （29） （30） （31） （32） In the formula: For users, For user collection, Typical daily users in summer and winter The demand for charging will increase in summer due to air conditioning and in winter due to heating. Typical Daily Users in Spring and Autumn The charging needs; , These are typical days in summer and winter, and typical days in spring and autumn, for users. The overall effect; This refers to the total number of charging stations, including existing stations and candidate stations. Two pairs of users at the typical day charging stations in spring and autumn. The utility; , users respectively Select stations on typical summer and winter days and typical spring and autumn days. The probability of; , users respectively Expected queuing time at station j on typical summer / winter days and typical spring / autumn days; , Charging stations are designated for typical summer / winter days and typical spring / autumn days, respectively. In the Hourly time-of-use electricity pricing For users Arrival distance, , , These are the weighting coefficients for distance, waiting time, and electricity price, respectively. , , These are the sensitivity coefficients for distance, waiting time, and price, respectively. (5) Economic constraints: Total investment budget constraint: The total cost of planning and upgrading charging stations must not exceed the total project budget to ensure that the plan is economically affordable; （33） In the formula: This represents the maximum allowed total investment budget for the project. Investment payback period constraint: The present value of the net income of the project within the specified payback period must reach a certain percentage of the investment cost to ensure that the investment has reasonable profitability; （34） In the formula: For the required investment payback period, For the project during the investment payback period Annual operating revenue For the project during the investment payback period Annual operating and maintenance costs For the discount rate, As the minimum return on investment coefficient, the project must recover at least a certain percentage of the investment within the payback period; (6) Service coverage constraints: The total service range of all charging stations must meet or exceed the prescribed minimum standards to ensure that there are no service blind spots and achieve equalization of basic public services; （35） In the formula: the distance from any user to their nearest charging station must not exceed [a certain distance]. To ensure full coverage For users To the charging station distance, To specify the maximum permitted service distance; (7) Variable type constraints Binary constraints on state variables: （36） State change decision constraints: （37） Non-negativity constraint on capacity: （38） Time-of-use electricity price upper and lower limits constraints for typical summer and winter days and typical spring and autumn days: （39） , The upper and lower limits of the time-of-use electricity price are determined by the regulations of the target planning area, and the upper and lower limits of the electricity price are assumed to remain stable during the planning period. S3.4: Under the constraints in S3.3, minimize the total system cost respectively. And maximize user satisfaction The time-of-use electricity prices on peak load days in summer and winter, and on regular days in spring and autumn, and the key decision variables of charging stations. Post-planning capacity To find the optimal variables, the total system cost is obtained. maximum value and minimum value and user satisfaction maximum value and minimum value .

5. The method for planning and pricing electric vehicle charging stations based on existing charging stations according to claim 4, characterized in that, The specific process of S4 is as follows: S4.1: Parameter initialization settings; setting population size Maximum number of iterations ;Set state decision Upper and lower limits, planned capacity Upper and lower limits, charging stations On the two typical days of summer and winter and spring and autumn hourly time-of-use electricity price and The upper and lower limits; For decision variables, the upper and lower bounds are defined as follows: for state variables... : , For post-planned capacity : , ,in For the maximum permissible capacity; for typical daily electricity prices and : , , , To define the permitted range of electricity prices; S4.2: Chaotic Mapping Generates the Initial Population The hybrid encoding strategy employs a core approach of designing a solution vector that fully represents a specific planning scheme, unifying integer and continuous variables within a single solution vector. The encoding structure is as follows: Assume the planning scheme has… One charging station, with a planning period of [number] days. Year; Each hummingbird individual encodes all decision variables, including site status variables, capacity configuration, and the time-of-use electricity price structure for two typical days in summer / winter and spring / autumn, as follows: （40） charging station for The total number of variables coded for each charging station is: （41） A solution vector Dimensions for: （42） In the formula: For population size, State decision variables, For the planned capacity, and Charging stations On the two typical days of summer and winter and spring and autumn, on the 1st Hourly electricity pricing; Based on the Logistic mapping formula, generate chaotic sequences: （43） In the formula: It is the chaotic value generated in the m-th iteration, and its value ranges between (0,1); According to The calculated next chaotic sequence value, ; According to formula (43), perform no less than N iterations to generate a chaotic sequence; then, extract an unused chaotic value from the generated chaotic sequence in sequence. Chaos value Mapping to individuals through linear transformation The The actual range of values ​​for each decision variable ,get : （44） In the formula: For the first The first hummingbird individual The values ​​of each decision variable at the initial time. For the first The lower bound of each decision variable. For the first Upper bounds of the decision variables: individual The decision variables are all initialized according to formula (44) to obtain the individual Initialization solution vector : （45） Perform on each individual in the population The initialization process yields the initial population; S4.3: Calculate the initial population fitness First, each individual in the initial population is decoded. Then, the vector values ​​of each individual are used for simulation calculations to obtain the total system cost for each individual. and user satisfaction The value is then used to calculate the overall fitness of each individual. : （46） （47） In the formula: These are weighting coefficients, which are fixed values. and These are the total system cost The maximum and minimum values, and These are user satisfaction The maximum and minimum values ​​are obtained from step S3.4; It is set to 10 6 -10 8 A positive penalty coefficient on the order of magnitude; The total constraint violation degree is determined by the number of constraints violated by the solution. Penalty items It will drastically increase the fitness value. This guides the algorithm to abandon infeasible solutions and turn to search for feasible solution regions; The formula for calculating the total constraint violation rate (CV) is as follows: （48） In the formula: The quantity that violates the inequality constraint; if This indicates that the constraint is satisfied and the violation is 0; if This indicates that the constraint has been violated; the amount of violation is... This positive value itself; the deviation of the equality constraint. It refers to the absolute difference between the values ​​on the left and right sides of the equation constraint; and The weights of each constraint; Decoding each individual in the population specifically refers to: decoding the state variables. Forced rounding and boundary truncation are performed, and state consistency correction is applied. For each individual in the population Variables representing state decisions Perform forced rounding and boundary truncation: （49） In the formula: This is a rounding function that ensures the final result is an integer. It is the discrete integer state value obtained after decoding, which strictly belongs to the set {-1,0,1}; Based on the discretized Modify the relevant variables to satisfy the logical rules: Rule 1: If Then forced ; Rule 2: If and Then set ; Rule 3: If but This is an illegal operation; please correct it to: ; S4.4: Population Iterative Update Based on the fitness value of each individual obtained in step S4.3, the individual with the smallest fitness value is selected as the current global historical best solution, and the population is iteratively updated. Each individual in the population executes guided flight and territory flight strategy updates with a certain probability. The update result is first decoded, then a temporary solution for each individual is obtained through greedy selection, and finally the final update vector for each individual is obtained through non-uniform mutation. The population achieves one iteration update. The flight guidance strategy update process is as follows: Each hummingbird With a certain probability The position is updated by following the guide hummingbird in the population, using the following formula: （50） In the formula: This represents the current iteration number. , For random vectors, and For the first Two different hummingbirds are randomly selected from the population in the next iteration. As a chaotic perturbation factor, it enhances global exploration capabilities. It is a vector, where each element represents the upper limit of the allowed values ​​for each decision variable in the optimization problem; It is also a vector, where each element represents the lower bound of the allowed values ​​for each decision variable in the optimization problem; The individual with the best current fitness is the guide hummingbird; The process for updating the flight strategy in the aforementioned area is as follows: With probability Execution simulates a hummingbird's fine-grained search within a local area: If guided flight is not executed, the hummingbird searches locally within its own territory, simulating the behavior of guarding a food source. The position update formula is: （51） In the formula: It is a random number. Another hummingbird was randomly selected from the population; The specific process of greedy selection is as follows: For the The individual, in the iteration to the _th At that time, two alternative new schemes were generated through guided flight and domain flight strategies. and Decode these two schemes and then calculate their fitness values. And select the option with the smaller fitness value as its next generation. temporary new location : （52） In the formula: This indicates that the solution is a temporary result in the current iteration, and is the temporary solution ultimately chosen by the algorithm for each individual. Generated for use in the next generation temporary solution, This indicates that the candidate solution was generated using a guided flight strategy. This indicates that the candidate solution was generated using a domain flight strategy; , express , Corresponding to the decoded result, The fitness function is a function where a smaller value indicates a better solution. The specific process of obtaining the final update vector for each individual through non-uniform mutation is as follows: The mutation probability of each individual decreases exponentially with the number of iterations: （53） In the formula: In the first The mutation probability of a generation The initial mutation probability ranges from 0.3 to 0.

5. The attenuation coefficient controls the rate at which the probability decays, and its value ranges from 4 to 6. Temporary solution for individual n For each decision variable, a probability-based decision is made regarding whether to mutate, using an adaptive step size; for non-uniform mutations of continuous variables, first generate... random numbers within the range ,like Then, perform mutation on the variable; then calculate the non-uniform variable length: （54） In the formula: This represents the distance from the current variable value to its boundary. for Random numbers within a range For shape parameters, Control the step size decay pattern; Finally, based on the non-uniform variation in asynchronous length, the continuous variable of the individual is randomly selected to mutate upwards or downwards: Upward mutation: （55） Downward mutation: （56） For continuous variables, ensure that the mutated value remains within the allowable range: （57） For discrete variables of individuals, a dedicated mutation discrete state transition for integer variables is used; first, generate... random numbers within the range ,like Then, mutate the variable; then randomly select one from two valid discrete states other than the current value; if the current value is... The new value is or ; （58） Based on the discretized Modify relevant variables to satisfy logical rules: Rule 1: If Then forced ; Rule 2: If and Then set ; Rule 3: If but This is an illegal operation; please correct it to: ; S4.5: Knowledge Transfer Flight Updates Population For each individual in the population that implements one iteration update in S4.4, calculate the fitness of each individual in the population according to the method in S4.3, and perform iterative updates of the population according to the method in S4.

4. Every certain number of generations, perform knowledge transfer flight to update the population, eliminate inferior individuals, and introduce new random explorations. The specific process of knowledge transfer and population renewal is as follows: Setting the first The +1st iteration requires performing knowledge transfer flight to update the population, when the... When +1 iterations are completed, select individuals from all individuals in the current population whose fitness function is optimal. The individual with the smallest value is defined as the optimal elite solution for the current generation. and make the fitness function The individual with the largest value is defined as the optimal elite solution for the current generation and the worst-case global solution. : （59） （60） In the formula: In the first The globally optimal elite solution found in generation +1. In the first The worst-case global solution found in generation +1. This represents the parameter that makes the function achieve its minimum value. This represents the parameter that makes the function reach its maximum value. The fitness function is used to evaluate the quality of the solution. In the first +1 generation population The solution vector of each individual; Then, explore and perturb the vicinity of the elite individual to generate new individuals: （61） In the formula: For random disturbance factors, ; Immediately after the migration flight, the newborn individuals Discretize the integer decision variables and correct the state consistency to ensure the feasibility of the new solution; Then, the worst individual in the original population is replaced with the newly generated individual, thus completing the knowledge transfer: （62） In the formula: For the population obtained through knowledge transfer flight updates, For the process The population obtained after +1 iteration update, "Indicates merging into a newly generated or selected high-quality individual" " "Indicates from the past" In the population obtained after +1 iterations, remove individuals marked as inferior. ; S4.6: Iteration Termination The updated population obtained through knowledge transfer flight in S4.5 is used as the initial population for the next iteration. The process of calculating the population fitness in S4.3 is repeated, as is the process of iterative population update in S4.

4. Every certain number of generations, the process of updating the population through knowledge transfer flight in S4.5 is performed, and then the processes in S4.3 and S4.4 are repeated. This process is continued until the maximum number of iterations is reached. Iterative updates stop; the population has passed... After several iterations, the final optimized population individuals are obtained, which is the optimized solution set of the decision variables.

6. The method for planning and pricing electric vehicle charging stations based on existing charging stations according to claim 5, characterized in that, The specific process of S5 is as follows: The Pareto optimal solution set is extracted from the optimal solution set of the decision variables in S4 using the fast non-dominated sorting algorithm: ,untie Dominant Solution If and only if both of the following conditions are met: Condition one: （63） Condition two: （64） In the formula: and Decision variables Two distinct solution vectors; express The total system cost, express User satisfaction; If solution 1 dominates solution 2, it means that solution 1 is superior to solution 2 in every aspect; if solution 1 is no worse than solution 2 in terms of total system cost and user satisfaction, and at least one of these two aspects is significantly better, then... This is the desired governing solution; All dominant solutions selected from the optimal solution set of the decision variables in S4 constitute the Pareto optimal solution set. The crowding degree of each Pareto optimal solution is calculated: （65） In the formula: To solve The crowding level is such that the larger the value, the more open the solution is around it, and the higher its priority during the selection process, thus ensuring the diversity of the solution set. Let be a Pareto optimal solution for the congestion degree to be calculated. Representing the The objective function is the total system cost. Or user satisfaction ; and To sort by the value of a certain objective function and then find the solutions that are immediately adjacent to each other. The previous and next solutions; , The objective function for the Pareto optimal solution set The maximum and minimum values; Based on the total system cost of each Pareto optimal solution He Zhe user satisfaction The total system cost The horizontal axis represents user satisfaction. Using the y-axis as the vertical axis, plot a two-dimensional scatter plot of decision references; simultaneously, using the congestion level of each Pareto optimal solution as the vertical axis, plot the corresponding total system cost. He Zhe user satisfaction The x-axis represents the coordinates, and the y-axis represents the total system cost. - Crowding curve, user satisfaction - Crowding curve; Based on the decision-making requirements of the target planning area, select the final electric vehicle charging station planning and pricing strategy: 1) When the decision-making requirement for the target planning area is based on the total system cost To minimize it, we start from the total system cost. - Select the congestion curve that corresponds to the highest congestion level and the highest total system cost. The minimum Pareto optimal solution is the final electric vehicle charging station planning and pricing strategy; 2) When the decision-making requirement for the target planning area is user satisfaction To maximize, consider user satisfaction. - Select the congestion level from the congestion curve that corresponds to the highest user satisfaction. The largest Pareto optimal solution is the final electric vehicle charging station planning and pricing strategy; 3) When the decision requirement for the target planning area is to balance the total system cost With user satisfaction At that time, calculate the cost of improving marginal satisfaction. The Pareto optimal solution corresponding to the maximum value of this ratio is the final electric vehicle charging station planning and pricing strategy; The specific calculation process is as follows: First, each Pareto optimal solution is calculated according to the total system cost. Sort by size from smallest to largest; if there are solutions with the same total system cost, consider user satisfaction. In ascending order, calculate the increment between adjacent solutions last. The solution that maximizes the increment is the final electric vehicle charging station planning and pricing strategy.

7. The method for planning and pricing electric vehicle charging stations based on existing charging stations according to claim 4, characterized in that, Weighting factors for distance, waiting time, and electricity price , , The analytic hierarchy process (AHP) combined with expert scoring is used to determine the weights of "distance", "waiting time", and "price". The judgment matrix is ​​constructed by comparing the relative importance of these three factors.

8. The method for planning and pricing electric vehicle charging stations based on existing charging stations according to claim 4, characterized in that, Sensitivity coefficients for distance, waiting time, and price , , The model was calibrated using historical selection data; by collecting actual user selection data among charging stations with different distances, prices, and waiting times, the maximum likelihood estimation method was used to infer the values ​​of the corresponding coefficients.

9. A method for planning and pricing electric vehicle charging stations based on existing charging stations according to claim 4, characterized in that, In S3.4, the total system cost maximum value and minimum value and user satisfaction maximum value and minimum value The results were obtained through iterative calculations using a genetic algorithm.

Images