A load forecasting method for electric vehicle charging station group based on variational equilibrium and energy state distribution evolution

Abstract

The application discloses a kind of based on variational equilibrium and energy state distribution evolution electric vehicle charging station group load forecasting method, first obtains charging station static attribute data, constructs charging demand potential function;Subsequently, establish the variational equilibrium model of site selection, solve the equilibrium allocation probability of vehicle to different charging station;Then construct vehicle state of charge probability density evolution equation and site queuing fluid dynamics equation, depict vehicle charging demand, state of charge migration and congestion state evolution process;On this basis, through non-local power response check site load is convolved aggregation, and combined with cross-station coupling correction term and high-order variational correction equation, obtain the charging station group load forecasting result of multiple time steps in the future.The application can consider the influence of multiple factors such as demand generation, site selection, state of charge change, queuing congestion and cross-station coupling simultaneously, improve the stability of electric vehicle charging station group load forecasting.

Description

Technical Field

[0001] This invention relates to the field of electric vehicle charging load prediction technology, and specifically to a method for predicting the load of electric vehicle charging station clusters based on variational equilibrium and energy state distribution evolution. Background Technology

[0002] With the continuous growth of electric vehicle ownership, public charging stations have become key nodes connecting urban energy networks and transportation networks. The load on charging stations is affected by a variety of factors, including vehicle travel demand, site selection behavior, remaining battery power, queuing congestion, dynamic electricity prices, weather changes, and regional functional attributes, exhibiting significant randomness, volatility, and spatiotemporal correlation.

[0003] In existing technologies, charging station load forecasting methods mostly focus on direct fitting based on historical time series, or utilize general statistical regression methods, shallow machine learning methods, and conventional deep learning methods for prediction. However, these methods typically analyze load changes only from the perspective of a single vehicle or a single station, lacking in-depth consideration of vehicle station selection behavior and congestion feedback mechanisms, and failing to characterize the inherent coupling relationship between demand generation and station allocation. Furthermore, existing technologies often lack unified modeling of state of charge distribution, queuing status, and inter-station coupling, resulting in insufficient interpretability and poor stability of prediction results. Therefore, how to jointly model from multiple levels, including demand-driven factors, station selection, energy state distribution, queuing dynamics, power aggregation, and inter-station coupling, to improve the accuracy, stability, and theoretical consistency of charging station cluster load forecasting is a pressing technical problem that needs to be solved. Summary of the Invention

[0004] To address the problem that existing technologies struggle to simultaneously consider factors such as demand generation, site selection, state of charge changes, queuing congestion, and cross-site coupling, this application proposes a load forecasting method and apparatus for electric vehicle charging station clusters. This method achieves accurate load forecasting based on physical mechanisms, improving the precision, stability, and interpretability of the forecasts.

[0005] Technical solution:

[0006] A load forecasting method for electric vehicle charging station clusters based on variational equilibrium and energy state distribution evolution includes the following steps:

[0007] S1. Obtain static attribute data of multiple charging stations and construct a standardized input dataset in the prediction time domain;

[0008] S2. Based on the input dataset, calculate the original charging demand intensity for each charging station;

[0009] S3. Using the original charging demand intensity as input, establish a variational equilibrium model for charging station selection, construct a variational equilibrium functional based on the generalized cost function, and solve the equilibrium allocation probability of vehicles facing each charging station under probability measure constraints.

[0010] S4. Using the original charging demand intensity and the balanced allocation probability as boundary conditions and driving terms, establish and solve the probability density equation describing the energy state evolution of vehicles in the station and the fluid dynamics equation describing the service state, to obtain the charge state probability density distribution, queuing and charging status of each charging station.

[0011] S5. Based on the state of charge probability density distribution, the initial load trajectory of each charging station is obtained by convolution integral of the state of charge probability density distribution through a nonlocal power response kernel.

[0012] S6. Based on the initial load time series, a coupling matrix reflecting the spatial and capacity correlation between stations is introduced, and cross-station collaborative correction is performed to obtain the corrected load time series;

[0013] S7. Perform high-order variational correction on the coupled-corrected load trajectory to output the final load prediction result of the charging station group.

[0014] Furthermore, in step S2, calculating the original charging demand intensity includes: constructing the comprehensive attraction potential function of the s-th charging station at time t. :

[0015] ,

[0016] in, This indicates the site capacity parameter. Indicates dynamic electricity price. Indicates the waiting time in the queue. This indicates the additional cost of the destination path. Indicates the activity level of regional functions. These are the weighting coefficients;

[0017] Constructing the regional charging demand driving potential function , which is the weighted spatial integral of the traffic density field, weather disturbance field, and travel activity intensity field within the study area;

[0018] according to and Calculate the original charging demand intensity : .

[0019] Furthermore, in step S3, the generalized cost function is expressed as:

[0020] ,

[0021] in, This represents the average detour distance a vehicle travels to reach charging station s. Indicates the waiting time in the queue. Indicates dynamic electricity price. This indicates a low battery risk item. ~ For cost weight parameters;

[0022] Variational equilibrium functional Represented as:

[0023] ,

[0024] in, The probability of equitable allocation of charging station s for vehicles. Under the condition of satisfying the probability normalization constraint Next, solve. The extreme value is obtained. .

[0025] Furthermore, in step S4, the probability density equation describing the energy state evolution of vehicles within the station is expressed as:

[0026] ,in, Let be the probability density function of a vehicle at station s with state of charge e at time t. The rate of change of the charged state. , For vehicle inflow and outflow items driven by the results of steps S2 and S3.

[0027] Furthermore, in step S4, the fluid dynamics equation describing the service state is:

[0028] ,

[0029] ,

[0030] in, The number of vehicles in the queue. The number of vehicles currently charging. The switching flow rate for transitioning from queuing to charging state. Service rate at departure stations.

[0031] Furthermore, switching flow rates Defined as:

[0032] ,

[0033] in, The number of charging piles at the site. This is the time step switching factor.

[0034] Furthermore, in step S5, the nonlocal power response kernel It is a function describing the effect of the state of charge e and the time interval on the instantaneous charging power, expressed as:

[0035] ,

[0036] in, The rated charging power of station s, For time decay parameters, These are the parameters for the state of charge response;

[0037] Initial load trajectory Calculated using the following formula:

[0038] .

[0039] Furthermore, in step S6, the coupling matrix is: The coupling weight , Let be the distance between station s and station r. and These are the capacity parameters for the corresponding sites. For distance scale parameters, For capacity scale parameters;

[0040] Using the coupling matrix W to analyze the initial load trajectory Cross-site collaborative correction is performed to obtain the coupled corrected load trajectory. : ,

[0041] in, and The initial load for neighboring sites r and k.

[0042] Furthermore, in step S7, the higher-order variational correction is achieved by constructing and solving the extremum problem of the following functional:

[0043] ,

[0044] in, To ultimately predict the load, The load trajectory is after coupling correction. To correct the weights;

[0045] Solving under constraints The following steps were taken to obtain information about Euler-Lagrange equation: ,

[0046] The solution result is used as the final predicted load trajectory.

[0047] Furthermore, the time derivative term in the probability density equation or the fluid dynamics equation adopts the Caputo fractional derivative. Replace it. It is a fractional order, and 0 < <1.

[0048] Furthermore, the present invention also provides a load forecasting device for electric vehicle charging station clusters, comprising:

[0049] The data acquisition module is used to acquire historical load data, dynamic electricity price data, traffic status data, weather data, and static attribute data of multiple charging stations to construct the input dataset in the prediction time domain.

[0050] The demand intensity determination module is used to construct the comprehensive attraction potential function and the regional charging demand driving potential function of each charging station based on the input dataset, so as to obtain the original demand intensity of each charging station.

[0051] The equilibrium allocation module is used to establish a variational equilibrium model for charging station selection and solve the equilibrium allocation probability of each charging station under the constraint of the site selection probability measure.

[0052] The state evolution module is used to establish the probability density evolution equation of the vehicle's state of charge and the hydrodynamic equation of the station queuing, and to obtain the state of charge distribution, queuing state and charging state of each charging station in the prediction time domain; the load aggregation module is used to perform convolution aggregation on the state of charge distribution based on the nonlocal power response kernel to obtain the initial load trajectory of each charging station.

[0053] The correction output module is used to perform cross-station coupling correction on the initial load trajectory to obtain the coupled corrected load trajectory, and construct a high-order variational correction functional to perform optimal correction on the coupled corrected load trajectory, and output the charging station group load prediction results for multiple future time steps.

[0054] Compared with the prior art, the present invention has at least the following beneficial effects:

[0055] (1) This invention starts from the combined attraction potential and the regional demand driving potential, and explicitly models the charging demand generation process, which can better reflect the impact of dynamic prices, traffic conditions, regional functions and congestion feedback on load formation.

[0056] (2) The present invention uses the variational equilibrium method to solve the allocation probability of the vehicle to different charging stations, rather than simply using empirical allocation or fixed rules. Therefore, it can more reasonably characterize the vehicle's equilibrium selection behavior among multiple stations.

[0057] (3) By constructing the vehicle charge state probability density evolution equation and the station queuing fluid dynamics equation, this invention achieves a joint description of energy state distribution and congestion state, thereby improving the interpretability of load formation mechanism.

[0058] (4) This invention achieves joint constraints on load trajectory smoothness, curvature change and station group synergy effect through nonlocal power response kernel aggregation, cross-station coupling correction and high-order variational correction, thereby improving the stability and continuity of prediction results. Attached Figure Description

[0059] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the embodiments will be briefly described below.

[0060] Figure 1 This is a flowchart of a method according to an embodiment of the present invention;

[0061] Figure 2 This is a schematic diagram illustrating the coupling relationship between site selection balancing and queuing in an embodiment of the present invention. Detailed Implementation

[0062] To make the objectives, technical solutions, and advantages of this invention clearer, the following detailed description, in conjunction with the accompanying drawings and embodiments, further illustrates the invention. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of the invention.

[0063] like Figures 1 to 2 As shown, this invention discloses a load forecasting method for electric vehicle charging station clusters based on variational equilibrium and energy state distribution evolution, comprising the following steps:

[0064] S1. Data Acquisition and Processing: Acquire historical load, dynamic electricity price, traffic status, weather, and static attribute data of multiple charging stations to construct a standardized input dataset for the prediction time domain.

[0065] Historical load data reflects the past load levels of the charging stations, dynamic electricity price data reflects the temporal fluctuations in charging costs, traffic condition data characterizes the ease of vehicle arrival, weather data affects battery charging efficiency and user travel intentions, and static attribute data of the charging stations (including at least station capacity parameters, number of charging piles, and station geographical location) determines the station's service capacity. This embodiment constructs a standardized input dataset by performing preprocessing operations such as time alignment, missing value imputation, and scaling on the aforementioned multi-source heterogeneous data, providing reliable input support for subsequent physical mechanism-based model calculations.

[0066] S2. Calculation of Initial Demand Intensity: Based on the input dataset, construct the comprehensive attraction potential function and the regional charging demand driving potential function for each charging station, and calculate the initial demand intensity for each charging station at each time point. Specifically:

[0067] Based on the input dataset obtained in step S1, construct the comprehensive attraction potential function of the s-th charging station at time t. And construct the regional charging demand driving potential function. .

[0068]

[0069] in, This indicates the site capacity parameter. Indicates dynamic electricity price. Indicates the waiting time in the queue. This indicates the additional cost of the destination path. Indicates the activity level of regional functions. These are the weighting coefficients.

[0070] In this embodiment, the combined attraction potential function Weighting coefficients in , , , , This is used to quantify the contribution of each influencing factor to the charging station's adsorption capacity. Among them, The site capacity weight represents the ability of the charging station's physical capacity to drive charging demand. The electricity price weight represents the negative inhibitory effect of dynamic electricity pricing on user choice. Queue weight represents the negative penalty for queuing time; The path weight represents the path cost for a user to reach the charging station. As a weight for regional vitality, it represents the positive pull of economic activities in the surrounding area on charging demand.

[0071] The regional charging demand driving potential function is defined as:

[0072]

[0073] in, Indicates the spatial extent of the study area. Represents the regional traffic density field. Indicates weather disturbance field, Indicates the intensity of travel activities; ~ These are the corresponding weight parameters.

[0074] Based on the combined attraction potential function and the regional charging demand driving potential function, the original demand intensity of each charging station at each time point is calculated. :

[0075]

[0076] in, Indicates the time facing the station The generated initial demand intensity, This indicates the total number of charging stations.

[0077] This step outputs the raw demand intensity sequence for each charging station within the prediction time domain. This step explicitly models charging demand from two dimensions: "site attraction" and "regional driving force." The comprehensive attraction potential function quantifies the ability of a specific charging station to attract vehicles, influenced by factors such as station capacity, electricity price, and queuing time. The regional charging demand driving potential function quantifies the generation intensity of charging demand across the entire region, driven by factors such as traffic density, weather disturbances, and travel activity intensity. By combining these two approaches, the raw demand intensity of each charging station under unconstrained conditions can be calculated, thus achieving a mapping from macroscopic environmental data to microscopic site demand.

[0078] S3. Solving for Equilibrium Allocation Probability: Establish a variational equilibrium model for charging station selection. Construct a variational equilibrium functional based on the generalized cost function, and solve for the equilibrium allocation probability of vehicles to each charging station under probability measure constraints. Specifically,

[0079] Let the probability measure of a vehicle choosing charging station s be... The nonnegativity and normalization constraints are satisfied. Based on the average detour distance, queuing time, dynamic electricity price, and low electricity risk term of the station, a generalized cost function for station s is constructed. Based on this, a variational equilibrium functional for site selection is constructed, and a Lagrangian function is constructed under constraints. The first-order variation of the Lagrangian function is then performed to obtain the equilibrium conditions. For each discrete time step, the equilibrium allocation probability can be solved iteratively. In specific implementation, the initial allocation probability vector is used as the starting point for iteration, and the allocation probabilities of each site are repeatedly updated until the error between two adjacent iterations is less than a preset threshold. The equilibrium distribution probability of each charging station at each time point is obtained. The output of this step is a balanced probability sequence.

[0080] Let the probability measure of a vehicle choosing charging station s be... ,satisfy:

[0081] Constructing the variational equilibrium functional for site selection:

[0082] The generalized cost function of station s is:

[0083]

[0084] in, This represents the average detour distance a vehicle travels to reach charging station s. This indicates a low battery risk item. ~ The cost weight parameter.

[0085] Under constraints Construct the Lagrangian function below:

[0086] And according to the first-order variational condition: The probability of balanced distribution of each charging station is obtained by solving the problem.

[0087] Because users engage in game theory when choosing charging stations, simple empirical allocation rules are insufficient to accurately describe this dynamic equilibrium. This embodiment introduces a variational equilibrium model, modeling user selection behavior as a functional extremum problem under probability measure constraints. By solving this model, the equilibrium allocation probability of each charging station is obtained, which reflects the likelihood of a vehicle choosing each station after considering generalized costs (such as distance, time, and electricity price).

[0088] S4. Solving the State Evolution within the Station: Establish the vehicle charge state probability density evolution equation and the station queuing fluid dynamics equation. Combining the original demand intensity and equilibrium distribution probability, solve for the charge state probability density distribution, the number of queued vehicles, and the number of charging vehicles at each charging station in the predicted time domain. Specifically,

[0089] Let the probability density function of a vehicle at station s with state of charge e at time t be: ,in Based on factors such as station charging efficiency, station rated charging power, charging utilization rate, regional average driving speed, and ambient temperature, a probability density evolution equation for the vehicle's state of charge is established, which includes a state of charge evolution velocity term, an inflow term, and an outflow term.

[0090] In the specific implementation, the initial state-of-charge distribution and boundary conditions are first set; then the state-of-charge interval and the prediction time interval are discretized; and finally, a difference scheme is used to solve the problem step by step, thereby obtaining the probability density distribution sequence of the state of charge of each station in the prediction time domain. The output of this step is... The discrete results.

[0091] Let the probability density function of a vehicle at station s with state of charge e at time t be: ,in Then its evolution satisfies: The rate of change of the charged state is:

[0092] The inflow and outflow items are as follows:

[0093] in, For charging efficiency, Rated charging power for the station, To improve charging efficiency, The average driving speed in the area. For ambient temperature, For reference temperature, For departure service rate, and These are the kernel functions for the charge state distribution upon arrival and departure from the station, respectively.

[0094] Solve for the queuing state and the charging state:

[0095] Let the number of vehicles queuing at station s at time t be... The number of vehicles charging is Based on the intensity of the original demand Equilibrium distribution probability Switching flow rates and departure service rate Establish the queuing state evolution equation and the in-filling state evolution equation.

[0096] Among them, the switching flow rate is used to characterize the number of vehicles that move from the queuing state to the charging state; the waiting time response function is used to characterize the feedback effect of the congestion state on the site attraction potential and generalized cost.

[0097] In the specific solution, for each discrete time step, the switching flow rate is updated based on the number of queued vehicles and the number of charging vehicles in the previous time step, and then updated separately. and Simultaneously calculate the waiting time response value. The output of this step is the queuing state sequence, charging state sequence, and waiting time response sequence for each station in the prediction time domain.

[0098] The queuing and charging states of station s satisfy the following:

[0099] in, The number of vehicles in the queue. The number of vehicles currently charging. The switching flow rate for transitioning from queuing to charging is defined as:

[0100] in, The number of charging piles at the site. The time step switching factor is used; the waiting time response function of station s is defined as:

[0101] in, This is the site congestion attenuation coefficient. To prevent positive numbers with a denominator of zero.

[0102] The vehicle state-of-charge probability density evolution equation characterizes the microscopic migration of energy states during the charging process. It describes the evolution of the probability density of a vehicle under different states of charge over time using partial differential equations, where the evolution rate is influenced by physical factors such as charging power and ambient temperature. The station queuing fluid dynamics equation characterizes the dynamic flow of vehicles at charging stations, including queuing, charging, and leaving the station. The equilibrium distribution probability, as input, drives vehicles to flow into each station, thus affecting the state-of-charge distribution and queuing status. By jointly solving these two equations, a precise description of the microscopic mechanism of the charging process is achieved.

[0103] S5. Initial Load Trajectory Aggregation: Based on the nonlocal power response kernel, the probability density distribution of the state of charge is convolved and integrated to obtain the initial load trajectory of each charging station. Specifically,

[0104] Based on the probability density distribution of the state of charge obtained in step S4 Construct the initial load trajectory of station s at time t. The trajectory is composed of a nonlocal power response kernel. It is obtained by convolution and aggregation with the probability density distribution of charged states.

[0105] In practical implementation, the time and charge state variables are discretized, and the continuous integral form is transformed into a discrete summation form to obtain the initial load trajectory of each station in the prediction time domain. The output of this step is... .

[0106] The initial load trajectory of station(s) at time (t) is defined as:

[0107]

[0108] The power response kernel function is defined as follows:

[0109] in, For time decay parameters, These are the parameters for the state of charge response.

[0110] This step maps the microscopic vehicle state to the macroscopic site load. The state of charge distribution only describes the energy state of the vehicle, while the load is the power integral over time. The nonlocal power response kernel function defines the contribution weights of vehicles to the site power response under different state of charge. Through convolution aggregation operations, the microscopic state of charge probability density distribution is transformed into the macroscopic initial load trajectory. This process reflects the physical superposition effect of load generation.

[0111] S6. Cross-site Coupling Correction: Based on the coupling matrix reflecting the spatial and capacity correlation between sites, the initial load trajectory is corrected to obtain the coupled-corrected load trajectory. Specifically,

[0112] To characterize the spatial and capacity correlations between different charging stations, an inter-station coupling matrix is ​​introduced. The coupling matrix is ​​constructed based on the distance between sites and the differences in site capacity.

[0113] Based on the coupling matrix, the initial load trajectory Perform cross-site coupling correction to obtain the coupled-corrected load trajectory. The output of this step is the coupled-corrected load trajectory for each site in the prediction time domain.

[0114] The inter-site coupling matrix is ​​defined as follows:

[0115]

[0116] in,

[0117]

[0118] in, Let be the distance between station s and station r. and These are the capacity parameters for the corresponding sites;

[0119] The load trajectory after cross-site coupling correction is as follows:

[0120] Considering the spatial correlation and capacity complementarity among charging station clusters, load changes at a single station may cause load fluctuations at adjacent stations. This step constructs a coupling matrix between stations to weight and correct the initial load trajectory, thereby introducing the station cluster synergy effect into the prediction model and improving the spatial consistency of the prediction results.

[0121] S7. Higher-order variational correction: Construct a higher-order variational correction functional to solve the coupled and corrected load trajectory, and output the final predicted load of each charging station at multiple future time steps.

[0122] To obtain a smooth final predicted trajectory that satisfies consistency across the entire time domain, a higher-order variational correction functional is constructed and solved under the constraint of total quantity conservation.

[0123] In practical implementation, the corresponding Euler-Lagrange equation is obtained by solving the higher-order variational correction functional; then, a five-point difference scheme is used for discrete solution on the discrete time axis; finally, the predicted load trajectory of each charging station at multiple future time steps is obtained. The output of this step is the final prediction result.

[0124] Construct higher-order variational correction functionals:

[0125] And satisfy the constraints:

[0126]

[0127] Solving the higher-order variational correction functional yields the Euler-Lagrange equation:

[0128] The solution result is used as the final predicted load trajectory.

[0129] Example 2

[0130] Example 2 is a targeted enhancement and generalization of Example 1. The improvement lies in replacing the integer-order differential dynamics model used to describe the system state evolution in step S4 of Example 1 with a fractional-order differential dynamics model. That is, the charged state probability density evolution equation or queuing state evolution equation is extended to a fractional-order form to enhance the system's ability to characterize long-history memory effects. The fractional derivative is expressed in Caputo form as follows:

[0131]

[0132] in, This represents the Caputo fractional derivative. It is a fractional order, and 0 < <1.

[0133] In this extended implementation, only the time derivative term is replaced with a fractional derivative term, while the definitions of other variables, input data, and output results remain unchanged. This implementation is suitable for application scenarios where demand fluctuations have long-term correlations.

[0134] The complete execution process of the method of the present invention will be described below with reference to a specific application scenario:

[0135] Suppose there are N public charging stations within a city's study area, with a prediction time step of 1 hour and a prediction time domain length of 24 future time steps. First, historical load data, dynamic electricity price data, traffic status data, weather data, and static attribute data of each charging station are collected to form the original input dataset. Then, time alignment, missing value imputation, outlier handling, and scaling are performed on the original input dataset to obtain standardized input data.

[0136] Next, based on the standardized input data, the comprehensive attraction potential function of each charging station at each time point is calculated. (Reflecting the attractiveness of the charging station itself) and the potential function driving regional charging demand. (Reflecting macro-level travel intensity), and further deriving the original demand intensity. To determine "how many vehicles need charging".

[0137] Then, under the condition of satisfying the probability measure constraint, a variational equilibrium model for site selection is constructed, and a discrete iterative method is used to solve for the equilibrium allocation probability of vehicles flowing to each charging station in the next 24 time moments, under the principle of minimizing cost. .

[0138] Furthermore, based on the equilibrium allocation probability, the probability density distribution of the state of charge at each site is solved separately. Number of vehicles in queue Number of vehicles charging and waiting time response .

[0139] Based on this, the nonlocal power response kernel is used to convolve and aggregate the state of charge distribution to obtain the initial load trajectory of each site in the next 24 time steps. .

[0140] Subsequently, based on the inter-site coupling matrix The initial load trajectory is corrected by cross-site coupling to obtain the coupled corrected load trajectory. .

[0141] Finally, by constructing a higher-order variational correction functional and solving the corresponding discrete equations, the final predicted load trajectory of each charging station for the next 24 hours is obtained. By summing up the final forecast values ​​for all stations, the overall load forecast curve for the station cluster is obtained.

[0142] This embodiment demonstrates that the method of the present invention can simultaneously consider the combined effects of factors such as demand generation, site selection, state of charge evolution, queuing congestion, and cross-site coupling on load formation, thereby improving the stability, accuracy, and interpretability of the load prediction results for charging station clusters.

[0143] Finally, it should be noted that the above descriptions are merely preferred embodiments of the present invention and are not intended to limit the present invention. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or make equivalent substitutions for some of the technical features. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A load forecasting method for electric vehicle charging station clusters based on variational equilibrium and energy state distribution evolution, characterized in that, Includes the following steps: S1. Obtain static attribute data of multiple charging stations and construct a standardized input dataset in the prediction time domain; S2. Based on the input dataset, calculate the original charging demand intensity for each charging station; S3. Using the original charging demand intensity as input, establish a variational equilibrium model for charging station selection, construct a variational equilibrium functional based on the generalized cost function, and solve the equilibrium allocation probability of vehicles facing each charging station under probability measure constraints. S4. Using the original charging demand intensity and the balanced allocation probability as boundary conditions and driving terms, establish and solve the probability density equation describing the energy state evolution of vehicles in the station and the fluid dynamics equation describing the service state, to obtain the charge state probability density distribution, queuing and charging status of each charging station. S5. Based on the state of charge probability density distribution, the initial load trajectory of each charging station is obtained by convolution integral of the state of charge probability density distribution through a nonlocal power response kernel. S6. Based on the initial load time series, a coupling matrix reflecting the spatial and capacity correlation between stations is introduced, and cross-station collaborative correction is performed to obtain the corrected load time series; S7. Perform high-order variational correction on the coupled-corrected load trajectory to output the final load prediction result of the charging station group.

2. The prediction method according to claim 1, characterized in that, In step S2, calculating the original charging demand intensity includes: constructing the comprehensive attraction potential function of the s-th charging station at time t. : ， in, This indicates the site capacity parameter. Indicates dynamic electricity price. Indicates the waiting time in the queue. This indicates the additional cost of the destination path. Indicates the activity level of regional functions. These are the weighting coefficients; Constructing the regional charging demand driving potential function , which is the weighted spatial integral of the traffic density field, weather disturbance field, and travel activity intensity field within the study area; according to and Calculate the original charging demand intensity : .

3. The prediction method according to claim 1, characterized in that, In step S3, the generalized cost function is expressed as: ， in, This represents the average detour distance a vehicle travels to reach charging station s. Indicates the waiting time in the queue. Indicates dynamic electricity price. This indicates a low battery risk item. ~ For cost weight parameters; The variational equilibrium functional Represented as: ， in, The probability of equitable allocation of charging station s for vehicles. Under the condition of satisfying the probability normalization constraint Next, solve. The extreme value is obtained. .

4. The method according to claim 1 or 3, characterized in that, In step S4, the probability density equation describing the energy state evolution of vehicles within the station is expressed as: ,in, Let be the probability density function of a vehicle at station s with state of charge e at time t. The rate of change of the charged state. , For vehicle inflow and outflow items driven by the results of steps S2 and S3.

5. The prediction method according to claim 4, characterized in that, In step S4, the fluid dynamics equation describing the service state is: ， ， in, The number of vehicles in the queue. The number of vehicles currently charging. The switching flow rate for transitioning from queuing to charging state. Service rate at departure stations.

6. The prediction method according to claim 5, characterized in that, The switching flow rate Defined as: ， in, The number of charging piles at the site. This is the time step switching factor.

7. The prediction method according to claim 1, characterized in that, In step S5, the nonlocal power response kernel It is a function describing the effect of the state of charge e and the time interval on the instantaneous charging power, expressed as: ， in, The rated charging power of station s, For time decay parameters, These are the parameters for the state of charge response; The initial load trajectory Calculated using the following formula: 。 8. The prediction method according to claim 1, characterized in that, In step S6, the coupling matrix is: The coupling weight , Let be the distance between station s and station r. and These are the capacity parameters for the corresponding sites. For distance scale parameters, For capacity scale parameters; Using the coupling matrix W to analyze the initial load trajectory Cross-site collaborative correction is performed to obtain the coupled corrected load trajectory. : , in, and The initial load for neighboring sites r and k.

9. The prediction method according to claim 1, characterized in that, In step S7, the higher-order variational correction is achieved by constructing and solving the extremum problem of the following functional: ， in, To ultimately predict the load, The load trajectory is after coupling correction. To correct the weights; The solution is under constraints. The following steps were taken to obtain information about Euler-Lagrange equation: , The solution result is used as the final predicted load trajectory.

10. The prediction method according to claim 4 or 5, wherein the time derivative term in the probability density equation or the hydrodynamic equation employs the Caputo fractional derivative. Replace it. It is a fractional order, and 0 < <1.

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