Non-cooperative game-based electric vehicle charging scheduling method and system considering load

Abstract

The present application relates to electric vehicle charging scheduling technical field, proposed considering the non-cooperative game type electric vehicle charging scheduling method and system of load, including predicting the photovoltaic power generation capacity and EV's charging demand of future period;Each EV is regarded as a rational individual participant, and a non-cooperative game model is constructed with charging price and load fluctuation minimization as the target;Game solution, according to the predicted photovoltaic power generation capacity and EV's charging demand, for the non-cooperative game model, strategy update solution is solved by using distributed algorithm iteration, finally converges to Nash equilibrium state, obtains game solution result;According to the game solution result, the charging power of each EV is distributed and sent to each charging terminal to execute charging. By introducing future load prediction information, the electric vehicle charging scheduling is modeled as a non-cooperative game and solved by using a distributed iterative algorithm, realizing the real-time, fairness and scalability of power distribution.

Description

Technical Field

[0001] This invention relates to the technical field of electric vehicle charging scheduling, specifically to a non-cooperative game-theoretic method and system for electric vehicle charging scheduling that takes load into account. Background Technology

[0002] The statements in this section are merely background information related to the present invention and do not necessarily constitute prior art.

[0003] With the continuous increase in the number of electric vehicles (EVs), their electricity demand during morning and evening peak hours and concentrated charging periods is showing a significant upward trend. This causes the power distribution network to be subjected to peak surges in a short period of time, leading to problems such as load fluctuations, unstable power supply voltage, and frequency deviations. Photovoltaic-storage charging stations, as integrated energy infrastructure that combines photovoltaic power generation systems with energy storage devices, can utilize direct photovoltaic power generation during the day or energy storage systems for peak shaving, thereby reducing peak grid load, lowering operating costs, and improving the utilization rate of renewable energy. Therefore, efficient energy dispatch and management technologies for photovoltaic-storage charging stations have become a key research direction for alleviating grid pressure, ensuring the charging experience for electric vehicle users, and promoting the development of green transportation.

[0004] Existing energy dispatching systems for photovoltaic-storage charging stations mostly employ a centralized control model, where a central controller makes unified decisions based on global information. However, this model suffers from high computational complexity, heavy data communication load, and dispatch response delays when faced with multiple EVs simultaneously accessing the system and fluctuating charging demand, making it difficult to meet real-time requirements. Furthermore, traditional dispatching strategies generally treat EV charging as an independent task, ignoring the mutual influence between different vehicles in terms of power allocation and resource competition, resulting in a lack of fairness and adaptability in charging power allocation. In addition, existing methods often make decisions based on the current load state, which is insufficient in scenarios with rapidly changing charging loads. Summary of the Invention

[0005] To address the aforementioned problems, this invention proposes a non-cooperative game-based electric vehicle charging scheduling method and system that considers load. By introducing future load prediction information, the electric vehicle charging scheduling is modeled as a non-cooperative game and solved using a distributed iterative algorithm, achieving real-time, fair, and scalable power allocation.

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

[0007] One or more embodiments provide a non-cooperative game-theoretic electric vehicle charging scheduling method that takes load into account, including the following steps:

[0008] Acquire current meteorological data, grid-side data, photovoltaic-side data, and EV user reservation information to predict future photovoltaic power generation capacity and EV charging demand;

[0009] Treating each EV as a rational individual participant, we construct a non-cooperative game model with the goal of minimizing charging prices and load fluctuations, and define the utility function, strategy space and constraints of each EV.

[0010] To solve the game, based on the predicted photovoltaic power generation capacity and the charging demand of EVs, a distributed algorithm is used to iteratively update the strategy for the non-cooperative game model, eventually converging to the Nash equilibrium state to obtain the game solution result.

[0011] Based on the game theory solution, the charging power of each EV is allocated and sent to each charging terminal to perform charging.

[0012] One or more embodiments provide a non-cooperative game-theoretic electric vehicle charging scheduling system that takes load into account, including:

[0013] The information collection and forecasting module is configured to acquire current meteorological data, grid-side data, photovoltaic-side data, and EV user reservation information to predict the photovoltaic power generation capacity and EV charging demand in future periods.

[0014] The game engine module is configured to build non-cooperative game models for all EVs and solve for Nash equilibrium strategies to obtain game solution results.

[0015] The control execution module is configured to allocate charging power to each EV based on the game solution results and send it to each charging terminal to execute charging.

[0016] One or more embodiments provide a load-considered non-cooperative game-theoretic electric vehicle charging scheduling system, including an information acquisition device and a processor;

[0017] The processor is configured to execute the steps of the above-described non-cooperative game-theoretic electric vehicle charging scheduling method that takes load into account.

[0018] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0019] This invention incorporates future load forecasting information to assess photovoltaic power generation capacity and EV charging demand before charging power allocation, significantly reducing electricity purchase costs during peak charging periods. By modeling EV charging scheduling as a non-cooperative game problem, distributed optimization can be achieved without the need for global computation by a centralized controller, reducing computational complexity and data communication load. Using forecasting information to guide game theory solutions allows for the pre-balancing of future load fluctuations, improving the real-time performance and adaptability of scheduling. The introduction of Nash equilibrium solutions makes power allocation among EVs more equitable and effectively suppresses peak load fluctuations, thereby improving the overall operating efficiency and stability of the charging station.

[0020] The advantages of the present invention, as well as its additional advantages, will be described in detail in the following specific embodiments. Attached Figure Description

[0021] The accompanying drawings, which form part of this invention, are used to provide a further understanding of the invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute a limitation thereof.

[0022] Figure 1 This is a flowchart of the electric vehicle charging scheduling method according to Embodiment 1 of the present invention;

[0023] Figure 2 This is a schematic diagram of the electric vehicle charging scheduling system according to Embodiment 2 of the present invention;

[0024] Figure 3 This is a flowchart of the game-theoretic solution method in the electric vehicle charging scheduling process according to Embodiment 1 of the present invention;

[0025] Figure 4 This is a comparison diagram of the non-cooperative game scheduling method based on load prediction in Embodiment 1 of the present invention and the benchmark strategy in terms of unit charging cost;

[0026] Figure 5 This is a comparison chart of the unit charging price changes of the scheduling method of Embodiment 1 of the present invention under different vehicle deadline conditions;

[0027] Figure 6 This is a comparison chart of the unit charging price changes under different average charging demand conditions for the scheduling method of Embodiment 1 of the present invention. Detailed Implementation

[0028] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0029] It should be noted that the following detailed descriptions are exemplary and intended to provide further illustration of the invention. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains.

[0030] It should be noted that the terminology used herein is for describing particular embodiments only and is not intended to limit the exemplary embodiments of the present invention. As used herein, the singular form is intended to include the plural form as well, unless the context clearly indicates otherwise. Furthermore, it should be understood that when the terms "comprising" and / or "including" are used in this specification, they indicate the presence of features, steps, operations, devices, components, and / or combinations thereof. It should be noted that, without conflict, the various embodiments and features within those embodiments can be combined with each other. The embodiments will now be described in detail with reference to the accompanying drawings.

[0031] Example 1

[0032] In one or more of the technical solutions disclosed in the embodiments, such as Figures 1 to 6 As shown, the non-cooperative game-theoretic electric vehicle charging scheduling method considering load includes the following steps:

[0033] Step 1: Obtain current meteorological data, grid-side data, photovoltaic-side data, and EV user reservation information to predict the photovoltaic power generation capacity and EV charging demand in the future.

[0034] Step 2: Treat each EV as a rational individual participant, construct a non-cooperative game model with the goal of minimizing charging price and load fluctuation, and define the utility function, strategy space and constraints of each EV.

[0035] Step 3: Solve the game theory problem. Based on the predicted photovoltaic power generation capacity and the charging demand of EVs, a distributed algorithm is used to iteratively update the strategy for the non-cooperative game model. The solution eventually converges to the Nash equilibrium state, and the game theory solution is obtained.

[0036] Step 4: Based on the game theory solution, allocate the charging power of each EV and send it to each charging terminal to perform charging.

[0037] Furthermore, it also includes a real-time update phase: if a new EV is added or the prediction results are updated, the game modeling and solution process is re-entered to ensure the dynamic adaptability of the scheduling.

[0038] This implementation method acquires real-time meteorological data, power grid operation status data, photovoltaic power generation data, and EV user charging reservation information through an information acquisition module. It then uses a predictive model to estimate photovoltaic power generation capacity and EV charging load demand within a specific future time period. Each EV is abstracted as a rational game participant. Under a non-cooperative game framework, a joint optimization objective is set to minimize charging price and load fluctuations. A utility function and strategy space are constructed based on the constraints of each participant. The game-solving process employs a distributed iterative algorithm. Each EV updates its charging power strategy based on local information. The algorithm converges to a Nash equilibrium state within a finite number of steps, ensuring that each EV's strategy is optimal given the strategies of other vehicles. Finally, the system sends the power allocation results under the Nash equilibrium to each charging terminal, achieving coordination between charging execution and load control.

[0039] Compared to traditional centralized scheduling methods, this implementation effectively reduces computational complexity and communication pressure when facing high concurrency access from multiple vehicles, while improving the response speed and real-time performance of the scheduling system. By introducing a non-cooperative game theory mechanism, it significantly solves the problem of neglecting the mutual influence of different vehicles in power allocation and resource competition in traditional methods. Each EV not only considers its own charging needs during the game process but also needs to respond to changes in the strategies of other vehicles. When the system reaches a Nash equilibrium, it automatically achieves coordination and competitive balance among vehicles, thereby improving the fairness and adaptability of overall power allocation. In addition, by introducing a module for predicting photovoltaic power generation capacity and load demand, it breaks the limitation of traditional decision-making based solely on the current load state, giving the scheduling system forward-looking and dynamic adjustment capabilities, especially suitable for scenarios with rapidly changing charging loads, improving the efficiency of renewable energy utilization while ensuring the stable operation of the power grid. This method can also dynamically adapt to fluctuations in photovoltaic output, enhancing the system's ability to integrate fluctuating energy sources, further improving energy utilization and system stability.

[0040] Step 1 is the information prediction stage: acquire current meteorological data, grid-side data, photovoltaic-side data, and EV user reservation information, predict the time series of photovoltaic power generation capacity and EV charging demand for future periods based on machine learning models, and use the prediction information as input for subsequent game theory.

[0041] Meteorological data may include all-day / hourly horizontal irradiance (GHI), direct normal irradiance (DNI), diffuse horizontal irradiance (DHI), temperature, relative humidity, wind speed, wind direction, cloud cover, cloud height, air pressure, and probability of precipitation.

[0042] Grid-side data can include bus voltage, transformer load factor, feeder power flow, peak electricity price, flat electricity price, and off-peak electricity price.

[0043] Photovoltaic side data can include module temperature, array azimuth / tilt angle, inverter DC side voltage and current, historical active power output, etc.

[0044] EV user reservation information may include the number of electric vehicles expected to be connected in each time slot, the reserved arrival time of each vehicle, the planned departure time, the target state of charge (SOC), the current SOC value, the remaining charging capacity, and the maximum charging power, etc.

[0045] Furthermore, the machine learning model employs a multi-model fusion structure; specifically, it constructs a multi-model fusion network, such as... Figure 1 As shown, the network includes a Long Short-Term Memory (LSTM) subnetwork, a One-Dimensional Convolutional Neural Network (CNN-1D) subnetwork, and a Gradient Boosting Tree (XGBoost) subnetwork. These three subnetworks are cross-fused at the feature layer.

[0046] The LSTM subnetwork forecasts long-term trends. When the forecast target is EV charging demand, the input is a historical multi-day total station load time series; when the forecast target is photovoltaic (PV) power generation capacity, the input is a historical multi-day PV active power output time series. The output is the baseline load and predicted PV output values ​​for each future time slot. The forecast output of the LSTM subnetwork is denoted as... ;

[0047] The CNN-1D subnetwork is adjusted for short-term fluctuations. When the prediction target is EV charging demand, the input is short-term historical load and time characteristics, and the output is the predicted load. When the prediction target is photovoltaic power generation capacity, the input is short-term historical photovoltaic output and time characteristics, and the output is the load and the photovoltaic output correction. The prediction output of the CNN-1D subnetwork is denoted as... ;

[0048] To prevent special circumstances such as external abrupt changes, the XGBoost subnetwork takes EV user reservation information and vehicle behavior characteristics as inputs when the prediction target is EV charging demand, and meteorological abrupt changes (such as cloud cover changes, precipitation probability, etc.) as inputs when the prediction target is photovoltaic power generation capacity. It outputs the load driven by vehicle behavior and the predicted photovoltaic output value, respectively. The prediction output of the XGBoost subnetwork is denoted as... ;

[0049] To achieve deep cross-fusion of multi-source information, this embodiment introduces an adaptive fusion sub-network in the feature extraction stage: first, the intermediate feature vectors (i.e., the baseline load prediction value and the load correction value) of the LSTM and CNN-1D sub-networks are mapped to a unified dimension with the high-dimensional feature vector output by XGBoost, i.e., the load prediction value, to construct a feature sequence, and then the fusion weights are generated. This enables the unification of feature layer cross-fusion and decision layer adaptive weighted prediction.

[0050] Finally, to meet the independent input parameter requirements of the subsequent non-cooperative game model, this step outputs two independent sets of time series prediction results: predicted photovoltaic power generation capacity for future periods. Compared with the forecast of conventional charging demand for electric vehicles For both prediction targets mentioned above, the adaptive weighted fusion strategy described above is used for calculation. For any prediction target... For example, the final fusion result is:

[0051] ;

[0052] in, Indicates the first The predicted output of each sub-network for this objective (solar power output or charging demand) For the corresponding adaptive weight coefficients, satisfying and .

[0053] One feasible implementation method is adaptive weighting coefficients. A dynamic allocation strategy based on the prediction error of a sliding window is adopted. This strategy automatically adjusts the weights of each sub-model according to its performance in the most recent historical time period, and calculates the mean square prediction error of the m-th sub-model over the past W time slots. Then, the current adaptive weights are calculated using the inverse error method. :

[0054] ;

[0055] ;

[0056] Where W is the length of the sliding window; These are true observations of historical moments. This is a predicted value; To prevent smooth minima where the denominator is zero.

[0057] Another feasible implementation involves transforming the intermediate representation features of the three sub-models—LSTM, CNN-1D, and XGBoost—and calculating adaptive weights through attention and gating mechanisms. Same as subsequent step S13;

[0058] Furthermore, the training method for the constructed multi-model fusion network includes the following steps:

[0059] Step S11, Data Preprocessing: Collect historical load, electricity price, weather, and vehicle behavior data; impute missing values ​​and perform normalization; construct station-level historical load sequences, time feature sequences, and vehicle demand feature sequences to form a training sample set. Let the actual load of the nth sample in time slot t be denoted as... .

[0060] Step S12, Sub-model Training: Pre-train the three sub-models LSTM, CNN-1D, and XGBoost using the training sample set respectively, to obtain the prediction output of each sub-model in time slot t. , , ;

[0061] Step S13, Feature Unification Mapping and Cross-Fusion: Transform the intermediate representation features of the three sub-models LSTM, CNN-1D, and XGBoost during training, and calculate adaptive weights through attention and gating mechanisms. ;

[0062] Step S131: Map the intermediate representation features of the three sub-models LSTM, CNN-1D and XGBoost to a unified dimension, and concatenate them in order to form a feature sequence;

[0063] ;

[0064] in, This represents the intermediate representation features of the m-th model for input sample n at time step t. Represents the weight matrix. Indicates bias;

[0065] Each of the three models in this embodiment outputs its own predicted value. , , However, in addition to outputting predicted values, intermediate features can also be extracted from its hidden layers or penultimate layer.

[0066] Concatenate them sequentially to form a feature sequence:

[0067] ;

[0068] Step S132: Input the feature sequence into the adaptive fusion sub-network, perform multi-head attention fusion processing, and generate adaptive weights through a gating network. ,include:

[0069] Multi-head attention mechanism, used to explicitly model the correlation and importance among three types of features:

[0070] ;

[0071] Gating weights are generated dynamically based on operating conditions (such as photovoltaic output and load level) to produce weights for each sub-model. :

[0072] ;

[0073] in, As a gated network, it is implemented using a two-layer fully connected feedforward network (MLP);

[0074] Step S14: Based on the obtained fusion weights The prediction outputs of each sub-model at time slot t are fused to obtain the fused prediction result. The model parameters are adjusted based on the loss function to obtain the final trained multi-model fusion network.

[0075] The formula for calculating the fusion prediction result is as follows:

[0076] ;

[0077] The weight generation network and fusion layer parameters are trained using mean squared error (MSE) as the loss function. The loss function is as follows:

[0078] ;

[0079] Where N is the number of training samples and T is the length of the prediction time window.

[0080] Furthermore, it also includes online updates, with the prediction error calculated in real time over a sliding window during the runtime phase, and the mean square error within the window... Exceeding the preset threshold At this time, online fine-tuning of the weight generation network parameters is triggered, and the parameters are adjusted according to the gradient descent rule, as shown in the formula:

[0081] ;

[0082] in, Generate the network's parameter vector for the weights. For learning rate, Indicates about parameters The gradient vector is used to adaptively correct concept drift through online updates, thereby improving the accuracy of long-term predictions.

[0083] Specifically, taking a photovoltaic-storage charging station in a certain city as an example, the station has 20 charging terminals, simultaneously connecting 100 EVs during a certain period. First, an information collection and prediction module acquires historical meteorological data, grid load records, and user reservation behavior, and then uses a machine learning model to predict the time series of photovoltaic power generation capacity and EV charging demand for the next 12 hours. These prediction results will serve as important inputs for game theory modeling to identify peak periods that may lead to power conflicts in advance.

[0084] In step 2, the game modeling stage is as follows: each EV is regarded as a rational individual participant, and a non-cooperative game model is constructed with the goal of minimizing charging price and load fluctuation. The utility function, strategy space and constraints of each EV are defined.

[0085] Treating each EV as a rational individual participant, a non-cooperative game model is constructed with the goal of minimizing charging prices and load fluctuations. ,as follows:

[0086] ;

[0087] in, This refers to the participants, i.e., each EV; This indicates the charging power selected by vehicle i during the current time period; Let i represent the utility function of vehicle i, which represents the benefit obtained given its own policy and the policies of other vehicles.

[0088] The charging benefit function is as follows:

[0089] ;

[0090] in, Weighting based on user preferences As the benchmark value for benefits, For saturation rate, For vehicles Actual charging amount For vehicles The charging demand.

[0091] The electricity purchase cost function is as follows:

[0092] ;

[0093] in, For time-slot electricity pricing, For vehicles In the time slot The charging power; This represents the set of discrete time slots within the scheduling time window.

[0094] The fluctuation penalty function is as follows:

[0095] ;

[0096] in, The total system load, For reference load, This is a volatility penalty factor.

[0097] The penalty function for not meeting the requirements is as follows:

[0098] ;

[0099] in, This is a penalty factor for failing to meet requirements.

[0100] The utility function for each EV is constructed as follows: charging benefit function, electricity purchase cost function, fluctuation penalty function, and unmet demand penalty function.

[0101] ;

[0102] Furthermore, the user preference weights The method for determining this is as follows: The average satisfaction rate is calculated based on the user's historical charging behavior and then weighted and integrated with the user's initial preference weights. The calculation formula is as follows:

[0103] ;

[0104] in, Indicates the first The actual amount of electricity gained on the first charge. Indicates the required electricity. The initial user preference value. This is a weighting factor.

[0105] Furthermore, the aforementioned penalty factor for not meeting demand The setting method is as follows: after each round of scheduling, an adaptive update is performed based on the difference between user demand and actual power received. The update formula is:

[0106] ;

[0107] in, The learning rate is the penalty factor when a user's needs are repeatedly not met. Automatically increase to reflect the user's sensitivity to unmet needs.

[0108] Each EV strategy space is This indicates that the charging power meets the maximum charging power limit, which is limited by the vehicle hardware and the charging pile capacity.

[0109] The constraints for each EV include:

[0110] (1) Power boundary constraint: The actual charging power of electric vehicle i in time slot t is less than the maximum allowable charging power of electric vehicle i.

[0111] ;

[0112] in, Let represent the actual charging power decision variable (kW) of electric vehicle i in time slot t; This represents the maximum allowable charging power (kW) of electric vehicle i, which is determined by the minimum of the maximum input power allowed by the on-board battery management system (BMS) and the rated power of the current charging station.

[0113] (2) Energy demand constraint: The actual charging amount of electric vehicle i in time slot t shall not exceed the total energy demand expected to be replenished by electric vehicle i, which must satisfy:

[0114] ;

[0115] in, This represents the charging efficiency coefficient of electric vehicle i. Indicates the duration of a single scheduling slot; This represents the total energy demand (kWh) that electric vehicle i expects to replenish, which is the difference between the energy required at the target state of charge (SOC) and the initial state of charge (SOC).

[0116] (3) Time constraints: The time window must satisfy the time from the arrival time to the departure time, i.e.:

[0117] ,in, This refers to the arrival time at the station. This refers to the departure time.

[0118] (4) Station-level capacity constraint: the sum of the actual charging power of all electric vehicles i is less than the maximum capacity of the station, i.e.:

[0119] ;

[0120] in, This represents the set of all electric vehicles that are in a connected state during time slot t; The maximum capacity of the station; connections / queuing must ensure that each single time slot serves only one vehicle; if necessary, add ramp or switch penalty strategies to limit jitter.

[0121] Step 3, Game Theory Solution Stage: Based on the predicted photovoltaic power generation capacity and EV charging demand, a distributed algorithm is used to iteratively update the strategy for the non-cooperative game model, eventually converging to the Nash equilibrium state to obtain the game theory solution.

[0122] Specifically, a distributed algorithm is used iteratively to solve the policy update problem. This distributed algorithm can be an improved greedy optimal response dynamic algorithm. The improved greedy optimal response dynamic algorithm is used for policy update solving, such as... Figure 3 As shown, it includes the following steps:

[0123] Step 31: Initialize the EV list and charging requirements;

[0124] Specifically, upon receiving a charging task, the system first generates an EV list based on the information of the currently connected electric vehicles, recording parameters such as the remaining battery power, target battery power, maximum charging power, and available charging time for each EV.

[0125] Step 32: Obtain the operation-related forecast information obtained in Step 1, including the photovoltaic power generation capacity forecast sequence for future periods. Electric vehicle conventional charging demand forecast series , which serves as the environmental state input for subsequent game theory models;

[0126] Step 33: Based on the current prediction information of each EV, execute the non-cooperative strategy selection to iteratively update the utility function constructed for each EV, and update the charging power of each EV based on the Greedy Optimal Response Dynamic Algorithm with Proximal Term (BRD-Prox).

[0127] Specifically, an initial charging power strategy is set for each electric vehicle. And calculate the initial load of the system. With electricity price In the first In the round of iteration, a vehicle is selected in turn. The optimization subproblem, which is the object of the update, is defined using the dynamic algorithm based on the greedy optimal response with proximal terms:

[0128] ;

[0129] in, This represents the optimal charging power strategy vector for electric vehicle i after the (k+1)th iteration update; This represents the set of feasible strategies for the vehicle, including power cap, energy demand, and departure window constraints. This represents the real-time electricity price at the k-th iteration. This indicates that vehicles are not included. System load; These are the proximal coefficients, used to suppress oscillations and ensure convergence; For proximal terms, This represents the charging power decision of vehicle i in time slot t during the k-th cycle, used to constrain the current decision. The offset from the result of the previous iteration; For vehicles In the time slot The charging power; For reference load;

[0130] Update system load according to the new vehicle strategy. With electricity price :

[0131] ;

[0132] ;

[0133] in, For electricity price function, This is the electricity price smoothing factor.

[0134] This embodiment employs a greedy optimal response dynamic algorithm with proximal terms to effectively optimize the charging strategy of each EV in a distributed computing environment. The algorithm introduces proximal terms in each strategy update to limit excessive policy jumps and suppress oscillating behavior, thereby enhancing the algorithm's convergence stability and system robustness. Simultaneously, the greedy optimal response mechanism ensures that each EV adjusts its charging power towards the current optimal direction, improving the overall scheduling efficiency and convergence speed. By synchronously updating electricity prices and system load, the system achieves good dynamic response capabilities in a non-cooperative game environment, improving the system's applicability and scheduling quality in volatile environments.

[0135] Step 34: Determine whether the updated charging power of all EVs satisfies the Nash equilibrium state. If it does, then converge and output the game solution result. Otherwise, if it does not converge, return to step 33 to continue iterating until the convergence condition is met.

[0136] In each round, each EV independently calculates its own optimal power response and updates the strategy until the convergence condition is met.

[0137] ;in, Set value;

[0138] If convergence is confirmed, an equilibrium solution is output; otherwise, return to step 33 to continue iteration.

[0139] Specifically, it converges to Nash equilibrium within 20 rounds.

[0140] Step 4, Strategy Execution Phase: The power scheduling value of each EV is sent to the charging terminal through the control execution module, and the execution process is monitored and transmitted back.

[0141] Furthermore, after completing the strategy execution in step 4, the pricing mechanism is dynamically adjusted to reflect the degree of resource competition. Specifically, a dynamic electricity price factor is calculated based on the current total load. To achieve load peak shaving incentives and dynamic electricity price factors The dynamic calculation formula is as follows:

[0142] ;

[0143] in, This indicates the quasi-time-of-use electricity price. This represents the total load of the system in time slot t. Indicates the load threshold. This indicates that photovoltaic or renewable energy output is being generated. This represents the normalization factor for renewable capacity. This represents the adjustment coefficient. Smoothing factor; dynamic electricity price factor The subscript t indicates time slot t;

[0144] The feeder congestion refers to the total load of the system. Exceeding the rated capacity of the feeder The state at that time, its congestion indication function is defined as:

[0145] ;

[0146] Total load: ;

[0147] At the same time, based on the current total load Calculate the dynamic electricity price factor This enables load peak shaving incentives.

[0148] Dynamic electricity price factor In the calculation formula, the plus sign outside the square brackets indicates taking the maximum value between 0 and the current value; that is... , indicates taking the maximum value;

[0149] Furthermore, it also includes a real-time update method: if a new EV is detected, the predicted change in EV charging demand exceeds a set first threshold, or the predicted fluctuation in photovoltaic power generation exceeds a set second threshold, a local game update is automatically triggered to reconstruct the game relationship of the affected EV subset, ensuring that the scheduling is timely and robust.

[0150] Wherein, both the first threshold and the second threshold are set values;

[0151] Furthermore, the method for triggering local game updates and reconstructing the game relations of the affected EV subset during real-time updates includes the following steps:

[0152] Step 51, Event Detection: When a new electric vehicle is detected to be connected, or the charging demand of an existing electric vehicle changes beyond a set value, or the predicted fluctuation of renewable energy output exceeds a set threshold, a local game update is triggered.

[0153] Step 52, Subset Reconstruction: For the set of affected electric vehicles, reconstruct their utility functions to obtain the reconstructed subset, and freeze the existing charging strategies of unaffected vehicles unchanged;

[0154] Step 53, Iterative Update: Run the Greedy Optimal Response Dynamic Algorithm with Proximal Term (BRD-Prox) within the reconstructed subset, reuse the previous round of equalization results as initial values, and iteratively update to obtain the new charging power allocation;

[0155] Step 54: Result merging: Merge the updated subset equalization results with the original strategies for unaffected vehicles to form a new overall charging scheduling scheme, which will then serve as the input for subsequent scheduling rounds.

[0156] A further technical solution involves setting up a communication and synchronization module to achieve synchronous scheduling and parameter sharing among the charging piles.

[0157] The control method for synchronous scheduling and parameter sharing among charging piles includes the following steps:

[0158] Step 61, Clock Synchronization Control: Use Network Time Protocol (NTP) or Precision Time Protocol (PTP) to synchronize the local clocks of each charging pile and edge control node in the station, so that all charging piles and edge control nodes start the scheduling cycle and execute power commands under a unified time base.

[0159] Step 62: Configure the network topology. Based on the scale and reliability requirements of the charging stations, set the communication topology between the charging piles.

[0160] Optionally, a star topology can be used in small-scale sites, where edge control nodes aggregate and distribute scheduling parameters; in large-scale or high-reliability scenarios, a decentralized Gossip topology can be used, where each charging pile only exchanges parameters with its neighboring nodes, achieving consistency of parameters across the entire site after multiple iterations. After completing the topology selection, the corresponding communication link is established.

[0161] Step 63: Parameter periodic broadcasting and synchronization. Specifically, the parameter sharing period is set to Δt. At the beginning of each period, each charging pile or edge control node broadcasts parameters such as the current pile number, the set of electric vehicles on site, the local estimated total system load, the current charging power plan and the plan version number to its communication neighbor nodes. After receiving the parameters from the neighbors, each node aggregates and updates them according to the topology it adopts, thereby achieving periodic synchronization of scheduling information throughout the entire station.

[0162] Furthermore, it also includes fault detection and fault tolerance control. Each node checks the message timestamp in each cycle. If it fails to receive a message for several consecutive cycles, or if the received message timestamp exceeds the set validity period, the charging pile node is marked as an abnormal node. The corresponding charging pile automatically switches to conservative control mode, including limiting the maximum output power and adopting a fixed electricity price strategy to avoid abnormal nodes from impacting system scheduling. After the node is detected to have resumed normal communication, it is reinstated into the scheduling process.

[0163] To illustrate the effectiveness of the method described in this embodiment, simulation experiments were conducted using electric vehicle charging scenarios of different scales, as detailed below;

[0164] The experiment spanned a 24-hour time domain with a 15-minute time step, dividing the scheduling cycle into 96 discrete time slots. All scheduling decisions were executed within this time grid. Three scenarios were constructed: small (20 electric vehicles), medium (100 electric vehicles), and large (300 electric vehicles). Vehicle arrival times were generated using a Poisson process model based on historical statistics, while charging demand and departure cutoff times were generated using a truncated Gaussian distribution to characterize the randomness of user arrivals and demand variability. Baseline load and photovoltaic output were based on historical operating data from the target site. Photovoltaic output was predicted on a rolling basis within each scheduling time slot to reflect the intermittent nature of renewable energy. The feeder rated capacity was set to 400kW to examine the scheduling effect under different congestion levels.

[0165] The experimental evaluation metrics include: system peak-to-average ratio (PAR), total scheduling cost, unmet demand ratio, and convergence rounds of the game theory algorithm. The system PAR is used to evaluate the peak shaving and valley filling effect, the total scheduling cost reflects the overall charging cost on the user side, the unmet demand ratio measures service quality, and the convergence rounds are used to evaluate the computational and communication overhead of the distributed game theory method.

[0166] To verify the effectiveness of the method proposed in this invention, the following strategies were selected for comparison in the experiment, and are detailed in the appendix. Figures 4 to 6 The corresponding legend labels are as follows:

[0167] (1) Centralized optimal scheduling (corresponding to) Figure 5 , Figure 6 The "centralized approach" in this context assumes the existence of a central controller that holds all global information. By solving a global optimization problem, a theoretical lower bound on cost is obtained, which serves as an ideal benchmark for measuring the performance of various distributed algorithms.

[0168] (2) Greedy charging strategy: Charge the vehicle at maximum power as soon as it arrives, without considering electricity price and load conditions, as the most basic control group.

[0169] (3) Scheduling strategy based on time-of-use (TOU): Vehicles only adjust their charging time according to the fixed time-of-use price and do not participate in game interaction.

[0170] (4) Traditional non-cooperative game iterative method (corresponding to) Figure 4 The illustration of the "Model Based on Stackelberg Game" in the text, and Figure 5 , Figure 6 (Example of "Game 1" in the diagram): A standard distributed game strategy is used, without incorporating the proximal term correction and dynamic electricity price mechanism proposed in this embodiment. This method serves as a benchmark control group to verify the improvements in convergence speed and stationarity of this invention.

[0171] (5) The non-cooperative game scheduling method considering load proposed in this embodiment (corresponding to) Figure 4 The legend of "this model" in the text, and Figure 5 and Figure 6 The “Game 2” diagram in this embodiment is the core method proposed in this embodiment. It introduces proximal term regularization and dynamic electricity price factor. Under the premise of ensuring the privacy of distributed computing, the performance curve (Game 2) of this method is closest to the centralized optimal solution and is better than the benchmark game strategy.

[0172] Experimental results show that, in a medium-scale scenario (100 electric vehicles), the method in this embodiment reduces peak load by approximately 12% compared to the greedy strategy, effectively mitigating load spikes during peak hours. Compared to the non-cooperative game theory method without proximate terms, the number of convergence rounds is reduced by approximately 40%, and the non-satisfaction rate is close to 0, comparable to the results of centralized optimal scheduling. In a large-scale scenario (300 electric vehicles), the method in this embodiment maintains low communication and computational overhead while ensuring convergence, demonstrating good scalability.

[0173] In large-scale scenarios, such as those involving more than 300 electric vehicles, centralized optimal scheduling methods struggle to meet real-time requirements due to the exponentially increasing time required to solve integer programming problems as the number of participating vehicles increases. In contrast, the method in this embodiment maintains a stable convergence time even with an increasing number of participants, demonstrating good scalability and engineering deployability.

[0174] Further simulation results show that, under the same average charging demand level, the method in this embodiment actively moves more loads out of high-congestion periods by redistributing charging power in different scheduling time slots. This makes the unit charging cost decrease as the vehicle deadline extends, reflecting the priority guarantee capability for vehicles with more urgent deadlines and helping to improve overall fairness.

[0175] Figure 4 Typical experimental results are selected, with the unit of charging price expressed in cents (￠). The comparison between the method in this embodiment and the baseline strategy in terms of unit charging cost is presented. Under the same vehicle size and load level, the non-cooperative game-theoretic scheduling method considering load proposed in this embodiment maintains a lower unit charging cost across all test points. This demonstrates that the method in this embodiment can effectively move more charging activities out of high-congestion periods, thereby reducing the average cost on the user side and improving overall economic efficiency.

[0176] Figure 5 The curve showing the relationship between the charging unit price and the vehicle's deadline is displayed. The method in this embodiment (Game 2) can provide higher scheduling priority for vehicles with tight deadlines, thus ensuring timely completion of charging needs. When deadlines are more flexible, the method proactively shifts charging to low-load periods, causing the unit price to decrease, demonstrating the fairness and flexibility of the scheduling strategy. In contrast, the traditional game theory method (Game 1) fails to fully utilize low-price periods when deadlines are flexible, resulting in higher costs.

[0177] Figure 6 The study further presents the variation pattern of unit charging cost under different average charging demands. Experimental results show that as vehicle demand increases, the baseline strategy tends to accumulate load during peak hours, leading to price increases. However, the method in this embodiment (Game 2) can effectively smooth the demand distribution through future load forecasting and dynamic power adjustment, keeping the overall unit cost at a lower level under different demand scales, and is very close to the theoretically optimal centralized method.

[0178] Example 2

[0179] Based on Embodiment 1, this embodiment provides a non-cooperative game-theoretic electric vehicle charging scheduling system that considers load, such as Figure 2 As shown, it includes:

[0180] The information collection and forecasting module is configured to acquire current meteorological data, grid-side data, photovoltaic-side data, and EV user reservation information to predict the photovoltaic power generation capacity and EV charging demand in future periods.

[0181] The game engine module is configured to build non-cooperative game models for all EVs and solve for Nash equilibrium strategies to obtain game solution results.

[0182] The control execution module is configured to allocate charging power to each EV based on the game solution results and send it to each charging terminal to execute charging.

[0183] Furthermore, the game engine module includes:

[0184] The game modeling module is configured to treat each EV as a rational individual participant, construct a non-cooperative game model with the goal of minimizing charging price and load fluctuation, and define the utility function, strategy space and constraints of each EV.

[0185] The game theory solution module is configured to perform game theory solutions. Based on the predicted photovoltaic power generation capacity and the charging demand of EVs, it uses a distributed algorithm to iteratively update the strategy for a non-cooperative game model, eventually converging to a Nash equilibrium state to obtain the game theory solution result.

[0186] Furthermore, it also includes a real-time update module, which is configured to: automatically trigger a local game update and reconstruct the game relationship of the affected EV subset if a new EV is detected to be connected, the predicted change in the charging demand of the EV exceeds a set first threshold, or the predicted fluctuation in photovoltaic power generation exceeds a set second threshold.

[0187] Furthermore, the local game update method includes:

[0188] Event detection: When a new electric vehicle is detected joining, or the charging demand of an existing electric vehicle changes beyond a set value, or the predicted fluctuation in renewable energy output exceeds a set threshold, a local game update is triggered.

[0189] Subset reconstruction: For the set of affected electric vehicles, reconstruct their utility functions to obtain the reconstructed subset, and freeze the existing charging strategies of unaffected vehicles unchanged;

[0190] Iterative update: Run the Greedy Optimal Response Dynamic Algorithm with Proximal Term (BRD-Prox) within the reconstructed subset, reuse the previous round of equalization results as initial values, and iteratively update to obtain the new charging power allocation;

[0191] Result merging: The updated subset equalization results are merged with the original strategies for unaffected vehicles to form a new overall charging scheduling scheme, which is then used as input for subsequent scheduling rounds.

[0192] Furthermore, it also includes a communication and synchronization module: used to achieve synchronous scheduling and parameter sharing among the charging piles.

[0193] It should be noted that each module in this embodiment corresponds one-to-one with each step in embodiment 1, and their specific implementation process is the same, so it will not be repeated here.

[0194] Example 3

[0195] Based on Embodiment 1, this embodiment provides a non-cooperative game-theoretic electric vehicle charging scheduling system that takes load into account, including an information acquisition device and a processor;

[0196] The processor is configured to perform the steps of the load-considered non-cooperative game-theoretic electric vehicle charging scheduling method described in Example 1;

[0197] Information collection devices may include, but are not limited to:

[0198] Meteorological information acquisition module: Used to collect environmental parameters related to photovoltaic power generation in real time, including solar irradiance, temperature, humidity, weather conditions, etc., and transmit them to the processor for photovoltaic power generation capacity prediction.

[0199] Power grid operation information acquisition module: used to acquire power grid power supply status, real-time load, electricity price information, etc.

[0200] Photovoltaic power monitoring module: used to collect real-time output power and historical operating data of photovoltaic power generation system.

[0201] User reservation information collection module: used to receive charging reservation requests from EV users, including estimated arrival time, planned departure time, target SOC (state of charge), etc.

[0202] Vehicle access detection module: used to identify EV access events and collect parameters such as current SOC, battery capacity, and maximum charging power.

[0203] In the above system, the information acquisition device and the processor can be connected via wired or wireless communication; the processor can be an embedded industrial computer, a server, or an edge computing node configured with corresponding software modules.

[0204] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

[0205] While the specific embodiments of the present invention have been described above in conjunction with the accompanying drawings, this is not intended to limit the scope of protection of the present invention. Those skilled in the art should understand that various modifications or variations that can be made by those skilled in the art without creative effort based on the technical solutions of the present invention are still within the scope of protection of the present invention.

Claims

1. A non-cooperative game-based electric vehicle charging scheduling method considering load, characterized in that, Includes the following steps: Acquire current meteorological data, grid-side data, photovoltaic-side data, and EV user reservation information to predict future photovoltaic power generation capacity and EV charging demand; Treating each EV as a rational individual participant, we construct a non-cooperative game model with the goal of minimizing charging prices and load fluctuations, and define the utility function, strategy space and constraints of each EV. To solve the game, based on the predicted photovoltaic power generation capacity and the charging demand of EVs, a distributed algorithm is used to iteratively update the strategy for the non-cooperative game model, eventually converging to the Nash equilibrium state to obtain the game solution result. Based on the game theory solution, the charging power of each EV is allocated and sent to each charging terminal to perform charging. Calculate the dynamic electricity price factor based on the current total load. To achieve load peak shaving incentives and dynamic electricity price factors The calculation formula is: ； in, This indicates the quasi-time-of-use electricity price. This represents the total load of the system in time slot t. Indicates the load threshold. This indicates that photovoltaic or renewable energy output is being generated. This represents the normalization factor for renewable capacity. This represents the adjustment coefficient. Indicates the smoothing factor; This represents the congestion indicator function.

2. The non-cooperative game-theoretic electric vehicle charging scheduling method considering load as described in claim 1, characterized in that: The utility function for each EV includes a charging benefit function, an electricity purchase cost function, a fluctuation penalty function, and a demand shortfall penalty function.

3. The non-cooperative game-theoretic electric vehicle charging scheduling method considering load as described in claim 1, characterized in that: The strategy update solution is obtained through distributed iterative algorithm, including the following steps: Step 31: Initialize the EV list and charging requirements; Step 32: Obtain the predicted information, including the photovoltaic power generation capacity and EV charging demand for future periods; Step 33: Based on the current prediction information of each EV, execute the non-cooperative strategy selection to iteratively update the utility function constructed for each EV, and update the charging power of each EV based on the greedy optimal response dynamic algorithm with proximal terms. Step 34: Determine whether the updated charging power of all EVs satisfies the Nash equilibrium state. If it does, then converge and output the game solution result. Otherwise, if it does not converge, return to step 33 to continue iterating until the convergence condition is met.

4. The non-cooperative game-theoretic electric vehicle charging scheduling method considering load as described in claim 3, characterized in that: The optimization subproblem based on the greedy optimal response dynamic algorithm with proximal terms is defined as follows: ； in, This represents the set of feasible strategies for the vehicle, including power cap, energy demand, and departure window constraints. This indicates that vehicles are not included. System load; For proximal regularization, These are the proximal coefficients, used to suppress oscillations and ensure convergence; For vehicles In the time slot The charging power, For reference load; This represents the real-time electricity price at the k-th iteration. This represents the charging power decision of vehicle i in time slot t during the kth cycle.

5. The non-cooperative game-theoretic electric vehicle charging scheduling method considering load as described in claim 1, characterized in that: If a new EV is detected, the predicted change in EV charging demand exceeds the set first threshold, or the predicted fluctuation in photovoltaic power generation exceeds the set second threshold, a local game update is automatically triggered to reconstruct the game relationship of the affected EV subset.

6. A non-cooperative game-theoretic electric vehicle charging scheduling system considering load, characterized in that, Implementing the load-considered non-cooperative game-theoretic electric vehicle charging scheduling method as described in any one of claims 1-5, comprising: The information collection and forecasting module is configured to acquire current meteorological data, grid-side data, photovoltaic-side data, and EV user reservation information to predict the photovoltaic power generation capacity and EV charging demand in future periods. The game engine module is configured to build non-cooperative game models for all EVs and solve for Nash equilibrium strategies to obtain game solution results. The control execution module is configured to allocate charging power to each EV based on the game solution results and send it to each charging terminal to execute charging.

7. The non-cooperative game-theoretic electric vehicle charging scheduling system considering load as described in claim 6, characterized in that: The game engine module includes: The game modeling module is configured to treat each EV as a rational individual participant, construct a non-cooperative game model with the goal of minimizing charging price and load fluctuation, and define the utility function, strategy space and constraints of each EV. The game theory solution module is configured to perform game theory solutions. Based on the predicted photovoltaic power generation capacity and the charging demand of EVs, it uses a distributed algorithm to iteratively update the strategy for a non-cooperative game model, eventually converging to a Nash equilibrium state to obtain the game theory solution result.

8. The non-cooperative game-theoretic electric vehicle charging scheduling system considering load as described in claim 7, characterized in that: The game-solving module is configured to use a distributed algorithm for iterative policy updates, including the following steps: Step 31: Initialize the EV list and charging requirements; Step 32: Obtain the predicted information, including the photovoltaic power generation capacity and EV charging demand for future periods; Step 33: Based on the current prediction information of each EV, execute the non-cooperative strategy selection to iteratively update the utility function constructed for each EV, and update the charging power of each EV based on the greedy optimal response dynamic algorithm with proximal terms. Step 34: Determine whether the updated charging power of all EVs satisfies the Nash equilibrium state. If it does, then converge and output the game solution result. Otherwise, if it does not converge, return to step 33 to continue iterating until the convergence condition is met.

9. A non-cooperative game-theoretic electric vehicle charging scheduling system considering load, characterized in that: Includes information acquisition devices and processors; The processor is configured to perform the steps of the load-considered non-cooperative game-theoretic electric vehicle charging scheduling method according to any one of claims 1-5.

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