A flexibility probabilistic prediction and random optimization regulation method for electric vehicle cluster

Abstract

This invention relates to a method for probabilistic prediction and stochastic optimization control of electric vehicle (EV) clusters, comprising: reconstructing the cumulative charging capacity envelope of a single EV based on charging data to obtain the feasible charging capacity domain of the EV, and defining an individual charging satisfaction index; aggregating EVs level by level using an EV aggregator to form the cumulative charging capacity envelope of the EV cluster, obtaining the cluster's feasible charging capacity domain; predicting the cluster's adjustment flexibility probability based on GPR; establishing the EV cluster's feasible charging capacity domain and the cluster's charging satisfaction loss function, constructing a cluster-level optimization operation problem, solving the optimization operation problem to obtain the optimal charging trajectory of the EV cluster, and distributing the solution results to each EV based on the individual charging satisfaction of the EVs, thereby achieving real-time control of the EV cluster. Compared with existing technologies, this invention has advantages such as not relying on historical demand response data and achieving good control effects.

Description

Technical Field

[0001] This invention relates to the field of electric vehicle optimization and control, and in particular to a method for probabilistic prediction and stochastic optimization control of electric vehicle clusters. Background Technology

[0002] Electric vehicles (EVs) are one of the important means for humanity to solve serious problems such as energy shortages and environmental pollution. On the one hand, EVs can significantly reduce the transportation sector's dependence on fossil fuels; on the other hand, the aggregation of large-scale EV resources can make them a new type of demand-side flexibility resource with good regulatory capabilities, effectively improving the reliability and economy of power system operation. Therefore, governments around the world are actively promoting their rapid development through various means such as economic support, policy incentives, and mandatory regulations.

[0003] However, EV charging behavior is highly random, requiring accurate and reliable forecasting of charging load for effective optimization and demand-side management. Currently, charging load forecasting faces the following problems and challenges.

[0004] (1) Existing research mainly focuses on charging load curve prediction, rather than EV flexibility prediction, which fails to reflect the adjustable resource characteristics of EVs. For example, Niu Mutong et al. proposed a "Multi-Time-Scale Electric Vehicle Load Prediction Model Considering Seasonal Characteristics," which realizes EV charging load curve prediction at multiple time scales and is mainly used for future charging facility construction and distribution network scheduling planning; Chen Yong et al. proposed "Large-Scale Electric Vehicle Charging Load Prediction," which uses a combined prediction model to calculate the number of vehicles and predicts the load of different types of EVs based on the Monte Carlo method. None of the above literature addresses the issue of flexibility prediction. Prediction problems usually require historical statistical data, but EV demand response data is much less than charging load data, making EV flexibility prediction far more difficult than load prediction.

[0005] (2) Existing EV flexibility prediction methods are based on relatively idealistic assumptions. For example, VANDAEL S et al. proposed an "AScalable three-step approach for demand-side management of plug-in hybrid vehicles," which requires users to report their charging plans in advance, affecting the charging experience and making it difficult to guarantee user cooperation. Hou Hui et al. proposed a "Price and Incentive Demand Response Electric Vehicle Load Aggregator Scheduling Strategy," assuming that characteristic parameters such as EV arrival time, charging time, charging capacity, and daily mileage all follow a normal distribution and are independent of each other. However, actual charging data shows that their distribution is not a single normal distribution, and there is a significant correlation between the above parameters.

[0006] (3) Most existing studies use deterministic prediction methods (also known as point prediction), which can only provide expected values, but not confidence intervals and confidence levels. Considering the stochastic nature of EV charging behavior, deterministic prediction results cannot provide the predicted distribution, and the information they can provide is relatively limited. It is difficult for grid dispatchers or EV aggregators to judge the risks and uncertainties of decision-making.

[0007] In summary, predicting EV flexibility solely based on historical response data presents significant challenges: Currently, the limited number of demand response events makes it difficult to obtain sufficient training samples for prediction; furthermore, as EV penetration increases, vehicle-to-grid interactions will become more frequent and routine. However, the range of EV flexibility exhibited in each response is influenced by numerous factors, including the type of interaction, time period, incentive intensity, and control objectives, which will have a cascading impact on charging trajectories in subsequent periods. Summary of the Invention

[0008] The purpose of this invention is to provide a method for probabilistic prediction and stochastic optimization control of electric vehicle clusters, which achieves rapid and accurate prediction of flexibility without relying on a large amount of historical demand response data, and realizes effective response scheduling of EV clusters while ensuring that charging targets are achieved.

[0009] The objective of this invention can be achieved through the following technical solutions:

[0010] A method for probabilistic prediction and stochastic optimization control of electric vehicle clusters includes the following steps:

[0011] Step 1) Based on the charging data, reconstruct the cumulative charging envelope of a single electric vehicle to obtain the feasible charging domain of the electric vehicle, and define the individual charging satisfaction index of a single electric vehicle.

[0012] Step 2) Utilizing the additivity property of the power envelope, the electric vehicles are aggregated step by step based on the electric vehicle aggregator to form the cumulative charging power envelope of the electric vehicle cluster, thus obtaining the power feasible region of the electric vehicle cluster.

[0013] Step 3) Utilize the cumulative charging envelope of the electric vehicle cluster to predict the cluster's adjustment flexibility probability based on GPR.

[0014] Step 4) Based on the probability prediction results of adjustment flexibility, establish the feasible domain of electric vehicle cluster and the charging satisfaction loss function of the cluster, construct the cluster-level optimization operation problem, solve the optimization operation problem to obtain the optimal charging trajectory of electric vehicle cluster, and allocate the solution results to each electric vehicle based on the individual charging satisfaction of electric vehicles to realize real-time control of electric vehicle cluster.

[0015] The measurable data of the charging pile includes network access time, network disconnection time, charging amount, and charging power.

[0016] The specific steps for reconstructing the cumulative charging capacity envelope of a single electric vehicle based on charging data to obtain the feasible charging capacity domain of the electric vehicle are as follows:

[0017] For a single electric vehicle, assume t in Start charging as soon as you connect to the network, t out Let D represent the accumulated battery charge and E represent the battery charge in a single time period, then the charging behavior model of a single electric vehicle can be expressed as follows:

[0018]

[0019] In the formula: P k Let D be the charging power during time period k, η be the charging efficiency, and D be the charging power during time period k. k Let D be the cumulative charging power up to time period k, Δt be the optimized scheduling interval, and D be the cumulative charging power up to time period k. exp D represents the charging power requirement. min,k D max,k These represent the lower and upper bounds of the charging capacity up to time period k, respectively.

[0020] If electric vehicles can [t] in ,t out If the charging target is achieved during the period, the feasible region of its charging capacity is represented as a closed region of parallelograms, with its upper and lower envelopes representing the fastest and slowest charging trajectories, respectively, and containing all possible charging trajectories of the EV.

[0021] The individual charging satisfaction index for a single electric vehicle is defined as follows:

[0022]

[0023] In the formula: P N The numerator represents the rated charging power; the numerator is the remaining uncharged amount of the electric vehicle, the denominator is the maximum amount of electricity that the electric vehicle can be charged before leaving the grid, and Δt′ represents the control interval.

[0024] S k The size reflects the user's urgency to charge: S k The smaller the value, the lower the urgency; S k =0 indicates that charging is complete, S k =1 indicates that the electric vehicle must maintain its rated charging power until it leaves the grid in order to achieve the charging target. If the electric vehicle can achieve the charging target, then S k The value always remains within the range of [0,1].

[0025] The step-by-step aggregation of electric vehicles based on the electric vehicle aggregator specifically involves overlaying the charging behavior models of individual electric vehicles within the cluster. The aggregation information is as follows:

[0026]

[0027] In the formula: the subscript agg on the left side of the equation represents the aggregate value of the variable corresponding to the electric vehicle cluster, and n is the number of electric vehicles in the cluster.

[0028] The cumulative charging capacity envelope of the electric vehicle cluster is used to construct the energy feasible region of the electric vehicle cluster, which specifically includes the following constraints:

[0029]

[0030] In the formula: D agg,k E represents the cumulative charging power of the cluster up to time period k. agg,k This represents the charging power of the cluster during time period k; the upper and lower bounds P of the cluster's charging power during this time period are also shown. max,agg,k P min,agg,k Take P from the pre-configured time period in the past. agg,k The maximum and minimum values.

[0031] By utilizing the cumulative charging capacity envelope of the electric vehicle cluster, the fastest charging trajectory of the cluster is compared with the actual charging trajectory, thereby quantitatively describing the charging anxiety of the cluster and obtaining the satisfaction loss function of the cluster under T optimization periods:

[0032]

[0033] In the formula: λ is the cluster anxiety coefficient, which represents the degree of importance that the cluster attaches to charging anxiety.

[0034] Step 3) predicting the adjustment flexibility probability of the cluster based on GPR includes probability prediction for the upper envelope and probability prediction for the lower envelope. The probability prediction for the upper envelope includes the following steps:

[0035] Step 311) Treat the upper envelope time series of the cumulative charging amount of the electric vehicle cluster as a Gaussian process, that is:

[0036] {D max,agg,k}~GP(m(k),K(k,k′))

[0037] In the formula: m(k) is the mean function, K(k,k') is the covariance function, and D... max,agg,k This represents the aggregated value of the charging amount up to time period k after being aggregated by the aggregator.

[0038] Step 312) Use a smooth periodic kernel function of the following form as the covariance function:

[0039]

[0040] In the formula: σ f l and p are the hyperparameters to be identified, and p is the period of the envelope.

[0041] Step 313) Abbreviated as D = {D} max,agg,k} represents the historical samples of the cumulative charging power envelope of the cluster, with a quantity of n; D * =D max,agg,k* For the future k * The value to be predicted at time σ is the root mean square error of the electrical quantity measurement, and I is the value to be predicted at time σ. n If D is an n-order identity matrix, then D and D * It follows a joint Gaussian distribution as follows:

[0042]

[0043] In the formula:

[0044]

[0045] Step 314) If the conditional probability of the Gaussian process still follows a Gaussian distribution, then the future k * Time D * The distribution is as follows:

[0046]

[0047] Then future k * The expected value of the point prediction result on the envelope of the cumulative charging capacity of the time cluster is:

[0048]

[0049] The variance at the corresponding time point is:

[0050]

[0051] Step 315) Based on the pre-configured confidence level, the expected value of the point prediction result, and the variance at the corresponding time, determine the point prediction value and confidence interval of the upper envelope of the cumulative charging power of the electric vehicle cluster, and obtain the prediction result of the upper envelope of the cumulative charging power of the electric vehicle cluster, i.e., random variable.

[0052] The probability prediction of the lower envelope includes the following steps:

[0053] Step 321) Treat the time series envelope of the cumulative charging power of the electric vehicle cluster as a Gaussian process, that is:

[0054] {D min,agg,k}~GP(m(k),K(k,k′))

[0055] In the formula: m(k) is the mean function, K(k,k') is the covariance function, and D... min,agg,k This represents the aggregated value after aggregating the lower bound of the charging amount up to time period k through the aggregator.

[0056] Step 322) Use a smooth periodic kernel function of the following form as the covariance function:

[0057]

[0058] In the formula: σ f l and p are the hyperparameters to be identified, and p is the period of the envelope.

[0059] Step 323) Abbreviation: D' = {D min,agg,k} represents the historical samples of the envelope under the cumulative charging power of the cluster, with a quantity of n; D' * =D min,agg,k* For the future k * The value to be predicted at time σ is the root mean square error of the electrical quantity measurement, and I is the value to be predicted at time σ. n If D' is an n-order identity matrix, then D' and D' * It follows a joint Gaussian distribution as follows:

[0060]

[0061] In the formula:

[0062]

[0063] Step 324) If the conditional probability of the Gaussian process still follows a Gaussian distribution, then the future k * Time D' * The distribution is as follows:

[0064]

[0065] Then future k * The expected value of the point prediction result of the envelope of the time cluster under the cumulative charging power is:

[0066]

[0067] The variance at the corresponding time point is:

[0068]

[0069] Step 325) Based on the pre-configured confidence level, the expected value of the point prediction result, and the variance at the corresponding time, determine the point prediction value and confidence interval of the envelope of the cluster's cumulative charging power, and obtain the prediction result of the envelope of the electric vehicle cluster's cumulative charging power, i.e., the random variable.

[0070] The process of establishing the feasible domain of electric vehicle clusters based on the probability prediction results of adjustment flexibility and the cluster's charging satisfaction loss function, constructing an optimization operation problem at the cluster level, and solving the optimization operation problem to obtain the optimal charging trajectory of the electric vehicle cluster specifically includes the following steps:

[0071] Step 41) Determine the opportunity constraints of the electric vehicle cluster charging plan based on the adjustment flexibility probability prediction results:

[0072]

[0073] In the formula: α∈[0,1] is the confidence level, P r () represents probability;

[0074] Step 42) Use the probability addition formula to transform the chance constraint into a deterministic constraint:

[0075]

[0076] make:

[0077]

[0078] To obtain a unique solution, let the above equation... If the two corresponding random events have the same probability of occurring, then:

[0079]

[0080] Since the GPR prediction results follow a Gaussian distribution, let The cumulative distribution functions are F Dmin,k F Dmax,k Then the above equation is transformed into the following two sets of deterministic constraints:

[0081]

[0082] Step 43) Constructing an optimized operation problem at the electric vehicle cluster level:

[0083]

[0084] Step 44) Solve the optimization operation problem at the electric vehicle cluster level to obtain the optimal charging trajectory {E} of the electric vehicle cluster. agg,k}

[0085] The method of allocating the solution results based on individual charging satisfaction of electric vehicles to each electric vehicle to achieve real-time control of the electric vehicle cluster includes the following steps:

[0086] Step 45) Virtual bidding: Each electric vehicle bids based on its current charging satisfaction level S. k For virtual bid prices, in P NΔt′ represents the amount of electricity bid, forming a virtual bidding curve, which is then submitted to the aggregator.

[0087] Step 46) Virtual Clearing: Aggregators are sorted from highest to lowest virtual bid price to form an aggregation demand curve; let the current total energy consumption target of the cluster be E. agg,k Find E agg,k The intersection of the virtual clearing price S with the aggregated demand curve yields the virtual clearing price S. * This signal is then sent to each electric vehicle as a cluster control signal.

[0088] Step 47) After receiving the control signal, each electric vehicle shall respond autonomously to the control signal according to the following principle: if its bid price S k Higher than S * Then start charging; otherwise, pause charging.

[0089] Step 48) Repeat steps 45)-47) within the pre-configured control cycle to achieve real-time control of the electric vehicle cluster.

[0090] Compared with the prior art, the present invention has the following beneficial effects:

[0091] (1) This invention proposes a method for constructing the cumulative charging capacity envelope of EVs based on measurable data of charging piles. By combining physical models with data-driven methods, this invention does not require historical samples of demand response to predict the flexible adjustment capability of EV clusters, nor does it require users to report charging plans in advance. It can solve the problem of insufficient demand response events based solely on measurable charging data of charging piles. This ensures that the method described in this invention can have sufficient and accurate sample data for prediction.

[0092] (2) This invention proposes a method for predicting EV cluster flexibility using GPR. It does not require making assumptions about the shape of the regression curve and requires very few model hyperparameters to be determined. It is a highly practical regression method that can effectively, quickly and accurately predict cluster flexibility, thereby adapting to the highly random characteristics of charging load. At the same time, while giving the expected value of charging flexibility, it can also provide confidence intervals, providing more information for optimizing scheduling.

[0093] (3) This invention utilizes the characteristics of Gaussian distribution to easily transform stochastic optimization problems into deterministic optimization problems, thereby facilitating the solution and simplifying the calculation.

[0094] (4) The prediction method of the present invention does not require assumptions or limitations on the distribution of features such as grid connection / disconnection time, charging time and power, as well as the correlation between features, and therefore can be adapted to situations involving multiple charging locations (such as residential areas, commercial areas, workplaces, etc.).

[0095] (5) Compared with point prediction results, the probability prediction of the present invention can provide richer information about the adjustment capability of EV clusters. On the one hand, the power sector can use the flexible prediction results to intuitively judge the load reduction range of the EV cluster in a specific period. On the other hand, the feasible region of the EV cluster can be constructed based on the flexible prediction results, thereby establishing an optimization model and realizing stochastic optimization and internal coordination control of the EV cluster.

[0096] (6) This invention proposes a stochastic optimization control method for EV clusters that takes into account satisfaction, which can achieve effective response scheduling of EV clusters while ensuring that charging targets are met, thereby improving the reliability and economy of power system operation.

[0097] (7) The method described in this invention can ensure that the total charging power accurately tracks the cluster target at the cluster level; at the EV level, it can ensure that EVs with high charging urgency are charged first, and the optimized scheduling scheme is more reasonable and efficient.

[0098] (8) In real-time control, the aggregator coordinates with a unified virtual clearing price, eliminating the need for direct load control on each EV, which improves safety and reduces communication requirements.

[0099] (9) The EV has great autonomy in the method of the present invention: on the one hand, the EV can formulate a bidding curve according to its own charging needs; on the other hand, if the charging target is reached before the end of a control interval, the EV can stop charging immediately. Attached Figure Description

[0100] Figure 1 This is a flowchart of the method of the present invention;

[0101] Figure 2 A schematic diagram of the cumulative charging capacity envelope of an EV, where (a) represents the cumulative charging capacity envelope of a single EV and (b) represents the cumulative charging capacity envelope of an EV cluster.

[0102] Figure 3 A schematic diagram of the prediction results for the upper and lower envelopes of an electric vehicle cluster over a single period;

[0103] Figure 4 Here are the virtual demand curves for EVs, where (a) is the individual demand curve for EVs and (b) is the demand curve for EV clusters.

[0104] Figure 5 This is a schematic diagram of time-of-use electricity pricing in an embodiment of the present invention;

[0105] Figure 6 This is a schematic diagram of the GPR regression prediction results in an embodiment of the present invention;

[0106] Figure 7This is a comparison chart of the cumulative charging power before and after peak shaving in an embodiment of the present invention;

[0107] Figure 8 This is a schematic diagram of the optimal charging capacity for each optimized interval in this embodiment of the invention. Detailed Implementation

[0108] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments. These embodiments are based on the technical solution of the present invention and provide detailed implementation methods and specific operating procedures. However, the scope of protection of the present invention is not limited to the following embodiments.

[0109] This embodiment provides a method for probabilistic prediction and stochastic optimization control of electric vehicle clusters, such as... Figure 1 As shown, it includes the following steps:

[0110] Step 1) Based on the charging data, reconstruct the cumulative charging envelope of a single electric vehicle to obtain the feasible charging domain of the electric vehicle, and define the individual charging satisfaction index of a single electric vehicle.

[0111] The charging station can automatically record measurable data for each EV, including the time of network access (t). in Offline time t out Charging capacity D exp and charging power P EV The aforementioned characteristics require no user input and are unaffected by whether the EV participates in grid interaction. They reflect the user's own travel patterns, as well as the rated power of the EV and charging station. This charging information can be used to reconstruct the EV's cumulative charging envelope, thereby reflecting the EV's adjustment flexibility.

[0112] Based on charging data, the cumulative charging capacity envelope of a single electric vehicle is reconstructed, resulting in the feasible charging capacity region for the electric vehicle as follows:

[0113] For a single electric vehicle, assume t in Start charging as soon as you connect to the network, t out Let D represent the accumulated battery charge and E represent the battery charge in a single time period, then the charging behavior model of a single electric vehicle can be expressed as follows:

[0114]

[0115] In the formula: P k Let D be the charging power during time period k, η be the charging efficiency, and D be the charging power during time period k. k Let D be the cumulative charging power up to time period k, Δt be the optimized scheduling interval, and D be the cumulative charging power up to time period k. exp D represents the charging power requirement. min,k D max,kThese represent the lower and upper bounds of the charging capacity up to time period k, respectively.

[0116] If electric vehicles can [t] in ,t out If the charging target is achieved during the charging period, then the feasible region of its charging capacity is represented as a closed parallelogram region, whose upper and lower envelopes represent the fastest and slowest charging trajectories, respectively. The region contains all possible charging trajectories of the EV, such as... Figure 2 As shown in (a), the shape of the enclosed area is not affected by whether the EV participates in grid interaction. In free charging mode, the EV is usually charged as soon as it is connected to the grid, and the charging trajectory follows the upper envelope. Figure 2 (a) The feasible domain is reconstructed entirely based on the actual charging data of the EV, without requiring users to provide additional information such as charging behavior prediction.

[0117] The individual charging satisfaction index for a single electric vehicle is defined as follows:

[0118]

[0119] In the formula: P N The numerator represents the rated charging power; the denominator is the remaining uncharged amount of the electric vehicle, and the denominator is the maximum amount of electricity the electric vehicle can be charged before leaving the grid. Δt′ represents the control interval. Individual charging satisfaction index is applied in step 4) to regulate the electric vehicle cluster.

[0120] S k It can reflect the user's urgency for charging in real time and intuitively: S k The smaller the value, the lower the urgency; S k =0 indicates that charging is complete, S k =1 indicates that the electric vehicle must maintain its rated charging power until it leaves the grid to achieve its charging target. If the electric vehicle can achieve its charging target, then S k The value always remains within the range of [0,1].

[0121] Step 2) Utilizing the additivity property of the electric charge envelope, the electric vehicles are aggregated step by step by the electric vehicle aggregator to form the cumulative charging capacity envelope of the electric vehicle cluster, thus obtaining the feasible energy domain of the electric vehicle cluster.

[0122] Individual EVs exhibit extremely high randomness, but aggregators can effectively reduce overall randomness and create a load resource with considerable adjustment capacity.

[0123] The electric vehicle aggregator aggregates individual electric vehicles step by step by superimposing the charging behavior models of individual electric vehicles within the cluster. The aggregation information is as follows:

[0124]

[0125] In the formula: the subscript agg on the left side of the equation represents the aggregate value of the variable corresponding to the electric vehicle cluster, and n is the number of electric vehicles in the cluster.

[0126] The cumulative charging capacity envelope of the electric vehicle cluster is used to construct the energy feasible region of the electric vehicle cluster, which specifically includes the following constraints:

[0127]

[0128] In the formula: D agg,k E represents the cumulative charging power of the cluster up to time period k. agg,k This represents the charging power of the cluster during time period k; the upper and lower bounds P of the cluster's charging power during this time period are also shown. max,agg,k P min,agg,k Take P from the past week respectively agg,k The maximum and minimum values.

[0129] By overlaying the individual EV models within the cluster, we obtain, as follows: Figure 2 (b) shows the cumulative charging envelope of the electric vehicle cluster.

[0130] When regulating EV clusters, the charging anxiety of EV owners needs to be considered. By comparing the fastest charging trajectory of the cluster with the actual charging trajectory using the cumulative charging envelope of the EV cluster, the charging anxiety level of the cluster can be quantitatively described. Therefore, this invention defines the cluster satisfaction loss function for T optimization periods as follows:

[0131]

[0132] In the formula: λ is the cluster anxiety coefficient, which represents the degree of importance that the cluster attaches to charging anxiety.

[0133] When the actual charging trajectory of the cluster coincides with the fastest charging trajectory, the satisfaction loss is 0; the longer the charging plan is delayed, the higher the satisfaction loss. By combining equations (2) and (5), the satisfaction of individual EVs and the cluster can be quantitatively described respectively, thereby achieving real-time coordination and overall optimization.

[0134] Step 3) Utilize the cumulative charging envelope of the electric vehicle cluster to predict the cluster's adjustment flexibility probability based on GPR.

[0135] The cumulative charging capacity envelope is mainly determined by the travel patterns of EV users and is not affected by whether they participate in grid interaction. It has relatively stable time series characteristics and can therefore be predicted using GPR.

[0136] Step 3) Based on GPR, predict the adjustment flexibility probability of the cluster, including probability prediction for the upper envelope and probability prediction for the lower envelope.

[0137] Step 31) Probability prediction for the upper envelope:

[0138] Step 311) Treat the upper envelope time series of the cumulative charging amount of the electric vehicle cluster as a Gaussian process, that is:

[0139] {D max,agg,k}~GP(m(k),K(k,k′)) (6)

[0140] In the formula: m(k) is the mean function, K(k,k') is the covariance function, and D... max,agg,k This represents the aggregated value of the charging amount up to time period k, after being aggregated by the aggregator.

[0141] Step 312) Use a smooth periodic kernel function of the following form as the covariance function:

[0142]

[0143] In the formula: σ f l and p are the hyperparameters to be identified, and p is the period of the envelope.

[0144] Step 313) Abbreviated as D = {D} max,agg,k} represents the historical samples of the cumulative charging power envelope of the cluster, with a quantity of n; D * =D max,agg,k* For the future k * The value to be predicted at time σ is the root mean square error of the electrical quantity measurement, and I is the value to be predicted at time σ. n If D is an n-order identity matrix, then D and D * It follows a joint Gaussian distribution as follows:

[0145]

[0146] In the formula:

[0147]

[0148] Step 314) If the conditional probability of the Gaussian process still follows a Gaussian distribution, then the future k * Time D * The distribution is as follows:

[0149]

[0150] Then future k * The expected value of the point prediction result on the envelope of the cumulative charging capacity of the time cluster is:

[0151]

[0152] The variance at the corresponding time point is:

[0153]

[0154] Step 315) Based on the pre-configured confidence level, the expected value of the point prediction result, and the variance at the corresponding time, determine the point prediction value and confidence interval of the upper envelope of the cumulative charging power of the electric vehicle cluster, and obtain the prediction result of the upper envelope of the cumulative charging power of the electric vehicle cluster, i.e., random variable.

[0155] Step 32) Probability prediction of the lower envelope:

[0156] Step 321) Treat the time series envelope of the cumulative charging power of the electric vehicle cluster as a Gaussian process, that is:

[0157] {D min,agg,k}~GP(m(k),K(k,k′)) (13)

[0158] In the formula: m(k) is the mean function, K(k,k') is the covariance function, and D... min,agg,k This represents the aggregated value of the lower bound of the charging amount up to time period k, after being aggregated by the aggregator.

[0159] Step 322) Use a smooth periodic kernel function of the following form as the covariance function:

[0160]

[0161] In the formula: σ f l and p are the hyperparameters to be identified, and p is the period of the envelope.

[0162] Step 323) Abbreviation: D' = {D min,agg,k} represents the historical samples of the envelope under the cumulative charging power of the cluster, with a quantity of n; D' * =D min,agg,k* For the future k * The value to be predicted at time σ is the root mean square error of the electrical quantity measurement, and I is the value to be predicted at time σ. n If D' is an n-order identity matrix, then D' and D' * It follows a joint Gaussian distribution as follows:

[0163]

[0164] In the formula:

[0165]

[0166] Step 324) If the conditional probability of the Gaussian process still follows a Gaussian distribution, then the future k * Time D' * The distribution is as follows:

[0167]

[0168] Then future k * The expected value of the point prediction result of the envelope of the time cluster under the cumulative charging power is:

[0169]

[0170] The variance at the corresponding time point is:

[0171]

[0172] Step 325) Based on the pre-configured confidence level, the expected value of the point prediction result, and the variance at the corresponding time, determine the point prediction value and confidence interval of the envelope of the cluster's cumulative charging power, and obtain the prediction result of the envelope of the electric vehicle cluster's cumulative charging power, i.e., the random variable.

[0173] In this embodiment, Figure 3 The results of the upper and lower envelope predictions for a single period of electric vehicle clusters are presented.

[0174] Step 4) Based on the probability prediction results of adjustment flexibility, establish the feasible domain of electric vehicle cluster and the charging satisfaction loss function of the cluster, construct the cluster-level optimization operation problem, solve the optimization operation problem to obtain the optimal charging trajectory of electric vehicle cluster, and allocate the solution results to each electric vehicle based on the individual charging satisfaction of electric vehicles to realize real-time control of electric vehicle cluster.

[0175] Step 41) Determine the opportunity constraints of the electric vehicle cluster charging plan based on the adjustment flexibility probability prediction results:

[0176]

[0177] In the formula: α∈[0,1] is the confidence level, P r () represents probability;

[0178] Step 42) Use the probability addition formula to transform the chance constraint into a deterministic constraint:

[0179]

[0180] make:

[0181]

[0182] To obtain a unique solution, let the above equation... If the two corresponding random events have the same probability of occurring, then:

[0183]

[0184] Since the GPR prediction results follow a Gaussian distribution, let The cumulative distribution functions are F Dmin,k F Dmax,k Then the above equation is transformed into the following two sets of deterministic constraints:

[0185]

[0186] Step 43) Constructing an optimized operation problem at the electric vehicle cluster level:

[0187]

[0188] In the formula: the objective function takes into account the electricity cost of cluster charging and the loss of satisfaction; the constraint defines the feasible domain of the cluster's electricity, which is based on Equation (4), but takes into account the confidence level α.

[0189] In the above formula, the satisfaction loss function L s It contains the l2-norm, and all other norms are linear, making it an easy quadratic programming problem to solve.

[0190] Step 44) Solve the optimization operation problem at the electric vehicle cluster level to obtain the optimal charging trajectory {E} of the electric vehicle cluster. agg,k}

[0191] Next, the optimization objective needs to be reasonably allocated to each EV, which includes the following steps:

[0192] Step 45) Virtual bidding: Each electric vehicle bids based on its current charging satisfaction level S. k For virtual bid prices, in P N Δt′ represents the bid electricity amount, forming a pattern as follows: Figure 4 (a) shows the virtual bid curve, which is then submitted to the aggregator;

[0193] Step 46) Virtual Clearing: Aggregators sort virtual bids from highest to lowest, forming a virtual clearing pool. Figure 4 (b) shows the aggregated demand curve; let the current total energy consumption target of the cluster be E. agg,k Find E agg,k The intersection of the virtual clearing price S with the aggregated demand curve yields the virtual clearing price S. * This signal is then sent to each electric vehicle as a cluster control signal.

[0194] Step 47) After receiving the control signal, each electric vehicle shall respond autonomously to the control signal according to the following principle: if its bid price S k Higher than S * Then start charging; otherwise, pause charging.

[0195] Step 48) Repeat steps 45)-47) within the pre-configured control cycle to achieve real-time control of the electric vehicle cluster.

[0196] In this embodiment, the control cycle can be set to 5-15 minutes; each time it is executed, the priority order of each EV will be based on its S k The value is dynamically adjusted.

[0197] The EV cluster stochastic optimization control method based on satisfaction has the following characteristics: (1) At the cluster level, it can ensure that the total charging power accurately tracks the cluster target; at the EV level, it can ensure that EVs with high charging urgency are charged first; (2) The aggregator coordinates with a unified virtual clearing price, without the need to implement direct load control for each EV, which improves safety and reduces communication requirements; (3) EVs have great autonomy: on the one hand, EVs can formulate bidding curves according to their own charging needs; on the other hand, if the charging target is reached before the end of a control interval, the EV can stop charging immediately.

[0198] This embodiment references the publicly released field-tested charging dataset from Caltech as historical EV charging data. This dataset contains approximately 30,000 field charging data points spanning three years. Charging electricity prices are... Figure 5 The time-of-use electricity price is shown.

[0199] It's worth noting that in power system operation optimization problems, the start time is often set to 0:00. However, in actual EV cluster operation optimization problems, various charging scenarios are often included, such as residential areas and workplaces, meaning there are still many vehicles charging at 0:00. For ease of construction... Figure 2 The cumulative charging capacity envelope is optimized in this embodiment by setting the period from 7:00 AM to 7:00 AM the next day. This ensures that the number of vehicles charging in various charging areas is relatively small at the above start and end times.

[0200] In this embodiment, the calculation interval for the optimization problem is 0.5h, and the real-time control cycle for EV within the cluster is 5min.

[0201] Based on the aforementioned charging dataset and Equation (1), an eight-day cumulative charging envelope for the EV cluster was established. The first seven days were selected as the training set, and the eighth day (April 25, 2018) was selected as the validation set. The prediction interval was consistent with the optimization interval, which was 0.5h. The confidence level α was set to 95%, and the GPR prediction results are as follows: Figure 6 As shown.

[0202] To evaluate the prediction performance, this embodiment uses the mean absolute percentage error (MAPE) to assess the accuracy of point prediction, and the prediction interval normalized average width (PINAW) and prediction interval coverage proportion (PICP) to assess the sharpness and coverage of the prediction interval, respectively. The specific calculation formulas are as follows:

[0203]

[0204] In the formula: N is the number of prediction periods; For the point prediction result, X k The true value; U k and L k These are the upper and lower bounds of the prediction interval, respectively, when the predicted value for time segment i falls within the interval [L]. k U k [Internal time c] i Set the value to 1, otherwise set it to 0; R is the total range of the interval boundary.

[0205] The evaluation results are shown in Table 1.

[0206] Table 1 Evaluation Indicators for GPR Prediction Results

[0207]

[0208] From the MAPE metric, the predicted point values ​​deviate little from the actual values, effectively reflecting the changing trend of the envelope. From the PINAW metric, the confidence interval closely encloses the actual values, indicating high precision. Meanwhile, from the PICP metric, the confidence interval largely covers the actual values, thus the prediction results for this interval are relatively reliable. It's worth noting that PINAW and PICP are difficult to balance perfectly. In practice, the confidence level α can be adjusted as needed: a larger α results in better coverage (PICP) but worse precision (PINAW), leading to a more conservative estimate of the EV cluster's flexibility.

[0209] The EV aggregator was optimized based on the above prediction results and implemented real-time control within the day to track the optimization results.

[0210] First, consider the case where the EV cluster does not participate in peak shaving response. By solving the optimization operation problem of equation (25), the optimal cumulative charging power trajectory of the cluster is obtained, as follows: Figure 7 As shown by the dashed line, its slope represents the charging power, which is converted into the charging amount within each optimized interval (0.5h) as follows: Figure 8As shown, during the 10:00-11:00 period, the charging power of the charging cluster is 0 due to peak electricity pricing. Subsequently, influenced by charging anxiety, the charging trajectory rises rapidly and basically coincides with the upper envelope prediction boundary. Around 19:00, despite peak electricity pricing, the cluster still retains some charging power because the distance between the upper and lower envelopes is very narrow and the adjustable range is small. During non-off-peak electricity pricing periods such as 20:00 and 23:00, most vehicles choose to delay charging to reduce charging costs because they have sufficient charging time.

[0211] Next, we consider EV participation in peak shaving response. Due to the peak electricity price during the 10:00-11:00 period, many charging plans are delayed, resulting in a cluster charging power of up to 1834kW during the 11:00-13:00 period. Assume that the power sector requires the total charging power during this period not to exceed 1200kW. Then, based on the optimization operation problem in equation (25), we add the power constraint for the peak shaving period and re-optimize to obtain the following result. Figure 7 The optimal trajectory is shown by the solid line in the middle.

[0212] Depend on Figure 7 It can be visually observed that the cluster has significant flexibility in adjustment during the 11:00-13:00 period. After responding to the peak-shaving command, the slope of the charging trajectory decreases significantly during the response period; after the peak-shaving period, to compensate for the reduced charging load, the curve slope becomes noticeably steeper again from 13:00, coinciding with the upper envelope at 14:00. Corresponding to... Figure 8 In the process, it can be observed more intuitively that the charging power is constrained to within 1200kW during peak shaving periods, and then the charging load recovers rapidly.

[0213] The above analysis focuses on the cluster optimization effect; the following analysis examines the actual execution control effect. Using the satisfaction-based stochastic optimization and control method of this invention, from... Figure 8 It is evident that the actual charging load tracked the optimized results well for most of the time. However, due to prediction errors, there were tracking deviations during a few periods. For example, after 0:00 the next day, from... Figure 7 Notice that the true value of the cluster's envelope lies at the lower edge of the prediction interval, indicating that the prediction overestimated the cluster's charging power demand after 0:00. Correspondingly, from... Figure 8 As you can see, the actual charging power of the cluster after 0:00 is lower than the optimized result. During the aforementioned period, the interval prediction result of this embodiment reduces the point prediction error to a certain extent, making the optimization result more consistent with the actual situation and more feasible.

[0214] The preferred embodiments of the present invention have been described in detail above. It should be understood that those skilled in the art can make numerous modifications and variations based on the concept of the present invention without creative effort. Therefore, all technical solutions that can be obtained by those skilled in the art based on the concept of the present invention through logical analysis, reasoning, or limited experimentation on the basis of existing technology should be within the scope of protection defined by the claims.

Claims

1. A method for flexible probabilistic forecasting and stochastic optimization regulation of an electric vehicle cluster, characterized in that, Includes the following steps: Step 1) Based on the charging data, reconstruct the cumulative charging envelope of a single electric vehicle to obtain the feasible charging domain of the electric vehicle, and define the individual charging satisfaction index of a single electric vehicle. Step 2) Utilizing the additivity property of the power envelope, the electric vehicles are aggregated step by step based on the electric vehicle aggregator to form the cumulative charging power envelope of the electric vehicle cluster, thus obtaining the power feasible region of the electric vehicle cluster. Step 3) Utilize the cumulative charging envelope of the electric vehicle cluster to predict the cluster's adjustment flexibility probability based on GPR. Step 4) Based on the probability prediction results of adjustment flexibility, establish the feasible domain of electric vehicle cluster and the charging satisfaction loss function of the cluster, construct the cluster-level optimization operation problem, solve the optimization operation problem to obtain the optimal charging trajectory of electric vehicle cluster, and allocate the solution results to each electric vehicle based on the individual charging satisfaction of electric vehicles to realize real-time control of electric vehicle cluster. The method of allocating the solution results based on individual charging satisfaction of electric vehicles to each electric vehicle to achieve real-time control of the electric vehicle cluster includes the following steps: Step 45) Virtual Bidding: Each electric vehicle bids based on its current charging satisfaction level. S k For virtual bid price, For the amount of electricity to be bid, a virtual bidding curve is generated and submitted to the aggregator, whereby... P N Indicates the rated charging power. Indicates the control interval; Step 46) Virtual Clearing: Aggregators are sorted from highest to lowest virtual bid price to form an aggregation demand curve; assuming the current total energy consumption target of the cluster is... E agg,k Seeking E agg,k The intersection of the virtual clearing price and the aggregated demand curve yields the virtual clearing price. S * This signal is then sent to each electric vehicle as a cluster control signal. Step 47) After receiving the control signal, each electric vehicle shall respond autonomously to the control signal according to the following principles: if its bid price S k Higher than S * Then start charging; otherwise, pause charging. Step 48) Repeat steps 45)-47) within the pre-configured control cycle to achieve real-time control of the electric vehicle cluster. 2.The flexibility probabilistic forecasting and stochastic optimization regulation method of an electric vehicle cluster according to claim 1, characterized in that, The charging data includes network access time, network disconnection time, charging amount, and charging power. 3.The flexibility probabilistic forecasting and stochastic optimization regulation method of an electric vehicle fleet according to claim 1, characterized in that, The specific steps for reconstructing the cumulative charging capacity envelope of a single electric vehicle based on charging data to obtain the feasible charging capacity domain of the electric vehicle are as follows: For a single electric vehicle, assuming t in Always connect to the network and start charging. t out Leave at any time, use D This represents the cumulative battery charge. E If we represent the electricity consumption during a single time period, then the charging behavior model for a single electric vehicle can be represented as follows: In the formula: P k for k Charging power during the period For charging efficiency, D k As of the deadline k Cumulative charging capacity over a period of time, ∆ t To optimize the scheduling interval, D exp Indicates the charging power requirement. D min,k , D max,k They represent the deadlines up to k The lower and upper bounds of the charging capacity up to the specified time period; If electric vehicles can [ t in , t out If the charging target is achieved during the period, the feasible region of its charging capacity is represented as a closed region of parallelograms, with its upper and lower envelopes representing the fastest and slowest charging trajectories, respectively, and containing all possible charging trajectories of the EV. 4.The flexibility probabilistic forecasting and stochastic optimization regulation method of an electric vehicle fleet according to claim 3, characterized in that, The individual charging satisfaction index for a single electric vehicle is defined as follows: In the formula: P N This represents the rated charging power; the numerator is the remaining uncharged amount of the electric vehicle, and the denominator is the maximum amount of electricity the electric vehicle can be charged before disconnecting from the grid. Indicates the control interval; S k The size reflects the user's urgency to charge: S k The smaller the size, the lower the urgency. S k =0 indicates that charging is complete. S k =1 indicates that the electric vehicle must maintain its rated charging power until it leaves the grid to achieve its charging target. If the electric vehicle can achieve its charging target, then... S k The value always remains within the range of [0,1].

5. The method for probabilistic prediction and stochastic optimization control of electric vehicle clusters according to claim 3, characterized in that, The step-by-step aggregation of electric vehicles based on the electric vehicle aggregator specifically involves overlaying the charging behavior models of individual electric vehicles within the cluster. The aggregation information is as follows: In the formula: the subscript agg on the left side of the equation represents the aggregated value of the corresponding variable for the cluster of electric vehicles, n is the number of electric vehicles in the cluster.

6. The flexibility probabilistic forecasting and stochastic optimization regulation method of an electric vehicle fleet according to claim 5, characterized in that, The cumulative charging capacity envelope of the electric vehicle cluster is used to construct the energy feasible region of the electric vehicle cluster, which specifically includes the following constraints: In the formula: D agg,k Indicates the deadline k The cumulative charging power of the cluster during the time period E agg,k express k The charging capacity of the cluster during a given time period; the upper and lower bounds of the cluster's charging power during that time period. P max,agg,k , P min,agg,k Take the pre-configured time period from the past respectively P agg,k The maximum and minimum values.

7. The flexibility probabilistic forecasting and stochastic optimization regulation method of an electric vehicle fleet according to claim 6, characterized in that, By utilizing the cumulative charging capacity envelope of an electric vehicle cluster, the fastest charging trajectory of the cluster is compared with the actual charging trajectory, thereby quantitatively describing the charging anxiety level of the cluster. T The cluster satisfaction loss function under each optimization period: In the formula: is the cluster anxiety coefficient, indicating the importance of the cluster to the charging anxiety. 8.The flexibility probabilistic forecasting and stochastic optimization regulation method of an electric vehicle fleet according to claim 7, wherein, Step 3) predicting the adjustment flexibility probability of the cluster based on GPR includes probability prediction for the upper envelope and probability prediction for the lower envelope. The probability prediction for the upper envelope includes the following steps: Step 311) Treat the upper envelope time series of the cumulative charging amount of the electric vehicle cluster as a Gaussian process, that is: In the formula: m ( k ) is the mean function, K ( k , k ') is the covariance function. D max,agg,k Indicates the deadline k The upper bound of the charging amount up to the specified time period is the aggregated value after being aggregated by the aggregator; Step 312) Use a smooth periodic kernel function of the following form as the covariance function: wherein: f and is a hyperparameter to be identified, p is the period of the envelope. Step 313) Brief Note D ={ D max,agg,k } represents the historical samples of the envelope of the cluster's cumulative charging power, with a quantity of . n ; D * = D max,agg,k* For the future k * The value to be predicted at time [time] This is the root mean square error of the electrical quantity measurement. I n for n If the identity matrix is ​​of order 1, then D and D * It follows a joint Gaussian distribution as follows: In the formula: Step 314) If the conditional probability of the Gaussian process still follows a Gaussian distribution, then the future... k * time D * The distribution is as follows: Then the future k * The expected value of the point prediction result on the envelope of the cumulative charging capacity of the time cluster is: The variance at the corresponding time point is: Step 315) determining the point prediction value and the confidence interval of the upper envelope line of the cluster cumulative charging power based on the preconfigured confidence, the point prediction result expectation value and the variance of the corresponding moment, obtaining the prediction result of the upper envelope line of the cluster cumulative charging power, i.e. the random variable ; The probability prediction of the lower envelope includes the following steps: Step 321) Treat the time series of the cumulative charging capacity of the electric vehicle cluster as a Gaussian process, that is: In the formula: m ( k ) is the mean function, K ( k , k ') is the covariance function. D min,agg,k Indicates the deadline k The lower bound of the charging amount up to the specified time period is the aggregated value after being aggregated by the aggregator; Step 322) Use a smooth periodic kernel function of the following form as the covariance function: In the formula: f and is a hyperparameter to be identified, p is the period of the envelope. Step 323) Brief Note D’ ={ D min,agg,k } represents historical samples of the envelope under the cumulative charging power of the cluster, with a quantity of . n ; D’ * = D min,agg,k* For the future k * The value to be predicted at time [time] The root mean square error of the electrical quantity measurement. I n for n If the identity matrix is ​​of order 1, then D’ and D’ * It follows a joint Gaussian distribution as follows: In the formula: Step 324) If the conditional probability of the Gaussian process still follows a Gaussian distribution, then the future... k * time D’ * The distribution is as follows: Then the future k * The point prediction result of the lower envelope line of the cluster accumulated charging power is: The variance at the corresponding time point is: Step 325) determining the point prediction value and the confidence interval of the lower envelope of the cluster cumulative charging power based on the preconfigured confidence, the point prediction result expectation value and the variance of the corresponding moment, obtaining the prediction result of the lower envelope of the cluster cumulative charging power, i.e. the random variable .

9. The flexibility probabilistic forecasting and stochastic optimization regulation method of an electric vehicle fleet according to claim 8, characterized in that, The process of establishing the feasible domain of electric vehicle clusters based on the probability prediction results of adjustment flexibility and the cluster's charging satisfaction loss function, constructing an optimization operation problem at the cluster level, and solving the optimization operation problem to obtain the optimal charging trajectory of the electric vehicle cluster specifically includes the following steps: Step 41) Determine the opportunity constraints of the electric vehicle cluster charging plan based on the adjustment flexibility probability prediction results: In the formula: [0, 1] is a confidence level, P r () denotes a probability; Step 42) Use the probability addition formula to transform the chance constraint into a deterministic constraint: make: To obtain a unique solution, let the above equation , The probability of the corresponding two random events occurring is the same, then: Since the GPR prediction results follow a Gaussian distribution, let , The cumulative distribution functions are respectively , Then the above equation is transformed into the following two sets of deterministic constraints: Step 43) Constructing the optimization operation problem at the cluster level of the electric vehicle: Step 44) solving the optimal operation problem at the cluster level of the electric vehicles to obtain the optimal charging trajectory of the cluster of electric vehicles E agg,k}

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