Hybrid model large-scale electric vehicle load prediction method

Abstract

The invention discloses a hybrid model large-scale electric vehicle load prediction method, and the method comprises the steps: obtaining the actual measurement charging data of a certain charging operator, and carrying out the data normalization processing; extracting data features by using GAF, and performing sequence modeling on the extracted data features through an FMM model; improving an EM algorithm, and accepting a poor new solution by using a simulated annealing algorithm; performing parameter estimation on the FMM model based on GAF feature extraction by adopting an improved EM algorithm, and introducing an L-BFGS-B algorithm to further optimize the FMM model; and according to the optimized model, predicting the charging load of the electric vehicle in the region, and verifying the effectiveness and feasibility of the proposed method. The method can help a power grid operator to predict the charging load of the electric vehicle, optimizes power grid resource configuration, and avoids overload or resource waste.

Description

Technical Field

[0001] The present invention relates to the technical field of electric vehicle charging load prediction, and in particular to a hybrid model large-scale electric vehicle load prediction method. Background Art

[0002] With the growing demand for global energy transformation and environmental protection, electric vehicles (EVs) have been widely promoted and applied as a clean and efficient means of transportation. According to the International Energy Agency (IEA), the number of EVs has grown exponentially over the past few years and is expected to continue to grow rapidly in the future. However, the widespread adoption of EVs has also posed new challenges to the power system. In particular, the rapid growth of charging loads has profoundly impacted grid planning, operations, and stability. The spatiotemporal distribution of EV charging loads is highly uncertain and complex, influenced by a variety of factors, including user charging behavior, the distribution of charging facilities, electricity pricing policies, and traffic conditions.

[0003] Accurately forecasting electric vehicle charging load is crucial for grid operators, charging facility planners, and energy managers. Charging load forecasting can help grid operators optimize resource allocation, avoid grid overload and resource waste, and ensure stable grid operation. Currently, electric vehicle charging load forecasting techniques primarily rely on traditional statistical models and machine learning methods, but these methods have limitations. For example, existing models typically assume charging behavior follows a single distribution. However, in reality, peak charging hours and power demand differ significantly between weekdays and weekends. Traditional methods are unable to dynamically distinguish these changes in patterns and respond dynamically to changes in real-time charging data. Traditional models (such as single Gaussian distributions or time series models) assume charging behavior follows a single probability distribution and are unable to simultaneously adapt to the differentiated patterns of weekdays (requiring a logarithmic Gaussian distribution) and weekends (requiring a simple Gaussian distribution). Furthermore, they struggle to capture the nonlinear differences between weekdays and weekends. Furthermore, the traditional EM algorithm aims to minimize the overall error and lacks a phased optimization strategy tailored to different day types, resulting in inadequate model fit for local patterns (such as random charging on weekends). Traditional optimization algorithms, such as the EM algorithm, are prone to falling into local optimal solutions and have low computational efficiency, making them difficult to meet the needs of online predictions. They also struggle to effectively process large-scale, high-dimensional charging data, resulting in limited prediction accuracy. Furthermore, existing models often fail to distinguish between charging behavior on weekdays and weekends, making them incapable of adapting to changes in charging demand during different time periods. Summary of the Invention

[0004] In response to the above technical problems, this technical solution provides a hybrid model-based large-scale electric vehicle load forecasting method, which can effectively help grid operators predict electric vehicle charging load, optimize grid resource allocation, realize regional charging load forecasting, provide accurate data support for grid dispatching decisions, and avoid overload or resource waste; it can effectively solve the above problems.

[0005] The present invention is achieved through the following technical solutions:

[0006] A hybrid model-based large-scale electric vehicle load forecasting method comprises the following steps:

[0007] Step 1: Obtain the measured charging data of a charging operator and perform data normalization;

[0008] Step 2: Use GAF to extract data features and use the FMM model to perform sequence modeling on the extracted data features. The specific steps include:

[0009] Step 2.1: Map the normalized time series data to polar coordinates to generate the angle θ i and radius r i , the expression is:

[0010]

[0011] In the above formula, θ i Represents data points The corresponding angle range is [0,π]; Represents the i-th data point in the time series data; r i is a data point The corresponding radius is in the range [0,1]; λ is the length of the time series; i represents the index of the data point, i = 1, 2, ..., N; N represents the total number of data points;

[0012] Step 2.2: Generate the Gram matrix G by summing trigonometric functions j , which captures the correlation between data points, is expressed as:

[0013]

[0014] In the above formula, G j The Gram matrix is ​​a symmetric matrix a×a, cos(θ i +θ b ) represents a data point and the correlation between

[0015] Step 2.3: Transform the Gram matrix G j Visualized as a grayscale image I j(w,h), the expression is:

[0016] I j (w,h)=G j

[0017] In the above formula, I j (w,h) represents a grayscale image, with width w = a and height h = a; G j represents the Gram matrix, as the pixel values ​​of the image;

[0018] Step 2.4: Use FMM to perform sequence modeling on the extracted features to capture the probability distribution of charging behavior;

[0019] Step 3: Improve the EM algorithm and use the simulated annealing algorithm to accept the worse new solutions;

[0020] Step 4: Use the improved EM algorithm to estimate the parameters of the FMM model based on GAF feature extraction, and introduce the L-BFGS-B algorithm to further optimize the FMM model;

[0021] Step 5: Predict the electric vehicle charging load in the region based on the optimized model.

[0022] Furthermore, the data normalization process described in step 1 is to obtain the measured charging data from a charging operator and use the Z-score normalization formula:

[0023]

[0024] in, Represents the normalized data value; x ij Represents the data value before normalization; is the mean of feature j, N is the total number of data points; i is the index of the data point, i = 1, 2, ..., N;

[0025] is the standard deviation of feature j.

[0026] Furthermore, the modeling described in step 2.4 includes the steps of:

[0027] Step 2.4.1: Set the FMM probability density function:

[0028]

[0029] Where: f(t) represents the probability distribution function of the initial charging time; q is the number of mixed components; g q (t|θ q ) is the qth component function of FMM; θ q is the parameter vector of the component function; t represents the starting time of charging of the electric vehicle; αq is the mixing weight of the qth component function, usually α q Is a non-negative number and needs to satisfy

[0030] Step 2.4.2: Select the logarithmic Gaussian distribution as the component function for the FMM modeling of the weekday start charging time:

[0031]

[0032] Where, t represents the starting time of charging of the electric vehicle; exp represents the natural exponential function; lnt represents the natural logarithm of t; μ q and σ q are the mean and standard deviation of the logarithm of the qth Gaussian component distribution variable;

[0033] Step 2.4.3: Select the simple Gaussian distribution as the component function for the FMM modeling of the rest day starting charging time:

[0034]

[0035] Where t represents the starting time of charging of the electric vehicle; exp represents the natural exponential function; lnt represents the natural logarithm of t; μ q and σ q are the mean and standard deviation of the logarithm of the qth Gaussian component distribution variable, respectively.

[0036] Furthermore, the improved EM algorithm described in step 3 uses the EM algorithm to perform probabilistic estimation on the parameters of the finite mixture model. Through iterative optimization, the parameters of each component in the FMM are estimated to accurately describe the charging behavior of electric vehicles on weekdays and weekends. On this basis, the EM algorithm is improved and the simulated annealing algorithm is used to accept the poor new solution. The specific steps of step 3 include:

[0037] Step 3.1:

[0038] Initialize model parameters:

[0039]

[0040] Among them, t i represents the starting charging time of the i-th electric vehicle; N k Indicates the number of data points initially assigned to the kth group

[0041]

[0042] Among them, c k represents the mean; t i represents the starting charging time of the i-th electric vehicle; N kIndicates the number of data points initially assigned to the kth group

[0043]

[0044] Among them, the constraints N represents the total number of data points; N k represents the number of data points initially assigned to the k-th group; K represents the total number of groups; k represents the k-th group;

[0045] θ q is the parameter vector of the component function, using the mean c k : corresponding to θ q The mean parameter in ; the variance d k : corresponding to θ q The variance parameter in ; t represents the starting charging time of the electric vehicle; t i represents the starting charging time of the i-th vehicle; the mixing ratio e k :The weight of each group, satisfying

[0046] Step 3.2: Improve the EM algorithm and use the simulated annealing algorithm to accept the poor new solution. In the EM algorithm, by calculating the posterior probability of each data point belonging to each group, the updated posterior probability γi k , used for parameter optimization; the specific steps are as follows: Calculate the posterior probability of each data point belonging to each group:

[0047]

[0048] Among them, γ ik Express data point t i The posterior probability of belonging to the kth group; the mixing weight e k :The weight of each group, satisfying g k (t i ,c k ,d k ) expresses the probability density function of the kth group, which is g q (t|θ q ) specific implementation; represents the normalization factor, ensuring that the sum of the posterior probabilities of all groups is 1;

[0049] Step 3.3: Update the model parameters by maximizing the likelihood function and introduce the simulated annealing algorithm to avoid falling into the local optimum;

[0050] Step 3.4: Simulated annealing, temperature update: In the simulated annealing algorithm, the current temperature o 旧 Cool down to control the probability of the algorithm accepting a worse solution; input the current temperature o 旧, cooling rate r, update the temperature so that:

[0051] o 新 =r·o 旧

[0052] Among them, 新 Indicates the temperature after cooling; o 旧 Represents the temperature before cooling; r represents the cooling rate; the higher the temperature o, the more the algorithm tends to accept the worse new solution, and the lower the temperature o, the more the algorithm tends to accept the better solution.

[0053] Step 3.5: Iteration termination condition: Repeat steps 3.2 and 3.3 until the convergence condition is met or the maximum number of iterations is reached.

[0054] Furthermore, the specific operation method of step 3.3 includes the following steps:

[0055] Step 3.31: For the mean c k , variance d k Add random perturbations and get the new solution c′ k and d′ k :

[0056] c′ k =c k +ε c ,d′ k =d k +ε d

[0057] Among them, c′ k and d′ k Indicates a new solution; c k , d k Here represents the current solution; ε c and ε d is a random disturbance;

[0058] Step 3.32: Calculate the energy difference ΔE between the new solution and the current solution:

[0059] ΔE=Q(c′ k ,d′ k )-Q(c k ,d k )

[0060]

[0061] Where ΔE represents the energy difference between the new solution and the current solution, which determines whether to accept the new solution; Q(c′ k ,d′ k ) represents the expected likelihood function value of the new solution; Q(c k ,d k) is the expected likelihood function value; γ ik Express data point t i The posterior probability of belonging to the kth group; N represents the total number of data points; g k (t i ,c k ,d k ) expresses the probability density function of the kth group;

[0062] Step 3.33 Accept the new solution:

[0063] If ΔE<0, directly accept the new solution:

[0064] c k =c′ k ,d k =d′ k

[0065] If ΔE≥0, with probability p=e -ΔE / o Accept new interpretation:

[0066]

[0067] Among them, c′ k and d′ k Indicates a new solution; c k and d k Here represents the current solution; r represents a random number in the range [0,1]; p = e -ΔE / o represents the probability of accepting the new solution; o represents the current temperature.

[0068] Step 3.34: Update the mixture weight e k :

[0069]

[0070] Where N represents the total number of data points; represents the sum of the posterior probabilities of all data points for the kth group.

[0071] Furthermore, the L-BFGS-B algorithm described in step 4 is introduced to further optimize the FMM model. The specific operation method includes the following steps:

[0072] Step 4.1: Initialize parameters:

[0073] Input the parameters obtained by the improved EM algorithm: mean c k , variance d k and mixed density e k (i.e., the current solution output in step 3). Here, the parameters optimized by simulated annealing are directly used as the initial values. The L-BFGS-B algorithm will further optimize within the constraints without generating new solutions.

[0074] Constrain the lower and upper bounds of the parameters to:

[0075] c min ≤c k ≤c max ,d min ≤d k ≤d max ,e min ≤e k ≤e max ,

[0076] Get the optimized output parameters

[0077] Step 4.2: Define the objective function: The objective function is the negative log-likelihood function:

[0078]

[0079] Where f(θ) represents the objective function; θ=(c k ,d k ,e k ) represents the parameter set of the FMM model; N represents the total number of data points; K represents the total number of groups; k represents the kth group; g k (t i ,c k ,d k ) expresses the probability density function of the kth group; Indicates t i The logarithm of the likelihood function of the charging time of the i-th electric vehicle;

[0080] Step 4.3: Calculate the gradient of the objective function with respect to the parameters:

[0081]

[0082] in, Represents the gradient of the objective function f(θ) with respect to the parameter θ; θ=(c k ,d k ,e k ) represents the parameter set of the FMM model; Represents the mean c of the objective function f(θ) for the kth group k The partial derivative of Denotes the variance d of the objective function f(θ) for the kth group k The partial derivative of Represents the mixing weight e of the objective function f(θ) for the kth group k The partial derivative of

[0083] Step 4.4: Update parameters using the L-BFGS-B algorithm:

[0084]

[0085] Among them, θ 新 represents the updated parameter value; θ 旧 represents the current parameter value, which refers to the parameter value before the optimization algorithm is updated; η is the learning rate; Indicates that the objective function f(θ) is at the current parameter value θ 旧 The gradient at

[0086] Step 4.5: Iterate until convergence: Repeat steps 4.3 and 4.4 until the objective function converges or the maximum number of iterations is reached.

[0087] Furthermore, the specific operation method of step 5 is: input the FMM model parameters optimized by the L-BFGS-B algorithm As well as the demand data of charging power, time and duration of electric vehicles in the region, the charging load of electric vehicles in the region is predicted; the steps include:

[0088] Step 5.1: Generate the probability distribution of the optimized starting charging time based on the optimized FMM model:

[0089]

[0090] Where F(t) represents the probability distribution function of the optimized starting charging time; K represents the total number of groups; k represents the kth group; t represents the starting charging time of the electric vehicle; g k (t i ,c k ,d k ) expresses the probability density function of the kth group;

[0091] Step 5.2: Calculate the charging load of a single electric vehicle, for each starting charging time t i , calculate the corresponding charging load:

[0092]

[0093] Among them, P i (T) represents the charging load of the i-th electric vehicle at time T; T represents the time variable; P avg represents the average charging power of electric vehicles; t i represents the starting charging time of the i-th electric vehicle; τ represents the standard deviation of the charging time;

[0094] Step 5.3: Superimpose the charging loads of all electric vehicles in the area to obtain the total load forecast value:

[0095]

[0096] Among them, P total (T) represents the total charging charge of all electric vehicles in the area at time T; P i (T) represents the charging load of the i-th electric vehicle at time T; Z represents the number of electric vehicles in the area.

[0097] (3) Beneficial effects

[0098] The hybrid model-based large-scale electric vehicle load forecasting method proposed in this invention has the following advantages compared with the prior art:

[0099] (1) The present invention combines the Gram Angular Field (GAF) with the Finite Mixture Model (FMM). The GAF is used to convert time series data into a Gram Matrix in polar coordinates to capture the nonlinear time series characteristics of charging behavior (such as charging power fluctuation and time period correlation). The FMM is then used to model working days and rest days separately (logarithmic Gaussian and Gaussian distributions), thus solving the problem that traditional methods cannot distinguish charging modes of different date types.

[0100] (2) This invention embeds a simulated annealing mechanism into the M step of the EM algorithm. By randomly perturbing parameters (mean and variance) and accepting new solutions based on energy differential (ΔE) states, it breaks the traditional EM algorithm's strong dependence on initial values. This enables the EM algorithm to escape from local optimal solutions and find more optimal model parameters, thereby improving the model's global optimization capabilities.

[0101] (3) After the EM algorithm preliminarily estimates the parameters, the present invention introduces the L-BFGS-B algorithm to perform constrained optimization (e.g., the variance is non-negative) on the mean, variance, and mixing weight of the FMM. This solves the parameter drift problem of the EM algorithm caused by the nonlinearity of the probability density function. This enables the FMM model to better fit the data, further improving the prediction accuracy and being able to process large-scale data sets, making the model applicable to a wider range of electric vehicle charging load forecasting. BRIEF DESCRIPTION OF THE DRAWINGS

[0102] Figure 1 It is a schematic diagram of the overall process of the present invention.

[0103] Figure 2 This is a graph showing the charging results of electric vehicles predicted on weekdays and weekends in the present invention.

[0104] Figure 3 This is a diagram of the improved process of the EM algorithm in the present invention.

[0105] Figure 4 This is a diagram of the optimization parameter process of the L-BFGS-B algorithm in the present invention.

[0106] Figure 5 This is a comparison chart of the predicted value and actual value of the load prediction of the FMM model in the present invention. DETAILED DESCRIPTION

[0107] The following will be combined with the accompanying drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. The described embodiments are only part of the embodiments of the present invention, rather than all the embodiments. Under the premise of not departing from the design concept of the present invention, various modifications and improvements made by ordinary persons in this field to the technical solutions of the present invention should fall within the scope of protection of the present invention.

[0108] Example 1:

[0109] like Figure 1 As shown, a hybrid model scale electric vehicle load forecasting method includes the following steps:

[0110] Step 1: Obtain the measured charging data from a charging operator and perform data normalization. Data normalization involves obtaining the measured charging data from a charging operator and using the Z-score normalization formula:

[0111]

[0112] in, Represents the normalized data value; x ij Represents the data value before normalization; is the mean of feature j, N is the total number of data points; i is the index of the data point, i = 1, 2, ..., N; is the standard deviation of feature j.

[0113] Step 2: Use GAF to extract data features and use the FMM model to perform sequence modeling on the extracted data features. The specific steps include:

[0114] Step 2.1: Map the normalized time series data to polar coordinates to generate the angle θ i and radius r i , the expression is:

[0115]

[0116] In the above formula, θ i Represents data points The corresponding angle range is [0,π]; Represents the i-th data point in the time series data; r i is a data point The corresponding radius is in the range [0,1]; λ is the length of the time series; i represents the index of the data point, i = 1, 2, …, N; N represents the total number of data points.

[0117] Step 2.2: Generate the Gram matrix G by summing trigonometric functions j , which captures the correlation between data points, is expressed as:

[0118]

[0119] In the above formula, G j The Gram matrix is ​​a symmetric matrix a×a, cos(θ i +θ b ) represents a data point and The correlation between them.

[0120] Step 2.3: Transform the Gram matrix G j Visualized as a grayscale image I j (w,h), the expression is:

[0121] I j (w,h)=G j

[0122] In the above formula, I j (w,h) represents a grayscale image, with width w = a and height h = a; G j Represents the Gram matrix, as the pixel values ​​of the image.

[0123] Step 2.4: Use FMM to perform sequence modeling on the extracted features to capture the probability distribution of charging behavior; the modeling includes the following steps:

[0124] Step 2.4.1: Set the FMM probability density function:

[0125]

[0126] Where: f(t) represents the probability distribution function of the initial charging time; q is the number of mixed components; g q (t|θ q ) is the qth component function of FMM; θ q is the parameter vector of the component function; t represents the starting time of charging of the electric vehicle; α q is the mixing weight of the qth component function, usually α q Is a non-negative number and needs to satisfy

[0127] like Figure 2As shown in the figure, weekday charging peaks are concentrated during the morning and evening commutes (e.g., around 8:00 AM and 6:00 PM), consistent with the regular travel habits of office workers. Charging is more dispersed on weekends, with peaks occurring in the afternoon and evening (e.g., between 2:00 PM and 8:00 PM), reflecting residents' random travel (shopping, leisure activities). This allows the grid to dynamically adjust energy storage release strategies to balance loads throughout the day.

[0128] Step 2.4.2: Select the logarithmic Gaussian distribution as the component function for the FMM modeling of the weekday start charging time:

[0129]

[0130] Where, t represents the starting time of charging of the electric vehicle; exp represents the natural exponential function; lnt represents the natural logarithm of t; μ q and σ q are the mean and standard deviation of the logarithm of the qth Gaussian component distribution variable, respectively.

[0131] Step 2.4.3: Select the simple Gaussian distribution as the component function for the FMM modeling of the rest day starting charging time:

[0132]

[0133] Where t represents the starting time of charging of the electric vehicle; exp represents the natural exponential function; lnt represents the natural logarithm of t; μ q and σ q are the mean and standard deviation of the logarithm of the qth Gaussian component distribution variable, respectively.

[0134] Step 3: Improve the EM algorithm and use the simulated annealing algorithm to accept the worse new solutions.

[0135] The improved EM algorithm uses the EM algorithm to perform probability estimation on the parameters of the finite mixture model. Through iterative optimization, the parameters of each component in the FMM are estimated to accurately describe the charging behavior of electric vehicles on weekdays and weekends. On this basis, the EM algorithm is improved, and the simulated annealing algorithm is used to accept the poor new solution. The simulated annealing algorithm is introduced into the EM algorithm to avoid falling into the local optimum. The specific process is as follows. Figure 3 As shown, the steps include:

[0136] Step 3.1:

[0137] Initialize model parameters:

[0138]

[0139] Among them, t i represents the starting charging time of the i-th electric vehicle; N kIndicates the number of data points initially assigned to the kth group

[0140]

[0141] Among them, c k represents the mean; t i represents the starting charging time of the i-th electric vehicle; N k Indicates the number of data points initially assigned to the kth group

[0142]

[0143] Among them, the constraints N represents the total number of data points; N k represents the number of data points initially assigned to the k-th group; K represents the total number of groups; k represents the k-th group;

[0144] θ q is the parameter vector of the component function, using the mean c k : corresponding to θ q The mean parameter in ; the variance d k : corresponding to θ q The variance parameter in ; t represents the starting charging time of the electric vehicle; t i represents the starting charging time of the i-th vehicle; the mixing ratio e k :The weight of each group, satisfying

[0145] Step 3.2: Improve the EM algorithm and use the simulated annealing algorithm to accept the poor new solution. In the EM algorithm, by calculating the posterior probability of each data point belonging to each group, the updated posterior probability γ ik , used for parameter optimization; the specific steps are as follows: Calculate the posterior probability of each data point belonging to each group:

[0146]

[0147] Among them, γ ik Express data point t i The posterior probability of belonging to the kth group; the mixing weight e k :The weight of each group, satisfying g k (t i ,c k ,d k ) expresses the probability density function of the kth group, which is g q (t|θ q ) specific implementation; represents a normalization factor to ensure that the sum of the posterior probabilities of all groups is 1.

[0148] Step 3.3: Update the model parameters by maximizing the likelihood function and introduce a simulated annealing algorithm to avoid falling into the local optimum. The specific operation includes the following steps:

[0149] Step 3.31: For the mean c k , variance d k Add random perturbations and get the new solution c′ k and d′ k :

[0150] c′ k =c k +ε c ,d′ k =d k +ε d

[0151] Among them, c′ k and d′ k Indicates a new solution; c k , d k Here represents the current solution; ε c and ε d is a random perturbation. Step 3.32: Calculate the energy difference ΔE between the new solution and the current solution:

[0152] ΔE=Q(c′ k ,d′ k )-Q(c k ,d k )

[0153]

[0154] Where ΔE represents the energy difference between the new solution and the current solution, which determines whether to accept the new solution; Q(c′ k ,d′ k ) represents the expected likelihood function value of the new solution; Q(c k ,d k ) is the expected likelihood function value; γ ik Express data point t i The posterior probability of belonging to the kth group; N represents the total number of data points; g k (t i ,c k ,d k ) expresses the probability density function of the kth group.

[0155] Step 3.33 Accept the new solution:

[0156] If ΔE<0, directly accept the new solution:

[0157] c k =c′ k ,d k =d′k

[0158] If ΔE≥0, with probability p=e -ΔE / o Accept new interpretation:

[0159]

[0160] Among them, c′ k and d′ k Indicates a new solution; c k and d k Here represents the current solution; r represents a random number in the range [0,1]; p = e -ΔE / o represents the probability of accepting the new solution; o represents the current temperature.

[0161] Step 3.34: Update the mixture weight e k :

[0162]

[0163] Where N represents the total number of data points; represents the sum of the posterior probabilities of all data points for the kth group.

[0164] Step 3.4: Simulated annealing, temperature update: In the simulated annealing algorithm, the current temperature o 旧 Cool down to control the probability of the algorithm accepting a worse solution; input the current temperature o 旧 , cooling rate r, update the temperature so that:

[0165] o 新 =r·o 旧

[0166] Among them, 新 Indicates the temperature after cooling; o 旧 Represents the temperature before cooling; r represents the cooling rate; the higher the temperature o, the more the algorithm tends to accept the worse new solution, and the lower the temperature o, the more the algorithm tends to accept the better solution.

[0167] Step 3.5: Iteration termination condition: Repeat steps 3.2 and 3.3 until the convergence condition is met or the maximum number of iterations is reached.

[0168] Step 4: Use the improved EM algorithm to estimate the parameters of the FMM model based on GAF feature extraction, and introduce the L-BFGS-B algorithm to further optimize the FMM model; Figure 4 As shown, the specific operation method includes the following steps:

[0169] Step 4.1: Initialize parameters:

[0170] Input the parameters obtained by the improved EM algorithm: mean ck , variance d k and mixed density e k (i.e., the current solution output in step 3). Here, the parameters optimized by simulated annealing are directly used as the initial values. The L-BFGS-B algorithm will further optimize within the constraints without generating new solutions.

[0171] Constrain the lower and upper bounds of the parameters to:

[0172] c min ≤c k ≤c max ,d min ≤d k ≤d max ,e min ≤e k ≤e max ,

[0173] Get the optimized output parameters

[0174] Step 4.2: Define the objective function: The objective function is the negative log-likelihood function:

[0175]

[0176] Where f(θ) represents the objective function; θ=(c k ,d k ,e k ) represents the parameter set of the FMM model; N represents the total number of data points; K represents the total number of groups; k represents the kth group; g k (t i ,c k ,d k ) expresses the probability density function of the kth group; Indicates t i The logarithm of the likelihood function of the charging time of the i-th electric vehicle.

[0177] Step 4.3: Calculate the gradient of the objective function with respect to the parameters:

[0178]

[0179] in, Represents the gradient of the objective function f(θ) with respect to the parameter θ; θ=(c k ,d k ,e k ) represents the parameter set of the FMM model; Represents the mean c of the objective function f(θ) for the kth group k The partial derivative of Denotes the variance d of the objective function f(θ) for the kth groupk The partial derivative of Represents the mixing weight e of the objective function f(θ) for the kth group k The partial derivative of .

[0180] Step 4.4: Update parameters using the L-BFGS-B algorithm:

[0181]

[0182] Among them, θ 新 represents the updated parameter value; θ 旧 represents the current parameter value, which refers to the parameter value before the optimization algorithm is updated; η is the learning rate; Indicates that the objective function f(θ) is at the current parameter value θ 旧 The gradient at .

[0183] Step 4.5: Iterate until convergence: Repeat steps 4.3 and 4.4 until the objective function converges or the maximum number of iterations is reached.

[0184] Step 5: Predict the charging load of electric vehicles in the region based on the optimized model, such as Figure 5 shown.

[0185] Input the FMM model parameters optimized by the L-BFGS-B algorithm As well as the demand data of charging power, time and duration of electric vehicles in the region, the charging load of electric vehicles in the region is predicted; the steps include:

[0186] Step 5.1: Generate the probability distribution of the optimized starting charging time based on the optimized FMM model:

[0187]

[0188] Where F(t) represents the probability distribution function of the optimized starting charging time; K represents the total number of groups; k represents the kth group; t represents the starting charging time of the electric vehicle; g k (t i ,c k ,d k ) expresses the probability density function of the kth group.

[0189] Step 5.2: Calculate the charging load of a single electric vehicle, for each starting charging time t i , calculate the corresponding charging load:

[0190]

[0191] Among them, P i(T) represents the charging load of the i-th electric vehicle at time T; T represents the time variable; P avg represents the average charging power of electric vehicles; t i represents the starting charging time of the i-th electric vehicle; τ represents the standard deviation of the charging time.

[0192] Step 5.3: Superimpose the charging loads of all electric vehicles in the area to obtain the total load forecast value:

[0193]

[0194] Among them, P total (T) represents the total charging charge of all electric vehicles in the area at time T; P i (T) represents the charging load of the i-th electric vehicle at time T; Z represents the number of electric vehicles in the area.

[0195] The optimized FMM model is simulated and verified, and the fitting coefficient and root mean square error are used as evaluation indicators, which are defined as follows:

[0196]

[0197] Among them, R 2 is the fitting coefficient; M represents the total number of samples; P m is the true value of the charging load of the mth node; is the fitted value of the charging load of the mth node; is the true mean; R 2 The value range is 0-1, R 2 Values ​​closer to 1 indicate better fitting.

[0198]

[0199] Among them, RMSE is the root mean square error. The smaller the RMSE, the higher the prediction accuracy of the model.

[0200] <![CDATA[R 2 ]]> RMSE Traditional FMM 0.86 178.65 Optimized FMM 0.97 139.53

[0201] By implementing the above steps and then comparing and analyzing the results, it can be concluded that the results confirm the significant effect of the optimized FMM model in improving prediction accuracy. This invention significantly improves the accuracy and robustness of electric vehicle charging load prediction through multi-algorithm fusion and optimization, providing a scientific basis for power grid planning and operation, and has important practical value and promotion prospects.

[0202] The description of the above embodiments is only used to help understand the method of the present invention and its core concept; at the same time, for those skilled in the art, according to the concept of the present invention, there will be changes in the specific implementation methods and application scopes. In summary, the content of this specification should not be understood as limiting the present invention.

Claims

1. A hybrid model-based large-scale electric vehicle load forecasting method, characterized by: Including steps: Step 1: Obtain the measured charging data of a charging operator and perform data normalization; Step 2: Use GAF to extract data features and perform sequence modeling on the extracted data features through the FMM model; The specific steps include: Step 2.1: Map the normalized time series data to polar coordinates to generate the angle θ i and radius r i , the expression is: In the above formula, θ i Represents data points The corresponding angle range is [0,π]; Represents the i-th data point in the time series data; r i is a data point The corresponding radius is in the range [0,1]; λ is the length of the time series; i represents the index of the data point, i = 1, 2, ..., N; N represents the total number of data points; Step 2.2: Generate the Gram matrix G by summing trigonometric functions j , which captures the correlation between data points, is expressed as: In the above formula, G j The Gram matrix is ​​a symmetric matrix a×a, cos(θ i +θ b ) represents a data point and the correlation between Step 2.3: Transform the Gram matrix G j Visualized as a grayscale image I j (w,h), the expression is: I j (w,h)=G j In the above formula, I j (w,h) represents a grayscale image, with width w = a and height h = a; G j represents the Gram matrix, as the pixel values ​​of the image; Step 2.4: Use FMM to perform sequence modeling on the extracted features to capture the probability distribution of charging behavior; Step 3: Improve the EM algorithm and use the simulated annealing algorithm to accept the worse new solutions; Step 4: Use the improved EM algorithm to estimate the parameters of the FMM model based on GAF feature extraction, and introduce the L-BFGS-B algorithm to further optimize the FMM model; Step 5: Predict the electric vehicle charging load in the region based on the optimized model.

2. The hybrid model large-scale electric vehicle load forecasting method according to claim 1, characterized in that: The data normalization process described in step 1 is to obtain the measured charging data from a charging operator and use the Z-score normalization formula: in, Represents the normalized data value; x ij Represents the data value before normalization; is the mean of feature j, N is the total number of data points; i is the index of the data point, i = 1, 2, ..., N; is the standard deviation of feature j.

3. The hybrid model large-scale electric vehicle load forecasting method according to claim 1, characterized in that: The modeling described in step 2.4 includes the following steps: Step 2.4.1: Set the FMM probability density function: Where: f(t) represents the probability distribution function of the initial charging time; q is the number of mixed components; g q (t|θ q ) is the qth component function of FMM; θ q is the parameter vector of the component function; t represents the starting time of charging of the electric vehicle; α q is the mixing weight of the qth component function, usually α q Is a non-negative number and needs to satisfy Step 2.4.2: Select the logarithmic Gaussian distribution as the component function for the FMM modeling of the weekday start charging time: Where, t represents the starting time of charging of the electric vehicle; exp represents the natural exponential function; lnt represents the natural logarithm of t; μ q and σ q are the mean and standard deviation of the logarithm of the qth Gaussian component distribution variable; Step 2.4.3: Select the simple Gaussian distribution as the component function for the FMM modeling of the rest day starting charging time: Where t represents the starting time of charging of the electric vehicle; exp represents the natural exponential function; lnt represents the natural logarithm of t; μ q and σ q are the mean and standard deviation of the logarithm of the qth Gaussian component distribution variable, respectively.

4. The hybrid model large-scale electric vehicle load forecasting method according to claim 3, characterized in that: The improved EM algorithm described in step 3 uses the EM algorithm to perform probability estimation on the parameters of the finite mixture model. Through iterative optimization, the parameters of each component in the FMM are estimated to accurately describe the charging behavior of electric vehicles on weekdays and weekends. On this basis, the EM algorithm is improved and the simulated annealing algorithm is used to accept the poor new solution. The specific steps of step three include: Step 3.1: Initialize model parameters: mean Among them, t i represents the starting charging time of the i-th electric vehicle; N k Indicates the number of data points initially assigned to the kth group variance Among them, c k represents the mean; t i represents the starting charging time of the i-th electric vehicle; N k Indicates the number of data points initially assigned to the kth group Mixing density Among them, the constraints N represents the total number of data points; N k represents the number of data points initially assigned to the k-th group; K represents the total number of groups; k represents the k-th group; θ q is the parameter vector of the component function, using the mean c k : corresponding to θ q The mean parameter in ; the variance d k : corresponding to θ q The variance parameter in ; t represents the starting charging time of the electric vehicle; t i represents the starting charging time of the i-th vehicle; the mixing ratio e k :The weight of each group, satisfying Step 3.2: Improve the EM algorithm and use the simulated annealing algorithm to accept the poor new solution. In the EM algorithm, by calculating the posterior probability of each data point belonging to each group, the updated posterior probability γ ik , used for parameter optimization; the specific steps are as follows: Calculate the posterior probability of each data point belonging to each group: Among them, γ ik Express data point t i The posterior probability of belonging to the kth group; the mixing weight e k :The weight of each group, satisfying g k (t i ,c k ,d k ) expresses the probability density function of the kth group, which is g q (t|θ q ) specific implementation; represents the normalization factor, ensuring that the sum of the posterior probabilities of all groups is 1; Step 3.3: Update the model parameters by maximizing the likelihood function and introduce the simulated annealing algorithm to avoid falling into the local optimum; Step 3.4: Simulated annealing, temperature update: In the simulated annealing algorithm, the current temperature o 旧 Cool down to control the probability of the algorithm accepting a worse solution; input the current temperature o 旧 , cooling rate r, update the temperature so that: o 新 =r·o 旧 Among them, 新 Indicates the temperature after cooling; o 旧 Represents the temperature before cooling; r represents the cooling rate; the higher the temperature o, the more the algorithm tends to accept the worse new solution, and the lower the temperature o, the more the algorithm tends to accept the better solution. Step 3.5: Iteration termination condition: Repeat steps 3.2 and 3.3 until the convergence condition is met or the maximum number of iterations is reached.

5. The hybrid model large-scale electric vehicle load forecasting method according to claim 4, characterized in that: The specific operation method of step 3.3 includes the following steps: Step 3.31: For the mean c k , variance d k Add random perturbations and get the new solution c′ k and d′ k : c′ k =c k +e c ,d′ k =d k +e d Among them, c′ k and d′ k Indicates a new solution; c k , d k Here represents the current solution; ε c and ε d is a random disturbance; Step 3.32: Calculate the energy difference ΔE between the new solution and the current solution: ΔE=Q(c′ k ,d′ k )-Q(c k ,d k ) Where ΔE represents the energy difference between the new solution and the current solution, which determines whether to accept the new solution; Q(c′ k ,d′ k ) represents the expected likelihood function value of the new solution; Q(c k ,d k ) is the expected likelihood function value; γ ik Express data point t i The posterior probability of belonging to the kth group; N represents the total number of data points; g k (t i ,c k ,d k ) expresses the probability density function of the kth group; Step 3.33 Accept the new solution: If ΔE<0, directly accept the new solution: c k =c′ k ,d k =d′ k If ΔE≥0, with probability p=e -ΔE / o Accept new interpretation: Among them, c′ k and d′ k Indicates a new solution; c k and d k Here represents the current solution; r represents a random number in the range [0,1]; p = e -ΔE / o represents the probability of accepting the new solution; o represents the current temperature. Step 3.34: Update the mixture weight e k : Where N represents the total number of data points; represents the sum of the posterior probabilities of all data points for the kth group.

6. The hybrid model large-scale electric vehicle load forecasting method according to claim 1, characterized in that: The L-BFGS-B algorithm described in step 4 is introduced to further optimize the FMM model. The specific operation method includes the following steps: Step 4.1: Initialize parameters Input the parameters obtained by the improved EM algorithm: mean c k , variance d k and mixed density e k , constrain the upper and lower bounds of the parameters to: c min ≤c k ≤c max ,d min ≤d k ≤d max ,e min ≤e k ≤e max , Get the optimized output parameters Step 4.2: Define the objective function: The objective function is the negative log-likelihood function: Where f(θ) represents the objective function; θ=(c k ,d k ,e k ) represents the parameter set of the FMM model; N represents the total number of data points; K represents the total number of groups; k represents the kth group; g k (t i ,c k ,d k ) expresses the probability density function of the kth group; Indicates t i The logarithm of the likelihood function of the charging time of the i-th electric vehicle; Step 4.3: Calculate the gradient of the objective function with respect to the parameters: in, Represents the gradient of the objective function f(θ) with respect to the parameter θ; θ=(c k ,d k ,e k ) represents the parameter set of the FMM model; Represents the mean c of the objective function f(θ) for the kth group k The partial derivative of Denotes the variance d of the objective function f(θ) for the kth group k The partial derivative of Represents the mixing weight e of the objective function f(θ) for the kth group k The partial derivative of Step 4.4: Update parameters using the L-BFGS-B algorithm: Among them, θ 新 represents the updated parameter value; θ 旧 represents the current parameter value, which refers to the parameter value before the optimization algorithm is updated; η is the learning rate; Indicates that the objective function f(θ) is at the current parameter value θ 旧 The gradient at Step 4.5: Iterate until convergence: Repeat steps 4.3 and 4.4 until the objective function converges or the maximum number of iterations is reached.

7. The hybrid model large-scale electric vehicle load forecasting method according to claim 1, characterized in that: The specific operation method of step 5 is: input the FMM model parameters optimized by the L-BFGS-B algorithm As well as the demand data on charging power, time and duration of electric vehicles in the region, the charging load of electric vehicles in the region is predicted; include step: Step 5.1: Generate the probability distribution of the optimized starting charging time based on the optimized FMM model: Where F(t) represents the probability distribution function of the optimized starting charging time; K represents the total number of groups; k represents the kth group; t represents the starting charging time of the electric vehicle; g k (t i ,c k ,d k ) expresses the probability density function of the kth group; Step 5.2: Calculate the charging load of a single electric vehicle, for each starting charging time t i , calculate the corresponding charging load: Among them, P i (T) represents the charging load of the i-th electric vehicle at time T; T represents the time variable; P avg represents the average charging power of electric vehicles; t i represents the starting charging time of the i-th electric vehicle; τ represents the standard deviation of the charging time; Step 5.3: Superimpose the charging loads of all electric vehicles in the area to obtain the total load forecast value: Among them, P total (T) represents the total charging charge of all electric vehicles in the area at time T; P i (T) represents the charging load of the i-th electric vehicle at time T; Z represents the number of electric vehicles in the area.

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