A method for evaluating the frequency regulation effectiveness of electric vehicles

Abstract

The present application discloses a method for evaluating the utility of electric vehicle frequency regulation, which relates to the field of electric vehicle frequency regulation. The method converts a power feasible domain characterization model into a polyhedron set, and expands the dimension of each polyhedron in the polyhedron set to a unified charging and discharging period; constructs a feasible domain basis set based on the expanded polyhedron set; scales and translates the feasible domain basis set, and establishes an initial polyhedron-optimized maximum inner approximation model; models the uncertainty of the initial power and grid-entry and off-grid time of electric vehicles, and obtains distributed Brutus constraints that take into account multiple travel scenarios of electric vehicle users; integrates the distributed Brutus constraints and the initial polyhedron-optimized maximum inner approximation model, solves the integrated model for each electric vehicle, and adopts the inner approximation Minkoff aggregation method to obtain the maximum inner approximation aggregation feasible domain of the electric vehicle cluster; uses the obtained feasible domain to participate in system frequency regulation, and obtains the charging and discharging power that characterizes the frequency regulation utility of the electric vehicle cluster. The present application can improve the stability and reliability of electric vehicle frequency regulation resources.

Description

Technical Field

[0001] The present application relates to the field of electric vehicle frequency modulation, and in particular to a method for evaluating the utility of electric vehicle frequency modulation. Background Art

[0002] New power systems are facing the dual challenges of integrating a high proportion of renewable energy and power electronic equipment. As system moment of inertia continues to decrease, the system's frequency regulation capabilities and resource constraints are becoming increasingly prominent, necessitating the development of new frequency regulation resources. Compared to conventional units, whose retrofit ratio is gradually decreasing, demand-side resources such as electric vehicles (EVs) offer rapid and precise dynamic response capabilities and considerable cluster capacity, offering new solutions for addressing system frequency regulation challenges associated with the integration of large-scale renewable energy generation.

[0003] Existing research on electric vehicle aggregators (EVAs) participating in system frequency regulation has mostly achieved large-scale EV integration through centralized control or traditional aggregation methods. With centralized control, individual vehicles exhibit significant randomness and high variable dimensionality. Individually regulating individual EVs incurs significant communication and computational overhead, resulting in high computational complexity. Traditional aggregation methods typically employ exact aggregation using the Minkowski summation, but the efficiency of this approach decreases exponentially with increasing problem dimensionality and number. Currently, the exact aggregation model is typically simplified, employing a model with lower mathematical complexity to approximate the feasible domain of resources. Approximate aggregation methods are primarily categorized as external approximation and internal approximation. While external approximation offers high computational efficiency, the external approximation process increases the feasible domain of resource aggregation, potentially leading to unsolvable problems in actual scheduling. While internal approximation ensures feasibility, it suffers from poor approximation accuracy and high conservatism when dealing with heterogeneous resources at multiple time scales, such as EVs, resulting in a significant loss of flexibility in the feasible domain of resource aggregation. In addition, electric vehicle users are dispersed and random. The uncertainty of the initial power of electric vehicles and the time of entering and leaving the grid will cause the adjustable capacity boundary of the aggregated electric vehicles to present a strong random characteristic, which makes the frequency regulation utility evaluation results obtained by deterministic optimization scheduling at risk of being weakened or even completely ineffective. Summary of the Invention

[0004] The purpose of this application is to provide a method for evaluating the utility of electric vehicle frequency regulation, which can improve the stability and reliability of electric vehicle frequency regulation resources.

[0005] To achieve the above objectives, this application provides the following solutions:

[0006] The present application provides a method for evaluating the frequency regulation utility of electric vehicles, including: establishing a power feasible domain representation model for individual electric vehicles; converting the power feasible domain representation models of all individual electric vehicles in an electric vehicle cluster into a polyhedron set represented in a half-plane form in Euclidean space; augmenting the dimension of each polyhedron in the polyhedron set to a unified charging and discharging period to obtain an augmented polyhedron set; constructing a feasible domain basis set based on the augmented polyhedron set; scaling and translating the feasible domain basis set, and establishing a maximum inner approximation model for initial polyhedron optimization; modeling the uncertainty of the initial power and grid-entry and off-grid time of electric vehicles to obtain a distributed robust constraint that takes into account multiple travel scenarios of electric vehicle users; fusing the distributed robust constraint and the initial polyhedron set. A maximum inner approximation model for cell body optimization is used to obtain a final maximum inner approximation model; the final maximum inner approximation model is solved to obtain the optimal polyhedron of the electric vehicle individual, and the inner approximation Minkowski aggregation method is used to aggregate all the optimal polyhedrons to obtain the maximum inner approximation aggregation feasible domain of the electric vehicle cluster; a frequency regulation utility evaluation model is established when the electric vehicle cluster participates in the power system frequency regulation; based on the maximum inner approximation aggregation feasible domain of the electric vehicle cluster, the frequency regulation utility evaluation model is solved with the goal of minimizing the sum of the standard deviations of the net load of the power system to obtain the charging and discharging power of the electric vehicle cluster in each charging and discharging period; the charging and discharging power reflects the frequency regulation capacity of the electric vehicle cluster when it participates in the power system frequency regulation, and the frequency regulation capacity represents the frequency regulation utility of the electric vehicle cluster.

[0007] According to the specific embodiments provided in this application, this application has the following technical effects:

[0008] The present application provides a method for evaluating the frequency regulation utility of electric vehicles. Before aggregation, the dimensions of each polyhedron are expanded to a unified charging and discharging period to achieve effective aggregation of heterogeneous electric vehicle resources at multiple time scales; the uncertainty of the initial power of electric vehicles and the time of entering and leaving the grid are modeled to obtain distributed robust constraints that take into account multiple travel scenarios of electric vehicle users, and the process of processing the uncertainty factors of electric vehicle user behavior is integrated into the aggregation process to achieve the transformation from the deterministic boundary of the aggregation feasible domain to the robust boundary, effectively reducing the failure risk of the frequency regulation utility evaluation results when electric vehicles participate in system frequency regulation, which is conducive to fully utilizing the regulation capacity of large-scale electric vehicle resources and improving the stability and reliability of electric vehicle frequency regulation resources. BRIEF DESCRIPTION OF THE DRAWINGS

[0009] In order to more clearly illustrate the technical solutions in the embodiments of the present application or related technologies, the following briefly introduces the drawings required for use in the embodiments. Obviously, the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.

[0010] Figure 1 A flow chart of a method for evaluating the frequency modulation utility of an electric vehicle provided in one embodiment of the present application;

[0011] Figure 2 A schematic diagram of a reconstruction process provided in another embodiment of the present application;

[0012] Figure 3 A schematic diagram of the polymerization principle provided for another embodiment of the present application;

[0013] Figure 4 A schematic diagram of the robust boundary characterization results of small-scale EV aggregation in two time periods provided by another embodiment of the present application;

[0014] Figure 5 A schematic diagram briefly summarizes a method for evaluating the frequency modulation utility of an electric vehicle provided in one embodiment of the present application. DETAILED DESCRIPTION

[0015] The following will be combined with the drawings in the embodiments of this application to clearly and completely describe the technical solutions in the embodiments of this application. Obviously, the embodiments described are only part of the embodiments of this application, not all of the embodiments. Based on the embodiments in this application, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of this application.

[0016] In order to make the above-mentioned purposes, features and advantages of the present application more obvious and easy to understand, the present application is further described in detail below with reference to the accompanying drawings and specific implementation methods.

[0017] In an exemplary embodiment, Figure 1 As shown, a method for evaluating the frequency regulation utility of electric vehicles is provided, comprising the following steps 101 to 110. In which:

[0018] Step 101: Establish a power feasible domain representation model for an individual electric vehicle.

[0019] Step 102: Convert the power feasible domain representation model of all individual electric vehicles in the electric vehicle cluster into a polyhedron set represented in a half-plane form in Euclidean space.

[0020] Step 103: Expand the dimension of each polyhedron in the polyhedron set to a unified charge and discharge period to obtain an expanded polyhedron set.

[0021] Step 104: construct a feasible region basis set based on the augmented polytope set.

[0022] Step 105: scaling and translating the feasible domain basis set, and establishing an initial maximum inner approximation model for polyhedral optimization.

[0023] Step 106: Model the uncertainty of the initial power of the electric vehicle and the time of entering and leaving the grid, and obtain the distributed robust constraints that take into account multiple travel scenarios of electric vehicle users.

[0024] Step 107: Fusing the distributed robust constraint and the initial polyhedral optimized maximum inner approximation model to obtain a final maximum inner approximation model.

[0025] Step 108: Solve the final maximum inner approximation model to obtain the optimal polyhedron of the electric vehicle individual, and simultaneously aggregate all the optimal polyhedrons using the inner approximation Minkowski aggregation method to obtain the maximum inner approximation aggregation feasible region of the electric vehicle cluster.

[0026] Step 109: Establish a frequency regulation utility evaluation model when electric vehicle clusters participate in power system frequency regulation.

[0027] Step 110: Based on the maximum inner approximation aggregation feasible domain of the electric vehicle cluster and with the goal of minimizing the sum of the standard deviations of the net load of the power system, the frequency regulation utility evaluation model is solved to obtain the charging and discharging power of the electric vehicle cluster in each charging and discharging period; the charging and discharging power reflects the frequency regulation capacity of the electric vehicle cluster when participating in the frequency regulation of the power system, and the frequency regulation capacity represents the frequency regulation utility of the electric vehicle cluster.

[0028] By implementing the above steps 101 to 110, the dimensions of each polyhedron are expanded to a unified charging and discharging period before aggregation, thereby realizing effective aggregation of heterogeneous electric vehicle resources at multiple time scales; considering the uncertainty of the initial power of electric vehicles and the time of entering and leaving the grid, determining the distributed robust constraints that take into account multiple travel scenarios of electric vehicle users, integrating the uncertainty factor processing process of electric vehicle user behavior into the aggregation process, realizing the transformation of the deterministic boundary of the aggregation feasible domain to the robust boundary, effectively reducing the failure risk of the frequency regulation utility evaluation results when electric vehicles participate in system frequency regulation, and improving the stability and reliability of electric vehicle frequency regulation resources.

[0029] In another exemplary embodiment of the present application, the EV power feasible domain is affected not only by the battery's own charge and discharge power limitations, but also by the battery's power limitations. When an EV is connected to the grid, its power feasible domain representation model is:

[0030]

[0031] Where, P t C 、P t D They represent the charging and discharging power of the electric vehicle in time period t, They represent the maximum charging and discharging power of electric vehicles, E t represents the operating capacity of electric vehicles in time period t, Et-1 represents the operating capacity of electric vehicles in time period t-1, η C ,η D They represent the charging and discharging efficiency of electric vehicles, Δt represents the charging and discharging time, E max 、E min They represent the upper and lower limits of the battery operating capacity of electric vehicles, E exp represents the expected power value of the electric vehicle owner when leaving the grid, is the power value of the electric vehicle when it is off-grid, t arr , t dep They represent the time when electric vehicles enter and leave the grid respectively.

[0032] In another exemplary embodiment of the present application, the charging and discharging flexibility of a single EV can be characterized by its power and energy boundaries. The power feasible domain representation model of the above EV feasible domain is converted into a polyhedron set represented in the form of a half-plane in Euclidean space, and its compact form is:

[0033] Φ i ={P i ∈R 2m |M i P i ≤H i};

[0034]

[0035] Where, Φ i represents the power feasible region of the i-th electric vehicle, m represents the total number of charging and discharging periods, P i represents the charging and discharging power matrix of the i-th electric vehicle, P i =[P i C ,P i D ] T , P i C represents the charging power matrix of the i-th electric vehicle, P i D represents the discharge power matrix of the i-th electric vehicle, R 2m Represents a set of 2m-dimensional column vectors, M i The inequality coefficient matrix representing the feasible region of the i-th electric vehicle, H i The column vector representing the feasible region of the i-th electric vehicle; I m represents the identity matrix, U m 、U' m 、A 1×m 、A1' ×m Both represent the energy constraint coefficient matrix related to charge and discharge efficiency, They represent the maximum charging and discharging power of electric vehicles, E max 、E min They represent the upper and lower limits of the battery operating capacity of electric vehicles, E exp It represents the expected power value of the electric vehicle owner when leaving the grid, and E0 represents the initial power of the electric vehicle. i Expressed as a set of power constraints and energy constraints, within the feasible region, EV can be charged and discharged at any allowed power level.

[0036] In another exemplary embodiment of the present application, since the charge and discharge periods of each EV are different, the dimensions of each matrix will be different and cannot be directly aggregated. Therefore, the dimensions of each polytope are first preprocessed and expanded to 24 charge and discharge periods. The above step 103 expands the dimensions of each polytope in the polytope set to a unified charge and discharge period as follows:

[0037] The dimensions of each polyhedron in the polyhedron set are uniformly expanded to 24 charge and discharge periods, and the inequality coefficient matrix of the expanded feasible domain is obtained as follows:

[0038]

[0039] Where, represents the charging power matrix of the i-th electric vehicle after augmentation, Represents a 145×48 matrix.

[0040] By calculating the coefficient matrix M of each EV inequality i After pre-processing, the EV charging and discharging periods after augmentation are all 24 periods. Both are 145×48 matrices.

[0041] In another exemplary embodiment of the present application, a feasible domain basis set Φ0 is constructed, and the values ​​of the parameters in the inequality coefficient matrix M0 and column vector H0 corresponding to the basis set are specified by averaging all EV parameters in the aggregate quotient. Then the above step 104 can be replaced by the following steps 201 to 204:

[0042] Step 201: Collect charging and discharging data of the electric vehicle cluster; the charging and discharging data includes the time of each electric vehicle entering and leaving the grid, initial power, required power, charging and discharging power, maximum charging and discharging efficiency and battery capacity.

[0043] Step 202: Based on the charging and discharging data of the electric vehicle cluster, average the same elements in the inequality coefficient matrix of the augmented feasible region of the electric vehicle cluster to obtain the inequality coefficient matrix corresponding to the basis set.

[0044] Step 203: Based on the charging and discharging data of the electric vehicle cluster, average the same elements in the column vector of the augmented feasible region of the electric vehicle cluster to obtain the column vector corresponding to the basis set.

[0045] Step 204: Determine the feasible region basis set according to the inequality coefficient matrix corresponding to the basis set and the column vector corresponding to the basis set.

[0046] In another exemplary embodiment of the present application, after constructing a feasible domain basis set Φ0, an affine transformation is performed, and the above step 105 can be replaced by the following steps 301 to 308:

[0047] Step 301: Introduce scaling factors and translation factors, scale and translate the feasible region basis set, and obtain the internal equivalent feasible region of the electric vehicle individual:

[0048] Φ' i =β i Φ0+ν i ={P i ∈R 2m |M0(P i -ν i )≤β i H0};

[0049] Where Φ' i represents the power feasible region Φ of the i-th electric vehicle i The internal equivalent feasible region of β i represents the scaling factor of the i-th electric vehicle, ν i represents the translation factor of the i-th electric vehicle, Φ0 represents the feasible region basis set, P i represents the charging and discharging power matrix of the i-th electric vehicle, P i =[P i C ,P i D ] T , P i C represents the charging power matrix of the i-th electric vehicle, P i D represents the discharge power matrix of the i-th electric vehicle, R 2m Represents a set of 2m-dimensional column vectors, M0 represents the inequality coefficient matrix corresponding to the basis set, and H0 represents the column vector corresponding to the basis set.

[0050] The internal equivalent feasible region can also be called the internal approximate feasible region. i ∈R, used to scale the basis set and determine the size of the feasible region, R represents the set of real numbers; ν i ∈R m×1 , which is used to translate the basis set and determine the location of the feasible region.

[0051] Step 302: Establish the optimal polyhedral inclusion problem model as follows:

[0052]

[0053] In order to obtain the maximum inner approximation area of ​​a single EV, the scaling factor β of the i-th EV is i and the translation factor ν i Optimization was performed and the above-mentioned optimal polyhedral inclusion problem model was established.

[0054] Step 303: high-dimensional variables are introduced through the strong duality principle to transform the optimal polyhedral inclusion problem model into a linear programming problem model; the linear programming problem model is:

[0055]

[0056] Where G represents a high-dimensional variable; represents the charging power matrix of the i-th electric vehicle after augmentation, Represents a 145×48 matrix.

[0057] Given the difficulty of accurately calculating the volume of high-dimensional polytopes, this application does not directly solve the optimization problem in the above equation. Instead, it introduces the high-dimensional variable G through the strong duality principle, transforming it into an easily solvable convex programming problem. Based on Farkas's lemma, the above optimal polytope inclusion problem model is equivalent to the above linear programming problem model.

[0058] Step 304: The difference coefficient matrix composed of row vectors that are different from M0 is recorded as m1, and the redundant constraint is determined as m1P i ≤h1; wherein h1 represents the undetermined parameter vector; the redundant constraint represents a set of hyperplanes tangent to the feasible domain basis set.

[0059] Considering the heterogeneity of EV resources, as the scale of EVs increases, the solution rate of the above convex programming problem is still difficult to meet the aggregation time requirement. To further improve the computational efficiency, this application introduces a reconstruction process of the polyhedron structure. By reconstructing M0, the polyhedron feasible domain of the basis set is deformed to have the same structure as the feasible domain space of each EV, avoiding the introduction of high-dimensional variables and simplifying the solution of the above convex programming problem. Figure 2 .

[0060] Now with Φ0 and Φ i Take the example to illustrate the reconstruction process. Compare the coefficient matrices of the two and record The matrix composed of row vectors that are different from M0 is m1. For the polyhedron Φ0, a series of additional linear constraints m1P are added to Φ0.i ≤h1, if the following formula is satisfied, then m1P i ≤h1 is a redundant constraint, and adding or deleting it will not change the original polytope.

[0061]

[0062] Where: column vector h1 is the unknown parameter.

[0063] To obtain a more accurate solution, the value of h1 should ensure the validity of the above formula as much as possible. The optimal value of each element in h1 can be obtained by solving the linear programming model in the following step 305.

[0064] Step 305: Establish a linear programming model of the undetermined parameter vector as follows:

[0065]

[0066] Where m1(s) and h1(s) represent the sth row of the difference coefficient matrix and the undetermined parameter vector, respectively.

[0067] Step 306: Solve the linear programming model of the undetermined parameter vector to obtain the undetermined parameter vector, and substitute the solved undetermined parameter vector into the redundant constraint.

[0068] Step 307: Replace the constraint formula at the corresponding position in the feasible domain basis set with the redundant constraint that has been substituted into the undetermined parameter vector, and generate a new feasible domain basis set:

[0069]

[0070] In the formula, Φ0' represents the new feasible domain basis set, M'0 represents the coefficient matrix formed by removing the difference coefficient matrix from M0, and H'0 represents the column vector formed by removing the corresponding column vector elements from the difference coefficient matrix from H0. Represents the column vector corresponding to the reconstructed basis set.

[0071] The above reconstruction process realizes the deformation of Φ0, and the reconstructed M0 is Exactly the same.

[0072] Step 308: Based on the new feasible domain basis set, the initial maximum inner approximation model for polyhedral optimization is established as:

[0073]

[0074] In another exemplary embodiment of the present application, in order to take into account the uncertainty of the electric vehicle's initial power and the time it takes to connect to and disconnect from the grid, step 106 may be replaced by the following steps 401 to 403:

[0075] Step 401: Establish uncertainty conditions taking into account the initial power:

[0076]

[0077] Where, Respectively All elements in the s'th row and the sth row, They represent the s'th and sth rows of the reconstructed feasible domain basis set column vectors, respectively. i (s') represents the s'th row of the inequality column vector corresponding to the feasible region of the i-th electric vehicle, ε s represents the allowed violation probability of the constraint in row s, Σ(s) represents the s-th row of the covariance matrix of the initial power distribution, μ(s) represents the s-th row of the empirical mean vector of the initial power distribution, ε represents the allowed violation probability, and L represents C u The number of elements contained in C n Indicates H i The set of the first 4m rows without uncertainty parameter E0, C u Indicates H i The set of the last (2m+1) rows containing the uncertainty parameter E0.

[0078] Step 402: Construct a method for describing the influence of network access and network disconnection time. The box uncertainty set of uncertainty is:

[0079]

[0080] Where U represents the box uncertainty set, represents the inequality coefficient matrix of the feasible region of the i-th electric vehicle in the n-th scenario, m n Indicates the total number of charging and discharging periods of EV in the nth scenario, and They represent the time of entering and leaving the grid after considering fluctuations, Δt n represents the value of the fluctuation number of electric vehicles entering and leaving the grid in the nth scenario, t arr , t dep They represent the time when electric vehicles enter and leave the grid, and t represents the time period.

[0081] Step 403: Combining the box uncertainty set and the uncertainty condition taking into account the initial power quantity, the distributed robust constraint taking into account multiple travel scenarios of electric vehicle users is obtained as follows:

[0082]

[0083] Where, β i,n 、ν i,nThey represent the scaling factor and translation factor of the i-th electric vehicle in the n-th scenario respectively.

[0084] For example, the specific implementation process of steps 401 to 403 is as follows:

[0085] Based on the generalized moment information of the initial power distribution, the empirical mean vector and covariance matrix of the initial power are used to construct the fuzzy set of its probability distribution:

[0086]

[0087] Where: D represents the fuzzy set of the initial power probability distribution; f(H i ) indicates H i The probability distribution function of . E[·] is the expectation operator, μ and Σ represent the empirical mean vector and covariance matrix of the initial power distribution, respectively.

[0088] Considering that the initial charge of EV E0 is only constrained by the right column vector of energy, that is, H i The (2m+1) rows after , therefore the uncertainty of the EV initial power is expressed as the matrix H i The uncertainty of H i Treated as a random variable, a joint chance constraint is introduced to describe the uncertainty of the user's initial power consumption:

[0089]

[0090] Where ε is the allowed violation probability and 1-ε is the confidence level. This formula indicates that the probability of satisfying the EV energy constraint under the condition of initial power uncertainty should be no less than the given confidence level.

[0091] The above joint chance constraint is processed in the distributionally robust framework and re-described as the following distributionally robust joint chance constraint (DRJCC):

[0092]

[0093] Where inf represents the lower bound of a set (or the largest element in the lower bound).

[0094] Combining the above formula with the inner approximation Minkowski aggregation process in step S102, the above DRJCC is introduced when considering the maximum inner approximation problem. The constraints of the above optimal polyhedral inclusion problem can be written in the following DRJCC form:

[0095]

[0096] This formula represents the calculation of Hi In the process of uncertainty aggregation, the maximum inner approximate polytope Φ' i Still included in the original EV feasible region Φ i The probability of is not less than the given confidence level. Through the reconstruction process, the above formula can be equivalently transformed into the following form under the framework of the maximum inner approximation problem in S102:

[0097]

[0098] According to the formula:

[0099]

[0100] Where: y 0 (x) is the part of the objective function that is unrelated to the random variable, y(x) T is the part of the objective function related to the random variable, represents a random variable, μ represents the mean vector of the random variable, and Σ represents the covariance matrix of the random variable.

[0101] The above formula can be equivalently transformed into the following linear programming problem, completing the transformation from the deterministic condition to the uncertain condition taking into account the initial power:

[0102]

[0103] Where: Represents matrices respectively All elements in the s'th row and the sth row; They represent the sth and s'th rows of the reconstructed basis set polytope column vectors respectively; H i (s') represents the s'th row of the inequality column vector corresponding to the EV feasible region; C n Indicates H i The set of the first 4m rows that do not contain the uncertainty parameter E0; C u Indicates H i The set of the (2m+1) rows containing the uncertainty parameter E0; s is the allowed violation probability of the constraint in row s; L is C u The number of elements contained in .

[0104] For each EV, considering that its on-grid and off-grid time may fluctuate in the previous and next time periods, the on-grid and off-grid time will affect the dimension of the feasible domain, so its uncertainty is expressed as the matrix The uncertainty of the grid connection and disconnection time is determined by constructing the following box uncertainty set to describe the matrix Uncertainty:

[0105]

[0106] Where: represents the feasible region inequality coefficient matrix of the i-th EV in the n-th scenario; and They represent the time of entering and leaving the grid after considering fluctuations; Δt n Indicates the value of the EV's on-grid and off-grid period fluctuations in the nth scenario; m n Indicates the total number of charging and discharging periods of the EV in the nth scenario.

[0107] Incorporating various scenarios of grid connection and disconnection time fluctuations into the above DRJCC, it is transformed into the following distributionally robust optimization (DRO) constraint form that takes multiple scenarios into account:

[0108]

[0109] Where: β i,n 、ν i,n They represent the scaling factor and translation factor of the i-th EV in the n-th scenario respectively; U is the box uncertainty set of the time of entering and leaving the grid.

[0110] In another exemplary embodiment of the present application, in order to accurately characterize the robust boundary of the feasible region for large-scale EV aggregation, based on the uncertainty factor modeling in step 106, the maximum inner approximation problem in the aggregation process of step 105 is transformed into the following form (the final maximum inner approximation model):

[0111]

[0112] Where, β i,n 、ν i,n denote the scaling factor and translation factor of the ith electric vehicle in the nth scenario, λ n represents the probability of the nth scene; ψ represents the confidence set of the fuzzy distribution of scene probability, K represents the total number of scenes, Respectively represent the s'th row and sth row of the reconstructed feasible domain basis set column vector, Respectively All elements in the s'th row and the sth row in H i (s') represents the s'th row of the inequality column vector corresponding to the feasible region of the i-th electric vehicle, ε s represents the allowed violation probability of the constraint in row s, Σ(s) represents the s-th row of the covariance matrix of the initial power distribution, μ(s) represents the s-th row of the empirical mean vector of the initial power distribution, ε represents the allowed violation probability, and L represents C u The number of elements contained in C n Indicates H i The set of the first 4m rows without uncertainty parameter E0, Cu Indicates H i The set of the last (2m+1) rows containing the uncertainty parameter E0, U represents the box uncertainty set.

[0113] In another exemplary embodiment of the present application, the above-mentioned final maximum inner approximation model has a two-layer structure. The inner layer problem determines the probability distribution of the worst scenario of on-grid and off-grid time by minimizing the EV scaling factor, and the outer layer problem solves the maximum scaling factor of a single EV through the inner approximation Minkowski reconstruction aggregation method to determine the maximum inner approximation feasible domain. When the inner layer model solves the probability distribution of the worst scenario of on-grid and off-grid time, in order to make the scenario probability fluctuate within a certain range and fit the actual data, a comprehensive norm constraint including 1-norm and ∞-norm is set to construct a confidence set of the fuzzy distribution of the scenario probability. Then the above step 108 uses the inner approximation Minkowski aggregation method to solve the final maximum inner approximation model. When , a comprehensive norm constraint including 1-norm and ∞-norm is set, and the confidence set of the fuzzy distribution of scene probability is constructed as follows:

[0114]

[0115] Where, Γ T represents the probability distribution vector of the on-grid and off-grid time scenarios, Γ T =(λ1,λ2,···,λ K ), λ1 represents the probability of the first scenario, λ2 represents the probability of the second scenario, λ K represents the probability of the Kth scenario; represents the probability distribution vector of the initial scenario of on-grid and off-grid time, λ1 0 represents the probability of the first initial scene, represents the probability of the second initial scenario, represents the probability of the Nth initial scene; ||·||1 represents the 1-norm; ||·|| ∞ represents the ∞-norm; θ1, θ ∞ Respectively represent the deviation values ​​allowed by the 1-norm and ∞-norm constraints; θ1, θ ∞ The value of is determined by the confidence level and the statistical sample situation of the scene.

[0116] Set the scene probability set {λ k}Satisfy the confidence constraint:

[0117]

[0118] Where M represents the number of scene samples.

[0119] Let the right side of the inequality in the confidence constraint be equal to the confidence γ (that is, there is at least a probability of γ fuzzy distribution in the given set), then In the formula, γ1 represents the confidence corresponding to the 1-norm constraint, γ ∞ Indicates the confidence corresponding to the ∞-norm constraint.

[0120] In another exemplary embodiment of the present application, steps 104 to 108 constitute an inner approximation reconstruction aggregation process, which aggregates each EV polytope set. The aggregation principle is as follows: Figure 3 As shown. The inner approximation reconstruction aggregation process mainly includes three steps: basis set construction, affine transformation and cluster integration. Step 104 corresponds to the basis set construction step, steps 105 to 108 to obtain the optimal polyhedron correspond to the affine transformation step, and step 108 "aggregating the optimal polyhedron to obtain the maximum inner approximation aggregation feasible domain of the electric vehicle cluster" corresponds to the cluster integration step. Among them, the affine transformation and isomorphic polyhedron summation process can be expressed as:

[0121] Φ' i =β i Φ0+ν i ={P i ∈R 2m |M0(P i -ν i )≤β i H0}.

[0122]

[0123] The second formula above reflects the inclusion relationship among the feasible region of the inner approximation Minkowski aggregation of the present application, the feasible region of the traditional inner approximation Minkowski aggregation and the feasible region of the exact Minkowski aggregation.

[0124] After optimizing the scaling factor and translation factor of each EV, the feasible region of the EV cluster’s maximum inner approximation aggregation can be expressed as:

[0125]

[0126] The robust boundary characterization results of small-scale EV aggregation in two periods are as follows: Figure 4 shown. Figure 4 P1 and P2 represent the first charge and discharge period and the second charge and discharge period respectively.

[0127] In another exemplary embodiment of the present application, the power system frequency deviation is mainly caused by the fluctuation of load demand and renewable energy power generation, and the magnitude of the system active power fluctuation can be measured by the net load standard deviation within the AGC (Automatic Generation Control) assessment period, as shown below:

[0128]

[0129] Where: δ represents the standard deviation of the net load during the AGC assessment period; Π represents the total length of the assessment period; and They represent the net load power, EV charging and discharging power, and load power excluding EV in the nth period during the tth assessment time. and They represent the wind power and photovoltaic power generation power in the nth period within the tth assessment time respectively.

[0130] The utility of large-scale EVs participating in system frequency regulation is evaluated. With the goal of minimizing the sum of the standard deviations of the system net load, the charging and discharging power of large-scale EVs participating in system frequency regulation is optimized based on the robust boundary described. The frequency regulation utility evaluation model is established as follows:

[0131]

[0132] Where, δ t′ represents the standard deviation of the net load in the assessment period t′, T represents the total charging and discharging period of the electric vehicle cluster participating in the system frequency regulation, π represents the total length of the assessment period, represents the charging and discharging power of the electric vehicle cluster in the nth period within the assessment time period t′, P t′ represents the charge and discharge power of the electric vehicle cluster at time t′, N represents the total number of electric vehicles in the cluster, Φ represents the maximum inner approximation aggregation feasible region of the electric vehicle cluster, P represents the charge and discharge power matrix of the electric vehicle cluster, R 2m represents the set of 2m-dimensional column vectors, M0 represents the inequality coefficient matrix corresponding to the basis set, ν i represents the translation factor of the i-th electric car, β i represents the scaling factor of the i-th electric vehicle, and H0 represents the column vector corresponding to the basis set.

[0133] The above formula provides the optimal optimization method for EV cluster charging and discharging power, which minimizes the sum of the system's net load standard deviations while accounting for the randomness of EV user behavior. This invention optimizes the EV cluster charging and discharging power to maintain a low net load standard deviation for the grid, contributing to grid frequency stability.

[0134] Figure 5This is a brief summary of the method of this application: S101, establish a model to represent the feasible domain of individual EV power, convert it into a polyhedron set expression, and preprocess the dimensions of each polyhedron; S102, establish an inner approximation Minkowski aggregation model to aggregate each EV polyhedron set, and introduce a reconstruction process of the polyhedron structure to simplify the solution of the aggregation process, and establish the deterministic boundary of the feasible domain of large-scale EV aggregation; S103, establish an uncertainty set of EV initial power and grid connection and disconnection time, and model the uncertainty of EV user travel information. S104, incorporate the uncertainty of EV user travel information into the aggregation process, and based on the aggregation process of step S102, accurately characterize the robust boundary of the feasible domain of large-scale EV aggregation; S105, based on the robust boundary of the feasible domain, apply it to system frequency regulation and evaluate the frequency regulation utility of large-scale EV participation in system frequency regulation by minimizing the standard deviation of the system net load. The method proposed in this application is universal, which is conducive to fully utilizing the regulation capabilities of large-scale EV resources, improving the stability and reliability of EV frequency regulation resources, and ensuring the stability of system frequency. It is of great significance for large-scale EVs to participate in vehicle-grid interaction.

[0135] The method of the present application has significant effects: first, the inner approximation Minkowski aggregation method is used to achieve the aggregation of the feasible domain of large-scale EVs, and the reconstruction process is introduced in the affine transformation process, which further improves the computational efficiency and approximation accuracy of the aggregation. Secondly, considering that the traditional inner approximation method can only aggregate EV clusters with exactly the same charging and discharging periods, the dimensions of each polyhedron are preprocessed before aggregation, and they are uniformly expanded to 24 charging and discharging periods to achieve effective aggregation of heterogeneous EV resources at multiple time scales. In addition, considering that EV user behavior has a certain degree of randomness and dispersion, if the aggregator only participates in the subsequent optimization process with the aggregated feasible domain boundary under the above-mentioned deterministic conditions, the obtained frequency regulation utility evaluation results will be weakened or even completely invalid. Therefore, the uncertainty of the EV initial power and the time of entering and leaving the grid is modeled, and the uncertainty factor processing process is integrated into the above-mentioned aggregation process to achieve the transformation of the deterministic boundary of the aggregated feasible domain to the robust boundary. Finally, the obtained robust boundary is used to participate in system frequency regulation to achieve efficient evaluation of the frequency regulation utility of EV frequency regulation resources. The electric vehicle frequency regulation utility evaluation method proposed in this application, which takes into account feasible domain reconstruction aggregation and robust boundary characterization, can take into account both computational efficiency and approximation accuracy when aggregating large-scale heterogeneous EV resources. At the same time, it can effectively reduce the failure risk of frequency regulation utility evaluation results when EVs participate in system frequency regulation, improve the stability and reliability of EV frequency regulation resources, and ensure the stability of system frequency. It has very important application value for scientific research institutions and the industrial and commercial sectors to realize electric vehicle participation in grid interaction technology and use electric vehicle aggregation technology to participate in system frequency regulation.

[0136] The technical features of the above embodiments can be combined arbitrarily. To make the description concise, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0137] This document uses specific examples to illustrate the principles and implementation methods of this application. The description of the above examples is only intended to help understand the method and core concept of this application. At the same time, for those skilled in the art, based on the concept of this application, there may be changes in the specific implementation methods and application scope. In summary, the content of this specification should not be understood as limiting this application.

Claims

1. A method for evaluating the frequency modulation utility of electric vehicles, characterized in that: include: Establish a power feasible domain representation model for individual electric vehicles; The power feasible domain representation model of all individual electric vehicles in the electric vehicle cluster is converted into a polyhedral set represented in the form of a half-plane in Euclidean space; Augmenting the dimensions of each polyhedron in the polyhedron set to a uniform charge and discharge period to obtain an augmented polyhedron set; Constructing a feasible domain basis set according to the augmented polytope set; scaling and translating the feasible domain basis set, and establishing an initial maximum inner approximation model for polyhedral optimization; Model the uncertainty of electric vehicle initial power and grid connection and disconnection time to obtain distributed robust constraints that take into account multiple travel scenarios of electric vehicle users; Fusing the distributed robust constraint and the initial polyhedral optimized maximum inner approximation model to obtain a final maximum inner approximation model; Solving the final maximum inner approximation model to obtain the optimal polyhedron of the electric vehicle individual, and simultaneously aggregating all the optimal polyhedrons using the inner approximation Minkowski aggregation method to obtain the maximum inner approximation aggregation feasible region of the electric vehicle cluster; Establish a frequency regulation utility evaluation model when electric vehicle clusters participate in power system frequency regulation; According to the maximum inner approximation aggregation feasible domain of the electric vehicle cluster, with the goal of minimizing the sum of the standard deviations of the net load of the power system, the frequency regulation utility evaluation model is solved to obtain the charging and discharging power of the electric vehicle cluster in each charging and discharging period; the charging and discharging power reflects the frequency regulation capacity of the electric vehicle cluster when participating in the frequency regulation of the power system, and the frequency regulation capacity represents the frequency regulation utility of the electric vehicle cluster.

2. The method for evaluating the frequency modulation utility of electric vehicles according to claim 1, characterized in that: The power feasible domain characterization model is: Where, They represent the charging and discharging power of the electric vehicle in time period t, They represent the maximum charging and discharging power of electric vehicles, E t represents the operating capacity of electric vehicles in time period t, E t-1 represents the operating capacity of electric vehicles in time period t-1, η C ,η D They represent the charging and discharging efficiency of electric vehicles, Δt represents the charging and discharging time, E max 、E min They represent the upper and lower limits of the battery operating capacity of electric vehicles, E exp represents the expected power value of the electric vehicle owner when leaving the grid, is the power value of the electric vehicle when it is off-grid, t arr , t dep They represent the time when electric vehicles enter and leave the grid respectively.

3. The method for evaluating the frequency modulation utility of electric vehicles according to claim 1, characterized in that: The polytope set is: Φ i ={P i ∈R 2m |M i P i ≤H i }; Where, Φ i represents the power feasible region of the i-th electric vehicle, m represents the total number of charging and discharging periods, P i represents the charging and discharging power matrix of the i-th electric vehicle, represents the charging power matrix of the i-th electric vehicle, represents the discharge power matrix of the i-th electric vehicle, R 2m Represents a set of 2m-dimensional column vectors, M i The inequality coefficient matrix representing the feasible region of the i-th electric vehicle, H i The column vector representing the feasible region of the i-th electric vehicle; I m represents the identity matrix, U m 、U' m 、A 1×m 、A1' ×m Both represent the energy constraint coefficient matrix related to charge and discharge efficiency, They represent the maximum charging and discharging power of electric vehicles, E max 、E min They represent the upper and lower limits of the battery operating capacity of electric vehicles, E exp It represents the expected power value of the electric vehicle owner when leaving the grid, and E0 represents the initial power of the electric vehicle.

4. The method for evaluating the frequency modulation effectiveness of electric vehicles according to claim 3, characterized in that: Increasing the dimensions of each polyhedron in the polyhedron set to a uniform charge and discharge period specifically includes: The dimensions of each polyhedron in the polyhedron set are uniformly expanded to 24 charge and discharge periods, and the inequality coefficient matrix of the expanded feasible domain is obtained as follows: Where, represents the charging power matrix of the i-th electric vehicle after augmentation, Represents a 145×48 matrix.

5. The method for evaluating the frequency modulation utility of electric vehicles according to claim 4, characterized in that: According to the augmented polytope set, a feasible domain basis set is constructed, specifically including: Collecting charging and discharging data of the electric vehicle cluster; the charging and discharging data includes each electric vehicle's grid entry and exit time, initial power, required power, charging and discharging power, maximum charging and discharging efficiency, and battery capacity; According to the charging and discharging data of the electric vehicle cluster, the same element in the inequality coefficient matrix of the augmented feasible region of the electric vehicle cluster is averaged to obtain the inequality coefficient matrix corresponding to the basis set; According to the charging and discharging data of the electric vehicle cluster, the same element in the column vector of the augmented feasible region of the electric vehicle cluster is averaged to obtain the column vector corresponding to the basis set; The feasible domain basis set is determined according to the inequality coefficient matrix corresponding to the basis set and the column vector corresponding to the basis set.

6. The method for evaluating the frequency modulation effectiveness of electric vehicles according to claim 1, characterized in that: The feasible domain basis set is scaled and translated, and an initial maximum inner approximation model for polyhedral optimization is established, specifically including: Introducing the scaling factor and translation factor, scaling and translating the feasible domain basis set, the internal equivalent feasible domain of the electric vehicle individual is obtained as: Φ' i =β i Φ0+ν i ={P i ∈R 2m |M0(P i -ν i )≤β i H0}; where Φ' i represents the power feasible region Φ of the i-th electric vehicle i The internal equivalent feasible region of β i represents the scaling factor of the i-th electric vehicle, ν i represents the translation factor of the i-th electric vehicle, Φ0 represents the feasible region basis set, P i represents the charging and discharging power matrix of the i-th electric vehicle, represents the charging power matrix of the i-th electric vehicle, represents the discharge power matrix of the i-th electric vehicle, R 2m represents the set of 2m-dimensional column vectors, M0 represents the inequality coefficient matrix corresponding to the basis set, and H0 represents the column vector corresponding to the basis set; The optimal polyhedral inclusion problem model is established as: By introducing high-dimensional variables through the strong duality principle, the optimal polyhedral inclusion problem model is transformed into a linear programming problem model; the linear programming problem model is: Where G represents a high-dimensional variable; represents the charging power matrix of the i-th electric vehicle after augmentation, Represents a 145×48 matrix; Will The difference coefficient matrix composed of row vectors that are different from M0 is recorded as m1, and the redundant constraint is determined as m1P i ≤h1; wherein h1 represents the undetermined parameter vector; the redundant constraint represents the set of hyperplanes tangent to the feasible domain basis set; The linear programming model of the undetermined parameter vector is established as: Where m1(s) and h1(s) represent the sth row of the difference coefficient matrix and the undetermined parameter vector, respectively; Solving the linear programming model of the undetermined parameter vector to obtain the undetermined parameter vector, and substituting the solved undetermined parameter vector into the redundant constraint; Replace the constraint formula in the corresponding position of the feasible domain basis set with the redundant constraint that has been substituted into the undetermined parameter vector, and generate a new feasible domain basis set: ; Where Φ0' represents the new feasible domain basis set, M'0 represents the coefficient matrix formed by removing the difference coefficient matrix from M0, and H'0 represents the column vector formed by removing the corresponding column vector elements from the difference coefficient matrix from H0. Represents the column vector corresponding to the reconstructed basis set; According to the new feasible domain basis set, the initial maximum inner approximation model of polyhedral optimization is established as:

7. The method for evaluating the frequency modulation effectiveness of electric vehicles according to claim 6, characterized in that: The uncertainty of the initial charge and on-grid and off-grid time of electric vehicles is modeled to obtain distributed robust constraints that take into account multiple travel scenarios of electric vehicle users, including: The uncertainty condition considering the initial charge is established as: Where, Respectively All elements in the s'th row and the sth row, They represent the s'th and sth rows of the reconstructed feasible domain basis set column vectors, respectively. i (s') represents the s'th row of the inequality column vector corresponding to the feasible region of the i-th electric vehicle, ε s represents the allowed violation probability of the constraint in row s, Σ(s) represents the s-th row of the covariance matrix of the initial power distribution, μ(s) represents the s-th row of the empirical mean vector of the initial power distribution, ε represents the allowed violation probability, and L represents C u The number of elements contained in C n Indicates H i The set of the first 4m rows without uncertainty parameter E0, C u Indicates H i The set of the last (2m+1) rows containing the uncertainty parameter E0; Constructed to describe the influence of on-grid and off-grid time The box uncertainty set of uncertainty is: Where U represents the box uncertainty set, represents the inequality coefficient matrix of the feasible region of the i-th electric vehicle in the n-th scenario, m n Indicates the total number of charging and discharging periods of EV in the nth scenario, and They represent the time of entering and leaving the grid after considering fluctuations, Δt n represents the value of the fluctuation number of electric vehicles entering and leaving the grid in the nth scenario, t arr , t dep They represent the time when the electric vehicle enters and leaves the grid, and t represents the time period; Combining the box uncertainty set and the uncertainty condition of the initial power, the distributed robust constraint considering multiple travel scenarios of electric vehicle users is obtained as follows: Where, β i,n 、ν i,n They represent the scaling factor and translation factor of the i-th electric vehicle in the n-th scenario respectively.

8. The method for evaluating the frequency modulation effectiveness of electric vehicles according to claim 1, characterized in that: The final maximum inner approximation model is: Where, β i,n 、ν i,n denote the scaling factor and translation factor of the ith electric vehicle in the nth scenario, λ n represents the probability of the nth scene; ψ represents the confidence set of the fuzzy distribution of scene probability, K represents the total number of scenes, Respectively represent the s'th row and sth row of the reconstructed feasible domain basis set column vector, Respectively All elements in the s'th row and the sth row in H i (s') represents the s'th row of the inequality column vector corresponding to the feasible region of the i-th electric vehicle, ε s represents the allowed violation probability of the constraint in row s, Σ(s) represents the s-th row of the covariance matrix of the initial power distribution, μ(s) represents the s-th row of the empirical mean vector of the initial power distribution, ε represents the allowed violation probability, and L represents C u The number of elements contained in C n Indicates H i The set of the first 4m rows without uncertainty parameter E0, C u Indicates H i The set of the last (2m+1) rows containing the uncertainty parameter E0, U represents the box uncertainty set.

9. The method for evaluating the frequency modulation utility of electric vehicles according to claim 8, characterized in that: In solving the final maximum inner approximation model When , a comprehensive norm constraint including 1-norm and ∞-norm is set, and the confidence set of the fuzzy distribution of scene probability is constructed as: Where, Γ T represents the probability distribution vector of the on-grid and off-grid time scenarios, Γ T =(λ1,λ2,···,λ K ), λ1 represents the probability of the first scenario, λ2 represents the probability of the second scenario, λ K represents the probability of the Kth scenario; represents the probability distribution vector of the initial scenario of on-grid and off-grid time, represents the probability of the first initial scene, represents the probability of the second initial scenario, represents the probability of the Nth initial scene; ||·||1 represents the 1-norm; ||·|| ∞ represents the ∞-norm; θ1, θ ∞ Represent the deviation values ​​allowed by the 1-norm and ∞-norm constraints respectively; Set the scene probability set {λ k }Satisfy the confidence constraint: Where M represents the number of scene samples; Let the right side of the inequality in the confidence constraint be equal to the confidence γ, then In the formula, γ1 represents the confidence corresponding to the 1-norm constraint, γ ∞ Indicates the confidence corresponding to the ∞-norm constraint.

10. The method for evaluating the frequency modulation utility of electric vehicles according to claim 1, characterized in that: The frequency modulation utility evaluation model is: Where, δ t′ represents the standard deviation of the net load in the assessment period t′, T represents the total charging and discharging period of the electric vehicle cluster participating in the system frequency regulation, π represents the total length of the assessment period, represents the charging and discharging power of the electric vehicle cluster in the nth period within the assessment time period t′, P t′ represents the charge and discharge power of the electric vehicle cluster at time t′, N represents the total number of electric vehicles in the cluster, Φ represents the maximum inner approximation aggregation feasible region of the electric vehicle cluster, P represents the charge and discharge power matrix of the electric vehicle cluster, R 2m represents the set of 2m-dimensional column vectors, M0 represents the inequality coefficient matrix corresponding to the basis set, ν i represents the translation factor of the i-th electric car, β i represents the scaling factor of the i-th electric vehicle, and H0 represents the column vector corresponding to the basis set.

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