A large-scale traffic user equilibrium regulation method considering charging behavior

Abstract

The present invention belongs to the field of electronic traffic coupling networks, and discloses a large-scale traffic user equilibrium regulation method considering charging behavior. The present invention improves the traditional sensitivity analysis technology to make it applicable to the user equilibrium problem considering charging behavior. Based on the improved sensitivity analysis technology, the present invention obtains the response of traffic flow to social regulation signals through the sensitivity analysis of the traffic user equilibrium problem. The present invention makes full use of the convex property of the user equilibrium problem to help quickly solve the optimal scheduling problem of a large-scale power-traffic coupling network with the user equilibrium as the response model.

Description

Technical Field

[0001] The present invention relates to an optimal operation algorithm for a power-traffic coupling network, which is a fast solution method applicable to large-scale traffic networks and belongs to the field of operation optimization of power-traffic coupling systems. Background Art

[0002] With the continuous expansion of the scale of electric vehicles, the charging power of electric vehicles and the scale of charging stations have also increased accordingly. This has led to a high degree of coupling between the power system and the traffic system, which may in turn cause negative impacts on the power-traffic coupling network, such as load overload in low-voltage areas, voltage over-limit at local nodes, and traffic line congestion during peak hours. Therefore, a large number of researchers have studied corresponding adjustment strategies from the perspective of the power-traffic coupling system, using the optimal power flow model and the user equilibrium model as the basic models for power and traffic respectively to reduce operating costs.

[0003] However, when the user equilibrium problem is regarded as the lower-level problem and interacts with other social entities (such as power grids or charging service providers), it is often modeled as a mathematical programming problem with equilibrium constraints (MPEC). This type of model often needs to introduce a large number of 0-1 variables as auxiliary variables, and thus is transformed into a mixed integer programming problem containing a large number of 0-1 variables, and its solution complexity is a huge challenge in large-scale networks. Summary of the Invention

[0004] The purpose of the present invention is to overcome at least one deficiency of the prior art and provide a large-scale traffic user equilibrium regulation method considering charging behavior.

[0005] The technical solution adopted by the present invention is as follows:[[]]

[0006] In the first aspect of the present invention, there is provided:[[]]

[0007] A large-scale traffic user equilibrium regulation method considering charging behavior, comprising the following steps:[[]]

[0008] S1. Construct a traffic network model based on the user equilibrium model, specifically including:[[]]

[0009] Represent the traffic network by a directed graph where and respectively represent the sets of nodes and edges in the directed graph, and there are and ; represents the number of elements in the set; a subset of the node set It includes nodes with fast charging stations, forming a set of charging nodes. Electric vehicles can choose to charge at any charging node; the travel demands in the transportation network are expressed using origin-destination pairs, and an origin-destination pair is represented by a tuple, , where both the origin s and the destination t belong to , and the travel demand belongs to the travel demand set , while the origin-destination tuple belongs to the origin-destination set ;

[0010] S2. Convert the charging behavior of electric vehicles into a generalized transportation behavior;

[0011] S3. Through sensitivity analysis technology, extract the response of the traffic flow allocation result to small perturbations, achieve the solution, and determine the large-scale traffic user equilibrium regulation strategy.

[0012] In some examples of large-scale traffic user equilibrium regulation methods, in step S2, converting the charging behavior of electric vehicles into a generalized transportation behavior specifically includes:

[0013] In some examples of large-scale traffic user equilibrium regulation methods, convert the charging behavior into the driving process on the "hyperedge" to achieve the compatibility of sensitivity analysis technology with the charging behavior of electric vehicles. The number of electric vehicle charging users is used as a kind of edge flow , and the edge flow of the entire transportation system is extended to a generalized edge flow ; the edge-path matrix and the charging-path matrix are extended to a generalized edge-path matrix .

[0014] In some examples of large-scale traffic user equilibrium regulation methods, step S3 specifically includes:

[0015] S31: Analyze and remove redundant paths in the traffic network path set and simplify the corresponding constraints:

[0016] Obtain the gradient of the number of electric vehicle charging users with respect to the perturbation based on the sensitivity analysis technology extended by the "hyperedge" ; the KKT condition system of the user equilibrium model is as follows:

[0017]

[0018]

[0019]

[0020]

[0021] where is used to represent the cost on the edge and the cost at the charging station; and are the Lagrange multipliers of the non - negativity constraint of path flow and the flow conservation constraint respectively, is equivalent to where ; in this KKT system, the traffic flow allocation result and are obtained by solving the lower - level user equilibrium problem, and all symbols are known values; for the set of paths whose path costs are equal to the minimum path costs of the corresponding origin - destination pairs, it is defined as the "equilibrium path set", that is ;

[0022] S32: Analyze the mathematical relationships in the traffic network, further simplify the constraints, and the path flow and the generalized edge flow satisfy the linear equation system relationship:

[0023] S33: Judge whether the left - hand coefficient matrix of the above - mentioned linear equation system is a column - full - rank matrix. If so, execute S34; otherwise, continue to complete the operation of S33, find the maximal linearly independent group of the left - hand coefficient matrix, use "~" to represent the corresponding set of the maximal linearly independent group, and represent the KKT system as:

[0024]

[0025] ;

[0026] S34: Calculate the response of the target traffic network variables with respect to the perturbation value based on the implicit function theory.

[0027] In some examples of large - scale traffic user equilibrium regulation methods, the specific operation for determining the response in step S34 is:

[0028] According to the implicit function theory, represent the gradients of the path flow and the Lagrange multiplier with respect to the perturbation value as:

[0029]

[0030]

[0031]

[0032] Based on the generalized edge - path matrix , transform the gradient based on the path flow into the gradient based on the generalized edge flow:

[0033] .

[0034] In some examples of large-scale traffic user equilibrium regulation methods, in step S31, the constraints of the simplified KKT condition system are as follows:

[0035]

[0036]

[0037] 。

[0038] In some examples of large-scale traffic user equilibrium regulation methods, the equilibrium regulation is the optimal pricing regulation of charging service providers, the optimal scheduling of emergency power supply fleets or emergency maintenance fleets when structural failures occur in the power-traffic coupling network, and charging regulation.

[0039] In some examples of large-scale traffic user equilibrium regulation methods, the equilibrium regulation is the optimal pricing regulation of charging service providers, and the mathematical expression of the traffic network model is:

[0040]

[0041]

[0042]

[0043]

[0044]

[0045] Where is the traffic flow allocated to traffic network edge a, is the number of electric vehicle users at fast charging station e; is the time taken for an electric vehicle to travel on edge a, is the time consumed for an electric vehicle to charge at fast charging station e, and the two are functions of edge flow and fast charging station electric vehicle users respectively; is the set of traffic flows allocated to all paths.

[0046] The second aspect of the present invention provides:

[0047] A computer-readable storage medium storing one or more programs, the one or more programs including instructions that, when executed by a computing device, cause the computing device to execute the method described in the first aspect of the present invention.

[0048] The third aspect of the present invention provides:

[0049] A computing device, comprising:

[0050] One or more processors, a memory, and one or more programs, wherein the one or more programs are stored in the memory and configured to be executed by the one or more processors, and the one or more programs include steps for performing the method described in the first aspect of the present invention.

[0051] The beneficial effects of the present invention are:

[0052] The equilibrium regulation method of some examples of the present invention is a basic solution tool that can be embedded in the optimal scheduling problem of any power-transportation coupled network with the user equilibrium problem as the lower-layer response problem. For example, in terms of price signal guidance, when decision-makers use charging prices, tolls, charging station access fees, or charging subsidies at designated locations to guide vehicles to charge orderly in terms of time and space, this method can be used as an evaluation tool for decision-makers to estimate the impact of the strategies to be proposed; for example, when typhoons or floods occur and structural failures occur in the power-transportation coupled network, when the emergency rescue department conducts the optimal scheduling of the optimal emergency power supply fleet or the emergency repair fleet, this method can be used as a sub-module of the large-scale scheduling problem to accelerate the solution of the problem and support rapid scheduling in emergency scenarios; from the perspective of charging service providers, charging service providers can formulate the optimal price of charging stations based on the method disclosed in the present invention, thereby improving their own operating efficiency.

[0053] In terms of the specific solution effect, taking the optimal pricing problem of charging service providers as an example. The algorithm for solving the optimal pricing problem of charging service providers based on sensitivity analysis proposed by the present invention can significantly improve the calculation efficiency compared with the mathematical programming method based on the KKT conditions, and there will be no obvious loss of optimality at the same time. Experimental results show that compared with the mathematical programming method, the proposed method can reduce the calculation time by up to 82.3% at most, and there is only a 0.5% loss of the objective function value. Description of the Drawings

[0054] Figure 1 is a flowchart of a large-scale traffic user equilibrium regulation method considering charging behavior of the present invention.

[0055] Figure 2 is a schematic diagram of the "hyperedge" transformation of the present invention, where "s" represents any pre-order node of the charging node "e", and "t" represents any post-order node of the charging node. Detailed Embodiments

[0056] The following further illustrates the technical solutions of the present invention with reference to examples.

[0057] Refer to Figure 1 , a large-scale traffic user equilibrium regulation method considering charging behavior, includes the following steps:

[0058] S1. Construct a traffic network model based on the user equilibrium model;

[0059] S2. Transform the electric vehicle charging behavior into a generalized traffic behavior;

[0060] S3. Through sensitivity analysis technology, extract the response of the traffic flow allocation result to small perturbations to achieve the solution.

[0061] Specifically, for S1, constructing a traffic network model based on the user equilibrium model includes:

[0062] Represent the traffic network by a directed graph where and represent the sets of nodes and edges in the directed graph respectively, and there are and . represents the number of elements in the set. A subset of the node set contains the nodes where fast charging stations are built, and becomes the charging node set. Electric vehicles can choose to charge at any charging node. Use the origin-destination pair to represent the traffic travel demand in the traffic network, and the origin-destination pair is represented by a tuple , where the origin s and the destination t both belong to , the traffic demand belongs to the traffic demand set , and the origin-destination tuple belongs to the origin-destination set . To represent the phenomenon that electric vehicle users choose one of several possible paths through the navigation software when traveling, the present invention uses an edge-path matrix to record which edges of the traffic network each path passes through. At the same time, the present invention uses a charging-path matrix to record the charging locations corresponding to each path. The set stores the indices of all paths, and then distinguishes which origin-destination pair each path belongs to through the origin-destination pair-path matrix .

[0063] For the typical optimal pricing model of charging service providers, it includes the upper-layer optimal pricing problem of charging service providers and the lower-layer user equilibrium problem. Among them, the lower-layer user equilibrium problem describes the distribution of traffic flow in the traffic network when all electric vehicle users adopt the minimum path cost (including driving time, charging time and charging price). Its mathematical model is as follows:

[0064]

[0065]

[0066]

[0067]

[0068]

[0069] where is the traffic flow allocated to edge a of the transportation network, and is the number of electric vehicle users at fast charging station e. is the time taken for an electric vehicle to travel on edge a, and is the time consumed for an electric vehicle to charge at fast charging station e. They are respectively functions of edge flow and the number of electric vehicle users at the fast charging station . is the set of traffic flows allocated to all paths. The first and second constraints characterize the mathematical relationship between edge flow and path flow. The third constraint is the flow conservation constraint, where the sum of the traffic flows for each origin-destination pair is equal to the traffic demand. The third constraint requires that the path flow is not less than zero, which also implies that the edge flow is not less than zero.

[0070] S2. Convert the electric vehicle charging behavior into a generalized traffic behavior, specifically including:

[0071] The present invention improves the sensitivity analysis technology to consider the electric vehicle charging behavior. By converting the charging behavior into a driving process on a "hyper-arc" (see Figure 2 ), the compatibility of the sensitivity analysis technology with the electric vehicle charging behavior is achieved. Through this conversion, the number of electric vehicle charging users can be regarded as a kind of edge flow , and the edge flow of the entire transportation system is extended to a generalized edge flow . The edge-path matrix and the charging-path matrix can be extended to a generalized edge-path matrix .

[0072] S3. Through the sensitivity analysis technology, extract the response of the traffic flow allocation result to small perturbations to achieve the solution, specifically:

[0073] S31: Analyze and remove redundant paths in the transportation network path set and simplify the corresponding constraints:

[0074] The present invention uses the sensitivity analysis technology based on the "hyper-arc" extension to obtain the gradient of the number of electric vehicle charging users with respect to perturbations . The KKT condition system of the user equilibrium model is as follows:

[0075]

[0076]

[0077]

[0078]

[0079] where is used to represent the cost on the edge and the cost at the charging station. and are the Lagrange multipliers of the non - negativity constraint of path flow and the flow conservation constraint respectively. Based on the aforementioned "hyper - edge transformation", is equivalent to where . In this KKT system, the traffic flow allocation results and have been obtained by solving the lower - level user equilibrium problem, and all symbols are known values. For the set of paths whose path cost is equal to the minimum path cost of the corresponding origin - destination pair, it is defined as the "equilibrium path set", that is . According to the definition of user equilibrium, for the non - equilibrium path set, its path traffic flow must be equal to 0 and it has no impact on the system, so it is directly removed, and all matrices and sets related to the path are reduced accordingly. For all the reduced sets, use " " for annotation. The first line of the KKT condition , according to the definition, the cost of the equilibrium path set is equal to the corresponding minimum path cost, so is equal to 0, that is, the complementary slackness constraint can be removed from the KKT system, and the constraints of the simplified KKT condition system are as follows:

[0080]

[0081]

[0082]

[0083] S32: Analyze the mathematical relationships in the traffic network and further simplify the constraints:

[0084] The path flow and the generalized edge flow satisfy the following relationship of a linear equation system:

[0085]

[0086] This linear equation system shows that when the generalized edge flow and the traffic demand are given, if the rank of the left - hand side coefficient matrix is less than the number of columns of this matrix, then the path flow There are infinitely many solutions, and there must be a set of solutions that are strictly greater than 0. Therefore, the third row of the above-reduced KKT system can be further removed.

[0087] S33: Determine whether the left coefficient matrix of the above linear equations is a column full-rank matrix. If so, execute S34; otherwise, continue with the S33 operation: find the maximum linearly independent group of the left coefficient matrix. Specifically:

[0088] When using the implicit function theory to find the derivative of variables in the KKT system, it is necessary to ensure that the variables are continuous and unique within the perturbation neighborhood. Although according to the mathematical properties of the user equilibrium problem, it is known that the generalized link flow and the corresponding Lagrange multipliers are uniquely existent when they are twice continuously differentiable with respect to the link travel time and the charging time. However, as analyzed above, there are infinitely many solutions for the path flow. Therefore, by finding the maximum linearly independent group of the left coefficient matrix of the above linear equations, the path flow under this combination can represent the remaining path flows through linear combination. Use "~" to represent the corresponding set of the maximum linearly independent group. So far, the KKT system is further simplified as:

[0089]

[0090]

[0091] S34: Calculate the response of the target traffic network variables with respect to the perturbation value based on the implicit function theory. Specifically:

[0092] According to the implicit function theory, the gradients of the path flow and the Lagrange multipliers with respect to the perturbation value can be written as:

[0093]

[0094]

[0095]

[0096] Then, based on the generalized link-path matrix , transform the gradient based on the path flow into the gradient based on the generalized link flow:

[0097] .

[0098] The algorithm effect is verified in a medium-sized traffic network with 74 nodes and 258 links in eastern Massachusetts and a medium-large traffic network with 1057 nodes and 2535 links in Winnipeg.

[0099] For the optimal pricing models of charging service providers for the above two transportation systems, path sets of different scales are generated respectively. The present invention uses the proposed solution algorithm and the mathematical programming method based on KKT to solve them respectively.

[0100] The calculation results are shown in Table 1 and Table 2. In Table 1 and Table 2, "-" indicates that the algorithm fails to complete the solution within the set solution time (2 hours).

[0101] Table 1 Calculation Results in Eastern Massachusetts

[0102]

[0103] Table 2 Calculation Results in Winnipeg

[0104]

[0105] As can be seen from Table 1, the proposed method is significantly superior to the mathematical programming method in terms of computational efficiency. In the efficiency performance of the first three path sets, it reduces by 53.8%, 82.7% and 82.8% respectively, and the mathematical programming method cannot complete the solution for the fourth path set within two hours. In terms of optimality, the proposed method loses 0.08%, 0.19% and 0.53% of the objective function value respectively, which is obviously acceptable in practical applications. As can be seen from Table 2, the mathematical programming method completely loses the ability to complete the solution within a limited time in a larger-scale transportation network.

[0106] Comparing Table 1 and Table 2 comprehensively, since the mathematical essence of the mathematical programming method is to solve a mixed integer programming problem, the time complexity increases exponentially as the number of 0-1 variables increases; however, for the method of this example, the calculation time is mainly composed of matrix inversion and finding a maximal linearly independent group. Since most of the matrices involved are sparse and positive definite, the good matrix properties make the inversion time very fast, and the Gaussian-Jordan elimination method is used to find the maximal linearly independent group, and its computational complexity is polynomial complexity O(n^3), where n is the matrix dimension. Therefore, the overall computational efficiency still shows an acceptable performance in a large-scale network.

[0107] In summary, compared with the mathematical programming method, although the solution method of this example can only guarantee convergence to a local optimal solution, its computational efficiency is significantly superior to the mathematical programming method based on the KKT conditions.

[0108] The above is a further detailed description of the present invention, which should not be regarded as a limitation on the specific implementation of the present invention. For those of ordinary skill in the technical field to which the present invention pertains, any simple deduction or substitution without departing from the concept of the present invention falls within the protection scope of the present invention.

Claims

1. A large-scale traffic user equilibrium regulation method considering charging behavior, comprising the following steps: S1. Construct a traffic network model based on the user equilibrium model, specifically including: The transportation network is represented by a directed graph where and represent the sets of nodes and edges in the directed graph respectively, and there are and ; represents the number of elements in the set; a subset of the node set contains the nodes where fast charging stations are built and becomes the charging node set. Electric vehicles can choose to charge at any charging node; the travel demands in the transportation network are expressed using origin-destination pairs, and the origin-destination pairs are represented by a tuple , where both the origin s and the destination t belong to , the travel demand belongs to the travel demand set , and the origin-destination tuple belongs to the origin-destination set ; S2. Convert the electric vehicle charging behavior into a generalized traffic behavior, specifically including: Convert the charging behavior into a driving process on "hyper-edges" to achieve the compatibility of sensitivity analysis technology with the charging behavior of electric vehicles, and the number of electric vehicle charging users As a kind of edge flow , the edge flow of the entire traffic system is extended to a generalized edge flow ; Edge-path matrix and charging-path matrix are extended to a generalized edge-path matrix ; S3. Through sensitivity analysis technology, extract the response of the traffic flow allocation result under perturbations to achieve the solution and determine the large-scale traffic user equilibrium regulation strategy. Step S3 specifically includes: S31: Analyze and remove redundant paths in the traffic network path set and simplify the corresponding constraints: Sensitivity analysis technology based on "hyperedge" expansion to obtain the gradient of the number of electric vehicle charging users with respect to perturbations ; The KKT condition system of the user equilibrium model is as follows: ， ， ， ， Among them and are respectively used to represent the cost on the edge and the cost at the charging station, ; and are respectively the Lagrange multipliers of the non - negativity constraint of path flow and the flow conservation constraint, is equivalent to where ; In this KKT condition system, the generalized edge flow and the set of all path - allocated traffic flows are obtained by solving the lower - layer user equilibrium problem, and all symbols are known values; for the set of paths whose path cost is equal to the minimum path cost of the corresponding origin - destination pair, it is defined as the "equilibrium path set", that is ; S32: Analyze the mathematical relationships in the transportation network. For all the reduced sets, use " " for annotation to further simplify the constraints. The relationship between the path flow and the generalized edge flow satisfies the linear equations : S33: Determine whether the left coefficient matrix of the above linear equation system is a column full-rank matrix. If so, execute S34; otherwise, continue with the S33 operation to find the maximum linearly independent group of the left coefficient matrix, and use "~" to represent the corresponding set of the maximum linearly independent group. Represent the KKT condition system as: ， ； S34: Calculate the response of the target traffic network variables to perturbations based on the implicit function theory. The specific operation is: According to the implicit function theory, the path flow and the Lagrange multiplier are expressed as gradients with respect to the perturbation as follows: ， ， ， Based on the generalized edge-path matrix , the gradient based on path flow is transformed into the gradient based on generalized edge flow: 。 2. The large-scale traffic user equilibrium regulation method according to claim 1, characterized in that In step S31, the constraints of the simplified KKT condition system are as follows: ， ， 。 3. The large-scale traffic user equilibrium regulation method according to claim 1, wherein The equilibrium regulation is the optimal pricing regulation of the charging service provider, the optimal scheduling of the emergency power supply fleet or the emergency maintenance fleet when a structural failure occurs in the power-traffic coupling network, and the charging regulation.

4. The large-scale traffic user equilibrium regulation method according to claim 3, characterized in that The equilibrium regulation is the optimal pricing regulation of the charging service provider. The mathematical expression of the traffic network model is: ， ， ， ， ， Among them is the traffic flow assigned to the traffic network edge a, , is the number of electric vehicle users at the fast charging station e, ; is the time taken for the electric vehicle to travel on edge a, is the time consumed for the electric vehicle to charge at the fast charging station e. The two are respectively functions of the edge flow and the fast charging station electric vehicle users ; is the set of traffic flows assigned to all paths, .

5. A computer-readable storage medium storing one or more programs, characterized in that, The one or more programs include instructions that, when executed by a computing device, cause the computing device to execute the method according to any one of claims 1 to 4.

6. A computing device, characterized in that, Including: One or more processors, a memory, and one or more programs, where the one or more programs are stored in the memory and configured to be executed by the one or more processors. When the one or more programs are executed, the steps in the method according to any one of claims 1 to 4 are implemented.

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