Large-scale traffic user balance regulation and control method considering charging behavior

Abstract

The invention belongs to the field of electronic traffic coupling networks, and discloses a large-scale traffic user balance regulation and control method considering charging behaviors. The traditional sensitivity analysis technology is improved, so that the method is suitable for the user equalization problem considering the charging behavior. Based on an improved sensitivity analysis technology, response of traffic flow to social regulation signals is obtained through sensitivity analysis of a traffic user equalization problem. According to the method, the convex property of the user equalization problem is fully utilized, and rapid solving of the large-scale power-traffic coupling network optimization scheduling problem with user equalization as a response model is assisted.

Description

Technical Field

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

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

[0003] However, when the user equilibrium problem is used as a 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 requires the introduction of a large number of 01 variables as auxiliary variables, thus being transformed into a mixed integer programming problem containing large-scale 01 variables. The complexity of its solution is a huge challenge in large-scale networks. Summary of the invention

[0004] The object of the present invention is to overcome at least one shortcoming of the prior art and to provide a method for balancing and regulating large-scale traffic users taking charging behavior into consideration.

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

[0006] The first aspect of the present invention provides:

[0007] A large-scale traffic user balanced regulation method considering charging behavior includes the following steps:

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

[0009] The traffic network is constructed through a directed graph Indicates that and Represent the sets of nodes and edges in a directed graph, respectively, and there is and ; Indicates the number of elements in a collection; a subset of a node collection The nodes with fast charging stations are included as charging node sets. Electric vehicles can choose to charge at any charging node. The start-end pair is used to express the travel demand in the transportation network. The start-end pair is represented by a tuple. , where the starting point s and the end point t both belong to , transportation demand Belongs to the traffic demand set , and the start and end point tuples belong to the start and end point set ;

[0010] S2, transforming electric vehicle charging behavior into a generalized transportation behavior;

[0011] S3. Through sensitivity analysis technology, the response of traffic flow distribution results under small disturbances is extracted, the solution is achieved, and the equilibrium control strategy for large-scale traffic users is determined.

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

[0013] In some examples of large-scale traffic user equilibrium control methods, the charging behavior is converted into the driving process on the "super edge", and the sensitivity analysis technology is compatible with the charging behavior of electric vehicles. As a side flow , the edge flow of the entire traffic system is expanded into a generalized edge flow ; Edge-path matrix and the charge-path matrix Expanded to a generalized edge-path matrix .

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

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

[0016] Obtaining the gradient of the number of electric vehicle charging users with respect to disturbance based on the sensitivity analysis technology of “hyperedge” expansion ; The KKT condition system of the user equilibrium model is as follows:

[0017]

[0018]

[0019]

[0020]

[0021] in is used to represent the cost at the edge and the cost at the charging station; and are the Lagrange multipliers of the path flow non-negativity constraint and flow conservation constraint, respectively. Equivalent to ,in ; In this KKT system, the traffic flow distribution results and It is obtained by solving the lower-layer user equilibrium problem, and all symbols are known values; the path set whose path cost is equal to the minimum path cost of the corresponding start-end pair 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 generalized edge flow satisfy the linear equation system Relationship:

[0023] 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 to complete S33 operation, find the maximal linear independent group of the left coefficient matrix, use "~" to represent the corresponding set of the maximal linear independent group, and express the KKT system as:

[0024]

[0025] ;

[0026] S34: Calculate the response of the target traffic network variable to the disturbance value based on implicit function theory.

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

[0028] According to implicit function theory, the path flow and Lagrange multipliers The gradient with respect to the perturbation value is expressed as:

[0029]

[0030]

[0031]

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

[0033] .

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

[0035]

[0036]

[0037] .

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

[0039] In some examples of the balanced regulation method for large-scale traffic users, the balanced regulation is the optimal pricing regulation of the charging service provider, and the mathematical expression of the traffic network model is:

[0040]

[0041]

[0042]

[0043]

[0044]

[0045] in is the traffic flow allocated to edge a of the traffic network, is the number of electric vehicle users at fast charging station e; is the time the electric car spends traveling on edge a, is the time consumed by electric vehicles to charge at the fast charging station e, and the two are the edge flow and fast charging station electric vehicle users Function of is the set of all path-assigned traffic flows.

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

[0047] A computer-readable storage medium storing one or more programs, wherein the one or more programs include instructions, and when the instructions are executed by a computing device, the computing device executes the method according to 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 executing the method described in the first aspect of the present invention.

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

[0052] The balanced control method of some examples of the present invention is a basic solving tool, which can be embedded in any optimization scheduling problem of the power-transportation coupling network with the user equilibrium problem as the underlying 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 in an orderly manner at the temporal and spatial levels, this method can be used as an evaluation tool for decision makers to estimate the impact of the proposed strategy; for example, when a typhoon or flood occurs, a structural failure occurs in the power-transportation coupling network, and the emergency rescue department is performing the optimal scheduling of the optimal emergency power supply fleet or emergency maintenance fleet, this method can be used as a submodule of the large-scale scheduling problem, accelerating the solution of the problem and supporting 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 specific solution effects, the optimal pricing problem of charging service providers is taken as an example. The algorithm for solving the optimal pricing problem of charging service providers based on sensitivity analysis proposed in this invention can significantly improve the calculation efficiency compared with the mathematical programming method based on KKT conditions, and there will be no obvious loss of optimality. Experimental results show that compared with the mathematical programming method, the proposed method can reduce the calculation time by up to 82.3%, and there is only a 0.5% loss in the objective function value. BRIEF DESCRIPTION OF THE DRAWINGS

[0054] Figure 1 It is a flow chart of some large-scale traffic user balanced control methods considering charging behavior of the present invention.

[0055] Figure 2 It is a schematic diagram of the “hyperedge” conversion of the present invention, wherein “s” represents any preceding node of the charging node “e”, and “t” represents any succeeding node of the charging node. DETAILED DESCRIPTION

[0056] The technical solution of the present invention is further explained below in conjunction with examples.

[0057] Reference Figure 1 , a large-scale traffic user balanced regulation method considering charging behavior, comprising the following steps:

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

[0059] S2, transforming electric vehicle charging behavior into a generalized transportation behavior;

[0060] S3. Through sensitivity analysis technology, the response of traffic flow distribution results under small disturbances is extracted to achieve the solution.

[0061] Specifically, S1,constructs the traffic network model based on the user equilibrium model including:

[0062] The traffic network is constructed through a directed graph Indicates that and Represent the sets of nodes and edges in a directed graph, respectively, and there is and . Indicates the number of elements in a collection. A subset of a node collection The nodes with fast charging stations are included as charging node sets. Electric vehicles can choose to charge at any charging node. The start-end pair is used to express the travel demand in the transportation network. The start-end pair is represented by a tuple. , where the starting point s and the end point t both belong to , transportation demand Belongs to the traffic demand set , and the start and end point tuples belong to the start and end point set In order to represent the phenomenon that electric car users choose one of several possible routes through navigation software when traveling, the present invention uses the edge-path matrix Record which edges of the traffic network each path will pass through. At the same time, the present invention uses the charging-path matrix Record the charging position corresponding to each path. Store the indices of all paths, and then use the start-end pair-path matrix Distinguish the start-end pair to which each path belongs.

[0063] For a typical charging service provider's optimal pricing model, it includes the optimal pricing problem of the upper-level charging service provider and the lower-level user equilibrium problem. The lower-level 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] in is the traffic flow allocated to edge a of the traffic network, is the number of electric vehicle users at fast charging station e. is the time the electric car spends traveling on edge a, is the time consumed by electric vehicles to charge at the fast charging station e, and the two are the edge flow and fast charging station electric vehicle users function. is the set of all path-allocated traffic flows. The first and second constraints characterize the mathematical relationship between edge flows and path flows. The third constraint is the flow conservation constraint, where the sum of the traffic flows of each start-end pair is equal to the traffic demand. The third constraint requires that the path flow is not less than zero, and it also implies that the edge flow is not less than zero.

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

[0071] The present invention improves the sensitivity analysis technique to take into account the charging behavior of electric vehicles by converting the charging behavior into a driving process on a "hyper-arc" (see Figure 2 ), thereby achieving compatibility of sensitivity analysis technology with electric vehicle charging behavior. Through this transformation, the number of electric vehicle charging users Can be considered as a kind of edge flow , the edge flow of the entire traffic system is expanded into a generalized edge flow . Edge-path matrix and the charge-path matrix can be expanded to a generalized edge-path matrix .

[0072] S3, through sensitivity analysis technology, extract the response of traffic flow distribution results under small disturbances and solve them, specifically:

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

[0074] The present invention adopts the sensitivity analysis technology based on "hyperedge" expansion to obtain the gradient of the number of electric vehicle charging users with respect to the disturbance. The KKT condition system of the user equilibrium model is as follows:

[0075]

[0076]

[0077]

[0078]

[0079] in is used to represent the cost at the edge and the cost at the charging station. and are the Lagrange multipliers of the non-negative constraint of path flow and the conservation constraint of flow, respectively. Based on the aforementioned “hyperedge conversion”, Equivalent to ,in In this KKT system, the traffic flow distribution results and It has been obtained by solving the lower-layer user equilibrium problem, and all symbols are known values. The set of paths whose path cost is equal to the minimum path cost of the corresponding start-end pair is defined as the "equilibrium path set", that is, According to the user equilibrium definition, for the non-equilibrium path set, the path traffic flow is always equal to 0, and it will not affect the system, so it is directly removed, and all matrices and sets related to the path are reduced accordingly. For all reduced sets, use " " is marked. The first line of the KKT condition , by 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 relaxation constraint can be removed from the KKT system, and the constraints of the simplified KKT conditional system are as follows:

[0080]

[0081]

[0082]

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

[0084] The path flow and generalized edge flow satisfy the following linear equations:

[0085]

[0086] This linear equation system shows that when the generalized edge flow and traffic demand are given, if the rank of the coefficient matrix on the left is less than the number of columns of the matrix, then the path flow There are infinitely many solutions, and there must be a set of solutions strictly greater than 0, so 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 equation system is a column full rank matrix. If so, execute S34, otherwise continue to complete the S33 operation: find the maximum linear independent group of the left coefficient matrix, specifically:

[0088] When using implicit function theory to find the derivative of a variable in a KKT system, it is necessary to satisfy the requirement that the variable is continuous and unique in the perturbation neighborhood. and the corresponding Lagrange multiplier in the path travel time and charging time The generalized edge flow only exists when it is second-order continuously differentiable. However, as shown in the above analysis, there are infinite solutions for the path flow. Therefore, by finding the maximal linearly independent group of the coefficient matrix on the left side of the above linear equations, the path flow under this combination can represent the remaining path flows through linear combinations. Use "~" to represent the corresponding set of maximal linearly independent groups. At this point, the KKT system is further simplified as:

[0089]

[0090]

[0091] S34: Calculate the response of the target traffic network variable to the disturbance value based on implicit function theory, specifically:

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

[0093]

[0094]

[0095]

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

[0097] .

[0098] The algorithm was verified on a medium-sized transportation network with 74 nodes and 258 edges in eastern Massachusetts and a medium-to-large transportation network with 1057 nodes and 2535 edges in Winnipeg.

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

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

[0101] Table 1 Calculation results for Eastern Massachusetts

[0102]

[0103] Table 2 Winnipeg calculation results

[0104]

[0105] As shown in Table 1, the proposed method is significantly better than the mathematical programming method in terms of computational efficiency. The efficiency of the first three path sets is reduced by 53.8%, 82.7% and 82.8% respectively, and the mathematical programming method cannot solve 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 shown in Table 2, the mathematical programming method completely loses the ability to complete the solution in a limited time in a larger-scale transportation network.

[0106] Comprehensively comparing Table 1 and Table 2, since the mathematical essence of the mathematical programming method is to solve a mixed integer programming problem, the time complexity increases exponentially with the increase of 01 variables; however, for the method of this example, the calculation time is mainly composed of matrix inversion and finding the maximum linearly independent group. Since the matrices involved are mostly sparse and positive definite, the good matrix properties make the inversion time very fast, and the Gauss-Jordan elimination method is used to find the maximum linearly independent group. Its computational complexity is polynomial complexity O (n^3), n is the matrix dimension, so the overall computational efficiency still maintains considerable performance in large-scale networks.

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

[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 ordinary technicians in the technical field to which the present invention belongs, simple deduction or replacement without departing from the concept of the present invention is within the protection scope of the present invention.

Claims

1. A method for balancing and regulating large-scale traffic users considering charging behavior, comprising the following steps: S1. Construct a traffic network model based on the user equilibrium model, including: The traffic network is constructed through a directed graph Indicates that and Represent the sets of nodes and edges in a directed graph, respectively, and there is and ; Indicates the number of elements in a collection; a subset of a node collection The nodes with fast charging stations are included as charging node sets. Electric vehicles can choose to charge at any charging node. The start-end pair is used to express the travel demand in the transportation network. The start-end pair is represented by a tuple. , where the starting point s and the end point t both belong to , transportation demand Belongs to the traffic demand set , and the start and end point tuples belong to the start and end point set ; S2, transforming electric vehicle charging behavior into a generalized transportation behavior; S3. Through sensitivity analysis technology, the response of traffic flow distribution results under small disturbances is extracted, the solution is achieved, and the equilibrium control strategy for large-scale traffic users is determined.

2. The method for balancing and controlling large-scale traffic users according to claim 1 is characterized in that: In step S2, converting the electric vehicle charging behavior into a generalized traffic behavior specifically includes: The charging behavior is converted into the driving process on the "super edge" to achieve the compatibility of sensitivity analysis technology with electric vehicle charging behavior. As a side flow , the edge flow of the entire traffic system is expanded into a generalized edge flow ; Edge-path matrix and the charge-path matrix Expanded to a generalized edge-path matrix .

3. The method for balancing and controlling large-scale traffic users according to claim 1 or 2, characterized in that: Step S3 specifically includes: S31: Analyze and remove redundant paths in the traffic network path set, and simplify the corresponding constraints: Obtaining the gradient of the number of electric vehicle charging users with respect to disturbance based on sensitivity analysis technology based on "hyperedge" expansion ; The KKT condition system of the user equilibrium model is as follows: ， ， ， ， in is used to represent the cost at the edge and the cost at the charging station; and are the Lagrange multipliers of the path flow non-negativity constraint and flow conservation constraint, respectively. Equivalent to ,in ; In this KKT system, the traffic flow distribution results and It is obtained by solving the lower-layer user equilibrium problem, and all symbols are known values; the path set whose path cost is equal to the minimum path cost of the corresponding start-end pair is defined as the "equilibrium path set", that is, ; S32: Analyze the mathematical relationships in the traffic network, further simplify the constraints, and the path flow and generalized edge flow satisfy the linear equation system Relationship: 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 to complete S33 operation to find the maximal linear independent group of the left coefficient matrix. Use "~" to represent the corresponding set of the maximal linear independent group. The KKT system is expressed as: ， ； S34: Calculate the response of the target traffic network variable to the disturbance value based on implicit function theory.

4. The method for balancing and controlling large-scale traffic users according to claim 3 is characterized in that: The specific operation of step S34 to determine the response is: According to implicit function theory, the path flow and Lagrange multipliers The gradient with respect to the perturbation value is expressed as: ， ， ， Based on the generalized edge-path matrix , converting the gradient based on path flow into the gradient based on generalized edge flow: 。 5. The method for balancing and controlling large-scale traffic users according to claim 3 is characterized in that: In step S31, the constraints of the simplified KKT condition system are as follows: ， ， 。 6. The method for balancing and controlling large-scale traffic users according to claim 1 is characterized in that: The balanced regulation includes optimal pricing regulation of charging service providers, optimal scheduling of emergency power supply fleets or emergency maintenance fleets when structural failures occur in the power-transportation coupling network, and charging regulation.

7. The method for balancing and controlling large-scale traffic users according to claim 6 is 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: ， ， ， ， ， in is the traffic flow allocated to edge a of the traffic network, is the number of electric vehicle users at fast charging station e; is the time the electric car spends traveling on edge a, is the time consumed by electric vehicles to charge at the fast charging station e, and the two are the edge flow and fast charging station electric vehicle users Function of is the set of all path-assigned traffic flows.

8. A computer-readable storage medium storing one or more programs, characterized in that: The one or more programs include instructions, which, when executed by a computing device, cause the computing device to perform the method of any one of claims 1 to 7.

9. A computing device, characterized in that include: 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 executing any one of the methods of claims 1 to 7.

Images