A bi-level game model and equilibrium solution method for power-traffic coupled network considering elastic demand behavior of electric vehicles

Abstract

The application aims to provide a power-traffic coupling network double-layer game model and equilibrium solving method considering the elastic demand behavior of electric vehicles, establish a hybrid traffic flow model containing the demand elasticity and charging behavior of electric vehicles, realize the coupling of urban power traffic network, consider the optimization target and operation constraint of the coupling network equilibrium problem, adopt a quasi-variational inequality framework to represent the elastic hybrid traffic user equilibrium state, and establish a mathematical optimization model of the urban power traffic coupling network, in view of the non-convexity of the problem, decouple the problem into a double-layer convex optimization problem by adopting an outer layered fixed point iteration, solve the inner layer equilibrium problem based on a viscous projection approximation algorithm, and form a complete method for solving the double-layer game equilibrium state. The application can provide an accurate and effective analysis means for the equilibrium state of the power traffic coupling network, and realize the fine modeling of the actual problem.

Description

Technical Field

[0001] This invention belongs to the technical fields of integrated energy network optimization and operation, and power-transportation coupled network optimization. Specifically, it relates to a two-layer game model and equilibrium solution method for power-transportation coupled networks that considers the elastic demand behavior of electric vehicles. It includes a method for solving the two-layer game model and equilibrium solution method for power-transportation coupled networks that considers the elastic demand behavior of electric vehicles, specifically designed based on a quasi-variable inequality framework and employing layered fixed-point iteration and sticky projection approximation algorithms. Background Technology

[0002] With the continuous increase in the number of electric vehicles, urban transportation networks are gradually becoming electrified. To meet the charging demands of electric vehicles, the power grid has established numerous fast-charging facilities to provide charging services. Meanwhile, electric vehicle users also adopt different travel strategies based on their charging needs. Since the power distribution network and transportation belong to different sectors, traditional collaborative optimization methods struggle to achieve mutual cooperation and win-win outcomes, leading to low efficiency in the utilization of public resources and high operating costs. Therefore, researching how to accurately describe the impact of electric vehicle behavior on the power-transportation network is of great value and significance.

[0003] Currently, most studies on the optimization of power-transport coupled networks only consider the network equilibrium state under the condition of fixed user demand, without taking into account the impact of user travel costs on user travel intentions within the transportation network. Traffic congestion and high charging costs lead users to adopt different travel strategies, thus affecting changes in network demand. Conversely, under smooth traffic conditions, users' travel intentions increase significantly. The user game equilibrium state under power-transport coupled networks that consider elastic demand more effectively reflects the actual distribution of network demand. Therefore, it is essential to consider the elastic demand of transportation users in the game model of power-transport networks.

[0004] The game-theoretic equilibrium problem of the power-transportation coupled network can be transformed into a two-level optimization problem. The distribution network achieves economical operation by setting electric vehicle charging prices, while transportation users choose the path with the lowest travel cost based on their own needs. The power grid and transportation network are coupled; the optimal power flow operation of the power grid can be reduced to an optimization problem with second-order cone constraints, while the game-theoretic equilibrium problem among transportation network users involves nonlinear complementary constraints. Therefore, when considering both together, non-convex optimization is often involved, making it difficult to effectively model, analyze, and solve using traditional methods. Summary of the Invention

[0005] This invention relates to the field of integrated energy network optimization and operation, providing a solution method for the equilibrium of a power-transportation coupled network considering the elastic demand of electric vehicles in urban power-transportation energy networks. The method includes: establishing a hybrid traffic flow model incorporating the elastic demand and charging behavior of electric vehicles, thus achieving coupling of the urban power-transportation network; considering the optimization objective and operational constraints of the coupled network equilibrium problem, employing a quasi-variableal inequality framework to characterize the equilibrium state of elastic hybrid traffic users, and establishing a mathematical optimization model for the urban power-transportation coupled network; addressing the non-convexity of the problem, using outer-layer layered fixed-point iteration to decouple the problem into a bi-layer convex optimization problem, and solving the inner-layer equilibrium problem based on a sticky projection approximation algorithm, forming a complete method for solving the bi-layer game equilibrium state. This invention provides accurate and effective analytical means for the equilibrium state of power-transportation coupled networks, enabling refined modeling of practical problems.

[0006] The specific technical solution adopted by this invention to solve its technical problem is as follows:

[0007] A two-layer game model for a power-transportation coupled network that considers the elastic demand behavior of electric vehicles, characterized by:

[0008] Couple the energy power grid with the transportation network through electric vehicle charging stations;

[0009] Considering the optimization objective and operational constraints of the coupled network equilibrium problem, a quasi-variable inequality framework is adopted to characterize the equilibrium state of elastic mixed traffic users.

[0010] In the inner game, traffic flow makes travel decisions based on the charging price given by the power grid, eventually reaching user equilibrium and forming a charging demand distribution. In the outer game, the power grid optimizes network operation based on the charging load distribution and extracts the marginal price of this state as the charging price for traffic network users.

[0011] Furthermore, the optimization objective of the distribution network is:

[0012]

[0013] Among them, a n b n b0 and b0 are both power generation cost coefficients. For the active power output of the generator, Inject active power into the main network nodes.

[0014] Furthermore, distribution network constraints include: active and reactive power balance constraints, branch start and end voltage constraints, branch power flow constraints, line current and node voltage magnitude constraints, main grid input power range constraints, and active power reduction and reactive power output constraints of DG.

[0015] Distribution network constraints specifically include:

[0016]

[0017]

[0018]

[0019]

[0020]

[0021]

[0022]

[0023]

[0024] Where Π(n) represents the set of all end nodes of all lines with n as the first node; The active power injected by the power source at node n; The reactive power injected into the power source at node n; These are the active power and reactive power flowing through the line, respectively. Let n be the active load at node n; These are the resistance and reactance of the circuit, respectively. For node reactive power load; It is the square of the line current amplitude.

[0025] In the traffic network equilibrium constraint, for any origin-destination traffic demand to OD, the travel time of routes with non-zero flow is the same and no greater than the travel time of routes with zero flow. This state is defined as the user equilibrium state UE. The traffic allocation principle based on the user equilibrium state is the user equilibrium principle. Based on this, the following are constructed: road segment form time function, traffic flow conservation constraint, and individual user travel cost function.

[0026] Furthermore, the hybrid user equilibrium model employs a method to determine the optimal travel route for each user based on the charging and travel needs of both electric vehicle (EV) and non-EV users. If an EV user needs to charge, their route will include a charging segment, while other vehicles that do not need to charge will use routes that do not include a charging segment. For any travel demand, the travel time for routes with non-zero traffic is the same and no greater than the travel time for routes with zero traffic. Simultaneously, it requires that any travel demand equals the demand function value corresponding to the minimum travel cost of the user in equilibrium, thereby determining the user's travel demand in the network. If the travel cost is too high, there is no travel demand.

[0027] The specific logical expression of the hybrid user load balancing model is as follows:

[0028]

[0029]

[0030]

[0031]

[0032]

[0033] In the formula: the superscript {·}={e,g} indicates that the relationship holds for both electric vehicles (i.e., electric vehicles) and non-electric vehicles (i.e., non-electric vehicles); Let h represent the set of user demand pairs for electric vehicles and non-electric vehicles in the network, and the set of all feasible paths, respectively. w Indicates traffic flow. For users' travel costs, To minimize the user's travel cost in equilibrium state, Let M be the actual demand, α be the negative elasticity parameter of the Logit model, and M be the actual demand. j A measure of attraction for users to reach their destination.

[0034] Furthermore, considering that all electric and non-electric vehicle users in the transportation network choose their travel routes according to the minimum travel cost, and further considering the impact of user elastic demand on cost under equilibrium state, a Logit negative exponential model is constructed to describe the negative correlation between elastic demand and travel cost.

[0035] Treating user equilibrium as a quasi-variable inequality problem, the traffic network constraints considered include the constraints between road segments and path flows, the non-negativity and conservation of path flows, the relationship between path time and road segment time, the conversion between path travel time and cost, hybrid user equilibrium allocation constraints, and the road segment time function, namely:

[0036]

[0037]

[0038]

[0039]

[0040]

[0041]

[0042]

[0043]

[0044]

[0045]

[0046]

[0047] Where: Ω T (ξ * ) represents the set of variable constraints for the equilibrium traffic flow, Δ E / Δ G Let Q be the demand-path correlation coefficient matrix. e* (ξ * ) and Q g* (ξ * ) represents the elastic demand for electric vehicles and non-electric vehicles under equilibrium conditions, which is determined by the unknown equilibrium travel cost ξ. * Let w be the shape parameter of the function; For electric vehicle charging station collection, c n The maximum capacity of the charging station; n∈k indicates that the road segment passes through the charging station node n; Free driving time on the road section The charging time required for an electric vehicle; For road segment capacity; w0 is the path-path correlation coefficient; w0 is the time-cost conversion coefficient. υ is the charging price for charging station n (passed by the road segment k); D The energy demand for charging individual electric vehicles.

[0048] Furthermore, the equilibrium solution method for the two-layer game model of the power-transportation coupled network considering the elastic demand behavior of electric vehicles is characterized by:

[0049] The established power grid model is subjected to second-order cone relaxation treatment; and the quasi-variable inequality framework is used to describe the equilibrium problem of the transportation network considering the elastic demand and charging behavior of electric vehicles, and the network equilibrium state is transformed into a mathematical optimization model.

[0050] The two-layer game problem and equilibrium state of the power-transportation coupled network are then solved by using a hierarchical fixed-point iteration method and a sticky projection approximation algorithm. Specifically, the outer layer achieves the decoupling solution of the power network and transportation network optimization problem through hierarchical fixed-point iteration, while the inner layer considers the equilibrium problem of the transportation network with elastic demand and is solved by the sticky projection approximation algorithm.

[0051] Furthermore, the established power grid model undergoes second-order cone relaxation; and using a quasi-variable inequality framework, the equilibrium problem of the transportation network considering the elastic demand and charging behavior of electric vehicles is described, transforming the network equilibrium state into a mathematical optimization model, specifically including:

[0052] The negative correlation between elastic demand and travel costs is described by introducing a Logit negative exponential model:

[0053]

[0054] In the formula Let M be the actual demand, α be the negative elasticity parameter of the Logit model, and M be the actual demand. j The attractiveness measure for users to reach their destination; the elastic demand characteristic function represents how user demand increases as travel costs decrease or the attractiveness measure of the destination increases.

[0055] By considering the elastic demand response of electric vehicles, a hybrid user equilibrium that takes into account the elastic demand on the user side is adopted, and its logical expression is as follows:

[0056]

[0057]

[0058]

[0059]

[0060] In the formula: the superscript {·} = {e, g} indicates that the relationship holds for both electric vehicles and non-electric vehicles; Let h represent the set of user demand pairs for electric vehicles and non-electric vehicles in the network, and the set of all feasible paths, respectively. w Indicates traffic flow. For users' travel costs, The minimum travel cost for users in equilibrium state;

[0061] To effectively model the above complex equilibrium conditions, an equivalent nonlinear complementarity problem is constructed as follows:

[0062]

[0063]

[0064]

[0065]

[0066] Further generalizing the variational inequality, we construct an equivalent quasi-variational inequality to describe the equilibrium state of elastic hybrid users; the problem is then transformed into the following quasi-variational inequality problem:

[0067]

[0068] in:

[0069]

[0070] In summary, through the above transformations and equivalences, the traffic flow equilibrium problem in the inner game of the power transportation two-layer game is transformed into a quasi-variable inequality problem, while the power grid optimization operation in the outer game is represented as a convex optimization problem with second-order cone constraints.

[0071] Furthermore, to address the non-convexity of the problem, an outer-layer fixed-point iteration is used to decouple the problem into a bi-layer convex optimization problem, and the inner-layer equilibrium problem is solved based on a viscous projection approximation algorithm.

[0072] Furthermore, the specific process of the hierarchical fixed-point iteration method is as follows:

[0073] 1) Initialization:

[0074] Input variables {λ 0 The initial value of} and the convergence error ε1; the number of iterations is set to k=0 and the iteration begins;

[0075] 2) Repeatedly solve the optimal power flow problem of the distribution network and the traffic user equilibrium subproblem, and iteratively update the marginal electricity price {λ}. k+1} and charging load distribution

[0076] ① Optimal power flow problem in distribution networks: Input Solve the optimal power flow problem of the distribution network and extract the marginal electricity price {λ} using dual variables. k+1};

[0077] ② Traffic User Equilibrium Subproblem: Input {λ k+1 The sticky projection approximation algorithm is used to solve the inner-layer traffic user game equilibrium problem QVI{λ. k+1 ,h,Q,Ω T}, to obtain the distribution of charging demand

[0078] 3) Until the convergence criterion is met:

[0079] {||λ k+1 -λ k ||,||p k+1 -p k ||}≤ε1

[0080] The final output is the charge distribution. and marginal electricity price {λ k+1 This serves as the final solution to the problem.

[0081] Furthermore, the specific process of solving the traffic user equilibrium subproblem using the designed sticky projection approximation algorithm is as follows:

[0082] 1) Initialize input:

[0083] ① The marginal electricity price {λ} obtained by solving the optimal power flow problem of the distribution network k+1},

[0084] ② Select the initial variable y 0 =(h 0 Q 0 )∈Ω T ,

[0085] ③ Choose the iteration parameters 0≤γ≤1 and the sequence The number of iterations is set to φ = 0;

[0086] 2) Repeat the following solution process:

[0087] ① Given the marginal electricity price {λ k+1} and the previous generation variable y φ =(h φ Q φ Solve for Λ T The projection point on

[0088]

[0089] ② Combining projection points and the previous generation variable y φ The sticky principle is used to update the current generation variable y. φ+1 ←(h φ+1 Q φ+1 ):

[0090]

[0091] ③ Determine whether the following convergence conditions are met:

[0092] ||y φ+1 -y φ ||≤ε2

[0093] When the conditions are met, the algorithm converges and exits the loop, outputting the obtained charging load distribution h. φ+1 And elastic demand Q φ+1 Otherwise, update φ = φ + 1 and return to step 1);

[0094] Step 1) Represents set Λ T Euclid norm projection on Defined as the mapping function vector of QVI; when γ is chosen to be appropriately small, it can ensure that the Lipschitz continuity condition is satisfied during the iteration process, thereby ensuring the convergence of the algorithm.

[0095] This invention and its preferred embodiments address the problems of existing technologies by introducing a quasi-variable inequality method and proposing a two-layer game model for the power-transportation coupled network that considers the elastic demand of electric vehicles. It also provides a method for solving the equilibrium game state of urban power-transportation networks that consider the elastic demand response of electric vehicles based on a hierarchical fixed-point iteration and sticky projection approximation algorithm.

[0096] First, a hybrid traffic flow model incorporating the elastic demand and charging behavior of electric vehicles is established. Based on this, a quasi-variational inequality framework characterizing the equilibrium state of elastic hybrid traffic users is proposed, and the equivalence relationship between the equilibrium state and the quasi-variational inequality is given. Second, based on the coupling characteristics between the power grid and the transportation network, a second-order cone programming model of the distribution network incorporating charging load is proposed. Finally, considering the physical interaction characteristics of the coupled network, a fixed-point framework with QVI is proposed to describe the complex game-theoretic behavior of the coupled network, and a two-layer fixed-point iterative algorithm is designed to solve the problem. Attached Figure Description

[0097] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments:

[0098] Figure 1 This is a schematic diagram of a traffic network according to an embodiment of the present invention;

[0099] Figure 2 This is a schematic diagram illustrating the relationship between elastic demand and network characteristics in an embodiment of the present invention;

[0100] Figure 3 This is a schematic diagram of a two-layer game framework for a power-transportation coupled network according to an embodiment of the present invention;

[0101] Figure 4 This is a schematic diagram of a power-transportation coupled network test system according to an embodiment of the present invention;

[0102] Figure 5 This is a schematic diagram showing the distribution of path traffic and travel costs for some demand pairs in an embodiment of the present invention;

[0103] Figure 6 This is a schematic diagram comparing the power grid operating costs of embodiments of the present invention;

[0104] Figure 7 This is a schematic diagram comparing flexible transportation demand in embodiments of the present invention;

[0105] Figure 8 This is a schematic diagram comparing the charging power distribution of electric vehicles according to an embodiment of the present invention;

[0106] Figure 9 This is a schematic diagram illustrating the changing pattern of power grid operating costs according to an embodiment of the present invention;

[0107] Figure 10 This is a schematic diagram illustrating the variation of charging load with parameters according to an embodiment of the present invention;

[0108] Figure 11 This is a schematic diagram illustrating the changing patterns of traffic flow on a road segment according to an embodiment of the present invention.

[0109] Figure 12 This is a schematic diagram of the error curve (outer layer) of the fixed-point algorithm in an embodiment of the present invention;

[0110] Figure 13 This is a schematic diagram of the error curve (inner layer) of the viscous projection approximation algorithm in an embodiment of the present invention;

[0111] Figure 14 This is a schematic diagram illustrating the implementation process of an embodiment of the present invention. Detailed Implementation

[0112] To make the features and advantages of this patent more apparent and understandable, specific embodiments are provided below for detailed explanation:

[0113] It should be noted that the following detailed descriptions are illustrative and intended to provide further explanation of this application. Unless otherwise specified, all technical and scientific terms used in this specification have the same meaning as commonly understood by one of ordinary skill in the art to which this application pertains.

[0114] like Figure 14 As shown, the model construction and solution process for solving the equilibrium state problem of urban power-transport coupled network based on hierarchical fixed-point iteration and viscous projection approximation algorithm provided by this invention can be specifically divided into the following steps:

[0115] S1: First, establish a user game equilibrium model for the power-transportation coupled network that considers the elastic demand of electric vehicles, realizing the coupling of the energy power grid and the transportation network; the two are coupled through electric vehicle charging stations, thereby achieving the coordinated operation of the entire city's integrated energy network. To meet the travel behavior of transportation network users and the charging behavior of electric vehicle users, electric vehicle charging stations provide users with fast charging facilities, such as... Figure 1 As shown.

[0116] S2: Establish energy flow models for the power grid and transportation network respectively. Considering the optimization objectives and operational constraints of the two networks, establish a mathematical optimization model for the urban power-transportation coupled network, as follows:

[0117] Distribution network optimization objectives:

[0118] The optimization objective of the power distribution network of the electric transportation network is shown in equation (1), where For the active power output of the generator, Inject active power into the main network nodes.

[0119]

[0120] a in the formula n b n b0 and b0 are both power generation cost coefficients.

[0121] Distribution network constraints:

[0122] This invention uses equations (6)-(15) to mathematically model the distribution network. The distribution network constraints of the mathematical optimization model of the urban power-transportation coupled network consider active and reactive power balance constraints, branch start-end voltage constraints, branch power flow constraints, line current and node voltage magnitude constraints, main grid input power range constraints, and active power reduction and reactive power output constraints of DG, namely:

[0123]

[0124]

[0125]

[0126]

[0127]

[0128]

[0129]

[0130] Where Π(n) represents the set of all end nodes of all lines with n as the first node; The active power injected by the power source at node n; The reactive power injected into the power source at node n; These are the active power and reactive power flowing through the line, respectively. Let n be the active load at node n; These are the resistance and reactance of the circuit, respectively. For node reactive power load; It is the square of the line current amplitude.

[0131] Transportation network equilibrium constraints:

[0132] For any origin-destination (OD) traffic demand, the travel time of routes with non-zero flow is the same and no greater than the travel time of routes with zero flow. This state is defined as the user equilibrium (UE) state. Based on this, the traffic allocation principle is the user equilibrium principle. This invention uses equations (9)-(11) to represent the segment-form time function, equations (12)-(13) to define the traffic flow conservation constraint, and equations (14)-(16) to establish the travel cost function of individual users. The established mathematical model of mixed traffic flow including electric vehicles is described as follows:

[0133]

[0134]

[0135]

[0136]

[0137]

[0138]

[0139]

[0140]

[0141] Where: w is the shape parameter of the function; For electric vehicle charging station collection, c n The maximum capacity of the charging station; n∈k indicates that the road segment passes through the charging station node n; Free driving time on the road section The charging time required for an electric vehicle; For road segment capacity; w0 is the path-path correlation coefficient; w0 is the time-cost conversion coefficient. The charging price for charging station n (passed by the road segment k); v D The energy demand for charging individual electric vehicles.

[0142] The two-layer game framework constructed in this way is as follows: Figure 3 As shown.

[0143] S3: Perform second-order cone relaxation on the established power grid model, and

[0144] S4: Using the framework of quasi-variable inequalities, the equilibrium problem of transportation networks considering the elastic demand and charging behavior of electric vehicles is described, and the network equilibrium state is transformed into a mathematical optimization model.

[0145] This invention further considers the impact of network travel costs on the travel needs of users such as electric vehicle users in actual transportation systems. This embodiment specifically studies, for example... Figure 2 The user equilibrium state of elastic demand is shown.

[0146] By introducing the Logit negative exponential model, the negative correlation between elastic demand and travel costs can be accurately described:

[0147]

[0148] In the formula Let M be the actual demand, α be the negative elasticity parameter of the Logit model, and M be the actual demand. j This is a measure of the attractiveness of a user's destination. The elastic demand characteristic function represents how user demand increases as travel costs decrease or the attractiveness of the destination increases, which aligns with reality.

[0149] By considering the elastic demand response of electric vehicles, this invention improves and extends the traditional user equilibrium, proposing a mixed user equilibrium (MUE) that considers the elastic demand on the user side, the logical expression of which is as follows:

[0150]

[0151]

[0152]

[0153]

[0154] In the formula: the superscript {·} = {e, g} indicates that the relationship holds true for both electric vehicles and non-electric vehicles. Let h represent the set of user demand pairs for electric vehicles and non-electric vehicles in the network, and the set of all feasible paths, respectively. w Indicates traffic flow. For users' travel costs, This represents the minimum travel cost for users in an equilibrium state.

[0155] In order to effectively model the above complex equilibrium conditions, the equivalent nonlinear complementarity problem of (18)-(21) is constructed as follows:

[0156]

[0157]

[0158]

[0159]

[0160] However, directly solving the nonlinear complementarity problem requires the introduction of binary variables, which is detrimental to the efficient solution of the equilibrium state and makes it difficult to apply to higher-dimensional scenarios involving electric vehicle behavior. Compared to nonlinear complementarity and mathematical programming methods, variational inequalities do not require the objective function to be a strictly linear convex function, can be applied to high-order nonlinear models, and do not require the introduction of integer variables, thus ensuring high efficiency in the solution. Therefore, this invention further generalizes variational inequalities, constructing equivalent quasi-variational inequalities to describe the equilibrium state of elastic hybrid users. The problem is transformed into the following quasi-variational inequality problem:

[0161]

[0162] in:

[0163]

[0164] In summary, through the above transformations and equivalences, the traffic flow equilibrium problem in the inner game of the power transportation two-layer game can be transformed into a quasi-variable inequality problem, and the power grid optimization operation in the outer game can be represented as a convex optimization problem with second-order cone constraints.

[0165] S5: A two-layer game problem and equilibrium state of a power-transportation coupled network are solved using a hierarchical fixed-point iteration method and a sticky projection approximation algorithm. Specifically, the outer layer uses hierarchical fixed-point iteration to decouple the optimization problems of the power network and the transportation network. Meanwhile, for the inner layer, which considers the equilibrium problem of the transportation network with elastic demand, a sticky projection approximation algorithm is designed for effective solution.

[0166] Solution method for the electricity-transportation two-level game problem:

[0167] Based on the established model, in the inner game, traffic flow makes travel decisions based on the charging price given by the power grid, ultimately reaching user equilibrium and forming a charging demand distribution. In the outer game, the power grid optimizes network operation based on the charging load distribution and extracts the marginal price of this state as the charging price for users of the transportation network. To address the above issues, a hierarchical fixed-point mapping containing QVI is designed to represent the two-layer game problem of electricity-transportation:

[0168]

[0169] Where: QVI{λ * ,h,Q,Ω T} represents the price parameter λ* Given the quasi-variable inequality, its relation to M 内 {λ * They are equivalent. The specific methods for solving the electricity-transportation two-level game problem are introduced below:

[0170] Outer layer solution: Fixed-point iterative algorithm

[0171] Based on the outer-layer game model described above, the game behavior between the outer power grid and the overall transportation network can be summarized as the interaction of price and charging load information, essentially a fixed-point mapping problem from charging price to its own value. Therefore, when the inner-layer game equilibrium solution and corresponding charging demand can be uniquely determined given a price, the outer-layer game equilibrium solution can be solved using a fixed-point iterative algorithm. The specific process is as follows:

[0172] Step 0 Initialization:

[0173] ① Initial values ​​of variables: {λ 0 Convergence error: ε1, Number of iterations: k = 0

[0174] Step 1 is repeated iteratively:

[0175] ② Solve the optimal power flow sub-problem (SOC-OPF) of the distribution network by extracting the marginal electricity price {λ} through dual variables. k+1}

[0176] ③ Solve the traffic user equilibrium subproblem, and use the sticky projection approximation algorithm to solve the quasi-variable inequality problem QVI{λ k+1 ,h,Q,Ω T}, to obtain the given marginal electricity price {λ k+1 Charging demand distribution under the inner-layer traffic user game equilibrium}

[0177] Step 3 continues until the iterative residuals of the charging demand distribution and marginal electricity price satisfy the following conditions:

[0178]

[0179] Step 4 outputs the final charging demand distribution. And marginal electricity price results {λ k+1}

[0180] Inner layer solution: Viscous projection approximation algorithm

[0181] In price {λ k+1 Given the given conditions, the inner-layer traffic user game problem is equivalent to the quasi-variable inequality problem QVI{λ k+1 ,h,Q,Ω T Since the feasible region of the variables includes the elastic demand Q at the final equilibrium state.* The presence of unknown parameters makes it difficult to solve directly using traditional methods. Considering that solving quasi-variable inequality problems is essentially a process of approximating the equilibrium solution with given variables, i.e., {h} φ Q φ}→{h * Q * Since φ = 1, 2, ..., the algorithm converges to have Q. φ ≈Q * And feasible region Ω T (ξ * The feasible region is uniquely determined. Therefore, this invention uses variable Q to represent Q within the feasible region. * Eliminate and define the relaxed feasible region Λ T as follows:

[0182]

[0183] Therefore, when the variables converge to the equilibrium solution, we have Λ T →Ω T (ξ * Based on this, the present invention designs a viscosity-based projection approximation algorithm to solve the QVI problem. The specific process is as follows:

[0184] 1) Initialize input:

[0185] ① The marginal electricity price {λ} obtained by solving the optimal power flow problem of the distribution network k+1},

[0186] ② Select the initial variable y 0 =(h 0 Q 0 )∈Ω T ,

[0187] ③ Choose the iteration parameters 0≤γ≤1 and the sequence Set the number of iterations to φ = 0

[0188] 2) Repetition:

[0189] ④ Given the price {λ} output by Algorithm 1 k+1} and the previous generation variable y φ =(h φ Q φ Solve for Λ T The projection point on

[0190]

[0191] ⑤ Combine projection points and the previous generation variable y φ The sticky principle is used to update the current generation variable y. φ+1 ←(hφ+1 Q φ+1 ):

[0192]

[0193] ⑥ Determine whether the following convergence conditions are met:

[0194] ||y φ+1 -y φ ||≤ε2

[0195] When the conditions are met, the algorithm converges and exits the loop, outputting the obtained charging load distribution h. φ+1 And elastic demand Q φ+1 Otherwise, update φ = φ + 1 and return to step 1.

[0196] In step 1 of the algorithm Represents set Λ T Euclid norm projection on Defined as the mapping function vector of QVI. When γ is chosen to be appropriately small, the Lipschitz continuity condition is guaranteed to be satisfied during the iteration process, thus ensuring the convergence of the algorithm.

[0197] Implementation Simulation Case Study

[0198] The following example will further illustrate the content of this invention.

[0199] Figure 4 This is a test coupled network topology diagram of a 45-node transportation network and a 56-node distribution network in Fuzhou area used in the implementation of this invention. The coupling information of charging stations in this test network is shown in Table 1, the relevant key parameter settings for the example are shown in Table 2, and the network and demand parameters of the transportation network are shown in Tables 3 and 4. The baseline value for traffic flow is 100 vehicles / pu. The simulation test is based on the MATLAB platform, and all sub-problems involving optimization in the algorithm are solved using the GUROBI (8.1.1) solver.

[0200] Table 1. Coupling Information Parameters of Charging Stations in Transportation Network

[0201]

[0202]

[0203] Table 2 shows the relevant parameters for the example.

[0204]

[0205] Table 3. Road segment parameters of the transportation network

[0206]

[0207]

[0208] Table 4 Traffic Demand Parameters

[0209]

[0210]

[0211] Table 5 presents a comparison of load distribution under different scenarios for the four charging stations in the coupled network. Observing the results in Table 5, it can be seen that in the network equilibrium state considering the elasticity of traffic user demand, the marginal price distribution of the four charging stations is relatively even, meaning that the congestion effect of each charging station on the power grid is comparable under equilibrium conditions. In contrast, under the inelastic scenario, the charging prices at different stations differ more significantly, and the overall price borne by users is higher.

[0212] Table 5: Results of the Marginal Electricity Price Calculation for Charging Stations

[0213]

[0214] Figure 5 The diagram presents the equilibrium path traffic and corresponding travel costs for some demand pairs. As shown in the figure, regardless of vehicle type, for the same demand pair, the cost to the user is the same for paths with available traffic. For other paths where the travel cost is greater than the equilibrium cost, the corresponding traffic volume is zero. These results demonstrate that the results obtained using the method of this invention conform to the concept of equilibrium.

[0215] Figure 6 The paper presents a comparison of grid operating costs under different scenarios. In all cases, the grid operating cost gradually increases with the number of iterations and eventually converges to an equilibrium state. The comparison shows that considering demand elasticity reduces the electric vehicle charging load connected to the grid, resulting in lower grid operating costs under elastic demand conditions compared to inelastic demand conditions. Furthermore, as the demand travel attraction measure increases, the grid operating cost gradually increases, but the rate of increase gradually decreases. This indicates that when the attraction measure is large, the elastic demand on the transportation side has a smaller impact on grid operation, and vice versa.

[0216] Figure 7 The changes in demand for electric vehicles and non-electric vehicles after considering elasticity are presented. Comparing the distribution of the six OD demand pairs in the figure, it can be seen that when considering the elasticity of electric vehicle demand, the demand decreases to varying degrees compared to the inelastic case. However, since the travel cost of non-electric vehicles is lower than that of electric vehicles (no charging cost), the travel demand is greater than in the inelastic case when the attraction measure is large. Furthermore, Figure 7Both (a) and (b) show that user elasticity demand increases with the increase of attraction measure. Therefore, considering demand elasticity and quantifying users’ travel intentions through measurement is of great significance for improving the power grid decision-making ability.

[0217] Figures 8-11 The variation patterns of charging power, grid operating cost, charging load, and the attraction measure and negative elasticity parameter of road traffic flow are presented in the figure.

[0218] 1) When the attraction measure is small, the change in grid operating costs is not significant when the negative elasticity parameter increases. For different negative elasticity parameters, the grid operating costs generally increase with the increase of the attraction measure, and it has a greater sensitivity compared to the negative elasticity parameter. Therefore, grid operating costs will be affected by both the travel intentions of traffic users and the degree of demand elasticity, with the former having a more significant impact.

[0219] 2) Figure 10 Taking charging stations 1 and 4 as examples, the variation pattern of charging load is presented. Clearly, the load at charging station 1 increases with the increase of the attraction measure. However, observing the corresponding contour plot shows that when the attraction measure is small, its change with the increase of the negative elasticity parameter is not significant. For charging station 4, when the negative elasticity parameter is greater than 1.4, the charging load shows an oscillating upward trend with the increase of the attraction measure; when the negative elasticity parameter is less than 1.4, the charging load first increases and then decreases. This phenomenon is mainly because the station is located far away, and it distributes part of the charging load when the demand level is low. However, when demand continues to increase, network congestion will continue to change dynamically, causing the road congestion cost for users choosing charging station 4 to be greater than choosing other stations, thus reducing the charging load at this station. Similarly, further increases in demand will lead to a surge in congestion at other stations. At this time, charging station 4 can distribute part of the load to ensure the optimal cost for users in the equilibrium state.

[0220] 3) Figure 11 The graph shows the traffic flow patterns on some road sections. As the elasticity of traffic demand increases, congestion in the city center will worsen, for example, sections 15-16, 10-20, 26-25, and 25-24. For sections farther from the center, the traffic flow increases slowly (e.g., sections 15-25 and 25-32) or remains almost unchanged (e.g., section 42-43). Therefore, the equilibrium results are consistent with the actual situation.

[0221] To test the effectiveness of the proposed two-layer fixed-point mapping algorithm, Figure 12The iterative error curves for route traffic and charging price are presented. As shown in the figures, the algorithm converges to equilibrium (error less than the given value of 10e-6) after 6 iterations, with a total iteration time of 791.197 seconds. Furthermore, the iterative error of route traffic in the figure and the iterative error of marginal price (LMP) in the right figure both gradually decrease with increasing iteration count, and their error curves show a rapid decrease in the first 4 iterations, after which the convergence speed gradually slows down. In fact, after the 4th iteration, the error has decreased to below 10e-4 and no longer decreases significantly with further iterations; therefore, this is called the error stability region. Given that this is a system-level game problem, the solution obtained within the stability region actually meets the accuracy requirements of most scenarios.

[0222] Figure 13 Taking the last fixed-point mapping iteration as an example, the iteration error curve of the inner viscous projection algorithm is presented. As shown in the figure, the error gradually decreases with the increase of the number of iterations. The errors are less than 10e-3 and 10e-4 at iterations of 152 and 460, respectively, with computation times of 23.65 seconds and 62.24 seconds, respectively. Simulation tests show that the algorithm finally converges in the 903rd iteration (error less than the given value of 10e-5), with a total computation time of 128.44 seconds. The results demonstrate that the proposed viscous projection approximation has high computational efficiency and adaptability for practical systems.

[0223] In summary, this invention establishes a two-layer game model for the power-transportation coupled network, considering the demand elasticity of electric vehicles and their charging behavior, based on quasi-variable inequality theory. Compared to traditional network game models that do not consider elastic demand, the proposed model framework better reflects the impact of user travel costs on user behavior intentions in the coupled network, as well as the changes in network demand elasticity caused by electricity price fluctuations, providing a more refined modeling and study of practical problems. Simulations based on a coupled network of a 45-node Fuzhou transportation network and a 56-node distribution network verify that the proposed two-layer fixed-point iteration and projection approximation algorithm has high computational efficiency, and for complex large-scale power-transportation coupled network equilibrium problems, the algorithm can achieve rapid convergence within a reasonable time. Furthermore, simulation results comparing demand elasticity and inelasticity scenarios with different attraction measures show that the game equilibrium solution considering the transportation demand side can improve the grid pricing strategy and reduce grid operating costs compared to the inelastic case, and the cost reduction is significantly correlated with the magnitude of the network attraction measure. This result reflects the necessity of considering elastic demand.

[0224] This patent is not limited to the above-described preferred embodiments. Anyone can derive other forms of two-layer game models and equilibrium solution methods for electric-transportation coupled networks that consider the elastic demand behavior of electric vehicles based on the inspiration of this patent. All equivalent changes and modifications made within the scope of this patent application shall fall within the scope of this patent.

Claims

1. A detection method for a two-layer game model of a power-transportation coupled network considering the elastic demand behavior of electric vehicles, characterized in that: Couple the energy power grid with the transportation network through electric vehicle charging stations; Considering the optimization objective and operational constraints of the coupled network equilibrium problem, a quasi-variable inequality framework is adopted to characterize the equilibrium state of elastic mixed traffic users. In the inner game, traffic flow makes travel decisions based on the charging price given by the power grid, eventually reaching user equilibrium and forming a charging demand distribution; in the outer game, the power grid optimizes network operation based on the charging load distribution and extracts the marginal price of this state as the charging price for traffic network users. The established power grid model is subjected to second-order cone relaxation treatment; and the quasi-variable inequality framework is used to describe the equilibrium problem of the transportation network considering the elastic demand and charging behavior of electric vehicles, and the network equilibrium state is transformed into a mathematical optimization model. Then, the two-layer game problem and equilibrium state of the power-transportation coupled network are solved by the hierarchical fixed-point iteration method and the sticky projection approximation algorithm: the outer layer achieves the decoupling solution of the power network and transportation network optimization problem through hierarchical fixed-point iteration, and the inner layer considers the transportation network equilibrium problem with elastic demand and is solved by the sticky projection approximation algorithm. The established power grid model is subjected to second-order cone relaxation; and using a quasi-variable inequality framework, the equilibrium problem of the transportation network considering the elastic demand and charging behavior of electric vehicles is described, transforming the network equilibrium state into a mathematical optimization model, specifically including: The negative correlation between elastic demand and travel costs is described by introducing a Logit negative exponential model: In the formula This represents the actual demand. For the negative elasticity parameter of the Logit model. The attractiveness measure for users to reach their destination; the elastic demand characteristic function represents how user demand increases as travel costs decrease or the attractiveness measure of the destination increases. By considering the elastic demand response of electric vehicles, a hybrid user equilibrium that takes into account the elastic demand on the user side is adopted, and its logical expression is as follows: In the formula: superscript This indicates that the relation holds true for both electric vehicles and non-electric vehicles; , Let represent the set of user demand pairs for electric vehicles and non-electric vehicles in the network, and the set of all feasible paths, respectively. Indicates traffic flow. For users' travel costs, The minimum travel cost for users in equilibrium state; To effectively model the above complex equilibrium conditions, an equivalent nonlinear complementarity problem is constructed as follows: Further generalizing the variational inequality, we construct an equivalent quasi-variational inequality to describe the equilibrium state of elastic hybrid users; the problem is then transformed into the following quasi-variational inequality problem: in: In summary, through the above transformations and equivalences, the traffic flow equilibrium problem in the inner game of the power transportation two-layer game is transformed into a quasi-variable inequality problem, while the power grid optimization operation in the outer game is represented as a convex optimization problem with second-order cone constraints.

2. The detection method for the two-layer game model of the power-transportation coupled network considering the elastic demand behavior of electric vehicles according to claim 1, characterized in that: The optimization objective of the distribution network is: in, , , All are power generation cost coefficients. For the active power output of the generator, Inject active power into the main network nodes.

3. The detection method for the two-layer game model of the power-transportation coupled network considering the elastic demand behavior of electric vehicles according to claim 1, characterized in that: Distribution network constraints include: active and reactive power balance constraints, branch start and end voltage constraints, branch power flow constraints, line current and node voltage magnitude constraints, main grid input power range constraints, and active power reduction and reactive power output constraints of DG. In the traffic network equilibrium constraint, for any origin-destination traffic demand to OD, the travel time of routes with non-zero flow is the same and no greater than the travel time of routes with zero flow. This state is defined as the user equilibrium state UE. The traffic allocation principle based on the user equilibrium state is the user equilibrium principle. Based on this, the following are constructed: road segment form time function, traffic flow conservation constraint, and individual user travel cost function.

4. The detection method for the two-layer game model of the power-transportation coupled network considering the elastic demand behavior of electric vehicles according to claim 1, characterized in that: Based on the charging and travel needs of electric vehicle users and non-electric vehicle users, the optimal travel route is determined for each user. If an electric vehicle user needs to charge, their travel route will include the charging segment, while other vehicles that do not need to charge will use routes that do not include the charging segment. For any travel demand, the travel time for routes with non-zero flow is the same and no greater than the travel time for routes with zero flow. At the same time, it is required that for any travel demand, the demand function value corresponding to the minimum travel cost of the user in the equilibrium state must be equal to determine the user's travel demand in the network. If the travel cost is too high, there is no travel demand.

5. The detection method for the two-layer game model of the power-transportation coupled network considering the elastic demand behavior of electric vehicles according to claim 4, characterized in that: Considering that all electric and non-electric vehicle users in the transportation network choose their travel routes according to the minimum travel cost, and further considering the impact of user elastic demand on cost under equilibrium state, a Logit negative exponential model is constructed to describe the negative correlation between elastic demand and travel cost. The user equilibrium problem is treated as a quasi-variable inequality problem. The traffic network constraints considered include the constraints between road segment and path flow, the non-negativity and conservation of path flow, the relationship between path time and road segment time, the conversion between path travel time and cost, mixed user equilibrium flow allocation constraints, and road segment time function.

6. The detection method for a two-layer game model of a power-transportation coupled network considering the elastic demand behavior of electric vehicles according to claim 1, characterized in that: To address the non-convexity of the problem, an outer-layer fixed-point iteration is used to decouple the problem into a bi-layer convex optimization problem, and the inner-layer equilibrium problem is solved based on a viscous projection approximation algorithm.

7. The detection method for a two-layer game model of a power-transportation coupled network considering the elastic demand behavior of electric vehicles according to claim 6, characterized in that: The specific process of the hierarchical fixed-point iteration method is as follows: 1) Initialization: Input variables , initial values ​​and convergence error The number of iterations is set to And begin iterating; 2) Repeatedly solve the optimal power flow problem of the distribution network and the equilibrium subproblem of traffic users, and continuously update the marginal electricity price. and charging load distribution ; ① Optimal power flow problem in distribution networks: Input Solve the optimal power flow problem of the distribution network and extract the marginal electricity price through dual variables. ; ② Traffic User Equilibrium Subproblem: Input The sticky projection approximation algorithm is used to solve the game equilibrium problem of inner-layer traffic users. Obtain the distribution of charging demand ; 3) Until the convergence criterion is met: The final output is the charge distribution. and marginal electricity price As the final solution to the problem.

8. The detection method for a two-layer game model of a power-transportation coupled network considering the elastic demand behavior of electric vehicles according to claim 7, characterized in that: The specific process of solving the traffic user equilibrium subproblem using the designed sticky projection approximation algorithm is as follows: 1) Initialize input: ① Obtain the marginal electricity price by solving the optimal power flow problem of the distribution network. , ② Select initial variables , ③ Select iteration parameters and sequence The number of iterations is set to ; 2) Repeat the following solution process: ①Given marginal electricity price and previous generation variables Solve The projection point on : ② Combining projection points and previous generation variables The sticky principle is used to update the current generation variables. : ③ Determine whether the following convergence conditions are met: When the conditions are met, the algorithm converges and exits the loop, outputting the obtained charging load distribution. and elastic demand Otherwise update (Return to step 1). Step 1) Represents a set Euclid norm projection on Defined as a vector of mapping functions in QVI; when Choosing an appropriately small value ensures that the Lipschitz continuity condition is satisfied during the iteration process, thereby guaranteeing the convergence of the algorithm.

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