Vehicle-road network continuous-time cooperative scheduling method and device based on polynomial approximation

Abstract

The application belongs to the technical field of power-traffic system collaborative operation, and specifically discloses a vehicle-road network continuous time collaborative scheduling method and equipment based on polynomial approximation. The application generates an alternative path set for different vehicles by adopting a traffic network expansion model based on graph theory, combines a user equilibrium model in a continuous time domain, accurately depicts the continuous space-time evolution of traffic flow and the dynamic fluctuation of charging load, and relieves the distortion caused by discrete time. Then, a continuous time power system optimal operation model is constructed, so that unit scheduling accurately responds to actual charging demand, and the scheduling mismatch risk caused by immature continuous time optimization is solved. Further, the two models are transformed from a function space to an algebra space through polynomial approximation, which greatly reduces the solving complexity, and finally the continuous time optimal scheduling plan is obtained by backstepping. Compared with the prior art, the application not only retains the high accuracy of continuous time, but also realizes efficient solving, and significantly improves the economy and safety of scheduling decision.

Description

Technical Field

[0001] This application belongs to the field of power-transportation system cooperative operation technology, specifically involving a vehicle-road network continuous-time cooperative scheduling method and device based on polynomial approximation. Background Technology

[0002] With the rapid growth of electric vehicle ownership, the coupling between the power system and the transportation system is becoming increasingly close. The spatiotemporal distribution of electric vehicle charging load is determined by the dynamic evolution of traffic flow, and its connection to the power grid profoundly affects the nodal power balance and operational economy of the power system. Therefore, conducting research on vehicle-road-grid coordinated optimization operation is of great significance for improving the overall operational efficiency of the power-transportation system.

[0003] Existing power-transportation coordinated scheduling methods are mainly based on discrete-time optimization frameworks. Within this framework, time-varying variables such as traffic flow, charging load, and power generation output are modeled as piecewise stepped curves, assuming that each variable remains constant within each time period. However, actual traffic flow exhibits continuous spatiotemporal evolution characteristics; the processes of vehicles traveling, queuing, and dispersing on road segments occur continuously, and the charging load also fluctuates dynamically as vehicles arrive at charging stations. Discrete-time modeling struggles to accurately depict the continuous propagation process of traffic flow within a time period and cannot precisely reflect the dynamic changes in charging load within a time period. This leads to biases in the assessment of flexibility resource requirements, potentially resulting in resource misallocation or increased operational risks in the scheduling scheme.

[0004] To address the aforementioned issues, some studies have attempted to improve modeling accuracy by shortening the scheduling period length. However, due to limitations in computational burden and the availability of prediction information, the period length cannot be infinitely refined, and continuous changes within the period are still ignored. Continuous-time optimization theory offers a new approach to solving these problems. By modeling time-varying variables as continuous smooth functions, it can fully characterize the dynamic processes within a time period. However, the application of continuous-time optimization in power-transportation coordinated scheduling is still immature, lacking an integrated continuous-time modeling and solution method that can simultaneously handle traffic flow delay propagation characteristics, user equilibrium behavior, and optimal power flow. Therefore, there is an urgent need to propose an optimized operation method that can accurately characterize the continuous spatiotemporal evolution of traffic flow, fully reflect the dynamic fluctuations of charging load, and achieve continuous-time integrated coordination of vehicles, roads, and the network. Summary of the Invention

[0005] To address the shortcomings of existing technologies, this application aims to provide a continuous-time collaborative scheduling method and device for vehicle-road networks based on polynomial approximation. This aims to solve the following problems: Currently, continuous-time optimization is still immature in the field of power-transportation collaborative scheduling, making it difficult to accurately characterize the continuous spatiotemporal evolution of traffic flow and fully reflect the dynamic fluctuations of charging load, resulting in scheduling mismatch or increased risks.

[0006] The first aspect of this application relates to a continuous-time collaborative scheduling method for vehicle-road networks based on polynomial approximation, comprising: step S10, constructing an extended traffic network model based on graph theory, the extended traffic network model being used to generate a set of alternative routes for different types of vehicles; step S20, based on the extended traffic network model, constructing a user equilibrium model of the traffic network in the continuous-time domain, the user equilibrium model being used to simulate vehicle travel behavior and output spatiotemporal distribution data of charging load; step S30, based on the spatiotemporal distribution data of charging load, constructing an optimal operation model of the power system in the continuous-time domain, the optimal operation model of the power system being used to formulate a unit scheduling plan with economic optimization as the objective; step S40, using the Bernstein polynomial approximation algorithm, transforming the solution space of the user equilibrium model of the traffic network and the optimal operation model of the power system from the function space to the algebraic space, obtaining a joint optimization model in algebraic form; step S50, based on the solution results of the joint optimization model in algebraic form, back-reasoning to obtain the optimal unit scheduling plan of the power system in the continuous-time domain.

[0007] In one embodiment, step S10 includes: hiding charging station nodes in the transportation network, abstracting the nodes in the transportation network as points, and abstracting the roads connecting the nodes as directed links to construct a first directed graph for path planning of the first type of vehicle; based on the first directed graph, adding self-circulating links for charging station nodes to construct a second directed graph for path planning of the second type of vehicle, wherein the self-circulating links are used to characterize the vehicle charging process; and generating alternative path sets for the first type of vehicle and the second type of vehicle respectively according to the first directed graph and the second directed graph.

[0008] In one embodiment, the traffic network user equilibrium model includes: a traffic flow delay propagation model and a user equilibrium criterion; step S20 includes: constructing a traffic flow delay propagation model based on the set of alternative paths output by the traffic network extended model; the traffic flow delay propagation model describes the dynamic propagation process of vehicles on the path through a time-varying correlation matrix, and determines the cumulative number of arrivals and departures of vehicles on roads and charging stations based on the first-in-first-out principle and the relationship between arrival and departure signals of vehicles on adjacent road segments; based on the cumulative number of arrivals and departures, determining the queuing status of vehicles on the road and the queuing status and charging status of vehicles at charging stations; constructing a user equilibrium criterion based on the queuing status and charging status; the user equilibrium criterion is used to calculate the comprehensive travel cost of vehicles choosing different paths at different departure times according to the queuing status and charging status, and determine the travel behavior of vehicles based on the comprehensive travel cost; and obtaining the spatiotemporal distribution data of charging load based on the traffic flow delay propagation model and the user equilibrium criterion.

[0009] In one embodiment, after step S20, the method further includes: introducing auxiliary variables and 0-1 variables to linearize the bilinear terms and complementary constraints in the traffic flow delay propagation model, thereby obtaining a linearized traffic network user equilibrium model.

[0010] In one embodiment, step S30 includes: taking minimizing the total operating cost of the system as the objective function, and setting the output constraints of the generator set and the transmission capacity constraints of the line; and, based on the power balance conditions of the power nodes, substituting the spatiotemporal distribution data of the charging load as known parameters into the objective function and the constraints to formulate a scheduling plan for the generator set in the continuous time domain.

[0011] In one embodiment, step S40 includes: step S41, using Bernstein polynomial approximation to express the continuous-time function variables in the traffic network user equilibrium model as algebraic forms of interpolation coefficients, and converting the complementary constraints and nonlinear terms in the traffic network user equilibrium model into algebraic mixed-integer linear constraints; step S42, using Bernstein polynomial approximation to express the continuous-time function variables in the power system optimal operation model as algebraic forms of interpolation coefficients, and converting the power system optimal operation model into an algebraic linear programming model.

[0012] In one embodiment, step S41 includes: performing Bernstein polynomial approximation on the one-dimensional continuous-time function variables in the traffic network user equilibrium model, representing them as cubic Bernstein polynomial interpolation coefficient vectors in each time segment, and applying continuity constraints to the interpolation coefficient vectors of adjacent time segments; performing Bernstein polynomial approximation on the two-dimensional continuous-time function variables in the traffic network user equilibrium model, representing them as cubic Bernstein polynomial interpolation coefficient matrices in each time and departure time grid, and applying continuity constraints to the interpolation coefficient matrices of adjacent grids; constraining the values ​​of the time-varying correlation matrix elements in the traffic network user equilibrium model to 0 or 1, and constraining their monotonically increasing nature in the time axis direction through the differential coefficient matrix; and converting the bilinear terms and complementary constraints in the traffic network user equilibrium model into a system of mixed integer linear inequalities in algebraic form by introducing auxiliary variables and 0-1 variables.

[0013] In one embodiment, step S42 includes: performing Bernstein polynomial approximation on the continuous-time function variables of generator output, node voltage phase angle, and charging power of charging stations in the optimal operation model of the power system, representing them as interpolation coefficient vectors of cubic Bernstein polynomials in each time segment, and applying continuity constraints to the interpolation coefficient vectors of adjacent time segments; and converting the objective function and all constraints in the optimal operation model of the power system into algebraic forms with respect to the interpolation coefficient vectors.

[0014] In one embodiment, step S50 includes: obtaining the interpolation coefficient vector obtained after solving the algebraic joint optimization model; and using a preset Bernstein polynomial basis function and the interpolation coefficient vector to perform calculations to reconstruct the unit's output time-series curve in the continuous time domain, which serves as the optimal scheduling plan.

[0015] In a second aspect, this application provides an electronic device, comprising: at least one memory for storing a program; and at least one processor for executing the program stored in the memory, wherein when the program stored in the memory is executed, the processor is configured to execute the method described in the first aspect or any possible implementation thereof.

[0016] Thirdly, this application provides a computer-readable storage medium storing a computer program that, when run on a processor, causes the processor to perform the method described in the first aspect or any possible implementation thereof.

[0017] Fourthly, this application provides a computer program product that, when run on a processor, causes the processor to perform the method described in the first aspect or any possible implementation thereof.

[0018] It is understood that the beneficial effects of the second to fourth aspects mentioned above can be found in the relevant descriptions in the first aspect mentioned above, and will not be repeated here.

[0019] Overall, the technical solutions conceived in this application have the following beneficial effects compared with the prior art: This application employs a graph-based traffic network extension model, which can generate alternative path sets for different types of vehicles, thereby finely characterizing the topological structure of the traffic network and the differentiated travel characteristics of vehicles. Based on this, a traffic network user equilibrium model in the continuous time domain is constructed, which breaks through the limitations of traditional discrete-time methods in characterizing the continuous spatiotemporal evolution of traffic flow, fully reflects the dynamic fluctuation characteristics of charging load, and avoids the distortion of load peaks or troughs caused by time discretization.

[0020] Furthermore, based on the spatiotemporal distribution data of the charging load, an optimal operation model of the power system in the continuous time domain is constructed, enabling the unit scheduling plan to accurately respond to the power demand brought about by actual traffic flow changes. This solves the problem of scheduling mismatch or increased risk caused by the immaturity of continuous time optimization in power-transportation coordinated scheduling.

[0021] Subsequently, a polynomial approximation algorithm was used to transform the solution space of the two models from the function space to the algebraic space, resulting in a joint optimization model in algebraic form. This significantly reduced the solution complexity of the continuous-time problem, transforming the originally difficult-to-compute infinite-dimensional optimization problem into a finite-dimensional algebraic problem that can be solved efficiently.

[0022] Finally, the optimal unit scheduling plan in the continuous time domain is derived from the solution results of the algebraic model. This not only retains the accuracy advantage of the continuous time model, but also overcomes the computational bottleneck. Compared with existing technologies, it achieves accurate capture of the spatiotemporal evolution of traffic flow and fluctuations in charging load, significantly improving the economy and safety of scheduling decisions.

[0023] Furthermore, this application constructs a traffic network user equilibrium model that takes into account the characteristics of traffic flow delay propagation on a continuous time scale. This model can accurately depict the continuous dynamic evolution of vehicle queuing, dissipation, and charging processes on roads and charging stations. It overcomes the shortcomings of discrete-time scheduling in describing the continuous changes in traffic flow and the dynamic fluctuations in charging load within a time period, and provides theoretical support for the accurate assessment of the spatiotemporal distribution of charging load.

[0024] Furthermore, this application utilizes Bernstein polynomial approximation theory to transform complex optimization problems in continuous-time function space into mixed-integer linear programming models in algebraic space, enabling the models to be solved efficiently using existing commercial solvers. This solves the problem of continuous-time optimization being difficult to compute in practical engineering and demonstrates good feasibility.

[0025] Furthermore, through continuous time-coordinated optimization, this application can more rationally formulate the power output plan of generator units in the power system, better match the spatiotemporal fluctuations of charging load, reduce the waste of reserve capacity or insufficient ramping caused by load forecast deviations and fluctuations within a time period, thereby reducing system operating costs and improving the economy and safety of power-transportation system operation. Attached Figure Description

[0026] Figure 1 This is a flowchart illustrating the continuous-time collaborative scheduling method for vehicle-road networks based on polynomial approximation provided in the embodiments of this application. Figure 2 This is a schematic diagram of the transportation network extension model provided in the embodiments of this application; Figure 3 This is a traffic system topology diagram used for simulation testing provided in the embodiments of this application; Figure 4 This is a power system topology diagram used for simulation testing provided in the embodiments of this application; Figure 5 These are the charging load dynamic curves of each charging station provided in the embodiments of this application; Figure 6 This is a schematic diagram of the structure of the electronic device provided in the embodiments of this application. Detailed Implementation

[0027] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.

[0028] In this application, the term "and / or" describes the relationship between related objects, indicating that three relationships can exist. For example, A and / or B can represent three cases: A existing alone, A and B existing simultaneously, and B existing alone. In this application, the symbol " / " indicates that the related objects are in an "or" relationship, for example, A / B means A or B.

[0029] In this application, the terms "first" and "second," etc., are used to distinguish different objects, not to describe a specific order of objects. For example, "first response message" and "second response message," etc., are used to distinguish different response messages, not to describe a specific order of response messages.

[0030] In the embodiments of this application, the terms "exemplary" or "for example" are used to indicate that something is an example, illustration, or description. Any embodiment or design that is described as "exemplary" or "for example" in the embodiments of this application should not be construed as being more preferred or advantageous than other embodiments or design. Specifically, the use of the terms "exemplary" or "for example" is intended to present the relevant concepts in a specific manner.

[0031] In the description of the embodiments of this application, unless otherwise stated, "multiple" means two or more, for example, multiple processing units means two or more processing units, multiple elements means two or more elements, etc.

[0032] In light of the background technology, this application proposes an embodiment of a continuous-time cooperative scheduling method for vehicle-road networks based on polynomial approximation. Please refer to... Figure 1 , Figure 1 This is a flowchart illustrating the continuous-time collaborative scheduling method for vehicle-road networks based on polynomial approximation provided in the embodiments of this application.

[0033] Polynomial approximation refers to using polynomial functions (such as Chebyshev polynomials, Legendre polynomials, or Bernstein polynomials) to approximate time-varying variables (such as traffic flow, charging load, and power generation output) in the continuous time domain, thereby transforming the optimization problem, which originally needed to be solved in an infinite-dimensional function space, into a numerical problem in a finite-dimensional algebraic space. Vehicle-road network refers to a coupled system composed of electric vehicles, road networks, and power networks. Continuous-time coordinated scheduling means that scheduling decisions no longer rely on discrete time step segments, but are based on unified planning using continuous-time functions, thus eliminating the accuracy loss caused by averaging within time periods. The core of this method lies in achieving the joint solution of dynamic traffic flow propagation and optimal power flow in the power system through polynomial approximation, avoiding the neglect of continuous processes within time periods under the traditional discrete-time framework.

[0034] In this embodiment, the method includes: Step S10: Construct an extended traffic network model based on graph theory. The extended traffic network model is used to generate a set of alternative routes for different types of vehicles.

[0035] It should be noted that graph theory is a branch of mathematics used to describe network structures composed of nodes and edges. In this embodiment, the traffic network extension model adopts a directed graph representation, where nodes represent intersections or charging station locations, and edges represent road segments. To accommodate the travel needs of different types of vehicles (such as private electric vehicles, logistics electric vehicles, and buses), the model adds virtual nodes and virtual edges to the basic road network to represent charging waiting times, path selection preferences, and time window constraints. In specific implementation, an adjacency matrix or adjacency list can be used to store topological relationships, and a set of alternative paths can be generated for each type of vehicle using a shortest path algorithm.

[0036] It should be noted that hypergraph or spatiotemporal network models can also be used to further refine path diversity. The effect of this model is that it provides a complete path candidate space for subsequent continuous-time user equilibrium models, ensuring that all feasible paths are included in the optimization scope and avoiding scheduling deviations caused by path omissions.

[0037] Step S20: Based on the extended traffic network model, construct a traffic network user equilibrium model in the continuous time domain. The traffic network user equilibrium model is used to simulate the travel behavior of vehicles and output the spatiotemporal distribution data of charging load.

[0038] It should be noted that the continuous time domain refers to a continuous interval of real numbers for time variables, rather than a discrete set of time points. The user equilibrium model for a transportation network can be built based on Wardrop's first principle (users choose the path that minimizes their travel costs), but it is extended to the continuous time dimension. In the model, the travel cost of each path consists of travel time, charging waiting time, and charging costs, and these costs are all continuous functions of time.

[0039] In practical implementation, variational inequalities or differential variational inequalities can be used to describe the user equilibrium conditions, combined with a continuous-time dynamic network loading model to simulate the continuous flow of vehicles on the road segment. The spatiotemporal distribution data of the charging load is output by this model, i.e., the charging power demand of each charging station at any given time, which is expressed as a continuous function of time. Alternatively, a continuous version based on the cellular transport model or a fluid dynamics model can also be used. The advantages of this model are that it can accurately characterize the continuous propagation of traffic flow (including queue formation and dissipation), allowing the instantaneous fluctuations of the charging load to be fully preserved, thereby providing a more realistic and flexible demand boundary for power system dispatching.

[0040] Step S30: Based on the spatiotemporal distribution data of charging load, construct the optimal operation model of the power system in the continuous time domain. The optimal operation model of the power system is used to formulate unit scheduling plans with the goal of economic optimization.

[0041] It should be noted that the objective of the optimal power system operation model is to minimize the total operating cost (including fuel cost, start-up and shutdown cost, and carbon emission cost) while satisfying safety constraints. Unlike traditional optimal power flow, this model treats generator output, energy storage charging and discharging power, and line power flow as continuous functions of time. Constraints may include: nodal power balance equations (presented in differential algebraic form), generator ramp rate limits (constraints involving derivatives), line thermal limits (inequalities that vary with time), and upper and lower limits of voltage amplitude.

[0042] In practical implementation, a continuous-time optimal power flow framework can be adopted, parameterizing the decision variables as a linear combination of polynomial basis functions. Alternatively, the pseudospectral method or collocation method can be used for discretization. The advantages of this model are: it can respond to continuous dynamic changes in charging load, formulate smooth unit scheduling plans without time-interval jumps, and avoid problems such as insufficient ramping or over-regulation caused by discretization, thereby improving the economy and security of power system operation.

[0043] Step S40: Using the Bernstein polynomial approximation algorithm, the solution spaces of the traffic network user equilibrium model and the power system optimal operation model are transformed from function space to algebraic space to obtain a joint optimization model in algebraic form.

[0044] It should be noted that the Bernstein polynomial approximation algorithm involves selecting a set of orthogonal polynomial basis functions to represent the unknown continuous functions in the original problem (such as path flow and node voltage phase angle) as a linear combination of basis functions. Through Galerkin projection or least squares fitting, the differential equations, integral equations, and variational inequalities are transformed into a system of algebraic equations concerning the combination coefficients. In this way, the optimization problem that originally needed to be solved in an infinite-dimensional function space is equivalently transformed into a finite-dimensional algebraic optimization problem (i.e., nonlinear programming or quadratic programming).

[0045] In practical implementation, the coefficients can be solved using spectral methods or adaptive pseudospectral methods. Alternatively, radial basis functions or wavelet bases can be used for approximation. The key benefits of this step are: significantly reduced computational complexity, enabling efficient solutions for continuous-time cooperative scheduling on existing computer hardware; and the convergence of polynomial approximation ensures that the error between the algebraic solution and the original continuous solution is controllable, thereby maintaining the physical accuracy of the scheduling scheme.

[0046] Step S50: Based on the solution results of the joint optimization model in algebraic form, the optimal unit scheduling plan of the power system in the continuous time domain is derived by reverse deduction.

[0047] It should be noted that the reverse calculation refers to using the basis function coefficients obtained in the previous steps to reconstruct the original continuous-time function through polynomial summation. For example, if the unit output is expressed as a weighted sum of several basis functions, then after solving for the coefficients, the output value at any given time can be directly calculated. These continuous functions constitute the optimal unit scheduling plan, including the output curves of each generator unit, the start-stop state switching times, and the energy storage charging and discharging strategies.

[0048] In practice, the algebraic solution can be substituted into the original polynomial expression to generate a time series or continuous curve for use by actuators (such as power plant controllers and energy management systems). Alternatively, the continuous curve can be recovered from discrete sampling points using interpolation or fitting methods. The advantage of this step is that the final output scheduling plan is continuous and can be directly applied to the real-time control of the actual power system (e.g., sent to the turbine speed control system or energy storage inverter) without the need for additional inter-time period interpolation or smoothing, thereby reducing command conversion errors and improving control accuracy.

[0049] In this embodiment, by employing a graph theory-based traffic network extension model, alternative path sets can be generated for different types of vehicles, thereby refining the topological structure of the traffic network and the differentiated travel characteristics of vehicles. Based on this, a traffic network user equilibrium model in the continuous time domain is constructed, which breaks through the limitations of traditional discrete-time methods in depicting the continuous spatiotemporal evolution of traffic flow, fully reflects the dynamic fluctuation characteristics of charging load, and avoids the distortion of load peaks or troughs caused by time discretization.

[0050] Furthermore, based on the spatiotemporal distribution data of the charging load, an optimal operation model of the power system in the continuous time domain is constructed. This enables the unit scheduling plan to accurately respond to the power demand brought about by changes in actual traffic flow, solving the problem of scheduling mismatch or increased risk caused by the immaturity of continuous-time optimization in power-traffic coordinated scheduling. Subsequently, a polynomial approximation algorithm is used to transform the solution space of the two models from the function space to the algebraic space, obtaining a joint optimization model in algebraic form. This significantly reduces the solution complexity of the continuous-time problem, transforming the originally difficult-to-compute infinite-dimensional optimization problem into a finite-dimensional algebraic problem that can be solved efficiently.

[0051] Finally, the optimal unit scheduling plan in the continuous time domain is derived from the solution results of the algebraic model. This not only retains the accuracy advantage of the continuous time model, but also overcomes the computational bottleneck. Compared with existing technologies, it achieves accurate capture of the spatiotemporal evolution of traffic flow and fluctuations in charging load, significantly improving the economy and safety of scheduling decisions.

[0052] Based on the above embodiments, this application provides a feasible implementation method.

[0053] It should be noted that this application assumes two types of vehicles on the transportation network: gasoline-powered vehicles and electric vehicles. Gasoline-powered vehicles travel from their origin to their destination without needing to charge or refuel, requiring only road sequence planning (conventional path selection). Electric vehicles, traveling from their origin to their destination, require at most one charging trip, necessitating both road sequence planning and charging decisions (generalized path selection).

[0054] Therefore, in this embodiment, step S10 includes: hiding the charging station nodes in the transportation network, abstracting the nodes in the transportation network as points, and abstracting the roads connecting the nodes as directed links to represent the vehicle driving process, so as to construct a first directed graph for path planning of the first type of vehicle (fuel vehicle). ; in the first directed graph Based on this, self-looping links are added to charging station nodes to represent the vehicle charging process, thereby constructing a second directed graph for path planning of the second type of vehicle (electric vehicle). The self-circulating link is used to characterize the vehicle's charging process.

[0055] Following the steps above, a similar result can be obtained. Figure 2 The transportation network extension model.

[0056] Understandably, this model achieves unified modeling for two different types of vehicle routing problems by constructing a directed graph in a hierarchical manner. Its core logic lies in the reasonable abstraction and simplification of complex real-world traffic elements.

[0057] It should be noted that the first directed graph omits charging station nodes, retaining only regular traffic nodes. This approach removes the charging attributes unnecessary for gasoline vehicles, simplifying the complex real-world road network into a pure traffic network. In this case, all roads are abstracted as directed links, primarily used to represent the vehicle's travel process and travel time cost.

[0058] It's important to note that the second directed graph encompasses all the elements of the first directed graph. Self-looping links are added at the original charging station node locations to specifically represent the vehicle's dwell time and charging process. At this point, the path planning no longer needs to consider the specific characteristics of each node. This means that when an electric vehicle plans its route through these nodes, the model allows it to choose whether to charge, thus addressing the range anxiety unique to electric vehicles.

[0059] Understandably, through this three-dimensional network representation system, the algorithm can perform pathfinding operations on directed graphs at two different levels, satisfying both the shortest path requirement for fuel vehicles and the energy replenishment constraints for electric vehicles.

[0060] Finally, based on the first directed graph Second directed graph , respectively generate alternative route sets for the first type of vehicle and the second type of vehicle.

[0061] In this embodiment, the traffic network user equilibrium model includes: a traffic flow delay propagation model and a user equilibrium criterion.

[0062] It should be noted that the traffic flow delay propagation model is responsible for simulating the dynamic movement of vehicles on roads and charging stations, including continuous behaviors such as driving, queuing, and charging. The user equilibrium criterion, based on the state data generated by this propagation process, calculates the comprehensive travel cost of vehicles choosing different paths at different departure times and determines the user's travel choice based on the principle of cost minimization. Together, they output the spatiotemporal distribution data of charging load, that is, the variation of charging power demand at each charging station at any given time with time and location. This model extends the user equilibrium theory under the traditional discrete-time framework to the continuous-time domain, accurately characterizing the continuous evolution of traffic flow.

[0063] Therefore, step S20 includes: constructing a traffic flow delay propagation model based on the set of alternative paths output by the traffic network extension model; the traffic flow delay propagation model describes the dynamic propagation process of vehicles on the path through a time-varying correlation matrix, and determines the cumulative number of arrivals and departures of vehicles on roads and charging stations based on the first-in-first-out principle and the relationship between arrival and departure signals of vehicles on adjacent road segments; based on the cumulative number of arrivals and departures, determining the queuing status of vehicles on the road and the queuing status and charging status at the charging station; constructing a user equilibrium criterion based on the queuing status and charging status; the user equilibrium criterion is used to calculate the comprehensive travel cost of vehicles choosing different paths at different departure times based on the queuing status and charging status, and determine the travel behavior of vehicles based on the comprehensive travel cost; and obtaining the spatiotemporal distribution data of charging load based on the traffic flow delay propagation model and the user equilibrium criterion.

[0064] Specifically, firstly, the relationship between departure flow and origin-destination (OD) demand is established using equations (1) and (2); secondly, a time-varying correlation matrix is ​​defined using equations (3) to (5) to describe the spatiotemporal location of vehicles on the path; then, the cumulative arrival / departure numbers for each road segment and charging station are calculated using equations (6) to (9); finally, the queuing status is determined using equations (10) to (15). The traffic flow delay propagation model is represented by the following equations (1) to (15): (1).

[0065] Equation (1) represents the supply and demand balance of fuel vehicles for each OD; and OD pairs respectively rs Total commuting demand for gasoline-powered vehicles and their alternative route set; This refers to the vehicle's departure time window. L and U These are the earliest and latest departure times of the vehicles, respectively. ; for From the path p Traffic flow departing from the entrance; For the set of OD pairs.

[0066] (2).

[0067] It should be noted that equation (2) represents the commuting supply and demand balance of electric vehicles for each OD; and OD pairs respectively rs The total commuting demand for electric vehicles and the set of alternative routes.

[0068] (3).

[0069] It should be noted that equation (3) is a time-varying correlation matrix that characterizes the dynamic propagation of vehicles along the path; and For path p With Link w The elements of the time-varying correlation matrix: if From the path p Vehicles departing from the entrance The time has passed the link w Entrance, then ,otherwise ;like From the path p Vehicles departing from the entrance The time has passed the link w Export, then ,otherwise ; For unit step function, For the step point, For vehicle-road-network system scheduling time window; For the total set of paths, we have ; For a set of links.

[0070] (4).

[0071] It should be noted that Equation (4) represents the first-in-first-out principle: on the same path, the vehicle that departs first always remains in the lead, that is, the first-in-first-out principle is satisfied on any link on the path; and These are the elements of the time-varying correlation matrix. exist and The value at time; and These are the elements of the time-varying correlation matrix. exist and The value at any given moment.

[0072] (5).

[0073] It should be noted that equation (5) represents the relationship between the arrival and departure signals of a vehicle on adjacent road segments along the path; if the path p The first link traversed is w but ,otherwise ; The step point is represented as The unit step function; For path pWith Link w The constant elements of the correlation matrix, if the path contains links w ,but ,otherwise ; For link w A set of links connected to the entry point.

[0074] (6).

[0075] It should be noted that equation (6) represents the cumulative number of vehicles arriving at each link over time; As of Time Link w The cumulative number of vehicles passing through the entrance. Bilinear term The corresponding auxiliary variables.

[0076] (7).

[0077] It should be noted that equation (7) represents the cumulative number of vehicles leaving each link over time; As of Time Link w The cumulative number of vehicles passing through the exit area. Bilinear term The corresponding auxiliary variables.

[0078] (8).

[0079] It should be noted that equation (8) represents the cumulative number of vehicles arriving and departing from each road over time; and As of Road at all times a The cumulative number of vehicles passing through the entrance and exit; A is the correlation matrix between roads and links, if the link w Corresponding vehicle on the road a Driving upwards, then ,otherwise ; For road sets.

[0080] (9).

[0081] It should be noted that equation (9) represents the cumulative number of vehicles arriving and departing at each charging station over time; and As of Moment Charging Station m The cumulative number of vehicles passing through the entrance and exit; B is the association matrix between the charging station and the link, if the linkw The corresponding vehicle at the charging station m Charging in the middle, then ,otherwise ; A collection of charging stations.

[0082] (10); (11); (12); (13).

[0083] (14); (15).

[0084] It should be noted that equation (10) represents the number of vehicles queuing on each road over time; for Road at all times a The number of vehicles queuing on the road; For roads a The free passage time. Equation (11) represents the number of vehicles queuing at each charging station over time; for Moment Charging Station m The number of vehicles queuing at each charging station. Equation (12) represents the number of vehicles charging at each charging station over time; for Moment Charging Station m The number of vehicles charging in the charging station. Equation (13) represents the charging time; in this application, the charging amount, rated charging power, and charging time of all vehicles charging in the charging station are set to the same constant, respectively. , and .

[0085] It should be noted that Equation (15) represents the relationship between the number of vehicles charging in the charging station and the capacity of the charging station (number of charging piles): if at a certain moment, the number of vehicles queuing in the charging station is 0, then the number of vehicles charging in the station is any value not greater than the capacity of the charging station; conversely, if the number of vehicles queuing is not 0, then the number of vehicles charging in the station is equal to the capacity of the charging station. For charging stations m The capacity.

[0086] Specifically, the user equilibrium criteria in the continuous time domain are as follows (16) to (21): (16).

[0087] It should be noted that equation (16) represents the time required for a vehicle departing from the path entrance at each time to pass through its subordinate links; for From the path p Vehicles departing from the entrance pass through the link w The time required.

[0088] (17).

[0089] It should be noted that Equation (17) represents the charging cost required for a vehicle departing from the path entrance at each time to pass through its subordinate links; for From the path p Vehicles departing from the entrance on the link w Charging costs on the device, and These are bilinear terms. and The corresponding auxiliary variables.

[0090] (18).

[0091] It should be noted that equation (18) represents the charging price corresponding to each link at each time point; and Links w and power nodes b exist Electricity price at any given time; Let be the association matrix between charging stations and power nodes. If the charging station m With power nodes b If connected, then ,otherwise .

[0092] (19).

[0093] It should be noted that equation (19) represents the comprehensive travel cost of the route; for From the path p The overall passage cost for vehicles departing from the entrance. This is the time-to-money conversion factor.

[0094] (20); (twenty one).

[0095] It should be noted that equation (20) represents the user equilibrium criterion for gasoline-powered vehicles; For OD rsThe optimal overall toll cost for gasoline-powered vehicles. Equation (21) represents the user equilibrium criterion for electric vehicles; For OD rs The optimal overall cost of travel for electric vehicles.

[0096] In this embodiment, after step S20, the method further includes: introducing auxiliary variables and 0-1 variables to linearize the bilinear terms and complementary constraints in the traffic flow delay propagation model, thereby obtaining a linearized traffic network user equilibrium model.

[0097] Specifically, the linearization method for the traffic network user equilibrium model that takes into account the characteristics of traffic flow delay propagation is as follows: (twenty two); (twenty three).

[0098] It should be noted that equation (22) represents the bilinear term in equation (6). Linearization; M For a relatively large constant, this application takes 10000. Equation (23) represents the bilinear term in equation (7). Linearization.

[0099] (twenty four); (25).

[0100] It should be noted that equation (24) represents the linearization of equation (14); For roads a The corresponding 0-1 auxiliary variables, and Represent Road at all times a The number of vehicles queuing on the platform is 0 and not 0. Equation (25) represents the linearization of equation (15); For charging stations m The corresponding 0-1 auxiliary variables, and Represent Moment Charging Station m The number of vehicles in the queue is 0 and not 0.

[0101] (26); (27).

[0102] It should be noted that equations (26) and (27) represent the bilinear terms in equation (17). Linearization.

[0103] (28).

[0104] It should be noted that equation (28) represents the bilinear term in equation (17). Linearization.

[0105] (29); (30).

[0106] It should be noted that equation (29) represents the linearization of equation (20); For path p The 0-1 auxiliary variables corresponding to gasoline-powered vehicles and These represent choosing and not choosing gasoline-powered vehicles, respectively. From the path p Starting from the entrance. Equation (30) represents the linearization of equation (21); For path p The 0-1 auxiliary variables corresponding to electric vehicles and These represent choosing and not choosing electric vehicles, respectively. From the path p Depart from the entrance.

[0107] In this embodiment, step S30 includes: taking minimizing the total operating cost of the system as the objective function, and setting the output constraints of the generator set and the transmission capacity constraints of the line; and, based on the power balance conditions of the power nodes, substituting the spatiotemporal distribution data of the charging load as known parameters into the objective function and the constraints to formulate a scheduling plan for the generator set in the continuous time domain.

[0108] Therefore, the optimal operating model of the power system in the continuous time domain is as follows: (31).

[0109] It should be noted that equation (31) represents the operating target of the power system; The total cost of unit dispatching in the power system; and Generator sets g exist The amount of output and marginal cost at any given moment.

[0110] (32).

[0111] It should be noted that equation (32) represents the approximate marginal cost of the generator set; and Generator sets g In the approximate piecewise linear function of the cost curve, the first...i The slope and intercept of the segment; It is the set of interval numbers for an approximate piecewise linear function.

[0112] (33).

[0113] It should be noted that equation (33) represents the power balance of power nodes; and They are nodes b The collection consisting of connected generator sets and charging stations; For a set of power nodes, For a collection of power lines, there are ; For charging stations m exist The charging power at any given time; For nodes b exist The normal load at any given time; and For nodes b and nodes d exist Voltage phase angle at any given moment; For the line The reactance; The dual multiplier of equation (33) is, in physical terms, a node. b exist Electricity price at any given moment.

[0114] (34); (35); (36); (37); (38).

[0115] It should be noted that equation (34) represents the charging power of the charging station; For charging stations m exist The number of charging vehicles at any given time; Equation (35) represents the power line power constraint; For the line The active capacity; Equation (36) represents the range of node voltage phase angle variation; and These are the upper and lower limits of the voltage phase angle, respectively; Equation (37) represents the setting of the voltage phase angle reference node; For reference node in The voltage phase angle at a given moment; Equation (38) represents the output range of the generator set; and Generator sets g The upper and lower limits of output.

[0116] In this embodiment, although the aforementioned linearization has transformed the model into a mixed-integer linear programming problem, the variables are still continuous-time functions. Therefore, it is necessary to further utilize Bernstein polynomial approximation to discretize these continuous-time function variables into finite algebraic coefficients in order to finally form a solvable algebraic optimization model. Step S40 includes: Step S41: Using Bernstein polynomial approximation, the continuous-time function variables in the traffic network user equilibrium model are expressed as algebraic forms of interpolation coefficients, and the complementary constraints and nonlinear terms in the traffic network user equilibrium model are converted into algebraic mixed-integer linear constraints.

[0117] Specifically, step S41 includes: approximating the one-dimensional continuous-time function variables in the traffic network user equilibrium model using Bernstein polynomials, representing them as cubic Bernstein polynomial interpolation coefficient vectors in each time segment, and applying continuity constraints to the interpolation coefficient vectors of adjacent time segments; approximating the two-dimensional continuous-time function variables in the traffic network user equilibrium model using Bernstein polynomials, representing them as cubic Bernstein polynomial interpolation coefficient matrices in each time and departure time grid, and applying continuity constraints to the interpolation coefficient matrices of adjacent grids; constraining the values ​​of the time-varying correlation matrix elements in the traffic network user equilibrium model to 0 or 1, and constraining their monotonically increasing nature in the time axis direction through the differential coefficient matrix; and converting the bilinear terms and complementary constraints in the traffic network user equilibrium model into a system of mixed integer linear inequalities in algebraic form by introducing auxiliary variables and 0-1 variables.

[0118] Therefore, the reconstruction method of the traffic network user equilibrium model based on Bernstein polynomial approximation is as follows (39) to (66): (39); (40).

[0119] It should be noted that equation (39) represents the algebraic equation obtained by approximating equation (1) with Bernstein polynomials; for exist Axis time period k The interpolation coefficient vector has a dimension of 4×1; K Let be the total number of possible departure times in the discrete time domain, then... Equation (40) represents the algebraic equation obtained by approximating (2) with Bernstein polynomials.

[0120] (41); (42).

[0121] It should be noted that equation (41) combined with equation (42) represents the algebraic constraints obtained by reconstructing equation (3) through Bernstein polynomial approximation; equation (41) will transform the function and The value is restricted to 0 or 1 (except for the step smoothing part); Equation (42) guarantees the function and exist Monotonically increasing in the axial direction; and They are respectively and exist Axis time period k and Axis time period t The interpolation coefficient matrix of the enclosed grid has a dimension of 4×4; This is the differential coefficient matrix, with a dimension of 4×4; T This represents the number of scheduling periods in the discrete time domain.

[0122] (43); (44).

[0123] It should be noted that equation (43) represents the algebraic constraint obtained by approximating equation (4) with Bernstein polynomials. Equation (44) represents the algebraic equation obtained by approximating equation (5) with Bernstein polynomials. It is a unit diagonal matrix with a dimension of 4×4.

[0124] (45); (46).

[0125] It should be noted that equation (45) represents the algebraic equation obtained by approximating equation (6) with Bernstein polynomials; for exist Axis time period t The interpolation coefficient vector has a dimension of 4×1; for exist Axis time period k and Axis time period t The interpolation coefficient matrix of the enclosed grid has a dimension of 4×4. Equation (46) represents the algebraic equation reconstructed by Bernstein polynomial approximation of equation (7); for exist Axis time period t The interpolation coefficient vector has a dimension of 4×1; for exist Axis time period k and Axis time period t The interpolation coefficient matrix of the enclosed grid has a dimension of 4×4.

[0126] (47); (48).

[0127] It should be noted that equation (47) represents the algebraic constraint obtained by reconstructing the bilinear linearization constraint (22) corresponding to equation (6) through Bernstein polynomial approximation. Equation (48) represents the algebraic constraint obtained by reconstructing the bilinear linearization constraint (23) corresponding to equation (7) through Bernstein polynomial approximation.

[0128] (49); (50).

[0129] It should be noted that equation (49) represents the algebraic equation obtained by approximating equation (8) with Bernstein polynomials; and They are respectively and exist Axis time period t The interpolation coefficient vector has a dimension of 4×1. Equation (50) represents the algebraic equation reconstructed by Bernstein polynomial approximation of equation (9); and They are respectively and exist Axis time period t The interpolation coefficient vector has a dimension of 4×1.

[0130] (51); (52).

[0131] It should be noted that equation (51) represents the algebraic equation obtained by approximating equation (10) with Bernstein polynomials; for exist Axis time period t The interpolation coefficient vector has a dimension of 4×1. Equation (52) represents the algebraic equation reconstructed by Bernstein polynomial approximation of equation (11); for exist The interpolation coefficient vector for the time interval t is 4×1.

[0132] (53).

[0133] It should be noted that equation (53) represents the algebraic equation obtained by approximating equation (12) with Bernstein polynomials; for exist The interpolation coefficient vector for the time interval t, with a vector dimension of 4×1; for exist The fourth element of the interpolation coefficient vector for the last time interval T of the axis.

[0134] (54); (55); (56); (57).

[0135] It should be noted that equation (54) represents the algebraic constraint obtained by reconstructing the equivalent linear constraint equation (24) of equation (14) through Bernstein polynomial approximation; for exist Axis time period t The interpolation coefficient vector has a dimension of 4×1. Equation (55) represents the algebraic constraint obtained by reconstructing the equivalent linear constraint (25) of equation (15) through Bernstein polynomial approximation; for exist Axis time period t The interpolation coefficient vector has a dimension of 4×1. Equation (56) represents the algebraic equation reconstructed by Bernstein polynomial approximation of equation (16); for exist The interpolation coefficient vector for axis time period k has a dimension of 4×1. Equation (57) represents the algebraic equation reconstructed by Bernstein polynomial approximation of equation (17); for exist The interpolation coefficient vector for axis time period k has a dimension of 4×1; and They are respectively and exist Axis time period k and Axis time period t The interpolation coefficient matrix of the enclosed grid has a dimension of 4×4.

[0136] (58); (59); (60).

[0137] It should be noted that equation (58) represents the algebraic equation obtained by approximating equation (18) with Bernstein polynomials; and They are respectively and exist Axis time period t The interpolation coefficient vector has a dimension of 4×1. Equations (59) and (60) respectively represent the bilinear terms in equation (17). The equivalent linear constraints (26) and (27) are approximated by Bernstein polynomials to reconstruct the algebraic constraints.

[0138] (61).

[0139] It should be noted that equation (61) represents the bilinear term in equation (17). The equivalent linear constraint (28) is approximated by Bernstein polynomials to reconstruct the algebraic constraints.

[0140] (62); (63); (64).

[0141] It should be noted that equation (62) represents the algebraic equation obtained by approximating equation (19) with Bernstein polynomials; for exist Axis time period kThe interpolation coefficient vector has a dimension of 4×1. Equation (63) represents the algebraic constraint obtained by reconstructing the equivalent linear constraint (29) of equation (20) through Bernstein polynomial approximation; for exist Axis time period k The interpolation coefficient vector has a dimension of 4×1. Equation (64) represents the algebraic constraint obtained by reconstructing the equivalent linear constraint (30) of equation (21) through Bernstein polynomial approximation; for exist Axis time period k The interpolation coefficient vector has a dimension of 4×1.

[0142] (65); (66); (67).

[0143] It should be noted that equation (65) is a Bernstein polynomial approximation of the next-dimensional function variable. Continuity constraints. and respectively function variables exist Axis time period t The 4th element of the interpolation coefficient vector and the time period t +1 is the first element of the interpolation coefficient vector.

[0144] It should be noted that equation (66) is a Bernstein polynomial approximation of the next-dimensional function variable. Continuity constraints. and respectively function variables exist Axis time period k The 4th element of the interpolation coefficient vector and the time period k +1 is the first element of the interpolation coefficient vector.

[0145] It should be noted that equation (67) represents the two-dimensional function variables under Bernstein polynomial approximation. Continuity constraints. function variables exist Axis time period k and Axis time period t The fourth element of the interpolation coefficient matrix of the enclosed grid; function variables exist Axis time period k +1 and Axis time period t The first row of the interpolation coefficient matrix of the enclosed grid; function variables exist Axis time period k and Axis time period t The fourth column element of the interpolation coefficient matrix of the enclosed grid; function variables exist Axis time period k and Axis time period t The first column element of the interpolation coefficient matrix of the grid enclosed by +1.

[0146] Step S42: Using Bernstein polynomial approximation, the continuous-time function variables in the optimal power system operation model are expressed as algebraic forms of interpolation coefficients, and the optimal power system operation model is transformed into an algebraic linear programming model.

[0147] Specifically, step S42 includes: performing Bernstein polynomial approximation on the continuous-time function variables of generator output, node voltage phase angle, and charging power of charging stations in the optimal operation model of the power system, representing them as interpolation coefficient vectors of cubic Bernstein polynomials in each time segment, and applying continuity constraints to the interpolation coefficient vectors of adjacent time segments; and converting the objective function and all constraints in the optimal operation model of the power system into algebraic forms with respect to the interpolation coefficient vectors.

[0148] Therefore, the power system optimal operation model reconstruction method based on Bernstein polynomial approximation is as follows: (68) to (76): (68).

[0149] It should be noted that equation (68) represents the algebraic objective obtained by reconstructing equation (31) through Bernstein polynomial approximation; and They are respectively and exist Axis time period t The interpolation coefficient vector has a dimension of 4×1.

[0150] (69); (70).

[0151] It should be noted that equation (69) represents the algebraic constraint obtained by approximating equation (32) with Bernstein polynomials. Equation (70) represents the algebraic equation obtained by approximating equation (33) with Bernstein polynomials. , , and They are respectively , , and exist The interpolation coefficient vector for the time interval t is 4×1.

[0152] (71).

[0153] It should be noted that equation (71) represents the algebraic constraint obtained by reconstructing equation (34) through Bernstein polynomial approximation; for exist Axis time period t The interpolation coefficient vector has a dimension of 4×1.

[0154] (72); (73); (74); (75).

[0155] It should be noted that equation (72) represents the algebraic constraint obtained by reconstructing equation (35) through Bernstein polynomial approximation. Equation (73) represents the algebraic constraint obtained by reconstructing equation (36) through Bernstein polynomial approximation. Equation (74) represents the algebraic constraint obtained by reconstructing equation (37) through Bernstein polynomial approximation. for exist Axis time period t The interpolation coefficient vector has a dimension of 4×1. Equation (75) represents the algebraic constraint obtained by approximating (38) with Bernstein polynomials.

[0156] (76).

[0157] It should be noted that equation (76) is a Bernstein polynomial approximation of the next-dimensional function variable. Continuity constraints. and respectively function variables exist Axis time period t The 4th element of the interpolation coefficient vector and the time period t +1 is the first element of the interpolation coefficient vector.

[0158] In this embodiment, step S50 includes: obtaining the interpolation coefficient vector obtained after solving the algebraic joint optimization model; and using the preset Bernstein polynomial basis functions and the interpolation coefficient vector to perform calculations to reconstruct the unit's output time-series curve in the continuous time domain, which serves as the optimal scheduling plan.

[0159] Therefore, the optimal unit scheduling plan for a power system in the continuous time domain is as follows: (77); (78).

[0160] Equation (77) represents the optimal unit scheduling plan of the power system in the continuous time domain. and These are, respectively, the unit output time-series curves and the interpolation coefficient vectors during the economically optimal operation of the power system; where... Belongs to the t Time segments [ t -1, t ], Let be the cubic Bernstein basis function vector on this segment. The curves of different segments are naturally connected by the continuity constraint equation (76). Equation (78) represents the calculation formula for the cubic Bernstein polynomial; The nth element of a 3rd-degree Bernstein polynomial vector; Let be the combination number, then we have .

[0161] Finally, this application constructs a traffic network user equilibrium model that takes into account the characteristics of traffic flow delay propagation on a continuous time scale. It can accurately characterize the continuous dynamic evolution of vehicle queuing, dissipation and charging processes on roads and charging stations. It overcomes the shortcomings of discrete-time scheduling in describing the continuous changes in traffic flow and the dynamic fluctuations of charging load within a time period, and provides theoretical support for the accurate assessment of the spatiotemporal distribution of charging load.

[0162] Furthermore, this application utilizes Bernstein polynomial approximation theory to transform complex optimization problems in continuous-time function space into mixed-integer linear programming models in algebraic space, enabling the models to be solved efficiently using existing commercial solvers. This solves the problem of continuous-time optimization being difficult to compute in practical engineering and demonstrates good feasibility.

[0163] Furthermore, through continuous time-coordinated optimization, this application can more rationally formulate the power output plan of generator units in the power system, better match the spatiotemporal fluctuations of charging load, reduce the waste of reserve capacity or insufficient ramping caused by load forecast deviations and fluctuations within a time period, thereby reducing system operating costs and improving the economy and safety of power-transportation system operation.

[0164] Furthermore, this application provides a specific example for demonstration, and the simulation settings are as follows: This section is in Figure 3 The 12-node transportation network shown Figure 4 The effectiveness of the proposed method was verified on the 18-node distribution network coupling test system shown. The test traffic network includes 19 road segments and 6 charging stations. The test distribution network has a radial topology and contains 17 lines. Substation S is connected to the power node B1 where the bus is located, and distributed generator sets G1, G2, and G3 are connected to power nodes B5, B13, and B18, respectively. The 6 charging stations are connected to the distribution network through coupling nodes. Charging stations 1 to 6 are located at traffic nodes T5, T6, T7, T8, T10, and T12, respectively, corresponding to power nodes B3, B12, B5, B13, B16, and B18.

[0165] To systematically evaluate the impact of differentiated traffic flow models and time discretization strategies on the accuracy of dynamic characterization of charging load, the economy of scheduling plans, and the efficiency of model solving, the following comparative scheme is set up. The specific scheme settings are as follows: Case I: A static traffic assignment model is used, without considering queuing dynamics, and the time step for the power-transportation system scheduling is 15 minutes.

[0166] Case II: A semi-dynamic traffic flow model is adopted, and the time step for power-transportation system scheduling is 15 minutes.

[0167] Case III: A discretized dynamic traffic flow model is adopted, and the time step for power-transportation system scheduling is 15 minutes.

[0168] Case IV: A discretized dynamic traffic flow model is adopted, and the time step for power-transportation system scheduling is 5 minutes.

[0169] Case V: The proposed continuous-time collaborative optimization method is adopted.

[0170] The evaluation employs a two-phase framework of planning and implementation: In the planning phase, each scheme formulates its unit output plan based on its corresponding mathematical model. In the implementation phase, the above plans and predictions are embedded into a ground truth environment constructed by a 5-second continuous traffic flow simulation. Due to differences in the accuracy of the traffic flow models of each scheme in characterizing the dynamic queuing process and the spatiotemporal distribution of charging load, a deviation occurs between the actual charging load and the planned prediction. Substation S maintains its planned output unchanged, while distributed units, as balancing resources, adjust their output under ramp-up constraints to mitigate the aforementioned charging load deviation, and the total implementation cost and deviation amount are evaluated.

[0171] Ultimately, the following results were obtained: 1. Accuracy Analysis of Charging Load and Traffic Flow Dynamics: The accuracy of each scheme in depicting the dynamic queuing process of traffic flow varies significantly. This difference directly determines the accuracy of road delay and bottleneck queuing predictions, and further influences the spatiotemporal distribution of charging load. Specifically, Case I completely fails to characterize departure time selection and queuing evolution, underestimating the total road delay by 92%. While Case II partially reflects the degree of road congestion, it cannot accurately capture the queuing generation and decay process and delay propagation, underestimating the total road delay by 65%. Although Cases III and IV introduce queuing dynamics, they are limited by the step approximation and the assumption of uniform distribution within the time period, underestimating the total road delay by 27% and 3%, respectively. These traffic flow prediction biases lead to a significant shift in the spatiotemporal distribution of electric vehicles arriving at charging stations, thus causing errors in charging load prediction. The overall quantitative error is shown in Table 1.

[0172] Table 1. Charging load and prediction error under different cases:

[0173] Specifically, the step approximations of Case III and IV cannot accurately depict the continuous dynamic process within a time period, resulting in significant intra-time deviations during the load ramp-up and pullback phases, such as... Figure 5 As shown in the shaded area. Meanwhile... Figure 5 The black line representing the true value is basically covered by the red line representing the scheme Case V. The simulation results verify the ability of the proposed continuous-time model to accurately characterize the queuing generation and extinction process and the spatiotemporal distribution of charging load, and provide a necessary model foundation for the precise coordination of transportation network and distribution network.

[0174] 2. Operational Economy and Safety Analysis: The model that does not consider queuing dynamics has the lowest cost but a deviation rate as high as 24.9% (Case I), which is not feasible in actual operation; the deviation rate of the 15-minute discrete dynamic model is 11.5% (Case III); the deviation rate of the 5-minute discrete dynamic model is 2.9% (Case IV). The proposed continuous-time model has a deviation rate of only 0.03%, as shown in Table 2.

[0175] Table 2. Operational economy and safety under different cases:

[0176] 3. Computational Efficiency Analysis: The increased complexity of the traffic flow model directly increases the solution burden, and the refinement of the time grid further leads to nonlinear expansion of the solution time. The solution time for the 15-minute discrete dynamic model is 52 minutes, and the solution time for the 5-minute discrete dynamic model is 201 minutes; the proposed continuous-time solution time is 73 minutes, which is 63.7% lower than the solution time of the 5-minute discrete dynamic model, as shown in Table 3.

[0177] Table 3. Computational efficiency under different cases:

[0178] The above results comprehensively verify that the proposed method has high commercial solvability while ensuring computational accuracy. At the same time, it fundamentally reduces the planning-realization deviation and adjustment costs, achieving a unity of accurate characterization, economic optimization and fast solution.

[0179] Based on the methods in the above embodiments, such as Figure 6 As shown in the illustration, this application provides an electronic device that may include a processor 100, a communication interface 200, a memory 300, and a communication bus 400. The processor, communication interface, and memory communicate with each other via the communication bus. The processor can invoke logical instructions stored in the memory to execute the methods described in the above embodiments.

[0180] Furthermore, the logical instructions in the aforementioned memory can be implemented as software functional units and, when sold or used as independent products, can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of this application, in essence, or the part that contributes to the prior art, or a portion of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of this application.

[0181] Based on the methods in the above embodiments, this application provides a computer-readable storage medium storing a computer program that, when run on a processor, causes the processor to execute the methods in the above embodiments.

[0182] Based on the methods in the above embodiments, this application provides a computer program product that, when run on a processor, causes the processor to execute the methods in the above embodiments.

[0183] It is understood that the processor in the embodiments of this application can be a central processing unit (CPU), or other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, transistor logic devices, hardware components, or any combination thereof. A general-purpose processor can be a microprocessor or any conventional processor.

[0184] The method steps in this application embodiment can be implemented in hardware or by a processor executing software instructions. The software instructions can consist of corresponding software modules, which can be stored in random access memory (RAM), flash memory, read-only memory (ROM), programmable read-only memory (PROM), erasable programmable read-only memory (EPROM), electrically erasable programmable read-only memory (EEPROM), registers, hard disks, portable hard disks, CD-ROMs, or any other form of storage medium known in the art. An exemplary storage medium is coupled to the processor, enabling the processor to read information from and write information to the storage medium. Of course, the storage medium can also be a component of the processor. The processor and the storage medium can reside in an ASIC.

[0185] In the above embodiments, implementation can be achieved entirely or partially through software, hardware, firmware, or any combination thereof. When implemented using software, it can be implemented entirely or partially as a computer program product. The computer program product includes one or more computer instructions. When the computer program instructions are loaded and executed on a computer, all or part of the processes or functions described in the embodiments of this application are generated. The computer can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable device. The computer instructions can be stored in a computer-readable storage medium or transmitted through the computer-readable storage medium. The computer instructions can be transmitted from one website, computer, server, or data center to another website, computer, server, or data center via wired (e.g., coaxial cable, fiber optic, digital subscriber line (DSL)) or wireless (e.g., infrared, wireless, microwave, etc.) means. The computer-readable storage medium can be any available medium that a computer can access or a data storage device such as a server or data center that integrates one or more available media. The available medium can be a magnetic medium (e.g., floppy disk, hard disk, magnetic tape), an optical medium (e.g., DVD), or a semiconductor medium (e.g., solid-state disk (SSD)).

[0186] It is understood that the various numerical designations used in the embodiments of this application are merely for the convenience of description and are not intended to limit the scope of the embodiments of this application.

[0187] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of this application and is not intended to limit this application. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of this application should be included within the scope of protection of this application.

Claims

1. A continuous-time cooperative scheduling method for vehicle-road networks based on polynomial approximation, characterized in that, include: Step S10: Construct an extended traffic network model based on graph theory, wherein the extended traffic network model is used to generate a set of alternative routes for different types of vehicles; Step S20: Based on the traffic network extended model, construct a traffic network user equilibrium model in the continuous time domain; the traffic network user equilibrium model is used to simulate vehicle travel behavior and output the spatiotemporal distribution data of charging load. Step S30: Based on the spatiotemporal distribution data of the charging load, construct an optimal operation model of the power system in the continuous time domain; the optimal operation model of the power system is used to formulate a unit scheduling plan with the goal of economic optimization; Step S40: Using the Bernstein polynomial approximation algorithm, the solution spaces of the traffic network user equilibrium model and the power system optimal operation model are transformed from function space to algebraic space to obtain a joint optimization model in algebraic form. Step S50: Based on the solution results of the joint optimization model in algebraic form, the optimal unit scheduling plan of the power system in the continuous time domain is obtained by reverse deduction.

2. The continuous-time cooperative scheduling method for vehicle-road networks based on polynomial approximation as described in claim 1, characterized in that, Step S10 includes: The charging station nodes in the transportation network are hidden, the nodes in the transportation network are abstracted as points, and the roads connecting the nodes are abstracted as directed links to construct a first directed graph for the first type of vehicle path planning; Based on the first directed graph, self-circulating links are added to the charging station nodes to construct a second directed graph for the second type of vehicle path planning. The self-circulating links are used to characterize the vehicle charging process. Based on the first directed graph and the second directed graph, alternative path sets are generated for the first type of vehicle and the second type of vehicle, respectively.

3. The continuous-time cooperative scheduling method for vehicle-road networks based on polynomial approximation as described in claim 1, characterized in that, The traffic network user equilibrium model includes: a traffic flow delay propagation model and a user equilibrium criterion; step S20 includes: Based on the set of alternative paths output by the traffic network extension model, a traffic flow delay propagation model is constructed. The traffic flow delay propagation model describes the dynamic propagation process of vehicles on the path through a time-varying correlation matrix, and determines the cumulative number of arrivals and departures of vehicles on roads and charging stations based on the first-in-first-out principle and the relationship between arrival and departure signals of vehicles on adjacent road segments. Based on the cumulative number of arrivals and departures, the queuing status of vehicles on the road and the queuing status and charging status at the charging station are determined. Based on the queuing status and the charging status, a user equilibrium criterion is constructed; the user equilibrium criterion is used to calculate the comprehensive travel cost of a vehicle choosing different routes at different departure times based on the queuing status and the charging status, and to determine the travel behavior of the vehicle based on the comprehensive travel cost. Based on the traffic flow delay propagation model and the user equilibrium criterion, the spatiotemporal distribution data of charging load are obtained.

4. The continuous-time cooperative scheduling method for vehicle-road networks based on polynomial approximation as described in claim 3, characterized in that, Step S20 is followed by: By introducing auxiliary variables and 0-1 variables, the bilinear terms and complementary constraints in the traffic flow delay propagation model are linearized to obtain a linearized traffic network user equilibrium model.

5. The continuous-time cooperative scheduling method for vehicle-road networks based on polynomial approximation as described in claim 1, characterized in that, Step S30 includes: The objective function is to minimize the total operating cost of the system, and constraints are set for the output of the generator sets and the transmission capacity of the lines. Based on the power balance conditions of the power nodes, the spatiotemporal distribution data of the charging load is substituted as known parameters into the objective function and constraints to formulate a scheduling plan for the units in the continuous time domain.

6. The continuous-time cooperative scheduling method for vehicle-road networks based on polynomial approximation as described in claim 1, characterized in that, Step S40 includes: Step S41: Using Bernstein polynomial approximation, the continuous-time function variables in the traffic network user equilibrium model are expressed as the algebraic form of interpolation coefficients, and the complementary constraints and nonlinear terms in the traffic network user equilibrium model are converted into algebraic mixed integer linear constraints. Step S42: Using Bernstein polynomial approximation, the continuous-time function variables in the optimal operation model of the power system are expressed as algebraic forms of interpolation coefficients, and the optimal operation model of the power system is transformed into an algebraic linear programming model.

7. The continuous-time cooperative scheduling method for vehicle-road networks based on polynomial approximation as described in claim 6, characterized in that, Step S41 includes: The one-dimensional continuous-time function variables in the traffic network user equilibrium model are approximated by Bernstein polynomials, and expressed as interpolation coefficient vectors of cubic Bernstein polynomials in each time segment, and a continuity constraint is applied to the interpolation coefficient vectors of adjacent time segments. The two-dimensional continuous-time function variables in the traffic network user equilibrium model are approximated by Bernstein polynomials. They are represented as the interpolation coefficient matrix of cubic Bernstein polynomials in the grid at each time and departure time, and continuity constraints are applied to the interpolation coefficient matrices of adjacent grids. The values ​​of the time-varying correlation matrix elements in the traffic network user equilibrium model are constrained to be 0 or 1, and their monotonically increasing nature in the time axis direction is constrained by the differential coefficient matrix. The bilinear terms and complementary constraints in the traffic network user equilibrium model are transformed into a system of mixed integer linear inequalities in algebraic form by introducing auxiliary variables and 0-1 variables.

8. The continuous-time cooperative scheduling method for vehicle-road networks based on polynomial approximation as described in claim 6, characterized in that, Step S42 includes: Bernstein polynomial approximation is performed on the continuous-time function variables of generator output, node voltage phase angle and charging station charging power in the optimal operation model of the power system. The variables are represented as interpolation coefficient vectors of cubic Bernstein polynomials in each time segment, and continuity constraints are applied to the interpolation coefficient vectors of adjacent time segments. The objective function and all constraints in the optimal operation model of the power system are converted into an algebraic form with respect to the interpolation coefficient vector.

9. The continuous-time cooperative scheduling method for vehicle-road networks based on polynomial approximation as described in claim 1, characterized in that, Step S50 includes: Obtain the interpolation coefficient vector obtained after solving the algebraic joint optimization model; By using the preset Bernstein polynomial basis functions and the interpolation coefficient vector, the output time sequence curve of the unit in the continuous time domain is reconstructed, which serves as the optimal unit scheduling plan.

10. An electronic device, characterized in that, Includes memory and one or more processors; The memory is coupled to the one or more processors, and the memory is used to store computer program code, the computer program code including computer instructions; The one or more processors invoke the computer instructions to cause the electronic device to execute the vehicle-road network continuous-time cooperative scheduling method based on polynomial approximation as described in any one of claims 1 to 9.

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