Train energy-saving optimization method and device and storage medium
Patent Information
- Application Number
- CN202410324238.3
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2024-03-20
- Publication Date
- 2025-09-23
Smart Images
Figure CN120688197A_ABST
Abstract
Description
Technical Field
[0001] The present disclosure relates to the field of rail transportation technology, and in particular to a train energy-saving optimization method, device, and storage medium. Background Art
[0002] The rail transit system is the foundation of my country's transportation system. It can improve people's quality of life and promote social and economic development. However, it is also a major energy consumer in the industrial system, consuming a large amount of energy every day. In order to reduce the energy consumption and greenhouse gas emissions of the rail transit system, train energy-saving optimization has always been one of the key technologies that has received much attention. Train energy-saving optimization includes two levels of optimization problems: the bottom level is the energy-efficient train control problem (EETC), which is the basis of the train energy-saving optimization problem. The upper level is the energy-efficient train timetable optimization problem (EETT). Current train energy-saving optimization methods usually have shortcomings such as low computational efficiency, long computation time, inability to guarantee optimality, and difficulty in handling complex line condition constraints. Summary of the Invention
[0003] In view of this, the present disclosure proposes a train energy-saving optimization method, device and storage medium.
[0004] According to one aspect of the present disclosure, a train energy-saving optimization method is provided. The method comprises:
[0005] Obtain line data and train parameters of train operation;
[0006] Determining a train energy-saving convex optimization model, the train energy-saving convex optimization model including an objective function and constraints, the constraints including constraints on convex relaxation auxiliary variables, the convex relaxation auxiliary variables being used to replace non-convex terms in the train energy-saving optimization model;
[0007] Based on line data and train parameters, the train energy-saving convex optimization model is solved with the minimum train operation energy consumption as the optimization goal to determine the train operation status information.
[0008] In one possible implementation, the train parameters include one or more of the following: train mass, resistance parameters, traction efficiency, braking feedback efficiency, maximum traction power, maximum braking power, maximum traction constant torque coefficient, and maximum braking constant torque coefficient.
[0009] In one possible implementation, the non-convex terms include the inverse term of the average speed in the subinterval and the square term of the speed in the subinterval. The constraint conditions for the convex relaxation auxiliary variables represent that the convex relaxation auxiliary variables are three-dimensional second-order cones. The optimal solution of the train energy-saving convex optimization model is obtained when the convex relaxation auxiliary variables are equal to the inverse term of the average speed in the subinterval and the square term of the speed in the subinterval, respectively.
[0010] In one possible implementation, the train energy-saving convex optimization model includes a train operation curve energy-saving convex optimization model. The objective function of the train operation curve energy-saving convex optimization model is the sum of the energy consumption of each subinterval. The constraints of the train operation curve energy-saving convex optimization model also include one or more of the following:
[0011] Energy consumption constraints in each sub-interval, constraints on train traction / braking force in each sub-interval, constraints on line speed limit in each sub-interval, constraints on running time, constraints on average speed in each sub-interval, constraints on line length in each sub-interval and boundary constraints.
[0012] In one possible implementation, the line data includes line length, line speed limit, line elevation, and the start and end positions of the phase zone; the train operation status information includes the optimized train operation speed curve and the optimized train traction / braking force curve; and each sub-interval is divided based on the line speed limit and line elevation.
[0013] In a possible implementation, the train energy-saving convex optimization model includes a train timetable energy-saving convex optimization model, and determining the train energy-saving convex optimization model includes:
[0014] Based on the running time allocation optimization model between stations and the energy-saving convex optimization model of the train running curve within each station, the train timetable energy-saving convex optimization model is determined. In the train timetable energy-saving convex optimization model, each station is divided into multiple sub-intervals.
[0015] In one possible implementation, the objective function of the train schedule energy-saving convex optimization model is the sum of the energy consumption between stations, and the energy consumption between each station is the sum of the energy consumption of each subinterval between stations. The constraints of the train schedule energy-saving convex optimization model also include one or more of the following:
[0016] Constraints on the running time between stations, energy consumption constraints within each sub-interval between stations, train traction / braking force constraints within each sub-interval between stations, line speed limit constraints within each sub-interval between stations, average speed constraints within each sub-interval between stations, line length constraints within each sub-interval between stations, and boundary constraints.
[0017] In a possible implementation, the line data also includes station and inter-station information, and the train operation status information also includes an optimized train operation schedule.
[0018] In a possible implementation, the objective function of the optimization model for distributing the operating time between stations is the sum of the energy consumption between stations, and the constraints of the optimization model for distributing the operating time between stations include constraints on the operating time between stations.
[0019] According to another aspect of the present disclosure, a train energy-saving optimization device is provided. The device includes:
[0020] An acquisition module is used to obtain line data and train parameters of train operation;
[0021] a determination module, configured to determine a train energy-saving convex optimization model, the train energy-saving convex optimization model including an objective function and constraints, the constraints including constraints on convex relaxation auxiliary variables, the convex relaxation auxiliary variables being used to replace non-convex terms in the train energy-saving optimization model;
[0022] The solution module is used to solve the train energy-saving convex optimization model based on line data and train parameters, with the minimum train operation energy consumption as the optimization goal, and determine the train operation status information.
[0023] In one possible implementation, the train parameters include one or more of the following: train mass, resistance parameters, traction efficiency, braking feedback efficiency, maximum traction power, maximum braking power, maximum traction constant torque coefficient, and maximum braking constant torque coefficient.
[0024] In one possible implementation, the non-convex terms include the inverse term of the average speed in the subinterval and the square term of the speed in the subinterval. The constraint conditions for the convex relaxation auxiliary variables represent that the convex relaxation auxiliary variables are three-dimensional second-order cones. The optimal solution of the train energy-saving convex optimization model is obtained when the convex relaxation auxiliary variables are equal to the inverse term of the average speed in the subinterval and the square term of the speed in the subinterval, respectively.
[0025] In one possible implementation, the train energy-saving convex optimization model includes a train operation curve energy-saving convex optimization model. The objective function of the train operation curve energy-saving convex optimization model is the sum of the energy consumption of each subinterval. The constraints of the train operation curve energy-saving convex optimization model also include one or more of the following:
[0026] Energy consumption constraints in each sub-interval, constraints on train traction / braking force in each sub-interval, constraints on line speed limit in each sub-interval, constraints on running time, constraints on average speed in each sub-interval, constraints on line length in each sub-interval and boundary constraints.
[0027] In one possible implementation, the line data includes line length, line speed limit, line elevation, and the start and end positions of the phase zone; the train operation status information includes the optimized train operation speed curve and the optimized train traction / braking force curve; and each sub-interval is divided based on the line speed limit and line elevation.
[0028] In one possible implementation, the train energy-saving convex optimization model includes a train schedule energy-saving convex optimization model, and a determination module for:
[0029] Based on the running time allocation optimization model between stations and the energy-saving convex optimization model of the train running curve within each station, the train timetable energy-saving convex optimization model is determined. In the train timetable energy-saving convex optimization model, each station is divided into multiple sub-intervals.
[0030] In one possible implementation, the objective function of the train schedule energy-saving convex optimization model is the sum of the energy consumption between stations, and the energy consumption between each station is the sum of the energy consumption of each subinterval between stations. The constraints of the train schedule energy-saving convex optimization model also include one or more of the following:
[0031] Constraints on the running time between stations, energy consumption constraints within each sub-interval between stations, train traction / braking force constraints within each sub-interval between stations, line speed limit constraints within each sub-interval between stations, average speed constraints within each sub-interval between stations, line length constraints within each sub-interval between stations, and boundary constraints.
[0032] In a possible implementation, the line data also includes station and inter-station information, and the train operation status information also includes an optimized train operation schedule.
[0033] In a possible implementation, the objective function of the optimization model for distributing the operating time between stations is the sum of the energy consumption between stations, and the constraints of the optimization model for distributing the operating time between stations include constraints on the operating time between stations.
[0034] According to another aspect of the present disclosure, a train energy-saving optimization device is provided, comprising: a processor; a memory for storing processor-executable instructions; wherein the processor is configured to implement the above method when executing the instructions stored in the memory.
[0035] According to another aspect of the present disclosure, a non-volatile computer-readable storage medium is provided, on which computer program instructions are stored, wherein the computer program instructions implement the above method when executed by a processor.
[0036] According to another aspect of the present disclosure, a computer program product is provided, including a computer-readable code, or a non-volatile computer-readable storage medium carrying the computer-readable code. When the computer-readable code runs in a processor of an electronic device, the processor in the electronic device executes the above method.
[0037] According to the embodiment of the present application, a train energy-saving convex optimization model can be determined, and based on the acquired line data and train parameters of the train operation, the train energy-saving convex optimization model can be solved with the minimum train operation energy consumption as the optimization goal, and the train operation status information can be determined. By introducing convex relaxation auxiliary variables for replacing non-convex terms in the train energy-saving optimization model, and making the constraints of the train energy-saving convex optimization model include constraints for convex relaxation auxiliary variables, the train energy-saving optimization problem can be converted into a second-order cone programming problem (i.e., a convex optimization problem), which can achieve a stable and fast solution effect, and can obtain the global optimal solution. It can also handle a variety of complex line constraints, thereby improving computing efficiency and saving computing resources.
[0038] Further features and aspects of the present disclosure will become apparent from the following detailed description of exemplary embodiments with reference to the attached drawings. BRIEF DESCRIPTION OF THE DRAWINGS
[0039] The accompanying drawings, which are incorporated in and constitute a part of the specification, illustrate exemplary embodiments, features, and aspects of the disclosure and, together with the description, serve to explain the principles of the disclosure.
[0040] Figure 1 A schematic diagram illustrating an application scenario according to an embodiment of the present application.
[0041] Figure 2 A flow chart of a train energy-saving optimization method according to an embodiment of the present application is shown.
[0042] Figure 3 A schematic diagram showing line data according to an embodiment of the present application is shown.
[0043] Figure 4 A schematic diagram showing the segmentation of train track sections according to an embodiment of the present application is shown.
[0044] Figure 5 A schematic diagram showing an optimized train running speed curve according to an embodiment of the present application is shown.
[0045] Figure 6 A schematic diagram showing inter-station line data of an operation embodiment of the present application is shown.
[0046] Figure 7 A schematic diagram illustrating verification of the effect of convex relaxation auxiliary variables on the exactness according to an embodiment of the present application is shown.
[0047] Figure 8 A schematic diagram showing a comparison of computational efficiency for processing large-scale problems according to an embodiment of the present application is shown.
[0048] Figure 9 A schematic diagram showing a comparison of computational efficiency for processing large-scale problems according to an embodiment of the present application is shown.
[0049] Figure 10 A schematic diagram showing a comparison of computational efficiency for processing large-scale problems according to an embodiment of the present application is shown.
[0050] Figure 11 A structural diagram of a train energy-saving optimization device according to an embodiment of the present application is shown.
[0051] Figure 12 It is a block diagram of a device 1900 for train energy-saving optimization according to an exemplary embodiment. DETAILED DESCRIPTION
[0052] Various exemplary embodiments, features, and aspects of the present disclosure will be described in detail below with reference to the accompanying drawings. The same reference numerals in the accompanying drawings represent elements with the same or similar functions. Although various aspects of the embodiments are shown in the accompanying drawings, the drawings are not necessarily drawn to scale unless otherwise indicated.
[0053] The word “exemplary” is used exclusively herein to mean “serving as an example, example, or illustration.” Any embodiment described herein as “exemplary” is not necessarily to be construed as preferred or advantageous over other embodiments.
[0054] In addition, numerous specific details are provided in the following detailed description to better illustrate the present disclosure. Those skilled in the art will appreciate that the present disclosure can be practiced without certain specific details. In some instances, methods, means, components, and circuits well known to those skilled in the art are not described in detail in order to highlight the main points of the present disclosure.
[0055] The rail transit system is the foundation of my country's transportation system, improving people's quality of life and promoting social and economic development. However, it is also a major energy consumer in the industrial system, consuming large amounts of energy every day. To reduce the energy consumption and greenhouse gas emissions of rail transit systems, train energy-saving optimization has always been a key technology that has attracted much attention. Train energy-saving optimization involves two levels of optimization problems: the bottom level is the train operation curve energy-saving optimization problem (EETC), which is the foundation of train energy-saving optimization problems; and the upper level is the train timetable energy-saving optimization problem (EETT). Current train energy-saving optimization methods often suffer from low computational efficiency, long computation time, inability to guarantee optimality, and difficulty handling complex line condition constraints.
[0056] In view of this, the present application provides a train energy-saving optimization method, device and storage medium. The method of the present application can determine a train energy-saving convex optimization model, and based on the acquired train operation line data and train parameters, solve the train energy-saving convex optimization model with the minimum train operation energy consumption as the optimization goal, determine the train operation status information, and by introducing convex relaxation auxiliary variables for replacing non-convex terms in the train energy-saving optimization model, and making the constraints of the train energy-saving convex optimization model include constraints for convex relaxation auxiliary variables, it is possible to convert the train energy-saving optimization problem into a second-order cone programming problem (i.e., a convex optimization problem), achieve a stable and fast solution effect, and obtain a global optimal solution, and be able to handle a variety of complex line constraints, thereby improving computing efficiency and saving computing resources.
[0057] Figure 1 Schematic diagram showing an application scenario according to an embodiment of the present application. Figure 1 As shown, a train energy-saving convex optimization model can be deployed on the train energy-saving optimization system of an embodiment of the present application. The train energy-saving convex optimization model can include a train operation curve energy-saving convex optimization model and a train timetable energy-saving convex optimization model. The train operation curve energy-saving convex optimization model can be used to solve the train operation curve energy-saving optimization problem EETC, and the train timetable energy-saving convex optimization model can be used to solve the train timetable energy-saving optimization problem EETT.
[0058] In the application scenario of the embodiment of the present application, the train energy-saving optimization system can obtain line data and train parameters of the train operation, use the train operation curve energy-saving convex optimization model or the train timetable energy-saving convex optimization model to solve the problem with the minimum train operation energy consumption as the optimization goal, and output the optimized train operation status information. Specifically, when the train operation curve energy-saving convex optimization model is used for solution, the output train operation status information may include the optimized train operation speed curve and the optimized train traction / braking force curve; when the train timetable energy-saving convex optimization model is used for solution, the output train operation status information may include the optimized train operation timetable. The output train operation status information may also include train operation energy consumption.
[0059] The train energy-saving optimization system of the embodiments of the present application can be deployed on a terminal device or server. The terminal device can be any one or more of a mobile phone, a foldable electronic device, a tablet computer, a desktop computer, a laptop computer, a handheld computer, a notebook computer, an ultra-mobile personal computer (UMPC), a netbook, a cellular phone, or a personal digital assistant (PDA). The embodiments of the present disclosure do not impose any particular restrictions on the specific type of terminal device, and the terminal device can have wired or wireless communication capabilities.
[0060] The server can be located locally or in the cloud, and can be a physical device or a virtual device, such as a virtual machine or container, and has wireless communication capabilities, wherein the wireless communication capabilities can be set in the chip (system) or other parts or components of the server. The wireless communication function can be implemented, for example, through mobile communication technologies such as 2G / 3G / 4G / 5G, as well as Wi-Fi, Bluetooth, frequency modulation (FM), digital radio, satellite communication, etc. Communication can also be carried out through wired connections to achieve interaction with other devices.
[0061] Figure 2 A flow chart of a train energy-saving optimization method according to an embodiment of the present application is shown. The method can be used in a terminal device or a server, such as Figure 2 As shown, the method may include:
[0062] Step S201: Acquire the line data and train parameters of the train.
[0063] Train parameters can be used to represent train characteristics. Train parameters may include one or more of the following: train mass M, resistance parameters (A, B, C), traction efficiency η t , Braking feedback efficiency η b , maximum traction power P t , Maximum braking power P b , maximum traction constant torque coefficient (tr1 and tr2), maximum braking constant torque coefficient (br1 and br2).
[0064] When solving the energy-saving convex optimization model of the train operation curve, the line data may include the line length S, line speed limit, line elevation, and the start and end positions of the phase zone. The line elevation can be used to represent the slope information in the line. When solving the energy-saving convex optimization model of the train schedule, the line data may also include station and inter-station information. Stations can be represented by station signs, and inter-station information may include the operating time range between each station. k is the inter-station identifier, and - and + can represent the lower and upper bounds of the inter-station running time respectively.
[0065] See also Figure 3 , shows a schematic diagram of line data according to an embodiment of the present application. Figure 3 As shown, the total length of the line is 100.8 km, and there are 18 stations along the line (see Figure 3 The line has 17 stations (marked 0-17) and 7 phase zones (gray areas in the figure). The line speed limit (red line in the figure), line elevation (blue line in the figure) and the start and end positions of the phase zones are shown in the figure.
[0066] Step S202: Determine a train energy-saving convex optimization model.
[0067] The train energy-saving convex optimization model may include an objective function and constraints. The objective function may be associated with the train operation energy consumption. The constraints include constraints on convex relaxation auxiliary variables. The convex relaxation auxiliary variables may be used to replace non-convex terms in the train energy-saving optimization model.
[0068] Among them, the train energy-saving convex optimization model may include a train running curve energy-saving convex optimization model, and the train running curve energy-saving convex optimization model can be used to solve the train running curve energy-saving optimization problem EETC. In the embodiment of the present application, discrete approximation processing can be used to divide the entire interval [0, S] of the train operation into N sub-intervals based on the line speed limit and the line elevation (i.e., the line slope). For example, based on relevant technologies, the intervals with different line speed limits or different line elevations can be divided. Among them, l0~l N-1 Represents the length of each subinterval, and the length of each subinterval can be different. Figure 4 , showing a schematic diagram of train track segmentation according to an embodiment of the present application. Figure 4 As shown, the horizontal axis represents the position and the vertical axis represents the running speed, S0~S N It can represent the starting and ending positions of each sub-interval, v0~v N The running speed at the start and end positions of each sub-interval can be determined separately.
[0069] The energy-saving convex optimization model of train operation curve can be expressed as formula (1):
[0070]
[0071] Among them, the objective function of the energy-saving convex optimization model of the train operation curve is the sum of the energy consumption of each sub-interval E n It can represent the operating energy consumption in the nth subinterval, where N is the number of subintervals. n The calculation method can be found in formula (2):
[0072]
[0073] Among them, S n and S n+1 They can represent the starting and ending positions of the nth subinterval respectively. n Indicates the traction force / braking force of the train in the nth subinterval. In this application, it is assumed that the traction force / braking force of the train remains constant in the subinterval of the line division, that is, when s∈[s n ,s n+1 ],u n is a fixed value. t represents the traction efficiency, η b Indicates the braking feedback efficiency.
[0074] This application introduces the convex relaxation auxiliary variable ω n and σ n , to replace the non-convex terms. Among them, the non-convex terms can include the inverse term of the average speed in the subinterval and the square term of the velocity in the subinterval (also called the quadratic term, ). and Thus, the energy-saving optimization problem (EETC) for train operation curves can be relaxed into a convex optimization problem. A convex optimization problem refers to a problem where both the objective function and the constraints are convex. A key property of a convex function is that the function value between any two points within its domain is always greater than or equal to the function value on the line segment between those two points and a point on the function graph. This property gives convex optimization problems several advantageous properties, such as the fact that the local optimal solution is also the global optimal solution.
[0075] Referring to formula (1), the constraints on the auxiliary variables of convex relaxation can include is the average speed in the nth subinterval, v n is the velocity of the starting position of the nth subinterval, It can represent a three-dimensional second-order cone. These two constraints can be used to represent the convex relaxation auxiliary variable as a three-dimensional second-order cone (i.e., the rotation second-order cone 2xy≥z 2 ,x,y≥0, x, y, z correspond to the three axes in the three-dimensional coordinate system respectively). The constraints for the auxiliary variables of convex relaxation can also include making ω n Satisfy the speed limit requirements within the sub-interval, that is, in formula (1) in, It can indicate the line speed limit within the nth sub-interval.
[0076] The constraints of the train operation curve energy-saving convex optimization model may also include one or more of the following:
[0077] Energy consumption constraints in each sub-interval, constraints on train traction / braking force in each sub-interval, constraints on line speed limit in each sub-interval, constraints on running time, constraints on average speed in each sub-interval, constraints on line length in each sub-interval and boundary constraints.
[0078] Referring to formula (1), the energy consumption constraints within each sub-interval may include: E n ≥u n l n η b as well as Among them, l n represents the length of the nth subinterval, M represents the mass of the train, A, B, and C represent the resistance parameters, Indicates the gravity component resistance caused by the line slope in the nth subinterval. In this application, the average speed in the nth subinterval is That is, the average of the speeds of the starting and ending positions of the nth subinterval, where v n is the velocity of the starting position of the nth subinterval, v n+1 is the speed of the end position of the nth subinterval. To approximate the integral term By introducing convex relaxation auxiliary variables, we can finally Convert to Where n∈0,1,…,N-1. The constraints on the train traction / braking force in each subinterval may include: u n ≤P t σ n 、 and u n ≥P b σ n Among them, tr1 and tr2 can represent the maximum traction constant torque coefficient, br1 and br2 can represent the maximum braking constant torque coefficient, P t It can represent the maximum traction power, P b Can indicate the maximum braking power.
[0079] Constraints on line speed limits within each sub-interval may include:
[0080] Runtime constraints can include: Where T represents the train running time constraint.
[0081] Constraints on the average speed of each sub-interval may include:
[0082] The constraints on the line length within each sub-interval may include: n =s n+1 -s n Among them, s n+1 Indicates the end point of the nth subinterval, s n Indicates the starting position of the nth subinterval.
[0083] Boundary constraints may include: s0 = 0, s N =S、v0=0,v N =0.
[0084] In this application, the energy-saving convex optimization model of the train running curve is obtained by introducing convex relaxation auxiliary variables, which converts the nonlinear programming problem into a second-order cone programming problem to achieve a fast and efficient solution to the energy-saving optimization problem of the train running curve. Since the feasible domain of the second-order cone programming problem is larger than that of the nonlinear programming problem, the accuracy of the second-order cone problem is proved in this application. It can be proved in this application that the optimal solution of the train energy-saving convex optimization model is when the convex relaxation auxiliary variables are equal to the inverse of the average speed in the subinterval and the square of the speed in the subinterval respectively. Obtain.
[0085] In proving that the optimal solution is When obtained, it can be converted into a proof that there are no constraints The exactness of the auxiliary variables of the convex relaxation. This application defines no constraints The Hammer function and the corresponding Lagrangian function of the model shown in formula (1) below can prove that the convex relaxation auxiliary variable σ n The accuracy of the proposed method can be verified, and an additional conclusion can be drawn: the optimal energy consumption between train stations decreases as the given running time increases.
[0086] Secondly, this application can prove by contradiction that the convex relaxation auxiliary variable The accuracy is not limited to special cases. This special case is: a very steep downhill line connected to a very steep uphill line, and the train must use the braking cruise model to maintain the speed limit allowed by the line on the downhill line. However, according to the train line construction standards, such an extreme line is impossible to appear. Therefore, it can be considered that the convex relaxation auxiliary variable ω in this application n It's exact.
[0087] Using a convex energy-saving optimization model for train operation curves, we can solve for each station separately to determine the optimal train operating state for inter-station operation at the optimal energy consumption. However, for a line with multiple stations, simply optimizing the energy consumption of each inter-station operation does not guarantee optimal energy consumption for the entire line. Instead, we need to comprehensively consider the energy-saving optimization of the entire line's schedule, i.e., the train schedule energy-saving optimization problem.
[0088] In the energy-saving optimization problem of train timetable, the energy consumed between the kth stations E(T k ) is related to the optimization of energy-saving operation curves between stations. Therefore, the train schedule optimization problem actually includes two levels of optimization, namely the upper-level optimization problem of the distribution of running time between stations and the lower-level energy-saving optimization problem of the operation curve between each station. The two-level optimization problems are coupled with each other, and contain complex line constraints. In order to solve the train schedule optimization problem with two levels of problems coupled with each other, this application further proposes a train schedule energy-saving convex optimization model based on the train operation curve energy-saving convex optimization model. The model of this application can be solved stably and quickly using methods such as the interior point method, and the model has only polynomial complexity. In this process, the optimization target in the train operation curve energy-saving convex optimization model can be transformed into the sum of energy consumption between multiple stations.
[0089] The train energy-saving convex optimization model may also include a train timetable energy-saving convex optimization model. In the train timetable energy-saving convex optimization model, each station interval may be divided into multiple subintervals, for example, N subintervals.
[0090] The intermediate stations other than the starting station and the terminal station in the multi-station interval can be regarded as special pass point constraints, so the train timetable energy-saving convex optimization model can be regarded as an energy-saving convex optimization model based on the train operation curve. At this time, the above proof conclusion (that is, the optimal solution of the train energy-saving convex optimization model is when the convex relaxation auxiliary variables are equal to the inverse of the average speed in the subinterval and the square of the speed in the subinterval respectively) The additional conclusion (i.e., the optimal energy consumption between train stations decreases with the increase of given running time) also holds true in the convex optimization model of train timetable energy conservation.
[0091] Based on the above, in step S202, you can:
[0092] Based on the running time allocation optimization model between stations and the energy-saving convex optimization model of the train running curve within each station, the energy-saving convex optimization model of the train timetable is determined.
[0093] In this application, the train parking time at each station is regarded as a fixed value, and the energy consumption J in the line is set in the optimization model of the running time allocation between stations. timetable Only the running time T between each station k The more trains L there are on a line, the longer the sum of the running time T between stations will be. And the number of trains L only affects the energy consumption in the line by affecting T. Therefore, in this application, the timetable optimization problem of multiple trains is simplified to the problem of allocating the running time between stations of a single train. The optimization model for the running time allocation between stations can be expressed as formula (3):
[0094]
[0095] Among them, the objective function of the operation time allocation optimization model between stations is the sum of the energy consumption between stations E(T k ) can represent the train running between the kth stations on the line, with a given running time of T k The minimum energy consumption when K is the number of stations. Can be Simplified, It can be regarded as a constant, where C represents the capacity of the line, α represents the train load factor, and c represents the capacity of a single train.
[0096] The constraints of the optimization model for the operation time allocation between stations may include constraints on the operation time between stations. See formula (3). The constraints on the operation time between stations may include: Among them, T k represents the train running time between stations, - and + represent the lower and upper bounds of the train running time between stations, and T represents the train running time constraint.
[0097] Since the number of trains L directly affects the total running time T of a single train between stations, that is, the larger L is, the larger T is. In this application, when facing the problem of allocating the running time between multiple trains, the number of trains L can be independently calculated by the conditions TC = Lh, h - ≤h≤h + TC - ≤TC≤TC + and Where TC is the train operation cycle, h is the departure interval, and - and + represent the lower and upper bounds, respectively.
[0098] The energy-saving convex optimization model of the train operation curve between stations can be found in the above formula (1).
[0099] By coupling the inter-station running time allocation optimization model and the train running curve energy-saving convex optimization model within each station, the train schedule energy-saving convex optimization model is determined as follows:
[0100]
[0101] The objective function of the train schedule energy-saving convex optimization model is the sum of the energy consumption between stations. The energy consumption between each station is the sum of the energy consumption of each sub-interval between stations. Refer to formula (4) and the objective function can be expressed as: Among them, E k,n It can represent the operating energy consumption in the nth subinterval of the kth station, where n∈{0,1,…,N-1} and k∈{1,2,…,K}.
[0102] The convex relaxation auxiliary variable ω is also introduced in the train schedule energy saving convex optimization model k,n and σ k,n , to replace the non-convex terms. Among them, the non-convex terms can include the inverse term of the average speed in the subinterval The square of the velocity in the sum subinterval Which meets and Therefore, the train timetable energy-saving optimization problem EETT can be relaxed and transformed into a convex optimization problem.
[0103] Referring to formula (4), the constraints on the auxiliary variables of convex relaxation can include is the average speed in the nth subinterval of the kth station, v k,n is the velocity of the starting position of the nth subinterval in the kth station interval, It can represent a three-dimensional second-order cone. These two constraints can be used to represent the convex relaxation auxiliary variable as a three-dimensional second-order cone. The constraints for the convex relaxation auxiliary variable can also include making ω k,n Satisfy the speed limit requirements within the sub-interval, that is, in formula (4) in, It can represent the line speed limit within the nth sub-interval in the kth station interval.
[0104] The constraints of the train schedule energy-saving convex optimization model may also include one or more of the following:
[0105] Constraints on the running time between stations, energy consumption constraints within each sub-interval between stations, train traction / braking force constraints within each sub-interval between stations, line speed limit constraints within each sub-interval between stations, average speed constraints within each sub-interval between stations, line length constraints within each sub-interval between stations, and boundary constraints.
[0106] Referring to formula (4), the constraints on the running time between stations can include: Among them, l k,n It represents the length of the nth subinterval in the kth station interval.
[0107] The energy consumption constraints for each sub-interval between stations may include: E k,n ≥u k,n l k,n η b 、 Among them, M gk,n represents the gravity component resistance caused by the line slope in the nth sub-interval of the kth station interval, represents the average speed in the nth subinterval of the kth station. k,n It represents the traction force / braking force of the train in the nth sub-interval of the kth station interval. In this application, it is assumed that the traction force / braking force of the train remains constant in the sub-intervals divided by the line.
[0108] The constraints on the train traction / braking force within each sub-interval between stations may include: u k,n ≤P t σ k,n 、 u k,n ≥P b σ k,n .
[0109] The speed limit constraints for each sub-interval between stations may include:
[0110] Constraints on the average speed of each sub-interval between stations may include: Among them, v k,n is the velocity of the starting position of the nth subinterval in the kth station, v k,n+1 is the velocity at the end position of the nth subinterval in the kth station interval.
[0111] The constraints on the line length within each sub-interval between stations may include: k,n =s k,n+1 -s k,n Among them, s k,n+1 Indicates the end position of the nth subinterval in the kth station interval, s k,n Indicates the starting position of the nth subinterval in the kth station interval.
[0112] Boundary constraints can include: v k,0 =0,v k,N = 0. Among them, Indicates the position of the starting point of the k-th station in the line, Indicates the location of the end point of the k-th station on the line.
[0113] Step S203 , based on the line data and train parameters, a train energy-saving convex optimization model is solved with the minimum train running energy consumption as the optimization goal to determine the train running status information.
[0114] In the case of solving the energy-saving convex optimization model of the train operation curve, the objects to be solved may include the above u n 、E n 、v n 、
[0115] σn 、ω n In the case of solving the train schedule energy-saving convex optimization model, the objects to be solved may include the above T k 、u k,n 、E k,n 、v k,n , σ k,n 、ω k,n .
[0116] The train energy-saving convex optimization model can be solved using methods such as the interior point method, and this application does not limit the solution method. The train operation status information can be used to represent the optimization result obtained by the solution.
[0117] When solving a train operation curve energy-saving convex optimization model, the resulting train operation status information can include the optimized train speed curve and the optimized train traction / braking force curve. The train speed curve represents the speed of the train at each location along the line, and the train traction / braking force curve represents the traction / braking force at each location along the line. The train operation status information can also include the energy consumption within each sub-interval during train operation.
[0118] See also Figure 5 , showing a schematic diagram of the optimized train speed curve according to an embodiment of the present application. Figure 5 As shown in the figure, the black line can represent the speed curve of the train running on the line after optimization. The red line can represent the speed limit at each location on the line, and the blue line can represent the elevation at each location on the line.
[0119] When solving a train timetable energy-saving convex optimization model, the obtained train operation status information may also include an optimized train speed curve and an optimized train traction / braking force curve. The train operation status information may also include an optimized train operation timetable. The train operation timetable may include the train's travel time and energy consumption between stations.
[0120] According to the embodiment of the present application, a train energy-saving convex optimization model can be determined, and based on the acquired line data and train parameters of the train operation, the train energy-saving convex optimization model can be solved with the minimum train operation energy consumption as the optimization goal, and the train operation status information can be determined. By introducing convex relaxation auxiliary variables for replacing non-convex terms in the train energy-saving optimization model, and making the constraints of the train energy-saving convex optimization model include constraints for convex relaxation auxiliary variables, the train energy-saving optimization problem can be converted into a second-order cone programming problem (i.e., a convex optimization problem), which can achieve a stable and fast solution effect, and can obtain the global optimal solution. It can also handle a variety of complex line constraints, thereby improving computing efficiency and saving computing resources.
[0121] In this application, the performance of the train energy-saving convex optimization model is verified by simulation test based on real line data and CRH3 train model. The CRH3 train model parameters can be obtained based on existing technology. The line data selected as test data can be found in Figure 6 , showing a schematic diagram of inter-station line data in operation according to an embodiment of the present application, including speed limit information (red line), start and end positions of phase separation zones (such as the start and end positions of the gray area), and elevation information (blue line).
[0122] The results obtained based on simulation experiments can be found in Figure 7 , showing a schematic diagram of verifying the effect of convex relaxation auxiliary variable accuracy according to an embodiment of the present application. Figure 7 As shown, the horizontal axis represents the position in the line, the vertical axis in the upper row represents the convex relaxation auxiliary variable σ, and the vertical axis in the lower row represents the convex relaxation auxiliary variable ω. The figures in the left column respectively show the convex relaxation auxiliary variables σ, ω and the corresponding variables in the special case (i.e., the very steep downhill line mentioned above is connected to a very steep uphill line, and the train must use the braking cruise model to maintain the line's allowed speed limit on the steep downhill line). v 2 The relationship diagram between ; the right column shows the convex relaxation auxiliary variables σ, ω and the corresponding variables in common cases v 2 As shown above, the convex relaxation auxiliary variable σ curve is consistent with the corresponding curve in both cases. coincides, that is, the convex relaxation auxiliary variable σ is exact. And the convex relaxation auxiliary variable ω curve is in special cases and the corresponding curve v 2 There is no overlap, meaning that in this case the convex relaxation auxiliary variable ω is not exact. However, as we noted above, due to the requirements for track slopes during construction, this special case is unlikely to occur on common lines. Therefore, we can assume that the convex relaxation auxiliary variable ω is exact on common lines.
[0123] The comparison of the optimization results between the train energy-saving optimization method of this application and other methods can be seen in Table 1:
[0124] Table 1
[0125] Optimization Results | Methods SOC CVX MILP RPM Energy consumption (kWh / km) 11.047 13.686 11.306 11.064 Run time error (s) 0.02 -32.08 -2.28 0 CPU time (s) 0.058 0.306 5.058 40.380
[0126] Here, SOC is the train energy-saving optimization method used in this application, CVX is another method, MILP is a mixed-integer linear programming method, and RPM is a radau pseudospectral method. The runtime error is the difference between the runtime calculated based on the verification model and the given runtime T.
[0127] As can be seen from the results in Table 1, our method is the most computationally efficient of all methods, with a CPU time of only 0.058s. Furthermore, our method achieves the lowest energy consumption of all methods, while the runtime error is only 0.02s, which is negligible compared to the total runtime.
[0128] The following further demonstrates the computational efficiency of the method of this application in handling large problems. Figure 8 、 Figure 9 and Figure 10 , showing a schematic diagram comparing the computational efficiency of processing large-scale problems according to an embodiment of the present application.
[0129] like Figure 8 As shown in FIG, the SOC of the method of the embodiment of the present application, as well as the CPU time of CVX and MILP, are shown as the number of circuit subinterval divisions N changes, where the number of circuit subinterval divisions N increases by 50 each time from 150 to 3000. Figure 8 It can be seen that the CPU time used for calculation by the method of the embodiment of the present application is almost linearly related to the number of line interval divisions N. Even when the number of divisions N reaches 3000, the CPU time of the method of the embodiment of the present application does not exceed 1.2 seconds. This shows that the method of the embodiment of the present application is also very efficient when dealing with large-scale problems.
[0130] like Figure 9 As shown in FIG, the method of the embodiment of the present application and the energy consumption of CVX and MILP are shown as the number N of line sub-interval divisions changes. Figure 10 As shown, it shows how the running time of the method of the embodiment of the present application, as well as CVX and MILP, changes with the number N of line subinterval divisions, where the number N of line subinterval divisions increases by 50 each time from 150 to 800.
[0131] from Figure 9 and Figure 10 It can be seen from the figure that the method of the embodiment of the present application uses a relatively accurate running time calculation method, so the energy consumption and running time errors obtained by the method fluctuate less as the number of line divisions N changes.
[0132] from Figure 10As can be seen in the figure, the mean and standard deviation of the runtime error obtained by the method of the embodiment of the present application are 0.012 and 0.014, respectively. The curve of the runtime error as the number of line segment divisions changes is basically a straight line. Similarly, the energy consumption curve obtained by the method of the embodiment of the present application as the number of segmentation N changes is also basically a straight line. Compared with the CVX method, the method of this paper can also achieve the results that CVX can achieve with a large number of line segmentation N and a relatively long time using a very small number of segmentation N.
[0133] This application also conducted a simulation experiment including train path envelope constraints, where the train path envelope constraints included train over-phase zone constraints and pass point constraints, verifying the ability of the method of the embodiment of this application to easily handle complex path envelope condition constraints. The method of the embodiment of this application can handle train pass point constraints well.
[0134] Under the premise that the total running time T of the train on the entire line remains unchanged, the comparison between the optimization results obtained by solving the train timetable energy-saving convex optimization model of the embodiment of the application and the benchmark results can be seen in Table 2:
[0135] Table 2
[0136]
[0137] As can be seen from Table 2, the method of the embodiment of the present application optimizes the allocation of operating time between each operating station, so that the final energy consumption is reduced by 8.8% compared with the baseline energy consumption.
[0138] The comparison of the results of solving the train timetable energy-saving convex optimization model of the embodiment of the present application and solving it using other methods can be seen in Table 3:
[0139] Table 3
[0140]
[0141] As can be seen from Table 3, the CPU time used by the method (SOC) of the embodiment of the present application is 0.391s, and the average CPU time between each operating station is only 0.021s. Compared with the time used by the MILP method and the PS method, it is much smaller. At the same time, the energy consumption obtained by the method of the embodiment of the present application is also the lowest, saving 8.88% compared to the baseline energy consumption. Overall, the method of the embodiment of the present application is the method with the highest computational efficiency and the lowest calculated energy consumption, demonstrating the huge potential value of the actual online application of the method of the embodiment of the present application.
[0142] Figure 11 The structure diagram of the train energy-saving optimization device according to an embodiment of the present application is shown. The device can be used in a terminal device or a server, such as Figure 11 As shown, the device may include:
[0143] The acquisition module 1101 is used to obtain line data and train parameters of the train operation;
[0144] A determination module 1102 is configured to determine a train energy-saving convex optimization model, where the train energy-saving convex optimization model includes an objective function and constraints, where the constraints include constraints on convex relaxation auxiliary variables, where the convex relaxation auxiliary variables are used to replace non-convex terms in the train energy-saving optimization model.
[0145] The solution module 1103 is used to solve the train energy-saving convex optimization model based on line data and train parameters with the minimum train operation energy consumption as the optimization goal, and determine the train operation status information.
[0146] In one possible implementation, the train parameters include one or more of the following: train mass, resistance parameters, traction efficiency, braking feedback efficiency, maximum traction power, maximum braking power, maximum traction constant torque coefficient, and maximum braking constant torque coefficient.
[0147] In one possible implementation, the non-convex terms include the inverse term of the average speed in the subinterval and the square term of the speed in the subinterval. The constraint conditions for the convex relaxation auxiliary variables represent that the convex relaxation auxiliary variables are three-dimensional second-order cones. The optimal solution of the train energy-saving convex optimization model is obtained when the convex relaxation auxiliary variables are equal to the inverse term of the average speed in the subinterval and the square term of the speed in the subinterval, respectively.
[0148] In one possible implementation, the train energy-saving convex optimization model includes a train operation curve energy-saving convex optimization model. The objective function of the train operation curve energy-saving convex optimization model is the sum of the energy consumption of each subinterval. The constraints of the train operation curve energy-saving convex optimization model also include one or more of the following:
[0149] Energy consumption constraints in each sub-interval, constraints on train traction / braking force in each sub-interval, constraints on line speed limit in each sub-interval, constraints on running time, constraints on average speed in each sub-interval, constraints on line length in each sub-interval and boundary constraints.
[0150] In one possible implementation, the line data includes line length, line speed limit, line elevation, and the start and end positions of the phase zone; the train operation status information includes the optimized train operation speed curve and the optimized train traction / braking force curve; and each sub-interval is divided based on the line speed limit and line elevation.
[0151] In one possible implementation, the train energy-saving convex optimization model includes a train schedule energy-saving convex optimization model, and the determination module 1102 is configured to:
[0152] Based on the running time allocation optimization model between stations and the energy-saving convex optimization model of the train running curve within each station, the train timetable energy-saving convex optimization model is determined. In the train timetable energy-saving convex optimization model, each station is divided into multiple sub-intervals.
[0153] In one possible implementation, the objective function of the train schedule energy-saving convex optimization model is the sum of the energy consumption between stations, and the energy consumption between each station is the sum of the energy consumption of each subinterval between stations. The constraints of the train schedule energy-saving convex optimization model also include one or more of the following:
[0154] Constraints on the running time between stations, energy consumption constraints within each sub-interval between stations, train traction / braking force constraints within each sub-interval between stations, line speed limit constraints within each sub-interval between stations, average speed constraints within each sub-interval between stations, line length constraints within each sub-interval between stations, and boundary constraints.
[0155] In a possible implementation, the line data also includes station and inter-station information, and the train operation status information also includes an optimized train operation schedule.
[0156] In a possible implementation, the objective function of the optimization model for distributing the operating time between stations is the sum of the energy consumption between stations, and the constraints of the optimization model for distributing the operating time between stations include constraints on the operating time between stations.
[0157] According to the embodiment of the present application, a train energy-saving convex optimization model can be determined, and based on the acquired line data and train parameters of the train operation, the train energy-saving convex optimization model can be solved with the minimum train operation energy consumption as the optimization goal, and the train operation status information can be determined. By introducing convex relaxation auxiliary variables for replacing non-convex terms in the train energy-saving optimization model, and making the constraints of the train energy-saving convex optimization model include constraints for convex relaxation auxiliary variables, the train energy-saving optimization problem can be converted into a second-order cone programming problem (i.e., a convex optimization problem), which can achieve a stable and fast solution effect, and can obtain the global optimal solution. It can also handle a variety of complex line constraints, thereby improving computing efficiency and saving computing resources.
[0158] In some embodiments, the functions or modules included in the device provided by the embodiments of the present disclosure can be used to execute the method described in the above method embodiments. The specific implementation can refer to the description of the above method embodiments. For the sake of brevity, it will not be repeated here.
[0159] The present disclosure also provides a computer-readable storage medium having computer program instructions stored thereon, wherein the computer program instructions implement the above method when executed by a processor. The computer-readable storage medium may be a volatile or non-volatile computer-readable storage medium.
[0160] An embodiment of the present disclosure further proposes an electronic device, comprising: a processor; and a memory for storing instructions executable by the processor; wherein the processor is configured to implement the above method when executing the instructions stored in the memory.
[0161] An embodiment of the present disclosure also provides a computer program product, including computer-readable code, or a non-volatile computer-readable storage medium carrying computer-readable code. When the computer-readable code runs in a processor of an electronic device, the processor in the electronic device executes the above method.
[0162] Figure 12 1 is a block diagram of a device 1900 for train energy-saving optimization according to an exemplary embodiment. For example, the device 1900 can be provided as a server or a terminal device. Figure 12 The apparatus 1900 includes a processing component 1922, which further includes one or more processors, and a memory resource represented by a memory 1932 for storing instructions, such as an application, that can be executed by the processing component 1922. The application stored in the memory 1932 may include one or more modules, each corresponding to a set of instructions. In addition, the processing component 1922 is configured to execute the instructions to perform the above-described method.
[0163] The device 1900 may also include a power supply component 1926 configured to perform power management of the device 1900, a wired or wireless network interface 1950 configured to connect the device 1900 to a network, and an input / output interface 1958 (I / O interface). The device 1900 may operate based on an operating system stored in the memory 1932, such as Windows Server 2003. TM , MacOS X TM , Unix TM ,Linux TM , FreeBSD TM or similar.
[0164] In an exemplary embodiment, a non-volatile computer-readable storage medium is also provided, such as a memory 1932 including computer program instructions that can be executed by the processing component 1922 of the apparatus 1900 to perform the above-described method.
[0165] The present disclosure may be a system, method and / or computer program product. The computer program product may include a computer-readable storage medium carrying computer-readable program instructions for causing a processor to implement various aspects of the present disclosure.
[0166] A computer-readable storage medium can be a tangible device that can hold and store instructions for use by an instruction execution device. A computer-readable storage medium can be, for example, but not limited to, an electrical storage device, a magnetic storage device, an optical storage device, an electromagnetic storage device, a semiconductor storage device, or any suitable combination thereof. More specific examples (a non-exhaustive list) of computer-readable storage media include: a portable computer disk, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or flash memory), a static random access memory (SRAM), a portable compact disc read-only memory (CD-ROM), a digital versatile disk (DVD), a memory stick, a floppy disk, a mechanical encoding device, such as a punch card or a raised structure in a groove on which instructions are stored, and any suitable combination thereof. As used herein, a computer-readable storage medium is not to be construed as a transient signal per se, such as a radio wave or other freely propagating electromagnetic wave, an electromagnetic wave propagating through a waveguide or other transmission medium (e.g., a light pulse through a fiber optic cable), or an electrical signal transmitted through an electrical wire.
[0167] The computer-readable program instructions described herein can be downloaded from a computer-readable storage medium to each computing / processing device, or downloaded to an external computer or external storage device via a network, such as the Internet, a local area network, a wide area network, and / or a wireless network. The network can include copper transmission cables, fiber optic transmission, wireless transmission, routers, firewalls, switches, gateway computers, and / or edge servers. The network adapter card or network interface in each computing / processing device receives the computer-readable program instructions from the network and forwards the computer-readable program instructions to be stored in the computer-readable storage medium in each computing / processing device.
[0168] The computer program instructions for performing the operations of the present disclosure may be assembly instructions, instruction set architecture (ISA) instructions, machine instructions, machine-dependent instructions, microcode, firmware instructions, state setting data, or source code or object code written in any combination of one or more programming languages, including object-oriented programming languages such as Smalltalk, C++, and conventional procedural programming languages such as "C" language or similar programming languages. Computer-readable program instructions may be executed entirely on a user's computer, partially on a user's computer, as an independent software package, partially on a user's computer, partially on a remote computer, or entirely on a remote computer or server. In the case of a remote computer, the remote computer may be connected to the user's computer via any type of network, including a local area network (LAN) or a wide area network (WAN), or may be connected to an external computer (e.g., utilizing an Internet service provider to connect via the Internet). In some embodiments, an electronic circuit, such as a programmable logic circuit, a field programmable gate array (FPGA), or a programmable logic array (PLA), may be personalized by utilizing the state information of the computer-readable program instructions. The electronic circuit may execute the computer-readable program instructions, thereby realizing various aspects of the present disclosure.
[0169] Various aspects of the present disclosure are described herein with reference to flowcharts and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the present disclosure. It should be understood that each block of the flowcharts and / or block diagrams, and combinations of blocks in the flowcharts and / or block diagrams, can be implemented by computer-readable program instructions.
[0170] These computer-readable program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, or other programmable data processing device, thereby producing a machine, so that when these instructions are executed by the processor of the computer or other programmable data processing device, a device is generated that implements the functions / actions specified in one or more blocks in the flowchart and / or block diagram. These computer-readable program instructions can also be stored in a computer-readable storage medium, where these instructions cause the computer, programmable data processing device, and / or other device to operate in a specific manner. Thus, the computer-readable medium storing the instructions comprises an article of manufacture that includes instructions for implementing various aspects of the functions / actions specified in one or more blocks in the flowchart and / or block diagram.
[0171] Computer-readable program instructions may also be loaded onto a computer, other programmable data processing apparatus, or other device so that a series of operational steps are performed on the computer, other programmable data processing apparatus, or other device to produce a computer-implemented process, thereby causing the instructions executed on the computer, other programmable data processing apparatus, or other device to implement the functions / actions specified in one or more blocks in the flowchart and / or block diagram.
[0172] The flow charts and block diagrams in the accompanying drawings show the possible architecture, functions and operations of the systems, methods and computer program products according to multiple embodiments of the present disclosure. In this regard, each box in the flow chart or block diagram can represent a part of a module, program segment or instruction, and the part of the module, program segment or instruction contains one or more executable instructions for realizing the prescribed logical function. In some alternative implementations, the functions marked in the box can also occur in a sequence different from that marked in the accompanying drawings. For example, two consecutive boxes can actually be executed substantially in parallel, and they can sometimes be executed in the opposite order, depending on the functions involved. It should also be noted that each box in the block diagram and / or flow chart, and the combination of the boxes in the block diagram and / or flow chart can be implemented by a dedicated hardware-based system that performs the prescribed function or action, or can be implemented by a combination of dedicated hardware and computer instructions.
[0173] While various embodiments of the present disclosure have been described above, the foregoing description is intended to be illustrative, non-exhaustive, and not limited to the disclosed embodiments. Many modifications and variations will be apparent to those skilled in the art without departing from the scope and spirit of the described embodiments. The terminology used herein is selected to best explain the principles of the embodiments, their practical applications, or technological improvements in the marketplace, or to enable others skilled in the art to understand the embodiments disclosed herein.
Claims
1. A train energy-saving optimization method, characterized in that: The method comprises: Obtain line data and train parameters of train operation; Determining a train energy-saving convex optimization model, the train energy-saving convex optimization model including an objective function and constraints, the constraints including constraints on convex relaxation auxiliary variables, the convex relaxation auxiliary variables being used to replace non-convex terms in the train energy-saving optimization model; Based on the line data and train parameters, the train energy-saving convex optimization model is solved with the minimum train operation energy consumption as the optimization goal to determine the train operation status information.
2. The method according to claim 1, characterized in that The non-convex terms include the inverse term of the average speed in the sub-interval and the square term of the speed in the sub-interval. The constraint conditions for the convex relaxation auxiliary variables indicate that the convex relaxation auxiliary variables are three-dimensional second-order cones. The optimal solution of the train energy-saving convex optimization model is obtained when the convex relaxation auxiliary variables are equal to the inverse term of the average speed in the sub-interval and the square term of the speed in the sub-interval, respectively.
3. The method according to claim 1, characterized in that The train energy-saving convex optimization model includes a train operation curve energy-saving convex optimization model, wherein the objective function of the train operation curve energy-saving convex optimization model is the sum of the energy consumption of each subinterval, and the constraints of the train operation curve energy-saving convex optimization model further include one or more of the following: Energy consumption constraints in each sub-interval, constraints on train traction / braking force in each sub-interval, constraints on line speed limit in each sub-interval, constraints on running time, constraints on average speed in each sub-interval, constraints on line length in each sub-interval and boundary constraints.
4. The method according to claim 3, characterized in that The line data includes line length, line speed limit, line elevation and start and end positions of the phase zone; the train operation status information includes an optimized train operation speed curve and an optimized train traction / braking force curve; and each sub-interval is divided based on the line speed limit and the line elevation.
5. The method according to claim 1, wherein The train energy-saving convex optimization model includes a train timetable energy-saving convex optimization model, and determining the train energy-saving convex optimization model includes: Based on the running time allocation optimization model between each station and the energy-saving convex optimization model of the train running curve within each station, the train timetable energy-saving convex optimization model is determined, in which each station is divided into multiple sub-intervals.
6. The method according to claim 5, characterized in that The objective function of the train schedule energy-saving convex optimization model is the sum of the energy consumption between stations, and the energy consumption between each station is the sum of the energy consumption of each subinterval between stations. The constraints of the train schedule energy-saving convex optimization model also include one or more of the following: Constraints on the running time between stations, energy consumption constraints within each sub-interval between stations, train traction / braking force constraints within each sub-interval between stations, line speed limit constraints within each sub-interval between stations, average speed constraints within each sub-interval between stations, line length constraints within each sub-interval between stations, and boundary constraints.
7. The method according to claim 5, characterized in that The line data also includes station and inter-station information, and the train operation status information also includes an optimized train operation schedule.
8. The method according to claim 5, characterized in that The objective function of the optimization model for allocating operating time between stations is the sum of energy consumption between stations, and the constraint conditions of the optimization model for allocating operating time between stations include constraints on the operating time between stations.
9. The method according to claim 1, wherein the train parameters include one or more of the following: train mass, resistance parameters, traction efficiency, braking feedback efficiency, maximum traction power, maximum braking power, maximum traction constant torque coefficient, and maximum braking constant torque coefficient.
10. A train energy-saving optimization device, characterized in that: The device comprises: An acquisition module is used to obtain line data and train parameters of train operation; a determination module, configured to determine a train energy-saving convex optimization model, wherein the train energy-saving convex optimization model includes an objective function and constraints, wherein the constraints include constraints on convex relaxation auxiliary variables, and the convex relaxation auxiliary variables are used to replace non-convex terms in the train energy-saving optimization model; A solution module is used to solve the train energy-saving convex optimization model based on the line data and train parameters with the minimum train operation energy consumption as the optimization goal, and determine the train operation status information.
11. A train energy-saving optimization device, characterized in that: include: processor; a memory for storing processor-executable instructions; The processor is configured to implement the method according to any one of claims 1 to 9 when executing the instructions stored in the memory.
12. A non-volatile computer-readable storage medium having computer program instructions stored thereon, characterized in that: When the computer program instructions are executed by a processor, the method according to any one of claims 1 to 9 is implemented.