A train energy-saving trajectory optimization method under coupling operation condition constraints

Abstract

The application discloses a train energy-saving trajectory optimization method under coupling operation condition constraints and relates to the technical field of rail transit operation control. The method comprises the following steps: a train dynamic kinematics model is built, a target function is constructed by taking traction energy consumption and ride comfort as targets, a train operation section is divided into a plurality of sub-sections, feasible working condition sequence combinations of the sub-sections are determined, a mixed integer linear programming model considering coupling constraints is constructed and solved, a globally optimal train operation speed trajectory and a corresponding discrete working condition sequence are obtained, discrete working condition control instructions in a full-line space domain are generated according to the globally optimal train operation speed trajectory and the corresponding discrete working condition sequence, the control instructions are issued to a train automatic operation system, and closed-loop energy-saving operation control is carried out. The method effectively overcomes the problem that a traditional strategy is discontinuous in an electric split phase area, realizes smooth transition of a driving state, accurately obtains a globally optimal solution, and significantly reduces total traction energy consumption of the system.

Description

Technical Field

[0001] This invention relates to the field of rail transit operation control technology, and in particular to a method for optimizing train energy-saving trajectories under coupled operating condition constraints. Background Technology

[0002] In high-speed rail train operation, different operation control and manipulation strategies can significantly impact the overall energy consumption of the high-speed rail network, particularly in optimizing system traction energy consumption. Inappropriate manipulation strategies may lead to a sharp increase in train traction energy consumption, or even overload the power supply system, increasing operating costs. Therefore, optimizing train operation is of great significance for cost reduction, efficiency improvement, and sustainable development of the high-speed rail system.

[0003] However, high-speed railway lines contain multiple electrical phase separation zones, requiring trains to de-energize and coast when passing through. Existing train trajectory optimization methods struggle to effectively handle the coupled constraints of electrical phase separation and speed limits, resulting in discontinuous speed curves. Because train speed curve optimization involves complex nonlinear processes and is highly coupled with spatial constraints such as electrical phase separation and speed limits, directly finding the global optimum is difficult and computationally burdensome. Some existing methods employ heuristic algorithms or dynamic programming to seek feasible solutions. However, these methods often struggle to balance solution quality and computational efficiency when dealing with complex coupled constraints, easily deviating from the optimal solution and causing excessive consumption of computational resources.

[0004] Therefore, proposing a train energy-saving trajectory optimization method under coupled operating condition constraints to solve the difficulties of the existing technology is a problem that urgently needs to be solved by those skilled in the art. Summary of the Invention

[0005] In view of this, the present invention provides a train energy-saving trajectory optimization method under coupled operating condition constraints, which effectively overcomes the problem of discontinuous operating strategy in the electrical phase separation region of traditional strategies, realizes smooth transition of driving state, accurately obtains the global optimal solution, and significantly reduces the total traction energy consumption of the system.

[0006] To achieve the above objectives, the present invention adopts the following technical solution: A method for optimizing train energy-saving trajectories under coupled operating condition constraints includes: S1. Construct a dynamic kinematic model of the train and build an objective function with traction energy consumption and ride comfort as optimization objectives; S2. Based on the coupling relationship between the line speed limit and the electrical phase separation, the train operating section is divided into several sub-sections, and the feasible operating condition sequence combination corresponding to each sub-section is determined. S3. Based on the feasible working condition sequence combination corresponding to each sub-interval, construct a mixed integer linear programming model considering coupling constraints and solve it to obtain the globally optimal train running speed trajectory and the corresponding discrete working condition sequence. S4. Generate discrete operating condition control commands in the entire line spatial domain based on the globally optimal train running speed trajectory and the corresponding discrete operating condition sequence. S5. Send control commands to the train automatic operation system to perform closed-loop energy operation control.

[0007] Optionally, in S1, a dynamic kinematic model of the train is constructed using the above method, specifically as follows: By simplifying the train as a proton, a dynamic kinematic model of the train can be constructed:

[0008]

[0009] in, The rotational mass factor; The mass of the train is expressed in kg. The instantaneous speed of the train is expressed in m / s. The traction force of the train is expressed in N (tonnes). Braking force of the train, measured in N; Basic resistance, in N; Additional resistance, in N; s The distance traveled by the train is expressed in meters (m). t Train travel time, in seconds; Basic resistance It is a physical quantity that is related to the train's operating speed in real time and is dependent on the train's model; additional resistance. Due to ramp resistance Curve resistance and tunnel resistance composition:

[0010]

[0011] Among them, China and This is the drag coefficient, which is related to the train model; Formula for calculating ramp resistance:

[0012] in, The value represents the slope in thousands; a positive value represents uphill and a negative value represents downhill. g It is the acceleration due to gravity;

[0013] Formula for calculating curve resistance:

[0014] in, This refers to the length of the train, measured in meters (m). The curve length is in meters (m).

[0015] The radius of the curve is in meters (m). Tunnel resistance calculation formula:

[0016] in, and These are the initial and final locations of the tunnel. , , The constant term is the drag coefficient. , , The drag coefficient is a linear term. , , This is the drag coefficient for the squared term.

[0017] Optionally, in the above method, in S1, an objective function is constructed with traction energy consumption and ride comfort as optimization objectives, specifically as follows: Traction energy consumption is determined by the integral of the traction or braking force output that varies with the train's position; Ride comfort is determined by the integral of the train's acceleration. The objective function constructed is:

[0018] in, The total travel time of the train. Indicates acceleration. The traction / braking force per unit mass. express The absolute value; and the range of values ​​for train traction and braking force is

[0019] ; In the formula, and They are respectively related to the train speed The varying lower / upper limit of traction force per unit mass. For speed The upper limit of braking force per unit mass varies.

[0020] Optionally, in the above method, in S2, based on the coupling relationship between the line speed limit and the electrical phase separation, the train operating section is divided into several sub-sections, and the feasible operating condition sequence combination corresponding to each sub-section is determined, specifically as follows: Based on the speed limit changes and electrical phase distribution between adjacent sub-sections, the train's operating sub-sections are divided into 5 types: Type I: When the speed limit is met When used for non-decreasing scenarios where the speed limit increases or adjacent sub-sections contain electrical phase separation, the operating condition sequence combination is: traction-cruise-coasting; Type II: When the speed limit is met When used in a scenario where the speed is limited and the coasting zone is decelerated without electrical phase separation, the operating sequence combination is: cruise-coasting-braking; Type III: When the speed limit is met , When used in scenarios where there is no electrically separated phase coasting region or the previous sub-region is an electrically separated phase coasting region, the working condition sequence combination is: traction-cruise-coasting-braking; Type IV: When the speed limit is met , When used in scenarios where there is no electric phase separation coasting region or the next sub-interval is an electric phase separation coasting region, the operating condition sequence combination is: cruise-coasting; Type V: Electrically separated phase idler region; in, , , These represent the speed limits for the current sub-interval, the previous sub-interval, and the next sub-interval, respectively.

[0021] Optionally, in S3 of the above method, a mixed-integer linear programming model considering coupling constraints is constructed and solved, specifically as follows: S301. Discretize the line running distance by treating the train's kinetic energy as a state variable. S302. Linearize the nonlinear dynamic constraints during train operation using piecewise affine functions; S303. Introduce binary decision variables for selecting indication conditions, transform the trajectory optimization problem into a mixed integer linear programming model, and solve it to obtain the globally optimal train speed trajectory and the corresponding discrete condition sequence.

[0022] Optionally, in the above method, S301, the train kinetic energy is used as a state variable to discretize the track running distance, specifically as follows: The line running distance is discretized, and the discretization interval is divided into... The number of sub-intervals, kinetic energy, and time points is: In sub-interval The number of discrete intervals within is: ; and The train's arrival location The initial kinetic energy and the moment of time are also the position. The corresponding final kinetic energy and time; It is an interval Internal traction, It is the first k The length of each interval; Representing an interval Traction energy consumption within; the objective function is described as: ; in, It is a suitable constant; The train dynamic kinematic model is rewritten as follows: ; ; in, , It is an interval The basic resistance within the system includes running resistance and air resistance; It is an interval Additional resistance on top, and Given by the verification formula, and ; The time constraint is obtained by solving the differential equation, based on the trapezoidal integral rule, for ,formula for: ; The constraint conditions for the resistance of segmented tunnels are expressed as follows:

[0023] Kinetic energy is used as a variable.

[0024] Optionally, in the above method, S302, a piecewise affine function is used to linearize the nonlinear dynamic constraints during train operation, specifically as follows: Transform it into a linear form using piecewise affine functions, and then fit it as... : ; in, , , Represents the linear coefficients at each stage. , , Represents the constant coefficients of each stage. , , , Indicates the segment boundary point, the train's maximum traction force It is a function of the train's real-time speed, and can be approximated using the PWA function as follows: ; in, , , Represents the linear coefficients at each stage. , , Represents the constant coefficients of each stage. , , , Indicates the segment boundary point.

[0025] Optionally, in S303, the trajectory optimization problem is transformed into a mixed-integer linear programming model, as described above: Based on piecewise affine functions The linear form introduces additional binary variables. and , when hour, ; when hour, ; Introducing binary variables express At the same time, real number variables are introduced. The following relation is satisfied: , get: ; The linear constraints are further transformed into: ; Substituting the linearized resistance into the train's kinematic equations and rearranging, we obtain the differential form: ; By analytically solving the differential form equations, the recurrence relation for updating the kinetic energy state within adjacent discrete intervals is derived: ; Among them, the correlation coefficient , , The definition is as follows: ; Based on the combination of the basic operating condition sequences of each sub-section of the train, let... For the set of all subintervals, For sub-range index; This is a collection of train operating conditions. For train operation status index; For binary decision variables, when the train is in the interval Select operating conditions If the value is 1, then the value is 0; otherwise, the objective function is: ; The constraint condition stipulates that the train can only choose one operating condition during the current sub-section's operation phase, expressed as: ; In the formula, Representing an interval Operating conditions are The corresponding index energy consumption at that time Representing an interval Operating conditions are The corresponding index for ride comfort; The train will depart from one station and stop at the terminal station, and the boundary conditions for high-speed train operation are: ; ; ; in, Indicates the number of subintervals. and These are the corresponding positions on the path. and The initial kinetic energy and the final kinetic energy at the point.

[0026] Optionally, in the above method, in S4, discrete control commands for the entire line's spatial domain are generated based on the globally optimal train speed trajectory and the corresponding discrete operating condition sequence. Specifically: The optimal velocity trajectory obtained by the global solution in step S3 Applied to the automatic train operation system as a reference target; The optimal binary decision variables obtained from solving mixed-integer linear programming The optimal discrete working condition sequence for each sub-interval Mapped to the actual line, this generates discrete operating condition control commands across the entire line's spatial domain. : .

[0027] Optionally, in S5, the control command is sent to the train automatic operation system to perform closed-loop functional operation control, as described above: It calculates the deviation between the current speed and the optimal trajectory in real time, and dynamically outputs traction or braking force under the working conditions constraints of the current position, so as to perform closed-loop energy operation control under multiple constraint coupling conditions.

[0028] As can be seen from the above technical solutions, compared with the prior art, the present invention provides a train energy-saving trajectory optimization method under coupled operating condition constraints, which has the following beneficial effects: The present invention effectively overcomes the problem of discontinuous operation strategy in the electric phase separation region by dividing the interval according to the coupling relationship between speed limit and electric phase separation and predefining the operating condition sequence, and realizes a smooth transition of driving state; by adopting the mixed integer linear programming method, the continuous design of train operating conditions is realized while accurately obtaining the global optimal solution, which significantly reduces the total traction energy consumption of the system. Attached Figure Description

[0029] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.

[0030] Figure 1 A flowchart of a train energy-saving trajectory optimization method under coupled operating condition constraints provided by the present invention; Figure 2 The sub-interval type partitioning diagram provided in a specific embodiment of the present invention; Figure 3 The speed trajectory optimization result diagram is provided in a specific embodiment of the present invention; Figure 4 The diagram shows the operating condition sequence adopted in a specific embodiment of the present invention. Detailed Implementation

[0031] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0032] Reference Figure 1As shown, this invention discloses a train energy-saving trajectory optimization method under coupled operating condition constraints, comprising: S1. Construct a dynamic kinematic model of the train and build an objective function with traction energy consumption and ride comfort as optimization objectives; S2. Based on the coupling relationship between the line speed limit and the electrical phase separation, the train operating section is divided into several sub-sections, and the feasible operating condition sequence combination corresponding to each sub-section is determined. S3. Based on the feasible working condition sequence combination corresponding to each sub-interval, construct a mixed integer linear programming model considering coupling constraints and solve it to obtain the globally optimal train running speed trajectory and the corresponding discrete working condition sequence. S4. Generate discrete operating condition control commands in the entire line spatial domain based on the globally optimal train running speed trajectory and the corresponding discrete operating condition sequence. S5. Send control commands to the train automatic operation system to perform closed-loop energy operation control.

[0033] Furthermore, in S1, a dynamic kinematic model of the train is constructed, specifically as follows: By simplifying the train as a proton, a dynamic kinematic model of the train can be constructed:

[0034]

[0035] in, The rotational mass factor; The mass of the train is expressed in kg. The instantaneous speed of the train is expressed in m / s. The traction force of the train is expressed in N (tonnes). Braking force of the train, measured in N; Basic resistance, in N; Additional resistance, in N; s The distance traveled by the train is expressed in meters (m). t Train travel time, in seconds; Basic resistance It is a physical quantity that is related to the train's operating speed in real time and is dependent on the train's model; additional resistance. Due to ramp resistance Curve resistance and tunnel resistance composition:

[0036]

[0037] in, and This is the drag coefficient, which is related to the train model; Formula for calculating ramp resistance:

[0038] in, The value represents the slope in thousands; a positive value represents uphill and a negative value represents downhill. g It is the acceleration due to gravity;

[0039] Formula for calculating curve resistance:

[0040] in, This refers to the length of the train, measured in meters (m). The curve length is in meters (m).

[0041] The radius of the curve is in meters (m). Tunnel resistance calculation formula:

[0042] in, and These are the initial and final locations of the tunnel. , , The constant term is the drag coefficient. , , The drag coefficient is a linear term. , , This is the drag coefficient for the squared term.

[0043] Furthermore, in S1, an objective function is constructed with traction energy consumption and ride comfort as optimization objectives, specifically: Traction energy consumption is determined by the integral of the traction or braking force output that varies with the train's position; Ride comfort is determined by the integral of the train's acceleration. The objective function constructed is:

[0044] in, The total travel time of the train. Indicates acceleration. The traction / braking force per unit mass. express The absolute value; and the range of values ​​for train traction and braking force is

[0045] ; In the formula, and They are respectively related to the train speed The varying lower / upper limit of traction force per unit mass. For speed The upper limit of braking force per unit mass varies.

[0046] Furthermore, in S2, based on the coupling relationship between the line speed limit and the electrical phase separation, the train operating section is divided into several sub-sections, and the feasible operating condition sequence combination corresponding to each sub-section is determined, specifically: Based on the speed limit changes and electrical phase distribution between adjacent sub-sections, the train's operating sub-sections are divided into 5 types: Type I: When the speed limit is met When used for non-decreasing scenarios where the speed limit increases or adjacent sub-sections contain electrical phase separation, the operating condition sequence combination is: traction-cruise-coasting; Type II: When the speed limit is met When used in a scenario where the speed is limited and the coasting zone is decelerated without electrical phase separation, the operating sequence combination is: cruise-coasting-braking; Type III: When the speed limit is met , When used in scenarios where there is no electrically separated phase coasting region or the previous sub-region is an electrically separated phase coasting region, the working condition sequence combination is: traction-cruise-coasting-braking; Type IV: When the speed limit is met , When used in scenarios where there is no electric phase separation coasting region or the next sub-interval is an electric phase separation coasting region, the operating condition sequence combination is: cruise-coasting; Type V: Electrically separated phase idler region; in, , , These represent the speed limits for the current sub-interval, the previous sub-interval, and the next sub-interval, respectively.

[0047] Furthermore, in S3, a mixed-integer linear programming model considering coupling constraints is constructed and solved, specifically as follows: S301. Discretize the line running distance by treating the train's kinetic energy as a state variable. S302. Linearize the nonlinear dynamic constraints during train operation using piecewise affine functions; S303. Introduce binary decision variables for selecting indication conditions, transform the trajectory optimization problem into a mixed integer linear programming model, and solve it to obtain the globally optimal train speed trajectory and the corresponding discrete condition sequence.

[0048] Furthermore, in S301, the train's kinetic energy is used as a state variable to discretize the track running distance, specifically as follows: The line running distance is discretized, and the discretization interval is divided into... The number of sub-intervals, kinetic energy, and time points is: In sub-interval The number of discrete intervals within is: ; and The train's arrival location The initial kinetic energy and the moment of time are also the position. The corresponding final kinetic energy and time; It is an interval Internal traction, It is the first k The length of each interval; Representing an interval Traction energy consumption within; the objective function is described as: ; in, It is a suitable constant; The train dynamic kinematic model is rewritten as follows: ; ; in, , It is an interval The basic resistance within the system includes running resistance and air resistance; It is an interval Additional resistance on top, and Given by the verification formula, and ; The time constraint is obtained by solving the differential equation, based on the trapezoidal integral rule, for ,formula for: ; The constraint conditions for the resistance of segmented tunnels are expressed as follows:

[0049] Kinetic energy is used as a variable.

[0050] Furthermore, in S302, piecewise affine functions are used to linearize the nonlinear dynamic constraints during train operation, specifically as follows: Transform it into a linear form using piecewise affine functions, and then fit it as... : ; in, , , Represents the linear coefficients at each stage. , , Represents the constant coefficients of each stage. , , , Indicates the segment boundary point, the train's maximum traction force It is a function of the train's real-time speed, and can be approximated using the PWA function as follows: ; in, , , Represents the linear coefficients at each stage. , , Represents the constant coefficients of each stage. , , , Indicates the segment boundary point.

[0051] Furthermore, in S303, the trajectory optimization problem is transformed into a mixed-integer linear programming model, specifically: Based on piecewise affine functions The linear form introduces additional binary variables. and , when hour, ; when hour, ; Introducing binary variables express At the same time, real number variables are introduced. The following relation is satisfied: , get: ; The linear constraints are further transformed into: ; Substituting the linearized resistance into the train's kinematic equations and rearranging, we obtain the differential form: ; By analytically solving the differential form equations, the recurrence relation for updating the kinetic energy state within adjacent discrete intervals is derived: ; Among them, the correlation coefficient , , The definition is as follows: ; Based on the combination of the basic operating condition sequences of each sub-section of the train, let... For the set of all subintervals, For sub-range index; This is a collection of train operating conditions. For train operation status index; For binary decision variables, when the train is in the interval Select operating conditions If the value is 1, then the value is 0; otherwise, the objective function is: ; The constraint condition stipulates that the train can only choose one operating condition during the current sub-section's operation phase, expressed as: ; In the formula, Representing an interval Operating conditions are The corresponding index energy consumption at that time Representing an interval Operating conditions are The corresponding index for ride comfort; The train will depart from one station and stop at the terminal station, and the boundary conditions for high-speed train operation are: ; ; ; in, Indicates the number of subintervals. and These are the corresponding positions on the path. and The initial kinetic energy and the final kinetic energy at the point.

[0052] Furthermore, in S4, based on the globally optimal train speed trajectory and the corresponding discrete operating condition sequence, discrete operating condition control commands are generated for the entire line's spatial domain, specifically: The optimal velocity trajectory obtained by the global solution in step S3 Applied to the automatic train operation system as a reference target; The optimal binary decision variables obtained from solving mixed-integer linear programming The optimal discrete working condition sequence for each sub-interval Mapped to the actual line, this generates discrete operating condition control commands across the entire line's spatial domain. : .

[0053] Furthermore, in S5, control commands are sent to the train automatic operation system for closed-loop energy-saving operation control, specifically as follows: It calculates the deviation between the current speed and the optimal trajectory in real time, and dynamically outputs traction or braking force under the working conditions constraints of the current position, so as to perform closed-loop energy operation control under multiple constraint coupling conditions.

[0054] In one specific embodiment, the CRH3-350 high-speed train is taken as the research object, the line length is set to 87km, and the CPLEX optimizer is used in the simulation environment to solve the constructed mixed integer linear programming model. This embodiment considers four electrical phase separation zones. Based on the speed limit changes and electrical phase separation distribution between adjacent sub-sections, the operating condition sequence types adopted by the train in the operating sub-sections include the following four types, such as... Figure 2 As shown: Type I: Speed ​​limit met The operating condition sequence combination is: traction-cruise-coast (MT-CR-CO). Type III: Speed ​​limit met , The operating condition sequence combination is: traction-cruise-coast-brake (MT-CR-CO-MB). Type IV: Speed ​​limit met , The operating condition sequence combination is: cruise-coast (CR-CO). Type V: Electrically separated phase idler region; Considering the numerous electrical phase separation and speed limiting coupling requirements in actual power lines, the simulation focused on comparing the operating results under the traditional unoptimized strategy and the optimized operating condition sequence strategy proposed in this patent. Figure 3 A comparison chart of the velocity trajectory optimization results. Figure 4 The operating condition sequence adopted is shown below. The optimal control command and speed trajectory results demonstrate that this algorithm can generate a smooth, continuous operating speed curve in complex coupled scenarios with multiple electrical phases. Compared to traditional unoptimized control methods, this optimization strategy saves at least 0.89% of traction energy consumption. These data fully verify the significant energy-saving advantages and engineering application feasibility of this optimization framework under actual complex operating conditions.

[0055] The various embodiments in this specification are described in a progressive manner. Similar or identical parts between embodiments can be referred to mutually. Each embodiment focuses on describing the differences from other embodiments. In particular, for system or system embodiments, since they are basically similar to method embodiments, the description is relatively simple, and relevant parts can be referred to the descriptions in the method embodiments. The systems and system embodiments described above are merely illustrative. The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the modules can be selected to achieve the purpose of this embodiment according to actual needs. Those skilled in the art can understand and implement this without creative effort.

[0056] The above description of the disclosed embodiments enables those skilled in the art to make or use the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method for optimizing train energy-saving trajectories under coupled operating condition constraints, characterized in that, include: S1. Construct a dynamic kinematic model of the train and build an objective function with traction energy consumption and ride comfort as optimization objectives; S2. Based on the coupling relationship between the line speed limit and the electrical phase separation, the train operating section is divided into several sub-sections, and the feasible operating condition sequence combination corresponding to each sub-section is determined. S3. Based on the feasible working condition sequence combination corresponding to each sub-interval, construct a mixed integer linear programming model considering coupling constraints and solve it to obtain the globally optimal train running speed trajectory and the corresponding discrete working condition sequence. Construct and solve a mixed-integer linear programming model considering coupling constraints, specifically as follows: S301. Discretize the line running distance by treating the train's kinetic energy as a state variable. S302. Linearize the nonlinear dynamic constraints during train operation using piecewise affine functions; S303. Introduce binary decision variables for selecting indication conditions, transform the trajectory optimization problem into a mixed integer linear programming model, and solve it to obtain the globally optimal train speed trajectory and the corresponding discrete condition sequence. In S301, the train's kinetic energy is used as a state variable to discretize the track running distance, specifically as follows: The line running distance is discretized, and the discretization interval is divided into... The number of sub-intervals, kinetic energy, and time points is: In sub-interval The number of discrete intervals within is: ； and The train's arrival location The initial kinetic energy and the moment of time are also the position. The corresponding final kinetic energy and time; It is an interval Internal traction, It is the first k The length of each interval; Representing an interval Traction energy consumption within; the objective function is described as: ； in, It is a suitable constant; The train dynamic kinematic model is rewritten as follows: ； ； in, , It is an interval The basic resistance within the system includes operating resistance and air resistance; It is an interval Additional resistance on top, and Given by the verification formula, and ; The time constraint is obtained by solving the differential equation, based on the trapezoidal integral rule, for ,formula for: ； The constraint conditions for the resistance of segmented tunnels are expressed as follows: Kinetic energy is used as a variable; In S302, piecewise affine functions are used to linearize the nonlinear dynamic constraints during train operation, specifically as follows: Transform it into a linear form using piecewise affine functions, and then fit it as... : ； in, , , Represents the linear coefficients at each stage. , , Represents the constant coefficients of each stage. , , , Indicates the segment boundary point, the train's maximum traction force It is a function of the train's real-time speed, and can be approximated using the PWA function as follows: ； in, , , Represents the linear coefficients at each stage. , , Represents the constant coefficients of each stage. , , , Indicates the segment boundary points; In S303, the trajectory optimization problem is transformed into a mixed-integer linear programming model, specifically: Based on piecewise affine functions The linear form introduces additional binary variables. and , when hour, ; when hour, ; Introducing binary variables express At the same time, real number variables are introduced. The following relation is satisfied: ， get: ； The linear constraints are further transformed into: ； Substituting the linearized resistance into the train's kinematic equations and rearranging, we obtain the differential form: ； By analytically solving the differential form equations, the recurrence relation for updating the kinetic energy state within adjacent discrete intervals is derived: ； Among them, the correlation coefficient , , The definition is as follows: ； Based on the combination of the basic operating condition sequences of each sub-section of the train, let... For the set of all subintervals, For sub-range index; This is a collection of train operating conditions. For train operation status index; For binary decision variables, when the train is in the interval Select operating conditions If the value is 1, then the value is 0; otherwise, the objective function is: ； The constraint condition stipulates that the train can only choose one operating condition during the current sub-section's operation phase, expressed as: ； In the formula, Representing an interval Operating conditions are The corresponding index energy consumption at that time Representing an interval Operating conditions are The corresponding index for ride comfort; The train will depart from one station and stop at the terminal station, and the boundary conditions for high-speed train operation are: ； ； ； in, Indicates the number of subintervals. and These are the corresponding positions on the path. and The initial kinetic energy and the final kinetic energy at the point; S4. Generate discrete operating condition control commands in the entire line spatial domain based on the globally optimal train running speed trajectory and the corresponding discrete operating condition sequence. S5. Send control commands to the train automatic operation system to perform closed-loop energy operation control.

2. The train energy-saving trajectory optimization method under coupled operating condition constraints according to claim 1, characterized in that, In S1, a dynamic kinematic model of the train is constructed, specifically as follows: By simplifying the train as a proton, a dynamic kinematic model of the train can be constructed: in, The rotational mass factor; The mass of the train is expressed in kg. The instantaneous speed of the train is expressed in m / s. The traction force of the train is expressed in N (tonnes). Braking force of the train, measured in N; Basic resistance, in N; Additional resistance, in N; s The distance traveled by the train is expressed in meters (m). t Train travel time, in seconds; Basic resistance It is a physical quantity that is related to the train's operating speed in real time and is dependent on the train's model; additional resistance. Due to ramp resistance Curve resistance and tunnel resistance composition: in, and This is the drag coefficient, which is related to the train model; Formula for calculating ramp resistance: in, The value represents the slope in thousands; a positive value represents uphill and a negative value represents downhill. g It is the acceleration due to gravity; Formula for calculating curve resistance: in, This refers to the length of the train, measured in meters (m). The curve length is in meters (m). The radius of the curve is in meters (m). Tunnel resistance calculation formula: in, and These are the initial and final locations of the tunnel. , , The constant term is the drag coefficient. , , The drag coefficient is a linear term. , , This is the drag coefficient for the squared term.

3. The train energy-saving trajectory optimization method under coupled operating condition constraints according to claim 2, characterized in that, In S1, the objective function is constructed with traction energy consumption and ride comfort as optimization objectives, specifically: Traction energy consumption is determined by the integral of the traction or braking force output that varies with the train's position; Ride comfort is determined by the integral of the train's acceleration. The objective function constructed is: in, The total travel time of the train. Indicates acceleration. The traction / braking force per unit mass. express The absolute value; and the range of values ​​for train traction and braking force is: ； In the formula, and They are respectively related to the train speed The varying lower / upper limit of traction force per unit mass. For speed The upper limit of braking force per unit mass varies.

4. The train energy-saving trajectory optimization method under coupled operating condition constraints according to claim 3, characterized in that, In S2, based on the coupling relationship between the line speed limit and the electrical phase separation, the train operating section is divided into several sub-sections, and the feasible operating condition sequence combination corresponding to each sub-section is determined, specifically as follows: Based on the speed limit changes and electrical phase distribution between adjacent sub-sections, the train's operating sub-sections are divided into 5 types: Type I: When the speed limit is met When used for non-decreasing scenarios where the speed limit increases or adjacent sub-sections contain electrical phase separation, the operating condition sequence combination is: traction-cruise-coasting; Type II: When the speed limit is met When used in a scenario where the speed is limited and the coasting zone is decelerated without electrical phase separation, the operating sequence combination is: cruise-coasting-braking; Type III: When the speed limit is met , When used in scenarios where there is no electrically separated phase coasting region or the previous sub-region is an electrically separated phase coasting region, the working condition sequence combination is: traction-cruise-coasting-braking; Type IV: When the speed limit is met , When used in scenarios where there is no electric phase separation coasting region or the next sub-interval is an electric phase separation coasting region, the operating condition sequence combination is: cruise-coasting; Type V: Electrically separated phase idler region; in, , , These represent the speed limits for the current sub-interval, the previous sub-interval, and the next sub-interval, respectively.

5. The train energy-saving trajectory optimization method under coupled operating condition constraints according to claim 1, characterized in that, In S4, based on the globally optimal train speed trajectory and the corresponding discrete operating condition sequence, discrete operating condition control commands are generated for the entire line's spatial domain. Specifically: The optimal velocity trajectory obtained by the global solution in step S3 Applied to the automatic train operation system as a reference target; The optimal binary decision variables obtained from solving mixed-integer linear programming The optimal discrete working condition sequence for each sub-interval Mapped to the actual line, this generates discrete operating condition control commands across the entire line's spatial domain. : 。 6. The train energy-saving trajectory optimization method under coupled operating condition constraints according to claim 5, characterized in that, In S5, control commands are sent to the train automatic operation system for closed-loop energy-saving operation control, specifically as follows: It calculates the deviation between the current speed and the optimal trajectory in real time, and dynamically outputs traction or braking force under the working conditions constraints of the current position, so as to perform closed-loop energy operation control under multiple constraint coupling conditions.

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