Train energy-saving operation control convex optimization model construction method for complex traction characteristics

Abstract

This invention discloses a method for constructing a convex optimization model for train energy-saving operation and control oriented towards complex traction characteristics. The method includes the following steps: collecting train operation data; constructing a basic convex optimization model for train energy-saving operation and control; constructing an inherent characteristic model of the traction system with natural characteristic zones and hybrid braking; constructing the relationship between efficiency, traction / braking force, and speed, introducing auxiliary variables, establishing the relationship between efficiency and train operation energy consumption, and constructing a convex model for train energy-saving operation and control based on the dynamic efficiency map of the motor; using positive and negative fitting faces to fit data to positive and negative surfaces, converting the dynamic efficiency map of the motor into a convex polynomial, and establishing the connection between dynamic efficiency and energy consumption; and obtaining real energy consumption data from power loss analysis of various components at the system level. This invention constructs a more accurate, highly adaptable, and robust train energy-saving operation and control model, reduces the model complexity at the traction drive system level, and improves the solution efficiency of complex models.

Description

Technical Field

[0001] This invention relates to the field of train energy-saving operation control technology, specifically to a method for constructing a convex optimization model for train energy-saving operation control oriented towards complex traction characteristics. Background Technology

[0002] Energy-efficient Train Control (EETC) refers to the acquisition of energy-efficient train operation trajectories or control strategies based on optimal control theory under various train operating conditions and traction constraints. The aim is to achieve minimum train operating energy consumption. Energy-efficient train control strategies are considered one of the most effective strategies for reducing traction energy consumption. Furthermore, with the development of intelligent rail transit and the continuous improvement of Automatic Train Operation (ATO) systems, proposing a train energy-efficient operation control model that can simultaneously achieve fast computational efficiency and high solution accuracy has become a fundamental requirement for modern optimization techniques to generate energy-efficient train operation trajectories or control strategies. In addition, modern rail transit traction and power supply network systems possess complex characteristics such as high dimensionality, nonlinearity, and spatiotemporal complexity. These complex characteristics are closely related to and have a significant impact on the energy consumption of rail transit systems. Ignoring these characteristics will seriously hinder further improvements in the overall energy efficiency of rail transit systems.

[0003] In the classic EETC model, to obtain the minimum operating energy consumption of the train, a train optimization model based on distance / time mixed integer linear programming is proposed. Piecewise linearization is used to handle nonlinear variables. It has good applicability in simple models, but it has significant drawbacks when dealing with the energy-saving operation control problem of trains with complex traction system characteristics. Using linearization to solve high-dimensional, nonlinear, and spatiotemporally complex systems will lead to large energy consumption errors. In addition, the number of linearization variables increases sharply with the increase of system complexity, which will lead to the problem of long model solution time due to too many variables. This is not conducive to updating the energy-saving control strategy when the train ATO occurs in emergency or special scenarios.

[0004] There is a lack of research on energy-saving train operation control that comprehensively considers the efficiency of complex traction systems, and research that can simultaneously meet the requirements of rapid efficiency calculation and energy consumption accuracy is also very limited. Current literature only simplifies the components of the traction system. The simplified efficiency model cannot reflect the real energy consumption and train trajectory. Moreover, the average efficiency is often used to replace the dynamic efficiency spectrum of the traction motor, which leads to a large deviation between the planned train speed trajectory and the optimal efficiency point under traction conditions, making it difficult to reflect the real operating efficiency and energy consumption of the train.

[0005] In existing train traction motors, induction motors are commonly used. The traction / braking characteristics of these motors often need to consider their natural characteristic range, but this crucial characteristic is almost entirely ignored in the literature, with only a very few studies addressing it. Furthermore, electric braking is limited by motor power and grid voltage drop. Train braking often requires combining electric braking with drag braking, air braking, or other mechanical braking modes. Train traction systems possess complex inherent traction characteristics that dynamically change with train speed. Typical trains exhibit power degradation at higher speeds and hybrid braking characteristics at lower speeds. These characteristics significantly impact energy efficiency during train operation. These complex inherent characteristics are highly correlated with energy consumption and safety; neglecting them could pose a threat to train operation safety. Summary of the Invention

[0006] To overcome the shortcomings and deficiencies of existing technologies, this invention provides a method for constructing a convex optimization model for train energy-saving operation and control oriented towards complex traction characteristics. This invention combines the inherent characteristics of motor dynamic efficiency maps, traction / braking natural characteristic zones and low-speed hybrid braking state switching, and the complex dynamic efficiency characteristics of various components of the traction system from the power grid to the train level to construct a more accurate, highly adaptable, and robust train energy-saving operation and control model. It proposes modeling and analysis of highly nonlinear and nonconvex variables, and uses methods including data preprocessing, data sampling, spatial transformation, and curve fitting to reduce the model complexity considering the traction drive system level, while improving the solution efficiency of complex models, providing important technical guidance for automatic train operation.

[0007] The second objective of this invention is to provide a system for constructing a convex optimization model for train energy-saving operation control oriented towards complex traction characteristics;

[0008] A third objective of this invention is to provide a computer-readable storage medium;

[0009] A fourth objective of this invention is to provide a computing device;

[0010] To achieve the above objectives, the present invention adopts the following technical solution:

[0011] This invention provides a method for constructing a convex optimization model for train energy-saving operation control oriented towards complex traction characteristics, comprising the following steps:

[0012] Collect real train parameter information and obtain real train operation curves;

[0013] Construct a basic convex model for train energy-saving operation and control;

[0014] By incorporating the modeling of inherent traction characteristics into the basic train energy-saving operation and control convex optimization model, an inherent characteristic model of the traction system with natural characteristic zone and hybrid braking is constructed.

[0015] By collecting, sampling and preprocessing measured dynamic efficiency data of traction motors, the relationship between efficiency, traction / braking force and speed is constructed. Auxiliary variables are introduced to establish the relationship between efficiency and train operation energy consumption, and a convex model of train energy-saving operation control based on the dynamic efficiency map of motors is constructed.

[0016] By using positive and negative fitting surfaces to fit the fitting data of positive and negative curved surfaces, the dynamic efficiency spectrum of the motor is converted into a convex polynomial, and the relationship between dynamic efficiency and energy consumption is established.

[0017] We obtain real energy consumption data by analyzing the power loss of each component at the system level.

[0018] As a preferred technical solution, the specific steps for constructing a basic train energy-saving operation control convex model include:

[0019] Based on the basic dynamics of trains, a distance-based discretization method is used to construct an optimization model for train energy-saving operation control strategy.

[0020] Pre-defined constraints, including constraints on train dynamics, kinematic relationships, resistance equations, and on-time performance, are used to construct a basic energy-saving operation and control model for the train;

[0021] The basic energy-saving operation and control model of the train is subjected to convex relaxation treatment using the auxiliary variable method, resulting in a basic convexized model of train energy-saving operation and control.

[0022] As a preferred technical solution, the constraints of train dynamics are expressed as follows:

[0023] ;

[0024] in, This represents the traction / braking force at the i-th distance interval. This represents the train running resistance that is positively correlated with train speed. This represents the length of the i-th distance interval. This indicates information about slope changes over a corresponding distance. This represents the velocity point that needs to be optimized at each discrete point. It's the quality of the train. Represents gravitational acceleration;

[0025] The constraints on on-time performance are expressed as follows:

[0026] The total time the train takes to travel within each section equals the target travel time indicated by the timetable. , is represented as:

[0027] ;

[0028] ;

[0029] in, This represents the average velocity at the i-th distance interval;

[0030] The basic energy-saving operation and control model of the train is subjected to convex relaxation treatment using the auxiliary variable method. Two auxiliary variables are added, represented as follows:

[0031] ;

[0032] ;

[0033] in, , Auxiliary variables are used for substitution. and This transforms non-convex constraints into linear expressions.

[0034] As a preferred technical solution, a traction system inherent characteristic model based on the natural characteristic zone and hybrid braking is constructed, and the specific steps include:

[0035] The traction motor has different characteristic regions, including the starting region, constant torque region, constant power region, and natural characteristic region. A three-stage traction and braking characteristic is used to simulate the inherent traction characteristics of a train under real-world operating conditions, satisfying the following constraints:

[0036] ;

[0037] in, Indicates the train's traction force. For maximum traction, This indicates the maximum speed in the constant torque region. This indicates the maximum speed in the constant power region. Indicates the maximum permissible speed;

[0038] When the train enters the braking phase, mechanical braking is used in the low-speed zone, supplemented by electric braking. When the speed exceeds the critical speed, the braking mode changes from mechanical braking to regenerative braking. The braking force-speed relationship expression under the hybrid braking mode is:

[0039] ;

[0040] in, This indicates the braking force considering both the natural characteristic zone and the hybrid braking mode. A sloping line used to indicate the change from mechanical braking to regenerative braking mode. For maximum regenerative braking force, This represents the linear fitting expression for the natural characteristic region, where parameters a, b, c, and d are all calculated from the measured data of the traction motor.

[0041] As a preferred technical solution, an auxiliary variable is introduced to establish the relationship between efficiency and train operation energy consumption, expressed as:

[0042] ;

[0043] ;

[0044] in, ≥0 indicates traction force. <0 indicates braking force. This indicates the efficiency at the corresponding traction force and velocity point. This indicates the efficiency at the corresponding braking force and speed point. This represents an auxiliary variable.

[0045] As a preferred technical solution, the fitting data of positive and negative fitting surfaces are processed using positive and negative fitting surfaces, specifically expressed as follows:

[0046] ;

[0047] in, These are the polynomial fitting coefficients for surfaces ① and ②. These are the polynomial fitting coefficients for surfaces ③ and ④. Surface ① represents the positively fitted surface, surface ② represents the positive extension of the negatively fitted surface, surface ③ represents the negatively fitted surface, and surface ④ represents the negative extension of the positively fitted surface. The distance is represented by f, the traction force or braking force is represented by v, and the speed is represented by v.

[0048] As a preferred technical solution, real energy consumption data is obtained by analyzing the power loss of each component at the system level. Specific steps include:

[0049] Establish traction power supply network Network voltage and the internal current flowing through the transformer The relationship is determined and fitted using a convex polynomial, which satisfies the following constraints:

[0050] ;

[0051] ;

[0052] in, This indicates the power loss of the transformer. This represents the internal resistance of the transformer that causes power loss.

[0053] Calculate the power losses of other system components, satisfying the following constraints:

[0054] ;

[0055] in, Indicates power loss. Indicates static loss efficiency. Used to indicate converters, gearboxes, or hubs.

[0056] To achieve the second objective mentioned above, the present invention adopts the following technical solution:

[0057] A system for constructing a convex optimization model for train energy-saving operation and control oriented towards complex traction characteristics includes: a train data acquisition module, a basic train energy-saving operation and control convex model construction module, a traction system inherent characteristic model construction module, a train energy-saving operation and control convex model construction module, a fitting processing module, a conversion module, and a power loss analysis module.

[0058] The train data acquisition module is used to collect real train parameter information and obtain the real train operation curve;

[0059] The basic train energy-saving operation and control convex model construction module is used to construct a basic train energy-saving operation and control convex model;

[0060] The traction system inherent characteristic model building module is used to add modeling of inherent traction characteristics to the basic train energy-saving operation control convex optimization model, and to build a traction system inherent characteristic model of natural characteristic region and hybrid braking.

[0061] The train energy-saving operation and control convex model construction module is used to collect, sample and preprocess measured dynamic efficiency data of traction motors, construct the relationship between efficiency, traction / braking force and speed, introduce auxiliary variables, establish the relationship between efficiency and train operation energy consumption, and construct a train energy-saving operation and control convex model based on the dynamic efficiency map of motors.

[0062] The fitting processing module is used to perform fitting data processing on positive and negative surfaces using positive and negative fitting surfaces.

[0063] The conversion module is used to convert the dynamic efficiency graph of the motor into a convex polynomial and establish the relationship between dynamic efficiency and energy consumption.

[0064] The power loss analysis module is used to obtain real energy consumption data from the power loss analysis of various components at the system level.

[0065] To achieve the third objective mentioned above, the present invention adopts the following technical solution:

[0066] A computer-readable storage medium includes a stored program that, when executed, implements the above-described method for constructing a convex optimization model for train energy-saving operation control oriented towards complex traction characteristics.

[0067] To achieve the fourth objective mentioned above, the present invention adopts the following technical solution:

[0068] A computing device includes a processor and a memory for storing processor-executable programs. When the processor executes the program stored in the memory, it implements the above-described method for constructing a convex optimization model for train energy-saving operation control oriented towards complex traction characteristics.

[0069] Compared with the prior art, the present invention has the following advantages and beneficial effects:

[0070] (1) Very few existing optimization algorithms can achieve a model solution speed of only milliseconds when the model complexity is high. This invention is based on the basic dynamic model of rail transit trains and adopts the convex optimization method to relax the model of complex and nonlinear variables related to speed into a convex model, which greatly improves the solution time of the model.

[0071] (2) Existing studies often use simplified traction characteristics, lacking an assessment of the impact of natural characteristic zones and hybrid braking modes on train energy-saving driving strategies, and cannot truly reflect the train traction / braking characteristics. This invention considers the inherent characteristics of the train traction system and uses convex relaxation and linearization methods to process the natural characteristic zones and hybrid braking modes, including air braking, resistor braking or other mechanical braking methods to assist electric braking force. The introduction of the above-mentioned natural characteristic zones and hybrid braking modes can obtain more realistic train traction / braking output characteristics and train speed trajectory.

[0072] (3) In the existing train energy-saving operation and control models, the average efficiency is used to calculate the efficiency of the motor, which simplifies the complexity of the model but reduces its accuracy. This invention uses the auxiliary variable method to process the dynamic efficiency spectrum of the traction motor, establishes the complex efficiency-traction / braking force relationship with auxiliary variables, and uses polynomial fitting to fit the intrinsic relationship between the three variables. After polynomial fitting, the variables and the energy consumption of train operation show a linear relationship. By verifying the convexity of the polynomial, the model of complex motor dynamic efficiency can be added to the basic train energy-saving operation and control convex model, which reduces the complexity of the model and improves the solution accuracy of the model.

[0073] (4) The present invention uses two surfaces, positive and negative, to process positive and negative three-dimensional data points. The model can select a more accurate fitting surface to replace a single fitting surface in order to obtain a higher fitting goodness and more realistic energy consumption data.

[0074] (5) This invention constructs a loss model from the traction power supply network to the wheel hub, realizes an efficiency evaluation framework from the power grid to the train level, and combines the auxiliary variable method to evaluate the power loss of system components including transformers, converters, gearboxes and wheel hubs. It proposes to use static loss efficiency to evaluate system loss and considers auxiliary equipment and other components independent of the train's operating state to construct an overall research framework, that is, to use the convex optimization method to realize the efficiency evaluation model from the power grid to the train level, and provide an important support framework for train energy-saving driving strategies and comprehensive energy consumption evaluation. Attached Figure Description

[0075] Figure 1 This is a flowchart illustrating the method for constructing a convex optimization model for train energy-saving operation control based on complex traction characteristics, as described in this invention.

[0076] Figure 2 This is a schematic diagram illustrating the construction process of the basic train energy-saving operation control convex model of the present invention;

[0077] Figure 3 This is a schematic diagram showing the different control regions of the traction motor of the present invention and their corresponding traction characteristics;

[0078] Figure 4 (a) is a simplified schematic diagram of the traction characteristic curve of the present invention;

[0079] Figure 4 (b) is a schematic diagram of the actual traction motor characteristic curves considering the natural characteristic zone and the hybrid braking mode in this invention;

[0080] Figure 5 A schematic diagram illustrating the research route for the actual traction motor characteristics considering both the natural characteristic region and the hybrid braking mode in this invention;

[0081] Figure 6 This is a schematic diagram illustrating the process of constructing a train energy-saving operation control convex model that considers the dynamic efficiency spectrum of the motor, as per the present invention.

[0082] Figure 7 This is a schematic diagram illustrating the use of positive and negative fitting surfaces to fit the dynamic efficiency spectrum of the traction motor according to the present invention.

[0083] Figure 8 This is a schematic diagram of the loss composition of the multiple components of the present invention. Detailed Implementation

[0084] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0085] Example

[0086] like Figure 1 As shown in the figure, this embodiment provides a method for constructing a convex optimization model for train energy-saving operation control oriented towards complex traction characteristics, including the following steps:

[0087] S1: Collect real train parameter information and obtain the real train operation curve;

[0088] This embodiment collects real train parameters, including train motor model, maximum permissible operating speed, maximum acceleration, track information, train timetable, speed limits, gradient, traction motor parameters, and other real parameter data. This real parameter data is input into the train energy-saving operation control strategy optimization model, which considers constraints such as speed limits, time, and energy conservation to obtain the train's actual operating curve. This embodiment uses a convex optimization method to transform the complex nonlinear, non-convex model into a convex model, thereby achieving rapid solution.

[0089] S2: As Figure 2 As shown, a basic convex model for train energy-saving operation and control is constructed;

[0090] In the first stage, based on fundamental train dynamics, a distance-based discretization method is used to construct an optimization model for energy-saving train operation control strategies. This model is built from constraints including train dynamics, kinematic relationships, resistance equations, and on-time performance. Train dynamics, in the discrete model, considers the train's operating state from one discrete point to another, where the work done by traction or braking force equals the sum of the change in train mechanical energy and the work done by resistance, satisfying the following constraints:

[0091] (1)

[0092] in, This represents the traction / braking force at the i-th distance interval. This represents the train running resistance that is positively correlated with train speed. This represents the length of the i-th distance interval. This indicates information about slope changes over a corresponding distance. This represents the velocity point that needs to be optimized at each discrete point. It's the quality of the train. This represents the acceleration due to gravity. In the context of train kinematics, assuming the intervals between each discrete segment are sufficiently small, and the train maintains uniform acceleration within that segment, the average velocity of that segment is... It can be represented as:

[0093] (2)

[0094] in, Let N represent the average speed at the i-th distance interval. To ensure discretization accuracy, N needs to be large enough so that the multiple uniformly accelerated motions of the train can approximate the actual variable acceleration operation.

[0095] To meet the requirements of the train timetable, the total travel time of the train within each section must equal the target travel time provided by the timetable. It satisfies the following constraints:

[0096] (3)

[0097] Variables in formula (1) Variables in formula (3) Both of these are speed-related nonlinear variables. To handle these two nonlinear variables, the auxiliary variable method will be used to perform convex relaxation on the above non-convex nonlinear train energy-saving operation control optimization model. Two auxiliary variables (or relaxation variables) will be added to achieve convex relaxation for handling speed-related variables, satisfying the following constraints:

[0098] (4)

[0099] (5)

[0100] in, , Auxiliary variables are used for substitution. and The purpose is to transform non-convex constraints into linear expressions. Equation (4) can be proven to be convex using the following formulas (5-a)-(5-d). Note that in the model... and The average value is always greater than 0, which guarantees that The validity of the inequality is such that the right-hand side of the inequality is always greater than 0. Formula (3) is a standard second-order cone programming constraint; the formula transformation does not change the feasible region (convex set) of the original expression. Therefore, when the constraint is satisfied... Under the condition that, the feasible region of the inequality constraint of formula (3) is a convex set.

[0101] (5-a)

[0102] (5-b)

[0103] (5-c)

[0104] (5-d)

[0105] Similarly, the convexity of formula (5) can be proven by the second-order condition of the convex function, that is, formula (5) satisfies the corresponding function. - , ( >0, >0), its feasible region R ++ (In the first and fourth quadrants of a two-dimensional Cartesian coordinate system) is an open convex set, satisfying the second-order condition for a convex function. The Hessian matrix of the corresponding function g is:

[0106] (6)

[0107] As shown above, formula (6) confirms that the feasible region corresponding to formula (4) is a convex set, satisfying the convex optimization condition. Thus, the above model is the most basic convexization model for train energy-saving operation control.

[0108] S3: Add modeling of complex inherent traction characteristics to the basic train energy-saving operation and control convex optimization model, that is, consider the natural characteristic region and the hybrid braking characteristics, and construct the inherent characteristic model of the traction system with natural characteristic region and hybrid braking.

[0109] In this embodiment, based on the optimal train operation control convex model, an inherent characteristic model of the traction system, including the natural characteristic region and hybrid braking, is constructed, such as... Figure 3 As shown, the different characteristic regions of the traction motor include the starting region, constant torque region, constant power region, and natural characteristic region. Specific implementation steps include:

[0110] The simplified traction characteristic curve is divided into two segments: constant traction force and constant power, as shown below. Figure 4 As shown in (a), considering that the actual traction / braking characteristic curve needs to take into account the natural characteristic region, that is, the power decline characteristic under high-speed operation, it is linearized. Figure 4 As shown in (b), this embodiment uses a three-stage traction and braking characteristic to simulate the inherent traction characteristics of a train in a real operating scenario, that is, to satisfy the following constraints:

[0111] (7)

[0112] in, Indicates the train's traction force. For maximum traction, This indicates the maximum speed (basic speed) in the constant torque region. This indicates the maximum speed (conversion speed) in the constant power region. The maximum permissible speed is indicated by formula (7). Formula (7) is used to represent the traction-speed relationship considering the three-segment working area. This embodiment considers the inherent traction characteristics of rail transit trains, that is, the output characteristics that are closer to the real traction characteristic curve.

[0113] When the train enters the braking phase, mechanical braking and auxiliary electric braking modes need to be considered in the low-speed zone. When the speed exceeds the critical speed, the braking mode changes from mechanical braking to regenerative braking mode. Formula (8) is the expression for the braking force-speed relationship under the mixed braking mode:

[0114] (8)

[0115] in, This indicates the braking force considering both the natural characteristic zone and the hybrid braking mode. A sloping line used to indicate the change from mechanical braking to regenerative braking mode. For maximum regenerative braking force, The expression for linear fitting of the natural characteristic region is given in formula (8). In formula (8), a, b, c, and d can all be obtained by calculation using the measured data of the traction motor.

[0116] like Figure 5 As shown, we first analyze the differences between the constant power characteristics and the natural characteristics region of the induction motor in the high-speed scenario, as well as the impact of different braking modes on the train's energy-saving driving strategy. Then, we model the simplified and real traction characteristics respectively, and add the above real characteristics into the train's energy-saving operation control model to explore the influence mechanism of the natural characteristics region and the hybrid braking mode on the train's energy-saving operation control.

[0117] S4: The traction motor is analyzed based on stator current, terminal voltage, load torque, traction force, etc. The two-dimensional traction efficiency graph undergoes data preprocessing and physical modeling, including:

[0118] In this embodiment, after sampling and preprocessing the original data, auxiliary variables are introduced for spatial transformation and curve fitting. Complex, non-convex, and nonlinear variables related to efficiency are made convex. This example makes non-convex problems convex, reducing the complexity and difficulty of the model and improving the solution efficiency of the model.

[0119] First, data sampling and preprocessing are performed on the traction motor efficiency profile. This involves sampling and preprocessing data based on the measured operating efficiency profile of the train traction motor (or referring to the motor efficiency characteristic curves provided by Advisor and CarSim software), including traction / braking torque, speed, and efficiency profile. Second, auxiliary variables are introduced to establish the three-dimensional relationship between speed, traction / braking force, and efficiency. It satisfies the following constraints:

[0120] (9)

[0121] in, Indicates traction force (+) or braking force (-). This indicates the efficiency at the corresponding traction force and velocity point. This indicates the efficiency at the corresponding braking force and speed point. This represents the train's energy consumption during operation. The relationship between traction / braking force and efficiency can be obtained through... Establish, its expression is as follows:

[0122] (10)

[0123] In formula (9) Using convex polynomial fitting requires that the Hessian matrix of the polynomial be positive semi-definite, and this constraint can be proven during the surface fitting process, when the goodness of fit between the original data points and the fitting surface is... A score of 0.99 is considered a high degree of fit.

[0124] like Figure 6 As shown, by collecting, sampling and preprocessing the measured dynamic efficiency data of the traction motor, the relationship between efficiency, traction / braking force and speed is constructed, and auxiliary variables are introduced to establish the relationship between efficiency and train operation energy consumption, so as to obtain a train energy-saving operation control convex model that considers the dynamic efficiency spectrum of the motor.

[0125] S4: To improve the fitting effect, such as Figure 7 As shown, the fitting of a single surface is extended to fitting using both positive and negative fitting surfaces, which improves the fitting accuracy and achieves a more efficient fitting.

[0126] In this embodiment, the auxiliary variable is fitted to a single surface to obtain the goodness of fit R. 2 Surface ⑤ with a value >0.99. Considering that when there are many data points, in order to fit the required surface and fit both positive and negative data points, a small number of key data points need to be discarded. Therefore, this invention uses two fitting surfaces to process the fitting data of the positive and negative surfaces to obtain a surface with a higher fitting goodness, namely, a positive fitting surface ① and a negative fitting surface ③ with a higher fitting goodness. The above-mentioned surfaces ① and ③ involve the processing of positive and negative extension surfaces in the FV plane, namely, the negative extension surface ④ of surface ① and the positive extension surface ② of surface ③. The fitting surface with a better fitting effect is selected by the following formula (11), thereby realizing the expansion from fitting one surface to fitting using two surfaces, positive and negative, achieving a higher fitting effect while realizing more accurate efficiency calculation:

[0127] (11)

[0128] in, These are the polynomial fitting coefficients for surface ① and the positively extended surface ②. These are the polynomial fitting coefficients for surface ③ and negative extension surface ④.

[0129] S5: Considering the dynamic efficiency of various components in the system, this section analyzes the dynamic efficiency of each component of the traction drive system, including the traction power supply network, transformer, rectifier, traction motor, gearbox, and wheel hub. Figure 8 As shown, this enables the acquisition of more accurate energy consumption data and power loss models, achieving system-level energy consumption assessment and efficiency calculation.

[0130] In this embodiment, based on the model considering dynamic efficiency, the power losses from the traction power supply network, transformers, converters, traction motors, and wheel hubs are calculated. First, the loss flowing through the transformer is established, i.e., the loss caused by the changing resistance of the current flowing through the transformer. Next, the efficiency of the rectifier, converter, and wheel hub during train operation is considered. Finally, the power losses of auxiliary devices are also included in the model. This embodiment comprehensively considers power losses and energy consumption assessments from the power grid to the train level, making the model closer to real-world train operation scenarios.

[0131] First, establish the traction power supply network. Network voltage and the internal current flowing through the transformer The relationship is determined and fitted using a convex polynomial, which satisfies the following constraints:

[0132] ;

[0133] (12)

[0134] in This indicates the power loss of the transformer. This represents the internal resistance of the transformer that causes power loss. Next, calculate the power losses of other system components, including the converter. The power loss calculations for gearboxes and hubs all use static loss efficiency, which satisfies the following constraint (13):

[0135] (13)

[0136] in, Indicates power loss. Represents the static loss efficiency, where These can be used to represent converters, gearboxes, or hubs, respectively. Furthermore, auxiliary devices typically include coolers, compressors, power electronics, and other equipment, independent of train operating conditions. In summary, the total power loss of system components... The following constraints must be satisfied:

[0137] (14)

[0138] This invention obtains a convex model for train energy-saving operation and control by using an auxiliary variable method to convexize non-convex variables. Secondly, considering the inherent characteristics of the actual traction system, the three-segment working interval is convexized and linearized. Thirdly, based on data preprocessing, data sampling, spatial transformation, and curve fitting, the motor dynamic efficiency spectrum is converted into a convex polynomial, thereby establishing the relationship between dynamic efficiency and energy consumption, reducing model complexity while improving solution efficiency. Finally, system-level energy consumption assessment is achieved, analyzing power loss from the power grid to the train wheel hub to obtain more realistic energy consumption data closer to industry standards. This invention can achieve pre-assessment of train operation energy consumption, providing important technical support for obtaining energy consumption and speed trajectory data of rail transit trains. Furthermore, this invention combines a complex model of system-level component losses, enabling millisecond-level solution speeds, providing crucial technical support for the field of energy-saving operation of rail transit trains.

[0139] Example 2

[0140] Except for the following technical contents, the technical contents of this embodiment are the same as those of Embodiment 1 above;

[0141] This embodiment provides a system for constructing a convex optimization model for train energy-saving operation and control oriented towards complex traction characteristics, including: a train data acquisition module, a basic train energy-saving operation and control convex model construction module, a traction system inherent characteristic model construction module, a train energy-saving operation and control convex model construction module, a fitting processing module, a conversion module, and a power loss analysis module.

[0142] In this embodiment, the train data acquisition module is used to collect real train parameter information and obtain the real train operation curve;

[0143] In this embodiment, the basic train energy-saving operation and control convex model construction module is used to construct a basic train energy-saving operation and control convex model;

[0144] In this embodiment, the traction system inherent characteristic model building module is used to add modeling of inherent traction characteristics to the basic train energy-saving operation control convex optimization model, and build the traction system inherent characteristic model of natural characteristic region and hybrid braking.

[0145] In this embodiment, the train energy-saving operation and control convex model construction module is used to collect, sample and preprocess the measured dynamic efficiency data of the traction motor, construct the relationship between efficiency, traction / braking force and speed, introduce auxiliary variables, establish the relationship between efficiency and train operation energy consumption, and construct a train energy-saving operation and control convex model based on the dynamic efficiency map of the motor.

[0146] In this embodiment, the fitting processing module is used to perform fitting data processing on positive and negative surfaces using positive and negative fitting surfaces;

[0147] In this embodiment, the conversion module is used to convert the dynamic efficiency spectrum of the motor into a convex polynomial, thereby establishing the relationship between dynamic efficiency and energy consumption.

[0148] In this embodiment, the power loss analysis module is used to obtain real energy consumption data from the power loss analysis of various components at the system level.

[0149] Example 3

[0150] This embodiment provides a computer-readable storage medium, which may be a storage medium such as ROM, RAM, disk, or optical disk. The computer-readable storage medium stores one or more programs. When the program is executed by a processor, it implements the method for constructing a convex optimization model for train energy-saving operation control oriented towards complex traction characteristics as described in Embodiment 1.

[0151] Example 4

[0152] This embodiment provides a computing device, which may be a desktop computer, laptop computer, smartphone, PDA handheld terminal, tablet computer or other terminal device with display function. The computing device includes a processor and a memory. The memory stores one or more programs. When the processor executes the program stored in the memory, it implements the method for constructing a convex optimization model for train energy-saving operation control oriented towards complex traction characteristics as described in Embodiment 1.

[0153] The above embodiments are preferred embodiments of the present invention, but the embodiments of the present invention are not limited to the above embodiments. Any changes, modifications, substitutions, combinations, or simplifications made without departing from the spirit and principle of the present invention shall be considered equivalent substitutions and shall be included within the protection scope of the present invention.

Claims

1. A method for constructing a convex optimization model for train energy-saving operation control oriented towards complex traction characteristics, characterized in that, Includes the following steps: Collect real train parameter information and obtain real train operation curves; The basic steps for constructing a convex model of train energy-saving operation control include: Based on the basic dynamics of trains, a distance-based discretization method is used to construct an optimization model for train energy-saving operation control strategy. Pre-defined constraints, including constraints on train dynamics, kinematic relationships, resistance equations, and on-time performance, are used to construct a basic energy-saving operation and control model for the train; The basic energy-saving operation and control model of the train is subjected to convex relaxation treatment using the auxiliary variable method to obtain the basic convex model of train energy-saving operation and control. The constraints of train dynamics are expressed as follows: ； in, This represents the traction / braking force at the i-th distance interval. This represents the train running resistance that is positively correlated with train speed. This represents the length of the i-th distance interval. This indicates information about slope changes over a corresponding distance. This represents the velocity point that needs to be optimized at each discrete point. It's the quality of the train. Represents gravitational acceleration; The constraints on on-time performance are expressed as follows: The total time the train takes to travel within each section equals the target travel time indicated by the timetable. , is represented as: ； ； in, This represents the average velocity at the i-th distance interval; The basic energy-saving operation and control model of the train is subjected to convex relaxation treatment using the auxiliary variable method. Two auxiliary variables are added, represented as follows: ； ； in, , Auxiliary variables are used for substitution. and This transforms non-convex constraints into linear expressions. By incorporating the modeling of inherent traction characteristics into the basic train energy-saving operation and control convex optimization model, an inherent characteristic model of the traction system with natural characteristic zone and hybrid braking is constructed. By collecting, sampling and preprocessing measured dynamic efficiency data of traction motors, the relationship between efficiency, traction / braking force and speed is constructed. Auxiliary variables are introduced to establish the relationship between efficiency and train operation energy consumption, and a convex model of train energy-saving operation control based on the dynamic efficiency map of motors is constructed. By using positive and negative fitting surfaces to fit the fitting data of positive and negative curved surfaces, the dynamic efficiency spectrum of the motor is converted into a convex polynomial, and the relationship between dynamic efficiency and energy consumption is established. We obtain real energy consumption data by analyzing the power loss of each component at the system level.

2. The method for constructing a convex optimization model for train energy-saving operation control oriented towards complex traction characteristics as described in claim 1, characterized in that, The specific steps for constructing an inherent characteristic model of the traction system with natural characteristic zones and hybrid braking include: The traction motor has different characteristic regions, including the starting region, constant torque region, constant power region, and natural characteristic region. A three-stage traction and braking characteristic is used to simulate the inherent traction characteristics of a train under real-world operating conditions, satisfying the following constraints: ； in, Indicates the train's traction force. For maximum traction, This indicates the maximum speed in the constant torque region. This indicates the maximum speed in the constant power region. Indicates the maximum permissible speed; When the train enters the braking phase, mechanical braking is used in the low-speed zone, supplemented by electric braking. When the speed exceeds the critical speed, the braking mode changes from mechanical braking to regenerative braking. The braking force-speed relationship expression under the hybrid braking mode is: ； in, This indicates the braking force considering both the natural characteristic zone and the hybrid braking mode. A sloping line used to indicate the change from mechanical braking to regenerative braking mode. For maximum regenerative braking force, This represents the linear fitting expression for the natural characteristic region, where parameters a, b, c, and d are all calculated from the measured data of the traction motor.

3. The method for constructing a convex optimization model for train energy-saving operation control oriented towards complex traction characteristics as described in claim 1, characterized in that, it introduces... An auxiliary variable is used to establish the relationship between efficiency and train operation energy consumption, expressed as follows: ； ； in, ≥0 indicates traction force. <0 indicates braking force. This indicates the efficiency at the corresponding traction force and velocity point. This indicates the efficiency at the corresponding braking force and speed point. Represents auxiliary variables. Indicates the length of distance.

4. The method for constructing a convex optimization model for train energy-saving operation control oriented towards complex traction characteristics as described in claim 1, characterized in that, The fitting data processing for positive and negative surfaces is performed using positive and negative fitting surfaces, specifically as follows: ； in, These are the polynomial fitting coefficients for surfaces ① and ②. These are the polynomial fitting coefficients for surfaces ③ and ④. Surface ① represents the positively fitted surface, surface ② represents the positive extension of the negatively fitted surface, surface ③ represents the negatively fitted surface, and surface ④ represents the negative extension of the positively fitted surface. The distance is represented by f, the traction force or braking force is represented by v, and the speed is represented by v.

5. The method for constructing a convex optimization model for train energy-saving operation control oriented towards complex traction characteristics according to claim 1, characterized in that, To obtain real energy consumption data from power loss analysis of each component at the system level, the specific steps include: Establish traction power supply network Network voltage and the internal current flowing through the transformer The relationship is determined and fitted using a convex polynomial, which satisfies the following constraints: ； ； in, This indicates the power loss of the transformer. This represents the internal resistance of the transformer that causes power loss. Calculate the power losses of other system components, satisfying the following constraints: ； in, Indicates power loss. Indicates static loss efficiency. Used to indicate converters, gearboxes, or hubs. ≥0 indicates traction force. <0 indicates braking force.

6. A system for constructing a convex optimization model for train energy-saving operation control oriented towards complex traction characteristics, characterized in that, The method for constructing a convex optimization model for train energy-saving operation and control oriented towards complex traction characteristics as described in any one of claims 1-5 includes: a train data acquisition module, a basic train energy-saving operation and control convex model construction module, a traction system inherent characteristic model construction module, a train energy-saving operation and control convex model construction module, a fitting processing module, a conversion module, and a power loss analysis module. The train data acquisition module is used to collect real train parameter information and obtain the real train operation curve; The basic train energy-saving operation and control convex model construction module is used to construct a basic train energy-saving operation and control convex model; The traction system inherent characteristic model building module is used to add modeling of inherent traction characteristics to the basic train energy-saving operation control convex optimization model, and to build a traction system inherent characteristic model of natural characteristic region and hybrid braking. The train energy-saving operation and control convex model construction module is used to collect, sample and preprocess measured dynamic efficiency data of traction motors, construct the relationship between efficiency, traction / braking force and speed, introduce auxiliary variables, establish the relationship between efficiency and train operation energy consumption, and construct a train energy-saving operation and control convex model based on the dynamic efficiency map of motors. The fitting processing module is used to perform fitting data processing on positive and negative surfaces using positive and negative fitting surfaces. The conversion module is used to convert the dynamic efficiency graph of the motor into a convex polynomial and establish the relationship between dynamic efficiency and energy consumption. The power loss analysis module is used to obtain real energy consumption data from the power loss analysis of various components at the system level.

7. A computer-readable storage medium comprising a stored program, characterized in that, When the program is executed, it implements the method for constructing a convex optimization model for train energy-saving operation control oriented towards complex traction characteristics as described in any one of claims 1-5.

8. A computing device, comprising a processor and a memory for storing a processor-executable program, characterized in that, When the processor executes the program stored in the memory, it implements the method for constructing a convex optimization model for train energy-saving operation control oriented towards complex traction characteristics as described in any one of claims 1-5.

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