A method for saving energy of a city rail comprehensive system based on multi-vehicle cooperative optimization

Abstract

The application discloses a kind of based on the energy-saving method of urban rail comprehensive system optimization of multi-vehicle cooperation, comprising the following steps: according to basic input data, establish train-line-net-graph comprehensive system coupling model;Establish the time-space-speed three-dimensional state network of train operation;According to train motion characteristics, determine the train control operating mode transfer rule between adjacent time stages in time-space-speed three-dimensional state network;The train state under each time stage of time-space-speed three-dimensional state network is reduced dimension, and effective state space domain is obtained;According to multiple body dynamic programming algorithm, train-line-net-graph comprehensive system coupling model, train control operating mode transfer rule and effective state space domain, output optimal collaborative multi-train three-dimensional trajectory.The application can significantly reduce the iteration number of tidal flow calculation, greatly improve the algorithm efficiency, can simultaneously optimize the running process of all trains in multi-train system, realize system state optimization.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of energy-saving operation of urban rail trains, and particularly relates to an energy-saving method for an urban rail comprehensive system based on collaborative optimization of multiple trains. BACKGROUND

[0002] In total power consumption of the urban rail system, about 50% is train traction energy consumption, regenerative braking energy accounts for more than 30% of the traction energy consumption, and about 40% of the regenerative braking energy cannot be utilized in actual operation. Therefore, to achieve energy saving of the urban rail system, there are mainly two ways: reducing traction energy consumption and improving regenerative braking energy utilization rate. The former can be achieved by traction motor optimization, equipment lightening, train shape optimization, etc., and the latter can be achieved by adding an inverter feedback device and an energy storage device, but the above-mentioned schemes need to change the topology of the existing system and a large amount of hardware investment, compared with which, train energy-saving driving technology is a better choice, which can achieve more considerable energy-saving effect than hardware modification, has smaller investment cost and is easy to implement.

[0003] The existing train energy-saving driving technology usually optimizes the operation process of the train as an independent individual, which is not consistent with the actual system. The dynamic operation process of the train is coupled with many factors. First, the operation line determines the maximum speed limit of the train movement with the position change and the slope resistance. Then, the train diagram specifies the arrival time and departure time of each train at each station under daily operation. Finally, the traction power supply system, in which the substation provides the required power for the train movement through the traction network. Therefore, only by comprehensively considering the vehicle-line-network-diagram coupled large system, modeling the system as a whole, and researching the train energy-saving driving technology at the system total energy consumption level, can the real system be more consistent, and the future engineering application can have more guiding significance and reference value.

[0004] In the daily operation of the urban rail system, there are multiple trains running on the line. The position and power of all trains at the same time determine the power flow distribution of the traction power supply system at the same time. The stop time, interval running time and interval running speed curve of all trains directly determine the dynamic coincidence state of the train group on the time axis. Therefore, to minimize the energy consumption of the vehicle-line-network-diagram comprehensive system, the operation process of multiple trains needs to be optimized collaboratively. The existing multi-train optimization technology has considerable limitations. Not only is the vehicle-line-network-diagram comprehensive system not modeled as a whole, but also the operation process of a specific train is usually optimized by presetting the running trajectory of the train, without realizing true collaboration. In addition, in order to reduce the complexity of the problem, the speed curve optimization and the timetable optimization of the train are usually carried out separately, and cannot achieve the same layer optimization.

[0005] In summary, it has important research significance and wide application prospect to analyze the energy saving of the train-line-network-diagram integrated system based on urban rail transit and avoid the system energy saving by only optimizing the operation process of a specific train. SUMMARY

[0006] In view of the above problems in the prior art, the energy saving method of the urban rail integrated system based on multi-vehicle cooperative optimization provided by the present application solves the problem of optimal cooperative energy saving operation of a train group in the urban rail transit direct-current traction power supply system.

[0007] To achieve the above-mentioned purposes, the technical scheme adopted by the present application is as follows:

[0008] The energy saving method of the urban rail integrated system based on multi-vehicle cooperative optimization comprises the following steps:

[0009] S1, establishing a train-line-network-diagram integrated system coupling model according to basic input data;

[0010] S2, establishing a time-space-speed three-dimensional state network of train operation;

[0011] S3, determining the train control working condition transfer rule between adjacent time stages of the time-space-speed three-dimensional state network in step S2 according to the train motion characteristics;

[0012] S4, reducing the dimension of the train state in each time stage of the time-space-speed three-dimensional state network in step S2 to obtain an effective state space domain;

[0013] S5, outputting an optimal cooperative multi-train three-dimensional trajectory according to the multi-agent dynamic programming algorithm, the train-line-network-diagram integrated system coupling model in step S1, the train control working condition transfer rule in step S3 and the effective state space domain in step S4.

[0014] The present application has the following beneficial effects:

[0015] (1) The present application establishes a train-line-network-diagram integrated system coupling model under the actual train operation scenario, which can reflect the operation constraints and energy flow relationship in the dynamic train operation process;

[0016] (2) The present application establishes an integrated circuit model of the urban rail direct-current traction power supply system and train operation, and proposes a corresponding power flow calculation method, which is suitable for the multi-train traction power supply system under any number of trains, and can significantly reduce the iteration number of power flow calculation;

[0017] (3) The system state space dimension reduction method adopted by the application closely combines the characteristics of the train operation process, filters out the state points that cannot appear in the train operation process, effectively reduces the state space of the optimization problem, and greatly improves the algorithm efficiency;

[0018] (4) The traditional multi-train cooperative optimization technology can only optimize the operation process of a specific train in a multi-train system based on the assumption that the running state of other trains is known, and cannot achieve system state optimization, while the application can optimize the operation process of all trains in a multi-train system, realize true multi-train cooperation, minimize the total power consumption of the substation in a running cycle of the multi-train, and can achieve system state optimization;

[0019] (5) The train timetable optimization problem and the speed curve optimization problem in the traditional technology are integrated into a comprehensive optimization problem in the same layer in the application, and the optimal running time, optimal speed curve and optimal stopping time of each train in each interval in the multi-train system can be obtained simultaneously under the premise of ensuring the total time of train operation in a week;

[0020] (6) The application can minimize the total power consumption of the substation in a running cycle of the multi-train, and the problem scenario and energy consumption model are very close to the actual urban rail system, which has important guiding significance and broad application prospect for daily energy-saving operation;

[0021] (7) The problem scenario and energy consumption model considered in the application are very close to the actual urban rail system, which has important guiding significance and broad application prospect for daily energy-saving operation;

[0022] (8) The multi-agent dynamic programming algorithm designed in the application can not only be used in the cooperative optimization of multi-train operation process, but also theoretically applied to the multi-stage optimal decision control problem of other multi-agent large systems. BRIEF DESCRIPTION OF DRAWINGS

[0023] Figure 1 It is a flow chart of an urban rail comprehensive system energy-saving method based on multi-train cooperative optimization;

[0024] Figure 2 It is a typical urban rail line structure diagram;

[0025] Figure 3 It is an equivalent circuit topology diagram of a multi-train direct current traction power supply system;

[0026] Figure 4 It is a flow chart of a multi-train direct current traction power supply system power flow calculation method;

[0027] Figure 5 It is a time-space-speed three-dimensional state network construction schematic diagram;

[0028] Figure 6 a schematic diagram of train control condition transfer rules between stages;

[0029] Figure 7 a schematic diagram of multi-agent dynamic programming algorithm under space-time-speed three-dimensional state network;

[0030] Figure 8 a flowchart of the multi-agent dynamic programming algorithm. DETAILED DESCRIPTION

[0031] The specific embodiments of the present application are described below to facilitate the understanding of the present application for those skilled in the art, but it should be clear that the present application is not limited to the scope of the specific embodiments, and for those skilled in the art, it is obvious that various changes are within the spirit and scope of the present application defined and determined by the appended claims, and all the inventions utilizing the concept of the present application are within the scope of protection.

[0032] As shown in Figure 1 a city rail integrated system energy saving method based on multi-vehicle cooperative optimization, comprising steps S1-S5:

[0033] S1, establishing a train-line-network-diagram integrated system coupling model according to basic input data.

[0034] In an optional embodiment of the present application, the present application first needs to obtain basic input data required for optimization, which includes city rail train data (train weight, traction / braking characteristics), line data (speed limit, slope, station location, substation location), diagram data (total travel time, maximum / minimum interval running time, maximum / minimum station stop time) and traction power supply system data (traction network distributed resistance, substation equivalent voltage, substation equivalent internal resistance). Then analyze the dynamic coupling mechanism of train operation process and line, diagram and traction power network in turn, and establish a "train-line-network-diagram" integrated system coupling model.

[0035] Specifically, in this step of the present application, a "train-line-network-diagram" integrated large system coupling model under the actual train operation scenario is established, which can reflect the operation constraints and energy flow relationship in the process of train dynamic operation; an integrated circuit model of city rail DC traction power supply system and train operation is established, and a corresponding power flow calculation method is proposed. The integrated circuit model and the corresponding power flow calculation method are suitable for multi-train traction power supply system under any number of trains, and can significantly reduce the number of iterations of power flow calculation.

[0036] Step S1 includes the following sub-steps:

[0037] S11, establishing a train-diagram coupling of a train-line-network diagram synthesis system coupling model according to basic input data.

[0038] As shown in the drawings, for a typical urban rail operation line, its structure is a two-way line, and trains run around the line in a periodic round, the present application first assumes that a line has M stations and N trains run, and then establishes a coupling relationship between a train diagram and train operation. Figure 2

[0039] Step S11 includes the following steps:

[0040] S111, establishing a train period total running time part of the train-diagram coupling, expressed as:

[0041]

[0042] Wherein: is the arrival time of train n at the (2M-1)th station it passes through, M is the total number of stations of the line, is the departure time of train n at the 1st station it passes through, T is the total running time of a train running around the line for one week.

[0043] S112, establishing a train interval running time part of the train-diagram coupling, expressed as:

[0044]

[0045] Wherein: is the minimum interval running time of train n in the mth interval it passes through, is the arrival time of train n at the (m+1)th station it passes through, is the departure time of train n at the mth station it passes through, is the maximum interval running time of train n in the mth interval it passes through.

[0046] Specifically, the present application establishes the train interval running time part of the train-diagram coupling according to the fact that the interval running time of each train in each interval must be kept within a reasonable range.

[0047] S113, establishing a train stop time part of the train-diagram coupling, expressed as:

[0048]

[0049] Wherein: is the minimum stop time of train n at the mth station it passes through, is the departure time of train n at the mth station it passes through, is the arrival time of train n at the mth station it passes through,​ is the maximum stop time of train n at the mth station it passes through.

[0050] Specifically, the train stop time of each train at each station is kept within a reasonable range, and the train stop time part of the train diagram coupling is established.

[0051] S114, establish the train cycle total running distance part of the train diagram coupling, which is represented as:

[0052] s n (T) = 2L

[0053] wherein s n (T) is the distance train n has run at time T, L is the length of a single track, and the up and down tracks are parallel and physically equal in length.

[0054] Specifically, the total running distance of each train running a week in the present application should be the sum of the lengths of the two-way tracks, and the length of a single track in the present application is L, so the train cycle total running distance part of the train diagram coupling can be obtained.

[0055] S12, establish the train-line coupling of the train-line-network-diagram integrated system coupling model according to the basic input data.

[0056] Step S12 includes the following sub-steps:

[0057] S121, establish the train longitudinal dynamics part of the train-line coupling according to Newton's second law, which is represented as:

[0058]

[0059] wherein x n is the position of train n, t n is the running time of train n, v n is the speed of train n, f n (v n ) is the traction force adopted by train n, b n (v n ) is the control force adopted by train n, a is the first running resistance coefficient of the train, b is the second running resistance coefficient of the train, c is the third running resistance coefficient of the train, m n is the mass of train n, g represents the acceleration of gravity, and θ(x n ) is the track gradient at the position of train n.

[0060] S122, establish the train dynamic running constraint part of the train-line coupling, which is represented as:

[0061]

[0062] wherein: F(v n ) is the maximum traction force that can be applied depending on the train speed, B(v n ) is the maximum braking force that can be applied depending on the train speed, f n (t) is the traction force adopted by the train n at time t, b n (t) is the control force adopted by the train n at time t, v n (x n ) is the speed of the train n at position x n , is the line speed limit at position x n of the train n, v n (x m ) is the speed of the train n at position x m , x m is the position of the station m.

[0063] S13, train-network coupling of the train-line-network-graph integrated system coupling model is established according to basic input data.

[0064] Specifically, since urban rail transit is usually powered by DC, and the regenerative braking energy of the train cannot be exchanged between different power supply sections, the present application models the DC traction power supply system under the condition that multiple trains exist in the same power supply section, and obtains the corresponding equivalent circuit topology model, as shown in Figure 3 .

[0065] Meanwhile, for the established DC traction power supply system and the corresponding equivalent circuit topology model, the present application proposes a corresponding power flow calculation method, as shown in Figure 4 . The model and method proposed by the present application are applicable to the multi-train traction power supply system under any number of trains, and based on this, the train-network coupling of the train-line-network-graph integrated system coupling model in the present application can be established.

[0066] S13 includes the following sub-steps:

[0067] S131, calculate the electric power at the node according to the train control force and speed, expressed as:

[0068]

[0069] wherein: is the electric power of the uplink train n, is the traction force of the uplink train n, is the speed of the uplink train n, and η is the efficiency of the train traction transmission system, is the braking force of the uplink train n, P aux is the power of the train auxiliary system, is the electric power of the downlink train n, is the traction force of the down train n, is the speed of the down train n, is the braking force of the down train n.

[0070] S132, according to the train position, the equivalent resistance between nodes is calculated, which is represented as:

[0071]

[0072] wherein: is the (n+1)th up equivalent resistance of the equivalent circuit, ρ1 is the resistivity of the catenary, ρ2 is the resistivity of the return rail, is the distance between the node n and the node (n+1) of the up train, is the (n+1)th down equivalent resistance of the equivalent circuit, is the distance between the node n and the node (n+1) of the down train.

[0073] Specifically, is the (n+1)th up equivalent resistance of the equivalent circuit, i.e., the equivalent resistance between the node n and the node (n+1) of the up train; is the (n+1)th down equivalent resistance of the equivalent circuit, i.e., the equivalent resistance between the node n and the node (n+1) of the down train.

[0074] S133, according to the equivalent resistance between nodes in the sub-step S132, the admittance matrix of the equivalent circuit is calculated.

[0075] The step S133 includes the following sub-steps:

[0076] S1331, according to the equivalent resistance between nodes in the sub-step S132, the self-admittance of the substation node in the diagonal element of the admittance matrix is calculated, which is represented as:

[0077]

[0078]

[0079] wherein: G 11 is the first diagonal element of the admittance matrix, R eq is the equivalent internal resistance of the substation, is the first up equivalent resistance of the equivalent circuit, is the first down equivalent resistance of the equivalent circuit, G PP is the Pth diagonal element of the admittance matrix, P is the total number of nodes of the equivalent circuit, is the (N u +1)th up equivalent resistance of the equivalent circuit, N u is the total number of up nodes of the equivalent circuit, the (i+1)th uplink equivalent resistance of the equivalent circuit, d the total number of downlink nodes of the equivalent circuit. d

[0080] S1332, according to the equivalent resistance between nodes in the sub-step S132, the self-admittance of the train node in the diagonal element of the admittance matrix is calculated, which is represented as:

[0081]

[0082] wherein: G (i+1)(i+1) the (i+1)th diagonal element of the admittance matrix, the ith uplink equivalent resistance of the equivalent circuit, the (i+1)th uplink equivalent resistance of the equivalent circuit, the (i-N u )th downlink equivalent resistance of the equivalent circuit, the (i-N u +1)th downlink equivalent resistance of the equivalent circuit.

[0083] S1333, according to the equivalent resistance between nodes in the sub-step S132, the mutual admittance of the adjacent nodes with discontinuous serial numbers in the non-diagonal element of the admittance matrix is calculated, which is represented as:

[0084]

[0085]

[0086] wherein: the element in the 1st row and the (N u +2)th column of the admittance matrix, the element in the (N u +2)th row and the 1st column of the admittance matrix, the element in the (N u +1)th row and the Pth column of the admittance matrix, the element in the Pth row and the (N u +1)th column of the admittance matrix.

[0087] S1334, according to the equivalent resistance between nodes in the sub-step S132, the mutual admittance of the adjacent nodes with continuous serial numbers in the non-diagonal element of the admittance matrix is calculated, which is represented as:

[0088]

[0089] wherein: G i(i+1) the element in the ith row and the (i+1)th column of the admittance matrix, G (i+1)i the element in the (i+1)th row and the ith column of the admittance matrix. ​

[0090] S1335, establish the admittance matrix according to the self-admittance of the substation node in the diagonal element of the admittance matrix in sub-step S1331, the self-admittance of the train node in the diagonal element of the admittance matrix in sub-step S1332, the mutual admittance of the adjacent nodes with discontinuous serial numbers in the non-diagonal element of the admittance matrix in sub-step S1333, and the mutual admittance of the adjacent nodes with continuous serial numbers in the non-diagonal element of the admittance matrix in sub-step S1334.

[0091] Specifically, all the remaining elements in the admittance matrix are 0, so that the admittance matrix G of the equivalent circuit can be obtained, which is expressed as:

[0092]

[0093] wherein: G 12 is the element of the 1st row and the 2nd column of the admittance matrix, G 1P is the element of the 1st row and the Pth column of the admittance matrix, G 21 is the element of the 2nd row and the 1st column of the admittance matrix, G 2P is the element of the 2nd row and the Pth column of the admittance matrix, G P1 is the element of the Pth row and the 1st column of the admittance matrix, G P2 is the element of the Pth row and the 2nd column of the admittance matrix.

[0094] S134, decompose the admittance matrix in sub-step S133 into an upper triangular matrix and a lower triangular matrix.

[0095] Specifically, because the admittance matrix is invertible, it can be decomposed into the product of a lower triangular matrix l and an upper triangular matrix u, which is expressed as:

[0096] G = l · u

[0097] wherein: G is the admittance matrix, l is the lower triangular matrix, and u is the upper triangular matrix.

[0098] S135, determine whether the current is the first time phase; if yes, set the initial value of the node voltage as the no-load voltage, otherwise set the initial value of the node voltage as the node voltage of the power flow distribution solved in the last time phase.

[0099] Specifically, because the train operation is a continuous motion process, i.e., the position and electric power of the train are continuously changed without sudden change, the power flow distribution of the equivalent circuit is continuously changed. The node voltage under the power flow distribution of the last state is taken as the initial value of the node voltage for the power flow calculation in the current state, which can greatly reduce the number of iteration calculations. The equation for setting the initial value of the node voltage is as follows:

[0100]

[0101] wherein: U0(k) is the voltage initial value of the first substation node at time stage k, U u(1) U(k) is the voltage matrix initial value of the up-bound train nodes at time stage k, U d(1) U(k) is the voltage matrix initial value of the down-bound train nodes at time stage k, U U0(k) is the voltage initial value of the second substation node at time stage k, U s1 U(k-1) is the voltage of the first substation node at time stage k-1 power flow distribution, U u U(k-1) is the voltage matrix of the up-bound train nodes at time stage k-1 power flow distribution, U d U(k-1) is the voltage matrix of the down-bound train nodes at time stage k-1 power flow distribution, U s2 U(k-1) is the voltage of the second substation node at time stage k-1 power flow distribution, [U0] P×1 U0 is a matrix of P rows and 1 column, where all elements are U0.

[0102] S136, calculate the node current initial value according to the node electric power in the sub-step S131 and the node voltage initial value in the sub-step S315, denoted as:

[0103]

[0104] Wherein: I0(r) is the rth iteration current of the first substation node, r is the iteration calculation number, I u(r) I(r) is the rth iteration current matrix of the up-bound train nodes, I d(r) I(r) is the rth iteration current matrix of the down-bound train nodes, I0(r) is the rth iteration current of the second substation node, U0(r) is the rth iteration voltage of the first substation node, U0 is the voltage of the substation, R eq R is the equivalent internal resistance of the substation, P u P is the electric power matrix of the up-bound train nodes, U u(r) P(r) is the rth iteration voltage matrix of the up-bound train nodes, P d P is the electric power matrix of the down-bound train nodes, U d(r) P(r) is the rth iteration voltage matrix of the down-bound train nodes, U0(r) is the rth iteration voltage of the second substation node.

[0105] S137, calculate the node voltage at power flow distribution according to the upper triangular matrix and the lower triangular matrix obtained in the sub-step S134 and the node current initial value in the sub-step S316:

[0106]

[0107] Wherein: U is the (r+1)th iteration voltage of the first substation node u(r+1) U is the (r+1)th iteration voltage matrix of the up-train node d(r+1) U is the (r+1)th iteration voltage matrix of the down-train node U is the (r+1)th iteration voltage of the second substation node, u is the upper triangular matrix of the admittance matrix, and l is the lower triangular matrix of the admittance matrix.

[0108] S138, judging whether the node voltage in the sub-step S137 converges, if yes, obtaining the power flow distribution of the equivalent circuit, otherwise jumping to the sub-step S136.

[0109] Specifically, the present application iteratively calculates until all the node voltages converge, and obtains the power flow distribution of the equivalent circuit, which is represented as:

[0110]

[0111] wherein: [ε] P×1 is a matrix of P rows and 1 column, wherein all elements are ε, and ε is the convergence accuracy of all node voltages in the iterative calculation.

[0112] S139, according to the power flow distribution in the sub-step S138, establishing the train-network coupling of the train-line-network-graph integrated system coupling model, which is represented as:

[0113]

[0114]

[0115] wherein: E s is the total energy consumption of the train-line-network-graph integrated system, i.e. the total electric energy consumed by the substations in the multi-train operation process, k is the kth time stage of the multi-train system on the time axis, K is the total number of time stages of the multi-train system in the whole operation process, P s (k) is the output power of the substation in the time stage k, δ s (k) is a 0-1 variable for judging whether the substation needs to supply energy to the train group, which divides the working mode of the substation into two cases, indicating that the internal diode rectifier device of the substation can only provide energy to the train group, when the regenerated braking energy generated in the train group is greater than the required traction energy consumption, the excess part of the energy cannot be recycled, but is usually consumed in the form of heat on the resistor.

[0116] Specifically, according to the proposed power flow calculation method, the power flow distribution of the traction power supply system under the determined state (position, speed, control force) of a plurality of trains at a certain time stage can be calculated, and the dynamic power of the substation can be calculated, the train-network coupling of the train-line-network-graph integrated system coupling model is established, and thus the energy consumption index of the train-line-network-graph integrated system can be determined.

[0117] S2, a time-space-speed three-dimensional state network of train operation is established.

[0118] In an optional embodiment of the present application, the power flow calculation method of the train-line-network-graph integrated system coupling model needs to be performed according to the state of each train at the same time. The present application divides the time stages based on the time axis, which is consistent with the energy consumption calculation mode of the train-line-network-graph integrated system; the whole train operation process is discretized into state points in the time-space-speed three-dimensional space, one state point is selected for each train at each time stage, and finally the state points of all time stages are connected to obtain the three-dimensional trajectory of a train in the whole operation process, which provides a state space basis for realizing the collaborative optimization of multiple trains, as shown in Figure 5 .

[0119] Step S2 includes the following sub-steps:

[0120] S21, the total running time of the train cycle is divided into a plurality of time stages according to equal time intervals.

[0121] S22, in each time stage in sub-step S21, the train operation state is discretized into state points on the space-speed plane according to equal position intervals and equal speed intervals, and a time-space-speed three-dimensional state network of the whole train operation process is established.

[0122] S3, according to the train motion characteristics, the train control working condition transfer rule between adjacent time stages of the time-space-speed three-dimensional state network in step S2 is determined.

[0123] In an optional embodiment of the present application, in the time-space-speed three-dimensional state network, the time, position and speed of each state point are determined, so the time difference, position difference and speed difference of two state points in adjacent time stages are also determined. Generally, it is difficult to realize the transfer between two state points by giving the train a constant force, and the present application realizes the transfer between two state points by the mode of double control working condition connection. Therefore, the present application provides eight control working conditions including single control working condition and double control working condition, which cover all possible state transfers in the time-space-speed three-dimensional state network, as shown in Figure 6The single control working conditions include maximum traction MT, coasting CO, maximum braking MB and stopping DW, and the double control working conditions include partial traction plus coasting double control working condition PT+CO, coasting plus partial braking double control working condition CO+PB, stopping plus partial traction double control working condition DW+PT and partial braking plus stopping double control working condition PB+DW. The train equivalent power under the state transition can be solved by calculating the corresponding double control working condition transition points, thereby providing a basis for calculating the state transition cost of the multi-train system in the subsequent optimization algorithm.

[0124] Step S3 includes the following sub-steps:

[0125] S31, determining the single control working condition and the double control working condition of the train operation according to the train motion characteristics.

[0126] Specifically, for a determined state point of a time stage k, the speed is known, and thus the maximum traction force and the maximum braking force are known, and the state points that can reach the next time stage by applying the maximum traction, coasting and maximum braking three single working conditions can be calculated in sequence. Then, the state points in the rectangle formed by the maximum traction state point and the coasting state point are obtained by the partial traction plus coasting double working condition transition; the state points in the rectangle formed by the coasting state point and the maximum traction state point are obtained by the coasting plus partial braking double working condition transition; if the speed of the state point of the current stage is not zero and the speed of the state point of the next stage is zero, the partial braking plus stopping double working condition transition is used; if the speed of the state point of the current stage is zero and the speed of the state point of the next stage is not zero, the stopping plus partial traction double working condition transition is used; if the speeds of the state points of the current stage and the next stage are both zero and the positions are consistent, the stopping working condition is represented.

[0127] In summary, there are 8 cases of train control working conditions between adjacent time stages, including 4 single control working conditions and 4 double control working conditions.

[0128] S32, calculating the transition point time of the double control working condition in the sub-step S31, which is represented as:

[0129]

[0130] wherein: is the transition point time of the double control working condition, t k is the time of the time stage k, v n (k) is the speed of the state point corresponding to the time stage k, is the transition point speed of the double control working condition, t k+1 is the time of the time stage k+1, v n (k+1) is the speed of the state point corresponding to the time stage k+1, x n (k+1) is the position of the state point corresponding to the time stage k+1, xn (k) is the position of the state point corresponding to the time stage k, is the first acceleration corresponding to the double-control mode, is the second acceleration corresponding to the double-control mode.

[0131] S33, the equivalent power of the transfer is calculated according to the transfer point time in step S32, and is represented as:

[0132]

[0133] wherein: P n (k, k+1) is the equivalent power of the train transferred in the double-control mode, m n is the mass of the train n, R n (v n (k), x n (k)) is the sum of the basic running resistance and the slope resistance of the train corresponding to the state point of the time stage k, PT+CO is the partial traction plus inertial running double-control mode, R n (v n (k+1), x n (k+1)) is the sum of the basic running resistance and the slope resistance of the train corresponding to the state point of the time stage k+1, CO+PB is the inertial running plus partial braking double-control mode, DW+PT is the stop station plus partial traction double-control mode, and PB+DW is the partial braking plus stop station double-control mode.

[0134] S4, the train state of each time stage of the time-space-speed three-dimensional state network in step S2 is reduced in dimension to obtain an effective state space domain.

[0135] In an optional embodiment of the present application, the train state of each time stage of the time-space-speed three-dimensional state network in step S2 is reduced in dimension to obtain an effective state space domain. The present application proposes a system state space dimension reduction method in this step, which closely combines the characteristics of the train running process and the corresponding timetable constraints, filters out the state points that cannot appear in the train running process, effectively reduces the state space of the optimization problem, and can greatly improve the algorithm efficiency.

[0136] Step S4 includes the following sub-steps:

[0137] S41, the train state of each time stage of the time-space-speed three-dimensional state network in step S2 is reduced in speed according to the line speed limit and the maximum running capacity of the train.

[0138] The present application is based on line speed limit, makes the train run the whole journey with maximum capacity, can obtain the maximum capacity speed curve, which determines the highest possible speed point corresponding to each position point, and the speed point higher than the curve is invalid state point, thereby reducing the train state space in the solving process by reducing the dimension of train state in each time stage of the time-space-speed three-dimensional state network in step S2.

[0139] S42, according to the running diagram time constraint and the maximum running capacity of the train, reducing the dimension of the train state in each time stage of the time-space-speed three-dimensional state network in step S2.

[0140] Specifically, step S41 only determines the upper limit of the train speed based on the position, which is irrelevant to time, while different time stages correspond to different time points. Based on this feature, the present application can calculate the position boundary that each train can reach in each time stage, and all the points outside the position interval are invalid state points, which greatly reduces the train state space in the solving process, thereby reducing the dimension of the train state in each time stage of the time-space-speed three-dimensional state network in step S2.

[0141] Step S42 includes the following sub-steps:

[0142] S421, determining the time interval of the final train arriving at the station according to the forward and backward calculation method, represented as:

[0143]

[0144] Wherein: is the earliest time of the final train n arriving at the mth station it passes through, max[] is the maximum value in the brackets, is the earliest time of the train n arriving at the mth station it passes through in forward calculation, is the earliest time of the train n leaving the mth station it passes through in backward calculation, is the latest time of the final train n arriving at the mth station it passes through, min[] is the minimum value in the brackets, is the latest time of the train n arriving at the mth station it passes through in forward calculation, is the latest time of the train n leaving the mth station it passes through in backward calculation.

[0145] Specifically, all trains start from zero time, and the earliest and latest time of each train arriving at each station can be calculated in forward direction by combining the upper and lower limits of the interval running time and the stop time:

[0146]

[0147]

[0148] wherein: is the minimum section running time of train n at the ith section it passes through, m represents the train n passes through m stations from the start, is the minimum stop time of train n at the ith station it passes through, is the earliest time of train n arriving at the mth station it passes through, calculated reversely, is the maximum stop time of train n at the mth station it passes through.

[0149] In addition, all trains need to run around the line for a week within the specified total running time, combined with the upper and lower limits of section running time and stop time, the earliest and latest time of each train arriving at each station can be calculated reversely:

[0150]

[0151]

[0152] wherein: is the maximum section running time of train n at the ith section it passes through, is the maximum stop time of train n at the ith station it passes through, is the latest time of train n arriving at the mth station it passes through, calculated reversely, is the minimum stop time of train n at the mth station it passes through.

[0153] The results of forward and reverse calculation are integrated to obtain the final earliest and latest time of each train arriving at and leaving each station.

[0154] S422, determine the time interval of the final train leaving the station according to the forward and reverse calculation method, which is represented as:

[0155]

[0156] wherein: is the earliest time of the final train n leaving the mth station it passes through, is the earliest time of train n leaving the mth station it passes through, calculated forwardly, is the earliest time of train n arriving at the mth station it passes through, calculated reversely, is the latest time of the final train n leaving the mth station it passes through, is the latest time of train n leaving the mth station it passes through, calculated forwardly, is the latest time of train n arriving at the mth station it passes through, calculated reversely.

[0157] Specifically, all trains are scheduled to depart from zero time, and the earliest and latest time of each train leaving each station can be calculated forwardly combining the upper and lower limits of the interval running time and the stop time:

[0158]

[0159]

[0160] wherein T is the total running time of a train running around a line for one round, the maximum interval running time of train n in the ith running interval it passes through, and M is the total number of stations of a line, the maximum stop time of train n in the ith station it passes through.

[0161] In addition, all trains need to run around a line for one round within the specified total running time, and the earliest and latest time of each train arriving at each station can be calculated reversely combining the upper and lower limits of the interval running time and the stop time:

[0162]

[0163]

[0164] The results of forward and reverse calculations can be integrated to obtain the final earliest and latest time of each train arriving at and leaving each station.

[0165] S423、According to the final train arrival station time interval in sub-step S421 and the final train departure station time interval in sub-step S422, the upper and lower boundaries of the position state point in the station stay time interval of the train are determined, which is expressed as:

[0166]

[0167] wherein x n,min (k) is the lower boundary of the corresponding position state point at t k (k), x n (m) is the position of the mth station passed through by train n, t k is the time corresponding to the kth time stage, x n,max (k) is the upper boundary of the corresponding position state point at t k (k).

[0168] S424、According to the final train arrival station time interval in sub-step S421 and the final train departure station time interval in sub-step S422, the upper and lower boundaries of the position state point in the station stay time interval of the train are determined, which is expressed as:

[0169]

[0170] wherein: is the position of train n after using the maximum capacity running time t of the mth running section, is the minimum section running time of train n in the ith section it passes through, is the latest time of the final train n to arrive at the (m+1)th station it passes through, is the earliest time of the final train n to arrive at the (m+1)th station it passes through.

[0171] S5, outputting the optimal coordinated multi-train three-dimensional trajectory according to the multi-agent dynamic programming algorithm, the train-line-network-graph integrated system coupling model in step S1, the train control working condition transfer rule in step S3, and the effective state space domain in step S4.

[0172] In an optional embodiment of the present application, the present application proposes a multi-agent dynamic programming algorithm, a schematic diagram of the method is shown in Figure 7 , and a flowchart of the method is shown in Figure 8 .

[0173] Specifically, according to the multi-agent dynamic programming algorithm, the train-line-network-graph integrated system coupling model in step S1, the train control working condition transfer rule in step S3, and the effective state space domain in step S4, the optimal joint decision is calculated, and the optimal joint state sequence from the initial time stage to the final time stage is obtained, that is, the time-space-speed three-dimensional trajectory of each train in the whole running is obtained. Correspondingly, the section running time, the stop time and the section running speed curve of each train are all optimized, the optimal coordination of multiple trains is realized, and the total energy consumption of the train-line-network-graph integrated system is minimized.

[0174] Step S5 includes the following sub-steps:

[0175] S51, determining the state point of each train in the initial time stage.

[0176] Specifically, in the first time stage, the present application gives the initial state point of each train, that is, the initial position and the initial speed of all trains are determined to be zero. Since there is only one state point for each train in the first time stage, the joint state is also unique, and the cumulative cost index of the joint state is set to zero.

[0177] S52, calculating the state points that can be transferred by each train in the next time stage according to the train control working condition transfer rule in step S3, and retaining the state points within the effective state space domain in step S4.

[0178] Specifically, for each state point of each train, the application calculates the state points that can be transferred to in the next time stage according to the train control working condition transfer rule in step S3, and judges whether the transferred state points are within the valid state space domain calculated in S4; if yes, they are retained, otherwise discarded.

[0179] S53, determine all joint states in the next time stage according to the state points within the valid state space domain retained in sub-step S52.

[0180] S54, judge whether the joint states in sub-step S53 correspond to multiple joint decisions; if yes, calculate the cumulative cost of each joint decision according to the train-line-network-graph integrated system coupling model in step S1, and retain the optimal joint decision according to the cumulative cost, and then enter sub-step S55, otherwise directly enter sub-step S55.

[0181] Specifically, the application lists all joint states in the next time stage, and for each joint state, judges whether it corresponds to multiple joint decisions; if yes, calculates the sum of the cumulative cost index of the joint state before transition and the transition cost of the joint decision, and retains the optimal joint decision. Then, the current joint state is added to the optimal joint state sequence from the initial time stage to the time stage before transition corresponding to the joint decision, as the optimal joint state sequence of the current joint state, and the corresponding cumulative cost index is recorded, while other joint decisions and corresponding sequences are discarded, otherwise, the optimal joint state sequence and cumulative cost index corresponding to the only joint decision are directly retained; (joint state: state combination of multiple trains in the stage. Joint decision: state transition combination of a certain joint state of multiple trains in the current time stage to a certain joint state in the next time stage).

[0182] S55, update the optimal sequence and cumulative cost of the joint state in sub-step S53.

[0183] S56, judge whether the last time stage is reached; if yes, output the optimal coordinated multi-train three-dimensional trajectory and end the operation, otherwise jump to sub-step S52.

[0184] When the algorithm reaches the last time stage, all trains have completed a round of operation and returned to the starting position with a speed of zero, so there is only one joint state. When the optimal joint decision of the joint state is calculated, the optimal joint state sequence from the initial time stage to the final time stage is obtained, i.e. the time-space-speed three-dimensional trajectory of each train in the whole running is obtained. Finally, the optimal coordinated multi-train three-dimensional trajectory is output and the operation is ended.

[0185] Those skilled in the art will appreciate that the embodiments described herein are presented for purposes of illustration and that the inventive principles are not limited to these particular embodiments. Other variations and modifications can be made to the embodiments without departing from the spirit and scope of the inventive principles.

Claims

1. A multi-vehicle coordination optimization-based urban rail integrated system energy-saving method, characterized in that, The method comprises the following steps: S1, establishing a train-line-network-graph integrated system coupling model according to basic input data; S2, establishing a time-space-speed three-dimensional state network of train operation; S3, determining train control working condition transfer rules between adjacent time stages of the time-space-speed three-dimensional state network in step S2 according to train motion characteristics; S4, reducing dimensions of train states in each time stage of the time-space-speed three-dimensional state network in step S2 to obtain an effective state space domain; S5, outputting optimal coordinated multi-train three-dimensional trajectories according to a plurality of individual dynamic programming algorithms, the train-line-network-graph integrated system coupling model in step S1, the train control working condition transfer rules in step S3, and the effective state space domain in step S4; Step S1 comprises the following sub-steps: S11, establishing train graph coupling of the train-line-network-graph integrated system coupling model according to basic input data; S12, establishing train line coupling of the train-line-network-graph integrated system coupling model according to basic input data; S13, establishing train network coupling of the train-line-network-graph integrated system coupling model according to basic input data; Step S2 comprises the following sub-steps: S21, dividing total train cycle operation time into a plurality of time stages according to equal time intervals; S22, discretizing train operation states into state points on a space-speed plane according to equal position intervals and equal speed intervals in each time stage in sub-step S21 to establish a time-space-speed three-dimensional state network of train operation throughout a whole journey; Step S3 comprises the following sub-steps: S31, determining single control working conditions and double control working conditions of train operation according to train motion characteristics; S32, calculating transfer point time of the double control working conditions in sub-step S31; S33, calculating equivalent power of transfer according to the transfer point time in sub-step S32. 2.The energy saving method of a city rail integrated system based on multi-vehicle cooperative optimization according to claim 1, characterized in that, Step S11 comprises the following sub-steps: S111, establishing a total train cycle operation time part of the train graph coupling, which is expressed as: wherein: is the number of stations on the line, is the number of stations on the line, is the arrival time of the train at the first station on its route, is the number of stations on the line, is the number of stations on the line, is the departure time of the train from the first station on its route, is the total running time of the train on the line for one round. S112, establishing a train section operation time part of the train graph coupling, which is expressed as: wherein: is the train the minimum section running time of the train at the section is the train the arrival time of the train at the station is the train the departure time of the train at the station is the train the maximum section running time of the train at the section S113, establishing a train stop station time part of the train graph coupling, which is expressed as: in: For train The first time it passed Minimum stopping time at each station, For train The first time it passed Departure times of each station For train The first time it passed Arrival times at each station, For train The first time it passed Maximum dwell time at each station; S114, establishing a total train cycle operation distance part of the train graph coupling, which is expressed as: wherein: is the train at the time distance traveled, is the length of the single-track section.

3. The energy saving method of a city rail integrated system based on multi-vehicle cooperative optimization according to claim 1, characterized in that, Step S12 comprises the following sub-steps: S121, establishing a train longitudinal dynamics part of the train line coupling according to Newton's second law, which is expressed as: in: For train Location, For train runtime For train speed, For train The traction force used For train The control force used This is the coefficient of the first running resistance experienced by the train. This is the second running resistance coefficient experienced by the train. This is the third running resistance coefficient experienced by the train. For train quality Represents gravitational acceleration. For train The gradient of the line at the location; S122, establishing a train dynamic operation constraint part of the train line coupling, which is expressed as: wherein: is the maximum tractive effort that can be applied depending on the train speed, is the maximum braking effort that can be applied depending on the train speed, is the train adopted tractive effort at time t, is the train adopted control effort at time t, is the train speed at position , is the train position , is the train speed at position , is the station position.

4. The energy saving method of a city rail integrated system based on multi-vehicle cooperative optimization according to claim 1, characterized in that, Step S13 comprises the following sub-steps: S131, calculating node electric power according to train control force and speed, which is expressed as: in: For the upward train electrical power, For the upward train traction force, For the upward train speed, For the efficiency of the train traction drive system. For the upward train Braking force, For the power of the train auxiliary system, For the down train electrical power, For the down train traction force, For the down train speed, For the down train Braking force; S132, calculating equivalent resistance between nodes according to train position, which is expressed as: wherein: Rup is the equivalent resistance of the up line, Rdown is the equivalent resistance of the down line, is the resistivity of the catenary, is the resistivity of the return rail, is the distance between the up train node and the node , Rup is the equivalent resistance of the up line, Rdown is the equivalent resistance of the down line, is the distance between the down train node and the node . S133, calculating an admittance matrix of the equivalent circuit according to the equivalent resistance between nodes in sub-step S132; S134, decomposing the admittance matrix in sub-step S133 into an upper triangular matrix and a lower triangular matrix; S135, judging whether the current is the first time stage; if yes, setting a node voltage initial value as no-load voltage, otherwise setting the node voltage initial value as a node voltage of a power flow distribution solved in the last time stage. S136, calculate the initial node current according to the initial node voltage and the initial node power at the node in sub-step S315, denoted as: in: The first substation node r The current of the next iteration r The number of iterations is calculated. The first node for the upward train r The next iteration current matrix The first downlink train node r The next iteration current matrix For the second substation node r The current of the next iteration The first substation node r Next iteration voltage. This refers to the voltage at the substation. This represents the equivalent internal resistance of the substation. This is the electrical power matrix for the uplink train node. The first of the upward train nodes r Next iteration voltage matrix This is the electrical power matrix for the downlink train nodes. The first downlink train node r Next iteration voltage matrix For the second substation node r Next iteration voltage; S137, calculate the node voltage under power flow distribution according to the upper triangular matrix and the lower triangular matrix in sub-step S134 and the initial node current in sub-step S316, denoted as: in: For the ()th node of the first substation r +1) iteration voltage, For the ()th node of the up-going train r +1) iteration voltage matrix, For the ()th of the downlink train node r +1) iteration voltage matrix, For the second substation node () r +1) iteration voltage, u The upper triangular matrix is ​​the admittance matrix. l It is a lower triangular matrix of the admittance matrix; S138, judge whether the node voltage in sub-step S137 converges, if yes, get the power flow distribution of the equivalent circuit, otherwise, jump to sub-step S136; S139, establish the vehicle-network coupling of the vehicle-line-network-graph integrated system coupling model according to the power flow distribution in sub-step S138, denoted as: wherein: is the total energy consumption of the train-line-network-graph synthesis system, is the number of time stages of the multi-train system on the time axis, is the total number of time stages of the multi-train system over the whole operation, is the number of time stages is the output power of the substation in time stage is a 0-1 variable that determines whether the substation needs to supply energy to the train group.​ 5. The urban rail integrated system energy-saving method based on multi-vehicle collaborative optimization according to claim 1, characterized in that, Calculate the transition point time of the double-control operating mode in sub-step S31, denoted as: wherein: is the time instant of the transition point between the two control regimes, denotes the time instant of the beginning of the time phase , is the speed of the state point corresponding to the time phase , is the speed of the transition point between the two control regimes, is the time instant of the beginning of the time phase , is the time instant of the beginning of the time phase , is the position of the state point corresponding to the time phase , is the position of the state point corresponding to the time phase , is the first acceleration corresponding to the two control regimes, is the second acceleration corresponding to the two control regimes. Calculate the equivalent power of the transition according to the transition point time in sub-step S32, denoted as: wherein: is the equivalent power of the train for the double control mode transition, is the mass of the train, is the time period, is the sum of the basic running resistance and the slope resistance of the train at the corresponding state point, is the partial traction plus idling double control mode, is the time period, is the sum of the basic running resistance and the slope resistance of the train at the corresponding state point, is the idling plus partial braking double control mode, is the time period, is the sum of the basic running resistance and the slope resistance of the train at the corresponding state point, is the partial braking plus station double control mode.

6. The energy saving method of a city rail integrated system based on multi-vehicle cooperative optimization according to claim 1, characterized in that, Step S4 includes the following sub-steps: S41, reduce the speed dimension of the train state at each time stage of the time-space-speed three-dimensional state network in step S2 according to the line speed limit and the maximum running capacity of the train; S42, reduce the position dimension of the train state at each time stage of the time-space-speed three-dimensional state network in step S2 according to the timetable time constraint and the maximum running capacity of the train.

7. The energy saving method of a city rail integrated system based on multi-vehicle cooperative optimization according to claim 6, characterized in that, Step S42 includes the following sub-steps: S421, determine the final train arrival station time interval according to the forward-backward calculation method, denoted as: wherein: is the final train arriving at the first station it passes through at the earliest time, is the maximum value taken over the bracket, is the earliest time at which the train arrives at the first station it passes through in the forward calculation, is the latest time at which the train leaves the first station it passes through in the backward calculation, is the final train arriving at the first station it passes through at the latest time, is the minimum value taken over the bracket, is the latest time at which the train arrives at the first station it passes through in the forward calculation, is the earliest time at which the train leaves the first station it passes through in the backward calculation; S422, determine the final train departure station time interval according to the forward-backward calculation method, denoted as: wherein: is the final train leaves the first station it passes through at the earliest time, is the train leaves the first station it passes through at the earliest time, is the train arrives at the first station it passes through at the earliest time, is the final train leaves the first station it passes through at the latest time, is the train leaves the first station it passes through at the latest time, is the train arrives at the first station it passes through at the latest time; S423, determine the upper and lower boundaries of the position state point in the train stay time interval at the station according to the final train arrival station time interval in sub-step S421 and the final train departure station time interval in sub-step S422, denoted as: wherein: is the lower boundary of the position state point corresponding to the time instant , is the position of the train passing through the th station, is the position of the train at the th time phase, is the upper boundary of the position state point corresponding to the time instant S424, determine the upper and lower boundaries of the position state point not in the train stay time interval at the station according to the final train arrival station time interval in sub-step S421 and the final train departure station time interval in sub-step S422, denoted as: wherein: is the train is the position of the train after the maximum capacity run time of the is the train is the minimum section run time of the train in the section it is passing through, is the latest time of arrival of the final train at the station it is passing through, is the earliest time of arrival of the final train at the station it is passing through. is the final train is the earliest time of arrival of the final train at the station it is passing through. 8.The energy saving method of a city rail integrated system based on multi-vehicle cooperative optimization according to claim 1, characterized in that, Step S5 includes the following sub-steps: S51, determine the state points of each train at the initial time stage; S52, calculate the state points that each train can transfer to at the next time stage according to the train control operating mode transition rule in step S3 and retain the state points within the effective state space domain in step S4; S53, determine all joint states at the next time stage according to the state points retained within the effective state space domain in sub-step S52; S54, judge whether the joint state in sub-step S53 corresponds to multiple joint decisions; if yes, calculate the cumulative cost corresponding to each joint decision according to the vehicle-line-network-graph integrated system coupling model in step S1, and retain the optimal joint decision according to the cumulative cost, then enter sub-step S55, otherwise, directly enter sub-step S55; S55, update the optimal sequence and cumulative cost of the joint state in sub-step S53; S56, judging whether the last time stage is reached; if yes, outputting the optimal coordinated multi-train three-dimensional trajectory and ending the operation, otherwise jumping to the sub-step S52.

Images