A train operation diagram optimization method considering passenger flow impact and power supply system energy saving

Abstract

The present invention discloses a train operation diagram optimization method that considers the impact of passenger flow and energy saving of the power supply system, proposes an urban rail train operation diagram optimization method that considers the comprehensive energy saving index of the power supply system, combines the operation diagram optimization process with power supply calculation and comprehensive energy saving index evaluation, and considers the train delay time limit and interval passenger flow changes, takes the train stop time and tracking interval as decision variables, establishes a double-layer train operation diagram optimization model, and uses a processor multi-core parallel computing method to accelerate the model solution. The present invention has the characteristics of considering actual train operation changes and comprehensively improving the energy saving rate of the power supply system. It is suitable for the optimization calculation of the comprehensive energy saving of the train operation diagram, and can provide a basis for the urban rail operation department to formulate the train energy-saving operation diagram.

Description

Technical Field

[0001] The present invention belongs to the field of rail transportation, and in particular relates to a train operation diagram optimization method that takes into account the impact of passenger flow and energy saving of a power supply system. Background Art

[0002] The technical background of energy-saving optimization of train operation diagrams stems from the growing energy consumption demand and environmental protection requirements of rail transit systems. With the acceleration of urbanization, rail transit has become a key component of urban public transportation, and its high energy consumption problem needs to be solved urgently. By optimizing the train operation diagram, energy consumption can be significantly reduced while ensuring train transportation efficiency and punctuality. For example, the regenerative braking technology of modern electric traction systems can convert the kinetic energy of trains into electrical energy and feed it back to the power grid. The effective use of this technology depends on the reasonable design of the operation diagram, so that the operation between trains is coordinated and consistent, reducing energy waste. In addition, the intelligent dispatching system optimizes train speed, stop time and operation frequency by analyzing traffic data and demand changes in real time, further improving the energy-saving efficiency of the system. With the increasingly stringent environmental protection regulations of various countries, rail transit needs to improve the sustainable development capabilities of the system while reducing energy consumption and carbon emissions.

[0003] The challenges faced in the process of optimizing train operation diagrams are closely related to the widespread application of modern energy-saving devices and the dynamic changes in the operating environment. First, with the application of regenerative braking technology, trains convert kinetic energy into electrical energy and feed it back to the power grid when braking. Although this technology can reduce energy consumption, its efficient use depends on the coordination between trains and the adaptability of the power system. As the transmission and utilization of regenerative braking power become more complicated, traditional operation diagram optimization methods alone can no longer fully utilize this energy. For example, the effectiveness of energy feedback depends on whether other trains can use this energy at the right time, otherwise it will lead to energy waste. Although the emergence of flexible traction power supply systems has improved the flexibility of the system, it has also increased the complexity of energy flow and management, making the optimization of operation diagrams more difficult.

[0004] In addition, changes in passenger flow also have a direct impact on the traction and braking energy consumption of the train, which in turn affects the optimization of the operation diagram. The huge difference in passenger flow during peak and trough periods requires trains to adopt different acceleration and braking strategies in different time periods. For example, during peak periods with large passenger flows, trains need to start and stop more frequently, resulting in higher energy consumption. During trough periods, trains may run at lower speeds or reduce the frequency to save energy. This dynamic change in passenger flow increases the uncertainty of train energy consumption, making the operation diagram optimization more flexible and dynamic. In addition, the passenger flow characteristics between different lines and stations are also different, which requires the operation diagram to be differentiated and optimized across the entire network. This complex multi-factor change poses a huge challenge to the optimization of the train operation diagram, and traditional optimization methods have been difficult to cope with. Summary of the invention

[0005] The present invention aims to optimize the train operation diagram by taking into account the passenger flow change and the comprehensive energy saving of the power supply system. The present invention provides a train operation diagram optimization method taking into account the passenger flow influence and the energy saving of the power supply system.

[0006] The present invention provides a train operation diagram optimization method that considers the impact of passenger flow and power supply system energy saving, specifically: establishing a double-layer train operation diagram optimization model, the upper layer is an operation diagram optimization model that considers the comprehensive energy saving index of the power supply system, generates feasible solutions for multi-train tracking intervals and stop times, drives the lower layer of the train timing energy saving optimization model that considers the change of interval passenger flow, and on the basis of restoring the operation trajectories of multiple vehicles, calls the power supply system simulation module, generates comprehensive energy saving indicators, and obtains the optimal solution through the iterative solution method of the intelligent algorithm.

[0007] The upper layer is an operation diagram optimization model that considers the comprehensive energy-saving indicators of the power supply system, which generates feasible solutions for multi-train tracking intervals and stop times, and drives the lower layer train timing energy-saving optimization model that considers changes in section passenger flow. On the basis of restoring the operation trajectories of multiple vehicles, the power supply system simulation module is called to generate comprehensive energy-saving indicators, and the optimal solution is obtained through the iterative solution method of intelligent algorithms.

[0008] Taking into account the comprehensive energy-saving index of the power supply system and the train delay time limit index, the normalization idea is adopted to establish the upper-level operation diagram optimization model as follows:

[0009]

[0010] in: is the normalized objective function, f1 is the comprehensive energy-saving index of the urban rail traction power supply system, and f 1,0 is the comprehensive energy-saving index of the urban rail traction power supply system before the operation diagram optimization, f2 is the train delay time limit index, and f 2,0It is the allowable delay time limit indicator of all trains before the operation diagram optimization. The weights of f1 and f2 are equal. After the operation diagram optimization, the energy consumption of the power supply system is reduced while the train deviation time is minimized.

[0011] constraint:

[0012]

[0013] Formulas (2)-(8) respectively represent: train stop time constraint, tracking interval constraint, section operation time constraint, overall stop time constraint of all trains at all stations, overall tracking interval constraint of all trains, single train delay time constraint, and overall delay time constraint of all trains.

[0014] In formula (1):

[0015]

[0016] In formula (9), f1∈[0,f 1,0 ], are the arrival and departure times of train i at each station before the operation diagram optimization, are the arrival and departure times of train i at each station after the operation diagram is optimized; It is the sum of all the traction work and electricity in the rectification condition of the whole line, that is, the traction energy consumption; It is the sum of all the traction work and electricity in the inverter condition of the whole line, that is, the feedback energy; N is the amount of electricity returned by the main substations along the entire line; r is the number of traction stations along the entire line, N m The number of main offices in the entire line; T r,rec is the duration of the rectification condition of the rth traction station, T r,inv is the duration of the inverter condition of the rth traction station, τ is the simulation time; P r,rec (t) is the active power of the rth traction under rectification condition at time t, P r,inv (t) is the active power of the rth traction under the inverter condition at time t, P m (t) is the return power of the mth main substation at time t.

[0017] In formula (1):

[0018]

[0019] In formula (10), are the times when train i arrives at and leaves station s according to the planned operation diagram; are the times when train i arrives at and leaves station s according to the optimized operation diagram; N is the total number of stations, and M is the total number of trains.

[0020] In formulas (2)-(7), are the minimum and maximum stop time of train i at station s respectively; are the minimum tracking interval and the maximum tracking interval between train i and train i+1 respectively; Δh is the secondary adjustment of the tracking interval, Δh∈[0,5]; T i,s,s+1 is the running time of train i in interval s, s+1; are the minimum and maximum sum of the stop time of all trains at each station, are the minimum and maximum values ​​of the sum of all train tracking intervals respectively; D i , are the delay time of train i, the minimum delay time of train i, and the maximum delay time of train i respectively; D total , They are respectively the sum of all train delay times, the minimum value of the sum of all train delay times, and the maximum value of the sum of all train delay times.

[0021]

[0022] in: S = {1,2,…,s,…,N} is the set of stations, and I = {1,2,…,i,M} is the set of trains.

[0023] The lower layer establishes a train timing energy-saving optimization model that takes into account changes in interval passenger flow. Changes in interval passenger flow cause changes in train weight, which in turn affects changes in train traction energy consumption. Based on the existing train timing energy-saving model, the train weight is considered as a variable, and the lower layer train timing energy-saving optimization model is established as follows:

[0024] min{f T,i,g},min{f E,i,g} (12)

[0025]

[0026] In formula (12), f T,i,g is the delay time limit index of train i running in section g, calculated by formula (14); f E,i,g is the traction energy consumption index of train i running in section g, which is calculated by formula (15).

[0027] f T,i,g =|T i,g (λ i,g ,v i,g )-T i,g | (14)

[0028] In formula (14), T i,g (λi,g ,v i,g ) is the number of train i in the gth interval with λ i,g 、v i,g The actual time of runtime, λ i,g is the coasting control coefficient, v i,g is the target speed of train i in section g, T i,g is the planned running time of train i in the g-th section.

[0029]

[0030] In formula (15), μ i,g is the traction force utilization coefficient of train i in section g, 0≤μ i,g ≤1;M i,g is the weight of train i when running in section g after considering passenger flow; f max,i,g (v i,g ,M i,g ) is when the train speed is v i,g 、The vehicle weight is M i,g The maximum traction force at i is the electromechanical efficiency of train i; is the time when train i arrives at station s+1, is the time when train i leaves station s.

[0031] Formula (13) represents: interval running time constraint, speed constraint, acceleration constraint; δ max The maximum deviation allowed between the actual running time and the planned running time; lim (l i,g ) is the position l i,g The speed limit at a i,g (t), a i,g (t-1) are the accelerations of train i at time t and time t-1 in the g-th interval, Δt is the simulation interval, Δa max is the maximum value of the acceleration rate of change.

[0032] The upper-level operation diagram optimization model uses the multi-train optimized operation trajectory as a driving force to calculate the power flow of the urban rail power supply system, solve the operation diagram optimization model, and generate the optimization solution set {h i,i+1 ,T i,S};h i,i+1 represents the tracking interval between the i-th train and the i+1-th train, T i,S represents the stop time of the i-th train at each station; the lower optimization model is based on the coasting control coefficient λ i,g 、Train target speed v i,gThe train operation process is divided, and a fixed-step target speed search algorithm is used to solve the train timing energy-saving optimization model considering the changes in section passenger flow, and generate multi-train optimized operation trajectories as the input of the upper optimization model.

[0033] The beneficial technical effects of the present invention are:

[0034] The operation diagram optimization method proposed in the present invention has the characteristics of considering actual train operation changes and comprehensively improving the energy-saving rate of the power supply system, and is suitable for the optimization calculation of the comprehensive energy saving of the train operation diagram; the present invention provides a feasible solution for optimizing the operation diagram of the power supply system of energy-saving equipment taking into account the influence of passenger flow, and can provide a basis for urban rail operating departments to formulate train energy-saving operation diagrams. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] Figure 1 It is a schematic diagram of the double-deck train operation diagram optimization model of the present invention.

[0036] Figure 2 It is a schematic diagram of parallel solution of the operation diagram optimization model of the present invention.

[0037] Figure 3 It is the train energy interaction diagram in the present invention. DETAILED DESCRIPTION

[0038] The present invention will be further described in detail below in conjunction with the accompanying drawings and specific embodiments.

[0039] The present invention provides a train operation diagram optimization method that considers the impact of passenger flow and power supply system energy saving, specifically: establishing a double-layer train operation diagram optimization model, the upper layer is an operation diagram optimization model that considers the comprehensive energy saving index of the power supply system, generates feasible solutions for multi-train tracking intervals and stop times, drives the lower layer of the train timing energy saving optimization model that considers the change of interval passenger flow, and on the basis of restoring the operation trajectories of multiple vehicles, calls the power supply system simulation module, generates comprehensive energy saving indicators, and obtains the optimal solution through the iterative solution method of the intelligent algorithm.

[0040] The upper layer is an operation diagram optimization model that considers the comprehensive energy-saving indicators of the power supply system, which generates feasible solutions for multi-train tracking intervals and stop times, and drives the lower layer train timing energy-saving optimization model that considers changes in section passenger flow. On the basis of restoring the operation trajectories of multiple vehicles, the power supply system simulation module is called to generate comprehensive energy-saving indicators, and the optimal solution is obtained through the iterative solution method of intelligent algorithms.

[0041] Taking into account the comprehensive energy-saving index of the power supply system and the train delay time limit index, the normalization idea is adopted to establish the upper-level operation diagram optimization model as follows:

[0042]

[0043] in: is the normalized objective function, f1 is the comprehensive energy-saving index of the urban rail traction power supply system, and f 1,0 is the comprehensive energy-saving index of the urban rail traction power supply system before the operation diagram optimization, f2 is the train delay time limit index, and f 2,0 It is the allowable delay time limit indicator of all trains before the operation diagram optimization. The weights of f1 and f2 are equal. After the operation diagram optimization, the energy consumption of the power supply system is reduced while the train deviation time is minimized.

[0044] constraint:

[0045]

[0046]

[0047] Formulas (2)-(8) respectively represent: train stop time constraint, tracking interval constraint, section operation time constraint, overall stop time constraint of all trains at all stations, overall tracking interval constraint of all trains, single train delay time constraint, and overall delay time constraint of all trains.

[0048] In formula (1):

[0049]

[0050] In formula (9), f1∈[0,f 1,0 ], are the arrival and departure times of train i at each station before the operation diagram optimization, are the arrival and departure times of train i at each station after the operation diagram is optimized; It is the sum of all the traction work and electricity in the rectification condition of the whole line, that is, the traction energy consumption; It is the sum of all the traction work and electricity in the inverter condition of the whole line, that is, the feedback energy; N is the amount of electricity returned by the main substations along the entire line; r is the number of traction stations along the entire line, N m The number of main offices in the entire line; T r,rec is the duration of the rectification condition of the rth traction station, T r,inv is the duration of the inverter condition of the rth traction station, τ is the simulation time; P r,rec (t) is the active power of the rth traction under rectification condition at time t, P r,inv (t) is the active power of the rth traction under the inverter condition at time t, P m (t) is the return power of the mth main substation at time t.

[0051] In formula (1):

[0052]

[0053] In formula (10), are the times when train i arrives at and leaves station s according to the planned operation diagram; are the times when train i arrives at and leaves station s according to the optimized operation diagram; N is the total number of stations, and M is the total number of trains.

[0054] In formulas (2)-(7), are the minimum and maximum stop time of train i at station s respectively; are the minimum tracking interval and the maximum tracking interval between train i and train i+1 respectively; Δh is the secondary adjustment of the tracking interval, Δh∈[0,5]; T i,s,s+1 is the running time of train i in interval s, s+1; are the minimum and maximum sum of the stop time of all trains at each station, are the minimum and maximum values ​​of the sum of all train tracking intervals respectively; D i , are the delay time of train i, the minimum delay time of train i, and the maximum delay time of train i respectively; D total , They are respectively the sum of all train delay times, the minimum value of the sum of all train delay times, and the maximum value of the sum of all train delay times.

[0055]

[0056] in: S = {1,2,…,s,…,N} is the set of stations, and I = {1,2,…,i,M} is the set of trains.

[0057] The lower layer establishes a train timing energy-saving optimization model that takes into account changes in interval passenger flow. Changes in interval passenger flow cause changes in train weight, which in turn affects changes in train traction energy consumption. Based on the existing train timing energy-saving model, the train weight is considered as a variable, and the lower layer train timing energy-saving optimization model is established as follows:

[0058] min{f T,i,g},min{f E,i,g}(12)

[0059]

[0060] In formula (12), f T,i,g is the delay time limit index of train i running in section g, calculated by formula (14); f E,i,g is the traction energy consumption index of train i running in section g, which is calculated by formula (15).

[0061] f T,i,g =|T i,g (λ i,g ,v i,g )-T i,g | (14)

[0062] In formula (14), T i,g (λ i,g ,v i,g ) is the number of train i in the gth interval with λ i,g 、v i,g The actual time of runtime, λ i,g is the coasting control coefficient, v i,g is the target speed of train i in section g, T i,g is the planned running time of train i in the g-th section.

[0063]

[0064] In formula (15), μ i,g is the traction force utilization coefficient of train i in section g, 0≤μ i,g ≤1;M i,g is the weight of train i when running in section g after considering passenger flow; f max,i,g (v i,g ,M i,g ) is when the train speed is v i,g 、The vehicle weight is M i,g The maximum traction force at i is the electromechanical efficiency of train i; is the time when train i arrives at station s+1, is the time when train i leaves station s.

[0065] Formula (13) represents: interval running time constraint, speed constraint, acceleration constraint; δ max The maximum deviation allowed between the actual running time and the planned running time; lim (l i,g ) is the position l i,g The speed limit at a i,g (t), a i,g (t-1) are the accelerations of train i at time t and time t-1 in the g-th interval, Δt is the simulation interval, Δa max is the maximum value of the acceleration rate of change.

[0066] like Figure 1 The schematic diagram of the double-layer train operation diagram optimization model is shown in the figure. The upper optimization model uses the multi-train optimized operation trajectory as a drive to calculate the power flow of the urban rail power supply system, solve the operation diagram optimization model, and generate the optimization solution set {h i,i+1 ,Ti,S}.h i,i+1 represents the tracking interval between the i-th train and the i+1-th train, T i,S represents the stop time of the i-th train at each station. The lower optimization model uses the coasting control coefficient λ i,g 、Train target speed v i,g The train operation process is divided, and the fixed step target speed search algorithm in the literature is used to solve the train timing energy-saving optimization model considering the changes in section passenger flow and generate multi-train optimal operation trajectories as the input of the upper optimization model.

[0067] The solution of the two-level optimization model is as follows:

[0068] Step 1: Initialize the simulation conditions of the operation diagram optimization model considering the comprehensive energy-saving index of the power supply system: Initialize the salp population, set the total number of salp individuals to M, the number of iterations of the operation diagram optimization model k = 0, and the maximum number of iterations k max , tracking interval optimization range, stop time optimization range, planned operation diagram tracking interval, planned operation diagram stop time. Set the stop time T of train i at station s i,s and the tracking interval h between train i and train i+1 i,i+1 .

[0069] Step 2: Load train, line, passenger flow and operation diagram data; initialize the simulation conditions of the train timing energy-saving optimization model considering the change of interval passenger flow: generate the initial solution of multi-train tracking interval and stop time from the operation diagram optimization model considering the comprehensive energy-saving index of the power supply system, and transfer it to the train timing energy-saving optimization model considering the change of interval passenger flow, let i = 1, g = 1, λ i,g =0, the target speed level y=0, v i,g =v max,i,g .

[0070] Step 3: According to v i,g and speed limit information, re-divide the ramp, and i,g 、v i,g Divide the train operation process into sections and complete the speed connection of train i in section g.

[0071] Step 4: Calculate T i,g (λ i,g ,v i,g ), if T i,g (λ i,g ,v i,g )≠T i,g , then use the fixed step target speed search algorithm and modify v i,g , until T i,g (λ i,g ,v i,g )=Ti,g , save the train i section running record R i,g (λ i,g ,v i,g ).

[0072] Step 5: Let λ i,g =λ i,g +Δλ, if λ i,g ≤0.25, then let v i,g =v max,i,g , g++, go to Step 3; otherwise, select the traction energy consumption index f E,i,g The smallest R i,g (λ i,g ,v i,g ) is the final optimization result of train i in interval g.

[0073] Step 6: Load the optimized operation trajectories of multiple trains; start the operation diagram optimization parallel solution simulator. The parallel solution diagram is as follows: Figure 2 shown.

[0074] Step 7: Initialize the number of iterations of power flow calculation j, voltage convergence accuracy ε, traction station status W, simulation start and stop time, simulation duration τ, and power supply system AC side node admittance matrix Y ac , DC side node admittance matrix Y dc .

[0075] Step 8: Read the position and power data of each train at the current simulation time t; perform the DC side power flow calculation of the AC / DC alternating iterative urban rail traction power supply system at time t, and update the voltage U of all nodes on the DC side dc , Node current I dc .

[0076] Step 9: Judgement | j,dc -U j－1,dc |<ε Whether the convergence condition is met, if so, continue to judge whether the traction state W is stable (if W is stable, set t=t+1 and go to step 10, otherwise adjust W and return to step 8), otherwise set j=j+1 and return to step 8.

[0077] Step 10: Perform AC-DC alternating iteration of the urban rail traction power supply system at time t to calculate the AC side power flow and update the voltage U of all nodes on the AC side ac , Node current I ac .

[0078] Step 11: Judgement | j,ac -U j－1,ac |<ε convergence condition is satisfied, if so, continue to judge whether t<τ is satisfied (if so, set t=t+1 and return to step 8, otherwise go to step 12), otherwise set j=j+1 and return to step 10.

[0079] Step 12: Multiple threads calculate the target function Sort by fitness and record the best individual salps; evaluate the comprehensive energy-saving index of the power supply system and output the optimal solution set of the k-th iteration tracking interval and stop time; if k <k max , perform individual differential mutation of salps, set k = k + 1, return to step 2, otherwise output the optimal solution set of the run graph optimization. The schematic diagram of multi-threaded parallel computing is as follows Figure 2 shown.

[0080] Based on this, we can obtain the optimized stop time of the train at each station and the tracking interval between two vehicles. The train energy interaction diagram is shown in Figure 3 As shown, the red part is the train traction energy consumption, the green part is the train braking energy consumption, and the dotted line part represents the overlapping interval of the train traction time and braking time.

Claims

1. A train operation diagram optimization method considering passenger flow impact and power supply system energy saving, characterized in that: Specifically: a double-decker train timetable optimization model is established. The upper layer is a timetable optimization model that takes into account the comprehensive energy-saving indicators of the power supply system, which generates feasible solutions for multi-train tracking intervals and stop times, and drives the lower layer's train timing energy-saving optimization model that takes into account changes in section passenger flow. On the basis of restoring the running trajectories of multiple vehicles, the power supply system simulation module is called to generate comprehensive energy-saving indicators, and the optimal solution is obtained through an intelligent algorithm iterative solution method.

2. A train operation diagram optimization method considering passenger flow impact and power supply system energy saving according to claim 1, characterized in that: The upper-layer operation diagram optimization model is specifically: in: is the normalized objective function, f1 is the comprehensive energy-saving index of the urban rail traction power supply system, and f 1,0 is the comprehensive energy-saving index of the urban rail traction power supply system before the operation diagram optimization, f2 is the train delay time limit index, and f 2,0 It is the allowable delay time limit index of all trains before the operation diagram optimization. The weights of f1 and f2 are equal. After the operation diagram optimization, the energy consumption of the power supply system is reduced while the train deviation time is minimized. constraint: Formulas (2)-(8) respectively represent: train stop time constraint, tracking interval constraint, interval operation time constraint, overall stop time constraint of all trains at all stations, overall tracking interval constraint of all trains, single train delay time constraint, and overall delay time constraint of all trains; In formula (1): In formula (9), f1∈[0,f 1,0 ], are the arrival and departure times of train i at each station before the operation diagram optimization, are the arrival and departure times of train i at each station after the operation diagram is optimized; It is the sum of all the traction work and electricity in the rectification condition of the whole line, that is, the traction energy consumption; It is the sum of all the traction work and electricity in the inverter condition of the whole line, that is, the feedback energy; N is the amount of electricity returned by the main substations along the entire line; r is the number of traction stations along the entire line, N m The number of main offices in the entire line; T r,rec is the duration of the rectification condition of the rth traction station, T r,inv is the duration of the inverter condition of the rth traction station, τ is the simulation time; P r,rec (t) is the active power of the rth traction under rectification condition at time t, P r,inv (t) is the active power of the rth traction under the inverter condition at time t, P m (t) is the return power of the mth main substation at time t; In formula (1): In formula (10), are the times when train i arrives at and leaves station s according to the planned operation diagram; are the arrival and departure times of train i at station s according to the optimized operation diagram; N is the total number of stations, and M is the total number of trains; In formulas (2)-(7), are the minimum and maximum stop time of train i at station s respectively; are the minimum tracking interval and the maximum tracking interval between train i and train i+1 respectively; Δh is the secondary adjustment of the tracking interval, Δh∈[0,5]; T i,s,s+1 is the running time of train i in interval s, s+1; are the minimum and maximum sum of the stop time of all trains at each station, are the minimum and maximum values ​​of the sum of all train tracking intervals respectively; D i , are the delay time of train i, the minimum delay time of train i, and the maximum delay time of train i respectively; D total , They are respectively the sum of all train delay times, the minimum value of the sum of all train delay times, and the maximum value of the sum of all train delay times; in: S = {1,2,…,s,…,N} is the set of stations, and I = {1,2,…,i,M} is the set of trains.

3. The train operation diagram optimization method considering passenger flow impact and power supply system energy saving according to claim 1 is characterized in that: The train timing energy-saving optimization model of the lower layer is specifically: my{f T,i,g },min{f E,i,g }(12) In formula (12), f T,i,g is the delay time limit index of train i running in section g, calculated by formula (14); f E,i,g is the traction energy consumption index of train i running in section g, calculated by formula (15); f T,i,g =|T i,g (λ i,g ,v i,g )-T i,g | (14) In formula (14), T i,g (λ i,g ,v i,g ) is the number of train i in the gth interval with λ i,g 、v i,g The actual time of runtime, λ i,g is the coasting control coefficient, v i,g is the target speed of train i in section g, T i,g is the planned running time of train i in the g-th section; In formula (15), μ i,g is the traction force utilization coefficient of train i in section g, 0≤μ i,g ≤1;M i,g is the weight of train i when running in section g after considering passenger flow; f max,i,g (v i,g ,M i,g ) is when the train speed is v i,g 、The vehicle weight is M i,g The maximum traction force at i is the electromechanical efficiency of train i; is the time when train i arrives at station s+1, is the time when train i leaves station s; Formula (13) represents: interval running time constraint, speed constraint, acceleration constraint; δ max The maximum deviation allowed between the actual running time and the planned running time; lim (l i,g ) is the position l i,g The speed limit at a i,g (t), a i,g (t-1) are the accelerations of train i at time t and time t-1 in the g-th interval, Δt is the simulation interval, Δa max is the maximum value of the acceleration rate of change.

4. The train operation diagram optimization method considering passenger flow impact and power supply system energy saving according to claim 1 is characterized in that: The upper-level operation diagram optimization model is driven by the multi-train optimized operation trajectory to perform power flow calculation of the urban rail power supply system, solve the operation diagram optimization model, and generate an optimization solution set {h i,i+1 ,T i,S };h i,i+1 represents the tracking interval between the i-th train and the i+1-th train, T i,S represents the stop time of the i-th train at each station; The lower optimization model is based on the inertial control coefficient λ i,g 、Train target speed v i,g The train operation process is divided, and a fixed-step target speed search algorithm is used to solve the train timing energy-saving optimization model considering the changes in section passenger flow, and generate multi-train optimized operation trajectories as the input of the upper optimization model.

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