A method for optimizing operation characteristics of a city rail train timetable and a bidirectional converter

Abstract

The application discloses a kind of urban rail train timetable and bidirectional converter operating characteristic optimization method, comprising the following steps: obtaining train data and line data;Generate the fixed number of all day feasible departure strategy of departure and corresponding timetable set;Calculate train speed curve;Calculate the train power and running position of each time when train runs in all sections of the whole line;The minimum cost under different timetable and the corresponding comprehensive scheme of bidirectional converter operating parameter are obtained by particle swarm algorithm;Output the timetable of minimum cost and bidirectional converter no-load voltage, limit voltage and droop slope scheme.The application comprehensively considers the transmission, utilization and feedback of regenerative braking energy of DC reversible traction power supply system by train timetable and bidirectional converter operating parameter characteristics, while meeting the requirements of reducing economic cost and reducing traction network voltage fluctuation rate, thereby improving train operation efficiency and operation safety.

Description

Technical Field

[0001] This invention relates to the field of comprehensive optimization of train operation and power supply parameters, specifically to a method for optimizing urban rail train timetables and bidirectional converter operating characteristics. Background Technology

[0002] Most existing studies are based on the optimization of the operating characteristics of bidirectional converters under the fixed train departure strategy, which ignores the impact of train group operation strategy on the energy transmission, utilization and feedback process of reversible traction power supply system, resulting in room for further optimization of the optimization results.

[0003] Existing technology (Chen Wen. Voltage Optimization Control Strategy for Urban Rail Traction Substations Based on Bidirectional Converters [D]. Beijing: Beijing Jiaotong University, 2022) studies an offline optimization method for the operating characteristics of urban rail traction substations based on bidirectional converters under the premise of fixed train departure intervals. This method aims to minimize energy consumption costs and voltage fluctuation range by changing parameters such as the no-load voltage and droop slope of the bidirectional converter. However, this technology has the following drawbacks:

[0004] 1) The discounted value of the off-line operating costs throughout the entire life cycle of the bidirectional converter is not considered.

[0005] 2) The optimization of train timetable and bidirectional converter operating characteristics was not comprehensively considered under the constraint of fixed train departures within a single day time window.

[0006] 3) The coordination and optimization between energy consumption costs, bidirectional converter installation costs and voltage fluctuations were not comprehensively considered. Summary of the Invention

[0007] To address the aforementioned shortcomings in existing technologies, this invention provides a method for optimizing urban rail train timetables and bidirectional converter operating characteristics, which solves the problem that existing technologies fail to balance economic costs and traction network voltage stability.

[0008] To achieve the above-mentioned objectives, the technical solution adopted by this invention is as follows:

[0009] A method for optimizing urban rail train timetables and bidirectional converter operating characteristics is provided, comprising the following steps:

[0010] S1. Obtain train data and route data;

[0011] S2. Use a brute-force search algorithm to search for the departure intervals of adjacent trains to generate a set of all feasible departure strategies for the whole day with a fixed number of departures and the corresponding timetables.

[0012] S3. Based on the maximum value principle, calculate the speed of the train at each moment during the set interval running time in all sections of the entire line, and obtain the speed curve;

[0013] S4. Calculate the train power and running position at each moment when the train is running in all sections of the entire line, based on the speed curve;

[0014] S5. Based on the train power and running position at each moment during operation, the particle swarm optimization algorithm is used to obtain the minimum cost and corresponding bidirectional converter operating parameters comprehensive scheme under different timetables.

[0015] S6. Output the timetable and bidirectional converter no-load voltage, limiting voltage and droop slope scheme with the lowest output cost, and complete the optimization of urban rail train timetable and bidirectional converter operation characteristics.

[0016] Furthermore, the train data in step S1 includes the train mass M; the line data includes the number of traction substations N, the number of sections Q, the travel time R of trains in each section of the entire line for both directions R, the dwell time at each station D, the total daily time window T, the number of trains departing in one direction on a single day S, the headway between the first trains in both directions K, and the maximum headway between two adjacent trains H. max Minimum value H min Distance distance ΔH, traction substation no-load voltage range Voltage range limitation and the range of droop slope [k] min ,k max ].

[0017] Furthermore, the specific method for step S2 is as follows:

[0018] A brute-force search algorithm is used to search for a set of all-day departure strategies and corresponding timetables that satisfy the following constraints:

[0019]

[0020]

[0021]

[0022]

[0023] in This represents the dwell time of the train traveling north at the nth station. This represents the travel time of the northbound train in the q-th section; The departure interval between the s-th and s+1-th trains in the northbound direction; This represents the dwell time of the train traveling south at the nth station. This represents the travel time of the down-line train in the q-th section; This represents the departure interval between the s-th and s+1-th down-line trains.

[0024] Furthermore, the specific method for step S4 is as follows:

[0025] According to the formula:

[0026]

[0027]

[0028] Obtain the train power at time d in the m-th operating section. and running location in Let be the running speed at time d in the m-th running interval; η is the power conversion efficiency. Let be the train traction force at time d in the m-th operating section; Let M be the braking force of the train at time d in the m-th operating section; M is the train mass. Let be the running speed at time d0+1 of the m-th running interval; Let be the running speed at time d0 of the m-th running interval.

[0029] Furthermore, the specific method of step S5 includes the following sub-steps:

[0030] S5-1, Input the power curve of the train running in all sections of the entire line, and set the basic unit price C0 of the bidirectional converter, unit capacity cost c, life cycle years L, electricity price a, annual discount rate r, number of payment periods p, and three-dimensional particle (U). no U lim The linear weights α and β of the cost function are given by (k), (k), and (k), respectively.

[0031] S5-2, Calculate Timetable X j Power-location-time data of all running trains within the next total time window T;

[0032] S5-3, Initialize Particle Swarm Velocity and location in and These represent the no-load voltage U. no Limiting voltage U lim and the droop slope k; and These represent the no-load voltage U. no Limiting voltage U lim The search speed for the droop slope k;

[0033] S5-4. The voltage matrix U(t) and current matrix I(t) of all traction substations at time t within the total time window are obtained through power flow calculation.

[0034] S5-5. Calculate the total output energy consumption E of the reversible substation within a single day's total time window based on the voltage matrix U(t) and the current matrix I(t). sub and the average voltage fluctuation rate of all substations along the line Through the open-circuit voltage U no Limiting voltage U lim Calculate the rated power P of the bidirectional converter inverter using the droop slope k. max ;

[0035] S5-6, Based on the rated power P of the bidirectional converter inverter max Calculate the installation cost C over the entire life cycle of the bidirectional converter. inv And electricity cost C cost And based on the installation cost C over the entire life cycle of the bidirectional converter inv Electricity cost C cost and the average voltage fluctuation rate of all substations Calculate the cost function C;

[0036] S5-7. Determine whether to end the iteration. If yes, obtain the minimum cost and corresponding bidirectional converter operating parameter integrated scheme under different timetables; otherwise, calculate the fitness value according to the cost function C, update the global optimal position, local optimal position, particle velocity and particle position of the particle swarm according to the fitness value, and return to step S5-5.

[0037] Furthermore, the specific method of step S5-4 includes the following sub-steps:

[0038] S5-4-1. Input train power-time data, set the initial time to 0, the initial iteration count to 0, and the voltage matrix U. (0) (0) and current matrix I (0) (0), set the maximum number of iterations w max And the iteration accuracy ε;

[0039] S5-4-2. Construct the nodal admittance matrix Y(t) at time t;

[0040] S5-4-3, According to the formula:

[0041] U(w+1)(t)=Y(t)⁻¹I(w)(t)

[0042] Calculate the voltage matrix U at time t in the next iteration. (w+1) (t); where I (w) (t) represents the current matrix at time t during the current iteration;

[0043] S5-4-4. Determine whether the difference between the voltage matrices corresponding to two adjacent iterations at time t is less than the iteration precision ε, or whether the current iteration number w is greater than the maximum iteration number w. max If so, output the voltage matrix U(t) and current matrix I(t) at the current moment and proceed to step S5-4-5; otherwise, increment the iteration count by 1 and return to step S5-4-3.

[0044] S5-4-5, Switch the operating condition of the reversible substation, update the current time, and reset the current iteration count to 0;

[0045] S5-4-6. Determine if the current time is less than the total time window for a single day. If so, return to step S5-4-2; otherwise, end.

[0046] Furthermore, the specific method for step S5-5 is as follows:

[0047] According to the formula:

[0048]

[0049]

[0050] Obtain the total output energy consumption E of the reversible substation within the total time window of a single day. sub and the average voltage fluctuation rate of all substations along the line Where T is the total time window for a single day; N is the number of traction substations included in the line data; U n (t) represents the voltage matrix of the nth traction substation at time t; I n (t) represents the current matrix of the nth traction substation at time t; E(U n ) represents the average voltage value of the nth traction substation on the grid side within the total time window of a single day; σ(U n ) represents the standard deviation of the grid-side voltage value of the nth substation within the total time window of a single day.

[0051] Furthermore, the specific methods for steps S5-6 are as follows:

[0052] According to the formula:

[0053] C inv =N(C0+P) max c)

[0054]

[0055]

[0056]

[0057] Obtain the installation cost C over the entire life cycle of the bidirectional converter. inv Electricity cost C cost Cost function C and rated power P of bidirectional converter inverter max Where N is the number of traction substations included in the line data; C0 is the basic unit price of the bidirectional converter; c is the unit capacity cost; a is the electricity price; r is the annual discount rate for electricity; p is the number of payment periods for electricity throughout the year; and L is the total life cycle time.

[0058] Furthermore, the specific method for determining whether to end the iteration in step S5-7 is to determine whether the maximum number of iterations has been reached.

[0059] The beneficial effects of this invention are as follows: This invention comprehensively considers the transmission, utilization, and feedback of regenerative braking energy in a DC reversible traction power supply system based on train timetables and bidirectional converter operating parameter characteristics. With the optimization objectives of low economic cost and low traction network voltage fluctuation rate throughout the entire life cycle of the bidirectional converter, and constraints of the planned number of train departures within a daily time window, acceptable departure intervals, and inverter operating characteristics, a collaborative optimization method for train timetables and bidirectional converter operating characteristics is proposed. As a supplement and improvement to existing technologies, by setting weights, the optimization results simultaneously meet the requirements of reducing economic costs and reducing traction network voltage fluctuation rate, thereby improving train operation efficiency and operational safety. Attached Figure Description

[0060] Figure 1 This is a flowchart illustrating the method. Detailed Implementation

[0061] The specific embodiments of the present invention are described below to enable those skilled in the art to understand the present invention. However, it should be understood that the present invention is not limited to the scope of the specific embodiments. For those skilled in the art, various changes are obvious as long as they are within the spirit and scope of the present invention as defined and determined by the appended claims. All inventions utilizing the concept of the present invention are protected.

[0062] like Figure 1 As shown, the method for optimizing the urban rail train timetable and bidirectional converter operating characteristics includes the following steps:

[0063] S1. Obtain train data and route data;

[0064] S2. Use a brute-force search algorithm to search for the departure intervals of adjacent trains to generate a set of all feasible departure strategies for the whole day with a fixed number of departures and the corresponding timetables.

[0065] S3. Based on the maximum value principle, calculate the speed of the train at each moment during the set interval running time in all sections of the entire line, and obtain the speed curve;

[0066] S4. Calculate the train power and running position at each moment when the train is running in all sections of the entire line, based on the speed curve;

[0067] S5. Based on the train power and running position at each moment during operation, the particle swarm optimization algorithm is used to obtain the minimum cost and corresponding bidirectional converter operating parameters comprehensive scheme under different timetables.

[0068] S6. Output the timetable and bidirectional converter no-load voltage, limiting voltage and droop slope scheme with the lowest output cost, and complete the optimization of urban rail train timetable and bidirectional converter operation characteristics.

[0069] The train data in step S1 includes the train mass M; the line data includes the number of traction substations N, the number of sections Q, the travel time R of trains in each section of the entire line for both directions R, the dwell time at each station D, the total daily time window T, the number of trains departing in one direction on a single day S, the headway between the first trains in both directions K, and the maximum headway between two adjacent trains H. max Minimum value H min Distance distance ΔH, traction substation no-load voltage range Voltage range limitation and the range of droop slope [k] min ,k max ].

[0070] The specific method for step S2 is as follows: Use a brute-force search algorithm to search for all-day departure strategies and corresponding timetable sets that satisfy the following constraints:

[0071]

[0072]

[0073]

[0074]

[0075] in This represents the dwell time of the train traveling north at the nth station. This represents the travel time of the northbound train in the q-th section; The departure interval between the s-th and s+1-th trains in the northbound direction; This represents the dwell time of the train traveling south at the nth station. This represents the travel time of the down-line train in the q-th section; This represents the departure interval between the s-th and s+1-th down-line trains.

[0076] The specific method for step S4 is as follows: According to the formula:

[0077]

[0078]

[0079] Obtain the train power at time d in the m-th operating section. and running location in Let be the running speed at time d in the m-th running interval; η is the power conversion efficiency. Let be the train traction force at time d in the m-th operating section; Let M be the braking force of the train at time d in the m-th operating section; M is the train mass. Let be the running speed at time d0+1 of the m-th running interval; Let be the running speed at time d0 of the m-th running interval.

[0080] The specific method of step S5 includes the following sub-steps:

[0081] S5-1, Input the power curve of the train running in all sections of the entire line, and set the basic unit price C0 of the bidirectional converter, unit capacity cost c, life cycle years L, electricity price a, annual discount rate r, number of payment periods p, and three-dimensional particle (U). no U lim The linear weights α and β of the cost function are given by (k), (k), and (k), respectively.

[0082] S5-2, Calculate Timetable X j Power-location-time data for all running trains within the next total time window T;

[0083] S5-3, Initialize Particle Swarm Velocity and location in and These represent the no-load voltage U. no Limiting voltage U lim and the droop slope k; and These represent the no-load voltage U. no Limiting voltage U lim The search speed for the droop slope k;

[0084] S5-4. The voltage matrix U(t) and current matrix I(t) of all traction substations at time t within the total time window are obtained through power flow calculation.

[0085] S5-5. Calculate the total output energy consumption E of the reversible substation within a single day's total time window based on the voltage matrix U(t) and the current matrix I(t). sub and the average voltage fluctuation rate of all substations along the line Through the open-circuit voltage U no Limiting voltage U lim Calculate the rated power P of the bidirectional converter inverter using the droop slope k. max ;

[0086] S5-6, Based on the rated power P of the bidirectional converter inverter max Calculate the installation cost C over the entire life cycle of the bidirectional converter. inv And electricity cost C cost And based on the installation cost C over the entire life cycle of the bidirectional converter inv Electricity cost C cost and the average voltage fluctuation rate of all substations Calculate the cost function C;

[0087] S5-7. Determine whether to end the iteration. If yes, obtain the minimum cost and corresponding bidirectional converter operating parameter integrated scheme under different timetables; otherwise, calculate the fitness value according to the cost function C, update the global optimal position, local optimal position, particle velocity and particle position of the particle swarm according to the fitness value, and return to step S5-5.

[0088] The specific method of step S5-4 includes the following sub-steps:

[0089] S5-4-1. Input train power-time data, set the initial time to 0, the initial iteration count to 0, and the voltage matrix U. (0) (0) and current matrix I (0) (0), set the maximum number of iterations w max And the iteration accuracy ε;

[0090] S5-4-2. Construct the nodal admittance matrix Y(t) at time t;

[0091] S5-4-3, According to the formula:

[0092] U(w+1)(t)=Y(t)⁻¹I(w)(t)

[0093] Calculate the voltage matrix U at time t in the next iteration. (w+1) (t); where I (w) (t) represents the current matrix at time t during the current iteration;

[0094] S5-4-4. Determine whether the difference between the voltage matrices corresponding to two adjacent iterations at time t is less than the iteration precision ε, or whether the current iteration number w is greater than the maximum iteration number w.max If so, output the voltage matrix U(t) and current matrix I(t) at the current moment and proceed to step S5-4-5; otherwise, increment the iteration count by 1 and return to step S5-4-3.

[0095] S5-4-5, Switch the operating condition of the reversible substation, update the current time, and reset the current iteration count to 0;

[0096] S5-4-6. Determine if the current time is less than the total time window for a single day. If so, return to step S5-4-2; otherwise, end.

[0097] The specific method for step S5-5 is as follows: According to the formula:

[0098]

[0099]

[0100] Obtain the total output energy consumption E of the reversible substation within the total time window of a single day. sub and the average voltage fluctuation rate of all substations along the line Where T is the total time window for a single day; N is the number of traction substations included in the line data; U n (t) represents the voltage matrix of the nth traction substation at time t; I n (t) represents the current matrix of the nth traction substation at time t; E(U n ) represents the average voltage value of the nth traction substation on the grid side within the total time window of a single day; σ(U n ) represents the standard deviation of the grid-side voltage value of the nth substation within the total time window of a single day.

[0101] The specific method for steps S5-6 is as follows: According to the formula:

[0102] C inv =N(C0+P) max c)

[0103]

[0104]

[0105]

[0106] Obtain the installation cost C over the entire life cycle of the bidirectional converter. inv Electricity cost C cost Cost function C and rated power P of bidirectional converter inverter maxWhere N is the number of traction substations included in the line data; C0 is the basic unit price of the bidirectional converter; c is the unit capacity cost; a is the electricity price; r is the annual discount rate for electricity; p is the number of payment periods for electricity throughout the year; and L is the total life cycle time.

[0107] The specific method for ending the iteration in step S5-7 is as follows: if the maximum number of iterations is reached, then the iteration ends.

[0108] In one embodiment of the present invention, the specific method for updating the global optimal position, local optimal position, particle velocity, and position of the particle swarm is as follows:

[0109] The reciprocal of the cost function of the j-th particle is taken as the fitness value of the j-th particle, according to the formula:

[0110]

[0111]

[0112] Update the global and local optimal positions of the particle swarm; where This represents the local optimal position of the particle swarm in the (d+1)th iteration. This represents the local optimal position of the particle swarm in the d-th iteration; F represents the position of the j-th particle in the (d+1)-th iteration; j Let be the fitness value of the j-th particle; This represents the global optimal position of the particle swarm in the d-th iteration;

[0113] According to the formula:

[0114]

[0115]

[0116] Update particle velocity and position; where Let represent the velocity of the j-th particle in the (d+1)-th iteration; y is the inertia weight. Let c1 and c2 represent the velocity of the j-th particle in the d-th iteration; c1 and c2 are both learnable parameters; r1 and r2 are both random numbers between 0 and 1. t represents the position of the j-th particle in the (d+1)-th iteration; t represents time.

[0117] In summary, compared to previous work on optimizing the operating characteristics of bidirectional converters, this invention, by simultaneously considering the impact of train timetables and the operating characteristics of bidirectional converters on the transmission, utilization, and feedback of regenerative braking energy in reversible traction power supply systems, can achieve minimum economic costs and minimum grid voltage fluctuations, thereby realizing coordinated optimization of train departure strategies and bidirectional converter operating characteristics. This method fully considers the discounted value of train operating costs at different times, improves the economic cost calculation model for traction power supply systems containing bidirectional converters, and achieves refined modeling.

Claims

1. A method for optimizing urban rail train timetables and bidirectional converter operating characteristics, characterized in that, Includes the following steps: S1. Obtain train data and route data; S2. Use a brute-force search algorithm to search for the departure intervals of adjacent trains to generate a set of all feasible departure strategies for the whole day with a fixed number of departures and the corresponding timetables. S3. Based on the maximum value principle, calculate the speed of the train at each moment during the set interval running time in all sections of the entire line, and obtain the speed curve; S4. Calculate the train power and running position at each moment when the train is running in all sections of the entire line, based on the speed curve; S5. Based on the train power and running position at each moment during operation, the particle swarm optimization algorithm is used to obtain the minimum cost and corresponding bidirectional converter operating parameters comprehensive scheme under different timetables. S6. Output the timetable and bidirectional converter no-load voltage, limiting voltage and droop slope scheme with the lowest output cost, and complete the optimization of urban rail train timetable and bidirectional converter operation characteristics. The specific method of step S5 includes the following sub-steps: S5-1. Input the power curve of the train running in all sections of the entire line, and set the basic unit price of the bidirectional converter. Unit capacity cost c Total life cycle years L Electricity unit price a Annual discount rate r Annual payment period p Three-dimensional particles and the linear weights of the cost function and ; S5-2, Calculate the timetable Lower total time window T Power-location-time data for all operating trains within the system; S5-3, Initialize Particle Swarm Velocity and location ;in , and These represent the no-load voltage. Limiting voltage and droop slope ; , and These represent the no-load voltage. Limiting voltage and droop slope Search speed; S5-4. Obtain the times of all traction substations within the total time window through power flow calculation. t voltage matrix and current matrix ; S5-5, Based on voltage matrix and current matrix Calculate the total output energy consumption of the reversible substation within the total time window of a single day. and the average voltage fluctuation rate of all substations along the line ; through no-load voltage Limiting voltage and droop slope Calculate the rated power of the bidirectional converter inverter. ; S5-6, Based on the rated power of the bidirectional converter inverter Calculate the installation cost over the entire lifecycle of a bidirectional converter. and electricity costs And based on the installation cost over the entire life cycle of the bidirectional converter Electricity costs and the average voltage fluctuation rate of all substations Calculate the cost function C ; S5-7. Determine whether the iteration should end. If yes, obtain the minimum cost and corresponding bidirectional converter operating parameter integrated scheme under different timetables; otherwise, based on the cost function... C Calculate the fitness value, update the global optimal position, local optimal position, particle velocity and particle position of the particle swarm based on the fitness value, and return to step S5-5. The specific methods for steps S5-6 are as follows: According to the formula: Obtain the installation cost over the entire lifecycle of the bidirectional converter. Electricity costs Cost function C and the rated power of bidirectional converter inverter ;in N The number of traction substations included in the line data; This is the basic unit price of a bidirectional converter; c Cost per unit capacity; This refers to the unit price of electricity. r The annual discount rate for electricity costs; p This refers to the number of payment periods for electricity bills throughout the year; L For the entire lifecycle time.

2. The method for optimizing urban rail train timetables and bidirectional converter operating characteristics according to claim 1, characterized in that, The train data in step S1 includes train mass. M The line data includes the number of traction substations. N Number of intervals Q Travel time of trains in both directions on all sections of the line R Stop times at each station D Total time window per day T Single-day one-way train departures S The first train departure interval in both directions K The maximum value of the departure interval between two adjacent trains Minimum value , a long walk traction substation no-load voltage range Voltage range limitation and droop slope range .

3. The method for optimizing urban rail train timetables and bidirectional converter operating characteristics according to claim 2, characterized in that, The specific method for step S2 is as follows: A brute-force search algorithm is used to search for a set of all-day departure strategies and corresponding timetables that satisfy the following constraints: in For the up train at the n Stop time at each station; For the up train at the q The running time of each interval; For the up train at the s Next and first s +1 train departure interval; For the down train at the n Stop time at each station; For the down train at the q The running time of each interval; For the down train at the s Next and first s +1 train departure interval.

4. The method for optimizing urban rail train timetables and bidirectional converter operating characteristics according to claim 1, characterized in that, The specific method for step S4 is as follows: According to the formula: Get the m The first operating interval d Train power at any time and running location ;in For the first m The first operating interval d The speed of operation at any given moment; To improve the efficiency of power conversion; For the first m The first operating interval d The traction force of the train at any given moment; For the first m The first operating interval d The braking force of the train at any moment; For train quality; For the first m The first operating interval The speed of operation at any given moment; For the m-th running interval The speed at which the machine runs at any given moment.

5. The method for optimizing urban rail train timetables and bidirectional converter operating characteristics according to claim 1, characterized in that, The specific method of step S5-4 includes the following sub-steps: S5-4-1. Input train power-time data, set the initial time to 0, the initial iteration count to 0, and the voltage matrix. and current matrix Set the maximum number of iterations. and iteration accuracy ; S5-4-2, Construction t Nodal admittance matrix at time 1 ; S5-4-3, According to the formula: Calculate the next iteration t Voltage matrix at time 1 ;in Indicates the current iteration process t The current matrix at time t; S5-4-4, Determine if both are t Is the difference between the voltage matrices corresponding to two adjacent iterations at a given time less than the iteration precision? or the current iteration number w Is it greater than the maximum number of iterations? If so, output the voltage matrix at the current time. and current matrix Proceed to step S5-4-5; otherwise, increment the iteration count by 1 and return to step S5-4-3. S5-4-5, Switch the operating condition of the reversible substation, update the current time, and reset the current iteration count to 0; S5-4-6. Determine if the current time is less than the total time window for a single day. If so, return to step S5-4-2; otherwise, end.

6. The method for optimizing urban rail train timetables and bidirectional converter operating characteristics according to claim 1, characterized in that, The specific method for step S5-5 is as follows: According to the formula: Obtain the total output energy consumption of reversible substations within a single day's total time window. and the average voltage fluctuation rate of all substations along the line ;in T For the total time window of a single day; N The number of traction substations included in the line data; Indicates the first n A traction substation t Voltage matrix at time t; Indicates the first n A traction substation t The current matrix at time t; , For the first n The average value of the grid-side voltage of each traction substation within a single day's total time window; For the first n The standard deviation of the grid-side voltage value of a substation within a single day's total time window.

7. The method for optimizing urban rail train timetables and bidirectional converter operating characteristics according to claim 1, characterized in that, The specific method for determining whether to end the iteration in step S5-7 is to determine whether the maximum number of iterations has been reached.

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