An online energy-saving optimization control method for subway trains based on on-board energy storage

Abstract

The invention discloses an online energy-saving optimization control method for a subway train based on on-board energy storage. Under the premise of considering the existence of basic resistance, train traction / braking force, slope additional force, etc., a train dynamics model is established with the train position as the independent variable and the speed and time as the state variables; then the length of the subway running line is discretized, and the train dynamics model and the forces it is subjected to are discretized; a train traction / braking force switching scheme is established, and a mode switching sequence when the train travels between multiple stations is specified; a charging and discharging strategy of an on-board supercapacitor is designed; a train energy-saving operation optimization problem is constructed; and according to constraint conditions combined with a state recursive equation, the optimal energy-saving driving strategy from the current position of the train to the end point is solved, and each time the train travels to a new discrete point, the optimal strategy is obtained in real time and updated. The method makes full use of the mode switching idea and has the advantages of rolling optimization, online train control, and reasonable use of train braking energy.

Description

Technical Field

[0001] The invention relates to the technical field of train operation optimization, and in particular to an online energy-saving optimization control method for a subway train based on on-board energy storage. Background Art

[0002] At present, there are three main types of energy-saving operation optimization for trains: the first is to rely on discrete generation of the optimal energy-saving speed curve of the train, and then run according to the curve during operation, but it may face interference, and the speed error in actual operation will be accumulated, and eventually deviate from the optimal solution obtained offline; the second is to combine offline with online, first obtain the optimal solution of the speed curve offline, and during driving, first run according to the first mode in the optimal solution, and then go to the offline optimal solution, and repeat the above steps until the train reaches the destination. This can eliminate the impact of interference during operation on the speed, but a large amount of energy will be generated when the train brakes, and this energy will be wasted; the third is to combine offline with energy storage devices, considering that the energy storage device will absorb the braking energy generated by the train, and then get the optimal speed curve offline, but it will face the situation where interference causes the speed to deviate from the optimal solution.

[0003] In summary, currently there is no train energy-saving optimization method that can both eliminate interference effects during train operation and reasonably use the generated regenerative braking energy. Summary of the invention

[0004] The purpose of the present invention is to provide a new energy-saving operation optimization method for subway trains, which uses position as an independent variable to obtain the state of the train online, uses an on-board supercapacitor to absorb the braking energy generated by the train, and provides energy to the train when the train accelerates, and uses a dynamic programming algorithm to solve the optimal switching control sequence and the optimal modal sequence of the train in real time. This method has the advantages of making full use of the idea of ​​model prediction rolling optimization, online control of the train, and reasonable use of braking energy.

[0005] To achieve the above object, the present invention provides the following technical solutions:

[0006] An online energy-saving optimization control method for a subway train based on on-board energy storage, characterized in that it comprises the following steps:

[0007] Step 1: Establish a train dynamics model with train position as the independent variable and speed and time as the state variables; when the train is running, it is regarded as a mass point, and the train traction characteristics, basic resistance, and track slope are taken into account:

[0008]

[0009]

[0010] Among them, t(s) is the time when the train reaches position s, v(s) is the speed of the train when it reaches position s, m is the mass of the train and the passengers in the train, f(s,σ) is the traction or braking force of the train at position s when the mode is σ, r(v) is the basic resistance acting on the train, and g(s) is the slope additional resistance of the train at position s, which is negative for uphill sections and positive for downhill sections. g(s) and r(v) are expressed as

[0011]

[0012] r(v)=ω1+ω2v+ω3v 2 (4)

[0013] G(s) represents the track slope at position s on the line, g is the acceleration due to gravity; the first two terms in (4) represent the mechanical resistance of the train, the last term represents the air resistance of the train, ω1, ω2, ω3 are the empirical coefficients of the train running resistance, which are determined by the train itself.

[0014] Step 2: Discretize the length of the subway line, and discretize the train dynamics model and the forces it is subjected to:

[0015] The total running distance of the train [0, S] is divided into K equally spaced segments Δs, where K is the total number of discrete segments. If the discretized point is not a station, the nearest station is used as the discretized point, and then used as the initial point to discretize again with the same spacing until the end point. The discretized station is represented as

[0016] s0=0,s1,…,s k ,…s K-1 ,s K =S (5)

[0017] Among them, k is the discrete point index that the train travels to in real time, s k is the kth Δs position. For a line with n stations, the station and the speed at the station are expressed as

[0018] p k ,k∈{1,2,…,n} (6)

[0019]

[0020] Among them, p k is the station at the kth discrete point, is the location of the station, and the discrete train dynamics model is expressed as

[0021]

[0022]

[0023] where v k =v(s k ) and t k =t(s k ) represent the train at position s k The corresponding speed and time at f k (σ k )=f(s k ,σ k ) is the train at position s k At, the mode is σ k The traction / braking force on the train at this time, g(s k ) and r(v k ) is the additional force and resistance on the ramp experienced by the train after discretization.

[0024] Step 3: Establish a train traction / braking force switching scheme with four different modes such as maximum traction, cruising, inertia, and maximum braking; specify the mode switching sequence when the train travels between multiple stations:

[0025] The first mode is the maximum traction mode MT:

[0026] f k (σ k )=F(v k )σ k =MT (10)

[0027] Among them, F(v(s k )) is the traction force of the train during operation.

[0028] The second mode is the cruise mode SH:

[0029] f k (σ k )=r(v k )+g(s k )σ k =SH (11)

[0030] Among them, r(v k )、g(s k ) is the basic resistance during train operation and the additional resistance on slope.

[0031] The third mode is the idle mode CS:

[0032] f k (σ k )=0σ k =CS(12)

[0033] The fourth mode is the maximum braking mode MB:

[0034] f k(σ k )=B(v k )σ k =MB (13)

[0035] Among them, B(v(s k )) is the braking force during train operation.

[0036] The mode switching sequence when a train travels between multiple stations is specified as follows:

[0037] MT→SH→CS→MB→MT→…→MB(14)

[0038] Step 4: Design the charging and discharging strategy of the on-board supercapacitor:

[0039] The on-board supercapacitor starts discharging if the following conditions are met:

[0040]

[0041] The on-board supercapacitor starts charging if the following conditions are met:

[0042]

[0043] in, The train travels to position s k The power at the time can be obtained by Find, P SC,dis is the discharge power of the on-board supercapacitor used, and in actual operation P SC,ch is the charging power of the on-board supercapacitor used, and in actual operation Yes k Always monitor the charge state of the supercapacitor. In order to increase its service life and achieve the purpose of protection, the energy in the supercapacitor cannot be completely discharged. Defined as t k The remaining energy in the supercapacitor at the moment With total energy E SC Ratio of:

[0044]

[0045]

[0046] in, is the train at position s k The remaining energy of the supercapacitor when it is started at time t0, t k The train travels to position s k The time when the supercapacitor is turned off; P SC,ch and PSC,dis Cannot appear at the same time.

[0047] Step 5: Construct a train energy-saving operation optimization problem, which is to find the minimum value of the accumulated work of the train traction force under the condition of on-board energy storage:

[0048] The final objective function to be optimized is expressed as

[0049]

[0050] in, For the train at position s k The energy consumed by driving for Δt time, is the energy provided by the on-board capacitor during the time t1→t2 when the train consumes energy, and E is the net energy consumption of the train excluding the energy supplied by the on-board energy storage when the train travels between multiple stations.

[0051] Step 6: Design line conditions including speed limits and total train running time constraints:

[0052]

[0053] Among them, p1, p2, …, p n are the stations on the subway lines, v min (s k ),v max (s k ) are respectively the train running to s k The minimum and maximum values ​​of the driving speed allowed at the time, T total is the total time required for the train to complete the entire line, t K It is the actual total running time when the train runs to the Kth discrete point, i.e., the terminal point, and δ is the error allowed in the total running time.

[0054] Step 7: Determine the state recursion equation:

[0055]

[0056] Among them, ψ k =[s k ,v k ,t k ] is the state of the train at the kth discrete position point, ψ K =[S,0,t K ] is the status of the train at the end of the line, E * (ψ k ) is from the terminal state ψ K To state ψ k The minimum energy consumption, L(ψ k-1 ,σ k-1 ) is the train in mode σk-1 Under control, from state ψ k To state ψ k-1 The change in energy consumption, E * (ψ K ) is the terminal state ψ K energy consumption.

[0057] Step 8: Considering the online calculation of on-board energy storage, it is mainly divided into offline search for the optimal driving strategy for the remaining routes when at the station and online search for the optimal driving strategy between stations when driving between stations:

[0058] Step 8.1: Set k = 0 and initialize s k ,v k ,t k ,σ k ;

[0059] Step 8.2: Get the terminal state ψ of the train K =[S,0,t K ], operating constraints and the current train’s real-time position s k , the dynamic programming algorithm uses the state recursion equation to reversely solve the optimal driving strategy of the train from the end point with the goal of minimizing energy consumption;

[0060] Step 8.3: When solving for the position s k If the energy consumption is not the minimum, return to step 8.2 and continue to calculate other points at this position until the energy consumption is minimized;

[0061] Step 8.4: Let k = k-1, determine whether it is at the real-time position, if not, return to step 8.2 to continue searching;

[0062] Step 8.5: Generate the optimal modal driving strategy set σ for the remaining routes;

[0063] Step 8.6: Select the first mode in the generated optimal mode driving strategy set as the next operating mode of the train;

[0064] Step 8.7: Update train speed and travel time;

[0065] Step 8.8: Determine whether the real-time power under the current train mode reaches the starting condition of the on-board supercapacitor. If not, directly execute step 8.10;

[0066] Step 8.9: After the on-board supercapacitor is turned on, the recursive equation is calculated to consider the situation where the on-board supercapacitor supplies power or absorbs energy;

[0067] Step 8.10: Use the dynamic programming algorithm to calculate the optimal energy consumption E(ψ k-1 );

[0068] Step 8.11: When solving for the position s k If the energy consumption is not the minimum, return to step 8.10 to continue calculating other points at this position until the energy consumption is minimized;

[0069] Step 8.12: Determine whether the current location is a station, if so, return to step 8.3 for calculation;

[0070] Step 8.13: Let k = k-1, determine whether it is at the real-time position, if not, return to step 8.7 to continue searching;

[0071] Step 8.14: Generate the control strategy of the train at each position in real time;

[0072] Step 8.15: Determine whether the current position is the end point. If not, return to step 8.7 to continue searching;

[0073] Step 8.16: End the calculation.

[0074] Compared with the existing methods, the advantages of the present invention are as follows:

[0075] The present invention discloses an online energy-saving optimization control method for subway trains based on an on-board energy storage device. The method takes into account the basic resistance, train traction / braking characteristics, additional resistance on ramps, speed limit and total running time limit during train operation, establishes a train dynamics model with train position as an independent variable, speed and time as state variables, and discretizes the model. The train running mode switching sequence between multiple stations is specified, and a train energy-saving optimization problem considering on-board energy storage is constructed. The state recursive equation is determined, and the optimal driving strategy of the train is solved by using a dynamic programming algorithm for two situations: running between stations and stopping at stations. The method makes full use of the mode switching idea and has the advantages of rolling optimization, online train control, and reasonable use of train braking energy. BRIEF DESCRIPTION OF THE DRAWINGS

[0076] Figure 1 This is a flow chart of an online energy-saving optimization control method for a subway train based on an on-board supercapacitor according to the present invention;

[0077] Figure 2 It is a simulation diagram of train position, speed, on-board supercapacitor switch control strategy and train driving strategy according to a specific embodiment of the present invention;

[0078] Figure 3 It is a simulation diagram of train position, train power, grid power and on-board supercapacitor power according to a specific implementation manner of the present invention. DETAILED DESCRIPTION

[0079] In order to clearly illustrate the present invention, the present invention is further described in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, rather than all the embodiments. Based on the embodiments in the invention, all other embodiments obtained by other persons in the art without creative work should be within the scope of protection of the present invention.

[0080] It is particularly noted that the terms train, line, etc. in the specification and claims of the present invention are used to refer to objects that meet specific conditions in general, not to refer to a specific object.

[0081] like Figure 1 As shown, the present invention is an online energy-saving optimization control method for a subway train based on on-board energy storage, and the method specifically comprises:

[0082] Step 1: Establish a train dynamics model with train position as the independent variable, speed and time as the state variables:

[0083]

[0084]

[0085] This embodiment uses the Yizhuang Line of Beijing Subway. The passenger mass of the Yizhuang Line train is m=300t, t(s) is the time when the train reaches position s, v(s) is the speed of the train when it reaches position s, f(s,σ) is the traction or braking force of the train at position s and mode σ, r(v) is the basic resistance acting on the train, g(s) is the slope additional resistance of the train at position s, g(s) and r(v) are expressed as

[0086]

[0087] r(v)=ω1+ω2v+ω3v 2 (25)

[0088] G(s) represents the track slope at position s on the line, g = 9.8 m / s 2 ,

[0089] ω1=2.965, ω2=-0.064, ω3=3.858.

[0090] Step 2: Discretize the length of the subway line, and discretize the train dynamics model and the forces it is subjected to:

[0091] The total length of the Yizhuang line is 23 km, divided into 767 stations with an equal interval of 30 m. The discrete stations are represented as follows:

[0092] s0=0,s1=30,…,s k ,sK =S (26)

[0093] Among them, K = 766, S = 23000, k is the index of the discrete point to which the train travels in real time, s k is the kth 30m position. There are 14 stations on the Yizhuang Line. The stations and the speeds at the stations are expressed as

[0094] p k ,k∈{1,2,…,n} (27)

[0095]

[0096] Where n = 14, p k is the station at the kth discrete point, is the location of the station, and the discrete train dynamics model is expressed as

[0097]

[0098]

[0099] where v k =v(s k ) and t k =t(s k ) represent the train at position s k The corresponding speed and time at f k (σ k )=f(s k ,σ k ) is the train at position s k At, the mode is σ k The traction / braking force on the train at this time, g(s k ) and r(v k ) is the additional force and resistance on the ramp experienced by the train after discretization, and the parameter value is equal to that before discretization.

[0100] Step 3: Establish a train traction / braking force switching scheme with four different modes such as maximum traction, cruising, inertia, and maximum braking; specify the mode switching sequence when the train travels between multiple stations:

[0101] f k (σ k )=F(v k )σ k =MT (31)

[0102] f k (σ k )=r(v k )+g(s k )σ k =SH (32)

[0103] f k (σ k )=0σ k =CS (33)

[0104] f k (σ k )=B(v k )σ k =MB (34)

[0105]

[0106] Among them, the traction and braking force at each position are expressed as

[0107]

[0108] The mode switching sequence when a train travels between multiple stations is specified as follows:

[0109] MT→SH→CS→MB→MT→…→MB(37)

[0110] Step 4: Design the charging and discharging strategy of the on-board supercapacitor:

[0111] The on-board supercapacitor starts discharging if the following conditions are met:

[0112]

[0113] The on-board supercapacitor starts charging if the following conditions are met:

[0114]

[0115] in, The train travels to position s k The power at the time can be obtained by Find, P SC,dis =585kW, and in actual operation P SC,ch =4378kW, and in actual operation Yes k Always monitor the charge state of the supercapacitor. In order to increase its service life and achieve the purpose of protection, the energy in the supercapacitor cannot be completely discharged. Defined as t k The remaining energy in the supercapacitor at the moment With total energy E SC =6.8kWh ratio:

[0116]

[0117]

[0118] in, is the train at position s k The remaining energy of the supercapacitor when it is started at time t0, t k The train travels to position s k The time when the supercapacitor is turned off; P SC,ch and P SC,dis Cannot appear at the same time.

[0119] Step 5: Construct a train energy-saving operation optimization problem, which is to find the minimum value of the accumulated work of the train traction force under the condition of on-board energy storage:

[0120] The final objective function to be optimized is expressed as

[0121]

[0122] in, For the train at position s k The energy consumed by traveling for Δt time, Δt is the time required for the train to travel 30m. is the energy provided by the on-board capacitor during the time t1→t2 when the train consumes energy, and E is the net energy consumption of the train excluding the energy supplied by the on-board energy storage when the train travels between multiple stations.

[0123] Step 6: Design line conditions including speed limits and total train running time constraints:

[0124]

[0125] Where n = 14, p1, p2, ..., p 14 are the stations on the subway lines, v min (s k ),v max (s k ) are respectively the train running to s k The minimum and maximum values ​​of the driving speed allowed at the time, T total =1601s,t K It is the actual total running time when the train runs to the Kth discrete point, i.e. the terminal point, δ = 20s.

[0126] Step 7: Determine the state recursion equation:

[0127]

[0128] Among them, ψ k =[s k ,v k ,t k] is the state of the train at the kth discrete position point, ψ K =[23000,0,1601] is the status of the train at the end of the line, E * (ψ k ) is from the terminal state ψ K To state ψ k The minimum energy consumption, L(ψ k-1 ,σ k-1 ) is the train in mode σ k-1 Under control, from state ψ k To state ψ k-1 The change in energy consumption, E * (ψ K ) is the terminal state ψ K energy consumption.

[0129] Step 8: Considering the online calculation of on-board energy storage, it is mainly divided into offline search for the optimal driving strategy for the remaining routes when at the station and online search for the optimal driving strategy between stations when driving between stations:

[0130] Step 8.1: Set k = 0 and initialize s k =0,v k =0,t k =0,σ k =MT;

[0131] Step 8.2: Get the terminal state ψ of the train K =[23000,0,1601], operation constraints and the current train's real-time position s k , the dynamic programming algorithm uses the state recursion equation to reversely solve the optimal driving strategy of the train from the end point with the goal of minimizing energy consumption;

[0132] Step 8.3: When solving for the position s k If the energy consumption is not the minimum, return to step 8.2 and continue to calculate other points at this position until the energy consumption is minimized;

[0133] Step 8.4: Let k = k-1, determine whether it is at the real-time position, if not, return to step 8.2 to continue searching;

[0134] Step 8.5: Generate the optimal modal driving strategy set σ for the remaining routes;

[0135] Step 8.6: Select the first mode in the generated optimal mode driving strategy set as the next operating mode of the train;

[0136] Step 8.7: Update train speed and travel time;

[0137] Step 8.8: Determine whether the real-time power under the current train mode reaches the starting condition of the on-board supercapacitor. If not, directly execute step 8.10;

[0138] Step 8.9: After the on-board supercapacitor is turned on, the recursive equation is calculated to consider the situation where the on-board supercapacitor supplies power or absorbs energy;

[0139] Step 8.10: Use the dynamic programming algorithm to calculate the optimal energy consumption E(ψ k-1 );

[0140] Step 8.11: When solving for the position s k If the energy consumption is not the minimum, return to step 8.10 to continue calculating other points at this position until the energy consumption is minimized;

[0141] Step 8.12: Determine whether the current location is a station, if so, return to step 8.3 for calculation;

[0142] Step 8.13: Let k = k-1, determine whether it is at the real-time position, if not, return to step 8.7 to continue searching;

[0143] Step 8.14: Generate the control strategy of the train at each position in real time;

[0144] Step 8.15: Determine whether the current position is the end point. If not, return to step 8.7 to continue searching;

[0145] Step 8.16: End the calculation.

[0146] After the calculation is completed, the simulation results are obtained. The total running time is T total The simulation diagram of train position, speed, on-board supercapacitor switch control strategy and train driving strategy is shown in Figure 1. Figure 2 As shown in the figure, the train position, train power, grid power and on-board supercapacitor power simulation diagram are as follows Figure 3 As shown. It can be seen that under the premise of meeting the punctuality requirement, the on-board supercapacitor supplies power to the train or absorbs the generated regenerative braking energy in real time when conditions are met, thereby reducing the power supply energy consumption of the power grid during train operation, and obtaining and updating the real train status in real time, using the dynamic programming method to search for the optimal driving strategy for the remaining lines, truly achieving online control of the train, eliminating interference effects, and reducing train operation errors.

Claims

1. A subway train online energy-saving optimization control method based on on-board energy storage, characterized in that: The following steps are involved: Step 1: Establish a train dynamics model with train position as the independent variable, speed and time as the state variables, and consider train traction characteristics, basic resistance, and track slope: Where t(s) is the time when the train reaches position s, v(s) is the speed of the train when it reaches position s, m is the mass of the train and the passengers, f(s,σ) is the traction or braking force on the train when the mode is σ at position s, r(v) is the basic resistance acting on the train, g(s) is the slope additional resistance on the train at position s, which is negative for uphill sections and positive for downhill sections. g(s) and r(v) are expressed as r(v)=ω1+ω2v+ω3v 2 (4) G(s) represents the track slope at position s on the line, g is the acceleration of gravity; the first two terms in (4) represent the mechanical resistance of the train, the last term represents the air resistance of the train, and ω1, ω2, ω3 are the empirical coefficients of the train running resistance; Step 2: Discretize the length of the subway line, and discretize the train dynamics model and the forces it is subjected to: The total running distance of the train [0, S] is divided into K equally spaced segments Δs, where K is the total number of discrete segments. If the discretized point is not a station, the nearest station is used as the discretized point, and then used as the initial point to discretize again with the same spacing until the end point. The discretized station is expressed as s0=0,s1,…,s k ,…s K-1 ,s K =S (5) Among them, k is the index of the discrete point to which the train travels in real time, s k is the kth Δs position, the station and the speed at the station are represented by p k ,k∈{1,2,…,n}(6) Where n is the number of sites, p k is the station at the kth discrete point, is the location of the station, and the discrete train dynamics model is expressed as where v k =v(s k ) and t k =t(s k ) represent the train at position s k The corresponding speed and time at f k (σ k )=f(s k ,σ k ) is the train at position s k At, the mode is σ k The traction / braking force on the train at this time, g(s k ) and r(v k ) is the additional force and resistance on the ramp experienced by the train after discretization; Step 3: Establish a train traction / braking force switching scheme with four different modes: maximum traction, cruising, inertia, and maximum braking; specify the mode switching sequence when the train travels between multiple stations: The first mode is the maximum traction mode MT: f k (s k )=F(v k )s k =MT(10) Among them, F(v(s k )) is the traction force of the train during operation; The second mode is the cruise mode SH: f k (s k )=r(v k )+g(s k )s k =SH(11) Among them, r(v k )、g(s k ) is the basic resistance of the train during operation and the additional resistance on the slope; The third mode is the idle mode CS: f k (s k )=0σ k =CS(12) The fourth mode is the maximum braking mode MB: f k (σ k )=B(v k ) σ k =MB (13) Among them, B(v(s k )) is the braking force of the train during operation; The mode switching sequence when a train travels between multiple stations is specified as follows: MT→SH→CS→MB→MT→…→MB(14) Step 4: Design the charging and discharging strategy of the on-board supercapacitor: The on-board supercapacitor starts discharging if the following conditions are met: The on-board supercapacitor starts charging if the following conditions are met: in, The train travels to position s k The power at the time is given by Find, P SC,dis is the discharge power of the on-board supercapacitor used. P SC,ch is the charging power of the on-board supercapacitor used. Yes k The state of charge of the supercapacitor at time t k The remaining energy in the supercapacitor at the moment With total energy E SC Ratio of: in, is the train at position s k The remaining energy of the supercapacitor when it is started at time t0, t k The train travels to position s k The time when the supercapacitor is turned off, P SC,ch and P SC,dis Cannot appear at the same time; Step 5: Construct the energy-saving operation optimization problem of the train and find the minimum value of the accumulated work of the train traction force under the condition of on-board energy storage: The final objective function to be optimized is expressed as in, For the train at position s k The energy consumed by driving for Δt time, is the energy provided by the on-board capacitor during the time t1→t2 when the train consumes energy, and E is the net energy consumption of the train when traveling between multiple stations excluding the energy provided by the on-board energy storage; Step 6: Design line conditions including speed limits and total train running time constraints: Among them, p1, p2, …, p n are the stations on the subway lines, v min (s k ),v max (s k ) are respectively the train running to s k The minimum and maximum values ​​of the driving speed allowed at the time, T total is the total time required for the train to complete the entire line, t K is the actual total running time when the train runs to the Kth discrete point, i.e., the terminal point, and δ is the error allowed for the total running time; Step 7: Determine the state recursion equation: Among them, ψ k =[s k ,v k ,t k ] is the state of the train at the kth discrete position point, ψ K =[S,0,t K ] is the status of the train at the end of the line, E * (ψ k ) is from the terminal state ψ K To state ψ k The minimum energy consumption, L(ψ k-1 ,σ k-1 ) is the train in mode σ k-1 Under control, from state ψ k To state ψ k-1 The change in energy consumption, E * (ψ K ) is the terminal state ψ K Energy consumption; Step 8: Considering the online calculation of on-board energy storage, it is divided into offline search for the optimal driving strategy for the remaining routes when at a station and online search for the optimal driving strategy between stations when driving between stations; The optimal driving strategy in step 8 is as follows: Step 8.1: Set k = 0 and initialize s k ,v k ,t k ,σ k ; Step 8.2: Get the train's terminal state ψ K =[S,0,t K ], operating constraints and the current train’s real-time position s k , the dynamic programming algorithm uses the state recursion equation to solve the optimal driving strategy of the train from the end point in reverse according to the minimum energy consumption; Step 8.3: When solving for the position s k If the energy consumption is not the minimum, return to step 8.2 and continue to calculate other points at this position until the energy consumption is minimized; Step 8.4: Let k = k-1, determine whether it is at the real-time position, if not, return to step 8.2 to continue searching; Step 8.5: Generate the optimal modal driving strategy set σ for the remaining routes; Step 8.6: Select the first mode in the generated optimal mode driving strategy set as the next operating mode of the train; Step 8.7: Update train speed and travel time; Step 8.8: Determine whether the real-time power under the current train mode reaches the starting condition of the on-board supercapacitor. If not, directly execute step 8.10; Step 8.9: After the on-board supercapacitor is turned on, the recursive equation is calculated to consider the situation where the on-board supercapacitor supplies power or absorbs energy; Step 8.10: Use the dynamic programming algorithm to calculate the optimal energy consumption E(ψ k-1 ); Step 8.11: When solving for the position s k If the energy consumption is not the minimum, return to step 8.10 to continue calculating other points at this position until the energy consumption is minimized; Step 8.12: Determine whether the current location is a station, if so, return to step 8.3 for calculation; Step 8.13: Let k = k-1, determine whether it is at the real-time position, if not, return to step 8.7 to continue searching; Step 8.14: Generate the control strategy of the train at each position in real time; Step 8.15: Determine whether the current position is the end point. If not, return to step 8.7 to continue searching; Step 8.16: End the calculation.

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