CN103963805A - Energy-saving method of train operation of urban mass transit - Google Patents

Abstract

The invention belongs to the technical field of urban mass transit and particularly relates to an energy-saving method of train operation of the urban mass transit. The energy-saving method comprises the steps of 1, analyzing operation matching rules of adjacent trains and computing the size of utilized regeneration energy; 2, establishing an optimization model of the train operation by taking the utilized regeneration energy as the target; 3, solving the optimization model to obtain an energy-saving time table of the train operation of the urban mass transit. By means of the energy-saving method, energy consumption during train operation is reduced, and security of an overhead line system is improved. Furthermore, the energy-saving method has the advantages of (1) being high in operation speed and applicable to large-scale computer simulation by adopting an integer programming method; (2) considering comprehensive factors, being high in modeling accuracy and strong in applicability of the planned operation time table; (3) being capable of embedded into hardware of a train energy-saving driving auxiliary system in an online mode, easy to implement, low in cost and wide in application range.

Description

Energy-saving method for running of urban rail transit train

Technical Field

The invention belongs to the technical field of urban rail transit, and particularly relates to an energy-saving method for running of an urban rail transit train.

Background

Along with the rapid development of urban rail transit transportation industry, rail transit lines are opened in a plurality of cities such as Beijing, Shanghai, Guangzhou and the like in China, and the operation mileage reaches 1970 kilometers. During the 'twelve-five' period, there will be 19 cities in China with newly built rail transit lines 1800 kilometers, and the total investment exceeds one trillion yuan. Urban rail transit is used as a main line of urban public transport and a main artery for passenger flow transportation, and is the basis for solving urban traffic jam. However, the energy consumption of urban rail transit is also very large. Taking Beijing as an example, the total annual traction power consumption exceeds 3 hundred million degrees. Therefore, under the era background of global rapid development of low-carbon economy, the research on the urban rail transit energy-saving technology undoubtedly has important practical significance. The energy-saving and emission-reducing work is well done, and the energy use efficiency is improved, so that the energy-saving and emission-reducing work is necessary and urgent.

Regenerative braking is a braking technique used in an electric railway train, in which a motor is converted into a generator mode during braking, and kinetic energy of the train is converted into electric energy for use. Generally, a small part of the regenerative energy generated by braking the train is utilized by the vehicle-mounted auxiliary equipment of the train, and most of the regenerative energy is fed back to a contact network (or a third rail) and is used by being pulled by an adjacent train in the same power supply section. The energy fed back to the contact network can be consumed by heating of heating resistors on the line if the energy cannot be used by other trains in time in a traction manner, so that danger caused by overhigh voltage of the contact network is prevented. Regenerative braking has been widely used in urban rail transit trains at home and abroad, for example, london subway, madrid subway, new york subway, beijing subway (airport line, No. 15 line, chang' ping line, yazao line, and house mountain line) and the like adopt a regenerative braking and air braking mode.

At present, when an urban rail transit train operates, the indexes such as punctuality, operation efficiency and average travel speed are mainly considered, the reduction of the consumption of train operation energy and the danger caused by overhigh voltage of a contact network during regenerative braking are not considered.

Disclosure of Invention

The invention aims to provide an energy-saving method for urban rail transit train operation, aiming at the problems of high energy consumption and network contact safety of the existing urban rail transit train operation, which is characterized by comprising the following steps of:

step 1, analyzing the operation matching rules of adjacent trains, and calculating the magnitude of the utilized regenerative energy;

step 2, establishing an optimization model of train operation by taking the utilized regenerative energy as a target;

and 3, solving the optimization model to obtain an energy-saving schedule of the running of the urban rail transit train.

The step 1 of calculating the magnitude of the utilized regenerative energy mainly comprises the following steps:

step 101, determining that the time when a first vehicle stops at a first station is 0 time;

step 102, calculating the time when the train i leaves the station n:

<math> <mrow> <msubsup> <mi>t</mi> <mi>in</mi> <mn>1</mn> </msubsup> <mrow> <mo>(</mo> <mi>X</mi> <mo>)</mo> </mrow> <mo>=</mo> <munderover> <mi>&Sigma;</mi> <mrow> <mi>k</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>n</mi> </munderover> <msub> <mi>x</mi> <mi>k</mi> </msub> <mo>+</mo> <munderover> <mi>&Sigma;</mi> <mrow> <mi>k</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow> <mi>n</mi> <mo>-</mo> <mn>1</mn> </mrow> </munderover> <msub> <mi>t</mi> <mi>k</mi> </msub> <mo>+</mo> <mrow> <mo>(</mo> <mi>i</mi> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> <mi>h</mi> <mo>;</mo> </mrow> </math>

wherein X is { h, X ═ h_nN1, 2, N-1 represents a set of these decision variables, N, k represents a station, x represents a station, and_nstopping time of the train at the nth station, wherein N represents the total number of stations on the line, i represents the train, h represents the departure interval of the train, and x_kIndicating the stop time of the train at each station k,indicating the moment at which the train leaves the station n and starts to pull, t_kRepresenting the running time of the train between the nth stations;

step 103, calculating the time when the train i finishes the traction and the coasting among the nth stations, the time when the train i finishes the coasting and the braking among the nth stations and the time when the train i finishes the braking and reaches the station n +1 among the nth stations:

$\left\{\begin{array}{c}{t}_{\mathrm{in}}^2\left(X\right)=t_{\mathrm{in}}^1\left(X\right)+t_n^a\\ t_{\mathrm{in}}^3\left(X\right)=t_{\mathrm{in}}^2\left(X\right)+t_n^c\\ t_{\mathrm{in}}^4\left(X\right)=t_{\mathrm{in}}^3\left(X\right)+t_n^b\end{array}\right.$

wherein,indicating the moment when the train leaves the station n to start traction,indicating the moment when the train starts to coast after the traction between the nth stations is completed,indicating the moment when the train completes starting braking while coasting between the nth stations,indicating the time when the braking of the train is completed between the nth stations and reaches the station n +1,representing the traction time of the train between the nth stations,indicating the braking time of the train between the nth stations,representing the coasting time of the train between the nth stations, wherein X represents a set of decision variables;

step 104, calculating a speed-time curve of the train i between the nth stations:

<math> <mrow> <msub> <mi>v</mi> <mi>in</mi> </msub> <mrow> <mo>(</mo> <mi>X</mi> <mo>,</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfenced open='{' close=''> <mtable> <mtr> <mtd> <msubsup> <mi>a</mi> <mi>n</mi> <mn>1</mn> </msubsup> <mrow> <mrow> <mo>(</mo> <mi>t</mi> <mo>-</mo> <msubsup> <mi>t</mi> <mi>in</mi> <mn>1</mn> </msubsup> <mrow> <mo>(</mo> <mi>X</mi> <mo>)</mo> </mrow> <mo>)</mo> </mrow> <mo>,</mo> </mrow> </mtd> <mtd> <mi>if</mi> <msubsup> <mi>t</mi> <mi>in</mi> <mn>1</mn> </msubsup> <mrow> <mo>(</mo> <mi>X</mi> <mo>)</mo> </mrow> <mo>&le;</mo> <mi>t</mi> <mo>&lt;</mo> <msubsup> <mi>t</mi> <mi>in</mi> <mn>2</mn> </msubsup> <mrow> <mo>(</mo> <mi>X</mi> <mo>)</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <msubsup> <mi>a</mi> <mi>n</mi> <mn>1</mn> </msubsup> <msubsup> <mi>t</mi> <mi>n</mi> <mi>a</mi> </msubsup> <mo>-</mo> <msubsup> <mi>a</mi> <mi>n</mi> <mn>2</mn> </msubsup> <mrow> <mo>(</mo> <mi>t</mi> <mo>-</mo> <msubsup> <mi>t</mi> <mi>in</mi> <mn>2</mn> </msubsup> <mrow> <mo>(</mo> <mi>X</mi> <mo>)</mo> </mrow> <mo>)</mo> </mrow> <mo>,</mo> </mtd> <mtd> <mi>if</mi> <msubsup> <mi>t</mi> <mi>in</mi> <mn>2</mn> </msubsup> <mrow> <mo>(</mo> <mi>X</mi> <mo>)</mo> </mrow> <mo>&le;</mo> <mi>t</mi> <mo>&lt;</mo> <msubsup> <mi>t</mi> <mi>in</mi> <mn>3</mn> </msubsup> <mrow> <mo>(</mo> <mi>X</mi> <mo>)</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <msubsup> <mi>a</mi> <mi>n</mi> <mn>1</mn> </msubsup> <msubsup> <mi>t</mi> <mi>n</mi> <mi>a</mi> </msubsup> <mo>-</mo> <msubsup> <mi>a</mi> <mi>n</mi> <mn>2</mn> </msubsup> <msubsup> <mi>t</mi> <mi>n</mi> <mi>c</mi> </msubsup> <mo>-</mo> <mrow> <mo>(</mo> <mi>t</mi> <mo>-</mo> <msubsup> <mi>t</mi> <mi>in</mi> <mn>3</mn> </msubsup> <mrow> <mo>(</mo> <mi>X</mi> <mo>)</mo> </mrow> <mo>)</mo> </mrow> <mo>,</mo> </mtd> <mtd> <mi>if</mi> <msubsup> <mi>t</mi> <mi>in</mi> <mn>3</mn> </msubsup> <mrow> <mo>(</mo> <mi>X</mi> <mo>)</mo> </mrow> <mo>&le;</mo> <mi>t</mi> <mo>&lt;</mo> <msubsup> <mi>t</mi> <mi>in</mi> <mn>4</mn> </msubsup> <mrow> <mo>(</mo> <mi>X</mi> <mo>)</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> <mo>,</mo> </mtd> <mtd> <mi>if</mi> <msubsup> <mi>t</mi> <mi>in</mi> <mn>4</mn> </msubsup> <mrow> <mo>(</mo> <mi>X</mi> <mo>)</mo> </mrow> <mo>&le;</mo> <mi>t</mi> <mo>&lt;</mo> <msubsup> <mi>t</mi> <mrow> <mi>i</mi> <mrow> <mo>(</mo> <mi>n</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow> <mn>1</mn> </msubsup> <mrow> <mo>(</mo> <mi>X</mi> <mo>)</mo> </mrow> </mtd> </mtr> </mtable> </mfenced> </mrow> </math>

wherein,representing the traction acceleration of the train between the nth stations,representing the coasting acceleration of the train between the nth stations,representing the braking acceleration of the train between the nth stations,representing the traction time of the train between the nth stations,represents the coasting time of the train between the nth stations, t represents the train i running time,indicating the moment when the train leaves the station n to start traction,indicating the moment when the train starts to coast after the traction between the nth stations is completed,indicating the moment when the train completes starting braking while coasting between the nth stations,indicating the time when the braking of the train is completed between the nth stations and reaches the station n +1,representing the moment when the train leaves the station n +1 and starts to pull, and X represents a set of decision variables;

step 105, calculating the energy required by the traction of the train i at the moment t:

<math> <mrow> <msub> <mi>f</mi> <mi>in</mi> </msub> <mrow> <mo>(</mo> <mi>X</mi> <mo>,</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>=</mo> <mi>m</mi> <mrow> <mo>(</mo> <msubsup> <mi>v</mi> <mi>in</mi> <mn>2</mn> </msubsup> <mrow> <mo>(</mo> <mi>X</mi> <mo>,</mo> <mi>t</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>-</mo> <msubsup> <mi>v</mi> <mi>in</mi> <mn>2</mn> </msubsup> <mrow> <mo>(</mo> <mi>X</mi> <mo>,</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>)</mo> </mrow> <mo>/</mo> <msub> <mrow> <mn>2</mn> <mi>&eta;</mi> </mrow> <mn>1</mn> </msub> </mrow> </math>

wherein eta is₁Representing the traction efficiency of the train motor, i.e. the ratio of electric energy to kinetic energy of the train, m being the trainThe mass of the vehicle is measured by the weight sensor,representing the speed of train i +1 between the nth stations at time t,representing the speed of the train i +1 between nth stations at the time t, wherein X represents a set of decision variables;

step 106, calculating the regenerative energy generated by braking the train i at the moment t:

<math> <mrow> <msub> <mi>g</mi> <mi>in</mi> </msub> <mrow> <mo>(</mo> <mi>X</mi> <mo>,</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>=</mo> <mi>m</mi> <mrow> <mo>(</mo> <msubsup> <mi>v</mi> <mi>in</mi> <mn>2</mn> </msubsup> <mrow> <mo>(</mo> <mi>X</mi> <mo>,</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>-</mo> <msubsup> <mi>v</mi> <mi>in</mi> <mn>2</mn> </msubsup> <mrow> <mo>(</mo> <mi>X</mi> <mo>,</mo> <mi>t</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>)</mo> </mrow> <msub> <mi>&eta;</mi> <mn>2</mn> </msub> <mrow> <mo>(</mo> <mn>1</mn> <mo>-</mo> <mi>&beta;</mi> <mo>)</mo> </mrow> <mo>/</mo> <mn>2</mn> </mrow> </math>

wherein eta is₂The conversion efficiency is expressed, namely the ratio of the kinetic energy of the train to the regenerated electric energy, beta represents the transmission loss of the regenerated energy on a contact net or a third rail,indicates that the train i +1 is between the nth stations at the time tThe speed of the motor vehicle is set to be,representing the speed of the train i +1 between the nth stations at the time t;

step 107: calculating the regenerated energy utilized in the whole running process of the I train:

<math> <mrow> <mi>F</mi> <mrow> <mo>(</mo> <mi>X</mi> <mo>)</mo> </mrow> <mo>=</mo> <munderover> <mi>&Sigma;</mi> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow> <mi>I</mi> <mo>-</mo> <mn>1</mn> </mrow> </munderover> <munderover> <mi>&Sigma;</mi> <mrow> <mi>n</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow> <mi>N</mi> <mo>-</mo> <mn>1</mn> </mrow> </munderover> <munder> <mi>&Sigma;</mi> <mrow> <mi>t</mi> <mo>&Element;</mo> <msub> <mi>T</mi> <mi>in</mi> </msub> </mrow> </munder> <mi>min</mi> <mo>{</mo> <msub> <mi>f</mi> <mi>in</mi> </msub> <mrow> <mo>(</mo> <mi>X</mi> <mo>,</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>,</mo> <msub> <mi>g</mi> <mrow> <mrow> <mo>(</mo> <mi>i</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> <mrow> <mo>(</mo> <mi>n</mi> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow> </msub> <mrow> <mo>(</mo> <mi>X</mi> <mo>,</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>}</mo> </mrow> </math>

wherein, T_inIndicating that train i is at the nth stationCoincidence time of inter-traction and braking of train I +1 between N-1 th stations, wherein I represents total number of trains, N represents total number of stations on line, and g_(i+1)(n-1)(X, t) regenerative energy generated by braking of train i +1 between the (n-1) th stations at time t, f_in(X, t) represents the energy required for the train i to pull at time t.

The optimization model of the train operation in the step 2 is as follows:

<math> <mfenced open='{' close='' separators=''> <mtable> <mtr> <mtd> <mi>max</mi> <mi>F</mi> <mrow> <mo>(</mo> <mi>X</mi> <mo>)</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mi>s</mi> <mo>.</mo> <mi>t</mi> <mo>.</mo> <msub> <mi>l</mi> <mi>h</mi> </msub> <mo>&le;</mo> <mi>h</mi> <mo>&le;</mo> <msub> <mi>u</mi> <mi>h</mi> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>l</mi> <mi>T</mi> </msub> <mo>&le;</mo> <munderover> <mi>&Sigma;</mi> <mrow> <mi>n</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow> <mi>N</mi> <mo>-</mo> <mn>1</mn> </mrow> </munderover> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mi>n</mi> </msub> <mo>+</mo> <msub> <mi>t</mi> <mi>n</mi> </msub> <mo>)</mo> </mrow> <mo>&le;</mo> <msub> <mi>u</mi> <mi>T</mi> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>l</mi> <mi>n</mi> </msub> <mo>&le;</mo> <msub> <mi>x</mi> <mi>n</mi> </msub> <mo>&le;</mo> <msub> <mi>u</mi> <mi>n</mi> </msub> <mo>,</mo> <mi>n</mi> <mo>=</mo> <mn>1,2</mn> <mo>.</mo> <mo>.</mo> <mo>.</mo> <mo>,</mo> <mi>N</mi> <mo>-</mo> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <mi>h</mi> <mo>,</mo> <msub> <mi>x</mi> <mi>n</mi> </msub> <mo>&Element;</mo> <mi>Z</mi> <mo>,</mo> <mi>n</mi> <mo>=</mo> <mn>1,2</mn> <mo>,</mo> <mo>.</mo> <mo>.</mo> <mo>.</mo> <mo>,</mo> <mi>N</mi> <mo>-</mo> <mn>1</mn> <mo>.</mo> </mtd> </mtr> </mtable> </mfenced> </math>

wherein F (X) is the regenerated energy utilized in the whole running process of the I train, h is the departure interval of the train, [ l [ ]_h,u_h]Representing the train departure interval constraint window, x_nFor the stop time of the train at the nth station, t_nFor the total running time of the train between the nth stations, [ l_T,u_T]Represents the total travel time constraint window, [ l_n,u_n]Representing a stop time constraint window, h and x, for a train at station n_nAll belong to integers, N is the serial number of the station, N is the total number of the station, and T is the total travel time.

The invention has the beneficial effects that: the invention realizes the reduction of train operation energy consumption and the improvement of contact network safety, and has the following advantages: (1) the method of integer programming is adopted, the operation speed is high, and therefore, the method is suitable for large-scale computer simulation; (2) the method has the advantages that the comprehensive modeling precision of the considered factors is high, and the made operation schedule has high applicability; (3) the system can be embedded into the hardware of the train energy-saving driving auxiliary system in an off-line manner, and is easy to implement, low in cost and wide in application range.

Drawings

FIG. 1 is a flow chart of an energy-saving train operation method according to the present invention;

FIG. 2 is a schematic diagram of a network structure of an urban rail transit power supply system;

FIG. 3 is a schematic diagram of inter-train energy matching;

fig. 4 is a schematic diagram of a train operation process.

Detailed Description

The preferred embodiments will be described in detail below with reference to the accompanying drawings.

The invention provides an energy-saving method for running of an urban rail transit train, which comprises the following steps:

1. analyzing the operation matching rule of the adjacent trains, and calculating the magnitude of the utilized regenerative energy;

2. establishing an optimization model of train operation by taking the utilized regenerative energy as a target;

3. and solving the optimization model to obtain an energy-saving schedule of the running of the urban rail transit train.

The loss in the transfer and conversion process of the regenerated energy in the running process of the urban rail transit train comprises the following steps:

(a) when the braking train regeneratively brakes, the kinetic energy is converted into the loss in the electric energy process;

(b) electric energy is transmitted from a braking train to a traction train through a power grid, and loss occurs in the transmission process;

(c) the traction train converts the absorbed electric energy into loss in the process of train kinetic energy through a series of transmission systems.

The method analyzes the transmission process of the regenerated energy in the train based on the network structure of the urban rail transit power supply system. As shown in fig. 2, a train i and a train i +1 are two trains located in the same power supply section, the train i leaves a station n and is in a traction working condition and needs to absorb electric energy, and the train i +1 arrives at the station n and is in a braking working condition and generates electric energy through regenerative braking. At this time, the regenerative energy generated by the train i +1 is absorbed and utilized by the train i through the third rail transmission. The arrows in the figure indicate the direction of energy transfer. By reasonably adjusting the departure time of the train i and the arrival time of the train i +1, the portion of the regenerative energy generated by the train i +1, which is utilized by the train i, can be increased. Based on the periodicity of the urban rail transit timetable, the utilization rate of the regenerated energy of the whole line can be improved by reasonably adjusting the departure time and arrival time of the whole line train.

The process of calculating the amount of the regenerative energy to be used in step 1 is shown in fig. 1, and mainly includes:

step 101, determining that the time when a first vehicle stops at a first station is 0 time;

step 102, calculating the time when the train i leaves the station n:

<math> <mrow> <msubsup> <mi>t</mi> <mi>in</mi> <mn>1</mn> </msubsup> <mrow> <mo>(</mo> <mi>X</mi> <mo>)</mo> </mrow> <mo>=</mo> <munderover> <mi>&Sigma;</mi> <mrow> <mi>k</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>n</mi> </munderover> <msub> <mi>x</mi> <mi>k</mi> </msub> <mo>+</mo> <munderover> <mi>&Sigma;</mi> <mrow> <mi>k</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow> <mi>n</mi> <mo>-</mo> <mn>1</mn> </mrow> </munderover> <msub> <mi>t</mi> <mi>k</mi> </msub> <mo>+</mo> <mrow> <mo>(</mo> <mi>i</mi> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> <mi>h</mi> <mo>;</mo> </mrow> </math>

wherein X is { h, X ═ h_nN1, 2, N-1 represents a set of these decision variables, N, k represents a station, N represents the total number of stations on the line, i represents a train, h represents a train departure interval, and x represents a train departure interval_kIndicating the stop time of the train at each station k,indicating the moment at which the train leaves the station n and starts to pull, t_kRepresenting the running time of the train between the nth stations;

step 103, calculating the time when the train i finishes the traction and the coasting among the nth stations, the time when the train i finishes the coasting and the braking among the nth stations and the time when the train i finishes the braking and reaches the station n +1 among the nth stations:

$\left\{\begin{array}{c}{t}_{\mathrm{in}}^2\left(X\right)=t_{\mathrm{in}}^1\left(X\right)+t_n^a\\ t_{\mathrm{in}}^3\left(X\right)=t_{\mathrm{in}}^2\left(X\right)+t_n^c\\ t_{\mathrm{in}}^4\left(X\right)=t_{\mathrm{in}}^3\left(X\right)+t_n^b\end{array}\right.$

wherein:indicating the moment when the train starts to coast after the traction between the nth stations is completed,indicating the moment when the train completes starting braking while coasting between the nth stations,indicating the time when the braking of the train is completed between the nth stations and reaches the station n +1,representing the traction time of the train between the nth stations,indicating the braking time of the train between the nth stations,representing the coasting time of the train between the nth stations;

step 104, calculating a speed-time curve of the train i between the nth stations:

<math> <mrow> <msub> <mi>v</mi> <mi>in</mi> </msub> <mrow> <mo>(</mo> <mi>X</mi> <mo>,</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfenced open='{' close=''> <mtable> <mtr> <mtd> <msubsup> <mi>a</mi> <mi>n</mi> <mn>1</mn> </msubsup> <mrow> <mrow> <mo>(</mo> <mi>t</mi> <mo>-</mo> <msubsup> <mi>t</mi> <mi>in</mi> <mn>1</mn> </msubsup> <mrow> <mo>(</mo> <mi>X</mi> <mo>)</mo> </mrow> <mo>)</mo> </mrow> <mo>,</mo> </mrow> </mtd> <mtd> <mi>if</mi> <msubsup> <mi>t</mi> <mi>in</mi> <mn>1</mn> </msubsup> <mrow> <mo>(</mo> <mi>X</mi> <mo>)</mo> </mrow> <mo>&le;</mo> <mi>t</mi> <mo>&lt;</mo> <msubsup> <mi>t</mi> <mi>in</mi> <mn>2</mn> </msubsup> <mrow> <mo>(</mo> <mi>X</mi> <mo>)</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <msubsup> <mi>a</mi> <mi>n</mi> <mn>1</mn> </msubsup> <msubsup> <mi>t</mi> <mi>n</mi> <mi>a</mi> </msubsup> <mo>-</mo> <msubsup> <mi>a</mi> <mi>n</mi> <mn>2</mn> </msubsup> <mrow> <mo>(</mo> <mi>t</mi> <mo>-</mo> <msubsup> <mi>t</mi> <mi>in</mi> <mn>2</mn> </msubsup> <mrow> <mo>(</mo> <mi>X</mi> <mo>)</mo> </mrow> <mo>)</mo> </mrow> <mo>,</mo> </mtd> <mtd> <mi>if</mi> <msubsup> <mi>t</mi> <mi>in</mi> <mn>2</mn> </msubsup> <mrow> <mo>(</mo> <mi>X</mi> <mo>)</mo> </mrow> <mo>&le;</mo> <mi>t</mi> <mo>&lt;</mo> <msubsup> <mi>t</mi> <mi>in</mi> <mn>3</mn> </msubsup> <mrow> <mo>(</mo> <mi>X</mi> <mo>)</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <msubsup> <mi>a</mi> <mi>n</mi> <mn>1</mn> </msubsup> <msubsup> <mi>t</mi> <mi>n</mi> <mi>a</mi> </msubsup> <mo>-</mo> <msubsup> <mi>a</mi> <mi>n</mi> <mn>2</mn> </msubsup> <msubsup> <mi>t</mi> <mi>n</mi> <mi>c</mi> </msubsup> <mo>-</mo> <mrow> <mo>(</mo> <mi>t</mi> <mo>-</mo> <msubsup> <mi>t</mi> <mi>in</mi> <mn>3</mn> </msubsup> <mrow> <mo>(</mo> <mi>X</mi> <mo>)</mo> </mrow> <mo>)</mo> </mrow> <mo>,</mo> </mtd> <mtd> <mi>if</mi> <msubsup> <mi>t</mi> <mi>in</mi> <mn>3</mn> </msubsup> <mrow> <mo>(</mo> <mi>X</mi> <mo>)</mo> </mrow> <mo>&le;</mo> <mi>t</mi> <mo>&lt;</mo> <msubsup> <mi>t</mi> <mi>in</mi> <mn>4</mn> </msubsup> <mrow> <mo>(</mo> <mi>X</mi> <mo>)</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> <mo>,</mo> </mtd> <mtd> <mi>if</mi> <msubsup> <mi>t</mi> <mi>in</mi> <mn>4</mn> </msubsup> <mrow> <mo>(</mo> <mi>X</mi> <mo>)</mo> </mrow> <mo>&le;</mo> <mi>t</mi> <mo>&lt;</mo> <msubsup> <mi>t</mi> <mrow> <mi>i</mi> <mrow> <mo>(</mo> <mi>n</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow> <mn>1</mn> </msubsup> <mrow> <mo>(</mo> <mi>X</mi> <mo>)</mo> </mrow> </mtd> </mtr> </mtable> </mfenced> </mrow> </math>

wherein,representing the traction acceleration of the train between the nth stations,representing the coasting acceleration of the train between the nth stations,representing the braking acceleration of the train between the nth stations;

step 105, calculating the energy required by the traction of the train i at the moment t:

<math> <mrow> <msub> <mi>f</mi> <mi>in</mi> </msub> <mrow> <mo>(</mo> <mi>X</mi> <mo>,</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>=</mo> <mi>m</mi> <mrow> <mo>(</mo> <msubsup> <mi>v</mi> <mi>in</mi> <mn>2</mn> </msubsup> <mrow> <mo>(</mo> <mi>X</mi> <mo>,</mo> <mi>t</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>-</mo> <msubsup> <mi>v</mi> <mi>in</mi> <mn>2</mn> </msubsup> <mrow> <mo>(</mo> <mi>X</mi> <mo>,</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>)</mo> </mrow> <mo>/</mo> <msub> <mrow> <mn>2</mn> <mi>&eta;</mi> </mrow> <mn>1</mn> </msub> </mrow> </math>

wherein eta is₁The traction efficiency of the train motor, namely the proportion of converting electric energy into train kinetic energy, is shown, m is the train mass,indicates that the train i +1 is at the time tThe speed between the n-th station is,representing the speed of the train i +1 between the nth stations at the time t;

step 106, calculating the regenerative energy generated by braking the train i at the moment t:

<math> <mrow> <msub> <mi>g</mi> <mi>in</mi> </msub> <mrow> <mo>(</mo> <mi>X</mi> <mo>,</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>=</mo> <mi>m</mi> <mrow> <mo>(</mo> <msubsup> <mi>v</mi> <mi>in</mi> <mn>2</mn> </msubsup> <mrow> <mo>(</mo> <mi>X</mi> <mo>,</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>-</mo> <msubsup> <mi>v</mi> <mi>in</mi> <mn>2</mn> </msubsup> <mrow> <mo>(</mo> <mi>X</mi> <mo>,</mo> <mi>t</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>)</mo> </mrow> <msub> <mi>&eta;</mi> <mn>2</mn> </msub> <mrow> <mo>(</mo> <mn>1</mn> <mo>-</mo> <mi>&beta;</mi> <mo>)</mo> </mrow> <mo>/</mo> <mn>2</mn> </mrow> </math>

wherein eta is₂The conversion efficiency, namely the ratio of the kinetic energy of the train to the regenerated electric energy is expressed, beta represents the transmission loss of the regenerated energy on a contact net (or a third rail),representing the speed of train i +1 between the nth stations at time t,representing the speed of the train i +1 between the nth stations at the time t;

step 107: calculating the regenerated energy utilized in the whole running process of the I train:

<math> <mrow> <mi>F</mi> <mrow> <mo>(</mo> <mi>X</mi> <mo>)</mo> </mrow> <mo>=</mo> <munderover> <mi>&Sigma;</mi> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow> <mi>I</mi> <mo>-</mo> <mn>1</mn> </mrow> </munderover> <munderover> <mi>&Sigma;</mi> <mrow> <mi>n</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow> <mi>N</mi> <mo>-</mo> <mn>1</mn> </mrow> </munderover> <munder> <mi>&Sigma;</mi> <mrow> <mi>t</mi> <mo>&Element;</mo> <msub> <mi>T</mi> <mi>in</mi> </msub> </mrow> </munder> <mi>min</mi> <mo>{</mo> <msub> <mi>f</mi> <mi>in</mi> </msub> <mrow> <mo>(</mo> <mi>X</mi> <mo>,</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>,</mo> <msub> <mi>g</mi> <mrow> <mrow> <mo>(</mo> <mi>i</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> <mrow> <mo>(</mo> <mi>n</mi> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow> </msub> <mrow> <mo>(</mo> <mi>X</mi> <mo>,</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>}</mo> </mrow> </math>

wherein, T_inIndicating the coincidence time of traction of the train I between the nth stations and braking of the train I +1 between the nth-1 stations, wherein I indicates the total number of trains, and g_(i+1)(n-1)(X, t) regenerative energy generated by braking between the (n-1) th stations at time t of the train i + 1.

Fig. 3 shows a situation of matching the energies of two adjacent trains i and i + 1. In the figure, the area of the solid line trapezoidal region represents the energy required for train traction, the area of the dashed line trapezoidal region represents the regenerative energy generated by train braking, and the gray overlapping region represents the portion of the regenerative energy utilized by the traction train generated by braking the train. And (4) solving an expression of the regenerative energy utilized by the drawn train, and establishing an energy-saving operation diagram optimization model of the urban rail transit train by taking the expression as a target.

The optimization model of the train operation diagram is as follows:

<math> <mfenced open='{' close='' separators=''> <mtable> <mtr> <mtd> <mi>max</mi> <mi>F</mi> <mrow> <mo>(</mo> <mi>X</mi> <mo>)</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mi>s</mi> <mo>.</mo> <mi>t</mi> <mo>.</mo> <msub> <mi>l</mi> <mi>h</mi> </msub> <mo>&le;</mo> <mi>h</mi> <mo>&le;</mo> <msub> <mi>u</mi> <mi>h</mi> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>l</mi> <mi>T</mi> </msub> <mo>&le;</mo> <munderover> <mi>&Sigma;</mi> <mrow> <mi>n</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow> <mi>N</mi> <mo>-</mo> <mn>1</mn> </mrow> </munderover> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mi>n</mi> </msub> <mo>+</mo> <msub> <mi>t</mi> <mi>n</mi> </msub> <mo>)</mo> </mrow> <mo>&le;</mo> <msub> <mi>u</mi> <mi>T</mi> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>l</mi> <mi>n</mi> </msub> <mo>&le;</mo> <msub> <mi>x</mi> <mi>n</mi> </msub> <mo>&le;</mo> <msub> <mi>u</mi> <mi>n</mi> </msub> <mo>,</mo> <mi>n</mi> <mo>=</mo> <mn>1,2</mn> <mo>.</mo> <mo>.</mo> <mo>.</mo> <mo>,</mo> <mi>N</mi> <mo>-</mo> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <mi>h</mi> <mo>,</mo> <msub> <mi>x</mi> <mi>n</mi> </msub> <mo>&Element;</mo> <mi>Z</mi> <mo>,</mo> <mi>n</mi> <mo>=</mo> <mn>1,2</mn> <mo>,</mo> <mo>.</mo> <mo>.</mo> <mo>.</mo> <mo>,</mo> <mi>N</mi> <mo>-</mo> <mn>1</mn> <mo>.</mo> </mtd> </mtr> </mtable> </mfenced> </math>

wherein F (X) is the regenerated energy utilized in the whole running process of the I train, h is the departure interval of the train, [ l [ ]_h,u_h]Representing the train departure interval constraint window, x_nFor the stop time of the train at the nth station, t_nFor the total running time of the train between the nth stations, [ l_T,u_T]Represents the total travel time constraint window, [ l_n,u_n]Representing a stop time constraint window, h and x, for a train at station n_nAll belong to integers, N is the serial number of the station, N is the total number of the station, and T is the total travel time.

The above algorithm can be implemented by using some common computer languages, such as C # language, C + + language and Matlab language. And finally, solving the optimization model by adopting a genetic algorithm to obtain an energy-saving schedule of the running of the urban rail transit train.

In this embodiment, fig. 4 describes the physical meanings of some parameters, and it is assumed that the values of the parameters are as follows: i20, m 287080kg, $a_n^1=0.8m/s2,$ $a_n^2=0.02m/s^2,$ $a_n^{3}1m/s^2,$ η₁＝0.7，η₂＝0.8，β＝0.05，l_h＝90s，l_n＝360s，l_T＝1850s，u_T＝1890s。

the method comprises the following steps:

step 1, determining that the time when a first vehicle stops at a first station is 0 time;

step 2, calculating the time when the train i leaves the station n;

step 3, calculating the time when the train i finishes the traction and the coasting among the nth stations, the time when the coasting among the nth stations finishes the braking and the time when the braking among the nth stations finishes and reaches the station n + 1:

step 4, calculating a speed-time curve of the train i between the nth stations;

step 5, calculating the energy required by the traction of the train i:

step 6, calculating the regenerative energy generated by braking the train i;

step 7, calculating the regeneration energy utilized by all trains on the whole line;

step 8, establishing an optimization model of train operation;

and 9, designing an algorithm solving model.

The energy-saving schedule of train operation is obtained as shown in the table I:

TABLE I energy-saving timetable for train operation obtained according to the method provided by the invention

The above description is only for the preferred embodiment of the present invention, but the scope of the present invention is not limited thereto, and any changes or substitutions that can be easily conceived by those skilled in the art within the technical scope of the present invention are included in the scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the claims.

Claims (3)

1. An energy-saving method for running of an urban rail transit train is characterized by comprising the following steps:

step 1, analyzing the operation matching rules of adjacent trains, and calculating the magnitude of the utilized regenerative energy;

step 2, establishing an optimization model of train operation by taking the utilized regenerative energy as a target;

and 3, solving the optimization model to obtain an energy-saving schedule of the running of the urban rail transit train.

2. The method of claim 1, wherein the step 1 of calculating the amount of the utilized regenerative energy mainly comprises:

step 101, determining that the time when a first vehicle stops at a first station is 0 time;

step 102, calculating the time when the train i leaves the station n:

<math> <mrow> <msubsup> <mi>t</mi> <mi>in</mi> <mn>1</mn> </msubsup> <mrow> <mo>(</mo> <mi>X</mi> <mo>)</mo> </mrow> <mo>=</mo> <munderover> <mi>&Sigma;</mi> <mrow> <mi>k</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>n</mi> </munderover> <msub> <mi>x</mi> <mi>k</mi> </msub> <mo>+</mo> <munderover> <mi>&Sigma;</mi> <mrow> <mi>k</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow> <mi>n</mi> <mo>-</mo> <mn>1</mn> </mrow> </munderover> <msub> <mi>t</mi> <mi>k</mi> </msub> <mo>+</mo> <mrow> <mo>(</mo> <mi>i</mi> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> <mi>h</mi> <mo>;</mo> </mrow> </math>

wherein X is { h, X ═ h_nN1, 2, N-1 represents a set of these decision variables, N, k represents a station, x represents a station, and_nstopping time of the train at the nth station, wherein N represents the total number of stations on the line, i represents the train, h represents the departure interval of the train, and x_kIndicating the stop time of the train at each station k,indicating the moment at which the train leaves the station n and starts to pull, t_kRepresenting the running time of the train between the nth stations;

step 103, calculating the time when the train i finishes the traction and the coasting among the nth stations, the time when the train i finishes the coasting and the braking among the nth stations and the time when the train i finishes the braking and reaches the station n +1 among the nth stations:

$\left\{\begin{array}{c}{t}_{\mathrm{in}}^2\left(X\right)=t_{\mathrm{in}}^1\left(X\right)+t_n^a\\ t_{\mathrm{in}}^3\left(X\right)=t_{\mathrm{in}}^2\left(X\right)+t_n^c\\ t_{\mathrm{in}}^4\left(X\right)=t_{\mathrm{in}}^3\left(X\right)+t_n^b\end{array}\right.$

wherein,indicating the moment when the train leaves the station n to start traction,indicating the moment when the train starts to coast after the traction between the nth stations is completed,indicating the moment when the train completes starting braking while coasting between the nth stations,indicating the time when the braking of the train is completed between the nth stations and reaches the station n +1,representing the traction time of the train between the nth stations,indicating the braking time of the train between the nth stations,representing the coasting time of the train between the nth stations, wherein X represents a set of decision variables;

step 104, calculating a speed-time curve of the train i between the nth stations:

<math> <mrow> <msub> <mi>v</mi> <mi>in</mi> </msub> <mrow> <mo>(</mo> <mi>X</mi> <mo>,</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfenced open='{' close=''> <mtable> <mtr> <mtd> <msubsup> <mi>a</mi> <mi>n</mi> <mn>1</mn> </msubsup> <mrow> <mrow> <mo>(</mo> <mi>t</mi> <mo>-</mo> <msubsup> <mi>t</mi> <mi>in</mi> <mn>1</mn> </msubsup> <mrow> <mo>(</mo> <mi>X</mi> <mo>)</mo> </mrow> <mo>)</mo> </mrow> <mo>,</mo> </mrow> </mtd> <mtd> <mi>if</mi> <msubsup> <mi>t</mi> <mi>in</mi> <mn>1</mn> </msubsup> <mrow> <mo>(</mo> <mi>X</mi> <mo>)</mo> </mrow> <mo>&le;</mo> <mi>t</mi> <mo>&lt;</mo> <msubsup> <mi>t</mi> <mi>in</mi> <mn>2</mn> </msubsup> <mrow> <mo>(</mo> <mi>X</mi> <mo>)</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <msubsup> <mi>a</mi> <mi>n</mi> <mn>1</mn> </msubsup> <msubsup> <mi>t</mi> <mi>n</mi> <mi>a</mi> </msubsup> <mo>-</mo> <msubsup> <mi>a</mi> <mi>n</mi> <mn>2</mn> </msubsup> <mrow> <mo>(</mo> <mi>t</mi> <mo>-</mo> <msubsup> <mi>t</mi> <mi>in</mi> <mn>2</mn> </msubsup> <mrow> <mo>(</mo> <mi>X</mi> <mo>)</mo> </mrow> <mo>)</mo> </mrow> <mo>,</mo> </mtd> <mtd> <mi>if</mi> <msubsup> <mi>t</mi> <mi>in</mi> <mn>2</mn> </msubsup> <mrow> <mo>(</mo> <mi>X</mi> <mo>)</mo> </mrow> <mo>&le;</mo> <mi>t</mi> <mo>&lt;</mo> <msubsup> <mi>t</mi> <mi>in</mi> <mn>3</mn> </msubsup> <mrow> <mo>(</mo> <mi>X</mi> <mo>)</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <msubsup> <mi>a</mi> <mi>n</mi> <mn>1</mn> </msubsup> <msubsup> <mi>t</mi> <mi>n</mi> <mi>a</mi> </msubsup> <mo>-</mo> <msubsup> <mi>a</mi> <mi>n</mi> <mn>2</mn> </msubsup> <msubsup> <mi>t</mi> <mi>n</mi> <mi>c</mi> </msubsup> <mo>-</mo> <mrow> <mo>(</mo> <mi>t</mi> <mo>-</mo> <msubsup> <mi>t</mi> <mi>in</mi> <mn>3</mn> </msubsup> <mrow> <mo>(</mo> <mi>X</mi> <mo>)</mo> </mrow> <mo>)</mo> </mrow> <mo>,</mo> </mtd> <mtd> <mi>if</mi> <msubsup> <mi>t</mi> <mi>in</mi> <mn>3</mn> </msubsup> <mrow> <mo>(</mo> <mi>X</mi> <mo>)</mo> </mrow> <mo>&le;</mo> <mi>t</mi> <mo>&lt;</mo> <msubsup> <mi>t</mi> <mi>in</mi> <mn>4</mn> </msubsup> <mrow> <mo>(</mo> <mi>X</mi> <mo>)</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> <mo>,</mo> </mtd> <mtd> <mi>if</mi> <msubsup> <mi>t</mi> <mi>in</mi> <mn>4</mn> </msubsup> <mrow> <mo>(</mo> <mi>X</mi> <mo>)</mo> </mrow> <mo>&le;</mo> <mi>t</mi> <mo>&lt;</mo> <msubsup> <mi>t</mi> <mrow> <mi>i</mi> <mrow> <mo>(</mo> <mi>n</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow> <mn>1</mn> </msubsup> <mrow> <mo>(</mo> <mi>X</mi> <mo>)</mo> </mrow> </mtd> </mtr> </mtable> </mfenced> </mrow> </math>

wherein,representing the traction acceleration of the train between the nth stations,representing the coasting acceleration of the train between the nth stations,representing the braking acceleration of the train between the nth stations,indicating train is at the n-thThe traction time between the stations is determined,represents the coasting time of the train between the nth stations, t represents the train i running time,indicating the moment when the train leaves the station n to start traction,indicating the moment when the train starts to coast after the traction between the nth stations is completed,indicating the moment when the train completes starting braking while coasting between the nth stations,indicating the time when the braking of the train is completed between the nth stations and reaches the station n +1,representing the moment when the train leaves the station n +1 and starts to pull, and X represents a set of decision variables;

step 105, calculating the energy required by the traction of the train i at the moment t:

<math> <mrow> <msub> <mi>f</mi> <mi>in</mi> </msub> <mrow> <mo>(</mo> <mi>X</mi> <mo>,</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>=</mo> <mi>m</mi> <mrow> <mo>(</mo> <msubsup> <mi>v</mi> <mi>in</mi> <mn>2</mn> </msubsup> <mrow> <mo>(</mo> <mi>X</mi> <mo>,</mo> <mi>t</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>-</mo> <msubsup> <mi>v</mi> <mi>in</mi> <mn>2</mn> </msubsup> <mrow> <mo>(</mo> <mi>X</mi> <mo>,</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>)</mo> </mrow> <mo>/</mo> <msub> <mrow> <mn>2</mn> <mi>&eta;</mi> </mrow> <mn>1</mn> </msub> </mrow> </math>

wherein eta is₁The traction efficiency of the train motor, namely the proportion of converting electric energy into train kinetic energy, is shown, m is the train mass,representing the speed of train i +1 between the nth stations at time t,representing the speed of the train i +1 between nth stations at the time t, wherein X represents a set of decision variables;

step 106, calculating the regenerative energy generated by braking the train i at the moment t:

<math> <mrow> <msub> <mi>g</mi> <mi>in</mi> </msub> <mrow> <mo>(</mo> <mi>X</mi> <mo>,</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>=</mo> <mi>m</mi> <mrow> <mo>(</mo> <msubsup> <mi>v</mi> <mi>in</mi> <mn>2</mn> </msubsup> <mrow> <mo>(</mo> <mi>X</mi> <mo>,</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>-</mo> <msubsup> <mi>v</mi> <mi>in</mi> <mn>2</mn> </msubsup> <mrow> <mo>(</mo> <mi>X</mi> <mo>,</mo> <mi>t</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>)</mo> </mrow> <msub> <mi>&eta;</mi> <mn>2</mn> </msub> <mrow> <mo>(</mo> <mn>1</mn> <mo>-</mo> <mi>&beta;</mi> <mo>)</mo> </mrow> <mo>/</mo> <mn>2</mn> </mrow> </math>

wherein eta is₂The conversion efficiency is expressed, namely the ratio of the kinetic energy of the train to the regenerated electric energy, beta represents the transmission loss of the regenerated energy on a contact net or a third rail,representing the speed of train i +1 between the nth stations at time t,representing the speed of the train i +1 between the nth stations at the time t;

step 107: calculating the regenerated energy utilized in the whole running process of the I train:

<math> <mrow> <mi>F</mi> <mrow> <mo>(</mo> <mi>X</mi> <mo>)</mo> </mrow> <mo>=</mo> <munderover> <mi>&Sigma;</mi> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow> <mi>I</mi> <mo>-</mo> <mn>1</mn> </mrow> </munderover> <munderover> <mi>&Sigma;</mi> <mrow> <mi>n</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow> <mi>N</mi> <mo>-</mo> <mn>1</mn> </mrow> </munderover> <munder> <mi>&Sigma;</mi> <mrow> <mi>t</mi> <mo>&Element;</mo> <msub> <mi>T</mi> <mi>in</mi> </msub> </mrow> </munder> <mi>min</mi> <mo>{</mo> <msub> <mi>f</mi> <mi>in</mi> </msub> <mrow> <mo>(</mo> <mi>X</mi> <mo>,</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>,</mo> <msub> <mi>g</mi> <mrow> <mrow> <mo>(</mo> <mi>i</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> <mrow> <mo>(</mo> <mi>n</mi> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow> </msub> <mrow> <mo>(</mo> <mi>X</mi> <mo>,</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>}</mo> </mrow> </math>

wherein, T_inIndicating the coincidence time of traction of a train I between the nth stations and braking of a train I +1 between the nth-1 stations, wherein I indicates the total number of trains, N indicates the total number of stations on a line, and g_(i+1)(n-1)(X, t) regenerative energy generated by braking of train i +1 between the (n-1) th stations at time t, f_in(X, t) represents the energy required for the train i to pull at time t.

3. The method according to claim 1, wherein the optimization model of the train operation in the step 2 is as follows:

<math> <mfenced open='{' close='' separators=''> <mtable> <mtr> <mtd> <mi>max</mi> <mi>F</mi> <mrow> <mo>(</mo> <mi>X</mi> <mo>)</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mi>s</mi> <mo>.</mo> <mi>t</mi> <mo>.</mo> <msub> <mi>l</mi> <mi>h</mi> </msub> <mo>&le;</mo> <mi>h</mi> <mo>&le;</mo> <msub> <mi>u</mi> <mi>h</mi> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>l</mi> <mi>T</mi> </msub> <mo>&le;</mo> <munderover> <mi>&Sigma;</mi> <mrow> <mi>n</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow> <mi>N</mi> <mo>-</mo> <mn>1</mn> </mrow> </munderover> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mi>n</mi> </msub> <mo>+</mo> <msub> <mi>t</mi> <mi>n</mi> </msub> <mo>)</mo> </mrow> <mo>&le;</mo> <msub> <mi>u</mi> <mi>T</mi> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>l</mi> <mi>n</mi> </msub> <mo>&le;</mo> <msub> <mi>x</mi> <mi>n</mi> </msub> <mo>&le;</mo> <msub> <mi>u</mi> <mi>n</mi> </msub> <mo>,</mo> <mi>n</mi> <mo>=</mo> <mn>1,2</mn> <mo>.</mo> <mo>.</mo> <mo>.</mo> <mo>,</mo> <mi>N</mi> <mo>-</mo> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <mi>h</mi> <mo>,</mo> <msub> <mi>x</mi> <mi>n</mi> </msub> <mo>&Element;</mo> <mi>Z</mi> <mo>,</mo> <mi>n</mi> <mo>=</mo> <mn>1,2</mn> <mo>,</mo> <mo>.</mo> <mo>.</mo> <mo>.</mo> <mo>,</mo> <mi>N</mi> <mo>-</mo> <mn>1</mn> <mo>.</mo> </mtd> </mtr> </mtable> </mfenced> </math>

wherein F (X) is the regenerated energy utilized in the whole running process of the I train, h is the departure interval of the train, [ l [ ]_h,u_h]Representing the train departure interval constraint window, x_nFor the stop time of the train at the nth station, t_nFor the total running time of the train between the nth stations, [ l_T,u_T]Represents the total travel time constraint window, [ l_n,u_n]Representing a stop time constraint window, h and x, for a train at station n_nAll belong to integers, N is the serial number of the station, N is the total number of the station, and T is the total travel time.