CN103963805A

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

Info

Publication number: CN103963805A
Application number: CN201410172427.XA
Authority: CN
Inventors: 宁滨; 杨欣; 唐涛; 步兵
Original assignee: Beijing Jiaotong University
Current assignee: Beijing Jiaotong University
Priority date: 2014-04-25
Filing date: 2014-04-25
Publication date: 2014-08-06

Abstract

The invention belongs to the technical field of urban rail transit, and in particular relates to an energy-saving method for the operation of urban rail transit trains, comprising: 1. analyzing the operation matching rules of adjacent trains, and calculating the amount of regenerative energy used; 3. Solve the optimization model to obtain the energy-saving timetable of urban rail transit train operation. The present invention realizes the reduction of train operation energy consumption and the improvement of catenary safety, and has the following advantages: (1) adopts the method of integer programming, and the running speed is fast, so it is suitable for large-scale computer simulation; (2) the method considers The accuracy of comprehensive modeling of factors is high, and the applicability of the developed operating schedule is strong; (3) It can be embedded offline in the hardware of the train energy-saving driving assistance system, which is easy to implement, low in cost, and wide in application.

Description

Energy-saving method for urban rail transit train operation

技术领域technical field

本发明属于城市轨道交通技术领域，尤其是涉及一种城市轨道交通列车运行的节能方法。The invention belongs to the technical field of urban rail transit, and in particular relates to an energy-saving method for running an urban rail transit train.

背景技术Background technique

伴随着城市轨道交通运输事业的迅猛发展，我国目前已经有北京、上海、广州等多个城市开通了轨道交通线路，运营里程达1970公里。“十二五”期间，我国还将有19个城市新建轨道交通线路1800多公里，总投资超过一万亿元。城市轨道交通作为城市公共交通的主干线、客流运送的大动脉，是解决城市交通拥堵的治本之策。然而，城市轨道交通的能耗也是非常巨大的。以北京市为例，年均牵引用电总量超过3亿度。因此，在全球大力发展低碳经济的时代背景下，城市轨道交通节能技术的研究无疑具有重要的现实意义。做好节能减排工作、提高能源使用效率，十分必要并且形势紧迫。With the rapid development of urban rail transportation, Beijing, Shanghai, Guangzhou and other cities in my country have opened rail transit lines, with an operating mileage of 1,970 kilometers. During the "Twelfth Five-Year Plan" period, there will be more than 1,800 kilometers of new rail transit lines in 19 cities in my country, with a total investment of more than one trillion yuan. As the main line of urban public transportation and the main artery of passenger flow, urban rail transit is the fundamental solution to urban traffic congestion. However, the energy consumption of urban rail transit is also very huge. Taking Beijing as an example, the total annual traction electricity consumption exceeds 300 million kWh. Therefore, under the background of the global development of low-carbon economy, the research on energy-saving technology of urban rail transit undoubtedly has important practical significance. It is very necessary and urgent to do a good job in energy conservation and emission reduction, and to improve energy efficiency.

再生制动是一种使用在电气化铁路列车上的制动技术，在制动时把电动机转换成发电机模式，将列车的动能转换成电能加以利用。通常来讲，制动列车产生的再生能量除一小部分被自身的车载辅助设备利用外，大部分反馈到接触网(或第三轨)上，被同一供电区间内的相邻列车牵引使用。反馈到接触网的这部分能量，若不能及时被其他列车牵引使用，就会被线路上的发热电阻发热消耗掉，以防止接触网电压过高带来危险。再生制动已在国内外城市轨道交通列车上得到了广泛应用，例如，伦敦地铁、马德里地铁、纽约地铁、北京地铁(机场线、15号线、昌平线、亦庄线、房山线)等均采用再生制动+空气制动的制动方式。Regenerative braking is a braking technology used on electrified railway trains. During braking, the electric motor is converted into a generator mode, and the kinetic energy of the train is converted into electrical energy for use. Generally speaking, except a small part of the regenerative energy generated by the braking train is utilized by its own on-board auxiliary equipment, most of the regenerative energy is fed back to the catenary (or the third rail) and used by adjacent trains in the same power supply section. If this part of the energy fed back to the catenary cannot be pulled and used by other trains in time, it will be consumed by the heating resistor on the line to prevent the danger caused by the excessive voltage of the catenary. Regenerative braking has been widely used in urban rail transit trains at home and abroad, for example, London Metro, Madrid Metro, New York Metro, Beijing Metro (Airport Line, Line 15, Changping Line, Yizhuang Line, Fangshan Line) etc. The braking method of regenerative braking + air braking.

目前，城市轨道交通列车运行时，主要考虑准时性、运行效率、平均旅行速度等指标，没有考虑到减少列车运行能量的消耗，以及再生制动时接触网电压过高所带来的危险。At present, when urban rail transit trains are running, they mainly consider indicators such as punctuality, operating efficiency, and average travel speed, without considering the reduction of energy consumption in train operation and the danger of excessive catenary voltage during regenerative braking.

发明内容Contents of the invention

本发明的目的在于，针对目前城市轨道交通列车运行能耗高和接触网安全性的问题，提出一种城市轨道交通列车运行的节能方法，其特征在于，包括以下步骤：The object of the present invention is to, aim at the problem that current urban rail transit train operation energy consumption height and catenary safety, propose a kind of energy-saving method of urban rail transit train operation, it is characterized in that, comprises the following steps:

步骤1、分析相邻列车的运行匹配规则，计算利用的再生能量的大小；Step 1, analyze the operation matching rules of adjacent trains, and calculate the size of the regenerative energy utilized;

步骤2、以利用的再生能量为目标，建立列车运行的优化模型；Step 2, with the utilization of regenerative energy as the target, an optimization model for train operation is established;

步骤3、求解优化模型，得到城市轨道交通列车运行的节能时刻表。Step 3. Solve the optimization model to obtain the energy-saving timetable for urban rail transit train operation.

所述步骤1中计算利用的再生能量的大小主要包括：The size of the regenerative energy calculated and utilized in the step 1 mainly includes:

步骤101、确定第一辆车停在第一站的时刻为0时刻；Step 101, determine that the time when the first vehicle stops at the first stop is time 0;

步骤102、计算列车i离开车站n的时刻：Step 102, calculate the moment when train i leaves station n:

${t t}_{in in}^{11} ((X x)) = = {Σ Σ}_{k k = = 11}^{n no} {x x}_{k k} + + {Σ Σ}_{k k = = 11}^{n no - - 11} {t t}_{k k} + + ((i i - - 11)) h h;;$

其中，X＝{h,x_n,n＝1,2,......,N-1}代表这些决策变量的集合，n、k表示车站，x_n为列车在第n个车站停车时间，N表示线路上的车站总数，i表示列车，h表示列车发车间隔，x_k表示列车在各个车站k的停站时间，表示列车离开车站n开始牵引的时刻，t_k表示列车在第n个站间的运行时间；Among them, X={h,x _n ,n=1,2,...,N-1} represents the set of these decision variables, n and k represent stations, and x _n represents the train stopping at the nth station Time, N represents the total number of stations on the line, i represents the train, h represents the train departure interval, x _k represents the stop time of the train at each station k, Indicates the moment when the train leaves station n and starts traction, and t _k indicates the running time of the train between stations n;

步骤103、计算列车i在第n个站间牵引完成开始惰行的时刻、在第n个站间惰行完成开始制动的时刻以及在第n个站间制动完成到达车站n+1的时刻：Step 103, calculate the moment when train i completes the traction between the n stations and starts to coast, the moment when it completes the coasting between the n stations and starts braking, and the moment when the braking between the n stations is completed and arrives at station n+1:

$\{\begin{matrix} {t t}_{in in}^{22} ((X x)) = = {t t}_{in in}^{11} ((X x)) + + {t t}_{n no}^{a a} \\ {t t}_{in in}^{33} ((X x)) = = {t t}_{in in}^{22} ((X x)) + + {t t}_{n no}^{c c} \\ {t t}_{in in}^{44} ((X x)) = = {t t}_{in in}^{33} ((X x)) + + {t t}_{n no}^{b b} \end{matrix}$

其中，表示列车离开车站n开始牵引的时刻，表示列车在第n个站间牵引完成开始惰行的时刻，表示列车在第n个站间惰行完成开始制动的时刻，表示列车在第n个站间制动完成到达车站n+1的时刻，表示列车在第n个站间的牵引时间，表示列车在第n个站间的制动时间，表示列车在第n个站间的惰行时间，X代表决策变量的集合；in, Indicates the moment when the train leaves station n and starts pulling, Indicates the moment when the train completes traction and starts to coast at the nth station, Indicates the moment when the train coasts and starts to brake at the nth station, Indicates the moment when the train completes braking between stations n and arrives at station n+1, Indicates the traction time of the train between the n stations, Indicates the braking time of the train between stations n, Indicates the idling time of the train between the n stations, and X represents the set of decision variables;

步骤104、计算列车i在第n个站间速度-时间曲线：Step 104, calculate the speed-time curve of train i at the nth station:

${v v}_{in in} ((X x,, t t)) = = \{\begin{matrix} {a a}_{n no}^{11} ((t t - - {t t}_{in in}^{11} ((X x)))),, & if if {t t}_{in in}^{11} ((X x)) \leq \leq t t < < {t t}_{in in}^{22} ((X x)) \\ {a a}_{n no}^{11} {t t}_{n no}^{a a} - - {a a}_{n no}^{22} ((t t - - {t t}_{in in}^{22} ((X x)))),, & if if {t t}_{in in}^{22} ((X x)) \leq \leq t t < < {t t}_{in in}^{33} ((X x)) \\ {a a}_{n no}^{11} {t t}_{n no}^{a a} - - {a a}_{n no}^{22} {t t}_{n no}^{c c} - - ((t t - - {t t}_{in in}^{33} ((X x)))),, & if if {t t}_{in in}^{33} ((X x)) \leq \leq t t < < {t t}_{in in}^{44} ((X x)) \\ 00,, & if if {t t}_{in in}^{44} ((X x)) \leq \leq t t < < {t t}_{i i ((n no + + 11))}^{11} ((X x)) \end{matrix}$

其中，表示列车在第n个站间的牵引加速度，表示列车在第n个站间的惰行加速度，表示列车在第n个站间的制动加速度,表示列车在第n个站间的牵引时间，表示列车在第n个站间的惰行时间，t表示列车i运行时间，表示列车离开车站n开始牵引的时刻，表示列车在第n个站间牵引完成开始惰行的时刻，表示列车在第n个站间惰行完成开始制动的时刻，表示列车在第n个站间制动完成到达车站n+1的时刻，表示列车离开车站n+1开始牵引的时刻，X代表决策变量的集合；in, Indicates the traction acceleration of the train between the n stations, Indicates the idling acceleration of the train between the n stations, Indicates the braking acceleration of the train between stations n, Indicates the traction time of the train between the n stations, Indicates the idling time of the train between stations n, t indicates the running time of train i, Indicates the moment when the train leaves station n and starts pulling, Indicates the moment when the train completes traction and starts to coast at the nth station, Indicates the moment when the train coasts and starts to brake at the nth station, Indicates the moment when the train brakes at the nth station and arrives at station n+1, Indicates the moment when the train leaves station n+1 and starts traction, X represents the set of decision variables;

步骤105、计算列车i在t时刻牵引所需的能量：Step 105, calculate the energy required for traction of train i at time t:

${f f}_{in in} ((X x,, t t)) = = m m (({v v}_{in in}^{22} ((X x,, t t + + 11)) - - {v v}_{in in}^{22} ((X x,, t t)))) / / {22 η η}_{11}$

其中，η₁表示列车电机的牵引效率，即电能转化成列车动能的比例，m为列车质量，表示列车i+1在t时刻在第n个站间的速度，表示列车i+1在t时刻在第n个站间的速度，X代表决策变量的集合；Wherein, η ₁ represents the traction efficiency of the train motor, i.e. the ratio of electric energy into train kinetic energy, m is the train quality, Indicates the speed of train i+1 between stations n at time t, Indicates the speed of train i+1 between stations n at time t, and X represents the set of decision variables;

步骤106、计算列车i在t时刻制动产生的再生能量：Step 106, calculate the regenerative energy generated by the braking of train i at time t:

${g g}_{in in} ((X x,, t t)) = = m m (({v v}_{in in}^{22} ((X x,, t t)) - - {v v}_{in in}^{22} ((X x,, t t + + 11)))) {η η}_{22} ((11 - - β β)) / / 22$

其中，η₂表示转化效率，即列车动能转化成再生电能的比例，β表示再生能量在接触网或第三轨上的传输损耗，表示列车i+1在t时刻在第n个站间的速度，表示列车i+1在t时刻在第n个站间的速度；Among them, _η2 represents the conversion efficiency, that is, the ratio of train kinetic energy converted into regenerative electric energy, and β represents the transmission loss of regenerative energy on the catenary or the third rail, Indicates the speed of train i+1 between stations n at time t, Indicates the speed of train i+1 between stations n at time t;

步骤107：计算I辆列车跑完全程利用的再生能量：Step 107: Calculating the regenerative energy utilized by the I train to run the full distance:

$F f ((X x)) = = {Σ Σ}_{i i = = 11}^{I I - - 11} {Σ Σ}_{n no = = 11}^{N N - - 11} \underset{t t &Element; &Element; {T T}_{in in}}{Σ Σ} min min {{{f f}_{in in} ((X x,, t t)),, {g g}_{((i i + + 11)) ((n no - - 11))} ((X x,, t t))}}$

其中，T_in表示列车i在第n个站间牵引和列车i+1在第n-1个站间制动的重合时间，I表示列车总数，N表示线路上的车站总数，g_(i+1)(n-1)(X,t)列车i+1在t时刻在第n-1个站间制动产生的再生能量，f_in(X,t)表示列车i在t时刻牵引所需的能量。Among them, T _in represents the coincidence time of train i traction between n stations and train i+1 braking between n-1 stations, I represents the total number of trains, N represents the total number of stations on the line, g _{(i+ 1) (n-1)} (X, t) The regenerative energy generated by the braking of train i+1 at the n-1st station at time t, f _in (X, t) represents the traction required by train i at time t energy of.

所述步骤2中列车运行的优化模型为：The optimization model of train operation in described step 2 is:

$\{\begin{matrix} max max F f ((X x)) \\ s the s . . t t . . {l l}_{h h} \leq \leq h h \leq \leq {u u}_{h h} \\ {l l}_{T T} \leq \leq {Σ Σ}_{n no = = 11}^{N N - - 11} (({x x}_{n no} + + {t t}_{n no})) \leq \leq {u u}_{T T} \\ {l l}_{n no} \leq \leq {x x}_{n no} \leq \leq {u u}_{n no},, n no = = 1,2 1,2 . . . . . .,, N N - - 11 \\ h h,, {x x}_{n no} &Element; &Element; Z Z,, n no = = 1,2 1,2,, . . . . . .,, N N - - 11 . . \end{matrix}$

其中,F(X)为I辆列车跑完全程利用的再生能量，h为列车发车间隔，[l_h,u_h]表示列车发车间隔约束窗口，x_n为列车在第n个车站停车时间，t_n为列车在第n个站间的总体运行时间，[l_T,u_T]表示总体旅行时间约束窗口，[l_n,u_n]表示列车在车站n的停站时间约束窗口，h和x_n均属于整数，n为车站序号，N为车站总数，T为总体旅行时间。Among them, F(X) is the regenerative energy used by one train running the whole journey, h is the train departure interval, [l _h ,u _h ] represents the constraint window of the train departure interval, x _n is the stop time of the train at the nth station, t _n is the overall running time of the train between stations n, [l _T ,u _T ] represents the overall travel time constraint window, [l _n , u _n ] represents the stop time constraint window of the train at station n, h and Both x and _n are integers, n is the serial number of the station, N is the total number of stations, and T is the overall travel time.

本发明的有益效果在于：本发明实现列车运行能耗的减少和接触网安全性的提高，并具有如下优点：(1)采用整数规划的方法，运行速度快，因而适合于大规模的计算机模拟；(2)该方法考虑因素全面建模精度较高，制定出的运行时刻表适用性较强；(3)可离线嵌入列车节能驾驶辅助系统硬件中，易实现，费用低，应用范围广。The beneficial effects of the present invention are: the present invention realizes the reduction of train running energy consumption and the improvement of catenary safety, and has the following advantages: (1) the method of integer programming is adopted, and the running speed is fast, so it is suitable for large-scale computer simulation ; (2) The method considers factors with high modeling accuracy, and the developed running timetable has strong applicability; (3) It can be embedded offline in the hardware of the train energy-saving driving assistance system, which is easy to implement, low in cost, and wide in application.

附图说明Description of drawings

图1为本发明列车节能运行方法的流程图；Fig. 1 is the flowchart of train energy-saving operation method of the present invention;

图2城市轨道交通供电系统网络结构示意图；Fig. 2 Schematic diagram of urban rail transit power supply system network structure;

图3列车间能量匹配示意图；Figure 3 is a schematic diagram of energy matching between trains;

图4列车运行过程示意图。Figure 4 is a schematic diagram of the train running process.

具体实施方式Detailed ways

下面结合附图，对优选实施例作详细说明。The preferred embodiments will be described in detail below in conjunction with the accompanying drawings.

本发明提出的一种城市轨道交通列车运行的节能方法，包括以下步骤：A kind of energy-saving method of urban rail transit train operation that the present invention proposes, comprises the following steps:

1、分析相邻列车的运行匹配规则，计算利用的再生能量的大小；1. Analyze the operation matching rules of adjacent trains, and calculate the amount of regenerative energy used;

2、以利用的再生能量为目标，建立列车运行的优化模型；2. Establish an optimization model for train operation with the aim of utilizing the regenerative energy;

3、求解优化模型，得到城市轨道交通列车运行的节能时刻表。3. Solve the optimization model to obtain the energy-saving timetable for urban rail transit train operation.

城市轨道交通列车运行中再生能量传递、转换过程中的损耗包括：The losses during the transfer and conversion of regenerative energy during the operation of urban rail transit trains include:

(a)制动列车再生制动时，将动能转化为电能过程中的损耗；(a) During the regenerative braking of the braking train, the loss in the process of converting kinetic energy into electrical energy;

(b)电能从制动列车经过电网传递到牵引列车，传递过程中的损耗；(b) Electric energy is transmitted from the braking train to the traction train through the power grid, and the loss during the transmission process;

(c)牵引列车将吸收的电能经过一系列的传动系统，转化成列车动能过程中的损耗。(c) Loss in the process of converting the electric energy absorbed by the traction train into train kinetic energy through a series of transmission systems.

本方法基于城市轨道交通供电系统网络结构，分析了再生能量在列车间的传送过程。如图2所示，列车i和列车i+1是位于同一供电区间内的两列车，列车i离开车站n处于牵引工况，需要吸收电能，列车i+1到达车站n处于制动工况，再生制动产生电能。此时，列车i+1产生的再生能量通过第三轨传送被列车i吸收利用。图中箭头表示能量的传送方向。通过合理调整列车i的离站时刻和列车i+1的到站时刻，可使得列车i+1的产生的再生能量被列车i利用的部分增加。基于城市轨道交通时刻表的周期性，通过合理调整全线列车的离站时刻和到站时刻，便可提高整条线路再生能量的利用率。Based on the network structure of urban rail transit power supply system, this method analyzes the transfer process of regenerative energy between trains. As shown in Figure 2, train i and train i+1 are two trains located in the same power supply interval. Train i leaves station n and is in traction condition and needs to absorb electric energy. Train i+1 arrives at station n and is in braking condition. Regenerative braking generates electrical energy. At this time, the regenerative energy generated by train i+1 is transmitted by the third rail and absorbed by train i. The arrows in the figure indicate the direction of energy transmission. By rationally adjusting the departure time of train i and the arrival time of train i+1, the part of the regenerative energy generated by train i+1 that is utilized by train i can be increased. Based on the periodicity of the urban rail transit timetable, the utilization rate of regenerative energy of the entire line can be improved by reasonably adjusting the departure time and arrival time of the trains on the whole line.

步骤1中计算利用的再生能量的大小的过程如图1所示，主要包括：The process of calculating the size of the regenerative energy used in step 1 is shown in Figure 1, mainly including:

其中，X＝{h,x_n,n＝1,2,......,N-1}代表这些决策变量的集合，n、k表示车站，N表示线路上的车站总数，i表示列车，h表示列车发车间隔，x_k表示列车在各个车站k的停站时间，表示列车离开车站n开始牵引的时刻，t_k表示列车在第n个站间的运行时间；Among them, X={h,x _n ,n=1,2,...,N-1} represents the set of these decision variables, n and k represent stations, N represents the total number of stations on the line, and i represents train, h represents the train departure interval, x _k represents the stop time of the train at each station k, Indicates the moment when the train leaves station n and starts traction, and t _k indicates the running time of the train between stations n;

步骤103、计算列车i在第n个站间牵引完成开始惰行的时刻、在第n个站间惰行完成开始制动的时刻以及在第n个站间制动完成到达车站n+1的时刻：Step 103, calculate the moment when the train i completes the traction between the n stations and starts to coast, the moment when it completes the coasting between the n stations and starts braking, and the moment when the braking between the n stations is completed and arrives at station n+1:

其中：表示列车在第n个站间牵引完成开始惰行的时刻，表示列车在第n个站间惰行完成开始制动的时刻，表示列车在第n个站间制动完成到达车站n+1的时刻，表示列车在第n个站间的牵引时间，表示列车在第n个站间的制动时间，表示列车在第n个站间的惰行时间；in: Indicates the moment when the train completes traction and starts to coast at the nth station, Indicates the moment when the train coasts and starts to brake at the nth station, Indicates the moment when the train brakes at the nth station and arrives at station n+1, Indicates the traction time of the train between the n stations, Indicates the braking time of the train between stations n, Indicates the idling time of the train between the n stations;

其中，表示列车在第n个站间的牵引加速度，表示列车在第n个站间的惰行加速度，表示列车在第n个站间的制动加速度；in, Indicates the traction acceleration of the train between the n stations, Indicates the idling acceleration of the train between the n stations, Indicates the braking acceleration of the train between the n stations;

其中，η₁表示列车电机的牵引效率，即电能转化成列车动能的比例，m为列车质量，表示列车i+1在t时刻在第n个站间的速度，表示列车i+1在t时刻在第n个站间的速度；Wherein, η ₁ represents the traction efficiency of the train motor, i.e. the ratio of electric energy into train kinetic energy, m is the train quality, Indicates the speed of train i+1 between stations n at time t, Indicates the speed of train i+1 between stations n at time t;

其中，η₂表示转化效率，即列车动能转化成再生电能的比例，β表示再生能量在接触网(或第三轨)上的传输损耗，表示列车i+1在t时刻在第n个站间的速度，表示列车i+1在t时刻在第n个站间的速度；Among them, _η2 represents conversion efficiency, that is, the ratio of train kinetic energy converted into regenerative electric energy, and β represents the transmission loss of regenerative energy on the catenary (or the third rail), Indicates the speed of train i+1 between stations n at time t, Indicates the speed of train i+1 between stations n at time t;

其中，T_in表示列车i在第n个站间牵引和列车i+1在第n-1个站间制动的重合时间，I表示列车总数，g_(i+1)(n-1)(X,t)列车i+1在t时刻在第n-1个站间制动产生的再生能量。Among them, T _in represents the coincidence time of train i traction between n stations and train i+1 braking between n-1 stations, I represents the total number of trains, g _(i+1)(n-1) ( X, t) The regenerative energy generated by the braking of train i+1 at the n-1th station at time t.

图3所示，描述了相邻的两列车i和i+1的能量的匹配情形。图中实线梯形区域的面积表示列车牵引所需要的能量，虚线梯形区域的面积表示列车制动产生的再生能量，灰色的重叠区域表示制动列车产生的被牵引列车所利用的那部分再生能量。求出被牵引列车所利用的再生能量的表达式，以此为目标建立城市轨道交通列车节能运行图优化模型。As shown in Fig. 3, it describes the energy matching situation of two adjacent trains i and i+1. The area of the solid-line trapezoidal area in the figure represents the energy required for train traction, the area of the dotted-line trapezoidal area represents the regenerative energy generated by train braking, and the gray overlapping area represents the regenerative energy generated by the braking train and used by the traction train . The expression of regenerative energy used by traction trains is obtained, and an optimization model of energy-saving operation diagrams for urban rail transit trains is established based on this goal.

列车运行图的优化模型为：The optimization model of the train diagram is:

以上算法，可以用一些常用的计算机语言去实现，例如，C#语言、C++语言以及Matlab语言。最后采用遗传算法求解优化模型，得到城市轨道交通列车运行的节能时刻表。The above algorithms can be implemented with some commonly used computer languages, for example, C# language, C++ language and Matlab language. Finally, the genetic algorithm is used to solve the optimization model, and the energy-saving timetable for urban rail transit train operation is obtained.

本实施例中，图4描述了部分参数的物理意义，假设各参数取值如下：I＝20，m＝287080kg， $a_{n}^{1} = 0.8 m / s 2,$ $a_{n}^{2} = 0.02 m / s^{2},$ $a_{n}^{3} 1 m / s^{2},$ η₁＝0.7，η₂＝0.8，β＝0.05，l_h＝90s，l_n＝360s，l_T＝1850s，u_T＝1890s。In the present embodiment, Fig. 4 has described the physical meaning of some parameters, assumes that each parameter takes a value as follows: I=20, m=287080kg, $a_{no}^{1} = 0.8 m / the s 2,$ $a_{no}^{2} = 0.02 m / {the s}^{2},$ $a_{no}^{3} 1 m / {the s}^{2},$ η ₁ =0.7, η ₂ =0.8, β=0.05, l _h =90s, l _n =360s, l _T =1850s, u _T =1890s.

按照如下步骤：Follow the steps below:

步骤1确定第一辆车停在第一站的时刻为0时刻；Step 1 determines that the moment when the first car stops at the first stop is time 0;

步骤2计算列车i离开车站n的时刻；Step 2 calculates the moment when train i leaves station n;

步骤3计算列车i在第n个站间牵引完成开始惰行的时刻、在第n个站间惰行完成开始制动的时刻以及在第n个站间制动完成到达车站n+1的时刻：Step 3 Calculate the moment when train i completes traction at the n-th station and starts to coast, the moment when it completes the coasting at the n-th station and starts braking, and the moment when the braking at the n-th station completes and arrives at station n+1:

步骤4计算列车i在第n个站间速度-时间曲线；Step 4 calculates the speed-time curve between train i at the nth station;

步骤5计算列车i牵引所需的能量：Step 5 Calculate the energy required for traction of train i:

步骤6计算列车i制动产生的再生能量；Step 6 calculates the regenerative energy generated by the braking of train i;

步骤7计算全线所有列车利用的再生能量；Step 7 calculates the regenerative energy utilized by all trains on the whole line;

步骤8建立列车运行的优化模型；Step 8 sets up the optimization model of train operation;

步骤9设计算法求解模型。Step 9 Design an algorithm to solve the model.

得到列车运行的节能时刻表如表一所示：The energy-saving timetable for train operation is obtained as shown in Table 1:

表一按照本发明提供的方法得到列车运行的节能时刻表Table one obtains the energy-saving schedule of train operation according to the method provided by the present invention

以上所述，仅为本发明较佳的具体实施方式，但本发明的保护范围并不局限于此，任何熟悉本技术领域的技术人员在本发明揭露的技术范围内，可轻易想到的变化或替换，都应涵盖在本发明的保护范围之内。因此，本发明的保护范围应该以权利要求的保护范围为准。The above is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any person skilled in the art can easily conceive of changes or modifications within the technical scope disclosed in the present invention. Replacement should be covered within the protection scope of the present invention. Therefore, the protection scope of the present invention should be determined by the protection scope of the claims.

Claims

1. an energy-saving method for urban rail transit train operation, is characterized in that, comprises the following steps:

Step 1, analyze the operation matching rules of adjacent trains, and calculate the size of the regenerative energy utilized;

Step 2, with the utilization of regenerative energy as the target, an optimization model for train operation is established;

Step 3. Solve the optimization model to obtain the energy-saving timetable for urban rail transit train operation.

2. according to the described method of claim 1, it is characterized in that, the magnitude of the regenerative energy that calculates utilization in described step 1 mainly comprises:

Step 101, determine that the time when the first vehicle stops at the first stop is time 0;

Step 102, calculate the moment when train i leaves station n:

{t t}_{in in}^{11} ((X x)) = = {Σ Σ}_{k k = = 11}^{n no} {x x}_{k k} + + {Σ Σ}_{k k = = 11}^{n no - - 11} {t t}_{k k} + + ((i i - - 11)) h h;;

Among them, X={h,x _n ,n=1,2,...,N-1} represents the set of these decision variables, n and k represent stations, and x _n represents the train stopping at the nth station Time, N represents the total number of stations on the line, i represents the train, h represents the train departure interval, x _k represents the stop time of the train at each station k, Indicates the moment when the train leaves station n and starts traction, and t _k indicates the running time of the train between stations n;

Step 103, calculate the moment when the train i completes the traction between the n stations and starts to coast, the moment when it completes the coasting between the n stations and starts braking, and the moment when the braking between the n stations is completed and arrives at station n+1:

\{\begin{matrix} {t t}_{in in}^{22} ((X x)) = = {t t}_{in in}^{11} ((X x)) + + {t t}_{n no}^{a a} \\ {t t}_{in in}^{33} ((X x)) = = {t t}_{in in}^{22} ((X x)) + + {t t}_{n no}^{c c} \\ {t t}_{in in}^{44} ((X x)) = = {t t}_{in in}^{33} ((X x)) + + {t t}_{n no}^{b b} \end{matrix}

in, Indicates the moment when the train leaves station n and starts pulling, Indicates the moment when the train completes traction and starts to coast at the nth station, Indicates the moment when the train coasts and starts to brake at the nth station, Indicates the moment when the train brakes at the nth station and arrives at station n+1, Indicates the traction time of the train between the n stations, Indicates the braking time of the train between stations n, Indicates the idling time of the train between the n stations, and X represents the set of decision variables;

Step 104, calculate the speed-time curve of train i at the nth station:

{v v}_{in in} ((X x,, t t)) = = \{\begin{matrix} {a a}_{n no}^{11} ((t t - - {t t}_{in in}^{11} ((X x)))),, & if if {t t}_{in in}^{11} ((X x)) \leq \leq t t < < {t t}_{in in}^{22} ((X x)) \\ {a a}_{n no}^{11} {t t}_{n no}^{a a} - - {a a}_{n no}^{22} ((t t - - {t t}_{in in}^{22} ((X x)))),, & if if {t t}_{in in}^{22} ((X x)) \leq \leq t t < < {t t}_{in in}^{33} ((X x)) \\ {a a}_{n no}^{11} {t t}_{n no}^{a a} - - {a a}_{n no}^{22} {t t}_{n no}^{c c} - - ((t t - - {t t}_{in in}^{33} ((X x)))),, & if if {t t}_{in in}^{33} ((X x)) \leq \leq t t < < {t t}_{in in}^{44} ((X x)) \\ 00,, & if if {t t}_{in in}^{44} ((X x)) \leq \leq t t < < {t t}_{i i ((n no + + 11))}^{11} ((X x)) \end{matrix}

in, Indicates the traction acceleration of the train between the n stations, Indicates the idling acceleration of the train between the n stations, Indicates the braking acceleration of the train between stations n, Indicates the traction time of the train between the n stations, Indicates the idling time of the train between stations n, t indicates the running time of train i, Indicates the moment when the train leaves station n and starts pulling, Indicates the moment when the train completes traction and starts to coast at the nth station, Indicates the moment when the train coasts and starts to brake at the nth station, Indicates the moment when the train brakes at the nth station and arrives at station n+1, Indicates the moment when the train leaves station n+1 and starts traction, X represents the set of decision variables;

Step 105, calculate the energy required for traction of train i at time t:

{f f}_{in in} ((X x,, t t)) = = m m (({v v}_{in in}^{22} ((X x,, t t + + 11)) - - {v v}_{in in}^{22} ((X x,, t t)))) / / {22 η η}_{11}

Wherein, η ₁ represents the traction efficiency of the train motor, i.e. the ratio of electric energy into train kinetic energy, m is the train quality, Indicates the speed of train i+1 between stations n at time t, Indicates the speed of train i+1 between stations n at time t, and X represents the set of decision variables;

Step 106, calculate the regenerative energy generated by the braking of train i at time t:

{g g}_{in in} ((X x,, t t)) = = m m (({v v}_{in in}^{22} ((X x,, t t)) - - {v v}_{in in}^{22} ((X x,, t t + + 11)))) {η η}_{22} ((11 - - β β)) / / 22

Among them, _η2 represents the conversion efficiency, that is, the ratio of train kinetic energy converted into regenerative electric energy, and β represents the transmission loss of regenerative energy on the catenary or the third rail, Indicates the speed of train i+1 between stations n at time t, Indicates the speed of train i+1 between stations n at time t;

Step 107: Calculating the regenerative energy utilized by the I train to run the full distance:

F f ((X x)) = = {Σ Σ}_{i i = = 11}^{I I - - 11} {Σ Σ}_{n no = = 11}^{N N - - 11} \underset{t t &Element; &Element; {T T}_{in in}}{Σ Σ} min min {{{f f}_{in in} ((X x,, t t)),, {g g}_{((i i + + 11)) ((n no - - 11))} ((X x,, t t))}}

Among them, T _in represents the coincidence time of train i traction between n stations and train i+1 braking between n-1 stations, I represents the total number of trains, N represents the total number of stations on the line, g _{(i+ 1) (n-1)} (X, t) The regenerative energy generated by the braking of train i+1 at the n-1st station at time t, f _in (X, t) represents the traction required by train i at time t energy of.

3. according to the described method of claim 1, it is characterized in that, the optimization model of train operation in the described step 2 is:

\{\begin{matrix} max max F f ((X x)) \\ s the s . . t t . . {l l}_{h h} \leq \leq h h \leq \leq {u u}_{h h} \\ {l l}_{T T} \leq \leq {Σ Σ}_{n no = = 11}^{N N - - 11} (({x x}_{n no} + + {t t}_{n no})) \leq \leq {u u}_{T T} \\ {l l}_{n no} \leq \leq {x x}_{n no} \leq \leq {u u}_{n no},, n no = = 1,2 1,2 . . . . . .,, N N - - 11 \\ h h,, {x x}_{n no} &Element; &Element; Z Z,, n no = = 1,2 1,2,, . . . . . .,, N N - - 11 . . \end{matrix}

Among them, F(X) is the regenerative energy used by one train running the whole journey, h is the train departure interval, [l _h ,u _h ] represents the constraint window of the train departure interval, x _n is the stop time of the train at the nth station, t _n is the overall running time of the train between stations n, [l _T ,u _T ] represents the overall travel time constraint window, [l _n , u _n ] represents the stop time constraint window of the train at station n, h and Both x and _n are integers, n is the serial number of the station, N is the total number of stations, and T is the overall travel time.