CN111460633A - Train energy-saving operation method based on multi-target particle swarm algorithm - Google Patents

Train energy-saving operation method based on multi-target particle swarm algorithm Download PDF

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CN111460633A
CN111460633A CN202010193898.4A CN202010193898A CN111460633A CN 111460633 A CN111460633 A CN 111460633A CN 202010193898 A CN202010193898 A CN 202010193898A CN 111460633 A CN111460633 A CN 111460633A
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张永
谢志鸿
左婷婷
刘自力
单梁
邢宗义
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Nanjing University of Science and Technology
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Abstract

The invention discloses a train energy-saving operation method based on a multi-target particle swarm algorithm. The method comprises the following steps: setting train operation environment parameters including line data, train data and operation data; establishing a train kinematics model and a traction energy consumption calculation method; establishing a train energy consumption multi-objective optimization model by taking traction energy consumption and running time as optimization objectives; solving the optimization model by adopting a multi-objective particle swarm algorithm to obtain a plurality of groups of non-inferior solutions of the traction energy consumption and the running time of the train in a single interval; calculating non-inferior solutions of the traction energy consumption and the running time of the train in each section of the whole line, and selecting the optimal solution of each section by adopting a dynamic programming method, so that the energy consumption of the whole line of the train is minimum under the condition of meeting the requirement of the specified running time. The invention improves the searching efficiency of the energy-saving optimization problem of the train, effectively reduces the energy consumption of the train and improves the punctuality of train operation.

Description

Train energy-saving operation method based on multi-target particle swarm algorithm
Technical Field
The invention belongs to the technical field of train operation control, and particularly relates to a train energy-saving operation method based on a multi-target particle swarm algorithm.
Background
Along with the acceleration of the urbanization process of China, the urban scale is gradually enlarged, and the urban population is rapidly increased. The rail transit has been developed as an important component of a two-line urban public transport system due to the advantages of large traffic volume and high speed. While the urban rail transit is rapidly developed, the construction cost and the operation cost of each urban rail transit are also increased year by year. According to the statistical result of the power consumption and energy consumption of the urban rail transit, the energy consumption of the urban rail transit system mainly comprises the following steps: the system comprises a train traction power supply system, an air conditioning system, a lighting system, an escalator and the like, wherein the traction power supply accounts for 50% of all power consumption. The huge energy consumption is a very serious problem faced by urban rail transit at present. Therefore, how to effectively reduce the train traction energy consumption becomes a task to be solved urgently for each subway operation company, and has important practical significance.
The train energy-saving operation control is a multi-objective optimization problem, and an accurate mathematical model is difficult to establish to describe the train operation process. The traditional mathematical methods, such as numerical analysis, are difficult to obtain the accurate solution of the model, only approximate solution of the model can be obtained even if an iterative method is adopted, and local optimization is easy to fall into. The method for processing the energy-saving multi-target multi-constraint optimization problem of the train at present mainly comprises the steps of weighting a plurality of optimization targets and converting the multi-target into a single target for optimization, however, the method needs to rely on a large amount of experience accumulation on weighting coefficients, local optimization is easy to cause, and only one group of solutions can be obtained.
Disclosure of Invention
The invention aims to provide a train energy-saving operation method based on a multi-target particle swarm algorithm, which is high in search efficiency, so that the train energy consumption is effectively reduced, and the punctuality of train operation is improved.
The technical solution for realizing the purpose of the invention is as follows: a train energy-saving operation method based on a multi-target particle swarm algorithm comprises the following steps:
step 1: setting train operation environment parameters including line data, train data and operation data;
step 2: establishing a train kinematics model and a traction energy consumption calculation method;
and step 3: establishing a train energy consumption multi-objective optimization model by taking traction energy consumption and running time as optimization objectives;
and 4, step 4: solving the optimization model by adopting a multi-objective particle swarm algorithm to obtain a plurality of groups of non-inferior solutions of the traction energy consumption and the running time of the train in a single interval;
and 5: calculating non-inferior solutions of the traction energy consumption and the running time of the train in each section of the whole line, and selecting the optimal solution of each section by adopting a dynamic programming method, so that the energy consumption of the whole line of the train is minimum under the condition of meeting the requirement of the specified running time.
Further, the line data in the step 1 comprise station positions, inter-station distances, line curvature radiuses, line temporary speed limits and line ramp data; the train data comprises data of train traction, braking force, maximum train running speed and acceleration and train quality; the operation data comprises the running time between stations of the train, the planned departure interval and the stop time.
Further, the train kinematics model in the step 2 includes a method for calculating train traction, braking force, basic resistance and additional resistance, and the energy consumption for train traction is calculated by calculating train traction to do work, and the formula is as follows:
Pi＝Fi·vi＝M·ai·vi
Ei＝Pi·Δt
wherein, PiRepresents the average power of the traction force in the i period, in kW/h; eiIndicating traction inWork done in i time period, in kJ; fiRepresents the average tractive effort of the train over a period i, in kN; m represents train mass, aiRepresenting the average acceleration of the train over a period i, viRepresents the average speed of the train over the i period, and Δ t represents a unit time.
Further, the train energy consumption multi-objective optimization model in the step 3 comprises two optimization objectives of traction energy consumption and operation time, and a plurality of constraint conditions including speed constraint, parking precision constraint and comfort constraint;
step 3.1, establishing an optimization goal
(1) Energy consumption optimization objective
Energy consumption f for inter-station operation of trainECalculated using the formula:
Figure BDA0002416878800000021
in the formula, EiRepresenting the traction energy consumption of the train in the ith time period, and n representing the time interval number into which the train operation time is divided;
the consumption of the traction energy generated by the train only exists in the traction working condition and the cruising working condition, so that the energy consumption of the two operation intervals is only considered when the traction energy is calculated;
Figure BDA0002416878800000022
in the above formula, PiRepresenting the average traction power of the train during the ith time period, FiRepresenting the average tractive effort, v, of the train during the i time periodiThe average speed of the train in the time period i;
(2) time optimization objective
Optimizing the energy consumption of the subway train, and considering whether the subway running time can meet the requirement of a schedule or not, optimizing and evaluating the time index fTThe calculation was performed using the following formula:
Figure BDA0002416878800000031
in the formula TiRepresenting each of the discrete time intervals of the time,
Figure BDA0002416878800000032
representing the total time of operation between stations, TpRepresenting the planned operation time between the train stations;
the target function is the difference value between the actual train running time and the planned running time, and the smaller the value is, the closer the actual train running time is to the planned running time is represented;
step 3.2, establishing constraint conditions
(1) Speed constraint
In the running process of the train, the speed cannot exceed the speed limit value v specified by the located linemaxThe speed limit value is not a constant value and changes along with the change of the line condition, so the speed v of the train at any time should satisfy the following conditions:
v＜vmax
(2) parking accuracy constraint
The constraint conditions of the parking precision are as follows:
|S-Sp|≤25/100
wherein S represents an actual parking position of the train, SpRepresents a target parking point, | S-SpThe smaller the | is, the higher the parking precision of the train is;
(3) comfort restraint
The stability degree of the operation is measured by the change rate of the acceleration degree of the train, and the constraint conditions are as follows:
ai≤amax
Figure BDA0002416878800000033
wherein, aiAcceleration value of the train at any moment, amaxRepresents the maximum acceleration that the train can provide, a1,a2Is t1,t2The acceleration value, a,
Figure BDA0002416878800000034
the train acceleration change rate is the minimum and maximum critical value.
Further, the step 4 of solving the optimization model by adopting a multi-objective particle swarm algorithm to obtain multiple groups of non-inferior solutions of the traction energy consumption and the operation time of the train in a single interval comprises the following substeps:
step 4.1, population initialization: initializing a population, randomly generating the initial speed and position of each particle under the limit of constraint conditions, and calculating the fitness value of all initialized particles;
step 4.2, population updating: updating the speed and the position of the current individual according to the global optimal particle and the individual optimal particle, wherein the global optimal particle is a particle randomly selected from a non-inferior solution set, and the updating rule is as follows:
Vim k+1＝ωVim k+c1r1(Pim k-Xim k)+c2r2(Pgm k-Xim k)
Xim k+1＝Xim k+Vim k+1
in the above formula Vim k+1、Xim k+1Respectively the velocity and position of the particle at the k +1 th iteration, Vim k、Xim kRespectively the velocity and position of the particle at the kth iteration; omega is the inertial weight; m ═ 1,2, ·, M; 1,2, · · n; k is the number of iterations when the current calculation is performed; c. C1,c2Is an acceleration factor; r is1,r2Is in the interval [0,1 ]]Any two of (a); pim kIs the individual extremum of the ith particle; pgm kRepresenting a global extremum of the particle;
and 4.3, updating the individual optimal particles: updating the individual optimal particles according to the domination relationship of the current optimal particles of the new particle individuals, namely selecting the domination particles when the domination particles exist in the two particles, and otherwise, randomly selecting one particle from the two particles as the new individual optimal particle;
4.4, screening non-inferior solutions: screening non-inferior solutions is divided into two steps, wherein in the first step, a new non-inferior solution set is merged with an old non-inferior solution set to obtain a new non-inferior solution set; secondly, removing the dominated solution according to the domination relation in the non-inferior solution set obtained in the first step, and screening out a new non-inferior solution set;
and 4.5, stopping updating: and if the iteration times reach the set maximum iteration times, stopping calculation, and otherwise, returning to the step 4.2 to continuously update the particles.
Further, in step 5, the optimal solution of each interval is selected by using a dynamic programming method, so that the energy consumption of the whole train line is minimum when the requirement of the specified operation time is met, specifically as follows:
the problem of minimum train overall energy consumption is regarded as a solving process of N steps, and each step selects a decision in non-inferior solutions of each interval; the decision-making process is to make the system optimal, and the criterion is the value of energy consumption;
r for index function of k stagek(xk,uk(xk) For example) and the initial state of a phase and the index function values for a set of sub-policies starting from that phase
Figure BDA0002416878800000043
It is shown, assuming an optimal control strategy:
Figure BDA0002416878800000041
then
Figure BDA0002416878800000042
At stage k state xkThe decision variable taken is uk(xk) The decision process consisting of all N stage decisions is called a policy
Figure BDA0002416878800000051
u*It is shown that the optimal control strategy is,
Figure BDA0002416878800000052
represents the optimal decision variable, J1,N(u*) Representing an optimal index function under an optimal control strategy;
to find the optimal index function
Figure BDA0002416878800000053
And their corresponding u*First, make a request
Figure BDA0002416878800000054
And corresponding optimal control; the index function of the sub-strategy of the k-th stage is then expressed as:
Figure BDA0002416878800000055
uk,…uN-1representing a set of control strategies, rk(xk,uk(xk) Denotes an index function of the k-th stage, gN(xN) Is the state of the Nth stage, which has no control decision input;
the method comprises the steps of calculating the optimal decision and the optimal index function of each stage from the Nth stage according to known conditions, and obtaining the optimal index function of the whole process and the optimal decision corresponding to each state of each stage from the known reverse calculation to the first stage; and then, forward calculation is carried out from the first stage by using a state transition equation to obtain a system state sequence and a whole process optimal strategy.
Compared with the prior art, the invention has the following remarkable advantages: (1) in the searching process, local optimization is not easy to be trapped, and the optimization result is not a single solution but a group of non-inferior solution sets, so that the corresponding optimization result can be selected according to the actual operation requirement; (2) the method improves the searching efficiency of the energy-saving optimization problem of the train, effectively reduces the energy consumption of the train and improves the punctuality of train operation.
Drawings
FIG. 1 is a flow chart of the train energy-saving operation method based on the multi-target particle swarm algorithm.
FIG. 2 is a flow chart of the solving steps of the multi-target particle swarm optimization.
Fig. 3 is a graph of the non-degraded speed of the train optimization results.
Fig. 4 is a graph of energy consumption for non-inferior solution of train optimization results.
FIG. 5 is a non-inferior solution distribution diagram of a train multiple optimization result.
Fig. 6 is a graph of train speed versus distance versus energy consumption versus distance.
Fig. 7 is a graph of the train full-line optimized operation.
Detailed Description
With reference to fig. 1-2, the train energy-saving operation method based on the multi-target particle swarm algorithm comprises the following steps:
step 1: setting train operation environment parameters including line data, train data and operation data;
step 2: establishing a train kinematics model and a traction energy consumption calculation method;
and step 3: establishing a train energy consumption multi-objective optimization model by taking traction energy consumption and running time as optimization objectives;
and 4, step 4: solving the optimization model by adopting a multi-objective particle swarm algorithm to obtain a plurality of groups of non-inferior solutions of the traction energy consumption and the running time of the train in a single interval;
and 5: calculating non-inferior solutions of the traction energy consumption and the running time of the train in each section of the whole line, and selecting the optimal solution of each section by adopting a dynamic programming method, so that the energy consumption of the whole line of the train is minimum under the condition of meeting the requirement of the specified running time.
As a specific example, the line data in step 1 includes station positions, inter-station distances, line curvature radii, line temporary speed limits, and line ramp data; the train data comprises data of train traction, braking force, maximum train running speed and acceleration and train quality; the operation data comprises the running time between stations of the train, the planned departure interval and the stop time.
As a specific example, the train kinematics model in step 2 includes a calculation method of train traction, braking force, basic resistance and additional resistance, and calculates the traction energy consumption of the train by calculating train traction work, where the formula is as follows:
Pi＝Fi·vi＝M·ai·vi
Ei＝Pi·Δt
wherein, PiRepresents the average power of the traction force in the i period, in kW/h; eiRepresents the work done by the tractive effort during the i period, in kJ; fiRepresents the average tractive effort of the train over a period i, in kN; m represents train mass, aiRepresenting the average acceleration of the train over a period i, viRepresents the average speed of the train over the i period, and Δ t represents a unit time.
As a specific example, the train energy consumption multi-objective optimization model in the step 3 includes two optimization objectives of traction energy consumption and operation time, and a plurality of constraint conditions including a speed constraint, a parking precision constraint and a comfort constraint;
step 3.1, establishing an optimization goal
(1) Energy consumption optimization objective
Energy consumption f for inter-station operation of trainECalculated using the formula:
Figure BDA0002416878800000061
in the formula, EiRepresenting the traction energy consumption of the train in the ith time period, and n representing the time interval number into which the train operation time is divided;
the consumption of the traction energy generated by the train only exists in the traction working condition and the cruising working condition, so that the energy consumption of the two operation intervals is only considered when the traction energy is calculated;
Figure BDA0002416878800000071
in the above formula, PiRepresenting the average traction power of the train during the ith time period, FiRepresenting the average tractive effort, v, of the train during the i time periodiThe average speed of the train in the time period i;
(2) time optimization objective
Optimizing the energy consumption of the subway train, and considering whether the subway running time can meet the requirement of a schedule or not, optimizing and evaluating the time index fTThe calculation was performed using the following formula:
Figure BDA0002416878800000072
in the formula TiRepresenting each of the discrete time intervals of the time,
Figure BDA0002416878800000073
representing the total time of operation between stations, TpRepresenting the planned operation time between the train stations;
the target function is the difference value between the actual train running time and the planned running time, and the smaller the value is, the closer the actual train running time is to the planned running time is represented;
step 3.2, establishing constraint conditions
(1) Speed constraint
In the running process of the train, the speed cannot exceed the speed limit value v specified by the located linemaxThe speed limit value is not a constant value and changes along with the change of the line condition, so the speed v of the train at any time should satisfy the following conditions:
v＜vmax
(2) parking accuracy constraint
The constraint conditions of the parking precision are as follows:
|S-Sp|≤25/100
wherein S represents an actual parking position of the train, SpRepresents a target parking point, | S-SpThe smaller the | is, the higher the parking precision of the train is;
(3) comfort restraint
The stability degree of the operation is measured by the change rate of the acceleration degree of the train, and the constraint conditions are as follows:
ai≤amax
Figure BDA0002416878800000081
wherein, aiAcceleration value of the train at any moment, amaxRepresents the maximum acceleration that the train can provide, a1,a2Is t1,t2The acceleration value, a,
Figure BDA0002416878800000082
the train acceleration change rate is the minimum and maximum critical value.
As a specific example, the step 4 of solving the optimization model by using the multi-objective particle swarm algorithm to obtain multiple groups of non-inferior solutions of the traction energy consumption and the running time of the train in a single compartment includes the following substeps:
step 4.1, population initialization: initializing a population, randomly generating the initial speed and position of each particle under the limit of constraint conditions, and calculating the fitness value of all initialized particles;
step 4.2, population updating: updating the speed and the position of the current individual according to the global optimal particle and the individual optimal particle, wherein the global optimal particle is a particle randomly selected from a non-inferior solution set, and the updating rule is as follows:
Vim k+1＝ωVim k+c1r1(Pim k-Xim k)+c2r2(Pgm k-Xim k)
Xim k+1＝Xim k+Vim k+1
in the above formula Vim k+1、Xim k+1Respectively the velocity and position of the particle at the k +1 th iteration, Vim k、Xim kRespectively the velocity and position of the particle at the kth iteration; omega is the inertial weight; m ═1,2, ·, M; 1,2, · · n; k is the number of iterations when the current calculation is performed; c. C1,c2Is an acceleration factor; r is1,r2Is in the interval [0,1 ]]Any two of (a); pim kIs the individual extremum of the ith particle; pgm kRepresenting a global extremum of the particle;
and 4.3, updating the individual optimal particles: updating the individual optimal particles according to the domination relationship of the current optimal particles of the new particle individuals, namely selecting the domination particles when the domination particles exist in the two particles, and otherwise, randomly selecting one particle from the two particles as the new individual optimal particle;
4.4, screening non-inferior solutions: screening non-inferior solutions is divided into two steps, wherein in the first step, a new non-inferior solution set is merged with an old non-inferior solution set to obtain a new non-inferior solution set; secondly, removing the dominated solution according to the domination relation in the non-inferior solution set obtained in the first step, and screening out a new non-inferior solution set;
and 4.5, stopping updating: and if the iteration times reach the set maximum iteration times, stopping calculation, and otherwise, returning to the step 4.2 to continuously update the particles.
As a specific example, in step 5, the optimal solution of each interval is selected by using a dynamic programming method, so that the energy consumption of the whole train line is minimum when the requirement of the specified operation time is met, specifically as follows:
the problem of minimum train overall energy consumption is regarded as a solving process of N steps, and each step selects a decision in non-inferior solutions of each interval; the decision-making process is to make the system optimal, and the criterion is the value of energy consumption;
r for index function of k stagek(xk,uk(xk) For example) and the initial state of a phase and the index function values for a set of sub-policies starting from that phase
Figure BDA0002416878800000091
It is shown, assuming an optimal control strategy:
Figure BDA0002416878800000092
then
Figure BDA0002416878800000093
At stage k state xkThe decision variable taken is uk(xk) The decision process consisting of all N stage decisions is called a policy
Figure BDA0002416878800000094
u*It is shown that the optimal control strategy is,
Figure BDA0002416878800000095
represents the optimal decision variable, J1,N(u*) Representing an optimal index function under an optimal control strategy;
to find the optimal index function
Figure BDA0002416878800000096
And their corresponding u*First, make a request
Figure BDA0002416878800000097
And corresponding optimal control; the index function of the sub-strategy of the k-th stage is then expressed as:
Figure BDA0002416878800000098
uk,…uN-1representing a set of control strategies, rk(xk,uk(xk) Denotes an index function of the k-th stage, gN(xN) Is the state of the Nth stage, which has no control decision input;
the method comprises the steps of calculating the optimal decision and the optimal index function of each stage from the Nth stage according to known conditions, and obtaining the optimal index function of the whole process and the optimal decision corresponding to each state of each stage from the known reverse calculation to the first stage; and then, forward calculation is carried out from the first stage by using a state transition equation to obtain a system state sequence and a whole process optimal strategy.
The invention is described in further detail below with reference to the figures and the embodiments.
Examples
The simulation research is carried out by combining the actual data of the railway line in China, and the railway line with the total length of 17.5 kilometers is an underground line. The line is provided with 9 stations, 8 underground islands, 1 bottom side and 4 transfer stations. The station positions and the inter-station distances are shown in table 1, and the line slopes are shown in table 2.
TABLE 1 station position and inter-station distance table
Figure BDA0002416878800000101
TABLE 2 line slope data
Figure BDA0002416878800000102
The train parameters are shown in tables 3 and 4.
TABLE 3 train basic parameter table
Figure BDA0002416878800000103
TABLE 4 TRAIN TRACTION-TRAVELLING METER
Figure BDA0002416878800000111
The operation data are shown in tables 5 and 6.
TABLE 5 Interval runtime Table
Figure BDA0002416878800000112
TABLE 6 stop time table
Figure BDA0002416878800000113
And 4, solving the model in the step 3 by adopting a multi-target particle swarm algorithm in the step 4, wherein the updating of the particles has certain randomness, so that the final optimization results are different. The number and specific values of the non-inferior solutions obtained by each optimization are different, but they fluctuate within a small range. The non-inferior solutions of the results of one of the multiple simulations are shown in table 7.
TABLE 7 non-inferior solution of optimization results
Figure BDA0002416878800000114
Fig. 3 plots the lazy transition points for each speed curve, and fig. 4 plots the energy consumption values for each energy consumption curve at the lazy transition points. The non-inferior solutions resulting from this suboptimal result total 7 groups, with a minimum energy consumption of 8.83kW, a maximum energy consumption of 11.48kW, a minimum runtime of 83.67s, a maximum runtime of 88.73s, and the minimum energy consumption corresponds to the minimum runtime and the maximum energy consumption corresponds to the maximum runtime. And repeating the optimization calculation for a plurality of times, wherein the non-inferior solution set of the energy consumption and the time of the plurality of groups is shown in FIG. 5. Although the number of the non-inferior solutions, the energy consumption of the non-inferior solutions and the running time of the optimization results are different, the non-dominant relationship exists between the interior of each group of non-inferior solutions, and therefore the results verify the correctness of the Pareto non-inferior solutions.
A group of solutions with the minimum energy consumption, i.e., a fourth group of non-inferior solutions, is selected from the plurality of groups of non-inferior solutions, and the speed and energy consumption curves are plotted as shown in fig. 6. The train is converted from a traction working condition to a cruising working condition at 3520.8m, converted from the cruising working condition to an idle working condition at 3817.5m and converted from the idle working condition to a braking working condition at 4440.7 m. The total train interval running time is 88.73s, wherein the traction time is 17.03s, the cruising time is 18.6s, the coasting time is 43.8s, and the braking time is 9.3 s. The total traction energy consumption of the train is 8.83kW, wherein the energy consumption in the traction stage is 7.32kW, and the energy consumption in the cruise stage is 1.51 kW. Compared with the train operation curve under the non-optimized time-saving strategy, the train energy consumption is reduced by 3.27kW, the operation time is increased by 7.53s, and the energy-saving efficiency reaches 27.02%.
And (5) optimizing the train whole-line traction energy consumption by adopting a dynamic programming method according to the step 5, wherein the optimization result is shown in a table 8, and the train operation curve is shown in a figure 7.
TABLE 8 train Whole line operating results
Figure BDA0002416878800000121
The total operation time of the train under the time-saving strategy is 1144s, the operation energy consumption is 181.61kW, under the optimization strategy, the total operation time of the train is 1273s, the operation energy consumption is 146.64kW, the operation time is increased by 129.31s totally, the operation energy consumption is reduced by 33.97kW, the energy-saving optimization efficiency reaches 18.1%, and the energy-saving effect is remarkable.

Claims (6)

1. A train energy-saving operation method based on a multi-target particle swarm algorithm is characterized by comprising the following steps:
step 1: setting train operation environment parameters including line data, train data and operation data;
step 2: establishing a train kinematics model and a traction energy consumption calculation method;
and step 3: establishing a train energy consumption multi-objective optimization model by taking traction energy consumption and running time as optimization objectives;
and 4, step 4: solving the optimization model by adopting a multi-objective particle swarm algorithm to obtain a plurality of groups of non-inferior solutions of the traction energy consumption and the running time of the train in a single interval;
and 5: calculating non-inferior solutions of the traction energy consumption and the running time of the train in each section of the whole line, and selecting the optimal solution of each section by adopting a dynamic programming method, so that the energy consumption of the whole line of the train is minimum under the condition of meeting the requirement of the specified running time.
2. The train energy-saving running method based on the multi-target particle swarm algorithm according to claim 1, wherein the line data in the step 1 comprise data of station positions, inter-station distances, line curvature radii, line temporary speed limits and line ramps; the train data comprises data of train traction, braking force, maximum train running speed and acceleration and train quality; the operation data comprises the running time between stations of the train, the planned departure interval and the stop time.
3. The train energy-saving operation method based on the multi-target particle swarm algorithm according to claim 1, wherein the train kinematic model in the step 2 comprises a calculation method of train traction, braking force, basic resistance and additional resistance, the train traction energy consumption is calculated by calculating train traction to do work, and the formula is as follows:
Pi＝Fi·vi＝M·ai·vi
Ei＝Pi·Δt
wherein, PiRepresents the average power of the traction force in the i period, in kW/h; eiRepresents the work done by the tractive effort during the i period, in kJ; fiRepresents the average tractive effort of the train over a period i, in kN; m represents train mass, aiRepresenting the average acceleration of the train over a period i, viRepresents the average speed of the train over the i period, and Δ t represents a unit time.
4. The train energy-saving operation method based on the multi-target particle swarm algorithm according to claim 1, wherein the train energy consumption multi-target optimization model in the step 3 comprises two optimization targets of traction energy consumption and operation time, and a plurality of constraint conditions comprising speed constraint, parking precision constraint and comfort constraint;
step 3.1, establishing an optimization goal
(1) Energy consumption optimization objective
Energy consumption f for inter-station operation of trainECalculated using the formula:
Figure FDA0002416878790000011
in the formula, EiIndicating trains in the ith time periodN represents the number of time intervals into which the train operating time is divided;
the consumption of the traction energy generated by the train only exists in the traction working condition and the cruising working condition, so that the energy consumption of the two operation intervals is only considered when the traction energy is calculated;
Figure FDA0002416878790000021
in the above formula, PiRepresenting the average traction power of the train during the ith time period, FiRepresenting the average tractive effort, v, of the train during the i time periodiThe average speed of the train in the time period i;
(2) time optimization objective
Optimizing the energy consumption of the subway train, and considering whether the subway running time can meet the requirement of a schedule or not, optimizing and evaluating the time index fTThe calculation was performed using the following formula:
Figure FDA0002416878790000022
in the formula TiRepresenting each of the discrete time intervals of the time,
Figure FDA0002416878790000023
representing the total time of operation between stations, TpRepresenting the planned operation time between the train stations;
the target function is the difference value between the actual train running time and the planned running time, and the smaller the value is, the closer the actual train running time is to the planned running time is represented;
step 3.2, establishing constraint conditions
(1) Speed constraint
In the running process of the train, the speed cannot exceed the speed limit value v specified by the located linemaxThe speed limit value is not a constant value and changes along with the change of the line condition, so the speed v of the train at any time should satisfy the following conditions:
v＜vmax
(2) parking accuracy constraint
The constraint conditions of the parking precision are as follows:
|S-Sp|≤25/100
wherein S represents an actual parking position of the train, SpRepresents a target parking point, | S-SpThe smaller the | is, the higher the parking precision of the train is;
(3) comfort restraint
The stability degree of the operation is measured by the change rate of the acceleration degree of the train, and the constraint conditions are as follows:
ai≤amax
Figure FDA0002416878790000031
wherein, aiAcceleration value of the train at any moment, amaxRepresents the maximum acceleration that the train can provide, a1,a2Is t1,t2The acceleration value, a,
Figure FDA0002416878790000032
the train acceleration change rate is the minimum and maximum critical value.
5. The multi-target particle swarm algorithm-based train energy-saving operation method according to claim 1, wherein the step 4 of solving the optimization model by using the multi-target particle swarm algorithm to obtain multiple groups of non-inferior solutions of traction energy consumption and operation time of the train in a single interval comprises the following substeps:
step 4.1, population initialization: initializing a population, randomly generating the initial speed and position of each particle under the limit of constraint conditions, and calculating the fitness value of all initialized particles;
step 4.2, population updating: updating the speed and the position of the current individual according to the global optimal particle and the individual optimal particle, wherein the global optimal particle is a particle randomly selected from a non-inferior solution set, and the updating rule is as follows:
Vim k+1＝ωVim k+c1r1(Pim k-Xim k)+c2r2(Pgm k-Xim k)
Xim k+1＝Xim k+Vim k+1
in the above formula Vim k+1、Xim k+1Respectively the velocity and position of the particle at the k +1 th iteration, Vim k、Xim kRespectively the velocity and position of the particle at the kth iteration; omega is the inertial weight; m ═ 1,2, ·, M; 1,2, · · n; k is the number of iterations when the current calculation is performed; c. C1,c2Is an acceleration factor; r is1,r2Is in the interval [0,1 ]]Any two of (a); pim kIs the individual extremum of the ith particle; pgm kRepresenting a global extremum of the particle;
and 4.3, updating the individual optimal particles: updating the individual optimal particles according to the domination relationship of the current optimal particles of the new particle individuals, namely selecting the domination particles when the domination particles exist in the two particles, and otherwise, randomly selecting one particle from the two particles as the new individual optimal particle;
4.4, screening non-inferior solutions: screening non-inferior solutions is divided into two steps, wherein in the first step, a new non-inferior solution set is merged with an old non-inferior solution set to obtain a new non-inferior solution set; secondly, removing the dominated solution according to the domination relation in the non-inferior solution set obtained in the first step, and screening out a new non-inferior solution set;
and 4.5, stopping updating: and if the iteration times reach the set maximum iteration times, stopping calculation, and otherwise, returning to the step 4.2 to continuously update the particles.
6. The multi-target particle swarm algorithm-based train energy-saving operation method according to claim 1, wherein in the step 5, an optimal solution of each interval is selected by adopting a dynamic programming method, so that the train overall energy consumption is minimum under the condition of meeting the requirement of specified operation time, and the method specifically comprises the following steps:
the problem of minimum train overall energy consumption is regarded as a solving process of N steps, and each step selects a decision in non-inferior solutions of each interval; the decision-making process is to make the system optimal, and the criterion is the value of energy consumption;
r for index function of k stagek(xk,uk(xk) For example) and the initial state of a phase and the index function values for a set of sub-policies starting from that phase
Figure FDA0002416878790000048
It is shown, assuming an optimal control strategy:
Figure FDA0002416878790000041
then
Figure FDA0002416878790000042
At stage k state xkThe decision variable taken is uk(xk) The decision process consisting of all N stage decisions is called a policy
Figure FDA0002416878790000043
u*It is shown that the optimal control strategy is,
Figure FDA0002416878790000044
represents the optimal decision variable, J1,N(u*) Representing an optimal index function under an optimal control strategy;
to find the optimal index function
Figure FDA0002416878790000045
And their corresponding u*First, make a request
Figure FDA0002416878790000046
N-1, …,2,1 and corresponding optimal control; the index function of the sub-strategy of the k-th stage is then expressed as:
Figure FDA0002416878790000047
uk,…uN-1representing a set of control strategies, rk(xk,uk(xk) Denotes an index function of the k-th stage, gN(xN) Is the state of the Nth stage, which has no control decision input;
the method comprises the steps of calculating the optimal decision and the optimal index function of each stage from the Nth stage according to known conditions, and obtaining the optimal index function of the whole process and the optimal decision corresponding to each state of each stage from the known reverse calculation to the first stage; and then, forward calculation is carried out from the first stage by using a state transition equation to obtain a system state sequence and a whole process optimal strategy.
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