CN111409673A - Train quasi-point energy-saving operation method based on dynamic programming algorithm - Google Patents
Train quasi-point energy-saving operation method based on dynamic programming algorithm Download PDFInfo
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Abstract
The invention discloses a train punctual energy-saving operation method based on a dynamic planning algorithm, which is characterized in that a train model and an operation environment thereof are established by setting train operation line data and train parameters, an energy-saving optimization model for train operation is established by taking train punctuality and train traction energy consumption as optimization targets, constraint conditions such as travel time, speed limit, maximum train addition and deceleration and the like are fully considered, a train operation constraint function, namely an energy-saving optimization model constraint condition, is established, and the optimization model is solved by using the dynamic planning algorithm, so that an optimal train operation strategy of a train is obtained. The invention effectively improves the precision of train energy-saving optimization, has high optimization speed, has the advantage of wide optimal solution search range and reduces train energy consumption.
Description
Technical Field
The invention belongs to the field of train operation control, and particularly relates to a train punctual energy-saving operation method based on a dynamic programming algorithm.
Background
At present, rail transit has developed into an important component in an urban rail transit 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, and huge energy consumption is a very serious problem facing 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 existing energy-saving scheme reduces energy consumption mostly in an indirect mode, has low energy-saving rate and complex objective function, and can not directly make the system enter a next-stage operation strategy of the train in the multi-decision problem.
Disclosure of Invention
The invention aims to provide a train punctual energy-saving operation method based on a dynamic programming algorithm.
The technical solution for realizing the purpose of the invention is as follows: a train punctual energy-saving operation method based on a dynamic planning algorithm comprises the following steps:
Step 3, establishing a train operation quasi-point energy-saving optimization model, wherein the target function of the train operation quasi-point energy-saving optimization model is that the sum of train operation energy consumption and time offset is minimum, the constraint condition is a train operation limiting index and the basic parameters, and the solution is an optimal train operation strategy;
Step 4, determining an energy consumption-time cost function of the kth subinterval according to the target function;
Step 5, establishing a recursion relation model of energy consumption-time cost;
And 6, determining an optimal operation strategy of the train by utilizing a dynamic programming algorithm according to the recursive relation model of the energy consumption-time cost and the energy consumption-time cost function of the kth subinterval.
Preferably, the line data includes a ramp start-stop kilometer post and a corresponding gradient, a curve section start-stop kilometer post and a corresponding curvature, a speed limit section start-stop kilometer post and a corresponding speed limit, and the train parameters include a train marshalling mode, a length, a load grade, a davis equation, a maximum acceleration, a maximum speed, a traction characteristic curve and a braking characteristic curve.
Preferably, the train operation waypoint energy-saving optimization model established in step 3 includes:
An objective function:
Wherein J is the minimum value of energy consumption and time offset, f (v) is the unit traction force of the full level of the train at the speed v, u kffor the tractive force usage coefficient, Delta S, of the train in the kth sub-interval kfor the length of the kth sub-interval in the operating line,. DELTA.t kThe running time of the train in the kth subinterval is T, and the T is the travel time given by the timetable;
Constraint conditions are as follows:
Wherein M is the current total mass of the train, V is the running speed of the train, f is the frictional resistance borne by the train, s is the required parking position, sp is the actual parking position, C is the resultant force borne by the train, i is the line gradient thousandth, C is the line curvature data, V Tfor temporarily limiting the speed of the line, L cIs a train model parameter;
Preferably, the energy consumption-time cost function of the kth sub-interval determined in step 4 is specifically:
gk(ΔSk,ukf)＝ukff(v)ΔSk+λΔtk。
Preferably, the recursive relationship model of energy consumption-time cost established in step 5 is specifically:
Wherein J is the minimum value of energy consumption and time offset, f (v) is the unit traction force of the full-level position of the train when the speed v is kffor the tractive force usage coefficient, Delta S, of the train in the kth sub-interval kfor the length of the kth sub-interval in the operating line,. DELTA.t kThe operation time of the train in the kth subinterval is shown, and lambda is a relation coefficient of absolute value offset of energy consumption and time; g kEnergy consumption-time cost over the kth decision interval, J kThe minimum energy consumption-time cost is accumulated for the stages from nth to kth.
Preferably, the specific step of determining the optimal operation strategy of the train by using a dynamic programming algorithm according to the recursive relation model of the energy consumption-time cost and the energy consumption-time cost function of the kth sub-interval in the step 6 is as follows:
6.1, discretizing the train operation punctual energy-saving optimization model according to train operation subintervals, dividing the train operation process into N decision-making stages, and setting the end state of the last decision-making stage as 0;
6.2, obtaining a plurality of effective speed connections of the last decision stage according to the terminal state of the kth decision stage and a recursion relation model of energy consumption-time cost;
Respectively substituting the effective speed connections into an energy consumption time cost function to obtain a plurality of energy consumption time costs, and taking the speed connection corresponding to the lowest energy consumption time cost as the terminal state of the last decision stage;
6.3, repeating the step 6.2 to obtain the terminal state of each decision stage, and expressing the optimal decision from the terminal state of each stage to the terminal state of the last stage as a state transition equation;
And 6.4, storing the optimal decision of each stage and the intermediate calculation result in the backtracking recursion process into a backtracking record table to obtain the optimal operation strategy of the train.
Preferably, the state transition equation is:
xk+1＝h(xk,uk)
xkIs the state of the kth stage, u k(xk) For the decision of the kth stage, x k+1Is the state of the (k + 1) th stage.
Preferably, if the train operation time is adjusted at a later time or in the original schedule, λ is directly increased, λ is a coefficient of relation between energy consumption and an absolute value offset of time, an adjustment formula is that λ 2 is (λ 0+ λ 1)/2, (λ 1 is a coefficient greater than λ 2), and the step 6.2 is returned to, and the optimal decision of each stage is obtained again.
Compared with the prior art, the invention has the following remarkable advantages: when the train runs in a plurality of intervals, the state of the current stage is determined, and the selection can be made according to the current state variable, and the backtracking is carried out forward, so that the system directly enters the next stage, and the energy-saving efficiency is greatly improved.
Drawings
Fig. 1 is a flow chart of a train punctual energy-saving operation method based on a dynamic programming algorithm in the invention.
Fig. 2 is a diagram of the train punctual energy-saving optimal operating speed and energy consumption in the invention.
Detailed Description
As shown in fig. 1, a train quasi-point energy-saving operation method based on a dynamic programming algorithm includes the following steps:
And 3, establishing a train operation quasi-point energy-saving optimization model, wherein the target function of the train operation quasi-point energy-saving optimization model is that the sum of the energy consumption and the time offset of train operation is minimum, the constraint condition is the limiting index of train operation and the basic parameter, and the solution is the optimal operation strategy of the train.
In a further embodiment, the objective function of the train operation quasi-point energy-saving optimization model is as follows:
The optimization model is the minimum of the sum of the energy consumption and the travel time offset.
Wherein J is the minimum value of energy consumption and time offset, f (v) is the unit traction force of the full-level position of the train when the speed v is kffor the tractive force usage coefficient, Delta S, of the train in the kth sub-interval kfor the length of the kth sub-interval in the operating line,. DELTA.t kFor the running time of the train in the kth sub-interval, T is the corresponding travel time given by the timetable. And lambda is the relation coefficient of the absolute offset of the energy consumption and the time.
The constraint conditions are specifically as follows:
Wherein M is the current total mass of the train, V is the running speed of the train, f is the frictional resistance borne by the train, s is the required parking position, sp is the actual parking position, C is the resultant force borne by the train, i is the line gradient thousandth, C is the line curvature data, V Tfor temporarily limiting the speed of the line, L cThe train model and other parameters.
Step 4, determining an energy consumption-time cost function of the kth subinterval according to the objective function, specifically:
gk(ΔSk,ukf)＝ukff(v)ΔSk+λΔtk
Step 5, establishing a recursive relation model of energy consumption-time cost, wherein the recursive relation model of energy consumption-time cost is as follows:
Wherein: j is the minimum value of energy consumption and time offset, f (v) is the unit traction force of the full level of the train at the speed v, u kffor the tractive force usage coefficient, Delta S, of the train in the kth sub-interval kfor the length of the kth sub-interval in the operating line,. DELTA.t kThe operation time of the train in the kth subinterval is shown, and lambda is a relation coefficient of absolute value offset of energy consumption and time; g kEnergy consumption-time cost over kth decision interval; j. the design is a square kAccumulating the minimum energy consumption-time cost for the nth phase to the kth phase; the initial value of the energy consumption-time cost is 0.
Step 6, according to the recursive relation model of the energy consumption-time cost and the energy consumption-time cost function of the kth subinterval, the optimal operation strategy of the train is obtained by using a dynamic programming algorithm, and the specific steps are as follows:
6.1, discretizing the train operation punctual energy-saving optimization model according to train operation subintervals, dividing the train operation process into N decision-making stages, and setting the end state of the last decision-making stage as 0;
6.2, obtaining a plurality of effective speed connections of the last decision stage according to the terminal state of the kth decision stage and a recursion relation model of energy consumption-time cost;
Respectively substituting the effective speed connections into an energy consumption time cost function to obtain a plurality of energy consumption time costs, and taking the speed connection corresponding to the lowest energy consumption time cost as the terminal state of the last decision stage;
The effective speed connection is a motion process that the train can be shifted from the state of the current stage to the state of the next stage within the owned traction braking characteristic range;
The state of the train in any decision stage is the current speed of the train, an effective speed connection between adjacent decision stages forms state transition, the train is transitioned from a known initial state to a next state, on the premise that constraint conditions of a train operation punctual energy-saving optimization model are met, a plurality of possibilities exist, and the effective speed connection with the lowest energy consumption time cost can be obtained by substituting the possibilities meeting the constraint conditions into the energy consumption time cost function in the step 2.
6.3, repeating the step 6.2 to obtain the terminal state of each decision stage;
Expressing the optimal decision of the end state of each stage to the end state of the last stage as a state transition equation:
xk+1＝h(xk,uk)
The above equation shows that once state x kAnd decision u k(xk) The state of the next stage is determined and can be expressed by the above formula. I.e. if the initial state and a set of policies u are known 1(x1),u2(x2),...,uN(xN) And solving the state of the whole system process according to the state transition equation.
According to the energy consumption-time cost recursive relation model, backtracking is carried out from the kth subinterval to the previous subinterval according to the energy consumption-time cost recursive relation model, so that a plurality of effective speed connections of the train in each stage can be obtained, all possible energy consumption-time costs in the subinterval are continuously compared in each decision stage, the minimum value is found, and the minimum value is substituted in the next decision stage, so that the optimal decision and the corresponding state transfer equation in the corresponding state of each stage in the whole process can be obtained.
The train has only one state in the N +1 stage, namely V N+10, and in this state the train is at the end The minimum energy consumption-time cost and the time to reach the end point are obviously 0. The braking force coefficient u2 at this time is-1. The backtracking calculation is started from the Nth decision stage, because the end point has only one state, the energy consumption-time cost corresponding to the effective speed connection of any state and the end point in the Nth decision stage is the minimum energy consumption-time cost of the state, the energy consumption-time cost is counted into the corresponding table in the kth stage, and for any state i delta v kConsider all the states j Δ v for the next phase that make the speed connection active k+1And calculating and comparing all energy consumption-time costs, selecting the minimum value and the corresponding arrival time and traction/braking force coefficient thereof, recording the minimum value and the corresponding arrival time and traction/braking force coefficient into a corresponding table, and backtracking to the starting station to finish calculation.
And 6.4, storing the optimal decision of each stage and the intermediate calculation result in the backtracking recursion process into a backtracking record table to obtain the optimal operation strategy of the train. The intermediate calculation result comprises the minimum energy consumption-time cost when the state of the kth decision stage is operated to the last stage, the expected time reaching the last stage corresponding to the minimum energy consumption-time cost, and the optimal traction/braking force use coefficient to be exerted in the state;
the operation strategies of each subinterval obtained in the backtracking process can be recorded into a backtracking record table, as shown in table 1, the rows in the backtracking record table represent each decision stage, and the columns represent the speed of the train at that stage, and the elements when the speed is i △ v are recorded in the kth decision stage of the backtracking record table (J △ v) ki,tki,ukif/ukib). Wherein J kiIs the minimum energy consumption-time cost, t, for the state of the kth decision stage to run to the previous stage kiIs the predicted time to last phase, u, corresponding to the minimum energy consumption-time cost kif/ukibIs the optimum traction/braking force usage factor to be exerted in this state.
TABLE 1
In a further embodiment, if the train operation time is adjusted at a later point of the train or in the original schedule, the lambda is directly adjusted to be lambda 2, the step 6.2 is returned, the optimal decision of each stage is obtained again, the optimized train speed curve meets the requirement of effective connection of four working condition speeds, and the energy consumption per kilometer is reduced compared with that before the optimization. The method for determining the lambda 2 comprises the following steps:
If λ is adjusted to λ 1 so that the deviation of the expected operating time from the given operating time is less than the threshold value, the coefficient of the absolute deviation of the adjusted energy consumption from time is λ 2 ═ λ 0+ λ 1)/2.
Claims (8)
1. A train punctual energy-saving operation method based on a dynamic planning algorithm is characterized by comprising the following steps:
Step 1, setting train running line data and train parameters to construct a train model and a running environment thereof;
Step 2, dividing a train running interval with the length of S into N sub-intervals according to line parameters, ensuring that each divided sub-interval contains a specific slope value, a curve radius and a speed limit value, and ensuring that the length of each sub-interval is delta S k；
Step 3, establishing a train operation quasi-point energy-saving optimization model, wherein the target function of the train operation quasi-point energy-saving optimization model is that the sum of train operation energy consumption and time offset is minimum, the constraint condition is a train operation limiting index and the basic parameters, and the solution is an optimal train operation strategy;
Step 4, determining an energy consumption-time cost function of the kth subinterval according to the target function;
Step 5, establishing a recursion relation model of energy consumption-time cost;
And 6, determining an optimal operation strategy of the train by utilizing a dynamic programming algorithm according to the recursive relation model of the energy consumption-time cost and the energy consumption-time cost function of the kth subinterval.
2. The train waypoint energy-saving operation method based on the dynamic programming algorithm according to claim 1 wherein the route data includes a ramp start and stop kilometer post and a corresponding gradient, a curve section start and stop kilometer post and a corresponding curvature, a speed limit section start and stop kilometer post and a corresponding speed limit, and the train parameters include a train formation mode, a length, a load level, a davis equation, a maximum acceleration, a maximum speed, a traction characteristic curve and a braking characteristic curve.
3. The train quasi-point energy-saving operation method based on the dynamic programming algorithm according to claim 1, wherein the train operation quasi-point energy-saving optimization model established in the step 3 comprises:
An objective function:
Wherein J is the minimum value of energy consumption and time offset, f (v) is the unit traction force of the full level of the train at the speed v, u kffor the tractive force usage coefficient, Delta S, of the train in the kth sub-interval kfor the length of the kth sub-interval in the operating line,. DELTA.t kThe running time of the train in the kth subinterval is T, and the T is the travel time given by the timetable;
Constraint conditions are as follows:
Wherein M is the current total mass of the train, V is the running speed of the train, f is the frictional resistance borne by the train, s is the required parking position, sp is the actual parking position, C is the resultant force borne by the train, i is the line gradient thousandth, C is the line curvature data, V Tfor temporarily limiting the speed of the line, L cIs a train model parameter;
4. The train punctual energy-saving operation method based on the dynamic programming algorithm according to claim 1, characterized in that the energy consumption-time cost function of the kth subinterval determined in step 4 is specifically:
gk(ΔSk,ukf)＝ukff(v)ΔSk+λΔtk。
5. The train punctual energy-saving operation method based on the dynamic programming algorithm according to claim 1, characterized in that the recursive relational model of energy consumption-time cost established in step 5 is specifically:
Wherein J is the minimum value of energy consumption and time offset, f (v) is the unit traction force of the full-level position of the train when the speed v is kffor the tractive force usage coefficient, Delta S, of the train in the kth sub-interval kfor the length of the kth sub-interval in the operating line,. DELTA.t kThe operation time of the train in the kth subinterval is shown, and lambda is a relation coefficient of absolute value offset of energy consumption and time; g kEnergy consumption-time cost over the kth decision interval, J kThe minimum energy consumption-time cost is accumulated for the stages from nth to kth.
6. The train punctual energy-saving operation method based on the dynamic programming algorithm according to claim 1, characterized in that, the specific steps of determining the optimal operation strategy of the train by using the dynamic programming algorithm according to the recursive relation model of energy consumption-time cost and the energy consumption-time cost function of the kth subinterval in step 6 are as follows:
6.1, discretizing the train operation punctual energy-saving optimization model according to train operation subintervals, dividing the train operation process into N decision-making stages, and setting the end state of the last decision-making stage as 0;
6.2, obtaining a plurality of effective speed connections of the last decision stage according to the terminal state of the kth decision stage and a recursion relation model of energy consumption-time cost;
Respectively substituting the effective speed connections into an energy consumption time cost function to obtain a plurality of energy consumption time costs, and taking the speed connection corresponding to the lowest energy consumption time cost as the terminal state of the last decision stage;
6.3, repeating the step 6.2 to obtain the terminal state of each decision stage, and expressing the optimal decision from the terminal state of each stage to the terminal state of the last stage as a state transition equation;
And 6.4, storing the optimal decision of each stage and the intermediate calculation result in the backtracking recursion process into a backtracking record table to obtain the optimal operation strategy of the train.
7. The train punctual energy-saving operation method based on the dynamic programming algorithm according to claim 6, characterized in that the state transition equation is:
xk+1＝h(xk,uk)
xkIs the state of the kth stage, u k(xk) For the decision of the kth stage, x k+1Is the state of the (k + 1) th stage.
8. The train punctual energy-saving operation method based on the dynamic programming algorithm according to claim 6, characterized in that, if the train operation time in the train late or original schedule is adjusted, λ is directly adjusted to λ 2, and the step 6.2 is returned to, and the optimal decision of each stage is obtained again, wherein the determination method of λ 2 is as follows: if λ is adjusted to λ 1 so that the deviation of the expected operating time from the given operating time is less than the threshold value, the coefficient of the absolute deviation of the adjusted energy consumption from time is λ 2 ═ λ 0+ λ 1)/2.
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| CN113536204A (en) * | 2021-06-30 | 2021-10-22 | 武汉理工光科股份有限公司 | Intelligent fire fighting force dispatching method and device and storage medium |
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Application publication date: 20200714 |