Train multi-interval energy-saving operation curve planning method based on grouped knapsacks

Abstract

The invention provides a train multi-interval energy-saving operation curve planning method based on grouped knapsacks, and belongs to the technical field of train operation energy-saving optimizing.The method comprises the steps that the optimal control Pareto leading edge between stations is obtained, the time-energy consumption relation is obtained from an offline database, the operation time between the stations is further optimized and adjusted, and the optimal control Pareto leading edge is obtained; according to a single-interval energy-saving driving algorithm, an energy-saving operation curve of each interval is generated, so that the total energy consumption of the whole train line is minimum, the purpose of whole-line energy-saving driving is achieved, and the problems that the online operation time complexity is high and the calculation precision cannot be guaranteed are solved.

Description

Technical Field

[0001] The present invention belongs to the technical field of train operation energy-saving optimization, and in particular relates to a train multi-section energy-saving operation curve planning method based on grouping backpacks. Background Art

[0002] The operation process of a train between stations includes four control conditions: traction, cruising, coasting and braking. The ordered set of control conditions and their corresponding distances applied when the train departs from the platform and stops at the next station is called the train driving operation strategy. Each set of operation strategies corresponds to a certain operating time, traction energy consumption and regenerative braking energy consumption. When the utilization rate of regenerative energy is known, for a specified operating time between stations, there exists at least one set of operation strategies that minimizes the total energy consumption of the train between stations. This set of operation strategies is the optimal operation strategy under the current operating time conditions, and is also a non-dominated solution in the entire feasible domain, namely the Pareto solution. The set of all optimal operation strategies is the Pareto optimal solution set, and its corresponding "energy consumption-time" Pareto frontier is as follows: Figure 1 The red curve in the middle shows that if two Pareto solutions are selected on the Pareto frontier, the corresponding optimal running trajectory of the train is shown in the blue curve.

[0003] Due to the different line conditions between stations, the corresponding optimal operation Pareto frontiers are different, such as Figure 1 As shown in , the Pareto fronts between the two stations are represented by red and blue respectively. Figure 2 It can be seen that under the same running time conditions, the energy-saving effect of the additional running time allocated to the two stations is significantly different; for the same station, the energy-saving effect of adding on the basis of different running times is also significantly different. The total running time of the train is fixed, and the running time allocation strategy between stations determines the total traction energy consumption of the train running on the entire line.

[0004] Disadvantages of existing technology:

[0005] 1) The method of treating the entire line as a large interval for interpolation calculation results in high time complexity and cannot meet the requirements of online replanning;

[0006] 2) In the process of fitting the Pareto curve, the influence of regenerative braking energy is not considered, which may lead to excessive fitting complexity or inaccurate results;

[0007] 3) The current method of using priority queues to process Pareto curves has higher time and space complexity.

[0008] That is, there are technical problems such as the time complexity is too high to be used for online planning; the discrete accuracy is insufficient; and the time complexity is too high. Summary of the invention

[0009] In view of the above-mentioned deficiencies in the prior art, the present invention provides a train multi-section energy-saving operation curve planning method based on grouped backpacks, which solves the problems of high online calculation time complexity and inability to guarantee calculation accuracy.

[0010] In order to achieve the above purpose, the technical solution adopted by the present invention is: a train multi-section energy-saving operation curve planning method based on grouping backpack, comprising the following steps:

[0011] S1. Generate the maximum capacity operation curve according to the most energy-saving operation strategy of the single vehicle, and build an offline database through the discrete Pareto curve;

[0012] S2, initialization and parameter definition;

[0013] S3, perform outer loop processing, traverse from the first interval to the last interval, so as to calculate the total remaining time of the subsequent interval for the curve number traversal of the interval given the total surplus time and the selected curve of the previous interval, wherein each interval is regarded as a group, and the surplus time allocated to each interval is regarded as an item;

[0014] S4, perform middle-level loop processing, initialize the curve index number k to 0, traverse from the first curve to the last curve in the interval, and obtain the selected curve number that maximizes the total energy consumption reduction in the interval given the total surplus time of the subsequent interval, wherein the energy consumption reduction of each curve relative to the maximum capacity of the interval is regarded as its value, and it is required that a curve must be selected in each interval to achieve the maximum filling of the backpack;

[0015] S5, perform inner loop processing, traverse the surplus time in reverse order, and traverse from the total surplus time W of the whole line to find the curve combination selected in each interval under different total surplus time, wherein the problem of finding surplus time is converted into a grouping knapsack problem;

[0016] S6. Calculate the energy consumption reduction newEnergy brought by selecting the new curve number in the current interval. In response to the energy consumption reduction newEnergy being greater than the maximum energy consumption reduction dp[i][j], update the maximum energy consumption reduction dp[i][j] to be equal to the energy consumption reduction newEnergy, and record the curve number index obtained by the selected outer loop, middle loop, and inner loop processing, where dp[i][j] represents the maximum energy consumption reduction of the first i intervals under j surplus time;

[0017] S7, determine whether the traversal of the outer layer, the middle layer and the inner layer is completed, if so, proceed to step S8, otherwise update the traversal variable and return to step S3;

[0018] S8, obtaining the running time of each interval according to the single interval curve maximum capacity running time recorded by the Pareto curve in step S1 and the selected curve number index recorded in step S6;

[0019] S9. According to the running time of each section, the optimal driving strategy for a single section is used to generate the optimal operating conditions for each section, and the planning of the energy-saving running curve for multiple sections of the train is completed.

[0020] The beneficial effects of the present invention are as follows: the present invention is based on the most energy-saving driving strategy for a single vehicle, stores the Pareto curve of the train in each section as an offline database, and uses the energy consumption of the maximum capacity operating curve of each section as a benchmark. The surplus time that exceeds the maximum capacity operating time is reasonably allocated to each section. Each section is regarded as a group, each allocated surplus time is regarded as an item, and the energy consumption reduction of each curve relative to the maximum capacity operation of the section is regarded as its value. It is required to select a curve in each section to achieve the maximum filling of the backpack and ultimately achieve the goal of maximizing energy-saving quantification, that is, while allocating all surplus time, significantly reducing energy consumption, and after calculating the timetable, the optimal energy-saving operating condition sequence of each section is calculated based on the operation strategy calculation method under the given operating time, thereby achieving the goal of minimizing the total energy consumption under the full-line time allocation. That is, on the basis of the existing Pareto curve of a single vehicle in a single section, the present invention fully considers the influence of regenerative braking energy, thereby achieving the goal of minimizing the total energy consumption under the full-line time allocation.

[0021] Furthermore, the step S1 includes the following steps:

[0022] S101, generating maximum capacity operation curves under different vehicle weights in different intervals according to the most energy-saving operation strategy for a single vehicle;

[0023] S102, according to the maximum capacity operation curves under different vehicle weights in different intervals, obtain the maximum operation time T of interval i i,max and maximum energy consumption E i,max ;

[0024] S103, calculate the Pareto curve under a given surplus time, discretize the Pareto curve with a certain step length, and record the running time T of the kth curve i,k and energy consumption E i,k ;

[0025] S104. Based on the results of step S102 and step S103, an offline database for the Pareto curve of each section of the train is constructed.

[0026] The beneficial effect of the above further scheme is: the present invention can significantly improve the accuracy and efficiency of online calculations by constructing a "time-energy consumption" offline database based on the most energy-saving driving strategy. By using the existing database and performing a large amount of calculations in the offline stage, a more accurate calculation efficiency can be obtained.

[0027] Furthermore, the step S2 is specifically as follows:

[0028] Define dynamic programming array dp;

[0029] The meaning and size of dp[i][j] are defined as (m+1)×(W+1); where dp[i][j] represents the maximum energy consumption reduction of the first i intervals under the j surplus time, m represents the number of intervals, and W represents the total surplus time of the entire line, that is, the excess time of the operation plan time relative to the maximum capacity operation time;

[0030] Initialize all elements to negative infinity;

[0031] Define CurveChoices[i][j] to store the curve number index combination selected in the first i intervals and at the j surplus time;

[0032] The initial state dp[0][0]=0 is set, where dp[0][0]=0 means that the maximum energy consumption reduction of the entire line is 0 when the surplus time is 0.

[0033] Furthermore, the step S3 is specifically as follows:

[0034] Perform outer loop processing, initialize the interval number to i=1, and traverse from i=1 to i=m, where m represents the number of intervals;

[0035] According to the traversal results, under the given total surplus time and the selected curve in the previous interval, the selected curve number that can reduce the total energy consumption the most is selected by calculating the total remaining time of the subsequent intervals. Each time the step S3 is returned, the value of the interval number i is set to i+1. In response to the interval number i being greater than m, the step S8 is entered.

[0036] Furthermore, the step S4 is specifically as follows:

[0037] Perform middle-level loop processing, initialize the curve index k to 0, from k = 0 to k = n i Traverse, where n i represents the total number of curves in the i-th interval;

[0038] According to the traversal results, the selection curve number that maximizes the total energy consumption reduction in the interval is obtained under the condition of the total surplus time of the subsequent interval. Each time the step S4 is returned, the value of the curve index number k is set to k+1.

[0039] Further, the specific steps of step S5 are as follows:

[0040] Perform inner loop processing. Initialize the surplus time j = W, and traverse from the surplus time j = W to j = Curve[i][k].ΔTime. Each time step S5 is returned, set the value of the surplus time j to j - 1. If the surplus time j < Curve[i][k].ΔTime, then return to step S4, where j represents the surplus time, W represents the total surplus time of the entire line, that is, the time by which the operation plan time exceeds the maximum capacity operation time, Curve[i][k] represents the k-th curve in the i-th section, which is a structure including time and energy consumption, and ΔTime represents the surplus time by which this curve exceeds the maximum capacity operation curve of this section;

[0041] According to the traversal results, find the curve combinations selected for each section under different total surplus times, where the problem of finding the surplus time is transformed into a grouped knapsack problem.

[0042] Further, the expression of the objective function for transforming the problem of finding the surplus time into a grouped knapsack problem is as follows:

[0043]

[0044] where Z represents the objective function, m represents the number of sections, n i represents the total number of curves in the i-th section, E i_max represents the operating energy consumption under maximum capacity in the i-th section, E i,k represents the energy consumption when the k-th curve is adopted in the i-th section, x i,k is a decision variable. When the k-th curve is adopted in the i-th section, x i,k = 1, otherwise, x i,k = 0;

[0045] The constraint conditions for transforming the problem of finding the surplus time into a grouped knapsack problem are as follows:

[0046]

[0047]

[0048] where T i,k represents the energy consumption when the k-th curve is adopted in the i-th section, T i_max represents the operating time under maximum capacity in the i-th section, T total represents the total surplus time of the entire line.

[0049] The beneficial effect of the above further solution is that the present invention performs initialization and discrete processing of the offline database through the above operations.

[0050] Furthermore, the expression of the energy consumption reduction newEngergy brought about by selecting a new curve number in the current interval is as follows:

[0051] newEnergy=dp[i-1][j-Curve[i][k].ΔTime]+Curve[i][k].ΔEnergy

[0052] Curve[i][k].ΔTime=T i,k -T i_max

[0053] Curve[i][k].ΔEnergy=E i,k -E i_max

[0054] Where Curve[i][k] represents the information of the kth curve in the i-th interval, ΔTime represents the extra time of the curve relative to the maximum capacity curve in the interval, ΔEnergy represents the reduced energy consumption of the curve relative to the maximum capacity curve in the interval, Curve[i][k].ΔTime represents the time increase of the kth curve in the i-1th interval relative to the maximum capacity curve in the i-1th interval, Curve[i][k].ΔEnergy represents the energy consumption reduction of the kth curve in the i-1th interval relative to the maximum capacity curve in the i-1th interval, T i,k represents the energy consumption under the kth curve in the ith interval, T i_max represents the running time at the maximum capacity in the i-th interval, E i_max represents the operating energy consumption at the maximum capacity in the i-th interval, E i,k Represents the energy consumption under the kth curve in the i-th interval.

[0055] The beneficial effect of the above further solution is that the present invention updates the selected curve of the interval to reach the maximum value of the objective function in the remaining time when the curve information of the previous interval is known through a numerical comparison at each traversal. Because there is only one step of numerical comparison, the efficiency of online calculation is improved. BRIEF DESCRIPTION OF THE DRAWINGS

[0056] Figure 1 Schematic diagram of the Pareto frontier for optimal train operation in the background technology.

[0057] Figure 2 It is a schematic diagram of energy saving effect under different operating time allocations in the background technology.

[0058] Figure 3 Schematic diagram of the most energy-saving control strategy for a bicycle.

[0059] Figure 4 The figure is a flow chart of the method of the present invention. DETAILED DESCRIPTION

[0060] The specific implementation modes of the present invention are described below so that those skilled in the art can understand the present invention. However, it should be clear that the present invention is not limited to the scope of the specific implementation modes. For those of ordinary skill in the art, as long as various changes are within the spirit and scope of the present invention as defined and determined by the attached claims, these changes are obvious, and all inventions and creations utilizing the concept of the present invention are protected.

[0061] Example

[0062] Before describing the present invention, the theoretical results involved in the present invention are described first.

[0063] (1) Optimal energy-saving strategy for a single train and a single section:

[0064] The optimal control strategy for a single train is to reasonably insert the coasting condition on the basis of the maximum capacity curve to ensure energy saving while ensuring the punctual operation time of the section. The maximum capacity curve of a single train includes maximum traction, cruising, and maximum braking. The operating energy consumption at this time is the highest, and there is also surplus time. By finding the coasting starting point on the maximum capacity outer envelope curve, a four-stage operation strategy of "maximum traction-cruising-coasting-maximum braking" or "maximum traction-coasting-maximum braking" operating condition sequence is formed. By finding a curve that meets the operation time (such as Figure 3 The optimal operating condition sequence under a given operating time can be found by calculating the optimal curve of a single interval under a given surplus time, and the relationship between "time-energy consumption" can be obtained to form Figure 2 The Pareto curve shown in Figure 1 is used to establish an offline database.

[0065] (2) Convert the problem of finding surplus time into a grouping knapsack problem:

[0066] The surplus time of the entire line is regarded as the backpack capacity, the surplus time allocated to each interval is regarded as the item, and the energy consumption reduced by the curve relative to the maximum capacity curve of the interval is regarded as the value. The problem is transformed into how to reasonably allocate the surplus time to each interval so as to maximize the reduction of energy consumption. The objective function is modified accordingly:

[0067]

[0068] Where Z represents the objective function, m represents the number of intervals, and n i represents the total number of curves in the i-th interval, E i_maxrepresents the operating energy consumption at the maximum capacity in the i-th interval, E i,k represents the energy consumption (equivalent to the value of the item) under the kth curve in the ith interval, x i,k is a decision variable. When the kth curve is used in the i-th interval, x i,k =1, otherwise, x i,k =0.

[0069] In this embodiment, the interval is the grouping, which is called grouping in the grouped knapsack problem, and the interval in this problem is the grouping.

[0070] At the same time, the following constraints must be met:

[0071] 1. Only one curve can be selected in each interval:

[0072]

[0073] Among them, i represents the interval, m represents a total of m intervals on the entire line, and the maximum index number is m.

[0074] 2. The constraint of total surplus time of the whole line is:

[0075]

[0076]

[0077] Among them, T i,k represents the energy consumption (equivalent to the weight of the item) of the kth curve in the i-th group, T i_max represents the running time under the maximum capacity in the i-th group, T total Indicates the total surplus time of the entire line.

[0078] The solution can be obtained quickly by using two-dimensional dynamic programming.

[0079] (3) Define the data structure:

[0080] In the present invention, the following data structures are defined to support the implementation of the algorithm:

[0081] Curve structure: ΔTime: represents the extra time of this curve compared with the maximum capacity operation curve of this interval, in seconds (s); ΔEnergy: represents the energy consumption reduction of this curve compared with the maximum capacity operation curve of this interval, in kilowatt-hours (kWh).

[0082] (4) Create a dynamic programming array:

[0083] Define dp to represent the maximum energy consumption reduction in the first i intervals under the j surplus time, which is (m+1)×(W+1).

[0084] Initialize all elements to negative infinity (indicating an impossible state), that is: dp[i][j] = -∞, dp[i][j] represents the maximum energy consumption reduction of the first i intervals under j surplus time.

[0085] Define CurveChoices[i][j]: used to store the combination of the curve index selected in the first i intervals and at the jth rich time.

[0086] Set the initial state: dp[0][0] = 0, which means that the maximum energy consumption reduction of the entire line is 0 when the surplus time is 0.

[0087] (5) Three-layer loop traversal to obtain the optimal solution:

[0088] Outer loop: The independent variable is the interval number, traversing from the first interval to the last interval. The goal is to calculate the total remaining time of the subsequent interval given the total surplus time and the selected curve of the previous interval, so as to traverse the curve number of the interval.

[0089] The second loop: the independent variable is the selected curve number, traversing from the first curve to the last curve in the interval. The goal is to obtain the selected curve number that can maximize the total energy consumption reduction in the interval given the total surplus time of the subsequent interval.

[0090] Inner loop: The independent variable is the surplus time, and it is traversed in descending order from the maximum surplus time, and the traversal order is from back to front. The goal is to obtain the sequence number of the curve selected in each interval under different total surplus times, and at the same time ensure that only one curve can be selected in each interval, and the curve will not be selected repeatedly.

[0091] The present invention explains the above three-layer loop as follows: the outer loop changes to variable i; the middle loop changes to variable k; the inner loop changes to variable j. Taking variable ikj as an example in the loop, variable i is fixed first, then variable k is fixed, and variable j traverses once; after variable j traverses, variable k increments itself, then variable k is fixed again, and variable j traverses once again; after variable k traverses, variable i increments itself, and variables k and j are reset, and the above process is repeated.

[0092] (6) Update the dynamic programming array:

[0093] When traversing the curve value in reverse, calculate the new value:

[0094] newEnergy=dp[i-1][j-Curve[i][k].ΔTime]+Curve[i][k].ΔEnergy(5)

[0095] Among them, newEnergy represents the energy consumption reduction brought about by selecting a new curve number in the current interval, Curve[i][k] represents the information of the kth curve in the i-th interval, ΔTime represents the extra time of this curve relative to the maximum capacity operating curve of this interval, and ΔEnergy represents the energy consumption reduction of this curve relative to the maximum capacity operating curve of this interval.

[0096] That is, traversing the previous interval reserves surplus time for this curve number, and in this interval, this curve is selected to reduce energy consumption.

[0097] If newEnergy>dp[i][j], update: dp[i][j]=newEnergy.

[0098] Because dp[i][j] is initialized to -∞, it is guaranteed that the selected curve will be updated at least once in each interval, ensuring that each interval is allocated a reasonable running time.

[0099] At the same time, the index of the curve number selected for the interval is recorded: CurveChoices[i][j]=k, where CurveChoices[i][j] represents the curve number selected for the i-th interval when the surplus time is j.

[0100] (7) Generation of curves:

[0101] According to the maximum capacity running time of a single interval recorded by the Pareto curve and the recorded curve index number CurveChoices[i][W], the running time of each interval is obtained, and the operating condition sequence of each interval is generated online according to the most energy-saving driving strategy of a single vehicle.

[0102] Based on the above theoretical analysis, in order to achieve the purpose of the present invention, the present invention involves taking the most energy-saving driving strategy of a single section into consideration, establishing an offline database based on the Pareto curve of "time-energy consumption" under this strategy, and using the grouped knapsack method to allocate the running time of the entire line, thereby optimizing the schedule, using the optimal schedule planned online, and adopting the most energy-saving driving strategy to generate the operating condition sequence of each section, so as to achieve the purpose of energy-saving driving of the entire line. Figure 4 As shown, the present invention provides a train multi-section energy-saving operation curve planning method based on grouping backpacks, and its implementation method is as follows:

[0103] S1. Build an offline database, store the Pareto curves of each section of the train and perform discretization processing, and calculate the maximum capacity operation curve of a single section. The implementation method is as follows:

[0104] S102, according to the maximum capacity operation curves under different vehicle weights in different intervals, obtain the maximum operation time T of interval i i,max and maximum energy consumption Ei,max ;

[0105] S103, calculate the Pareto curve under a given surplus time, discretize the Pareto curve with a certain step length, and record the running time T of the kth curve i,k and energy consumption E i,k ;

[0106] S104. Based on the results of step S102 and step S103, an offline database for the Pareto curve of each section of the train is constructed.

[0107] In this embodiment, the maximum capacity curve is calculated in step S101, its energy consumption and time are obtained in step S102, and the energy consumption at other times is calculated in step S103 to form a Pareto curve.

[0108] In this embodiment, an offline database is established, and the maximum capacity operation curves under different intervals and vehicle weights are generated according to the most energy-saving operation strategy of a single vehicle, and the maximum operation time T of interval i is obtained. i,max and energy consumption E i,max , calculate the Pareto curve under a given surplus time, discretize it with a certain step size, and record the running time T of the kth curve i,k and energy consumption E i,k , the accuracy of the calculation results can be improved through a large number of discretizations.

[0109] S2. Initialize and define parameters, which are as follows:

[0110] Define dp array;

[0111] The meaning and size of dp[i][j] are defined as (m+1)×(W+1); where dp[i][j] represents the maximum energy consumption reduction of the first i intervals under j surplus time, m represents the number of intervals, and W represents the total surplus time of the entire line, that is, the excess time of the operation plan time relative to the maximum capacity operation time.

[0112] Initialize all elements to negative infinity;

[0113] Define CurveChoices[i][j] to store the curve number index combination selected in the first i intervals and at the j surplus time;

[0114] The initial state dp[0][0]=0 is set, where dp[0][0]=0 means that the maximum energy consumption reduction of the entire line is 0 when the surplus time is 0.

[0115] S3, perform outer loop processing, traverse from the first interval to the last interval, and calculate the total remaining time of the subsequent interval for the curve number traversal of the interval under the condition of the total surplus time and the selected curve of the previous interval, which is specifically as follows:

[0116] Perform outer loop processing, initialize the interval number to i=1, and traverse from i=1 to i=m, where m represents the number of intervals;

[0117] According to the traversal results, under the given total surplus time and the selected curve in the previous interval, the selected curve number that can reduce the total energy consumption the most is selected by calculating the total remaining time of the subsequent intervals. Each time the step S3 is returned, the value of the interval number i is set to i+1. In response to the interval number i being greater than m, the step S8 is entered.

[0118] In this embodiment, in the outer loop, the interval number is traversed. The goal is to calculate the total remaining time of the subsequent interval for the curve number traversal of the interval given the total surplus time and the selected curve of the previous interval. From i=1 to i=m, the interval number is initialized to i=1. Each time when returning to S3, i=i+1. If i>m, jump to step S7.

[0119] S4, perform middle-level loop processing, initialize the curve index number k to 0, traverse from the first curve to the last curve in the interval, and obtain the selected curve number that maximizes the total energy consumption reduction in the interval given the total surplus time of the subsequent interval, which is specifically:

[0120] Perform middle-level loop processing, initialize the curve index k to 0, from k = 0 to k = n i Traverse, where n i represents the total number of curves in the i-th interval;

[0121] According to the traversal results, the selection curve number that maximizes the total energy consumption reduction in the interval is obtained under the condition of the total surplus time of the subsequent interval. Each time the step S4 is returned, the value of the curve index number k is set to k+1.

[0122] In this embodiment, in the middle-level loop, the index numbers of each interval are traversed, and the goal is to obtain the selection curve number that maximizes the total energy consumption reduction in the interval given the total surplus time of the subsequent interval. From k = 0 to k = n i Traverse, initialize the curve index number to k = 0, each time you return to S4, k = k + 1, if k>n i , return to step S3.

[0123] S5. Perform inner loop processing to traverse the surplus time in reverse order, starting from the total surplus time W of the whole line and decreasingly traversing to find the curve combinations selected for each interval under different total surplus times. Among them, the problem of finding the surplus time is transformed into a grouped knapsack problem, which is specifically as follows:

[0124] Perform inner loop processing. Initialize the surplus time j = W. Traverse from the surplus time j = W to j = Curve[i][k].ΔTime. Each time step S5 is returned, let the value of the surplus time j be j - 1. If the surplus time j < Curve[i][k].ΔTime, then return to step S4, where j represents the surplus time, W represents the total surplus time of the whole line, that is, the time by which the operation plan time exceeds the maximum capacity operation time, Curve[i][k] represents the k-th curve of the i-th interval, which is a structure including time and energy consumption, and ΔTime represents the surplus time by which this curve exceeds the maximum capacity operation curve of this interval;

[0125] According to the traversal results, find the curve combinations selected for each interval under different total surplus times. Among them, the problem of finding the surplus time is transformed into a grouped knapsack problem.

[0126] In this embodiment, in the inner loop, the surplus time is traversed and processed from j = W to j = Curve[i][k].ΔTime. The goal is to obtain the curve numbers selected for each interval under different total surplus times, and at the same time ensure that each interval can select at most one curve and there will be no repeated selection of curves. Initialize j = W, and j = j - 1 each time step S5 is returned. If the surplus time j < Curve[i][k].ΔTime, return to step S4.

[0127] In this embodiment, the expression of the objective function for transforming the problem of finding the surplus time into a grouped knapsack problem is the above formula (1).

[0128] In this embodiment, the constraint conditions for transforming the problem of finding the surplus time into a grouped knapsack problem are the above formula (3) and formula (4).

[0129] S6. Calculate the energy consumption reduction amount newEnergy brought by selecting a new curve number for the current interval. In response to the energy consumption reduction amount newEnergy being greater than the maximum energy consumption reduction amount dp[i][j], update the maximum energy consumption reduction amount dp[i][j] to be equal to the energy consumption reduction amount newEnergy, and record the curve number indexes obtained from the processed outer loop, middle loop, and inner loop, where dp[i][j] represents the maximum energy consumption reduction amount for the first i intervals under the surplus time j;

[0130] S7. Determine whether the outer, middle, and inner loops have been traversed completely. If so, enter step S8; otherwise, update the traversal variables and return to step S3;

[0131] In this embodiment, the expression for calculating the energy consumption reduction newEnergy brought about by selecting a new curve number in the current interval is the above formula (5).

[0132] In this embodiment, traversing the previous curve reserves the surplus time allocated to this interval, and the energy consumption reduction of this curve is selected in this interval. Only numerical calculations are performed here, and the time complexity is O(i*j*k), which greatly improves the calculation efficiency, where ijk represents three variables: interval, surplus time, and curve number.

[0133] In this embodiment, dp[i][j] is checked and updated: if dp[i][j]=newEnergy, the index of the selected curve number is recorded: CurveChoices[i][j]=k.

[0134] S8, obtaining the running time of each interval according to the single interval curve maximum capacity running time recorded by the Pareto curve in step S1 and the selected curve number index recorded in step S6;

[0135] In this embodiment, the running time of each interval is output: according to the single interval curve maximum capacity running time recorded by the Pareto curve in step S1 and the selected curve number index CurveChoices[i][W] recorded in step S6, the running time T of each interval is output. i =T i,k Output.

[0136] S9. According to the running time of each section, the optimal driving strategy for a single section is used to generate the optimal operating conditions for each section, and the planning of the energy-saving running curve for multiple sections of the train is completed.

[0137] In summary, based on the above design, the present invention has the following effects:

[0138] (1) Based on the above background technology, the present invention adopts the single-vehicle optimal driving strategy, combined with the offline "time-energy consumption" database, to reasonably allocate the running time of the entire line online, and generate the optimal operating condition sequence under the energy-saving timetable. For the total energy consumption of a single train in a single section, an offline "time-energy consumption" database based on the most energy-saving driving strategy is established. Under the condition of keeping the total running time of the entire line unchanged, a grouped knapsack algorithm is adopted for the time allocation problem of each section, the running section is regarded as a group, the allocated running time is regarded as an item, and the total energy consumption is used as the evaluation standard. The goal is to reasonably allocate the surplus time with the lowest total energy consumption of the entire line within the specified time, so as to obtain the most energy-saving curve for each section based on the most energy-saving control strategy under the given time. At the same time, the algorithm design ensures low time complexity to cope with the dynamic re-planning requirements caused by the running time deviation. The present invention uses the knapsack algorithm to solve the problem in the online stage, and verifies the potential and feasibility of reducing energy consumption from a quantitative perspective. In addition, the method combines dynamic programming technology, and only performs one step of numerical calculation and comparison during traversal, which has low time complexity, can effectively deal with the punctuality problem that occurs during online operation, and realizes the timely re-planning function. This flexible adjustment mechanism not only improves the energy efficiency of the train, but also ensures the reliability of operation, and contributes new ideas and methods to energy conservation and emission reduction in modern railway transportation. That is, in online calculation, only one step of numerical comparison can increase the speed of calculation.

[0139] (2) The present invention proposes an optimization method based on the grouped knapsack method for the time allocation problem of a single train running on the entire line. Compared with the previous method of using a priority queue based on the Pareto curve of a single train and a single section and the method of inserting idling operation on the entire line, it has a significant energy consumption reduction effect and higher operating efficiency. The present invention fully considers the influence of regenerative braking energy and realizes the accuracy and efficiency improvement of online calculation by constructing an offline data database. The present invention not only optimizes the time allocation of the entire line and reduces energy consumption, but also combines dynamic programming technology with low time complexity, and can effectively deal with the punctuality problem that occurs during online operation, thereby realizing timely re-planning function.

Claims

1. A train multi-section energy-saving operation curve planning method based on grouping backpack, characterized in that: The following steps are involved: S1. Generate the maximum capacity operation curve according to the most energy-saving operation strategy of the single vehicle, and build an offline database through the discrete Pareto curve; S2, initialization and parameter definition; S3, perform outer loop processing, traverse from the first interval to the last interval, so as to calculate the total remaining time of the subsequent interval for the curve number traversal of the interval given the total surplus time and the selected curve of the previous interval, wherein each interval is regarded as a group, and the surplus time allocated to each interval is regarded as an item; S4, perform middle-level loop processing, initialize the curve index number k to 0, traverse from the first curve to the last curve in the interval, and obtain the selected curve number that maximizes the total energy consumption reduction in the interval given the total surplus time of the subsequent interval, wherein the energy consumption reduction of each curve relative to the maximum capacity of the interval is regarded as its value, and it is required that a curve must be selected in each interval to achieve the maximum filling of the backpack; S5, perform inner loop processing, traverse the surplus time in reverse order, and traverse from the total surplus time W of the whole line to find the curve combination selected in each interval under different total surplus time, wherein the problem of finding surplus time is converted into a grouping knapsack problem; S6. Calculate the energy consumption reduction newEnergy brought by selecting the new curve number in the current interval. In response to the energy consumption reduction newEnergy being greater than the maximum energy consumption reduction dp[i][j], update the maximum energy consumption reduction dp[i][j] to be equal to the energy consumption reduction newEnergy, and record the curve number index obtained by the selected outer loop, middle loop, and inner loop processing, where dp[i][j] represents the maximum energy consumption reduction of the first i intervals under j surplus time; S7, determine whether the traversal of the outer layer, the middle layer and the inner layer is completed, if so, proceed to step S8, otherwise update the traversal variable and return to step S3; S8, obtaining the running time of each interval according to the single interval curve maximum capacity running time recorded by the Pareto curve in step S1 and the selected curve number index recorded in step S6; S9. According to the running time of each section, the optimal driving strategy for a single section is used to generate the optimal operating conditions for each section, and the planning of the energy-saving running curve for multiple sections of the train is completed.

2. The train multi-section energy-saving operation curve planning method based on grouping backpack according to claim 1 is characterized in that: The step S1 comprises the following steps: S101, generating maximum capacity operation curves under different vehicle weights in different intervals according to the most energy-saving operation strategy for a single vehicle; S102, according to the maximum capacity operation curves under different vehicle weights in different intervals, obtain the maximum operation time T of interval i i,max and maximum energy consumption E i,max ; S103, calculate the Pareto curve under a given surplus time, discretize the Pareto curve with a certain step length, and record the running time T of the kth curve i,k and energy consumption E i,k ; S104. Based on the results of step S102 and step S103, an offline database for the Pareto curve of each section of the train is constructed.

3. The train multi-section energy-saving operation curve planning method based on grouping backpack according to claim 1 is characterized in that: The step S2 is specifically as follows: Define the dynamic programming array dp; The meaning and size of dp[i][j] are defined as (m+1)×(W+1); where dp[i][j] represents the maximum energy consumption reduction of the first i intervals under the j surplus time, m represents the number of intervals, and W represents the total surplus time of the entire line, that is, the excess time of the operation plan time relative to the maximum capacity operation time; Initialize all elements to negative infinity; Define the index combination of the curve number CurveChoices[i][j] selected in the first i intervals and at the j-th rich time for storage; Set the initial state dp[0][0]=0, where dp[0][0]=0 means that the maximum energy consumption reduction of the whole line is 0 when the rich time is 0.

4. The train multi-section energy-saving operation curve planning method based on grouping backpack according to claim 1 is characterized in that: The specific content of step S3 is as follows: Perform an outer loop process, initialize the interval number as i = 1, and traverse from i = 1 to i = m, where m represents the number of intervals; According to the traversal result, obtain the curve number selection that maximizes the total energy consumption reduction by calculating the total remaining time of the subsequent intervals under the given total rich time and the curves already selected in the previous intervals. Each time step S3 is returned, set the value of the interval number i to i + 1. When the interval number i is greater than m, enter step S8.

5. The train multi-section energy-saving operation curve planning method based on grouping backpack according to claim 1 is characterized in that: The specific content of step S4 is as follows: Perform middle-level loop processing, initialize the curve index k to 0, from k = 0 to k = n i Traverse, where n i represents the total number of curves in the i-th interval; According to the traversal results, the selected curve number that can maximize the total energy consumption reduction in the given subsequent interval is obtained. Each time the step S4 is returned, the value of the curve index k is set to k+1. If k>n i , return to step S3.

6. The train multi-section energy-saving operation curve planning method based on grouping backpack according to claim 1 is characterized in that: The specific content of step S5 is as follows: Perform an inner loop process, initialize the rich time j = W, and traverse from the rich time j = W to j = Curve[i][k].ΔTime. Each time step S5 is returned, set the value of the rich time j to j - 1. If the rich time j < Curve[i][k].ΔTime, return to step S4, where j represents the rich time, W represents the total rich time of the whole line, that is, the time that the operation plan time is more than the maximum capacity operation time, Curve[i][k] represents the k-th curve in the i-th interval, which is a structure body, and this structure body includes time and energy consumption, and ΔTime represents the rich time that this curve is more than the maximum capacity operation curve of this interval; According to the traversal result, find the curve combinations selected for each interval under different total rich times, where the problem of finding the rich time is transformed into a grouped knapsack problem.

7. The train multi-section energy-saving operation curve planning method based on grouping backpack according to claim 6 is characterized in that: The expression of the objective function for transforming the problem of finding the rich time into a grouped knapsack problem is as follows: Where Z represents the objective function, m represents the number of intervals, and n i represents the total number of curves in the i-th interval, E i_max represents the operating energy consumption at the maximum capacity in the i-th interval, E i,k represents the energy consumption under the kth curve in the ith interval, x i,k is a decision variable. When the kth curve is used in the i-th interval, x i,k =1, otherwise, x i,k =0; The constraint conditions for transforming the problem of finding the rich time into a grouped knapsack problem are as follows: Among them, T i,k represents the energy consumption under the kth curve in the ith interval, T i_max represents the running time at the maximum capacity in the i-th interval, T total Indicates the total surplus time of the entire line.

8. The train multi-section energy-saving operation curve planning method based on grouping backpack according to claim 1 is characterized in that: The expression of the energy consumption reduction newEnergy brought by selecting a new curve number in the current interval is as follows: newEnergy = dp[i - 1][j - Curve[i][k].ΔTime] + Curve[i][k].ΔEnergy Curve[i][k].ΔTime=T i,k -T i_max Curve[i][k].ΔEnergy=E i,k -E i_max Where Curve[i][k] represents the information of the kth curve in the i-th interval, ΔTime represents the extra time of the curve relative to the maximum capacity curve in the interval, ΔEnergy represents the reduced energy consumption of the curve relative to the maximum capacity curve in the interval, Curve[i][k].ΔTime represents the time increase of the kth curve in the i-1th interval relative to the maximum capacity curve in the i-1th interval, Curve[i][k].ΔEnergy represents the energy consumption reduction of the kth curve in the i-1th interval relative to the maximum capacity curve in the i-1th interval, T i,k represents the energy consumption under the kth curve in the ith interval, T i_max represents the running time at the maximum capacity in the i-th interval, E i_max represents the operating energy consumption at the maximum capacity in the i-th interval, E i,k Represents the energy consumption under the kth curve in the i-th interval.

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