CN113947287A

CN113947287A - Electric bus regional dispatching method and system

Info

Publication number: CN113947287A
Application number: CN202111101852.6A
Authority: CN
Inventors: 巫威眺; 林越; 曾坤
Original assignee: South China University of Technology SCUT
Current assignee: South China University of Technology SCUT
Priority date: 2021-09-18
Filing date: 2021-09-18
Publication date: 2022-01-18

Abstract

The invention discloses an electric bus regional dispatching method, which comprises the following steps: establishing a time expansion network model to explain the multi-bus yard scheduling problem of the pure electric buses; setting nodes and arcs of a time expansion network model, and setting the cost of the arcs; further establishing a dual-target integer programming model considering time-of-use electricity price and energy consumption control; processing double targets of a double-target integer programming model by adopting a dictionary order optimization method, and converting a double-target problem into a first target and a second target of a single-target model for solving; designing a branch pricing algorithm to solve the first target of the converted single-target model; taking the optimal solution obtained by the first target as an initial solution of a second target, and solving the second target of the converted single-target model through a commercial solver so as to complete electric bus regional dispatching; the method can reduce the cost, reduce the load peak value of the power grid, improve the safety of the power grid, and has good characteristic and stronger practical application prospect.

Description

Electric bus regional dispatching method and system

Technical Field

The invention relates to the research field of electric bus regional dispatching technology, in particular to an electric bus regional dispatching method and system considering time-of-use electricity price and energy consumption control.

Background

The electric bus has good environmental benefit and social benefit, and provides great development potential for future public transport systems. However, the large-scale adoption of electric buses faces huge obstacles, not only limited in operation range and long charging time, but also limited by the characteristics of the power grid, namely the time-of-use electricity price and the risk of peak load. On the one hand, the operating costs depend to a large extent on the time of use electricity prices and vehicle schedules. On the other hand, the charging demand imbalance caused by vehicle scheduling brings peak load risk, and poses potential threat to the safety of the power grid. Along with the popularization of the electric buses, people increasingly need to carefully design and manage the dispatching of the electric buses, so that the system cost can be reduced, and the safety of a power grid can be guaranteed.

In the electric bus dispatching problem in the pure electric region, the electric buses start from different places, complete a series of bus numbers, charge by utilizing free time and finally return to the original place. The vehicle executes the operation plan, and the operation plan comprises processes of departure, receiving, number of vehicles, waiting, empty running and charging.

In a conventional bus area scheduling model, the minimum total operating cost or the minimum fleet size is usually taken as an optimization target, wherein the total operating cost includes vehicle use cost, distance cost, waiting time cost, fuel replenishment cost and the like. However, in the problem of pure electric bus regional dispatching, the operation problem of a bus enterprise is involved, and the load problem of a power grid is also involved. After the electric bus is connected to a power grid, the urban power consumption is increased sharply, and due to uncertainty of daytime charging time and space, if the bus is charged intensively in a large scale, the load of the power grid is increased, and the safety of equipment is affected. However, the grid load problem and the bus enterprise cost problem conflict with each other in some aspects, the bus enterprise cost is optimal, and a plurality of vehicles are bound to be charged in a low electricity price period, so that the peak value of the grid load is increased. The peak value of the load of the power grid is reduced, the charging requirement of the vehicles is inevitably spread to each time period, and some vehicles may be charged in a high electricity price period, so that extra operation cost is brought to the public transportation enterprises. Therefore, in the pure electric bus regional dispatching model, the problem of operation cost of a bus enterprise needs to be considered, and the problem of lowest load peak value of a power grid needs to be considered.

Disclosure of Invention

The invention mainly aims to overcome the defects and shortcomings of the prior art, and provides an electric public transportation region scheduling method considering time-of-use electricity price and energy consumption control.

The first purpose of the invention is to provide an electric public transportation regional dispatching method;

the second purpose of the invention is to provide an electric public transportation regional dispatching system.

The first purpose of the invention is realized by the following technical scheme:

an electric bus regional dispatching method comprises the following steps:

establishing a time expansion network model, and explaining the multi-yard scheduling problem of the pure electric bus through the time expansion network model;

setting nodes and arcs of a time expansion network model, and setting the cost of the arcs;

according to the cost of nodes, arcs and arcs of the time expansion network model, a dual-standard integer programming model considering time-of-use electricity price and energy consumption control is established;

processing double targets of a double-target integer programming model by adopting a lexicographic order optimization method, wherein the double targets comprise a first target problem and a second target problem, and converting the double-target problem into a first target and a second target of a single-target model for solving;

designing a branch pricing algorithm, and solving a first target of the converted single-target model through the branch pricing algorithm;

and taking the optimal solution obtained by the first target as an initial solution of a second target, and solving the second target of the converted single-target model through a commercial solver, thereby completing electric bus regional dispatching.

Further, the establishing of the time expansion network model specifically includes:

the network is layered according to the parking lot to build a time expansion network model G ═ (V)_k,A_k) Wherein V is a set of kth layer nodes, and A is a set of kth layer arcs;

in the time expansion network, different layers represent different parking lots, and the number of vehicles can be specified to be completed by a certain parking lot; a node representing execution of a plan, the node comprising: a yard starting point or end point, a train number node and a charging plan node; an arc represents a feasible connection between two plans, the arc including: departure arc, receiving arc, number of cars connecting arc and charging arc.

Further, the cost of the set arc specifically is:

the cost in the multi-yard scheduling problem is embodied in the cost of the arc, which is set as:

wherein,

in order to be the arc of departure of the car,

is a connection arc for the number of the vehicle,

in order to be a charging arc,

in order to receive the arc of the vehicle,

representing slave nodesPoint i end position el_iTo node j starting position sl_jEmpty distance of c_dRepresenting a cost per unit distance, c_wRepresenting a unit latency fee, wherein the latency ID_ij＝st_j-et_i-DH_ij，st_jRepresents the start time, et, of node j_iIndicates the end time of node i, DH_ijIndicates the end position el of the slave node i_iTo node j starting position sl_jEmpty time of driving, c_vWhich represents a fixed cost per unit vehicle,

represents a charge fee;

cost of charging

The calculation formula of (2) is as follows:

wherein, P is the charging power of the electric bus, W (t) is the price of electricity at the time t, st_tFor the start time of the charging schedule t, et_tFor the end time of the charging schedule t, c_fThe cost is fixed for charging.

Further, the establishing of the dual-target integer programming model considering the time-of-use electricity price and energy consumption control according to the costs of the nodes, the arcs and the arcs of the time expansion network model specifically comprises:

the dual-standard integer planning model needs to consider the operation cost problem of the public transportation enterprise and also considers the lowest load peak value problem of the power grid; then there are:

Min L (3)

s.t.

wherein,

the time expansion network model is a Boolean variable and represents whether arcs from nodes i to j in the kth layer in the time expansion network model are selected or not;

the continuous variable represents the accumulated driving mileage from the k-th layer vehicle to the node i in the time expansion network model, and the variable is used for tracking whether the accumulated driving mileage of the vehicle exceeds the upper limit of the driving mileage;

representing the cost of the k-th layer nodes i to j;

representing the distance from the node i to the node j at the k layer; g represents the upper limit of the accumulated driving mileage of the bus; n represents the upper limit of the fleet scale;

representing the upper capacity limit of the yard k;

indicating charging plan T_jThe upper capacity limit of the located charging station; l represents a load peak value, and is the maximum number of vehicles charged in the same time period by each charging station;

in the objective function (2), minimizing the total cost is taken as an optimization objective; in the objective function (3), the load peak is minimized as a target; constraint (4) is a train number coverage constraint, which indicates that each train number has and is only executed by one bus; the constraint (5) is a flow conservation constraint, which means that all nodes except the starting point and the end point of the same layer need to obey the flow conservation constraint; constraint (6) is an accumulated traveled distance calculation formula, represents the accumulated traveled distance of the node j, and is equal to the accumulated traveled distance of the front node i plus the distance between the node i and the node j; constraint (7) indicates that the accumulated travel mileage is cleared to be 0 at the starting point or the charging station, and represents that the vehicle starts from the station or the vehicle is fully charged at the charging station; the constraint (8) indicates that the accumulated mileage cannot exceed the maximum mileage; constraint (9) is a fleet size limit, indicating that the number of vehicles cannot exceed the maximum fleet size; the constraint (10) is a yard capacity limit, indicating that the number of vehicles emanating from the yard cannot exceed the maximum capacity of the yard; the constraint (11) is a charging station capacity limit, indicating that the number of vehicles on the same charging plan cannot exceed the maximum capacity of the charging station; the constraint (12) is a load constraint, which indicates that the load of each charging station does not exceed a load peak value; the constraint (13) indicates that the decision variable is a0, 1 variable. The constraint (14) represents that the accumulated driving mileage of the vehicle is more than or equal to 0;

the constraint terms (6) and (8) are subjected to linearization processing because nonlinear terms exist; here, the large M method is used, and for the constraint (6), the following linear formula is used for substitution:

wherein M is a large normal amount; when in use

When the temperature of the water is higher than the set temperature,

it is obvious that

If true; when in use

When the temperature of the water is higher than the set temperature,

constraining(15) And (16) are relaxed;

similarly, for constraint (8), the following linear formula is used for substitution:

from this point, a dual-standard integer programming model is constructed.

Further, the method for processing the double targets of the double-target integer programming model by the lexicographic order optimization method converts the double-target problem into the first target and the second target of the single-target model for solving, and specifically comprises the following steps: the first objective is a minimum operation cost objective, and the second objective is a minimum load peak objective; converting the double targets of the double-target integer programming model into a minimized operation cost target of a minimized expense problem model and a minimized load peak target of a minimized load peak problem model;

wherein, the minimization cost problem model is as follows:

s.t.

Eqs:

obtaining an optimal solution when solving the first objective

Then, will restrict

Adding the load peak value into a constraint condition, and solving a minimized load peak value problem taking an objective function as a target; the model is as follows:

MinL (28)

s.t.

Eqs:

wherein,

is a Boolean type variable, a tableIndicating whether an arc from a node i to a node j at the k layer in the time expansion network model is selected;

representing the cost of the k-th layer nodes i to j;

representing the upper capacity limit of the yard k;

indicating charging plan T_jThe upper capacity limit of the located charging station; l denotes a load peak value, where the maximum number of vehicles charged for the same time period for each charging station.

Further, the branch pricing algorithm is designed, and the first target of the converted single-target model is solved through the branch pricing algorithm; the method specifically comprises the following steps: designing an efficient branch pricing algorithm, providing a special heuristic rule and a train number chain pool acceleration strategy, and solving by adopting the algorithm: the first objective is a minimum operating cost objective;

the minimum operation cost problem is solved by adopting a column generation algorithm, an original problem is converted into a column generation main problem and a subproblem, wherein the main problem is a set segmentation problem of a train number chain, and the subproblem is a shortest-path problem with resource limitation:

for the main problem:

limiting the main problem, i.e. solving the set segmentation problem of the train number chain, the solution model RMP _ COST is as follows:

(RMP_COST)

min∑_r∈Rc_rz_r (41)

s.t.

∑_r∈Rz_r≤N (45)

in the RMP _ COST model, the decision variable is z_rIndicating whether the train number chain r is selected; r is the set of train chains that bound the main problem, c_rFor the cost of the train time chain R e R,

the parameter is a Boolean type parameter and indicates whether the train number chain starts from a k train yard or not;

representing whether a train number chain r covers a node S belonging to S or not for a Boolean type parameter, wherein S is a train number set;

the method comprises the steps that a Boolean type parameter is used for representing whether a train number chain r covers a node T belonging to T, wherein T is a charging plan set; n represents the upper limit of the fleet size,

the upper limit of the capacity of the yard k is shown,

indicating charging plan T_tThe upper capacity limit of the located charging station;

in order to generate an objective function (41) that limits the constraints of the main question, representing a minimum operating cost, whose value is equal to the sum of the costs of the selected train chains; the constraint (42) represents a yard capacity constraint; the constraint (43) represents a train-number-unique coverage constraint; the constraint (44) represents a charging station capacity constraint; the constraint (45) represents a vehicle maximum size limit; the constraint (46) represents the value range of the decision variable, z_rIs a boolean variable;

for dual variables, linear relaxation, i.e. z, will usually limit the main problem_rChanging the Boolean type variable into the value range of [0, 1%]A continuous type variable of (1);

for the sub-problem:

for the minimization problem, when the inspection number of all the possible rows and columns is more than or equal to 0, the introduced rows are not used for improving the problem, and the minimization problem obtains an optimal value; for the major problem of train number chain set segmentation, the dual variables of the constraints (42) to (45) are respectively: alpha is alpha_k、β_s、γ_t、π(k∈K,s∈S,t∈T)；

The sub-problem is to find the train number chain with the minimum number of tests, namely to find the shortest path in the network, and the shortest path with resource limitation is the problem because the continuous mileage constraint of the train number chain needs to be considered; the subproblem model is as follows:

(SUBP_COST)

s.t.

wherein

Comprises the following steps:

in the SUB _ COST model, the decision variable is

And

is a boolean variable representing whether the arc (i, j) of the k-th layer is selected;

the accumulated driving mileage of the kth layer node i is obtained; g is the maximum driving range of the busA process;

an objective function (47) representing a minimum train pass number, whose value is equal to the sum of the paths of the various selected edges; the constraint (48) indicates that the train number chain is sent from the starting point and is only one; the constraint (49) is a flow conservation constraint, which means that all nodes except the starting point and the end point of the same layer need to obey the flow conservation constraint; constraint (50) is an accumulated traveled distance calculation formula, represents the accumulated traveled distance of the node j, and is equal to the accumulated traveled distance of the front node i plus the distance between the node i and the node j; constraint (51) represents that the starting point or the charging station is out, the accumulated driving mileage is cleared to be 0, and represents that the vehicle starts from the station or the vehicle is fully charged in the charging station; the constraint (52) indicates that the accumulated mileage cannot exceed the maximum mileage; constraint (53) indicates that the decision variable is a0, 1 variable; the constraint (54) represents that the accumulated driving mileage of the vehicle is more than or equal to 0;

the time expansion network is provided with a plurality of layers, and for each layer K belonging to K, the starting point theta can be independently calculated_kTo the end point theta_k' the shortest path problem, this process adopts the way of parallel computation; when the shortest path problem of each image layer is solved, taking the path with the minimum cost in all the image layers as an optimal solution, namely the optimal solution of the subproblems; and solving the shortest path problem with the resource limitation by adopting a label correction method.

Further, the label correction method specifically includes:

1) label definitions

Order to

Indicates the m-th starting point theta from the yard_kA path to node i; for the path

Label (R)

And path

Associated, having two resources

Wherein

Indicating the origin theta from the yard_kThe sum of the costs of the mth path to node i,

indicating the origin theta from the yard_kThe accumulated driving mileage of the mth path from the node i;

2) label extension

Label (R)

The maintenance adopts forward dynamic programming; in the label correction method, the side (i, j) and the path are corrected

Extending labels of i-nodes

Labels to j nodes

The label extension calculation rule is as follows:

the label extension conditions are as follows:

when the endurance mileage condition is met, the label is expanded, wherein the accumulated endurance mileage also needs to be distinguished whether the j node is a charging station, and if yes, the accumulated endurance mileage needs to be cleared;

3) label domination

The computation speed of the labeling algorithm depends on the number of labels that will be removed when a label is not part of the optimal solution; the label domination rule is used for removing labels which are not the optimal solution so as to accelerate the calculation speed; label (R)

Domination label

If and only if the following conditions are true simultaneously:

if label

Domination label

Then represents the label

Related path

Is not part of the optimal solution because of any pair

Is also applicable to

While

The cost of (2) is lower; therefore, the temperature of the molten metal is controlled,

and

will be removed;

first, the mark correction method needs initialization to set the starting point θ_kThe tag of (1) is set to (0,0), which indicates that the cost and the accumulated endurance mileage at the starting point are both 0; the label correction method needs to record the node number of label update, and check all arcs sent from a certain node in the next iteration, wherein the FIFO node processing rule is adopted, so the nodes are stored by using queues; when a certain node is processed, firstly, pairwise comparison is carried out on all labels of the node, and redundant and low-efficiency labels are deleted by using a label domination rule; if the label expansion condition (43) is met, label expansion is carried out on the label of the node; when the queue is empty, the algorithm backtracks to find the optimal path and the optimal solution.

Further, the branch pricing algorithm adopts a branch strategy, specifically:

branching the connection relation between the nodes:

when the solution of the linear relaxation limited main problem is not an integer, converting the solution of the set segmentation model into the solution of the time expansion network model, and branching the non-branched arcs (i, j); two sub-problems are obtained, each containing branch information x_ij0 and x_ij1 is ═ 1; for branch information x_ijDeleting arcs (i, j) on the time-expanding network as 0; and for branch information x_ij1, the arcs on the time expansion network can be deleted according to the unique constraint of the train number;

branch and boundThe tree has a global upper bound to record the value of the best integer solution found; adopt a depth-first search rule and always solve branch x preferentially_ij＝1；

Constructing an initial solution by adopting a heuristic algorithm, and converting the decimal solution into an integer solution;

the heuristic algorithm is used for solving the problem of the shortest path of the time expansion network to obtain a train number chain by continuously setting the cost of the arc on the time expansion network, and the solving method is the same as that of the subproblem; after the train number chain is obtained, adding the train number chain into a train number chain set, and deleting train number nodes covered on the time expansion network, and train yard nodes and charging nodes with the capacity reaching the upper limit; repeating the above process until all the vehicle numbers are covered

The method specifically comprises the following steps:

and (3) constructing an initial solution in a heuristic manner:

the purpose of constructing an initial solution in a heuristic manner is to make each train number chain cover more train numbers, simultaneously make the cost as small as possible, and simultaneously ensure that a solution scheme meets capacity constraint and vehicle quantity constraint; the step of heuristically constructing an initial solution is as follows:

step 1, time expansion network construction: setting the cost of the k-th layer arc ij as

v is a constant, which is a very small number,

the cost of the k-th layer arc ij; if the j node is a train number node, μ equals-1, otherwise μ equals 0, and the vehicle covers more trains by adding this item;

step 2, solving the shortest path problem of the time expansion network to obtain a train number chain, and deleting covered train number nodes, train yard nodes with the capacity reaching the upper limit and charging nodes; the obtained train number chain meets the endurance mileage constraint and does not conflict with covered train numbers, a full-capacity train yard and a charging station;

step 3, repeating the process of Step 2 until all the train number nodes are covered;

the initial solution also adds a manual train number chain which meets all constraint conditions of the main problem and consumes a large amount of cost so as to ensure the feasibility of the problem;

heuristic repair decimal solution:

when solving the subproblems of each branch-and-bound tree, the obtained solution is not an integer solution, at this time, a heuristic repairing decimal solution is adopted, and the method comprises the following steps:

step 1, selecting a train number chain which has the largest decimal solution and is not considered;

step 2, time expansion network construction: the cost of arc ij is set as

If the j node is a node covered by the train number chain, λ is-10, otherwise λ is 0;

step 3, solving the shortest path problem of the time expansion network to obtain a train number chain, and deleting covered train number nodes, train yard nodes with the capacity reaching the upper limit and charging nodes; the obtained train number chain meets the endurance mileage constraint and does not conflict with covered train numbers, a full-capacity train yard and a charging station;

and Step 4, repeating Step 1, Step 2 and Step 3 until all the train number nodes are covered.

Further, the train number chain pool acceleration strategy specifically includes:

the train number chain of the branch and bound tree child nodes utilizes the existing information of the father node, so that the solution of the child nodes is accelerated; designs a train number chain pool R_poolThe system is used for collecting all train number chains generated by each node of the branch and bound; if the node of the currently solved branch-and-bound tree is p, the initial train number chain set R of the main problem of the node p_pCan be driven from the train number chain pool R_poolGet in, but need to delete the train number chain that does not satisfy the branch constraint:

R_p＝R_pool-r (61)

wherein R ∈ R_poolAnd r does not satisfy the branch constraint of p;

in particular, for the branch-and-bound tree root node root,

R_rootit is made up of two parts: heuristically constructing a train number chain generated by an initial solution and an artificial train number chain with high cost;

after the node p is solved, merging the train number chain generated in the column generation process with the train number chain pool to obtain a new train number chain pool:

R_pool＝R_pool∪R_p (62)。

the second purpose of the invention is realized by the following technical scheme:

an electric bus regional dispatching system, comprising:

the time expansion network module is used for establishing a time expansion network model and explaining the pure electric bus multi-yard scheduling problem through the time expansion network model; setting nodes and arcs of a time expansion network model and setting the cost of the arcs;

the dual-target integer programming module is used for establishing a dual-target integer programming model considering time-of-use electricity price and energy consumption control according to nodes and arcs of the time expansion network model;

the conversion module is used for processing the double targets of the double-target integer programming model by adopting a lexicographic order optimization method and converting a double-target problem into a first target and a second target of a single-target model for solving;

the first target solving module is used for designing a branch pricing algorithm and solving a first target of the converted single-target model through the branch pricing algorithm;

the second target solving module is used for solving the second target of the converted single-target model through a commercial solver by taking the optimal solution obtained by the first target as the initial solution of the second target;

and the result output module is used for outputting the scheduling scheme.

Compared with the prior art, the invention has the following advantages and beneficial effects:

the invention explains the pure electric bus multi-yard scheduling problem by establishing a time expansion network model; setting the cost of an arc in a time expansion network; establishing a dual-target integer programming model considering time-of-use electricity price and energy consumption control; processing double targets by a dictionary sequence optimization method, and converting the double target problem into a single target for solving; and designing an efficient solving algorithm to solve the first target of the converted single-target model, and taking the optimal solution obtained by the first target as the initial solution of the second target so as to find a solution with a lower load peak value and a lower operation cost.

Drawings

FIG. 1 is a flow chart of a method of electric bus regional dispatching according to the invention;

fig. 2 is a flow chart of a scheduling method in embodiment 1 of the present invention;

fig. 3 is a schematic diagram of a time expansion network structure in embodiment 1 of the present invention;

FIG. 4 is a flowchart of a branch pricing algorithm in embodiment 1 of the present invention;

fig. 5 is a schematic view of the distribution of the yard and the charging stations in embodiment 1 of the present invention;

FIG. 6 is a time-of-use electricity price chart of Guangzhou city peak valley in example 1 of the present invention;

FIG. 7a is a graph showing the peak load value of each time zone of the charging station at the time when the second target is reduced by the peak load value from 12 hours to 14 hours in the embodiment 1 of the present invention;

FIG. 7b is a graph showing the peak load value of each time zone of the charging station when the charging vehicle is completely removed in the embodiment 1 of the present invention;

fig. 8 is a distribution diagram of the line condition and the bus route in embodiment 1 of the present invention;

FIG. 9 is a comparison graph of the results of the extended FIFO rule and the branch pricing algorithm calculation in the embodiment 1 of the present invention;

fig. 10a is a charging period and price distribution diagram obtained by the extended FIFO rule in embodiment 1 of the present invention;

fig. 10b is a charging period and price distribution diagram calculated by the branch pricing algorithm in embodiment 1 of the present invention;

fig. 11 is a structural diagram of an electric bus area dispatching system in embodiment 2 of the present invention.

Detailed Description

The present invention will be described in further detail with reference to examples and drawings, but the present invention is not limited thereto.

Example 1:

an electric bus region scheduling method is shown in fig. 1, and comprises the following steps:

Specifically, as shown in fig. 2, the contents are as follows:

first, model establishment

The invention discloses an electric bus regional dispatching method considering time-of-use electricity price and energy consumption control, which mainly adopts the following steps: establishing a time expansion network model to explain the multi-bus yard scheduling problem of the pure electric buses; setting the cost of an arc in a time expansion network; establishing a dual-target integer programming model considering time-of-use electricity price and energy consumption control; processing double targets by a dictionary sequence optimization method, and converting the double target problem into a single target for solving; designing an efficient solving algorithm to solve the first target of the converted single-target model; and calling a commercial solver to solve a second target of the converted single-target model.

1. Description of the problem

A certain bus company provides public transport service by using a large number of electric buses, and in daily operation, the vehicles need to be charged, and how to reasonably arrange charging is important content of an electric bus regional dispatching plan. In order to reduce the cost of public transport companies and reduce the peak value of the load of a power grid and improve the safety of the power grid, a scientific and reasonable electric public transport regional dispatching plan needs to be made.

The invention provides a solution for electric bus regional dispatching by considering the electricity prices in different periods and the peak value of the power grid load during charging.

2. Basic assumptions

(1) The travel time assumption is: the travel time for each train is assumed to be constant, and the travel time for different trains may be different in different time periods.

(2) The departure state is assumed: assuming that all electric buses can be fully charged at night, the accumulated endurance mileage is 0 when the buses are sent from the parking lot.

(3) Day charging hypothesis: the electric public transport allows the electric public transport to use free time to go to a charging station for charging in an operation time period, and the electric public transport is supposed to adopt a quick charging mode. The charging station can be arranged at a station and a parking lot, and can also be independently arranged at a certain position. The charging time of all the electric buses is equal to the full charging time of the electric buses, and the electric buses are charged with the maximum power, so that the electric quantity of each bus is full after the charging is finished.

3. Establishing a time expansion network model

In the multi-yard scheduling problem of the pure electric bus, in order to facilitate tracking the yard to which a certain vehicle belongs, the network is layered according to the yard to establish a time expansion network model G (V)_k,A_k) Wherein V is a set of kth layer nodes, and A is a set of kth layer arcs; a time-expanding network is shown in fig. 3.

In the time expansion network, different layers represent different parking lots, and the number of vehicles can be specified to be completed by a certain parking lot.

The node represents and executes a certain plan, and is divided into three types, namely: the train yard starting point or the terminal point, the train number node and the charging plan node. The train number node and the charging plan node are abstracts of the train number and the charging plan on a time expansion network, have the attributes of a starting time, a starting station, an ending time and an ending station, and have the same meaning as the train number and the charging plan.

Arcs represent viable connections between two plans, including departure arcs, number of trains connecting arcs, and charging arcs. The upper limit of the capacity of these arcs is 1, ensuring that each train is only executed by one vehicle. The departure arc is an arc connecting the start of the yard with each train number node, and represents a process of departure of the vehicle and execution of the train number. The receiving arc is an arc connecting each train number node with the terminal of the train yard and represents the process of vehicle receiving. The train number connection arc is an arc connecting a train number node or a charging plan node and the train number node, and corresponds to two situations under actual conditions: 1) waiting: the vehicle waits at the original station and executes the next time; 2) empty driving: and the vehicle runs to other stations in an empty state, waits and executes the train number. And the charging arc is an arc formed by connecting the train number node and the charging plan node, and represents that the vehicle travels to the charging station from the station where the current train number is located in an empty state, and the charging is finished.

In the time expansion network, S represents a vehicle secondary node set, T represents a charging node set, and theta_kDenotes a start point of the k-th layer, Θ'_kIndicating the yard end of the k-th layer. For a train number connecting or charging arc (i, j) ∈ A_kI belongs to S, j belongs to S and T, and the connection condition needs to be satisfied: st_j-et_i-DH_ijNot less than 0, wherein st_jRepresents the start time, et, of node j_iIndicates the end time of node i, DH_ijIndicates the end position el of the slave node i_iTo node j starting position sl_jThe empty time of driving. Feasible train number chain starting point theta from train yard_kStarting, passing through a series of train number nodes and charging plan nodes and meeting the endurance mileage limit, and finally returning to the yard terminal theta'_k. The problem of multi-yard scheduling is to search a plurality of feasible train number chains to ensure that the train number chains can be completely usedAnd covering the train number set S, and simultaneously meeting the capacity constraints of a train yard and a charging station.

4. Setting costs of arcs in a time-extended network

In the multi-yard scheduling problem, the cost items relate to the fixed cost of the vehicle, the cost of the driving distance, the cost of waiting time and the cost of charging. The charging cost includes a price of electricity cost and a fixed charging cost, and the price of electricity cost is related to the charging time, the charging power and the charging fee. Due to the time-of-use pricing mechanism, charging during peak hours pays more electricity than charging during low peak hours. Taking the peak-valley time-of-use electricity price of commercial electricity in Guangzhou city as an example, the electricity price is divided into three stages of peak, flat peak and low peak, wherein the peak electricity price is 0.97 yuan/kilowatt hour, and the low peak electricity price is 0.3 yuan/kilowatt hour, namely, the charging is carried out in the low peak period, and the charging cost is only one third of the peak period. The fluctuation of the electricity price influences the charging cost of the public transport, so the factor of the time-of-use electricity price needs to be considered in the model. In addition, in the charging activity, maintenance of a charging place, personnel expenses, and cost of battery depreciation are also factors to be considered, and these are charging fixed costs. For a charging plan T ∈ T, the charging cost

The calculation formula is as follows:

Thus, the cost of the arc may be calculated as follows:

wherein,

in order to be the arc of departure of the car,

is a connection arc for the number of the vehicle,

in order to be a charging arc,

in order to be the arc of departure of the car,

indicates the end position el of the slave node i_iTo node j starting position sl_jEmpty distance of c_dRepresenting a cost per unit distance, c_wRepresenting a unit latency fee, wherein the latency ID_ij＝st_j-et_i-DH_ij，st_jRepresents the start time, et, of node j_iIndicates the end time of node i, DH_ijIndicates the end position el of the slave node i_iTo node j starting position sl_jEmpty time of driving, c_vWhich represents a fixed cost per unit vehicle,

indicating a charge rate, that varies with the charging period.

And S3, establishing a dual-target integer planning model considering the time-of-use electricity price and energy consumption control.

In the pure electric bus regional dispatching model, the problem of operation cost of a bus enterprise needs to be considered, and the problem of lowest load peak value of a power grid needs to be considered.

Min L(4) s.t.

Wherein,

representing the cost of the k-th layer nodes i to j;

representing the upper capacity limit of the yard k;

indicating charging plan T_jThe upper capacity limit of the located charging station; l represents a load peak value, the maximum number of vehicles charged for the same time period for each charging station.

In the objective function (3), minimizing the total cost is taken as an optimization objective. In the objective function (4), the load peak is minimized as a target. Constraint (5) is a train number coverage constraint, meaning that each train number has and is only executed by one bus. Constraint (6) is a flow conservation constraint, which means that the flow conservation constraint needs to be observed for all nodes (except the starting point and the ending point) on the same layer. And the constraint (7) is an accumulated traveled distance calculation formula, represents the accumulated traveled distance of the node j, and is equal to the accumulated traveled distance of the front node i plus the distance between the node i and the node j. Constraint (8) indicates that at the origin or charging station, the accumulated mileage is cleared to 0, representing the vehicle leaving the station or the vehicle fully charged at the charging station. The constraint (9) indicates that the accumulated mileage cannot exceed the maximum mileage. The constraint (10) is a fleet size limit, indicating that the number of vehicles cannot exceed the maximum size of the fleet. The constraint (11) is a yard capacity limit, indicating that the number of vehicles emanating from the yard cannot exceed the maximum capacity of the yard. The constraint (12) is a charging station capacity limit, indicating that the number of vehicles on the same charging schedule cannot exceed the charging station maximum capacity. The constraint (13) is a load constraint, which means that the load of each charging station does not exceed a load peak. The constraint (14) indicates that the decision variable is a0, 1 variable. The constraint (15) indicates that the vehicle accumulated driving distance is greater than or equal to 0.

The constraint term (7) and the constraint term (9) are subjected to linearization processing because nonlinear terms exist. Here, the large M method is used, and for the constraint (7), the following linear formula is used for substitution:

where M is a large normal amount. When in use

When the temperature of the water is higher than the set temperature,

it is obvious that

If true; when in use

When the temperature of the water is higher than the set temperature,

the constraints (16), (17) are relaxed. Similarly, for constraint (9), the following linear formula is used for substitution:

thus, a mixed integer linear programming dual-target model is constructed.

And S4, processing the double targets by adopting a lexicographic order optimization method, and converting the double-target problem into a single target for solving.

The mixed integer linear programming dual-target model consists of two targets: a minimum operating cost target and a minimum load peak target. High-level information is known before optimization, and the importance degree of reducing the operation cost of the public transportation enterprise is generally greater than the importance degree of reducing the load peak value of a power grid. Therefore, a lexicographic order optimization method is adopted, namely under the condition of giving target preference information, a double-target problem is converted into a single target to be solved.

First, the objective function (4) and the load constraint (13) are not considered, and only the minimization cost problem is solved, which is obviously a single objective problem. Next, the second objective is further optimized when the first objective reaches the optimal value, that is, the minimum load peak is used as a secondary objective to solve under the condition that the operation cost is not worse than the solution obtained in the first objective. Wherein, the minimization cost problem model is as follows:

s.t.

Eqs:(5)-(12)

obtaining an optimal solution when solving the first objective

Then, will restrict

Adding to the constraint condition and solving the problem of minimizing load peak value by taking the objective function as a target. The model is as follows:

MinL (21)

s.t.

Eqs:(5)-(13)

wherein,

representing the cost of the k-th layer nodes i to j;

representing the upper capacity limit of the yard k;

indicating charging plan T_jThe upper capacity limit of the located charging station; l represents a load peak value where the maximum number of vehicles charged for the same time period for each charging station;

and S5, designing an efficient solving algorithm to solve the first target of the converted single-target model.

For the first target minimum operation cost, a high-efficiency branch pricing algorithm is designed, a special heuristic rule and a train number chain pool acceleration strategy are provided, and the algorithm is adopted for solving. FIG. 4 is a flow chart of a branch pricing algorithm.

The problem of the minimized operation cost is expressed as the selection problem of the train number chains, each train number chain meets the continuous voyage mileage constraint and the train number connection constraint, and all the train number chains meet the vehicle number constraint, the yard capacity constraint, the charging station capacity constraint and the train number unique constraint. However, the number of available train number chains is large, and it takes a long time to represent all the train number chains. Therefore, a column generation algorithm is adopted, and the algorithm is not used for processing all train number chains simultaneously, but is only used for carrying out optimization solution through limiting the main problem on the basis of the currently generated train number chains. And the other train number chains are selected to enter the train number chain pool only when the column generation subproblem is judged to be the optimal solution capable of improving and limiting the current main problem, otherwise, the train number chains are delayed all the time. Therefore, the column generation algorithm will only consider columns that can improve the optimal solution of the constraint main problem rather than all possible columns. The problem of the minimized operation cost is solved by adopting a column generation algorithm, and an original problem can be converted into a column generation main problem and a sub-problem, wherein the main problem is a set segmentation problem of a train number chain, and the sub-problem is a shortest path problem with resource limitation.

■ major problem

The constraint main problem is to solve the set segmentation problem of the train number chain, and the solution model RMP _ COST is as follows:

(RMP_COST)

min∑_r∈Rc_rz_r (25)

s.t.

∑_r∈Rz_r≤N (29)

to representThe upper limit of the capacity of the k-shaped parking lot,

indicating charging plan T_tThe upper capacity limit of the located charging station.

An objective function (25) represents the minimum operating cost, whose value is equal to the sum of the costs of the selected train chains. The constraints (26) represent yard capacity constraints. The constraint (27) represents a train unique coverage constraint. The constraint (28) represents a charging station capacity constraint. The constraint (29) represents a vehicle maximum size limit. The constraint (30) represents the value range of the decision variable, z_rIs a boolean variable.

To generate dual variables that limit the constraints of the main problem, the main problem is typically constrained to be relaxed linearly, i.e., z is_rChanging the Boolean type variable into the value range of [0, 1%]Is used as the continuous type variable.

■ subproblems

For the minimization problem, when the check number of all possible rows is greater than or equal to 0, the introduced rows do not improve the problem, and the minimization problem obtains an optimal value. For the major problem of train number chain set segmentation, let the dual variables of constraints (26) - (29) be: alpha is alpha_k、β_s、γ_tπ (K ∈ K, S ∈ S, T ∈ T), then the number of tests for the train number R ∈ R is:

cost of train number chain c_rThe expression can be made by the edge of the time-expanding network:

boolean type parameter

It can also be expressed in a similar manner:

substituting the formula (32) to the formula (35) into the formula (31) can obtain a time expansion network expression of the train number chain R ∈ R check number:

make the inspection number of each arc

In this way, sub-problems can be constructed based on the number of tests for each edge. The sub-problem is to find the train number chain with the minimum number of tests, namely to find the shortest path in the network, and the shortest path problem with resource limitation is caused by the consideration of the mileage constraint of the train number chain. The subproblem model is as follows:

(SUBP_COST)

s.t.

in the SUB _ COST model, the decision variable is

And

the accumulated driving mileage of the kth layer node i is obtained; g is the maximum driving mileage of the bus; .

An objective function (38) represents a minimum train pass number equal to the sum of the paths of the various selected edges. The constraint (39) indicates that the train number chain is only one from the starting point. The constraint (40) is a flow conservation constraint, which means that the flow conservation constraint is to be observed for all nodes (except for the start point and the end point) on the same layer. And the constraint (41) is an accumulated traveled distance calculation formula, represents the accumulated traveled distance of the node j, and is equal to the accumulated traveled distance of the front node i plus the distance between the node i and the node j. Constraint (42) indicates a starting or charging station out, and the accumulated mileage cleared to 0, representing the vehicle departing from the station or the vehicle fully charged at the charging station. The constraint (43) indicates that the accumulated mileage cannot exceed the maximum mileage. Constraints (44) indicate that the decision variables are 0,1 variables. The constraint (45) indicates that the vehicle accumulated driving distance is greater than or equal to 0.

Note that the time-expanding network has a plurality of layers, and for each layer K ∈ K, the starting point theta can be independently calculated_kTo the end point theta_k' shortest path problem, this process can be implemented in parallel computing. And when the shortest path problem of each layer is solved, taking the path with the minimum cost in all the layers as the optimal solution, namely the optimal solution of the subproblem. The shortest path problem of each layer is the shortest path problem with resource limitation, and the shortest path problem with resource limitation can be solved by adopting a label setting method or a label correction method.

But because of

It is possible to be negative and therefore there may be negatively weighted arcs in the network, which makes label setting unfeasible. Extended label correction is therefore employed.

The linear relaxation-limited main problem is not necessarily integer feasible and often requires the use of a branching strategy. Directly on the decision variable z in the main problem_rBranching is difficult because of the fixed decision variable z_rThe structure of the pricing problem is destroyed. When the decision variable z of a certain column_rWith a fix of 0, the sub-problem may generate a new column similar to that column, making the branching policy inefficient. Therefore, the connection relationship between the nodes can be branched.

In particular, when linear relaxation is limited to the solution of the subject matterWhen the number of the arcs is not an integer, converting the solution of the set segmentation model into the solution of the time expansion network model, and branching the non-branched arcs (i, j); two sub-problems are obtained, each containing branch information x_ij0 and x_ij1 is ═ 1; for branch information x_ijDeleting arcs (i, j) on the time-expanding network as 0; and for branch information x_ijArcs on the time-spreading network can be deleted according to the unique constraints of the train number 1. The branch strategy can embody the branch information on a time expansion network, and has convenience and feasibility.

The branch-and-bound tree has a global upper bound for recording the value of the best integer solution found. These integer solutions are derived from heuristic rules or the RMP solution is a branch-and-bound node of an integer. To obtain integer solutions faster, a depth-first search rule is employed, and branch x is always solved first_ij＝1。

Heuristic algorithms are generally able to obtain a feasible solution at a lower time cost. When the problem size is large, solutions to relax the main problem are usually not integer feasible, which makes it difficult to obtain integer solutions. It is only possible to update the upper bound when the solution yields an integer solution. In addition, the branch-and-bound tree root nodes often need to provide an initial solution that can keep the main problem feasible and reduce the number of iterations of the column generation algorithm. Therefore, a heuristic algorithm is required to construct an initial solution and convert the fractional solution into an integer solution.

Here, a new heuristic algorithm is proposed. This heuristic algorithm may operate on the time-expanding network such that the generated solution satisfies the branching conditions defined on the time-expanding network. The method obtains a train number chain by continuously setting the cost of the arc on the time expansion network and solving the problem of the shortest path of the time expansion network, and the solving method is the same as the subproblem. And after the train number chain is obtained, adding the train number chain into a train number chain set, and deleting the train number nodes covered on the time expansion network, the train yard nodes with the capacity reaching the upper limit and the charging nodes. The above process is repeated until all the vehicle passes have been covered.

Therefore, how to set a reasonable arc cost is very critical. The basic idea of parameter setting is as follows: firstly, approaching to decimal solution (decimal solution restoration) as much as possible; secondly, each train number chain covers the train number as much as possible; and the cost of the train number chain is minimum (the cost of empty running and the like is as low as possible).

■ heuristic construction of initial solution

At the root node of the branch-and-bound tree, an initial solution often needs to be given as a start. A better initial solution may keep the main problem feasible, thereby reducing the number of iterations of column generation. Generally speaking, vehicle fixed costs are a large proportion of the total cost, and a good solution requires that the number of vehicles be reduced as much as possible, which results in the need to cover more vehicle runs per vehicle. The purpose of heuristically constructing the initial solution is to make each train number chain cover more train numbers, make the cost as small as possible, and simultaneously ensure that the solution scheme meets the capacity constraint and the vehicle number constraint. The step of heuristically constructing an initial solution is as follows:

v is a constant, which is a very small number,

and Step 2, solving the shortest path problem of the time expansion network to obtain a train number chain, and deleting the covered train number nodes, the train yard nodes with the capacity reaching the upper limit and the charging nodes. The obtained train number chain meets the endurance mileage constraint and does not conflict with covered train numbers, a full-capacity train yard and a charging station;

step 3. repeat the process of Step 2 until all train number nodes are covered.

Heuristically constructing the initial solution may fail because stricter vehicle quantity or yard capacity constraints are set. Therefore, the initial solution also adds a chain of artificial trains that satisfy all the constraints of the main problem but with a high cost to ensure the feasibility of the problem.

■ heuristic repair decimal solution

When solving the subproblems of each branch-and-bound tree, the resulting solution is often not an integer solution. At this time, a heuristic rule is required to convert the decimal solution into an integer solution. The benefit of repair is that integer solutions can be obtained more quickly, thereby providing an upper bound for the algorithm and reducing the size of the branch-and-bound tree. The constructed train order chain needs to be more "like" a fractional solution, while similar to heuristically constructing the initial solution, the train order chain still needs to cover more trains while keeping the cost as small as possible. The step of heuristically repairing the decimal solution is as follows:

step 2, time expansion network construction: the cost of arc ij is set as

If the j node is the node covered by the train number chain, λ is-10, otherwise λ is 0.

And Step 3, solving the shortest path problem of the time expansion network to obtain a train number chain, and deleting the covered train number nodes, the train yard nodes with the capacity reaching the upper limit and the charging nodes. The obtained train number chain meets the endurance mileage constraint and does not conflict with covered train numbers, a full-capacity train yard and a charging station;

and Step 4, repeating the

steps

1, 2 and 3 until all train number nodes are covered.

When the branch-and-bound solution is used, the train number chain is generated by frequently calling the column generation process at each node, so that more time is consumed. The train number chain of the branch and bound tree child nodes utilizes the existing information of the father node, so that the solution of the child nodes is accelerated; designs a train number chain pool R_poolThe system is used for collecting all train number chains generated by each node of the branch and bound; if the node of the currently solved branch-and-bound tree is p, the initial train number chain set R of the main problem of the node p_pCan be driven from the train number chain pool R_poolGet but need to deleteTrain number chains that satisfy branch constraints:

R_p＝R_pool-r (43)

wherein R ∈ R_poolAnd r does not satisfy the branch constraint of p;

in particular, for the branch-and-bound tree root node root,

R_rootit is made up of two parts: and (4) heuristically constructing a train number chain generated by an initial solution and a manual train number chain with high cost.

R_pool＝R_pool∪R_p (44)

and S6, calling a commercial solver to solve a second target of the converted single-target model.

And for the second target minimum load peak value, adopting a mode of calling a commercial solver, and taking the optimal solution obtained by the first target as an initial solution of the second target so as to find a solution with a lower load peak value and a lower operation cost.

Second, example analysis

■ example 1

As shown in fig. 5, there are 5 yards and 4 charging stations, and the coordinates of the yards are: (26,23), (33,36), (43,29), (56,12), (58,41), the coordinates of the charging station are: (4,23), (12,2), (43,29), (57,39), wherein the points to be selected (43,29) are both yards and charging stations.

In the aspect of electric public transportation, the maximum driving mileage G is set to 250km and the charging time is set to 60min by referring to data of a BYD K7 bus. Cost aspect, set vehicle fixed cost G_v700 yuan, distance cost C_dIs 2.8 yuan, wait for cost C_w0.7 yuan, fixed cost of charging c_fIs 35 yuan. The electricity price adopts the peak-valley time-of-use electricity price in Guangzhou city, and the fluctuation condition of the electricity price along with time is shown in figure 6. It can be seen that the price of electricity is divided into different periods and low priceThe time period is 24: 00-08: 00, and the time period of high electricity price is 14: 00-17: 00 and 19: 00-22: 00.

In order to test data of different scale examples, the number of train runs was set to 50,100,200,400, the number of yards was set to 2,5,8, the number of charging stations was set to 2,4,6,8, and a total of 4 × 3 × 4 to 48 data. For all data, an upper limit of the number of node accesses is set to 200. For the case where the number of trains is 50,100,200, the upper limit of the solution time is set to 12 h. For the case that the number of train numbers is 400 and the number of yards is 2, the upper limit of the solving time is set to 24 h. For the case that the number of train numbers is 400 and the number of yards is 5 and 8, the upper limit of the solving time is set to be 48 h.

For these example data, the CPLEX and the branch pricing algorithm are respectively invoked to calculate the first target, and the results are shown in table 1 below:

TABLE 1

The first column | S | in the table represents the number of vehicle lots, the second column | K | in the table represents the number of vehicle yards, the third column l in the table represents the number of charging stations, the fourth to eighth columns in the table are the results of CPLEX calculations, the fourth column is the number of variables of the dual-target integer programming model, the fifth column is the lower bound, the sixth column is the best integer solution found, and the seventh column is a calculation formula

The eighth column of CPUs is the CPU time calculated by the program in units of s. The ninth to thirteenth columns are the results of the branch pricing calculation, the ninth column is the node visit number, and the tenth to thirteenth columns have the same meaning as the fifth to eighth columns. Columns five through seventh are '-', indicating that no feasible solution can be found by calling CPLEX. The tenth column and the twelfth column of '-' represent that the main problem of the root node is not solved completely, so that the lower bound and the gap value of the problem cannot be obtained. But the branch pricing algorithm runs heuristic rules at the root node, so a feasible solution can be obtained.

As can be seen from the table, CPLEX can quickly obtain the optimal solution in a small-scale calculation example, but when the number of variables exceeds 2 ten thousand, CPLEX can hardly obtain the optimal solution, and even a feasible solution can not be found. In contrast, the branch pricing algorithm has a slower solving speed than CPLEX in the small-scale calculation example, but a feasible solution can still be found in the large-scale calculation example, and the average value of gap is below 10%. However, in the problem that the number of variables exceeds 100 ten thousand, CPLEX and the branch pricing algorithm have difficulty finding a feasible solution. It is noted that the lower bound obtained by the branch pricing algorithm is generally better than that obtained by CPLEX.

Taking the calculation result of 400 turns as the initial solution of the second target calculation, and still calling CPLEX for calculation. To obtain a better solution, it was decided to set the RINS frequency to 20. The actual CPLEX calculation time of all data is 48h, and the results are calculated as the following table 2:

TABLE 2 Dual target calculation results

Fig. 7 shows the load peaks of the charging station for the respective time periods. Fig. 7(a) shows that the second target is reduced by the load peaks from 12 hours to 14 hours. Fig. 7(b) shows that the charging vehicle is completely subtracted.

As can be seen from the table, the second objective optimizes the load peaks while also optimizing the cost costs to a small extent. Illustrating that the calculation of the second target has an effect. It can be observed from the table that the second objective can be optimized well when the problem size is relatively small.

■ example 2

The Guangzhou university city is located in the small valley surrounding street of the area of the wine of Guangzhou city, the city areas are distributed on two sides of the Zhujiang, the area is 34.4 square kilometers in total, and the Guangzhou university city is a national first-class university park which is developed by high-grade talent culture, scientific research and communication in the south China and is an 'information port' and an 'intelligence center' in the south China. The city of Guangzhou university has twenty or more public transport lines, and tests are carried out by taking the circuits of the

lines

1, 2, 201 and 202 in the island as backgrounds. The line condition and the bus line distribution are shown in fig. 8, and the bus line condition is shown in table 3.

TABLE 3 bus line situation

The line length is measured by a hundred-degree map, and the one-way driving time is measured and calculated at the average bus operating speed of 20 km/h. The time of the first shift and the time of the last shift and the departure interval can be obtained by inquiring the car network, and the total number of the cars is 379. The operation time is 6:00-23:00, wherein the peak time is 7: 00-9: 00 and 16: 00-18: 00 in the morning, and the peak time is 21:00 and later in the evening. The four lines have 5 stations which are respectively as follows: the system comprises a southern general station of a city national archive, a western road general station of a college city, a sports center general station of the college city, a general station of the suing village of the college city, and a general station of the science center of the college city, wherein vehicles are dispatched and collected from the stations. In addition, at national archives south master station in city, still set up pure electric bus charging station, supply pure electric bus to charge. The maximum size of the vehicle is 100, assuming that the vehicle capacity of each of the central station and the charging station is 30. The schedule of the line is shown in table 4 below:

TABLE 4 running time table

The distance and time relationships between the various sites, as queried by the Baidu map, are shown in tables 5 and 6 below:

TABLE 5 inter-site distances

TABLE 6 inter-site time

In charging, a BYD K6 pure electric bus is taken as an original model, and the driving range of the bus is 260 kilometers. In the actual operation process, in order to prolong the service life of the battery and avoid the situation that the endurance mileage of the vehicle is insufficient, the endurance mileage is usually artificially reduced to avoid deep discharge, and here, the endurance mileage of the vehicle is set to 130 km. Taking the biddi quick-charging type charging device EVA080KG as an example, the quick-charging time of the vehicle is set to 30 minutes. In terms of cost, the fixed cost of the vehicle is 2000 yuan/vehicle, the cost of the driving distance is 3 yuan/km, the waiting cost is 0.1 yuan/min, and the fixed cost of charging is 50 yuan/time. The computer configuration and parameter settings are the same as the basic data of the simulation example.

Based on the principle of simplicity and feasibility, the public transport company mostly adopts a single-line scheduling mode. The main resources of the public transport enterprise under the mode are organized by taking a single bus line as a unit, the vehicles are divided according to the line and fixedly configured, and the charging station is arranged according to the line for attaching or taking care of the convenience of the operation of the single line. The problem of electric bus single-line scheduling can generally adopt an expanded FIFO rule. The expansion FIFO rule still adopts the FIFO rule to connect the train number, but when connecting the next train number, whether the remaining endurance mileage is safe needs to be judged. Safe driving range must be sufficient for the vehicle to return to the station or charging station, i.e. for

The following formula holds simultaneously:

g_i+DH(iθ′)≤DMAX (46)

equation (45) indicates that the vehicle range is sufficient to return to the nearest charging station, and equation (46) indicates that the vehicle range is sufficient to return to the yard. Therefore, when train connection is performed, the expanded FIFO rule is as shown in table 7 below:

TABLE 7 extended FIFO rule for connection of lots

For the real arithmetic problem, an expanded FIFO rule and a branch pricing algorithm are respectively adopted for solving. Wherein, the upper limit of the solving time of the branch pricing algorithm is set to be 72 hours, and the computer configuration is the same as the simulation example. The extended FIFO rule obtains a solution result using 39 vehicles in total, and the total cost is 97188.50 yuan. The branch pricing algorithm explores 88 nodes in total, the gap value is 6.14%, the obtained solving result uses 28 vehicles in total, and the total cost is 76062.78 yuan. It can be seen that the branch pricing algorithm gives better results than the FIFO rule.

TABLE 8 vehicle scheduling scheme

For convenience, the national archive center station of the shorthand city, the urban outer city western road station of the university, the urban sports center station of the university, the urban fringe village center station of the university and the central station of the urban fringe village of the university are A, B, C, D and E, DH represents empty driving, and Charge station charging is represented by Charge. FIG. 9 lists the comparison of cost and number of charging vehicles calculated by the extended FIFO rule and the branch pricing algorithm. As can be seen from fig. 9, the branch pricing algorithm yields results in which the number of vehicles is much better than the extended FIFO rule, which is achieved by increasing the number of charged vehicles and increasing the empty runs appropriately. It was also observed that while the branch pricing algorithm charges a greater number of vehicles than the extended FIFO rule, most vehicles are charged during the peak of the price, and therefore the cost of charging only rises slightly.

Fig. 10 shows the charging period and the electricity price distribution diagram, and as can be seen from fig. 10(a), the extended FIFO rule results in that the charging period selected by the vehicle is just in the peak period of the electricity price. Of course, there is a difference in charging period between different lines, and the loop 1 is mainly charged at 13 hours to 14 hours and 20 hours to 21 hours, and the loop 202 and the loop 2 are mainly charged intensively at 14 hours to 15 hours, and the loop 201 is mainly charged before and after 16 hours. Fig. 10(b) shows the result of the branch pricing algorithm calculation, and since the regional dispatching mode is adopted, it is not possible to distinguish which route the charged vehicle belongs to. As can be seen from fig. 10(b), the vehicles are more inclined to select the peak period of the electricity price for charging, and at the same time, the number of charging vehicles is lower than the result obtained by the extended FIFO rule.

The branch pricing algorithm can obtain a result with better cost in an actual calculation example, which shows that the algorithm has good characteristics and can be popularized to practical application.

Example 2

An electric bus regional dispatching system, as shown in fig. 11, includes:

and the result output module is used for outputting the scheduling scheme.

The above embodiments are preferred embodiments of the present invention, but the present invention is not limited to the above embodiments, and any other changes, modifications, substitutions, combinations, and simplifications which do not depart from the spirit and principle of the present invention should be construed as equivalents thereof, and all such changes, modifications, substitutions, combinations, and simplifications are intended to be included in the scope of the present invention.

Claims

1. An electric bus regional dispatching method is characterized by comprising the following steps:

establishing a time expansion network model through a time expansion network module, and explaining the pure electric bus multi-yard scheduling problem through the time expansion network model;

2. The electric bus regional dispatching method according to claim 1, wherein the time expansion network model is established as follows:

3. The electric bus regional dispatching method according to claim 2, wherein the cost of the set arc is specifically:

wherein,

in order to be the arc of departure of the car,

is a connection arc for the number of the vehicle,

in order to be a charging arc,

in order to receive the arc of the vehicle,

represents a charge fee;

cost of charging

The calculation formula of (2) is as follows:

4. The electric bus regional dispatching method according to claim 1, wherein a dual-target integer programming model considering time-of-use electricity price and energy consumption control is established according to the cost of nodes, arcs and arcs of the time expansion network model, and specifically comprises the following steps:

Min L (3)

s.t.

wherein,

representing the cost of the k-th layer nodes i to j;

representing the upper capacity limit of the yard k;

in the objective function (2), minimizing the total cost is taken as an optimization objective; in the objective function (3), the load peak is minimized as a target; constraint (4) is a train number coverage constraint, which indicates that each train number has and is only executed by one bus; the constraint (5) is a flow conservation constraint, which means that all nodes except the starting point and the end point of the same layer need to obey the flow conservation constraint; constraint (6) is an accumulated traveled distance calculation formula, represents the accumulated traveled distance of the node j, and is equal to the accumulated traveled distance of the front node i plus the distance between the node i and the node j; constraint (7) indicates that the accumulated travel mileage is cleared to be 0 at the starting point or the charging station, and represents that the vehicle starts from the station or the vehicle is fully charged at the charging station; the constraint (8) indicates that the accumulated mileage cannot exceed the maximum mileage; constraint (9) is a fleet size limit, indicating that the number of vehicles cannot exceed the maximum fleet size; the constraint (10) is a yard capacity limit, indicating that the number of vehicles emanating from the yard cannot exceed the maximum capacity of the yard; the constraint (11) is a charging station capacity limit, indicating that the number of vehicles on the same charging plan cannot exceed the maximum capacity of the charging station; the constraint (12) is a load constraint, which indicates that the load of each charging station does not exceed a load peak value; the constraint (13) represents that the decision variable is a0, 1 variable; the constraint (14) represents that the accumulated driving mileage of the vehicle is more than or equal to 0;

wherein M is a large normal amount; when in use

When the temperature of the water is higher than the set temperature,

it is obvious that

If true; when in use

When the temperature of the water is higher than the set temperature,

the constraints (15), (16) are relaxed;

from this point, a dual-standard integer programming model is constructed.

5. The electric bus regional dispatching method according to claim 1, wherein the two targets of the two-target integer programming model are processed by a lexicographic order optimization method, and a two-target problem is converted into a first target and a second target of a single-target model for solving, and specifically: the first objective is a minimum operation cost objective, and the second objective is a minimum load peak objective; converting the double targets of the double-target integer programming model into a minimized operation cost target of a minimized expense problem model and a minimized load peak target of a minimized load peak problem model;

wherein, the minimization cost problem model is as follows:

s.t.

Eqs:

obtaining an optimal solution when solving the first objective

Then, will restrict

MinL (19)

s.t.

Eqs:

wherein,

representing the cost of the k-th layer nodes i to j;

representing the upper capacity limit of the yard k;

6. The electric bus regional dispatching method as claimed in claim 1, wherein a branch pricing algorithm is designed, and a first target of the converted single-target model is solved through the branch pricing algorithm; the method specifically comprises the following steps: designing an efficient branch pricing algorithm, providing a special heuristic rule and a train number chain pool acceleration strategy, and solving by adopting the algorithm: the first objective is a minimum operating cost objective;

for the main problem:

(RMP_COST)

min∑_r∈Rc_rz_r (41)

s.t.

∑_r∈Rz_r≤N (29)

the upper limit of the capacity of the yard k is shown,

for the sub-problem:

(SUBP_COST)

s.t.

wherein

Comprises the following steps:

in the SUB _ COST model, the decision variable is

And

the accumulated driving mileage of the kth layer node i is obtained; g is the maximum driving mileage of the bus;

the time-expanding network has a plurality of layers, for each layerLayer K ∈ K, independently calculable from start θ_kTo the end point theta_k' the shortest path problem, this process adopts the way of parallel computation; when the shortest path problem of each image layer is solved, taking the path with the minimum cost in all the image layers as an optimal solution, namely the optimal solution of the subproblems; and solving the shortest path problem with the resource limitation by adopting a label correction method.

7. The electric bus regional dispatching method according to claim 6, wherein the label correction method is as follows:

1) label definitions

Order to

Label (R)

And path

Associated, having two resources

Wherein

2) label extension

Label (R)

Extending labels of i-nodes

Labels to j nodes

The label extension calculation rule is as follows:

the label extension conditions are as follows:

3) label domination

The computation speed of the labeling algorithm depends on the number of labels, when a label is not part of the optimal solutionThe tag is to be removed; the label domination rule is used for removing labels which are not the optimal solution so as to accelerate the calculation speed; label (R)

Domination label

If and only if the following conditions are true simultaneously:

if label

Domination label

Then represents the label

Related path

Is not part of the optimal solution because of any pair

Is also applicable to

While

and

will be removed;

8. The electric bus regional dispatching method according to claim 6, wherein the branch pricing algorithm adopts a branch strategy, specifically:

branching the connection relation between the nodes:

the branch-and-bound tree has a global upper bound for recording the value of the best integer solution found; adopt a depth-first search rule and always solve branch x preferentially_ij＝1；

The method specifically comprises the following steps:

and (3) constructing an initial solution in a heuristic manner:

v is a constant, which is a very small number,

heuristic repair decimal solution:

step 2, time expansion network construction: the cost of arc ij is set as

9. The electric bus regional dispatching method according to claim 6, wherein the train number chain pool acceleration strategy specifically comprises:

R_p＝R_pool-r (61)

wherein R ∈ R_poolAnd r does not satisfy the branch constraint of p;

is specially characterized in thatFor the root node root of the branch-and-bound tree,

R_pool＝R_pool∪R_p (62)。

10. the utility model provides an electronic public transit regional dispatch system which characterized in that includes:

and the result output module is used for outputting the scheduling scheme.