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CN110949149B - Electric vehicle charging positioning method and system - Google Patents

Electric vehicle charging positioning method and system Download PDF

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CN110949149B
CN110949149B CN201911270634.8A CN201911270634A CN110949149B CN 110949149 B CN110949149 B CN 110949149B CN 201911270634 A CN201911270634 A CN 201911270634A CN 110949149 B CN110949149 B CN 110949149B
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郑声俊
艾闯
李默涵
薛斐
赵明宇
孙广明
汪映辉
石进永
王刚
李�浩
李充
柯慧敏
王冬
李奕杰
张宇峰
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NARI Group Corp
Nari Technology Co Ltd
NARI Nanjing Control System Co Ltd
Hainan Power Grid Co Ltd
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Abstract

The invention discloses an electric vehicle charging positioning method and system, aiming at the problem of charging station site selection caused by randomness of the driving range of an electric vehicle and different charging requirements, establishing an expected flowing charging positioning model of the electric vehicle by analyzing the problem of deterministic flowing charging positioning, and carrying out heuristic solving analysis by using a tabu search algorithm aiming at the problem of electric vehicle random driving in the model so as to obtain an optimal positioning solution. Experimental data show that the tabu search algorithm can provide a high-quality solution in a short calculation time all the time, and theoretical support is provided for planning and positioning of the electric vehicle charging station.

Description

Electric vehicle charging positioning method and system
Technical Field
The invention particularly relates to an electric automobile charging positioning method and system, and belongs to the technical field of electric automobile driving safety.
Background
According to the report of the international energy agency, transportation accounts for nearly one fourth of the global energy-related carbon dioxide emission, so that the electric automobile becomes the best choice for replacing the traditional fuel oil automobile. At present, the holding capacity of electric vehicles is increased explosively, and as the last half year of 2019, the holding capacity of pure electric vehicles in China reaches 281 thousands of vehicles, which account for 81.74 percent of the total amount of new energy vehicles. The rapid development of electric vehicles urgently needs the construction of matched charging facilities, the number and the positions of charging stations need to be planned to reduce the investment cost of the charging facilities, and the charging requirements of regional electric vehicles are met in an optimized manner, and the optimization problem is called a mobile charging positioning problem. This problem is generally assumed to be deterministic and known when analyzing the driving range of an electric vehicle, but this does not correspond to the actual case of travel of an electric vehicle.
Therefore, the change of the driving range is more meaningful to be taken into the mobile charging positioning problem for practical application. In addition, the charging demand also has a non-negligible influence on the location problem of the charging station, and the coverage flow of the charging demand in the road network has a very high reference value for the location of the charging station.
Disclosure of Invention
The invention aims to overcome the defects of the prior art, provides a method and a system for positioning charging of an electric automobile, and solves the problems of difficult charging and random charging positions of the electric automobile.
In order to solve the technical problem, the invention provides a charging positioning method for an electric vehicle, which is characterized by comprising the following steps of:
by analyzing the problem of deterministic mobile charging positioning and considering the influence caused by the randomness of the driving mileage, an expected mobile charging positioning model of the electric automobile is established to ensure that the electric automobile realizes charging in all possible ranges;
and solving the expected mobile charging positioning model of the electric automobile to obtain the charging position of the electric automobile.
Further, the analyzing the deterministic flow charging localization problem comprises:
the deterministic flow charging localization problem is described using the FRLM formula, which is expressed as follows:
Max∑ q∈Q f q y q (1)
Figure BDA0002314057890000021
Figure BDA0002314057890000022
Figure BDA0002314057890000023
∑ j∈N\N' x j ＝p (5)
Figure BDA0002314057890000024
Figure BDA0002314057890000025
Figure BDA0002314057890000026
wherein Q is the journey, Q is the set of journeys of the electric automobile driver from the departure place to the destination in the road network, R is the journey of the electric automobile, f q Representing the flow of the electric vehicle in the journey q; y is q Indicates whether the trip q is covered; x is the number of k Indicating whether a charging station is established at node k; x is the number of j Indicating whether to open the charging station;
Figure BDA0002314057890000027
represents from O' q To D' q When passing after node k belongs to N q A set of nodes of (a); n is a set of road network nodes, N 'represents a set of repeating nodes, p is the number of charging stations to be built, O' q Starting point O for journey q q Repetition of, D' q For journey q destination D q Repetition of (A), (B), (C) and (C), N q Is O' q And D' q The set of nodes of the shortest path between them,
Figure BDA0002314057890000028
is from O' q To D' q When passing before node l belongs to N q The set of nodes of (a) is,
Figure BDA0002314057890000029
is a circulation section [ k, l]The length of the stroke q over which the stroke q runs,
Figure BDA00023140578900000210
are assigned variables.
Further, the influence of the randomness of the driving range is considered to include:
defining a continuous variable z taking into account the coverage probability of a trip q ∈[0,1]For all nodes l ∈ N q \{O' q Is assigned to a position located at the length of the loop segment
Figure BDA0002314057890000031
Charging station with a distance less than the distance traveled
Figure BDA0002314057890000032
Is expressed as:
Figure BDA0002314057890000033
wherein, R (omega) represents the driving distance of the electric automobile, wherein omega represents a given random condition; g represents an accumulated density function and defines
Figure BDA0002314057890000034
Further, the electric vehicle expected flow charging positioning model comprises:
obtaining an expected flowing charging positioning model of the electric automobile according to a formula FRLM for determinacy of a flowing charging position problem and the coverage probability of a stroke;
the expected flow charge localization model formula is as follows:
Max∑ q∈Q f q z q (10)
Figure BDA0002314057890000035
Figure BDA0002314057890000036
Figure BDA0002314057890000037
further, the solving of the expected flowing charging positioning model of the electric vehicle comprises:
and solving the expected mobile charging positioning model of the electric automobile by adopting a tabu search algorithm.
Correspondingly, the invention also provides an electric automobile charging positioning system which is characterized by comprising a charging positioning model establishing module and a charging positioning model solving module;
the charging positioning model establishing module is used for establishing an expected flowing charging positioning model of the electric automobile by analyzing the problem of deterministic flowing charging positioning and considering the influence caused by the randomness of the driving mileage so as to ensure that the electric automobile realizes charging in all possible ranges;
and the charging positioning model solving module is used for solving the expected mobile charging positioning model of the electric automobile to obtain the charging position of the electric automobile.
Further, in the charging location model building module, the analyzing the deterministic flowing charging location problem includes:
the deterministic flow charging localization problem is described using the FRLM formula, which is expressed as follows:
Max∑ q∈Q f q y q (1)
Figure BDA0002314057890000041
Figure BDA0002314057890000042
Figure BDA0002314057890000043
∑ j∈N\N' x j ＝p (5)
Figure BDA0002314057890000044
Figure BDA0002314057890000045
Figure BDA0002314057890000046
wherein Q is a journey, Q is a set of journeys of an electric vehicle driver from a departure place to a destination in the road network, R is a journey of the electric vehicle, f q Representing the flow of the electric vehicle in the journey q; y is q Indicates whether the trip q is covered; x is the number of k Indicating whether a charging station is established at node k; x is the number of j Indicating whether the charging station is opened;
Figure BDA0002314057890000047
represents from O' q To D' q When passing after node k belongs to N q A set of nodes of (a); n is a set of road network nodes, N 'represents a set of repeating nodes, p is the number of charging stations to be built, O' q Starting point O for journey q q Repetition of, D' q For journey q destination D q Repetition of (A), (B), (C) and (C), N q Is O' q And D' q The set of nodes of the shortest path between,
Figure BDA0002314057890000048
is from O' q To D' q When passing before node l belongs to N q The set of nodes of (a) is,
Figure BDA0002314057890000049
is a circulation section [ k, l]The length of the stroke q over which the stroke q runs,
Figure BDA0002314057890000051
are assigned variables.
Further, in the charging location model building module, the considering of the influence caused by the randomness of the traveled mileage includes:
defining a continuous variable z taking into account the coverage probability of a trip q ∈[0,1]For all nodes l ∈ N q \{O' q Is assigned to a position located at the length of the loop segment
Figure BDA0002314057890000052
Charging station with a distance less than the distance traveled
Figure BDA0002314057890000053
Is represented as:
Figure BDA0002314057890000054
wherein, R (omega) represents the driving distance of the electric automobile, wherein omega represents a given random condition; g represents a cumulative density function and defines
Figure BDA0002314057890000055
Further, in the charging location model building module, the electric vehicle expected mobile charging location model includes:
obtaining an expected flowing charging positioning model of the electric automobile according to a formula FRLM for determinacy of a flowing charging position problem and the coverage probability of a stroke;
the expected flow charge localization model formula is as follows:
Max∑ q∈Q f q z q (10)
Figure BDA0002314057890000056
Figure BDA0002314057890000057
Figure BDA0002314057890000058
further, in the charging location model solving module, the solving of the expected flowing charging location model of the electric vehicle includes:
and solving the expected mobile charging positioning model of the electric automobile by adopting a tabu search algorithm.
Compared with the prior art, the invention has the following beneficial effects: the invention realizes the charging positioning of the electric automobile, fully exerts the development potential of the electric automobile, and solves the problems of difficult charging and random charging positions of the electric automobile, thereby ensuring that the electric automobile is not interrupted due to insufficient electric quantity in the normal driving process.
Drawings
Fig. 1 is a flow chart of a tabu search algorithm.
Detailed Description
The invention is further described below with reference to the accompanying drawings. The following examples are only for illustrating the technical solutions of the present invention more clearly, and the protection scope of the present invention is not limited thereby.
Aiming at the randomness of the vehicle running range and the problem of location of a charging station caused by different charging requirements, the invention establishes the expected mobile charging positioning model of the electric vehicle, and utilizes a tabu search algorithm to carry out heuristic solving analysis aiming at the random problems of the running state of the electric vehicle, the residual electric quantity of a battery and the like in the model, thereby shortening the time for obtaining optimal positioning.
The invention discloses a charging positioning method of an electric automobile, which comprises the following steps:
firstly, establishing an expected mobile charging positioning model of the electric automobile by analyzing the problem of deterministic mobile charging positioning and considering the influence caused by the randomness of the driving mileage, and ensuring that the electric automobile realizes charging in all possible ranges;
the method specifically comprises the following steps:
(1) Put forward the formula of Flow Recharging Location Model (FRLM)
1) Description of the problem
Consider a road network G (N, a), where N represents a set of nodes and a represents a set of arcs linking the nodes. The demand is modeled as a set Q of predetermined trips to be taken by the driver of the electric vehicle, each trip Q of the set Q of trips corresponding to a given origin O q E N travel to given destination D q E N and return, assuming all drivers performing the trip q follow the pass O q And D q The shortest path therebetween, and there is no desire to deviate from this path for charging. Flow f of stroke q q Corresponding to the unit time of O q And D q The number of vehicles traveling in between. Where the distance between each pair of adjacent stations on the path is defined to not exceed the R range, then the journey q is said to be covered. However, as long as the distance between a pair of adjacent charging stations is greater than R, the journey q is considered uncovered. The optimization problem is therefore to determine the best positions to build a predetermined number p of charging stations in the road network in order to maximize the total flow of covered electric vehicles.
The concept of loop segments is introduced to facilitate modeling of the problem. Circulation section [ k, l ]]Defined as a sequence of consecutive arcs intersecting on the shortest path (outgoing and/or return direction) between node k and node l, it is noted that a loop segment [ O ] q ,l]Two different ways can be understood: driver from O q Go to l from start or go to and fro l → O q → l for each trip q, node O is replicated q And D q Is node O' q And D' q Prepared from (O' q ，O q ) And (D) q ，D′ q ) Added to A, circulating section [ O ] q ,l](corresponding [ k, D ] q ]) Represents from O q To l (from k to D) q ) Goes outwards and circulates the section [ O' q ,l](corresponding [ k, D' q ]) Representing a round trip to the origin (destination). Wherein the circulation section [ k, l ]]Length over stroke q
Figure BDA0002314057890000071
The definition is as follows:
(1) For k = O' q And l ∈ N q \{D' q }，
Figure BDA0002314057890000072
(2) For k ∈ N q \{O' q And l = D' q ，
Figure BDA0002314057890000073
(3) For k ∈ N q \{O q ,D q Are equal to l ∈ N q \{O q ,D q }，
Figure BDA0002314057890000074
(4) For k = O' q And l = D' q ，
Figure BDA0002314057890000075
Formula (1) represents if node k = O' q And node l is O' q And D' q On the set of nodes of shortest path therebetween or at D' q O 'is incorporated' q And D' q Define an interpretation for a loop segment, then the loop segment [ k, l ]]Is equal to twice the sum of the arc lengths between k and l, wherein the arc length (m, n) belongs to a subset of the set of consecutive arcs on the shortest path between k and l; in the same way, the conclusion of the formula (2) is the same as that of the formula (1); compared with the formula (1) and the formula (2), the formula (3) has no reciprocating process in the circulating section, and only advances in one direction, so that the circulating section [ k, l ]]Is equal to the sum of the arc lengths between k and l; formula (4) represents, if k = O' q And l = D' q Then cycle section [ k, l]Corresponding to always cycling between a starting point and an ending point, so its length is expressed as infinity.
The definitions of the symbols in the specific steps are shown in table 1.
TABLE 1 definition of symbols in the specific procedures
Figure BDA0002314057890000081
Figure BDA0002314057890000091
2) Put forward FRLM formula
In order to solve the problem of mobile charging location, the invention provides a formula FRLM, if a journey q is covered, after an open charging station in front of an electric vehicle is charged, each node l belongs to N q Should be reachable. Thus, in the case of coverage of the run q, it is necessary to cover for each node l ∈ N q Allocating a charging station within the range of the vehicle distance R
Figure BDA0002314057890000092
It is served so that the Electric Vehicle (EV) driver can charge the vehicle at node k and reach node l. If a charging station is established at node k, x k =1, otherwise 0; if the run q is covered, then y q And =1, otherwise 0.
Introducing a set of binary variables into formula FRLM
Figure BDA0002314057890000093
It is defined as follows, for each trip q, each node l ∈ N q \{O′ q And each node
Figure BDA0002314057890000094
Comprises the following steps:
Figure BDA0002314057890000095
for k ≠ O' q : if the battery of the electric vehicle is charged at the charging station located at the node k, so that the driver can at least drive out to the node l again,
Figure BDA0002314057890000096
otherwise, the value is 0;
Figure BDA0002314057890000097
for k = O' q : if sub-stroke l → O' q Charging of → l is ensured by the charging station of node l or a station thereafter, and the electric vehicle is in D' q To O' q Is traveling along the shortest path traversed by the return direction of (c),
Figure BDA0002314057890000098
the formula for FRLM is as follows:
Max∑ q∈Q f q y q (1)
Figure BDA0002314057890000099
Figure BDA00023140578900000910
Figure BDA00023140578900000911
∑ j∈N\N' x j ＝p (5)
Figure BDA0002314057890000101
Figure BDA0002314057890000102
Figure BDA0002314057890000103
in the formula (f) q For indicating electric vehicles in journey qFlow rate; y is q Representing whether the journey q is covered, if yes, 1; x is a radical of a fluorine atom k Indicating whether a charging station is built at the node k, and if yes, the node k is 1; x is the number of j Indicating whether the charging station is opened or not, wherein the opening is 1;
Figure BDA0002314057890000104
represents from O' q To D' q When passing after node k belongs to N q A set of nodes of (a);
Figure BDA0002314057890000105
represents from O' q To D' q When, the one that passed before node l belongs to N q The node set of (2); n' represents a set of repeating nodes.
The objective function (1) seeks to maximize the total coverage flux, calculated as a weighted sum of the coverage trips. Constraint equation (2) can be viewed as an assignment constraint, stating that if the trip q is covered, every node on the path, l ∈ N q \{O′ q All should be assigned to a single node
Figure BDA0002314057890000106
Constraint (3) defines the relationship between variable w and variable x, if the charging station at node k is not open, then EV cannot be charged at node k, and all variables corresponding to node k
Figure BDA0002314057890000107
Should be set to 0; constraint (4) is a range constraint that ensures that each node l on the path is assigned to a station with a distance less than R if journey q is covered, and all nodes corresponding to journey q if journey q is uncovered
Figure BDA0002314057890000108
All variables are set to 0, and the constraint (4) is not used; the constraint (5) sets the number of charging stations that have to be opened to a predetermined number p; constraints (6) - (8) define the problem variables.
(2) Considering the influence caused by the randomness of the driving mileage and considering the coverage probability of the journey in problem modeling
In practice, the driving range R of the electric vehicle is influenced by many uncertain factors, such as traffic conditions, weather or driving habits, and meanwhile, the randomness of the driving range is considered to have an important influence on problem modeling. In fact in the deterministic problem, whether a journey is covered depends on the position of the charging station, in contrast to when the driving range is random, the coverage becomes an accidental event. In this case, even if many charging stations are opened on the corresponding path, it may no longer be possible to ensure that charging is achieved for all possible ranges. Therefore, the coverage probability of the trip, i.e., the probability that the EV driver can make a round trip from the departure point to the destination without depleting the electric power, needs to be considered in the problem modeling. Defining a continuous variable z q ∈[0,1]Is the coverage probability of the run q. Here, z is q Defined as all nodes l ∈ N q \{O' q Is assigned to a position located at the length of the loop segment
Figure BDA0002314057890000111
Charging station with a distance less than the distance traveled
Figure BDA0002314057890000112
The joint probability of (a) can be obtained:
Figure BDA0002314057890000113
where R (ω) represents a travel distance of the electric vehicle, where ω represents a given random condition for which the value of the EV travel distance R (ω) is assumed to be the same in all road networks; g represents a cumulative density function. The second step of the equation calculates z using the assumption that the travel distance R (ω) is the same in all road networks q Is the probability that the distance traveled is greater than the longest cycle length traveled on trip q. In the third step of the equation, the probability is expressed using the cumulative density function G, where the fourth step of the equation holds because G is a non-decreasing function. Due to the fact that
Figure BDA0002314057890000114
Is a binary variable and G (0) =0, one can obtain
Figure BDA0002314057890000115
Thus, the fifth step of the equation is derived. Finally, by defining
Figure BDA0002314057890000116
The final result of the equation is obtained.
(3) Expected flow charging positioning model establishment
The expected flow charging location model (EFRLM) formula is as follows:
Max∑ q∈Q f q z q (10)
Figure BDA0002314057890000117
Figure BDA0002314057890000118
Figure BDA0002314057890000121
the constraint (11) states that if the journey q has a definite positive probability of coverage (z) q ≧ 0), then for each node l ∈ N q \{O' q During the journey q there must be a node k before node l is passed, so that the vehicle can be charged to reach node l. The constraint (12) will cover the probability variable z q And binary variables
Figure BDA0002314057890000122
Are linked together. The formula indicates the variable z q All zones [ k, l ] calculated as node 1 supplemented by charging stations at node k]Minimum coverage probability. The constraints (3), (5), (6) and (8) are guaranteed to be satisfied by deterministic equations.
And secondly, for the defect of long calculation time required for solving a large expected flowing charging positioning model, a taboo search heuristic algorithm is provided for solving and analyzing the expected flowing charging positioning model so as to obtain a high-quality solution in shorter calculation time:
for small and medium scale examples, a commercial Mixed Integer Linear Programming (MILP) solver may be used to solve for the stochastic flow charging localization model. However, when the size of the road network scale increases, the calculation time required to obtain an optimal solution may become very long. Tabu search can provide a high quality solution to general device location problems and is easy to develop and implement. The procedure for tabu search to solve the desired streaming charge location problem is as follows:
(1) Constructing an initial solution
The process of constructing the initial solution aims at obtaining a set of charging station numbers p that can provide good network coverage, for which the journey is based on its flow value f q When selecting a station to be opened, the descending order of (1) first considers a travel position where the vehicle flow rate is the maximum. When the number p of charging stations that need to be opened is reached, the process ends. However, the coverage probability is not minimized in the desired flow charging location model because its goal is to maximize the expected flow. Thus, when establishing an initial solution, this minimum probability is set as an input parameter and a set of initial number p of sites is established. At the end of the process, the objective function of the resulting solution is evaluated by examining the coverage (or coverage probability) of all trips.
(2) Evaluating an objective function for a given solution
To evaluate the objective function for a given solution, iterations of the runs are required to check which runs are covered and calculate the total (or expected) flow covered. In order to know whether the journey q is covered, the following steps are required: for each cycle segment of q in EFRLM, the probability z of coverage of the run q q Calculated as the minimum of its all-cycle segment coverage probabilities, and then by adding f q z q The target value is updated.
Taboo search algorithm referring to FIG. 1, firstFirstly, establishing an initial solution, and then, solving the optimal feasible solution Sol best Set as initial solution Sol init The optimum target value Obj best Set to an initial target value Obj init The number of iterations nblterwithroutimpr =0 of the tabu search is initialized. The process is realized by exploring Sol init Neighborhood to iteratively improve Sol best Two steps are performed when nblterWithoutImpr < maxWithoutImpr.
Step 1 comprises selecting a site s to open among | N | -p closed sites 1 ，
Figure BDA0002314057890000131
And should achieve the highest expected coverage among all possible open sites. This step may improve the expected coverage, but the solution obtained is not feasible since p +1 charging stations are involved. Therefore, at the end of this step, the tabu list addition s needs to be updated 1 Go to tabuoverest without updating the optimal solution Sol best 。
Step 2 comprises selecting a site s to close among the p +1 open sites 2 ，
Figure BDA0002314057890000132
And should achieve the highest expected coverage among all possible shut down sites. A scofflaw criterion is considered here, i.e. accepting to close a contra site, but will improve the optimal target value.
At the end of step 2, the tabu list needs to be updated, if it is improved after the last shutdown, the optimal solution needs to be updated, otherwise the number of iterations is increased without improvement. When there is no improved Obj best When the iteration number of the tabu search process reaches the maximum limit, the tabu search process is stopped. It is noted that in this process, two tabu lists are required, one for the most recently opened site and the other for the most recently closed site. Wherein the symbol definitions are shown in table 2.
TABLE 2 symbol definitions in tabu search Algorithm
Figure BDA0002314057890000133
Figure BDA0002314057890000141
And thirdly, verifying the feasibility of the method by calculation.
The invention evaluates the performance of the proposed accurate and heuristic solution method through the results of experimental data. All solution algorithms are written in the C + + language. The millp model is realized by using the Concert technology, and solved by using ILOG CPLEX 12.6.2 version. All tests were performed on a personal computer running under the Windows 10 operating system, equipped with Intel i5-3210M core 2Duo (2.50 GHz) and 8GB memory.
In numerical experiments, the road network used in the present invention was randomly generated. First, the | N | nodes are generated, and the coordinates of the nodes are uniformly distributed in [1,1000 ]] 2 And (4) internal random selection. The moving distance between each pair of nodes is calculated as the euclidean distance. The Kruskal algorithm is then applied to determine the minimum spanning tree of | N | -1 nodes, and experiments have also selected | N | additional arcs to be added to a, these arcs being the shortest potential arcs that have not been added to a, so that the order of each node remains below 4. Then M starting point to end point nodes are randomly selected from the nodes belonging to N. The deterministic range R is set to 250km. Assuming that the random range R (ω) follows a Gamma distribution, the shape parameter k is 50 and the scale parameter θ is 5.
The present invention considers the problem from two dimensions: i N | =100, m =50 and i N | =200, m =100, 5 network instances and sets of journeys to cover are randomly generated, for each of these 10 network instances, 9 possible station number p values need to be considered: p ∈ {1,2,3,4,5,10,15,20,25}, resulting in a set of 90 instances in total, where in the representation of each test instance, first represents | N |, then M, and finally p. For example, the example N100M50p10 represents testing a road network including 100 nodes, 50 start/end nodes and 10 charging stations open.
(1) Results of deterministic problems
This section analyzes the numerical performance of the formula FRLM for the deterministic flow charging location problem. Table 3 shows the results obtained with CPLEX on a random generation network. The experimental results show the calculated integrity gap, i.e. the relative difference between the optimal integer feasible solution and the linear relaxation value, the CPU time in seconds (setting the calculation time limit to 10 hours), the number of Branch & Bound nodes obtained by the algorithm within the time limit, while the remaining gap is defined as the relative difference between the optimal integer feasible solution and the optimal upper limit found within the time limit.
Table 3 numerical performance obtained using formula FRLM in random example (average 5 replicates)
Figure BDA0002314057890000151
Figure BDA0002314057890000161
First, from experimental results it can be observed that the average CPU time increases with the road network scale, because: as | N | and M increase, the formula calculation increases. It was also observed through experimental results that the average CPU time trend increased as the value of p increased, because: as long as p ≦ N/2, the number of possible combinations of site deployments may increase. It should be noted that there are exceptions to the small p-value using the formula FRLM. The calculations show that the average calculation time for the random instances is 422 seconds using the FRLM formula. In the random case, the average integrity gap for FRLM was 20.9%. Before finding the optimal solution, the average number of Branch & Bound nodes obtained by the algorithm is 10. Thus, although the order of magnitude of the constraint of the formula FRLM is large, its better compactness enables the mathematical solver CPLEX to solve deterministic variables of the problem more efficiently.
(2) Results of randomness problems
This section analyzes the formula EFRLM that solves the random flow charging location problem. The results in table 4 show that, when considering the randomness of the vehicle driving range and the charging station location problem caused by different charging requirements, the average calculation time of the random example is larger and larger with the increase of the road network (5753 seconds at the maximum of the road network).
Table 4 numerical performance obtained using the formula EFRLM in the random example (average 5 replicates)
Figure BDA0002314057890000171
(3) Performance using tabu search algorithms
As shown in the calculation results of table 4, for large examples, the CPU time required to solve the optimal solution of the MILP formula corresponding to the stochastic problem is still long. The heuristic solution method can obtain a high-quality solution in a short running time, so that the part solves the random problem by using a tabu search algorithm, and the setting is as follows: tabu list size Ntabu =5, maximum number of iterations maxwithoutjmpr =10 allowed without improving the target value, and minimum coverage probability is set to 60% when establishing an initial solution to the desired streaming charge location problem. Table 5 summarizes the results of the heuristic on the random instance of the random problem, where the average tabu gap is obtained, which is defined as the relative gap between the optimal solution found by the heuristic and the optimal solution, and the tabu search heuristic CPU time.
TABLE 5 tabu heuristic Performance of stochastic problem on random instances (5 replicates on average)
Figure BDA0002314057890000181
Figure BDA0002314057890000191
The results of table 5 show that the tabu heuristic provides a near-optimal solution in a short computation time. I.e., the tabu heuristic of EFRLP had an average gap of 0.9% over random instances with an average computation time of 35 seconds. Experimental results also show that for EFRLP, the tabu search heuristic can yield a near-optimal solution with significantly reduced computation time compared to the mathematical solver, i.e., the average computation time of the heuristic is reduced from 4792 to 35 seconds of the solver in all instances. For larger instances (random set of instances N200M100p15, N200M100p20, and N200M100p 25), this reduction is even more pronounced, reducing the average computation time from the solver 6h to 2min using the heuristic.
Correspondingly, the invention also provides an electric automobile charging positioning system which is characterized by comprising a charging positioning model establishing module and a charging positioning model solving module;
the charging positioning model establishing module is used for establishing an expected mobile charging positioning model of the electric automobile by analyzing the problem of deterministic mobile charging positioning and considering the influence caused by the randomness of the driving mileage so as to ensure that the electric automobile realizes charging in all possible ranges;
and the charging positioning model solving module is used for solving the expected mobile charging positioning model of the electric automobile to obtain the charging position of the electric automobile.
Further, in the charging location model building module, the analyzing the deterministic flowing charging location problem includes:
the deterministic flow charging location problem is described using the FRLM formula, which is expressed as follows:
Max∑ q∈Q f q y q (1)
Figure BDA0002314057890000201
Figure BDA0002314057890000202
Figure BDA0002314057890000203
∑ j∈N\N' x j ＝p (5)
Figure BDA0002314057890000204
Figure BDA0002314057890000205
Figure BDA0002314057890000206
wherein Q is a journey, Q is a set of journeys of an electric vehicle driver from a departure place to a destination in the road network, R is a journey of the electric vehicle, f q Representing the flow of the electric vehicle in the journey q; y is q Indicates whether the trip q is covered; x is a radical of a fluorine atom k Indicating whether a charging station is established at node k; x is the number of j Indicating whether the charging station is opened;
Figure BDA0002314057890000207
represents from O' q To D' q When passing after node k belongs to N q A set of nodes of (a); n is a set of road network nodes, N 'represents a set of repeating nodes, p is the number of charging stations to be built, O' q Starting from the journey q q Repetition of, D' q For journey q destination D q Repetition of (A), (B), (C) and (C), N q Is O' q And D' q The set of nodes of the shortest path between them,
Figure BDA0002314057890000208
is from O' q To D' q When passing before node l belongs to N q The set of nodes of (a) is,
Figure BDA0002314057890000209
is a circulation section [ k, l]The length of the stroke q over which the stroke q runs,
Figure BDA00023140578900002010
are assigned variables.
Further, in the charging location model building module, the considering of the influence caused by the randomness of the traveled mileage includes:
defining a continuous variable z taking into account the coverage probability of a trip q ∈[0,1]For all nodes l ∈ N q \{O' q Is assigned to a position located at the length of the loop segment
Figure BDA00023140578900002011
Charging station with a distance less than the distance traveled
Figure BDA00023140578900002012
Is represented as:
Figure BDA0002314057890000211
wherein, R (omega) represents the driving distance of the electric automobile, wherein omega represents a given random condition; g represents a cumulative density function and defines
Figure BDA0002314057890000212
Further, in the charging location model building module, the electric vehicle expected mobile charging location model includes:
obtaining an expected flowing charging positioning model of the electric automobile according to a formula FRLM for determinacy of a flowing charging position problem and the coverage probability of a stroke;
the expected flow charge localization model formula is as follows:
Max∑ q∈Q f q z q (10)
Figure BDA0002314057890000213
Figure BDA0002314057890000214
Figure BDA0002314057890000215
further, in the charging location model solving module, the solving of the expected flowing charging location model of the electric vehicle includes:
and solving the expected mobile charging positioning model of the electric automobile by adopting a tabu search algorithm.
As will be appreciated by one skilled in the art, embodiments of the present application may be provided as a method, system, or computer program product. Accordingly, the present application may take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, the present application may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, and the like) having computer-usable program code embodied therein.
The present application is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the application. It will be understood that each flow and/or block of the flow diagrams and/or block diagrams, and combinations of flows and/or blocks in the flow diagrams and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
The above description is only a preferred embodiment of the present invention, and it should be noted that, for those skilled in the art, several modifications and variations can be made without departing from the technical principle of the present invention, and these modifications and variations should also be regarded as the protection scope of the present invention.

Claims (4)

1. A charging positioning method for an electric automobile is characterized by comprising the following steps:
by analyzing the problem of deterministic mobile charging positioning and considering the influence caused by the randomness of the driving mileage, an expected mobile charging positioning model of the electric automobile is established to ensure that the electric automobile realizes charging in all possible ranges;
solving an expected flowing charging positioning model of the electric automobile to obtain a charging position of the electric automobile;
the analyzing deterministic streaming charging location problems includes:
the deterministic flow charging localization problem is described using the FRLM formula, which is expressed as follows:
Max∑ q∈Q f q y q (1)
Figure FDA0003828959610000011
Figure FDA0003828959610000012
Figure FDA0003828959610000013
∑ j∈N\N' x j ＝p (5)
Figure FDA0003828959610000014
Figure FDA0003828959610000015
Figure FDA0003828959610000016
wherein Q is the journey, Q is the set of journeys of the electric automobile driver from the departure place to the destination in the road network, R is the journey of the electric automobile, f q Representing the flow of the electric vehicle in the journey q; in the formula, k and l both represent nodes, k and l in each formula respectively represent nodes meeting conditions, and y q Indicates whether the trip q is covered; x is the number of k Indicating whether a charging station is established at node k; x is the number of j Indicating whether a charging station is opened, wherein j indicates a road network node;
Figure FDA0003828959610000017
represents from O' q To D' q That passes after node k belongs to N q A set of nodes of (a); n is a set of road network nodes, N 'represents a set of repeating nodes, p is the number of charging stations to be built, O' q Starting point O for journey q q Repetition of (1), D' q For journey q destination D q Repetition of (A), (B), (C) and (C), N q Is O' q And D' q The set of nodes of the shortest path between,
Figure FDA0003828959610000021
is from O' q To D' q When passing before node l belongs to N q The set of nodes of (a) is,
Figure FDA0003828959610000022
is a circulation section [ k, l]The length of the stroke q over which the stroke q runs,
Figure FDA0003828959610000023
is an assignment variable;
the influence of considering the randomness of the driving mileage includes:
defining a continuous variable z taking into account the coverage probability of a trip q ∈[0,1]For all nodes l ∈ N q \{O' q Is assigned to a position located at the length of the loop section
Figure FDA0003828959610000024
Charging station with a distance less than the distance traveled
Figure FDA0003828959610000025
Is represented as:
Figure FDA0003828959610000026
wherein, R (omega) represents the driving distance of the electric automobile, wherein omega represents a given random condition; g represents an accumulated density function and defines
Figure FDA0003828959610000027
The electric automobile expected flow charging positioning model comprises:
obtaining an expected flowing charging positioning model of the electric automobile according to a formula FRLM for determinacy of a flowing charging position problem and the coverage probability of a stroke;
the expected flow charge localization model formula is as follows:
Max∑ q∈Q f q z q (10)
Figure FDA0003828959610000028
Figure FDA0003828959610000029
Figure FDA00038289596100000210
2. the method as claimed in claim 1, wherein the step of solving the expected mobile charging location model of the electric vehicle comprises:
and solving the expected mobile charging positioning model of the electric automobile by adopting a tabu search algorithm.
3. The electric vehicle charging positioning system is characterized by comprising a charging positioning model establishing module and a charging positioning model solving module;
the charging positioning model establishing module is used for establishing an expected mobile charging positioning model of the electric automobile by analyzing the problem of deterministic mobile charging positioning and considering the influence caused by the randomness of the driving mileage so as to ensure that the electric automobile realizes charging in all possible ranges;
and the charging positioning model solving module is used for solving the expected mobile charging positioning model of the electric automobile to obtain the charging position of the electric automobile.
In the charging location model building module, the analyzing the deterministic flow charging location problem includes:
the deterministic flow charging localization problem is described using the FRLM formula, which is expressed as follows:
Max∑ q∈Q f q y q (1)
Figure FDA0003828959610000031
Figure FDA0003828959610000032
Figure FDA0003828959610000033
∑ j∈N\N’ x j ＝p (5)
Figure FDA0003828959610000034
Figure FDA0003828959610000035
Figure FDA0003828959610000036
wherein Q is a journey, Q is a set of journeys of an electric vehicle driver from a departure place to a destination in the road network, R is a journey of the electric vehicle, f q Representing the flow of the electric vehicle in the journey q; y is q Indicates whether the trip q is covered; x is a radical of a fluorine atom k Indicating whether a charging station is established at node k; x is the number of j Indicating whether the charging station is opened;
Figure FDA0003828959610000037
represents from O' q To D' q That passes after node k belongs to N q A set of nodes of (a); n is a set of road network nodes, N'Representing a repeating node set, p being the number of charging stations to be built, O' q Starting point O for journey q q Repetition of, D' q For journey q destination D q Repetition of (A), (B), (C) and (C), N q Is O' q And D' q The set of nodes of the shortest path between them,
Figure FDA0003828959610000041
is from O' q To D' q When passing before node l belongs to N q The set of nodes of (a) is,
Figure FDA0003828959610000042
is a circulation section [ k, l]The length over the course of the stroke q,
Figure FDA0003828959610000043
is an assignment variable;
in the charging location model building module, the consideration of the influence caused by the randomness of the traveled mileage includes:
considering the coverage probability of a run, a continuous variable z is defined q ∈[0,1]For all nodes l ∈ N q \{O' q Is assigned to a position located at the length of the loop segment
Figure FDA0003828959610000044
Charging station with a distance less than the distance traveled
Figure FDA0003828959610000045
Is expressed as:
Figure FDA0003828959610000046
wherein, R (omega) represents the driving distance of the electric automobile, wherein omega represents a given random condition; g represents a cumulative density function and defines
Figure FDA0003828959610000047
In the charging positioning model establishing module, the electric vehicle expected flowing charging positioning model includes:
obtaining an expected flowing charging positioning model of the electric automobile according to a formula FRLM for determinacy of a flowing charging position problem and the coverage probability of a stroke;
the expected flow charge localization model formula is as follows:
Max∑ q∈Q f q z q (10)
Figure FDA0003828959610000048
Figure FDA0003828959610000049
Figure FDA00038289596100000410
4. the charging positioning system for the electric vehicle as claimed in claim 3, wherein in the charging positioning model solving module, the solving of the expected flowing charging positioning model for the electric vehicle includes:
and solving the expected mobile charging positioning model of the electric automobile by adopting a tabu search algorithm.
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