CN115438840A - Site selection optimization method for electric vehicle power changing station with controllable average waiting time - Google Patents
Site selection optimization method for electric vehicle power changing station with controllable average waiting time Download PDFInfo
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Abstract
The invention relates to an electric automobile power station replacement site selection optimization method with controllable average waiting time, which comprises the following steps: step S1: based on behavior preference of an electric vehicle driver in battery replacement, with the serviceable range and construction budget of a battery replacement station as constraints and the maximized driver battery replacement requirement as a target, constructing a battery replacement station site selection optimization model under the background of service capability differentiation; step S2: based on the requirement of the driver for replacing the battery and the time for replacing the battery of the power change station, expanding a power change station site selection optimization model into a power change station site selection optimization model by using a queuing theory method; and step S3: and reconstructing a power station site selection optimization model by adopting variable replacement and equivalent transformation, so that the power station site selection optimization model can be solved by an accurate algorithm. The method disclosed by the invention considers the randomness of the battery replacement requirement of the driver, constructs a mathematical optimization model based on the queuing theory and the facility site selection planning theory, meets the requirement preference and the waiting time threshold constraint of the driver, and has the advantages of strong practicability and high service efficiency.
Description
Technical Field
The invention relates to the field of traffic operation management, in particular to a site selection optimization method for an electric automobile battery replacement station with controllable average waiting time.
Background
At present, the energy supplement mode of the pure electric vehicle comprises two modes of charging and battery replacement. In the charging mode, the electric automobile needs to be parked near a charging facility, the electric automobile can leave after the electric quantity of the battery reaches a satisfactory state, and the energy supplementing waiting time is more than 2 hours on average; and under the power changing mode, the battery of the electric automobile is allowed to be separated from the automobile body, the battery can be separated only by replacing a fully charged battery in the power changing station, and the energy supplementing waiting time is averagely not more than 10 minutes. Therefore, the electric automobile in the battery replacement mode can greatly shorten the energy supplementing waiting time and improve the vehicle using efficiency of a driver.
In 2021, the sales volume of the electric vehicle replacement in China is about 16 thousands of vehicles, the year-on-year growth is 162%, the sales volume of the electric vehicle replacement in 2025 is expected to reach 192 thousands of vehicles, and the reserve volume of the electric vehicle replacement at that time is expected to break through 400 thousands of vehicles. Meanwhile, the battery replacement demand of the battery replacement vehicle has shown a rapidly increasing trend. It is reported that the queuing waiting time of the battery replacement automobile drivers in the battery replacement station is far longer than the battery replacement time, and the queuing waiting time of part of the battery replacement stations even exceeds 1 hour. The battery replacement service capability will become a bottleneck restricting the development of the battery replacement mode.
There are two ways to improve the battery replacement capability: one is to update the capacity of the original battery replacement service network by shortening the battery replacement time and the battery storage capacity in the amplification station; and the other method is to expand the overall capacity of the urban power conversion service network by newly building a power conversion station. In the past years, although the battery replacement service provides enterprises to continuously increase the battery replacement speed of the battery replacement station, the average time for battery replacement is shortened from 10 minutes to 5 minutes, and even some enterprises can achieve 3 minutes, the phenomenon that drivers wait too long in line in the battery replacement station still often occurs. In 2021, the reserve of battery replacement stations in China is only about 1400 seats, and the service capability improved by updating the original battery replacement service network cannot adapt to the rapid growth of the current battery replacement vehicles. Therefore, expanding the overall capability of the urban battery replacement service network by means of newly building a battery replacement station becomes a key to break through the bottleneck.
The construction of the power conversion station has particularity and complexity, for example, a high-voltage power transmission network needs to be matched around the construction position of the power conversion station, and some alternative positions meeting the construction conditions need to be defined under the discussion of government departments and expert scholars. The problem of how to select the most suitable construction position from a plurality of alternative positions to be solved first when a new power station is built is solved. The existing research is usually developed based on a Covering Location theoretical model (Covering Location Problem), that is, under the constraint that a built power station can cover the replacement requirements of all drivers, a Location model minimizing the construction cost of the power station is built, or the power station construction budget is used as model constraint, a Location model targeting the maximized replacement requirement coverage is built, and finally, a certain heuristic algorithm (such as a genetic algorithm, a simulated annealing algorithm and a neighborhood search algorithm) is designed to solve the Problem model to obtain the optimal solution or the satisfactory solution of the Problem.
Although the existing research can solve the problem of site selection of the power station under the background of a certain specific problem, the following defects still exist: (1) Only whether the battery replacement requirement of a driver can be covered by the radiation range of the power replacement station is considered, and the problem of queuing waiting time after the driver arrives at the power replacement station is not considered, so that the phenomenon that the queuing waiting time is too long after the driver arrives at the power replacement station is sometimes caused; (2) When a driver is covered by a plurality of swapping stations at the same time, in order to obtain a global optimal solution of the objective function, part of drivers are arranged to be far swapped stations for replacing batteries, and fairness among the drivers is damaged. At present, no research has been made to provide a solution based on a comprehensive consideration of the above two points.
Disclosure of Invention
In order to solve the technical problem, the invention provides a site selection optimization method for an electric automobile battery replacement station with controllable average waiting time.
The technical solution of the invention is as follows: an electric vehicle power station location selection optimization method with controllable average waiting time comprises the following steps:
step S1: based on behavior preference of an electric vehicle driver in battery replacement, a replacement station location optimization model under the background of service capability differentiation is constructed by taking a battery replacement available range and construction pre-calculation as constraints and maximizing a driver battery replacement demand as a target;
step S2: based on the battery replacement requirement of the electric automobile driver and the replacement time of the battery replacement station, expanding the site selection optimization model of the battery replacement station into a site selection optimization model of the battery replacement station with controllable average waiting time of the driver by using a queuing theory method;
and step S3: and reconstructing the site selection optimization model of the power conversion station by adopting variable replacement and equivalent transformation, so that the site selection optimization model can be solved by an accurate algorithm.
Compared with the prior art, the invention has the following advantages:
1. the invention discloses an electric vehicle power station changing location optimization method with controllable average queuing time.
2. The method provided by the invention can simultaneously quantify the behavior preference of the driver for replacing the battery and the waiting time of queuing of the driver in the battery replacement station, not only meets the individual requirements of the driver, but also reduces the service waiting time of the driver, and has the advantage of high service efficiency.
3. The method provided by the invention can convert a random planning model into a mathematical model which can be solved by using an accurate algorithm, can obtain a global optimal solution under a system stable state, and has the characteristic of strong practicability.
Drawings
Fig. 1 is a flowchart of an optimization method for site selection of an electric vehicle battery replacement station with controllable average queuing time in the embodiment of the present invention;
FIG. 2 is a schematic diagram of a battery replacement requirement and an alternative power replacement station in an embodiment of the present invention;
fig. 3 is a schematic diagram of an optimal construction scheme of a power conversion station facility in an embodiment of the present invention.
Detailed Description
The invention provides an electric automobile power station changing location optimizing method with controllable average queuing time, which solves the problem of long waiting time for a driver to queue in a power station changing from the perspective of facility planning by the cross fusion of a facility location theory and a queuing theory, and has strong practicability and high service efficiency.
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings.
As shown in fig. 1, the method for optimizing site selection of an electric vehicle battery replacement station with controllable average queuing time provided by the embodiment of the invention comprises the following steps:
step S1: based on behavior preference of an electric vehicle driver for replacing batteries, a replacement station address selection optimization model under the background of service capability differentiation is constructed by taking a serviceable range and a construction pre-calculation of a replacement station as constraints and taking the maximized driver battery replacement requirement as a target;
step S2: based on the battery replacement requirement of an electric automobile driver and the replacement of a battery of a power station, expanding a power station site selection optimization model into a power station site selection optimization model with controllable average waiting time of the driver by using a queuing theory method;
and step S3: and reconstructing a power station site selection optimization model by adopting variable replacement and equivalent transformation, so that the power station site selection optimization model can be solved by an accurate algorithm.
In one embodiment, the step S1: based on behavior preference of an electric vehicle driver for replacing batteries, with a serviceable range and a construction budget of a power conversion station as constraints and a maximized driver battery replacement demand as a target, a power conversion station site selection optimization model under the background of poor service capability is constructed, and the power conversion station site selection optimization model specifically comprises an objective function (1) and a constraint function (2) -9:
wherein, the meaning of each parameter is as follows:
i: and (4) a potential position point set meeting the power station changing construction condition in the city, wherein I belongs to I.
J: and J belongs to J in the position point set generated by the requirement of replacing the battery of the driver in the city.
L: and (4) constructing a set of service capability types selected when the power station is changed, wherein L belongs to L.
r: the service radius that each power exchange station can cover.
d ij : the distance traveled from the ith position to the jth position, I ∈ I, J ∈ J.
I j : a subset of the set I in the sense of
Where r is the service radius.
J i : a subset of the set J having the meaning of
Where r is the service radius.
λ j : a numerical characterization of the battery replacement requirement generated at the jth location, J e J.
f i : and (4) the fixed cost required for constructing the power conversion station at the ith position point, such as the land use cost, I belongs to I.
v il : the variable cost of the L type of power station is built at the I position point, such as the cost of construction materials and instruments, I belongs to I, L belongs to L.
b: and building available budget of the power swapping station.
y i : and (4) a decision variable, which represents whether a power change station is built at the ith position point, is 1, otherwise, is 0, I belongs to I.
x ij : and (4) a decision variable which indicates whether the battery replacement station at the ith position point serves the battery replacement demand at the jth position point, wherein 1 is taken, and otherwise, 0,i belongs to I and J belongs to J is taken.
z il : and (4) a decision variable which indicates whether the ith type of power conversion station is built at the ith position point is 1, otherwise, 0,i belongs to I, and L belongs to L.
In the mathematical model of step S1, behavior preference of an electric vehicle driver in replacing batteries and differentiation of battery replacement station types are fully considered, wherein:
formula (1) is an objective function and consists of a calculation formula of the satisfied battery replacement requirement of the driver, and Max represents a scheme when the satisfied battery replacement requirement of the driver is maximum;
the formula (2) shows that the total investment of the current power station changing construction scheme cannot exceed the actual budget;
formula (3) shows that the power exchange station built at one position can only select one of a plurality of service types;
formula (4) shows that the driver can only select one of the battery replacement stations in all coverage areas to go to and receive the battery replacement service;
formula (5) indicates that a nearby driver can be served only after the power station is built at a certain position;
formula (6) shows that when there are multiple swapping stations capable of receiving service in the coverage area, the driver needs to go to one of the swapping stations with the closest distance, and the constraint characterizes the behavior preference of the driver when seeking the battery replacement service, that is, the driver tends to go to the swapping station with the closest distance to seek service;
equation (7) represents the decision variable x ij Can only take place between two integers 0 and 1;
equation (8) represents the decision variable y i Can only take place between two integers 0 and 1;
equation (9) represents the decision variable z il Can only occur between integers of 0 and 1.
In one embodiment, the step S2: comprehensively considering the battery replacement requirement of a driver and the characteristics of the battery replacement station during battery replacement, expanding the mathematical optimization model in the S1 into a site selection optimization model of the battery replacement station with controllable average waiting time of the driver based on a queuing theory method, and specifically comprising the following steps of:
step S21: digital characteristic Lambda for constructing battery replacement requirements faced by battery replacement station located at point i i Known from the basic concept of the queuing theory method
Step S22: constructing a battery change station at point i to provide battery replacementNumerical characteristic u of mean value of time required for service i Known from the basic knowledge of linear programming
Step S23: the method comprises the following steps of taking a power conversion station as a service desk, constructing a queuing system based on M/G/1 as a theory, and expanding a mathematical model in the step S1 into a power conversion station site selection optimization model for controlling the average waiting time of a driver by adjusting a maximum waiting time threshold parameter, wherein the power conversion station site selection optimization model specifically comprises an objective function (10) and a constraint function (11) -22:
wherein the meaning of each parameter is as follows:
i: and (4) a potential position point set in the city, I belongs to I, meeting the construction condition of the power station.
J: and J belongs to J in the position point set generated by the requirement of replacing the battery of the driver in the city.
L: and (4) constructing a set of service capability types selected when the power station is changed, wherein L belongs to L.
r: the service radius that each power change station can cover.
d ij : and the driving distance from the ith position to the jth position, I belongs to I, and J belongs to J.
I j : a subset of set I in the sense of
Where r is the service radius.
J i : a subset of the set J having the meaning of
Where r is the service radius.
λ j : a numerical characteristic of the battery replacement requirement generated at the jth position point, J ∈ J.
f i : and (4) the fixed cost required for constructing the power conversion station at the ith position point, such as the land use cost, I belongs to I.
v il : the variable cost of constructing the L-th type of power station at the I-th position point, such as the cost of construction materials and instruments, I belongs to I and L belongs to L.
b: and building available budget of the power swapping station.
y i : and (4) a decision variable, which represents whether a power swapping station is built at the ith position point, is 1, otherwise, 0 is selected, I belongs to I.
x ij : and a decision variable, which represents whether the battery replacement station at the ith position point is served by the battery replacement requirement of the jth position point, is 1, otherwise, 0 is selected, I belongs to I, and J belongs to J.
z il : and a decision variable, which represents whether the ith type of power change station is built at the ith position point, is 1, otherwise, 0 is selected, I belongs to I, and L belongs to L.
u l : and the service capability of the type I power change station, wherein L belongs to L.
u i : the average time required for the battery change station at point I to receive the battery change service, I ∈ I.
σ i : and the variance of the time required by the battery replacement service received by the battery replacement station at the point I is within the range I.
Λ i : and (3) digital characteristics of battery replacement requirements of the power change station at the point I, wherein I belongs to I.
T: and (4) the maximum acceptable waiting time threshold value is reached after the driver arrives at the power swapping station.
M: the mathematical expression represents the meaning of a large number of values.
The method adopted in step S23 fully incorporates the processing technology based on the queuing theory, so that the method is extended to a power station location optimization model capable of controlling the average waiting time of the driver by adjusting the maximum waiting time threshold T, wherein:
formula (10) is an objective function, and consists of a calculation formula of the satisfied driver battery replacement demand, and Max represents a scheme when the satisfied amount of the driver battery replacement demand is the maximum;
a formula (11) shows that the total investment of the construction scheme of the current power station cannot exceed the actual budget;
formula (12) shows that the power exchange station built at one position can only select one of a plurality of service types;
formula (13) shows that the driver can only select one of the battery replacement stations in all coverage areas to go to and receive the battery replacement service;
formula (14) indicates that a nearby driver can only be served after a power station is built at a certain position;
formula (15) shows that when there are multiple swapping stations which can receive service in the coverage area, the driver needs to go to one of the swapping stations which is closest to the driver;
formula (16) represents the numerical characteristics of the battery replacement requirements faced by the power conversion station at point i, depicting the customer arrival rate of the queuing model with the power conversion station as the service facility;
formula (17) represents the numerical characteristic of the average time required by the battery replacement station at the point i to provide the battery replacement service, and depicts the service level of the battery replacement station when the battery replacement service is provided;
the formula (18) indicates that the service capacity of the power conversion station is higher than the total demand of the service in the future, otherwise, the model is not established, and the constraint is an objective constraint condition of a queuing theory;
formula (19) shows that the average waiting time of the driver after the driver reaches the power conversion station is necessarily smaller than a preset threshold value T, the constraint is an important embodiment of the invention for fusing the queuing theory and the facility site selection theory, and the aim of controlling the average waiting time of the driver in the optimization model can be fulfilled by adjusting the threshold value T;
equation (20) represents the decision variable x ij Can only take place between two integers 0 and 1;
equation (21) represents the decision variable y i Can only take place between two integers 0 and 1;
equation (22) represents the decision variable z il Values of (c) can only be generated between two integers 0 and 1.
In one embodiment, the step S3: reconstructing the mathematical optimization model in the step S2 by adopting an equivalent transformation and variable replacement technology, so that the mathematical optimization model can be solved by an accurate algorithm, and the method specifically comprises the following steps:
step S31: and (3) carrying out equivalent transformation on the constraint conditions (19) in the mathematical model in the step S23, wherein the method comprises the following specific steps:
wherein the meaning of each parameter is as follows:
m: the mathematical expression represents the meaning of a large number of values.
T: and (4) the maximum acceptable waiting time threshold value is reached after the driver arrives at the power swapping station.
u i : the average time required for the battery change station at point I to receive the battery change service, I ∈ I.
Λ i : and (3) digital characteristics of battery replacement requirements of the power change station at the point I, I belongs to I.
y i : and (4) a decision variable, which represents whether a power change station is built at the ith position point, is 1, otherwise, is 0, I belongs to I.
σ i : and the variance of the time required by the battery replacement service received by the battery replacement station at the point I is within the range I.
The formula is an equivalent transformation formula of the constraint condition (19) in the mathematical model of the step S23, and has the same physical meaning as the constraint condition.
Step S22: three intermediate variables are newly established, which are as follows:
the step is the specific application of a mathematical variable replacement technology and three new intermediate variables are generated. The new intermediate variables play an auxiliary role in the model and have no actual physical meaning.
Step S33: substituting the three intermediate variables of the step S32 into the mathematical expression of the step S31 to obtain the transformed constraint condition, which is specifically as follows:
wherein the meaning of each parameter is as follows:
m: the mathematical expression represents the meaning of a large number of values.
T: and (4) the maximum acceptable waiting time threshold value is reached after the driver arrives at the power swapping station.
u i : the average time required for the battery change station at point I to receive the battery change service, I ∈ I.
Λ i : and (3) digital characteristics of battery replacement requirements of the power change station at the point I, I belongs to I.
y i : and (4) a decision variable, which represents whether a power swapping station is built at the ith position point, is 1, otherwise, 0 is selected, I belongs to I.
σ i : and the variance of the time required for receiving the battery replacement service at the battery replacement station at the point I, I belongs to the I.
A i : intermediate variables having the mathematical meaning of
i∈I
B i : intermediate variables having the mathematical meaning of
C i : intermediate variables having the mathematical meaning of
The step is the integration and application of equivalent transformation and variable replacement methods, the constraint conditions (19) in the mathematical model in the step S23 are reconstructed into an equivalent form in the step, the equivalent form and the constraint conditions (19) in the mathematical model in the step S23 have the same physical meaning, and due to the transformation on the mathematical form, the constraint can be used for obtaining an optimal solution through general mathematical optimization software.
Step S34: reconstructing the mathematical optimization model in step S23 based on step S32 and step S33, so that it can be solved by an accurate algorithm, specifically including an objective function (23) and a constraint function (24) -38:
wherein, the meaning of each parameter is as follows:
i: and (4) a potential position point set meeting the power station changing construction condition in the city, wherein I belongs to I.
J: and J belongs to J in the position point set generated by the requirement of replacing the battery of the driver in the city.
L: and (4) constructing a set of service capability types selected when the power station is changed, wherein L belongs to L.
r: the service radius that each power change station can cover.
d ij : and the driving distance from the ith position to the jth position, I belongs to I, and J belongs to J.
I j : a subset of set I in the sense of
Where r is the service radius.
J i : a subset of the set J having the meaning of
Where r is the service radius.
λ j : a numerical characterization of the battery replacement requirement generated at the jth location, J e J.
f i : and (4) the fixed cost required for constructing the power conversion station at the ith position point, such as the land use cost, I belongs to I.
v il : the variable cost of constructing the L-th type of power station at the I-th position point, such as the cost of construction materials and instruments, I belongs to I and L belongs to L.
b: and building available budget of the power swapping station.
y i : and (4) a decision variable, which represents whether a power change station is built at the ith position point, is 1, otherwise, is 0, I belongs to I.
x ij : and a decision variable, which represents whether the battery replacement station at the ith position point is served by the battery replacement requirement of the jth position point, is 1, otherwise, 0 is selected, I belongs to I, and J belongs to J.
z il : and (4) a decision variable which indicates whether the ith type of power conversion station is built at the ith position point is 1, otherwise, 0,i belongs to I, and L belongs to L.
u l : and the service capability of the type I power change station, wherein L belongs to L.
u i : when the power station at point i receives the average of the battery replacement serviceAnd I ∈ I.
σ i : and the variance of the time required for receiving the battery replacement service at the battery replacement station at the point I, I belongs to the I.
Λ i : and (3) digital characteristics of battery replacement requirements of the power change station at the point I, I belongs to I.
T: and (4) the maximum acceptable waiting time threshold value is reached after the driver arrives at the power swapping station.
M: the mathematical expression represents the meaning of a large number of values.
A i : intermediate variables having the mathematical meaning of
i∈I.
B i : intermediate variable having the mathematical meaning of B i ＝Λ i y i ，i∈I.
C i : intermediate variables having the mathematical meaning C i ＝u i Λ i ，i∈I.
In step S34, the quartic constraint planning model in step S23 is converted into a mixed integer quadratic planning model by new variables and constraints generated based on variable replacement, equivalent transformation, constraint reconstruction techniques, wherein:
formula (23) is an objective function, and is composed of a calculation formula of the satisfied driver battery replacement demand, and Max represents a scheme when the satisfied amount of the driver battery replacement demand is the maximum;
a formula (24) shows that the total investment of the current power station construction scheme cannot exceed the actual budget;
formula (25) shows that the power station built at one position can only select one of a plurality of service types;
formula (26) indicates that the driver can only select one of the battery replacement stations in all coverage areas to go to and receive the battery replacement service;
formula (27) indicates that a nearby driver can only be served after the power station is built at a certain position;
formula (28) indicates that when there are multiple swapping stations capable of receiving service in the coverage area, the driver needs to go to one of the swapping stations closest to the driver, and this constraint characterizes the behavior preference of the driver when seeking the battery replacement service, that is, the driver tends to go to the nearest swapping station to seek service;
formula (29) represents the numerical characteristics of the battery replacement requirements faced by the power change station at point i, characterizing the customer arrival rate of the queuing model with the power change station as the service facility;
formula (30) represents the numerical characteristic of the average time required by the power change station at the point i to provide the battery replacement service, and depicts the service level of the power change station when the power change station provides the battery replacement service;
the formulas (31) - (33) represent three additional intermediate variables, and have no actual physical meaning;
the formula (34) shows that the service capacity of the power conversion station is higher than the total demand of the previous service, otherwise, the model is not established, and the constraint is an objective constraint condition of a queuing theory;
the formula (35) indicates that the average waiting time of the driver after the driver arrives at the power swapping station must be less than a certain threshold value T, the constraint is an important embodiment for fusing the queuing theory and the facility site selection theory, and the aim of controlling the average waiting time of the driver in the optimization model can be fulfilled by adjusting the threshold value T;
equation (36) represents the decision variable x ij Can only take place between two integers 0 and 1;
equation (37) represents the decision variable y i Can only take place between two integers 0 and 1;
equation (38) represents the decision variable z il Values of (c) can only be generated between two integers 0 and 1.
The final optimization model given in the step enables the problem to be solved by an accurate algorithm, and improves the operability of the optimization model in the actual problem application process. For example, in a practical application, the model in step S34 may be introduced into business optimization software for solution, see the following example.
Now, as shown in fig. 2, the site selection problem of the power station is presented, and the research area is 5 × 5The battery replacement device is characterized by comprising 25 square small lattices with the side length of 10, wherein the central position of each small lattice is the position where the battery replacement requirement is generated, namely the position of an asterisk. The numbers below the asterisk are the numbers of each demand location, i.e., J = {1,2,3, \8230;, 25}; the numbers above the asterisk indicate the demand generated at that location, i.e. λ 1 ＝1，λ 2 ＝1，λ 3 ＝2，λ 4 ＝4，λ 5 ＝2，λ 6 ＝4，λ 7 ＝4，λ 8 ＝5，λ 9 ＝5， λ 10 ＝2，λ 11 ＝2，λ 12 ＝3，λ 13 ＝2，λ 14 ＝5，λ 15 ＝5，λ 16 ＝3，λ 17 ＝2，λ 18 ＝4，λ 19 ＝2，λ 20 ＝3， λ 21 ＝2，λ 22 ＝3，λ 23 ＝5，λ 24 ＝4，λ 25 And (5). The junction between grids is an alternative position for building a power conversion station and is represented by solid triangles in fig. 2. The number below the triangle a is the number for each alternative position, i.e., I = {1,2,3, \8230;, 16}; the number at the upper right of the triangle a represents the fixed cost required for building the power station at the position, namely f 1 ＝34，f 2 ＝41，f 3 ＝31，f 4 ＝45，f 5 ＝42，f 6 ＝48，f 7 ＝50，f 8 ＝49，f 9 ＝38，f 10 ＝30， f 11 ＝41，f 12 ＝34，f 13 ＝34，f 14 ＝36，f 15 ＝32，f 16 =45; its corresponding sigma 1 ＝2，σ 2 ＝2，σ 3 ＝1， σ 4 ＝2，σ 5 ＝2，σ 6 ＝2，σ 7 ＝2，σ 8 ＝1，σ 9 ＝2，σ 10 ＝1，σ 11 ＝2，σ 12 ＝2，σ 13 ＝2，σ 14 ＝1， σ 15 ＝2，σ 16 =1. The types of the existing two power conversion stations can be selected, namely L = {1,2}, wherein u is 1 ＝10，u 2 =15; and v is i1 ＝50，v i2 =100,i ∈ I. Assume a service radius of r =20; the driver can accept the most after arriving at the power stationThe large latency threshold is T =100; the construction budget is 40% of the total cost required to construct the most expensive power change stations at all locations, i.e., b =892. Distance d of each position point between the set I and the set J ij Determined by its physical location, in this case the linear distance between two points.
And (4) substituting the parameters into the model in the step S34, and calling a mathematical optimization solver, for example, gurobi Version 9.5.2, to obtain an optimal construction scheme of the power station replacement facility, which meets all constraint conditions, as shown in fig. 3. Wherein the content of the first and second substances,
indicating that a first type of power station needs to be built at the position, wherein I = {1,2,3,6,8,10,11}; the triangle is represented by a square shape of 963360, and the enclosure indicates that a second type of power exchange station needs to be built at the position, wherein I = {14,15}; and no power change station is built at other positions. In fig. 3, a connection line between the asterisk and the triangle a represents a service relationship between the demand position and the power swapping station position, for example, a battery replacement demand at the demand position {1,2,6,11} is forwarded to the power swapping station position 1 to seek service, a battery replacement demand at the demand position {2,5} is forwarded to the power swapping station position 2 to seek service, and so on, all service relationships can be obtained. The examples are complete.
Claims (4)
1. An electric vehicle power changing station site selection optimization method with controllable average waiting time is characterized by comprising the following steps:
step S1: based on the behavior preference of an electric vehicle driver for replacing batteries, a site selection optimization model of a battery replacement station under the background of service capability differentiation is constructed by taking the serviceable range and the construction budget of the battery replacement station as constraints and maximizing the battery replacement requirement of the driver as a target;
step S2: based on the battery replacement requirement of the electric automobile driver and the replacement of the battery of the power station, expanding the power station site selection optimization model into a power station site selection optimization model with controllable average waiting time of the driver by using a queuing theory method;
and step S3: and reconstructing the site selection optimization model of the power conversion station by adopting variable replacement and equivalent transformation, so that the site selection optimization model can be solved by an accurate algorithm.
2. The method for optimizing site selection of the electric vehicle battery replacement station with controllable average waiting time as claimed in claim 1, wherein the step S1: based on behavior preference of an electric vehicle driver in replacing batteries, with a battery replacement station serviceable range and a construction budget as constraints and a maximized driver battery replacement requirement as a target, a site selection optimization model of the battery replacement station under a background of service capability differentiation is constructed, and specifically comprises an objective function (1) and a constraint function (2) -9:
wherein the meaning of each parameter is as follows:
i: the method comprises the following steps that (1) a potential position point set which meets the construction conditions of a power station in a city belongs to I;
j: a position point set generated by the replacement requirement of a driver battery in a city, wherein J belongs to J;
l: a set of service capability types selected during the construction of the power change station belongs to L;
r: the service radius which can be covered by each power exchange station;
d ij : the driving distance from the ith position to the jth position, I belongs to I, and J belongs to J;
I j : a subset of set I in the sense of
Wherein r is the service radius;
J i : a subset of the set J having the meaning of
Wherein r is the service radius;
λ j : the digital characteristics of the battery replacement requirement generated at the jth position point, J belongs to J;
f i : the fixed cost required for building the electricity changing station at the ith position point, such as the land use cost, I belongs to I;
v il : the change cost of constructing the L type of power changing station at the ith position point, such as the cost of construction materials and instruments, I belongs to I, and L belongs to L;
b: building available budget of the power swapping station;
y i : a decision variable, which represents whether a power change station is built at the ith position point, if so, 1 is selected, otherwise, 0 is selected, I belongs to I;
x ij : a decision variable, which represents whether the battery replacement station at the ith position point serves the battery replacement requirement at the jth position point, is 1, otherwise, 0 is selected, I belongs to I, and J belongs to J;
z il : and a decision variable, which represents whether the ith type of power change station is built at the ith position point, is 1, otherwise, 0 is selected, I belongs to I, and L belongs to L.
3. The method for optimizing the site selection of the electric vehicle power switching station with controllable average waiting time according to claim 2, wherein the step S2: based on the battery replacement requirement of the electric automobile driver and the replacement time of the battery of the power exchanging station, the power exchanging station site selection optimization model is expanded into a power exchanging station site selection optimization model with controllable average waiting time of the driver by using a queuing theory method, and the method specifically comprises the following steps:
step S21: digital characteristic Lambda for constructing battery replacement requirement faced by battery replacement station located at point i i Known from the basic concept of the queuing theory method
Step S22: constructing a digital signature u of the mean of the times required for a battery change station located at point i to provide a battery change service i From the linear programming basic knowledge
Step S23: the method comprises the following steps of taking a power conversion station as a service desk, constructing a queuing system based on M/G/1 as a theory, and expanding a power conversion station site selection optimization model into a power conversion station site selection optimization model for controlling the average waiting time of a driver by adjusting a maximum waiting time threshold parameter, wherein the power conversion station site selection optimization model specifically comprises an objective function (10) and a constraint function (11) -22:
wherein the meaning of each parameter is as follows:
i: the method comprises the following steps that (1) a potential position point set which meets the construction conditions of a power station in a city belongs to I;
j: a position point set generated by the replacement requirement of a driver battery in a city, wherein J belongs to J;
l: the method comprises the steps that a set of service capability types selected during power station swapping is built, and L belongs to L;
r: the service radius which can be covered by each power exchange station;
d ij : the driving distance from the ith position to the jth position, I belongs to I, and J belongs to J;
I j : a subset of set I in the sense of
Wherein r is the service radius;
J i : a subset of the set J having the meaning of
Wherein r is the service radius;
λ j : the digital characteristics of the battery replacement requirement generated at the jth position point, J belongs to J;
f i : the fixed cost required for building the power change station at the ith position point is that I belongs to I;
v il : constructing the variation cost of the L type of power changing station at the ith position point, wherein I belongs to I and L belongs to L;
b: building available budget of the power swapping station;
y i : a decision variable, which represents whether a power changing station is built at the ith position point, is 1, otherwise, 0 is selected, I belongs to I;
x ij : a decision variable, which represents whether the battery replacement station at the ith position point serves the battery replacement requirement at the jth position point, is 1, otherwise, 0 is selected, I belongs to I, and J belongs to J;
z il : a decision variable, which indicates whether the ith type of power change station is built at the ith position point, is 1, otherwise, 0 is selected, I belongs to I, and L belongs to L;
u l : the service capability of the ith type of power change station, wherein L belongs to L;
u i : the average time required for receiving the battery replacement service at the battery replacement station at the point I belongs to the group I;
σ i : receiving the variance of the time required by the battery replacement service at a battery replacement station positioned at the point I, wherein I belongs to I;
Λ i : digital characteristics of battery replacement requirements of a power change station at a point I, wherein I belongs to I;
t: the maximum waiting time threshold value accepted by the driver after the driver reaches the power swapping station;
m: the mathematical expression represents the meaning of a large number of values.
4. The method for optimizing the site selection of the electric vehicle power switching station with controllable average waiting time according to claim 3, wherein the step S3: reconstructing the site selection optimization model of the power conversion station by adopting an equivalent transformation and variable replacement technology to enable the site selection optimization model to be solved by an accurate algorithm, and specifically comprises the following steps:
step S31: the constraint (19) is equivalently transformed, as follows:
wherein the meaning of each parameter is as follows:
m: the meaning of a very large numerical value is expressed in the mathematical expression;
t: the maximum waiting time threshold value accepted by the driver after the driver reaches the power swapping station;
u i : the average time required for receiving the battery replacement service at a battery replacement station positioned at the point I belongs to I;
Λ i : digital characteristics of battery replacement requirements of a power change station located at the point I, wherein I belongs to I;
y i : a decision variable, which represents whether a power changing station is built at the ith position point, is 1, otherwise, 0 is selected, I belongs to I;
σ i : the variance of the time required for receiving the battery replacement service at a battery replacement station at the point I belongs to I;
step S32: three intermediate variables are newly established, and the method comprises the following specific steps:
step S33: substituting the three intermediate variables of the step S32 into the mathematical expression of the step S31 to obtain an equivalent constraint condition, which is specifically as follows:
wherein, the meaning of each parameter is as follows:
m: the meaning of a very large numerical value is expressed in the mathematical expression;
t: the maximum acceptable waiting time threshold value is reached after the driver arrives at the power swapping station;
u i : the average time required for receiving the battery replacement service at the battery replacement station at the point I belongs to the group I;
Λ i : digital characteristics of battery replacement requirements of a power change station located at the point I, wherein I belongs to I;
y i : a decision variable, which represents whether a power change station is built at the ith position point, if so, 1 is selected, otherwise, 0 is selected, I belongs to I;
σ i : receiving the variance of the time required by the battery replacement service at a battery replacement station positioned at the point I, wherein I belongs to I;
A i : intermediate variables having the mathematical meaning of
B i : intermediate variables having the mathematical meaning of
C i : intermediate variables having the mathematical meaning of
Step S34: reconstructing the site selection optimization model in the step S23 based on the step S32 and the step S33, so that the site selection optimization model can be solved by an accurate algorithm, and specifically comprises an objective function (23) and a constraint function (24) - (38):
wherein the meaning of each parameter is as follows:
i: the method comprises the following steps that (1) a potential position point set which meets the construction conditions of a power station in a city belongs to I;
j: a position point set generated by the replacement requirement of a driver battery in a city, wherein J belongs to J;
l: the method comprises the steps that a set of service capability types selected during power station swapping is built, and L belongs to L;
r: the service radius which can be covered by each power exchange station;
d ij : the driving distance from the ith position to the jth position, I belongs to I, and J belongs to J;
I j : a subset of set I in the sense of
Wherein r is the service radius;
J i : a subset of the set J having the meaning of
Wherein r is the service radius;
λ j : the digital characteristics of the battery replacement requirement generated at the jth position point, J belongs to J;
f i : the fixed cost required for constructing the power conversion station at the ith position point, such as the land use cost, I belongs to I;
v il : the variable cost of constructing the L type of power station at the I-th position point, such as the cost of construction materials and instruments, I belongs to I, and L belongs to L;
b: building available budget of the power conversion station;
y i : a decision variable, which represents whether a power change station is built at the ith position point, if so, 1 is selected, otherwise, 0 is selected, I belongs to I;
x ij : a decision variable representing whether the battery replacement station at the ith position point serves the battery replacement demand of the jth position point is 1, otherwise, 0 is selected, I belongs to I, and J belongs to J;
z il : a decision variable, which indicates whether the ith type of power change station is built at the ith position point, is 1, otherwise, 0 is selected, I belongs to I, and L belongs to L;
u l : the service capability of the ith type of power change station, wherein L belongs to L;
u i : the average time required for receiving the battery replacement service at the battery replacement station at the point I belongs to the group I;
σ i : the variance of the time required for receiving the battery replacement service at a battery replacement station at the point I belongs to I;
Λ i : digital characteristics of battery replacement requirements of a power change station at a point I, wherein I belongs to I;
t: the maximum waiting time threshold value accepted by the driver after the driver reaches the power swapping station;
m: the meaning of a very large numerical value is expressed in the mathematical expression;
A i : intermediate variables having the mathematical meaning of
B i : intermediate variable having the mathematical meaning of B i ＝Λ i y i ，i∈I；
C i : intermediate variable having the mathematical meaning of C i ＝u i Λ i ，i∈I。
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