CN109492794B - Electric vehicle charging station optimal configuration modeling method based on two-step equivalence method - Google Patents

Electric vehicle charging station optimal configuration modeling method based on two-step equivalence method Download PDF

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CN109492794B
CN109492794B CN201811167738.1A CN201811167738A CN109492794B CN 109492794 B CN109492794 B CN 109492794B CN 201811167738 A CN201811167738 A CN 201811167738A CN 109492794 B CN109492794 B CN 109492794B
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electric vehicle
charging
vehicle charging
charging station
requirements
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CN109492794A (en
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李磊
李晓辉
赵新
徐亮
刘伟东
刘小琛
梁彬
陈彬
刘洋洋
谢秦
赵庆来
邹琪
杨光
李丹
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State Grid Corp of China SGCC
State Grid Tianjin Electric Power Co Ltd
Electric Power Research Institute of State Grid Tianjin Electric Power Co Ltd
Beijing State Grid Purui UHV Transmission Technology Co Ltd
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State Grid Corp of China SGCC
State Grid Tianjin Electric Power Co Ltd
Electric Power Research Institute of State Grid Tianjin Electric Power Co Ltd
Beijing State Grid Purui UHV Transmission Technology Co Ltd
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    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06Q—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES; SYSTEMS OR METHODS SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES, NOT OTHERWISE PROVIDED FOR
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    • Y02T—CLIMATE CHANGE MITIGATION TECHNOLOGIES RELATED TO TRANSPORTATION
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Abstract

The invention relates to a two-step equivalence method-based mathematical modeling method for optimal configuration of an electric vehicle charging station, which comprises the following specific execution steps of: step 1, establishing a basic optimal configuration model of an electric vehicle charging station containing different types of electric vehicle charging piles; step 2, optimizing the established optimal configuration model of the electric vehicle charging station by using a two-step equivalent method; and 3, performing relaxation optimization on the optimal configuration model of the electric vehicle charging station based on the two-step equivalent method optimization by using a second-order cone programming. The method provides and applies a two-step equivalence method, and after equivalence and some accurate relaxation, the provided optimization model is converted into a type of Mixed Integer Second Order Cone Programming (MISOCP), and the electric vehicle charging station programming method with the minimum annual charging social cost can be effectively solved through a proper mathematical method.

Description

Electric vehicle charging station optimal configuration modeling method based on two-step equivalence method
Technical Field
The invention belongs to the technical field of electric energy metering, and relates to a planning and modeling method for an electric vehicle charging station, in particular to a mathematical modeling method for optimal configuration of the electric vehicle charging station based on a two-step equivalence method.
Background
Electric vehicles have attracted increasing attention in the past decade as a huge alternative to traditional fossil fuel powered traffic, where greenhouse gas emissions are low and energy utilization is efficient. Against this background, electric vehicle advocates (e.g., governments, automobile companies, and energy companies) are actively promoting their popularity. The prevalence of electric vehicles is expected to grow rapidly in the foreseeable future. However, unlike the rapid refueling of conventional fossil fuel vehicles, electric vehicle charging activities require appropriate charging facilities and certain charging times. These inconveniences are global pain points for the vigorous development of the electric automobile industry, thereby bringing negative effects to the society of electric automobiles. While the efficiency and the relief of the described pain points, optimal planning of electric vehicles becomes a very important topic, and an optimal configuration scheme can meet the charging requirements of different vehicle owners with minimal social cost, thereby promoting the development of the electric vehicle industry.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provides an electric vehicle charging station optimal configuration mathematical modeling method based on a two-step equivalence method.
The technical problem to be solved by the invention is realized by adopting the following technical scheme:
a mathematical modeling method for optimal configuration of an electric vehicle charging station based on a two-step equivalence method is characterized by comprising the following steps of: the specific execution steps comprise:
step 1, establishing a basic optimal configuration model of an electric vehicle charging station containing different types of electric vehicle charging piles;
step 2, optimizing the established optimal configuration model of the electric vehicle charging station by using a two-step equivalent method;
and 3, performing relaxation optimization on the optimal configuration model of the electric vehicle charging station based on the two-step equivalent method optimization by using a second-order cone programming.
In step 1, the basic optimal configuration model of the electric vehicle charging station including the electric vehicle charging piles of different types includes:
(1) an objective function:
Figure GDA0001952719740000021
wherein the constants 4, 96 represent four seasons of the year and 15 minute time periods contained in one day, respectively, each season has an average of 65.25 weekdays and 26 weekends, and a total of 768 time periods are contained in the above formula,
(2) constraint conditions are as follows: comprising (a) a power flow constraint: (b) voltage amplitude constraint: (c) and (3) branch current constraint: (d) population balance constraints relating to electric vehicle charging: (e) and (3) restricting the driving distance after charging: (f) requirement constraint of charging facilities in electric vehicle charging stations: (g) and (5) charging power quality constraint.
Moreover, the objective function specifically includes:
(a) annual investment cost C of electric vehicle charging stationI：
Figure GDA0001952719740000022
(b) Annual grid consolidation cost CR：
Figure GDA0001952719740000023
(c) Annual usage and maintenance costs C for electric vehicle charging stationsO&M：
Figure GDA0001952719740000024
(d) Annual network loss cost
Figure GDA0001952719740000025
Figure GDA0001952719740000026
Moreover, the constraint conditions specifically include:
(a) and (3) power flow constraint:
Figure GDA0001952719740000027
Figure GDA0001952719740000028
Figure GDA0001952719740000029
(b) voltage amplitude constraint:
Figure GDA0001952719740000031
(c) and (3) branch current constraint:
Figure GDA0001952719740000032
(d) population balance constraints relating to electric vehicle charging:
Figure GDA0001952719740000033
Figure GDA0001952719740000034
Figure GDA0001952719740000035
(e) and (3) restricting the driving distance after charging:
Figure GDA0001952719740000036
Figure GDA0001952719740000037
Figure GDA0001952719740000038
(f) requirement constraint of charging facilities in electric vehicle charging stations:
Figure GDA0001952719740000039
Figure GDA00019527197400000310
Figure GDA00019527197400000311
(g) and (5) charging power quality constraint.
Moreover, the (g) charging power quality constraint includes four scenarios:
scene 1: the charging requirements of each type of electric automobile can be met by the corresponding charging pile;
Figure GDA00019527197400000312
the charging power on the electric vehicle charging station bus j is expressed as:
Figure GDA00019527197400000313
scene 2: part of the SCF charging requirements are transferred to the NCF, which is fully able to meet the original requirements and the transferred requirements due to the SCF shortage:
Figure GDA0001952719740000041
the charging power on the electric vehicle charging station bus j is expressed as:
Figure GDA0001952719740000042
scene 3: due to the shortage of NCFs, part of NCF charging requirements are transferred to FCFs, while FCFs can fully meet the original requirements and the transferred requirements:
Figure GDA0001952719740000043
the charging power on the electric vehicle charging station bus j is expressed as:
Figure GDA0001952719740000044
scene 4: SCFs are not sufficient to meet the corresponding charging requirements, while NCFs cannot meet the sum of their original and transferred requirements:
Figure GDA0001952719740000045
the charging power on the electric vehicle charging station bus j is expressed as:
Figure GDA0001952719740000046
further, the step 2 includes:
(1) replacing the equal sign in constraint equations (22), (24), (26), and (28) with a sign greater than or equal to does not affect the optimal solution of the proposed optimization model;
(2) neglecting preconditions constraint formula (21), (23), (25), (27), directly adding their corresponding constraints to the proposed optimization model does not bring any difference to the optimal solution,
the model becomes:
min(2)
s.t.(7)-(20)(29)-(32)。
further, the step 3 includes:
the standard SOCP problem consists of a linear objective function and some constraints of a certain type, including second-order cone constraints, linear equality constraints and linear inequality constraints, the standard form of SOCP is described as:
min fTx
Figure GDA00019527197400000511
Fx＝g (33)
in order to make the proposed optimization model conform to the standard form of SOCP, the variables in the following formula are substituted:
Figure GDA0001952719740000051
Figure GDA0001952719740000052
Figure GDA0001952719740000053
the constraints (a) (b) (c) are converted as follows:
Figure GDA0001952719740000054
Figure GDA0001952719740000055
Figure GDA0001952719740000056
Figure GDA0001952719740000057
Figure GDA0001952719740000058
further, the equal sign in (36) is relaxed to be equal to or greater than the symbol:
Figure GDA0001952719740000059
equation (42) is re-expressed as a standard second order cone in (43), thus transforming the proposed optimization model into the MISOCP type,
Figure GDA00019527197400000510
the model becomes:
min(2)
s.t.(12)-(20)(29)-(32)(37)-(41)(43)。
before establishing the optimal configuration mathematical modeling method of the electric vehicle charging station based on the two-step equivalent method, firstly establishing a model for generating the charging demand and load data of the electric vehicle, wherein the model comprises the following steps:
step 1: modeling the parking behavior of the electric automobile;
the requirements for parking behavior include three types of areas: residential areas, business areas and office building areas to obtain distribution curves required by electric vehicles parked in various areas;
step 2: modeling the charging behavior of the electric automobile;
and step 3: and (4) load modeling.
Moreover, according to the demand of the electric vehicle charging behavior, three charging facilities are planned: a Slow Charging Facility (SCF), a conventional charging facility (NCF), and a Fast Charging Facility (FCF),
the charging requirements of the electric automobile can be divided into three types, which respectively correspond to SCF, NCF and FCF, and the classification standard of the charging requirements is as follows:
Figure GDA0001952719740000061
the invention has the advantages and positive effects that:
1. in the planning stage, the multi-type charging facilities are considered to be installed in a mixed mode, and the new factor is also properly considered in the planning stage;
2. the invention provides an optimization model for determining an EVCSS allocation scheme by taking the minimization of the annual social cost of an EV charging system as a target;
3. in order to process the scene-based electric vehicle charging power quantization constraint, two-step equivalence is proposed and adopted;
4. the optimization model is transformed into the MISocp type using accurate SOCP relaxation, which can be solved efficiently in polynomial time.
Drawings
FIG. 1 is (A) a residential area; (B) a shopping area; (C) the electric automobile arrival time per unit value characteristic distribution in the office building area;
FIG. 2 is (A) a residential zone; (B) a shopping area; (C) the electric automobile parking time per unit value characteristic distribution in the writing building area;
FIG. 3 is a flow chart of an electric vehicle charging demand modeling at a certain day;
fig. 4 is a typical load profile for different situations: (A) the working day of the residential area; (B) weekends in residential areas; (C) the working day of the shopping area; (D) weekends in shopping areas; (E) working days of office building areas; (F) weekends in office building areas;
FIG. 5 is a functional urban area under study;
fig. 6 is an optimal electric vehicle charging station planning scheme under case 1;
FIG. 7 is a comparison of costs associated with different electric vehicle charging station planning scenarios.
Detailed Description
The present invention will be described in further detail with reference to the following embodiments, which are illustrative only and not limiting, and the scope of the present invention is not limited thereby.
A two-step equivalence method based mathematical modeling method for optimal configuration of an electric vehicle charging station provides and applies a two-step equivalence method, and after equivalence and some accurate relaxation, the provided optimization model is converted into a Mixed Integer Second Order Cone Programming (MISOCP) type, so that the electric vehicle charging station programming method for minimum annual charging social cost can be effectively solved through a proper mathematical method.
In order to achieve the above object, first, there is provided a model for generating electric vehicle charging demand and load data, including:
step 1: modeling the parking behavior of the electric automobile;
step 2: modeling the charging behavior of the electric automobile;
and step 3: and (4) load modeling.
The parking behavior of the electric vehicle is significantly influenced by the land utilization of the parking area, and three typical land utilization types, namely, residential areas, business areas and office building areas are considered, and the distribution curves required by the electric vehicles parked in various areas can be obtained through corresponding historical data.
Fig. 1 shows a typical distribution arrival value curve of electric vehicles in different regions.
Fig. 2 illustrates a display parking time profile.
In order to improve the accuracy of the obtained distribution curves, the statistical data of the weekdays and weekends are processed separately. The electric vehicle arrival time per time period in fig. 1 is expressed in per unit value, and the peak number of stops of the electric vehicle is taken as a standard value. And the probability of parking time for various electric vehicles in fig. 2 is equal to the proportion of all electric vehicles that they occupy all the day.
The charging behavior of electric vehicles in urban areas has two obvious characteristics: (1) most electric vehicle owners are willing to charge electric vehicles at the destination of travel; (2) they prefer to fully charge the electric vehicle battery every time it is charged. Charging at the destination provides great convenience to the owners of electric vehicles, as they can do things they like to do (e.g., work, shopping, and charging). ) During charging of the electric vehicle, rather than waiting in a boring manner. While fully charged batteries can effectively alleviate their "range anxiety". Furthermore, when charging an electric vehicle, the selection of the charging facility directly affects its specified charging time, and the owner of the electric vehicle will often make the most reasonable decision based on the current state of charge (SOC) and its scheduled parking time.
In this context, two basic principles are concluded, namely that the owner of the electric vehicle should follow the following two principles when selecting the charging facility: (1) the charging power of the facility selected in the rated parking time is high enough to ensure that the electric automobile is fully charged in the parking time; (2) when the plurality of charging facilities satisfy the principle (1), a charging facility with the lowest rated charging power is selected. Principle (1) is easily understood as "range anxiety". Principle (2) on the one hand, high-speed charging frequently has a negative effect on the economic life of the battery, and these effects tend to be severe as the charging power increases; on the other hand, unnecessary high-speed charging results in a short charging time, and the owner of the electric vehicle has to spend additional distance and time to move the fully charged electric vehicle before departing.
For the sake of simplicity and brevity of description, three typical charging facilities are considered in the electric vehicle charging station planning, which are named as a Slow Charging Facility (SCF), a Normal Charging Facility (NCF), and a Fast Charging Facility (FCF), respectively, according to a rated charging power, and the electric vehicle charging demand is classified into several types corresponding to the typical charging facilities. The charging demand distribution of each type is obtained by a monte carlo simulation method.
The charging requirements of the electric automobile can be divided into three types, which respectively correspond to SCF, NCF and FCF, and classification standards of the charging requirements are formulated in formula (1).
Figure GDA0001952719740000081
FIG. 3 shows a flow of the spatiotemporal distribution of the charging demand of electric vehicles in urban areas modeled by Monte Carlo simulation.
The power load is also an important factor to be considered in optimization planning, in actual life, the power load fluctuates all the time in a planning stage, prediction of load distribution of each passenger car is infeasible, after reasonable simplification, the power load is divided into different types, and the load type of a certain bus is assumed to be the same as the corresponding land. From the historical load data, the load distribution for each load type can be inferred.
Fig. 4 shows typical load curves for a number of scenarios (spring/summer/fall/winter weekdays and weekends). In this process, the diversity of load types is fully considered, for each load type, the load per unit value is based on the peak load.
In order to achieve the above object, the present invention provides a two-step equivalence method-based mathematical modeling method for optimal configuration of an electric vehicle charging station, wherein the strategy implementation steps include:
step 1, establishing a basic optimal configuration model of an electric vehicle charging station containing different types of electric vehicle charging piles;
step 2, optimizing the established optimal configuration model of the electric vehicle charging station by using a two-step equivalent method;
and 3, performing relaxation optimization on the optimal configuration model of the electric vehicle charging station based on the two-step equivalent method optimization by using a second-order cone programming.
In the step 1, the basic optimal configuration model of the electric vehicle charging station including the electric vehicle charging piles of different types includes:
(1) an objective function:
with the aim of minimizing the virtual size cost, the charge and discharge control of the aggregator of the first plug-in electric vehicle was studied:
Figure GDA0001952719740000091
wherein the content of the first and second substances,
the constants 4, 96 represent four seasons of the year and a 15 minute time period contained in one day, respectively. There are an average of 65.25 weekdays and 26 weekends per season, with a total of 768 time periods contained in the above equation (384 time periods from weekdays and 384 time periods from weekends).
(a) Annual investment cost C of electric vehicle charging stationI：
Figure GDA0001952719740000092
(b) Annual grid consolidation cost CR：
Figure GDA0001952719740000093
(c) Annual usage and maintenance costs C for electric vehicle charging stationsO&M：
Figure GDA0001952719740000094
(d) Annual network loss cost
Figure GDA0001952719740000095
Figure GDA0001952719740000096
(2) Constraint conditions are as follows:
(a) and (3) power flow constraint:
Figure GDA0001952719740000097
Figure GDA0001952719740000098
Figure GDA0001952719740000099
(b) voltage amplitude constraint:
Figure GDA0001952719740000101
(c) and (3) branch current constraint:
Figure GDA0001952719740000102
(d) population balance constraints relating to electric vehicle charging:
Figure GDA0001952719740000103
Figure GDA0001952719740000104
Figure GDA0001952719740000105
(e) and (3) restricting the driving distance after charging:
Figure GDA0001952719740000106
Figure GDA0001952719740000107
Figure GDA0001952719740000108
(f) requirement constraint of charging facilities in electric vehicle charging stations:
Figure GDA0001952719740000109
Figure GDA00019527197400001010
Figure GDA00019527197400001011
(g) and (3) charging electric energy quality constraint:
because in some cases, the charging requirement of the low-power-consumption electric vehicle may be transferred to the high-power charging facility, and it is difficult to accurately quantify the charging power of a certain parameter in the process of establishing the optimization model, the following four possible situations are analyzed according to the numerical relationship between the number of the charging facilities and the charging requirement of the electric vehicle, and the charging power on the j bus is taken as an example
Scene 1: the charging requirements of each type of electric automobile can be met by the corresponding charging pile;
Figure GDA00019527197400001012
the charging power on the electric vehicle charging station bus j is expressed as:
Figure GDA0001952719740000111
scene 2: part of the SCF charging requirements are transferred to the NCF, which is fully able to meet the original requirements and the transferred requirements due to the SCF shortage:
Figure GDA0001952719740000112
the charging power on the electric vehicle charging station bus j is expressed as:
Figure GDA0001952719740000113
scene 3: due to the shortage of NCFs, part of NCF charging requirements are transferred to FCFs, while FCFs can fully meet the original requirements and the transferred requirements:
Figure GDA0001952719740000114
the charging power on the electric vehicle charging station bus j is expressed as:
Figure GDA0001952719740000115
scene 4: SCFs are not sufficient to meet the corresponding charging requirements, while NCFs cannot meet the sum of their original and transferred requirements:
Figure GDA0001952719740000116
the charging power on the electric vehicle charging station bus j is expressed as:
Figure GDA0001952719740000117
the step 2 comprises the following steps:
(1) replacing the equal sign in constraint equations (22), (24), (26), and (28) with a sign greater than or equal to does not affect the optimal solution of the proposed optimization model.
Scene 1:
Figure GDA0001952719740000121
scene 2:
Figure GDA0001952719740000122
scene 3:
Figure GDA0001952719740000123
scene 4:
Figure GDA0001952719740000124
(2) neglecting the preconditions constraint equations (21), (23), (25), (27), directly adding their corresponding constraints to the proposed optimization model does not bring any difference to the optimal solution.
The model becomes:
min(2)
s.t.(7)-(20)(29)-(32)
the step 3 comprises the following steps:
the standard SOCP problem consists of a linear objective function and some constraints of a certain type, including second-order cone constraints, linear equality constraints and linear inequality constraints, and the standard form of SOCP can be described as:
min fTx
Figure GDA0001952719740000129
Fx＝g (33)
in order to make the proposed optimization model conform to the standard form of SOCP, the variables in the following formula are substituted:
Figure GDA0001952719740000125
Figure GDA0001952719740000126
Figure GDA0001952719740000127
the constraints (a) (b) (c) can be transformed as follows:
Figure GDA0001952719740000128
Figure GDA0001952719740000131
Figure GDA0001952719740000132
Figure GDA0001952719740000133
Figure GDA0001952719740000134
further, the equal sign in (36) is widened to be equal to or larger than the symbol as shown in (42).
Figure GDA0001952719740000135
Equation (42) can be re-expressed as a standard second order cone in (43) to convert the proposed optimization model to the MISOCP type.
Figure GDA0001952719740000136
The model becomes:
min(2)
s.t.(12)-(20)(29)-(32)(37)-(41)(43)。
example (c): a utility city is selected as the test system as shown in fig. 5. It is in fact a coupled system containing both electrical and geographic information, with the target area being provided by a 10 kv radial distribution system. For convenience, it is assumed that the destinations of the electric bus and the electric car are located at the geometric centers of the land blocks, and the distances therebetween. The two plots are equal to their geometric center and the electrical load/land use in the test system is divided into three typical types, indicated in different colors, depending on the actual situation.
To show the positive effect of considering multiple types of charging facilities in the planning phase, we analyzed four examples for comparison, where the difference is the candidate types of charging facilities to be installed, as shown in table 1, and in all cases FCFs were considered, since they are the only ones that can satisfy the charging facility type and shorter parking time requirements of low SOC electric vehicles. The optimal solution for the planning model under different conditions is shown in table 2.
An optimal electric vehicle charging station planning scheme for scenario 1 is illustrated in fig. 6. Wherein the number of installations of SCF, NCF and FCF are represented by statistical bars of different colors.
In fig. 7, the costs associated with different electric vehicle charging station planning schemes are compared from an economic perspective
In summary, the numerical results of the above-mentioned ingenious design cases show that a plurality of charging devices can be installed in a mixed manner in the electric vehicle charging system to properly meet different electric vehicle charging requirements, and meanwhile, the adoption of the charging device configured in this way can significantly reduce unnecessary cost of relatively expensive devices, thereby bringing significant economic benefits to the whole electric vehicle charging system. On the basis of actual planning, the charging facilities are reasonably and economically configured.
TABLE 1 candidate types of toll facility in different cases
SCF NCF FCF
Case
1 √ √ √
Case 2 √ × √
Case 3 × √ √
Case 4 × × √
To show the positive effect of considering multiple types of charging facilities in the planning phase, we analyzed four examples for comparison, where the difference is the candidate types of charging facilities to be installed, as shown in table 1, and in all cases FCFs were considered, since they are the only ones that can satisfy the charging facility type and shorter parking time requirements of low SOC electric vehicles. The optimal solution for the planning model under different conditions is shown in table 2.
An optimal electric vehicle charging station planning scheme for scenario 1 is illustrated in fig. 6. Wherein the number of installations of SCF, NCF and FCF are represented by statistical bars of different colors.
In fig. 7, the costs associated with different electric vehicle charging station planning schemes are compared from an economic perspective
In summary, the numerical results of the above-mentioned ingenious design cases show that a plurality of charging devices can be installed in a mixed manner in the electric vehicle charging system to properly meet different electric vehicle charging requirements, and meanwhile, the adoption of the charging device configured in this way can significantly reduce unnecessary cost of relatively expensive devices, thereby bringing significant economic benefits to the whole electric vehicle charging system. On the basis of actual planning, the charging facilities are reasonably and economically configured.
TABLE 2 optimal solution of planning model (hundred thousand dollars) under different conditions
Figure GDA0001952719740000141
Figure GDA0001952719740000151
Although the embodiments of the present invention and the accompanying drawings are disclosed for illustrative purposes, those skilled in the art will appreciate that: various substitutions, changes and modifications are possible without departing from the spirit and scope of the invention and the appended claims, and therefore the scope of the invention is not limited to the disclosure of the embodiments and the accompanying drawings.

Claims (4)

1. A mathematical modeling method for optimal configuration of an electric vehicle charging station based on a two-step equivalence method is characterized by comprising the following steps of: the two-step equivalence method is a type that after equivalence and some accurate relaxation, the proposed optimization model is converted into a mixed integer second-order cone planning, and the minimum annual charging social cost can be effectively solved through a proper mathematical method, and the method specifically comprises the following implementation steps of:
step 1, establishing a basic optimal configuration model of an electric vehicle charging station containing different types of electric vehicle charging piles;
the basic optimal configuration model of the electric vehicle charging station comprising different types of electric vehicle charging piles comprises the following steps:
(1) an objective function:
Figure FDA0003147236970000011
wherein the constants 4, 96 represent four seasons of the year and 15 minute time periods contained in one day, respectively, each season has an average of 65.25 weekdays and 26 weekends, and a total of 768 time periods are contained in the above formula,
the objective function specifically includes:
(a) annual investment cost C of electric vehicle charging stationI：
Figure FDA0003147236970000012
(b) Annual grid consolidation cost CR：
Figure FDA0003147236970000013
(c) Annual usage and maintenance costs C for electric vehicle charging stationsO&M：
Figure FDA0003147236970000014
(d) Annual network loss cost
Figure FDA0003147236970000015
Figure FDA0003147236970000016
(2) The constraint conditions specifically include:
(a) and (3) power flow constraint:
Figure FDA0003147236970000017
Figure FDA0003147236970000021
Figure FDA0003147236970000022
(b) voltage amplitude constraint:
Figure FDA0003147236970000023
(c) and (3) branch current constraint:
Figure FDA0003147236970000024
(d) population balance constraints relating to electric vehicle charging:
Figure FDA0003147236970000025
Figure FDA0003147236970000026
Figure FDA0003147236970000027
(e) and (3) restricting the driving distance after charging:
Figure FDA0003147236970000028
Figure FDA0003147236970000029
Figure FDA00031472369700000210
(f) requirement constraint of charging facilities in electric vehicle charging stations:
Figure FDA00031472369700000211
Figure FDA00031472369700000212
Figure FDA00031472369700000213
(g) charging power quality constraints;
(g) the charging power quality constraint includes four scenarios:
scene 1: the charging requirements of each type of electric automobile can be met by the corresponding charging pile;
Figure FDA0003147236970000031
the charging power on the electric vehicle charging station bus j is expressed as:
Figure FDA0003147236970000032
scene 2: part of the SCF charging requirements are transferred to the NCF, which is fully able to meet the original requirements and the transferred requirements due to the SCF shortage:
Figure FDA0003147236970000033
the charging power on the electric vehicle charging station bus j is expressed as:
Figure FDA0003147236970000034
scene 3: due to the shortage of NCFs, part of NCF charging requirements are transferred to FCFs, while FCFs can fully meet the original requirements and the transferred requirements:
Figure FDA0003147236970000035
the charging power on the electric vehicle charging station bus j is expressed as:
Figure FDA0003147236970000036
scene 4: SCFs are not sufficient to meet the corresponding charging requirements, while NCFs cannot meet the sum of their original and transferred requirements:
Figure FDA0003147236970000037
the charging power on the electric vehicle charging station bus j is expressed as:
Figure FDA0003147236970000038
step 2, optimizing the established optimal configuration model of the electric vehicle charging station by using a two-step equivalent method;
the method comprises the following steps:
(1) replacing the equal sign in constraint equations (22), (24), (26), and (28) with a sign greater than or equal to does not affect the optimal solution of the proposed optimization model;
(2) neglecting preconditions constraint formula (21), (23), (25), (27), directly adding their corresponding constraints to the proposed optimization model does not bring any difference to the optimal solution,
the model becomes:
min(2)
s.t.(7)-(20)(29)-(32)；
and 3, performing relaxation optimization on the optimal configuration model of the electric vehicle charging station based on the two-step equivalent method optimization by using a second-order cone programming.
2. The two-step equivalence method-based electric vehicle charging station optimal configuration mathematical modeling method according to claim 1, characterized in that: the step 3 comprises the following steps:
the standard SOCP problem consists of a linear objective function and some constraints of a certain type, including second-order cone constraints, linear equality constraints and linear inequality constraints, the standard form of SOCP is described as:
min fTx
Figure FDA0003147236970000041
Fx＝g (33)
in order to make the proposed optimization model conform to the standard form of SOCP, the variables in the following formula are substituted:
Figure FDA0003147236970000042
Figure FDA0003147236970000043
Figure FDA0003147236970000044
the constraints (a) (b) (c) are converted as follows:
Figure FDA0003147236970000045
Figure FDA0003147236970000046
Figure FDA0003147236970000047
Figure FDA0003147236970000048
Figure FDA0003147236970000049
further, the equal sign in (36) is relaxed to be equal to or greater than the symbol:
Figure FDA0003147236970000051
equation (42) is re-expressed as a standard second order cone in (43), thus transforming the proposed optimization model into the MISOCP type,
Figure FDA0003147236970000052
the model becomes:
min(2)
s.t.(12)-(20)(29)-(32)(37)-(41)(43)。
3. the two-step equivalence method-based electric vehicle charging station optimal configuration mathematical modeling method according to claim 1, characterized in that: before establishing the mathematical modeling method for optimal configuration of the electric vehicle charging station based on the two-step equivalence method, firstly establishing a model for generating the charging demand and load data of the electric vehicle, wherein the model comprises the following steps:
step 1: modeling the parking behavior of the electric automobile;
the requirements for parking behavior include three types of areas: residential areas, business areas and office building areas to obtain distribution curves required by electric vehicles parked in various areas;
step 2: modeling the charging behavior of the electric automobile;
and step 3: and (4) load modeling.
4. The two-step equivalence method-based electric vehicle charging station optimal configuration mathematical modeling method according to claim 1, characterized in that: according to the demand of the electric automobile charging behavior, three charging facilities are planned: a Slow Charging Facility (SCF), a conventional charging facility (NCF), and a Fast Charging Facility (FCF),
the charging requirements of the electric automobile can be divided into three types, which respectively correspond to SCF, NCF and FCF, and the classification standard of the charging requirements is as follows:
Figure FDA0003147236970000053
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