2018年美赛o奖论文d73156-construct all-electric network

1、Team Control Number73156For office use onlyFor office use onlyT1 T2T3 F1 F2F3 Problem ChosenD2018MCM/ICM Summary SheetConstruct all-electric networkThe transformation from gas vehicles to electric vehicles becomes a hot topic all overthe world. In order to get the schedule of the location of chargin

2、g stations and predict the process of transformation tendency, we establish several models to solve the questions.For question 1, we firstly establish a model based on queuing theory. Furthermore, we construct a multi-objective programming model based on information of the current Tesla charging net

3、work in the US. With the help of Matlab, we find that Tesla is on track to allow a complete switch to all-electric in the US. We obtain that the number of charging stations needed is about 1.7million when all gas vehicles transform to electric vehicles, and the distribution proportions of charging s

4、tations in urban, suburban and rural areas are 67:23:10.For question 2, we establish the site selection models of charging station for urban, suburban and rural areas of South Korea, separately. Combining with the programming model which we established in problem 1, we obtain the number, location an

5、d distribution of charging stations in Korea. We get the key factors that affect our plan are the building cost of chargers and the government investment. By considering six indexes, we establish a logistic model. Using this model, we firstly give the timeline of the full evolution to electric vehic

6、les. We find that the key factor for this situation is policy orientation. Then we further predict the number of the electric vehicles of urban and rural areas in South Korea separately. Through the logistic model, we obtain that South Korea should give preference to build charging station in cities

7、. Similarly, we find that the two key factors which influent our model most are wealth distribution and government investment. Additionally, we introduce a concept called lag index to measure the relationship between the car and the charging station.For question 3, we establish a classification syst

8、em through Q-type clustering model. According to different national conditions, we divide the countries into three categories. Through some analysis of the Q-type clustering model, we find out that the key factors that trigger the selection of different approaches to growing the network are policy o

9、rientation, wealth distribution and government investment. According to these factors, a targeted electric network development plan has been proposed.For question 4, to study the influence of various new technologies, we set several indicators to establish our models, such as GDP and OPH. By analyzi

10、ng our evaluation model, we find that these technologies impact the growth rate of electric vehicles, which contributes to the growing popularity of electric vehicles. Besides, the population of electric vehicles will be driven by these technologies.For question 5, we prepare a one-page handout for

11、the leaders identifying the key factors which they should consider as they return to their home country to develop a national plan tomigrate personal transportation towards all-electric cars and set a gas vehicle-ban date forT4 F4 different countries.更多数学建模资料请关注微店店铺“数学建模学习交流” /RH

12、O6PSpA数模乐园整理提供，更多数学建模资源请关注微信公众平台“数模乐园”或网站获取Key words: site selection model, logistic model, Q-type clustering model, electric networkTeam#73156Page 1 of 27Content1 Introduction.21.1 Background21.2. Restatement of the Problem31.2 Literature Review31.3 Our Work42 Assumptions and Justific

13、ations43 Distribute the charging stations in the US43.1 Concepts introduction.53.2 All-electric evaluation model63.2.1 The model construction.63.2.2 Model solution and analysis73.3 Distribution optimization model83.3.1 The model construction.83.3.2 Model solution and analysis94 Study on South Korea9

14、4.1 Urban charging station location model104.2 Suburban charging station location model124.3 Rural charging station location model124.4 Logistic model134.4.1 Index definition.134.4.2 The model construction.134.4.3 Model solution and analysis144.5 Answers of the Questions145 Create a classification s

15、ystem165.1 The model construction.175.2 Model solution and analysis176 Comment on the effect of new technologies186.1 The model construction.186.2 Model analysis187 Sensitivity Analysis198 Conclusions208.1 Strengths208.2 Weaknesses208.3 Model extension209 A Handout to the Leaders2010 Reference2111 A

16、ppendix.22Team#73156Page 2 of 271Introduction1.1 BackgroundNowadays, fossil fuel and the environment protection have become the hottest issues in the world 1. The main transportations all over the world are based on fossil oil, which has caused serious environmental pollutions. Since the resource of

17、 fossil fuels is limited and it always leads to the pollution, the transition of it to more clean energy is inevitable. In order to realize this aim, electric vehicles which are the representatives of new energy vehicles, have been recognized as the main development direction of the transformation i

18、n the automotive industry in the 21st century 2.It is well established that electric vehicles are high efficiency, low noise and nearly zero pollution 3. The advantages of electric vehicles are obvious. Hence, they have been widely used all over the world. To promote the large-scale development of e

19、lectric vehicles, it is necessary to improve the corresponding infrastructure. As an important part of the construction of electric vehicle facilities, charging stations are crucial to the development of the entire electric vehicle industry. Where and how many do we need to construct the charging st

20、ations? Selecting the correct location and estimating the number of charging stations are very important.1.2. Restatement of the ProblemWhen we transform the gasoline and fossil fuel cars to electric vehicles, we need to consider the network of charging stations and the growth of them over time. In

21、order to make a development schedule of the charging stations for a country, we are required to answer the following questions.1. Build a model to judge whether or not Tesla can switch to all-electric all over US. Distribute the charging stations in case of full electric.2. Select a country to deter

22、mine the number and location of charging stations. Make a timeline for the full evolution and find out the key factors that matter your model most.3. Consider whether the model is suitable for the countries with different geographies, population density distributions, and wealth distributions situat

23、ions, and discuss the feasibility of creating a classification system.4. Consider that how new technologies affect the analysis of the increasing use of electric vehicles.5. Write a one-page handout for the leaders to identify the key factors they should consider and set a gas vehicle-ban date.1.2 L

24、iterature ReviewUnder the pressure of energy conservation and low carbon, the research on the electric vehicles and the construction of charging station network have made great progress.In the planning of charging facilities, some researchers point out that the layout of charging stations are affect

25、ed by the number of electric vehicles 4. The construction of power stations needs to meet the requirements of traffic density. Only in this way can they develop in harmony. Taking California for example, we know that there are one million new energy vehicles in existence 5. By combining the supply a

26、nd demand ofTeam#73156Page 3 of 27California electricity, they build linear and nonlinear models, aiming at saving energy and reducing emissions. Wang 6 proposed a new method for the layout of charging station. In 6, they considered several influential factors such as technical level, holding capaci

27、ty and charging behavior of electric vehicles. However, the proposed load-shedding space segment prediction method does not take into the driving features, using mode and charging mode into account. The weight of the method is subjective and the prediction error is large.For selecting the location o

28、f charging stations, Holzman 7 aimed at minimizing the square distance of user-to-facility locations, and constructed the location selection model based on network planning. Then he discussed and expanded the model with specific conditions. Additionally, the authors 8 build the optimization model, w

29、hose algorithm was based on game theory. Hakimi 9 conducted a systematic study of the selection of facility location. He considers the location of one or more facilities within a network, providing that the total distance or the maximum distance between the facility and the point is minimized. The t

30、heory makes the selection of charging station furtherdeveloped on the basis of the original theory.However, the development of electric vehicles are still at the initial stage. The layout planning theory of charging facility is also under exploration and there are still very little studies about the

31、 network of charging stations. Although some achievements have been made, we still have lots of the uncertainties to study. In this paper, we propose a brand- new model to imply the location of charging stations. Furthermore, we extend our models to suit different circumstances.1.3 Our WorkFirstly,

32、we establish a multi-objective programming model to calculate the number of charging stations. Besides, we establish a site selection model to determine the distribution in urban, suburban and rural areas. Then we choose six indexes which affect the number of the electric vehicles. According these i

33、ndexes, we establish a logistic model to predict the number of the electric vehicles. We can find out the key factors through the predicted data. Furthermore, we can analyze the relationship among the different key factors. Next, we expand our model. We establish a classification system through Q-ty

34、pe clustering model to analyze the electric network development plan for countries in different categories. We also consider the effect of various new technologies, and analyze the status of each technology and the trend of future development. Finally, we write a handout for the leaders to offer the

35、m some effective advice on the development of electric network.2lAssumptions and JustificationsThe charging station which has been built cannot be removed. Since the construction of charging station costs a lot of manpower and financial resources, the demolition of it will cause greater losses.The c

36、andidate points of charging station are obtained through reasonable analysis and rigorous demonstration. Because if the charging station is built in an area with poor or unsafe conditions, it will lead to fewer cars to be charged.lTeam#73156Page 4 of 27lEach charging station will not break down duri

37、ng charging process. Because the charging station network will be regularly maintained.Vehicle arrival obeys to Poisson distribution. It is demonstrated in statistics.l3Distribute the charging stations in the USTask one requires us to determine whether Tesla is on track to allow a full switch toall-

38、electric in the US, and give the distribution of charging stations based on all-electric condition. Firstly, we searching the population density and car ownership per capita of different states of America. According to population density, we divided the United States into urban, suburban and rural a

39、reas. Secondly, the total amount of cars in each area is determined by the amount of car ownership per capita. According to queuing theory, we calculate the average waiting time for car charging. Then, we can get the number of supercharging stations theoretically needed. We compare it with the actua

40、l number of charging stations, determine whether or not the US can go all-electric. Finally, with the goal of minimum cost and minimum waiting time, we build a multi-objective optimization model to calculate the number of charging stations required in each region.3.1 Concepts introductionl Populatio

41、n densityLet i denote the population density, i.e. the number of people per square kilometer. The population distributions in the US are obtained from the US Census Bureau 10. We divide the United States into three regions based on the intensity of the population.When the population density is great

42、er than 150, the area is the urban. Similarly, when the population density is between 50 and 150, the area is suburban. Otherwise, the area is the rural. The dividing results are as follows.Figure 1: The population density distribution in the USCar ownership per capitalLet Hi denote the car ownershi

43、p per capita, which means the average number of cars owned by each individual. According to the U.S. official statistic 11, the overall car ownership per capita is 0.8. Wherein the car ownership per capita in urban, suburban, rural areas are 0.94, 0.83, 0.60 respectively.lConnectivity rateThe distan

44、ce between two adjacent electric vehicle charging stations has a great influence on the convenience of charging. The closer the charging station is, the higher the charging convenience will be. In general, a supercharging station can provide up to 170 miles of power. If the distance between two char

45、ging stations is less than or equal to this value, then the car can provide an endless stream of electricity. That is to say, theTeam#73156Page 5 of 27distribution of charging station is reasonable to satisfy the charging needs. Therefore, we define the connectivity rate to reflect the rationality o

46、f charging station distribution.connectivity rate = number of adjacent stations 170 miles awaynumber of all adjacent stations /2We find the locations of all the charging stations built and to be built from the Tesla website, and mark them on the US map. Then we connect all adjacent charging stations

47、 whose distance is less than 170 miles. The road map is shown as below.Figure 2: Connectivity diagramAs shown in figure 2, the coverage of the charging stations has basically covered the entire United States, especially in areas with a high population density. After calculation, we find that the con

48、nectivity rate has reached 71%. Therefore, we have initially judged that Tesla is making the United States on an all-electric track. Next, we will analyze in detail through modeling.3.2 All-electric evaluation model3.2.1 The model construction1) Actual number of electric vehiclesThe total number of

49、electric vehicles in a region will be affected by many factors.The macroscopic parameter of rangeis Si which stands for the acreage ofarea. Theithparameter Pirepresents the percentage of electric vehicles initharea. Hence, we canget the equation between the total number of electric vehicles and the

50、various factors.ni = ri Si Hi Pi2) Theoretical number of electric vehiclesWhen the number of electric vehicles reaches a certain level, there needs to be enough charging stations to serve it. Because the supercharging station is much more expensive than the destination charging station, we first con

51、sider the number of super charging station. According to the survey data of General Motors in the United States, the utilization rate of a public charging station is 35%. The electric vehicle can run T miles when charging once at a supercharging station. According to the average annualdriving distan

52、ceof the car and the average number of driving days, we canLDcalculate the number of times ( Nsc ) a car is charged on the supercharging station every day.L=NscDTThrough multiplying the total number of electric vehicles in each area by the average number of charging times each day, we can get the to

53、tal number of times all the vehicles in the area needs to be recharged daily. For the charging stations, these are the numberNitotalof charging vehicles they need to service each day,Team#73156Page 6 of 27Nitotal =Nsc ni .Vehicle arrival is a typical Poisson distribution event 12. The average servic

54、e timeof a supercharging station are t hours every day. There arevehicles arriving atcharging station every hour. Poisson distribution is expressed as follows,e- t (t)JPJ (t) =(J = 0,1, 2,.).J !A supercharging station can be viewed as a single service desk model M/M/1. The average service time per c

55、ar is . When the vehicle arrives at the charging station at a Poisson distribution, if at this time there are a number of vehicles are charging, then the vehicle must wait in line,2 Lq = ( -)If the average number of arrivals is greater than a certain degree, cars that arrive later cannot be fully ch

56、arged in time. Under the condition of stable system, the average waiting time will increase first, and then close to a stable value. That is the average waiting timeLq=.TqSCGiven a waiting time, we can calculate the total number of cars that a supercharging station can service nsc = t .3.2.2 Model s

57、olution and analysisIn a charging station, waiting time is generated when more vehicles are queued for charging. The longer the waiting time, the lower the quality of service. In order to make electric vehicles more convenient to charge, we have to shorten the waiting time for the car. Therefore, the number of charging stations need to be increased. The convenience index CIi is defined to reflect the ease of charging in each area.Nitotal n rCI =sciWhere ri denotes the actual number of supercharging stations.When the actual number of vehicles needed to be charged is less than themaxi