2012年数学建模美赛优秀论文

发布于:2021-09-28 18:04:23

Abstract
We develop a basic mathematical model for the electric vehicle using system. The model shows interactions of electric vehicles usage amount and various aspects. In environmental aspect, the pollutions electric vehicles produced is obviously less than internal combustion engine vehicles. In economic aspect, the energy cost of electric vehicle is far less than internal combustion engine vehicle, but due to the cost of production and batteries, the total cost is higher. In social aspect, the demand of electric vehicle is limited because of inconvenience. In order to increase the usage amount, extra investment is necessary. Applying the impact of every aspect to the basic model, we simplify the model to be an optimization model with the view of maximizing the total benefit. The constraint conditions are the amount of demand, generation capacity and the cost of electric vehicle. We work out the usage amount maximize the total benefit. We investigate the key factors that governments and vehicle manufacturers should consider. Governments take seriously whether the demand can be enhanced and whether the increase number would aggravate burden of electric power generation, possible policy changes to improve the situation including providing subsidy, building more battery charging stations and improving capacity of batteries recycling. The key factors that manufacturers should consider are how to lessen electric vehicle cost and how to expand sales volume. Our results show that the optimal popular rate is 37.5% at present, we estimate the amount of oil the world would save is 36833 million tonnes. Finally, we setup a model analyzing the proportions of each energy source, and the annual change rate. We have the result: 434 million MWh of coal-fired power, 183 million MWh of natural gas power, 198 million MWh of nuclear power and 144 million MWh of wind power.

Optimizing the Bene?t of Electric Vehicle Using System

February 15, 2011

1
1.1

Introduction
Background

An electric vehicle, also referred to as an electric drive vehicle, uses one or more electric motors for propulsion[?]1. Now the power unit of vehicle is divided into two major categories: electric motors and internal combustion engines. Gasoline and diesel burned in internal combustion engines produce nitrites of oxygen, vehicle-born monoxide, carbon dioxide and particle pollution, etc. These lead to air pollution that seriously threatens human health. In addition, greenhouse gases among them cause greenhouse effect and climatic change. Instead, electric vehicles have several advantages: energy ef?cient, environmentally friendly and energy dependence less. As industrial development and population growth, the energy crisis is becoming more obvious. Because of so many advantages over internal combustion engine vehicles, numerous countries vigorously encourage the development of electric vehicles.

1.2

Problem Restatement

Although electric vehicles have many advantages, controversies about the widespread use still exist. Pollution caused directly by electric vehicles is low, but there are hidden sources of pollutants associated with electric vehicles. If electricity on electric vehicles is converted from fossil fuels, energy loss and pollution still produce in the process of power generation. On one hand, the electric vehicle is limited by capacity and lifetime of a battery. This will greatly improve costs of electric vehicles. On the other hand, the time spent in charging in is much longer than pumping oil. This wastes users of electric vehicle much time to wait. So people wonder: whether electric vehicle is truly more energy-saving and environmental, whether its widespread use is feasible and bene?cial.

1

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In this paper, we expound various aspect impacts of the widespread use of electric vehicles and give rationalization suggestions for the governments and vehicle manufacturers. We calculate whether electric vehicles really can save fossil fuels, and work out amount of fossil fuels saving by widely using electric vehicles. To achieve the largest number of bene?ts to different aspects, we develop the model to con?rm the amount and type of electricity generation that conform to electric vehicle.

2

Basic Model

The widespread use of electric vehicles will affect the environment, social, economic, and many other aspects. And governments and automobile manufacturers play an important role on popularization of electric vehicles. So, we build a feedback effect model to solve problem. We use Figure 1 to show interactions of electric vehicles usage amount and all aspects. We assume that the sales volume is equal to usage amount.

Figure 1: Interactions of electric vehicle using system

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We develop the model, to analyze whether the widespread use of electric vehicles is feasible and bene?cial. First, we assume that the amount of global vehicles is unchanged in a certain time. And we presume that the demand of electric vehicles meets a time function. The research indicates that the pollution electric vehicles produce is obviously less than internal combustion engine vehicles. In the economic aspect, fuel cost of electric vehicle is far less than internal combustion engine vehicle. However, the price of electric vehicle is higher than internal combustion engine vehicles. Besides, electric vehicles need replace batteries on account of lifetime limit and the batteries are quite expensive. In the social aspect, the demand of electric vehicle is limited because of inconvenience, in order to increase the usage amount, extra investment is necessary. Total bene?t is comprised with environmental, economic and social factors. We de?ne that amount of electric vehicles is Nv . Environmental bene?t Bev and social bene?t Bs are the functions of Nv , economic bene?t Bec is a function about Nv and time t, the total bene?t is de?ned as below B = Bev (Nv ) + Bs (Nv ) + Bec (Nv ,t) So, the problem is transformed into ?nding the the maximum value of total bene?t in the some related constraint conditions. The main factor of limiting quantity is electric vehicle demand. The demand is less, because of the electric vehicles needing often charged and no suitable for long-distance transportation. Sales price is also a limiting factor: the higher the price, the less sales. According to the above, we have the conclusion Nv < N(D) where N(D) is maximum usage amount deduced by demand. The widespread use of electric vehicles will bring some other problems. For example, the large electricity consumption affects normal life especially at peak period. Electricity consumption always subjects to power generation level constraints. Consumption E(Nv ) and generating capacity Eg should comply with the following relationship Nv < N(Eg ) where N(Eg ) is the maximum of usage amount deduced by the capacity of electricity generation. Relation of the price and sales is inverse proportion. Nv < N(P) where N(P) is the maximum of usage amount deduced by price. We analyze concretely effects of the widespread use of electric vehicles to environment, economy, society.

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2.1

Health and Environment Impact

Automobile exhaust gas produces carbon monoxide (CO), nitrogen oxides (NOx ), volatile organic compound (VOCs), particulate matter (PM10 and PM2.5 ) lead compounds and sulfur compounds, etc, are also harmful substances. [2]. Whereas the diversity and complexity, we consider ?ve substances: nitrogen oxides, CO, PM and carbon dioxide. 2.1.1 Nitrogen Oxides

Nitric acid vapor and related particles produced in the reactions can harm human breathing system, cause central nervous system dysfunction, and even cause premature death in extreme cases. Studies of bronchial responsiveness among asthmatics suggest an increase in responsiveness at levels upwards from 200? g/m3 [3]. In respect of atmosphere pollution, NO is the catalytic agent of ozone decomposition. Hence, NO play a damage role for ozone layer. NO2 may decrease lung function and increase the risk of respiratory symptoms such as acute bronchitis and cough and phlegm, particularly in children[4]. We seek out date of year of 2005 whole nitrogen oxides that produce in various kinds of processes (Figure 2) [5].Through the table we ?nd that nitrogen oxides are mainly from vehicle exhaust. Every year there are about 6491821 ton of nitrogen oxides that occupied 35.5% of this emission.

Figure 2: National Nitrogen Oxides Emissions by Source Sector in 2005 Meanwhile we also ?nd emission date of nitrogen oxides from 1980 to 2009 (Figure 3), it is a set of many sites, the 90th percentile means the 90th site value in the data by ascending counts, so does the 10th percentile, and the mean is the mean value of all sites.

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We gain the conclusion that the national nitrogen oxides level decrease year by year. The national nitrogen oxides level was lower than national standard. However, the evidences emerged that respiratory disease morbidity of people living for a long time in association with annual NO2 concentration increase. In brief, nitrogen oxides are seriously harm

Figure 3: NO2 Air Quality, 1980-2009 for human respiratory system and ruinous to ozonosphere. As to automobile nitrogen oxides emission accounting for large part of total nitrogen oxides, the widespread use of electrics can substantially reduce nitrogen oxides emissions. And it is bene?cial for health and environment. 2.1.2 Carbon Monoxide

CO can cause harmful health effects by reducing oxygen delivery to the organs (like the heart and brain) and tissues, and leads to dysfunction of feeling, reaction, understanding and memory, etc. Blood circulation badly damaged even threatens human life. Carbon monoxide is mainly hazardous to human health, and has little in?uence on climate. We also collect the relevant data, such as national carbon monoxide emissions by different source sector in 2005 (Figure 4). It indicates that the amount of automobile CO emission accounting for half of total CO. And here is a set of data of 1980-2009 CO air quality (Figure 5), it shows that the CO air quality has an 80% decrease in national average from 1980 to 2009. Even so, the current CO concentration may damage the human blood system. If it spread with the electric vehicles instead of the fuel automobiles, the CO concentration could decrease more than a half. Therefore, we can see the CO emission is hazardous to human health, and the effect on climate change is inconspicuous. However, we should take decreasing CO concentration seriously in order to decreasing the incidence rate.

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Figure 4: National Carbon Monoxide Emissions by Source Sector in 2005

Figure 5: CO Air Quality, 1980-2009 2.1.3 Particulate Matter

The PM2.5 is the particles that is smaller than 2.5? m. The range of health effects is broad, but is predominantly to the respiratory and cardiovascular systems. All population is affected, but susceptibility to the pollution may vary with health or age[3]. We get the information about PM2.5 and PM10 by source sector in USA from the internet (Figure 6). This data indicates that the road dust is the main source of PM, and the source, on road vehicle, is only 3.04% in PM2.5 and 0.97% in PM10. So the amount of internal combustion engine vehicles changed is less in?uence on the total particulate matter. But even so, the widespread use of electric vehicles is good to decrease the amount of PM.

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Figure 6: The PM2.5 and PM10 Emissions by Source Sector 2.1.4 Carbon Dioxide

Carbon dioxide is a kind of greenhouse gas, as we all know, would produce the greenhouse effect which leads to increase of temperature. Within limits, greenhouse gases in the atmosphere ensure the suitable degree to people. Carbon dioxide makes a 9 to 26 percentages contribution to the greenhouse effect[6]. While, the transportation sources were responsible for about 27 percent of total U.S. GHG emissions in 2003(Figure 7), i.e. 1,866.7 Tg CO2 Eq (?gure 6, Tg CO2 Eq means million metric ton of Carbon dioxide equivalent)[7]. We also ?nd that the CO2 make contribution to the greenhouse gas ?oating from 78 percentages to 83 percentages. So, CO2 transportation produced aggravate the greenhouse effect. If using electric vehicles instead using internal combustion engine vehicles, it is effective for relieving the greenhouse effect. 2.1.5 Total reduced pollution

In above sections, we analyzed several typical pollutants from internal combustion engine vehicles operation, the harms to the human health and the environment are greatly negative in?uence. Now we quantitatively analyze total pollution reduction of fuel automobile quantity change caused. We use the 2005 American data including nitrogen oxides, carbon monoxide, particulate matter and carbon dioxide. In US, the transportation produces 1988 million metric tons carbon dioxide, and is 33.29% of total energyrelated carbon dioxide emissions in 2005[8]. Then we get the date of the 2005 pollutants changes that internal combustion engine vehicles instead of electric vehicles (Table 1)

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Figure 7: U.S. Greenhouse Gas Emissions by End-Use Economic Sector, 1990-2003 We rank these ?ve kinds of pollutants according severity of effect to the health and the Table 1: The Change of Pollutants after Spread the Electric Vehicles Kind Nitrogen Oxides Carbon Monoxide PM2.5 PM10 Carbon Dioxide Ratio of Total Substance 35.5% 58.78% 3.04% 0.97% 33.29% Quantity (Tonnes) 6,491,821 48,544,438 136,182 193,160 1,988,000,000

in?uence of climate. While 5 means is serious, 1 means is light. Then we evaluate the Table 2: The Grade of Pollutants on the effect with Health and Climate Kind Nitrogen Oxides Carbon Monoxide PM2.5 PM10 Carbon Dioxide Climate Health 4 1 3 3 5 5 5 4 4 1

effect of pollutant changes to the health and the in?uence of climate with comprehensive evaluation. We calculated as follow, ) ( 1 5 Ai j Ri Sj = ∑ 5 i=1 5 where S j is in?uence degree of widespread use of electric vehicles( climate j=1, health j=2);

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Ai j is de?ned as the effect of pollutant i to j; Ri stands for rate of pollutants change. Finally, we conclude that S1 = 0.152ˇ nS2 = 0.208. This is effect degree of climate cˇ and health in 2005 under American electric automobile comprehensive promotion. That is to say, if all internal combustion engine vehicles are instead by electric vehicles, the harm of these pollutants to climate could reduce by 15.2%, and to health reduce by 20.8%. 2.1.6 Pollution of Electric Vehicle

The main pollution of Electric vehicle is battery pollution. At present the common batteries include lead-acid battery, nickel hydrogen battery and lithium-ion battery. The lead pollution can cause brain and kidney damage, hearing impairment, and learning problems in children[?]10. The lead-acid vehicle battery recycling rates top 95% in the United States, and only about 5% of batteries may leave pollution. Because we have no reliable data of storage batteries using, we just estimate hundreds of millions cells of batteries being used in US. However, we could reduce the lead pollution through improve the battery recycling rate. The nickel hydrogen battery mainly contains nickel hydroxide and potassium hydroxide. It has few effects on environment and health. It has less ef?cient and higher energy density than lead-acid. As a result of high performance and low pollution, lithium-ion battery with further improvement will be the most suitable electric vehicle batteries. Because the pollution produced by lead-acid battery is obviously serious, nickel hydrogen battery and lithium-ion battery are more bene?cial to use in vehicle battery. And their performances should be improved, such as electric capacity, lifetime and recycling rate.

2.2

Social Impact

On the one hand, if the amount of electric vehicles becomes large, the demand of electric power will increase. When it goes beyond a limit value, the electric power will be cut off to insure the safety. One the other hand, if the capacitance of batteries is not large enough, the electric vehicles could not travel to destination. Both of two aspects above are the factors of social impact. In order to avoid the former, it is advisable to build a number of charging stations. We recommend that the users charge batteries at off-peak times to relieve stress of peaktimes. Four hundred and ?fty thousand dollars is needed to build a charging station. One charging station can serve the ?xed number of electric vehicles, so we have Ns = Nv kc

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where kc is the number of electric vehicles that one charging station can serve, Ns is the number of charging stations, and Nv is the number of electric vehicles. Collecting the data about charging time and the scale of charging stations, we ?nd that it takes 15 minutes at least to make a battery charge enough power[11], and one charging station can serve 100 electric vehicles at one time. There are 5 hours during off-peak time per day, we assume that charging stations charge batteries at the off-peak time and all electric vehicles charge in the charging stations . So we have kc = 2000. Building a charging station need $450000[12], so the investment in building charging stations is 450000Ns . The limit of capacitance is also a problem. How far an electric vehicle can travel that depends on the energy consumption of the vehicle and the capacitance of its battery, likewise, how far an internal combustion engine vehicle can travel depends on the energy consumption and the volume of its fuel tank. All the factors are varied with the type of vehicles. After searching, we ?nd that although the capacitance, volume and energy consumption is different, the distance that a vehicle can travel is approximate, they are approximate 600 kilometers for internal combustion engine vehicle and approximate 150 kilometers for electric vehicle. The consumers prefer to the one that can travel farther. So we have the demand of electric vehicles is 1 of the demand of normal vehicles. 4

2.3

Economic Impact

One of the most important objectives of manufacturing electric vehicles is to save energy. Transports consumed a lot of valuable non-renewable fossil fuel. And, the reserves of fossil fuel will be exhausted consequentially. Economy can bene?t from the widespread use of electric vehicles. Because of the follows: ? The energy consumption of electric vehicles is low, that is to say, ef?ciency will be improved. ? The electricity can be generated by the renewable energy, such as wind energy and solar energy. So the fossil fuel would be saved. That means save money. In addition, the nuclear energy is enough to generate electricity. ? The techniques to reduce the energy consumption of the electric vehicles will be improved. However, there are some weaknesses of widely using the electric vehicles: ? The cost of research is more than normal vehicles. ? The cost of batteries manufacture is extremely expensive. electricity. ? The lifetime of battery is restricted.

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The necessary electricity of electric vehicles is generated from ?ve parts. They are petroleum, nature gas, coal, renewable energy and nuclear. Petroleum, nature gas, and coal are fossil fuel, among them, petroleum and nature gas are also a part of the energy of transport. In fact, the amount of natural gas that can be saved is low, so we ignore it, just model the consumption of petroleum. Let E pe1 be the amount of petroleum using in normal vehicles, E pe2 be the amount of petroleum using to generate electricity for electric vehicles. E pe1 = v p E1 ηo

where E1 is the amount of energy normal vehicles using per 100 kilometer, v p is the proportion of petroleum using in transport, ηo is the ef?ciency of internal combustion engine. w p E2 E pe2 = ηm η p where E2 is the amount of energy electric vehicles using per 100 kilometer, w p is the proportion of petroleum using in electricity generation, ηm is the ef?ciency of electromotor, η p is the ef?ciency of generating electricity with petroleum. It is easy to ?nd that ηo = 0.4, ηm = 0.9,η p = 0.38. We use the data of 2009 U.S. Energy Information to solve

Figure 8: The Source of Electric Power it (Figure 8)[13]. From Figure 8 we can de?ne that v p = 0.94, w p = 0.01. We select RAV4 EV and RAV4 to make an example to compare[14]. RAV4 EV consumes 20 kWh electric energy per 100 kilometers, RAV4 consumes 8.5 L gasoline per 100 kilometers. Then we calculate out that E pe1 = 19.975L, E pe2 = 0.6086. Similarly, how much natural gas is saved can also be calculated. In order to conform to the reality, we set up a mathematic model to calculate the cost of vehicle whole life. We consider the cost of production C p , energy Ce , repair Cr , and

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batteries Cb . The total cost of vehicle in the whole life C is as below C = C p +Ce +Cr +Cb We also utilize the example of RAV4 EV and RAV4 to illustrate. Total distance of the both vehicles can travel in the whole life are 500000 kilometers. The price of petroleum is $0.36 per liter, so Ce is respectively $1095.5 and $35955. We de?ne C p is equal to the price of vehicle, so C is respectively $60000 and $30000. According to the scrap norm of vehicles, both usage limit time is 10 years. The cost of repair per year is respectively $450 and $1500, so C p the cost of repair during 10 years is respectively $4500 and $15000. Twelve replacements are necessary for the electric vehicle to travel the total distance, the price of a battery pack is $3000, so Cb is $36000. In conclusion, the cost of electric vehicle is $101600, and the cost of normal vehicle is $80955. The result indicates that the energy cost of electric vehicle is far below internal combustion engine vehicle, but the total cost is higher. We consider the main factors of electric vehicle are the cost of production, the price of batteries and the lifetime of batteries, while the main factors of internal combustion engine vehicle are the price of fuel and the cost of production. Hence, the reduction of petroleum will result in the cost of internal combustion engine vehicle rising. To improve the electric vehicle economic effectiveness, the efforts should be made to reduce the cost of production, develop cheap batteries and improve the life of batteries.

2.4
2.4.1

The Key Factors
Governments

We still use basic model to analyze the key factors that governments taken serious. Synthesizing in?uences of all aspects, both the advantages and the disadvantages, we believe promotion to electric vehicles is very necessary in the long term. So the government needs to consider how to reach maximum of total bene?t at each stage. We provide the following key factors, ? How to lessen electric vehicle cost. ? What strategies to execute. ? Whether the increase number would aggravate burden of electric power generation. In a word, the most important issue governments faced is how to ensure of total bene?t at each stage. To help promote electric vehicles, the government can implement policy as below. ? Governmental subsidy. If the governments give electric vehicle buyers certain subsidies, there would be more consumers choosing to buy electric vehicles.

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? Build more battery charging stations. To alleviate charging pressure and meet more demand, the governments could build more battery charging stations. ? Improving capacity of batteries recycling 2.4.2 Manufactures

The cost of electric vehicle research and development is expensive, and sales volume is less. Even at high price and high pro?t, the sales proceeds of electric vehicle is less than internal combustion engine vehicle. In order to the survival and development of enterprises, manufactures would continue to increase development and production of electric vehicles. Manufactures need to consider the factors as follows. ? Governmental subsidy. If the governments give electric vehicle buyers certain subsidies, there would be more consumers choosing to buy electric vehicles. ? How to expand sales volume. Hence, the most important issue manufactures should solve is technology improvement. ? Improve the performance of vehicle battery. ? Spread the advantages of vehicle battery.

3

How much oil the world would save

Utilizing the model outlined above, we can calculate how much oil one electric vehicle can save in America. Now what we should do is to estimate the amount of electric vehicles and to analyze the energy ?ow of other countries. As we analyzed above, there exists Nv that maximizes B. When time is unchanged, Bev and Bec only relate to the variable Nv . Bs is 0 before point D that represents the demand amount of electric vehicles. When Nv is larger than D, extra investment is necessary to make using electric vehicles more convenient. Let b be the derivative of B, so b increases with the increase of Nv , then decrease with the increase of Nv . Finally, it becomes negative. The following ?gure shows the variation of b. It is obvious that when b is 0, B reaches the maximum value. So the area of shaded part is the maximum value of B. We calculate that the effect degree of climate and health is respectively 0.152 and 0.208, the effect degree of economy is -0.255. The demand of electric vehicles is 1 of the demand of normal vehicles. At 4 present, the total number of vehicles is 1 billion[15], so D is 0.2 billion. When Nv is more than D, we consider that the extra investment are government subsidy and building charging stations. So we have the following equations. { b = 0.105Nv , Nv < D b = 0.105Nv ? 0.533(Nv ? D), Nv ≥ D

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Figure 9: The rate of total bene?t varies with the amount of electric vehicles Let b be 0, we can calculate that Nv = 0.375 billion. That is to say the popular rate of using electric vehicles is 0.375. In fact, there are some differences among every county in the amount of vehicles and energy ?ow. We divide all countries into two groups, OECD members and non OECD members[16]. Because the technology level and some other factors of non OECD countries is lower than OECD countries, they utilize more petroleum in transportation, v p = 0.94 in OECD countries, v p = 0.97 in non OECD countries. The consumption of petroleum relate to the amount of vehicles between OECD members and non OECD members. The data is from 1995 to 2006 as Table 3[17]. Table 3: The consumption of petroleum(Thousand Barrels per Day) Time 1995 1996 1997 1998 1999 2000

OECD 44968.31 46021.55 46775.81 46934.55 47869.69 47925.71 non OECD 25164.81 25649.20 26651.08 27118.39 27857.47 28786.19 Time 2001.00 2002.00 2003.00 2004.00 2005.00 2006.00

OECD 47987.81 47943.75 48653.10 49434.54 49824.31 49563.20 non OECD 29455.74 30145.67 31007.28 32973.13 34180.56 35416.20 We calculate the proportion of petroleum consumption, as the Figure 10. Observing ?gure, we ?t them to be a line. After that we can calculate the proportion of the amount of electric vehicles is 1.34 now. So the amount of vehicles in OECD countries is 0.57 billion, and the amount of vehicles in non OECD countries is 0.43 billion. The proportion of petroleum using in electricity generation w p is also different. But the difference is small, so we consider w p of the two groups approximately equal.

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1.85 1.8 1.75 1.7 1.65 1.6 1.55 1.5 1.45 1.4 1.35 0 2 4 6 8 10 12 14

Figure 10: The Proportion of Petroleum Consumption The amount of oil can be saved is Os = (E pe1 ? E pe2 )Nv L where Os is the amount of oil can be saved, C is the total distance one vehicle can travel in the whole life, the unit of it is 100 kilometers, E pe1 ? E pe2 is how much oil one electric vehicle can save. Considering the difference between the two groups, we have the ?nal result is 36833 million tonnes.

4
4.1

Model of Electric Generation
Total Electricity Demand

Electric generation need meet the demand of electric vehicles, so we deduce the equation as follows. Te = eN We de?ne that Te is the total demand per year, e is power consumption per year of an electric vehicle, and N is the total amount of vehicles. So we deduce generating capacity K = Te . Then we deal with the amount and type of the electricity generation that can ?t the structure feature of the U.S. power industry.

4.2

The Type of Electricity Generation in U.S.

The type of energy sources and electricity generation of the U.S. electric power industry main can be divided into coal, natural gas, nuclear, renewable, petroleum and other. We assume that annual electricity generation is respectively EG1 , EG2 , EG3 ,

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EG4 , EG5 and EG6 ,. The annual electricity capacity is respectively EC1 , EC2 , EC3 , EC4 , EC5 and EC6 . We calculate the initial assignment of electricity generation based on the feature of the national electricity generation with the below formula, pi = EGi , i = 1, 2, 3, 4, 5, 6 sumEGi

where pi is the proportion of each energy source. And we should calculate the trend that is the each type of yearly electricity generation change. We take the data of national annual electric capacity into computing, with below formula dECi rei = dt where rei is the annual change rate of energy source by each type; t is the time in year. Then, we also consider the generating pollution and economic problem[10],and transform the problem into quantizing their coef?cient after condition changing. At ?rst, we assess the ?ve types of electricity generation, where 1 means little in?uence, 5 means most in?uence. Then we multiply the pollution in?uence by the economy in?uence, and take the reciprocal product into normalization as follows, sei =
1 Effectpollution Effecteconomy

? 0.04

1 ? 0.04

Finally, we work out values of pollution and economic coef?cient sei . The larger the value is, the more the type effect on pollution and economy. Table 4: The Pollution and Cost of Electric Generation Kind Coal Natural Gas Nuclear Renewable Petroleum Pollution 5 3 1 1 4 Economy 1 2 5 4 3 0.17 0.13 0.17 0.22 0.05

4.3

The Amount of Electric Generation by Source Sector

After calculating the Tei ,pi , rei and sei , we work out the amount of each electricity generation type with the formula below. Tei = K ECi pi sei rei · sumpi sei rei EGi

Then we can get the electricity capacity in each type.

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4.4

The Compute about the Amount and Type of Electricity Capacity in U.S.

First of all, we get the amount of national cars in 2009 from the Internet, and is about 256million. A car consumes 20 kWh per 100 km, and a car can run for 50 thousand kilometers per year, so we can get the electric consumption of a car is 10 MWh per year. We have known the popular rate is 37.5%. And we can get. K = Te = 256 × 10 × 0.375million MWh = 960million MWh We use the American electricity data from 1998 to 2009[10].Then we pick up the data for the national electric generation and electric capacity (Table 5). With the former forTable 5: The Amount of Electricity Generation and Capacity in U.S. Coal Capacity (Megawatts) Generation (Thousand Megawatthours) 314,294 1,755,904 Renewables Capacity (Megawatts) Generation (Thousand Megawatthours) 149,230 412,642 Natural Gas 403,204 931,426 Other 888 11,929 Petroleum 56,781 38,938 Total 1,025,400 3,949,694 Nuclear 101,004 798,855

mula, we can calculate the percentage of each type of electricity generation(Figure 11). Then we analyze the data for American electricity capacity from 1998 to 2009(Figure 12). We ?nd the natural gas and renewable fast growth, the coal and nuclear ?atten out and the petroleum drops slightly. Besides, the other is negligible and we don’t analyze this aspect. We calculate the change of electrical capacity, and get the rate by each type of the electricity capacity (Table 6). Table 6: Processed Data Coal 1.0031 Natural 1.0094 Gas Petroleum 0.9884 Nuclear 1.0025 Renewables 1.0794 Other 0.9427

Because the petroleum is dropping in recent years, we do not consider it as a developable energy, and the other is short of the pollution and economic coef?cient. At last, the coal, natural gas nuclear and renewables are considered as the type of electricity generation. And we can work out the electricity capacity demand in each type with the former formula (Table 7).

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Figure 11: The U.S. Electric Generation by Source Sector

Figure 12: The Trend of Electrical Capacity in U.S. Table 7: Processed Data Coal Capacity Demand (Megawatts) 77,717 Natural Gas 79,370 Nuclear 25,075 Renewables 52,127

In 2009 (and 2010), wind generators were eligible for Federal production and investment tax credits or a cash grant in lieu of those tax credits [the 2005 Energy Policy Act], so we consider the wind as the renewable to afford the capacity. Now we get the amount and type of electricity generation that would be needed to support the electric vehicles. The assignment electricity generation is 434 million MWh of coal, 183 million MWh of natural gas, 198 million MWh of Nuclear and 144 million MWh of wind. And to afford the electricity capacity demand, the coal needs

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77.7 gigawatts, the natural gas needs 79.4 gigawatts, the nuclear needs 25.1 gigawatts and the wind needs 52.1 gigawatts.

5

Conclusion

After developing a model to understand the effects of components of the electric vehicle using model, and a model to solve the amount and type of electricity generation that would be needed to support the amount and type of electric vehicle in the former model, we have developed a scheme for the electric vehicle: ? Each Aspect Impact of the Widespread use of Electric Vehicles We analyze the four aspect impacts, and they are social impact, economic impact, health impact and climate impact. ? The Key Factors that Governments and Manufactures Consider The governments should consider the cost of electric vehicles, the strategies to execute and the electric power generation. The manufactures should consider the electric vehicles and the sales volume. ? The Amount of Saving Oil We ?nally work out the value is 36833 million tonnes in the world. ? The Amount and Type of Electric Generation After having the widespread rate of electric vehicles, we model a model of the amount and type of electricity generation. The demand of electric power generation is mainly the coal-?red power and natural gas power, a less demand is wind power, and least demand is nuclear power.

References
[1] Electric vehicle. http://en.wikipedia.org/wiki/Electric_vehicle.Accessed 12 Gebruary 2011 Publishing Company , 1984-1986. [2] Car pollution. http://en.wikipedia.org/wiki/Car_pollution.Accessed 12 Gebruary 2011 [3] World Health Organization, WHO Air quality guidelines for particulate matter, ozone, nitrogen dioxide and sulfur dioxide.2005 [4] Scienti?c Facts on Air Pollution. http://www.greenfacts.org/en/nitrogen-dioxideno2/index.htm.Accessed 12 Gebruary 2011 [5] Nitrogen Oxides. http://www.epa.gov/air/emissions/nox.htm.Accessed 12 Gebruary 2011

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[6] Greenhouse effect. http://en.wikipedia.org/wiki/Greenhouse_effect.Accessed 12 Gebruary 2011 [7] U.S. Environmental Protection Agency Of?ce of Transportation and Air Quality. Greenhouse Gas Emissions from the U.S. Transportation Sector 1990-2003. March 2006 [8] Energy Information Administration. U.S. Carbon Dioxide Emissions from Energy Sources 2008.May 2009 [9] Lead acid battery. http://en.wikipedia.org/wiki/Lead-acid_battery,Accessed 12 Gebruary 2011 [10] U.S. Energy Information Administration. Electric Power Annual 2009.January 2011 [11] Sha Yongkang. The analysis of the cost of electric vehicle. New energy vehicle 24-25. [12] Electric vehical charging station make in?nite money. 2010. http://energy.people.com.cn/GB/11676238.html Accessed 12 Gebruary 2011 [13] Primary Energy Flow by Source and Sector. 2009. http://www.eia.doe.gov/aer/pecss_diagram.html. Accessed 12 Gebruary 2011 [14] Yang Feng, Fu Jun. The comparison and analysis of the economical ef?ciency of electric vehicle economical ef?ciency. Journal of WUT(INFORMATION & MANAGEMENT ENGINEERING). 287-288. [15] Global vehicle population.2010. http://www.cngaosu.com/zhuanti/html/ gaoduanluntan/redianwentiyanjiutantao/2010/0531/60472.html Accessed 12 Gebruary 2011 [16] Member counties. http://www.oecd.org/countrieslist/0,3025,en _33873108_33844430_1_1_1_1_1,00.html Accessed 12 Gebruary 2011 [17] Files for the international energy annual .2006. http://www.eia.doe.gov/iea/. Accessed 12 Gebruary 2011


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