INTRODUCTION
Reasons for choosing the topic
As we know, fossil fuels are the main source of fuel for vehicles using traditional engines However, this supply is gradually becoming scarcer due to high demand and limited reserves In the UK, a fuel crisis is occurring due to scarcity of fuel as well as high prices due to imports from other countries.
Another cause that can affect fuel sources for vehicles is war Last year, we had to witness the highest gasoline price, mainly due to the war between Russia and Ukraine This war has a direct impact on the world economy as well as in Vietnam. The increase in gasoline prices also greatly affects the demand for using traditional vehicles.
The worldwide disruption created by the COVID-19 Pandemic has brought many positive impacts on the environment and climate The reduction of modern human activities on a global scale such as: a significant reduction in the need for planned travel has caused a large decrease in air pollution and water pollution in many areas. When the pandemic first occurred, environmental quality gradually improved as the air became cleaner as cities imposed blockade orders or social distancing.
In Vietnam, the General Department of Environment (Ministry of Natural Resources and Environment) said that comparing the results of air quality in northern cities from January 1 to April 2020, including the period of isolation. Society shows that the change in production and human activities is an important cause of changing air quality Compared to the same period of previous years, air quality also tends to improve, since people have reduced unnecessary movement due to the Covid-19 epidemic, which has contributed to a significant decrease in air quality carbon dioxide, methane, and carbon monoxide emissions This also shows that the influence of emission sources such as traffic and manufacturing activities has a significant impact on urban air quality.
Therefore, the application of electric vehicles to replace traditional vehicles is one of the methods to effectively solve those problems Currently, in big cities in Vietnam are starting to research and develop electric bus models to replace old buses And Vinbus is the first car company to successfully apply its electric bus model and is applied on a number of routes in Hanoi and Ho Chi Minh City.
Realizing that this is one of the potential solutions to develop the city, our group decided to research about the topic “DESIGN AND SIMULATION THE
ELECTRIC BUS” in order to calculate, research and check the preliminary assessment of the simulation model of an electric bus based on the Vinbus car including available parameters From there to evaluate whether the calculated results are consistent with the parameters of the model or not, and the greatest desire from the knowledge and research in the article, this will be the basis for research and development of a complete electric bus.
Research situation in Abroad and Vietnam
The Asia Pacific area has the world's largest electric bus market It is home to some of the world's most rapidly expanding and developed economies The region's development may be ascribed to the Chinese market's dominance as well as the existence of prominent OEMs in the nation, resulting in the Asia Pacific electric bus and coach market growing at an exponential rate.
The region's electric bus industry is expected to increase due to favorable legislation for electric buses, the availability of electric and electronic components, and quickly expanding charging infrastructure In January 2022, the Government of India would distribute 670 electric buses to the states of Maharashtra, Goa, Gujarat, and Chandigarh under Phase 2 of the FAME initiative Furthermore, 241 charging stations will be installed on the roads of Madhya Pradesh, Tamil Nadu, Kerala, Gujarat, and Port Blair.
During the projected period, North America is predicted to be the fastest-growing market For example, the US Federal Budget pledged USD 130 million in 2019 to expedite the implementation of zero-emission buses and automobiles Blue Bird will deliver its 400th electric school bus in North America in March 2021 The business intends to deploy 1,000 electric school buses by 2022 A growing number of such breakthroughs imply that the North American electric bus industry will increase tremendously in the future.
In Vietnam, Vinbus is the first electric bus to be operated and serve the travel needs of people However, the current use of Vinbus is only applied to 2 big cities, Hanoi and Ho Chi Minh City In Ho Chi Minh City, most of these cars are only driven around areas near Vinhome or places invested by Vingroup But there are still positive signs for the development of this type of traffic in the future On July 22,
2022, Deputy Prime Minister Le Van Thanh signed Decision 876/QD-TTg approving the Action Program on green energy transformation, reducing carbon and methane emissions of the transport sector The overall objective of the strategy is to develop a green transport system towards the goal of net greenhouse gas emissions to "zero" by 2050 The strategy sets a target that from 2025, 100% of buses will replace to invest in new electric vehicles and green energy From 2030, the rate of vehicles using electricity and green energy will reach at least 50%; 100% replacement taxi, new investment using electricity, green energy By 2050, 100% of buses and taxis will use electricity and green energy.
Therefore, the race for electric buses will not stop with Vinbus alone, transport companies invested and supported by car companies like Samco and some others are also starting the research and launching process products to keep up with the current trend of electric vehicles.
Aim of Research
The primary goal of this project is to develop a comprehensive parametric design approach for the drivetrain system of an electric bus This approach may identify both the ratings and maximum capabilities of the powerplant for a given vehicle's characteristics Motor power, torque, speed, and battery capacity are all rated The ratings in the suggested approach take into account the vehicle's maximum velocity and maximum acceleration rate in order to attain the hardest road conditions The suggested methodology's validation is discussed using the case study Vinbus The cars' performance is simulated and evaluated using two distinct driving cycles.
A parameter optimization technique for a medium-sized bus's power system based on the orthogonal test and secondary development of ADVISOR software The vehicle power system characteristics were matched and created based on vehicle theoretical knowledge and the needs of the vehicle power performance index The modeling of the vehicle's essential components was completed using the secondary development of MATLAB/Simulink and ADVISOR software Considering the impact of the number of battery packs, motor power model, wheel rolling resistance coefficient, and wind resistance coefficient on the power system design The dynamic performance and driving range of the entire vehicle were simulated using several design approaches, and the quality of the simulation findings was validated
3 by comparing and evaluating the simulation images The study material of this article gives a specific reference for the design of shuttle buses for the Electric Bus system, efficiently minimizes the testing costs of the vehicle development process,and provides a novel idea for the power system design of pure electric buses.
Research Method
− Learn about requirements and study calculating components on an electric bus.
− Build calculation formulas for force, speed, acceleration, and power of the vehicle on Matlap/Simulink software.
− Calculation and selection of Motor suitable for bus requirements: High Torque, Low Speed.
− Learn, build Driving Cycles for different bus driving conditions based on articles and European standards.
− Enter the calculated parameters into ADVISOR, run the model and study the results.
− Calculate and choose the right charger for the vehicle.
Research subjects
− The driving cycle has been selected and set up.
− Study the actual running routes of buses in Ho Chi Minh City.
Focus on researching and calculating, designing components of an electric bus based on an existing Vinbus The range is only the routes in Ho Chi Minh City The data is only obtained through the process of calculation and analysis.
• Chapter 3: ELECTRIC BUS CALCULATION AND DESIGN
LITERATURE SURVEY
Overview of Electric Bus
The global electric bus market was valued at 170 thousand units in 2020 and is predicted to grow at a CAGR of 16.0% from 192 thousand units in 2021 to 544 thousand units by 2028 According to our research, the global market will shrink by 14.1% in 2020, compared to the average year-on-year gain from 2017 to 2019. COVID-19 has had an unprecedented and catastrophic global impact, with the market seeing a severe impact on demand across all industries as a result of the pandemic The increase in CAGR is attributable to this market's demand and growth, which will return to pre-pandemic levels once the pandemic is over [1].
According to the United Nations Environment Program (UNEP), city buses contribute considerably to black carbon emissions from the transportation sector As a result, the UNEP is assisting 20 cities in Asia, Latin America, and Africa in developing and mapping low-emission public transportation networks that include e-buses Furthermore, in order to acquire public commitment, the UNEP, in partnership with the International Clean Transportation Council (ICCT) and regional partners, has given technical help to identify and eliminate hurdles, as well as support for the adoption and design of clean buses These government initiatives are anticipated to boost the expansion of the electric bus market throughout the forecast period [1].
The covid-19 outbreak has had a substantial influence on e-bus deployments. Several public transportation networks throughout the world are incurring major revenue losses as a result of the epidemic's decline in transit use According to the American Public Transportation Association (APTA), public transportation usage declined by 80% in April 2020, with passenger numbers falling by more than 60% for the rest of 2020 compared to 2019 The APTA predicts that this trend will continue in the short to medium term due to reasons such as increased remote work and an increase in private automobile ownership [1].
In Santiago, Chile, for example, there are 776 privately owned electric buses In this model, fleet owners acquire and maintain these buses before leasing them on long- term contracts to municipalities or transit providers This distinguishes operation from ownership This might pave the path for a large-scale transition to electric fleets As a result, these characteristics will influence market growth [1].
During the 33rd ASEAN summit in September 2016, member states decided to set a long-term goal of decreasing the region's greenhouse gas emissions by 20% Despite global progress in electric buses, ASEAN nations are still three to five years away from commercialization due to the high cost of components and the demand produced by a lack of know-how To fulfill the objective for greenhouse gas emissions, ASEAN countries are developing and testing a variety of prototype electric bus projects.
Brunei has just lately begun importing electric buses, and Shenglong New Energy Automobile Co., Ltd., a Chinese electric vehicle manufacturer, will soon establish an electric bus manufacturing plant in Berakas This factory will be developed in partnership with a Chinese corporation based in Guangxi and a company with ties to the Bruneian government.
The University of Indonesia in Jakarta displayed four electric vehicles created by the campus engineering department in Depok, West Java The Makara Electric Vehicle (MEV) initiative includes three municipal vehicles and one electric bus [2].
The Laotian government created the E-bus project and encouraged government employees to use more public electric buses, which are both economical and environmentally friendly The Japanese International Cooperation Agency (JICA) is funding the E-bus project, which is being operated by Lao Green Company in the UNESCO World Heritage town of Luang Prabang [2] [3].
Malaysia completed the first electric bus test in June 2015, and fifteen eco-buses were deployed for the Sunway Group's Bus Rapid Transit (BRT).
The Philippine government is encouraging the use of electric vehicles PhUV Inc., a local bus manufacturer, built approximately 20 electric minibuses known as e- jeepneys Several government towns, colleges, and commercial companies use e- jeepneys, including the country's electricity supplier, Manila Electric Co (Meralco), Ateneo de Manila University, and De La Salle University.
Singapore has committed to reducing emissions by 7% to 11% below "business as usual" BAU levels by 2020 The GreenLite, Singapore's first hydrogen and lithium- ion battery electric bus, was developed in 2011 by Nanyang TechnologicalUniversity (NTU), Tsinghua University, and Shanghai Sunlong Bus Co., Ltd [2].
The first electric buses bearing the VinBus name have arrived in Vietnam (Vinhomes Ocean Park, Gia Lam) According to Insideevs, the automobile is built and assembled at Hai Phong's Automobile Manufacture Complex VinBus is a Vingroup subsidiary that began operations in September 2019.
At the end of 2021, VinBus launched the first electric bus route in Hanoi, followed three months later by the first electric bus line in Ho Chi Minh City (HCMC) By the end of June 2022, Hanoi will have around 100 VinBus electric buses running on eight routes, HCMC will have 20 vehicles working on one route, and Phu Quoc will have 30 buses in the area.
The number of VinBus in operation is small in comparison to the over 5,000 buses currently in operation in Hanoi, HCMC, and Da Nang; however, it is a significant milestone because it is Vietnam's first electric bus and the first electric bus licensed operator to provide public transportation services [4] [5].
2.1.4 The Characteristic of Electric Bus
Buses are vehicles with large wheels, similar to ordinary passenger cars However, it has the distinction of operating on shorter routes Specifically, connecting urban points together, inter-districts, towns and cities Usually each province will have its own bus system.
Buses operate most days of the week Regardless of holidays, Saturday or Sunday. However, the transportation of the bus always follows a fixed time frame.
Depending on the distance between urban clusters, the number of vehicles distributed in that area, the travel needs of the people But each place will have a different running frequency Usually there is one every 15 minutes In densely populated areas or peak clusters, the frequency will be 5-10 minutes On the contrary, where few people have a need to use it, it will take 20 to 30 minutes for 1 turn [6].
Bus dynamics
We study the power and energy needs of the automobile powertrain in this section by applying physics concepts to the vehicle's motion First, analyze the fundamental vehicle load forces of aerodynamic drag, rolling resistance, and climbing resistance. This preliminary analysis allows for the quantification of a vehicle's power and energy requirements, as well as the conversion of these vehicle requirements of speed and accelerating or braking power into mechanical specifications of torque and speed for the electric motor.
2.2.1 Vehicle Load Forces and Dynamics Equation
Understanding vehicle driving needs and performance criteria is necessary for developing the electric powertrain In this section, the primary load forces of Rolling Resistance (F R ), Aerodynamic Drag (F D ), and Climbing Resistance acting on the vehicle (F c ), as illustrated in Figure 2.1 [7].
Figure 2.1 Forces acting on a vehicle moving uphill.
The slip between tire and road provides traction force, FT, and the engine or electric motor is the true power source for slip creation For acceleration or deceleration, the difference between the total of road loads and the traction force is used The dynamic equation of vehicle motion in the longitudinal direction is expressed by:
2.2.1.1 Basic Power, Energy, and Speed Relationships
According to [7], power is defined as work done per second The unit of power is the watt (W).
If a vehicle travels at a constant speed v, the power P required to move it is equal to the product of the force F and the speed In equation form: power = force ∗ speed
An object is said to possess energy if it can do work The unit of energy and work is the joule (J).
The energy E required to propel the vehicle at a constant speed is simply the product of power and time: energy = power ∗ time
The above equation can be rewritten to express the distance in terms of energy, speed, and power as follows: s = E v (2.8)
In [7] [8], the rolling resistance is the product of all frictional load forces caused by tire deformation on the road surface and friction inside the drivetrain The following equation describes rolling resistance FR:
In [7] [8], aerodynamic drag is the resistance of air to vehicle movement The vehicle's aerodynamic drag force F D and power P D are described as:
(2.11) v + v w : vehicle and wind are travelling in same direction v − v w : vehicle and wind are travelling in opposite direction
Depending on [8] whether the automobile is rising or descending an elevation, the vehicle load power might rise or decrease The downhill force or climbing resistance is provided by:
The downhill force is negative and can result in energy regeneration to the battery, a mode typically utilized in electrically driven cars to slow the vehicle rather than friction braking.
The gradeability of a vehicle is the highest slope that it can climb at a given speed.
It is the tangent of the incline angle, or the ratio of the climb to the run. θ = arctan %grade
It is sometimes expressed as a percentage, with tan 45° equaling 100% Table 2.1 shows several inclination angles and values.
Table 2.1 Incline angles and grade.
2.2.2 Power Train Traction Effort and Vehicle Speed
A power plant (electric motor), a gearbox (transmission), final drive include differential, drive shaft, and drive wheels comprise an automobile power train, as illustrated in Figure 2.2 The gearbox, final drive, differential, and drive shaft transfer torque and rotational speed from the power plant's output shaft to the drive wheels The gearbox provides a few gear ratios from its input shaft to its output shaft to adapt the torque-speed profile of the power plant to the load requirements. The final drive is often a set of gears that provide additional speed reduction and distribute torque to each wheel via the differential [7].
The torque on the drive wheels, transmitted from the power plant, is expressed as:
The tractive effort on the drive wheels can be expressed as:
Substituting Equation into yields the following result:
Figure 2.3 Tractive effort and torque on a drive wheel.
The rotating speed, in revolutions per minute (RPM), of the drive wheel can be expressed as:
The translational speed of the wheel center (vehicle speed) can be expressed as: πNN w r d
Substituting Equation 2.18 into Equation 2.19 yields v = πNN p r d
2.2.3.1 The maximum speed of a vehicle
In [7] [8] [9], a vehicle's maximum speed is the highest consistent cruising speed that it can accomplish at full power on a flat road When the tractive and resistive forces are in equilibrium, the maximum speed of a vehicle is determined with full torque from the traction source on a level road:
This equation states that the vehicle reaches its top speed when the tractive effort, represented by the left-hand side term in Equation 2.21, equals the resistance,
12 represented by the right-hand side terms The maximum speed of the vehicle is the junction of the tractive effort curve and the resistance curve.
It should be noted that certain cars have no intersection between the tractive effort and resistance curves due to a huge power plant or a large gear ratio The maximum speed of the vehicle is governed in this situation by the maximum speed of the power plant The maximum speed of the vehicle may be calculated using Equation 2.20: πNN p max r d
The gradeability of a vehicle is the highest gradient on which it can begin climbing from a standstill with all its wheels on the gradient at the time of start [7] [8] [9].
The tractive effort and resistance of a vehicle as it drives on a road with a minor gradient and constant speed may be extended to add gradeability, resulting in equilibrium Equation calculates this for modest angles:
In [7] [8] [9] ,the vehicle's acceleration performance is often characterized by the time and distance traversed from 0 to a specified high speed on flat terrain The vehicle's acceleration may be written:
(2.25) dt M T r 2 a f d and minimum road slop θminmin is considered Then, the total tractive force of becomes:
Then, the rated power of the traction motor P m depends on the maximum velocity Vmax, the total tractive force FT and it is expressed as:
Subtitute the Maximum Force into the equation:
2.2.4.1 Driving cycle design for testing Electric Bus
Follow [10], the urbanization and traffic levels in each city, as well as the specific working environment of each transportation business, demand actual variety, and maintaining simply one "urban" cycle would be unduly simple.
The structure of the cycles can be sketched as follows:
Figure 2.4 Structure of the cycles
The following need to be determined:
• The number of base cycles.
Number of different base cycles necessary After long discussion, 3 base cycles appear to offer a reasonable solution:
• Urban base cycle: Velocity is 12 km/h.
• Mixed base cycle: Velocity is 17 km/h.
• Suburban base cycle: Velocity is 27 km/h.
In [10], three different base cycles have been created to show urban traffic (SORT 1), mixed traffic (SORT 2), and suburban traffic (SORT 3) Each cycle includes an inactive time The period of standstill was changed to match the average pace of each cycle (e.g., distance vs time including stops) The stoppage % is primarily determined by actual experience.
SORT 1 (Urban traffic) is extensively covered This cycle has three trapezes that move at constant rates of 20 km/h, 30 km/h, and 40 km/h After each trapezoid, a 20-second respite is provided, giving the cycle a total idle time of 60 seconds The average speed (commercial speed) of this cycle is roughly 12 km/h.
The SORT 2 and 3 cycles consist of three basic trapezes The primary distinction between the SORT 3 cycle (suburban) and the SORT 1 and SORT 2 cycles is a shorter stop duration at each stop: 40 seconds as opposed to 60 seconds for SORT 1 and SORT 2 This is because the load has been statistically lessened.
EV Charging Method
The three primary charging methods are battery exchange, wireless charging, and conductive charging Figure 2.8 [11] illustrates the additional division of conductive charging into pantograph (Bottom-up and Top-down) and overnight charging.
Methods 2.3.1 Battery Swap Station (BSS)
The "Battery Exchange" strategy to battery swapping is based on paying the BSS owner a monthly rent for the battery The BSS's slow charging approach adds to a longer battery life [12] The BSS system may be connected more readily with locally produced Renewable Energy Sources (RES), such as solar and wind One of the primary advantages of this technology is that drivers may quickly replace a low battery without having to depart the vehicle Furthermore, the station's battery can participate in the V2G (vehicle-to-grid) initiative [13] [14].
However, because the BSS owner owns the EV batteries, this type of EV charging approach may be more expensive than refilling the ICE engine due to the BSS owner's high monthly lease charges This strategy necessitates the purchase of multiple expensive batteries as well as a large storage space, which might be costly in a congested area Furthermore, while the station may have a certain battery model, the automobiles' battery requirements may differ [15] [16].
This electromagnetic induction-based approach employs two coils The secondary coil is inside the automobile, while the primary coil is outside on the road WPT technology has lately sparked attention in EV applications because to its ability to
17 offer convenient and secure EV charging It can even charge while the car is driving and does not require a normal connector (but does require traditional coupling technology) [17].
Because inductive power transfer is often modest, the air space between the transmitter and receiver coils should be between 20 and 100 cm for effective power transmission [18] Eddy current loss is another issue in the WPT if the transmitter coil is not turned off Communication delays are likely because real-time information transfer between the transmitter and the EV is necessary [19] Figure 2.9 [20] illustrate of inductive charging for buses.
Figure 2.9 Illustration of inductive charging for buses 2.3.3 Conductive Charging (CC)
Conductive charging offers various charging capabilities, and has a high charging efficiency since it involves a direct electrical connection between the car and the charging input The two power charging levels (Level 2 and Level 3) are used for a public charging station [11].
Conductive charging provides a V2G capability, minimizes grid loss, maintains voltage, avoids grid overloading, supports active power, and may compensate for reactive power by using the vehicle's battery [21] [22].
Furthermore, a complex infrastructure, limited access to the electrical grid, and a consistent connector/charging level are necessary [23] The V2G technology requires extensive grid and vehicle connection Furthermore, because batteries must be charged and drained often during V2G operation, their lifespan is shortened. Table 2.2 summarizes the various types of charging stations, including BSS, WPT, and CC stations.
Table 2.2 Summary of reviews on charging methods
The two charging techniques indicated below are utilized for applications like as buses and vehicles that require larger battery capacity and faster charging:
− Overnight Depot Charging: The overnight depot charging system offers both slow and quick charging choices It is generally located at the end of the lines and functions as a night charging station It is the greatest option since delayed charging has little impact on the distribution system [24] However, the Pantograph charging approach is appropriate for applications requiring bigger battery capacities and rapid charging.
− Pantograph Charging: This technique of charging is a charging option This sort of charging infrastructure is used in applications with larger battery capacity and power requirements, such as buses and trucks While the cost of charging infrastructure rises, this charging technique requires less investment in the bus battery, cutting the overall cost of the bus [25] The following two types further divide pantograph charging:
− Top-down Pantograph: The charging system is referred to as an off-board top-down pantograph since it is positioned on the bus stop's roof The high
19 power direct current provided by this technology has previously been tested in Singapore, Germany, and the United States [26].
− Bottom-up Pantograph: Applications where the charging equipment is already built into the bus are ideal for this sort of charging technology.Another name for this is an on-board or bottom-up pantograph [26]
EV Charging Configuration for Electric Bus
Because buses in Vietnam routinely drive more than 100 kilometers per day, charge anxiety is a more serious issue than range anxiety Because it frequently enables more kW transfer and reduces the burden on the car, the off-board charger is a preferable solution for reducing charge anxiety The phrase "off-board charger" refers to a charger that provides DC power to the EV battery pack while being positioned outside of the vehicle The off-board EV charging system [27] depicted in Figure 2.10 (Table 2.2) employs both IEC mode 4 and SAE levels 1 and 2.
Figure 2.10 EV charging configuration for off-board
On the other hand, on-board charging, adds weight to the vehicle and delivers a lower kW transfer The weight, size, and cost constraints of single-phase on-board chargers limit the transfer of high power [27] [28] As a result, charging takes longer than with the off-board charging configuration Figure 2.11 [29] [30] depicts an EV charging solution with an on-board charger for AC (Modes 1 and 2 and Level
1 and 2 per IEC and SAE standards, respectively) The DC charging levels are listed in Table 2.2.
Figure 2.11 EV charging configuration for on-board
A variety of EV charging standards are utilized internationally to deal with EV charging infrastructure For example, whereas Japan and Europe use the CHAdeMO charging standard, the United States uses the IEEE and SAE standards The Standards Administration of China (SAC) uses GB/T standards, which are similar to IEC standards In SAE, the phrase "Level" is used to define the power level, but in IEC, the word "Mode" is used Table 2.3 summarizes the ICE and SAE charging standards.
In most homes or companies, Level 1/Mode 1 is used for overnight slow charging. Level 2/Mode 2 and Level 3/Mode 3 charging modes are utilized by both public and private charging stations, but mode 4 in IEC and SAE is intended for fast charging [11].
Table 2.3 IEC and SAE standards: Current and voltage level for AC and DC charging
DESIGN AND CALCULATION OF ELECTRIC BUS
Available Specifications
Figure 3.1 The parameter of Vinbus
Because numerous bus lines are due to start operating in Ho Chi Minh City, they must also be changed, and the length of the bus lines must be suitably reduced As a result, a short-distance electric bus power system must be designed We determined the pure electric vehicle power system with an battery pack as the power and a motor as the driving device after referring to the design of similar vehicles on the market and the actual needs of Ho Chi Minh City's public transportation system.
The design of the electric bus should fulfill the necessary criteria of the vehicle's power performance and operating range.
The key aspect influencing the power performance of pure electric cars is the matching of the power system parameters This study chooses a pure electric car as the research object and aligns the vehicle's entire vehicle power system to the needs of dynamic design Table 3.1 and 3.2 [31] [32]displays all of the vehicle parameters.
Table 3.1 Vehicle Parameters of pure Electric Bus
Table 3.2 Power Performance Requirements for pure Electric Vehicle
Dynamic Parameter [Unit] Symbol Value
Maximum cruising range for Sort 1 [km] S 1 142,2
Maximum cruising range for Short 2 [km] S 2 248
Maximum cruising range for Short 3 [km] S 3 304
Choosing Parameter
The key aspect influencing the power performance of pure electric cars is the matching of the power system parameters This study chooses a pure electric car as the research object and aligns the vehicle's entire vehicle power system to the needs of dynamic design Table 3.3 [31] [33] [34] displays all of the vehicle parameters.
Table 3.3 Coefficients of Vinbus Electric Vehicle.
Aside from the engine system, this electric bus contains subsystems and auxiliary electrical components such as an air conditioner, a steering hydraulic pump, and a coolant system, among others Their worth can be summarized as follows.
Types of electrical loads on cars are connected in parallel and can be divided into 3 types:
− Working load is not continuous
− The load works for a short period of time
Here are some component we divide they are three kind of auxiliaries component and the value of power as show on these table below [2] [33] [35]:
Table 3.4 Power dissipation of the connecting loads continue on the car.
Head light 20 Vehicle air compressor 3.000
Indicator light 30 Vehicle cooling system 500
Table 3.5 Power dissipation of cockroach loads section on the car
Head light 200 Rear fog light 20
Table 3.6 Working load in a short time
Calculation Parameter
According to [36] [37], the automobile dynamic performance index, choosing the best driving motor has an influence on its dynamic performance The power system must meet maximum speed, acceleration, maximum climbing slope, and rated torque The dynamic performance of pure electric vehicles must meet the driving force Ft delivered to the wheels by the motor while also overcoming vehicle resistance while driving The rolling resistance Ff caused by the road surface when driving, the air resistance caused by air friction The driving equation as follows:
It is possible to obtain by substituting the calculation formula for each force into formula that:
3.3.1.1 Determination of peak power and rated power of motor
In [31] [38], a pure electric vehicle's motor power matching has a direct influence on the vehicle's dynamic performance Matching appropriate motor power may boost not only the car's driving distance, but also its energy consumption. Furthermore, the peak power of the motor must fulfill the maximum grade and acceleration time standards.
The power needed by the motor while the vehicle is running at a constant speed with the maximum speed Vmax is:
The motor's maximum power P imax is dictated by the slope at constant speed.
Using the ascending slope as the design metric, At this point, the rising slope and the needed peak motor power is:
Where, uslo is the climbing speed, which is estimated to be 10 km/h.
The motor's maximum power Ptmax is dictated by its acceleration performance The ascending slope is zero while assessing the acceleration capability of pure electric cars The power required to accelerate on a horizontal road:
First, at the maximum velocity, the rated power is determined using (3.3) and (3.4).
At flat level, the needed power for a maximum velocity of 100 km/h is 130kW.When the gradeability is enhanced, the tractive power increases as well Depicts the motor power vs vehicle velocity at various gradeability levels for the VinbusElectric Vehicle.
The tractive power is 195 kW at 8.2% gradeability and a maximum velocity of 10 km/h The rated power used is determined by the vehicle's capacity to move up the grade road at maximum speed.
For the maximum power measured by the three power performance indices, the total power Pmax of the power source must meet the following formula:
3.3.1.2 Determination of peak speed and rated speed
The formulas of rated speed and peak speed of the motor are shown in Equations: n max =
(3.8) β where i is the reduction ratio of the electric vehicle; r is the tire radius, and the value was 0.47825 m; and β is 2~4 [31].
3.3.1.3 Determination of peak torque and rated torque
The rated power and rated speed of the motor determine the rated torque of the motor Then, the rated torque and maximum torque of the motor are expressed as:
Where T e is the rated torque of the motor, n e is the rated speed of the motor, T max is the maximum torque of the motor and λ p is 2–3 [31].
The important characteristics of the motor may be derived theoretically, and the rated speed and torque of the motor, as well as the maximum speed and torque, can be computed by selecting the motor's rated power and peak power The driving motor parameters are derived using the aforementioned design indicators and theoretical calculations, as well as data from the vehicle market and applicable national norms, as indicated in Table 3.7 and Table 3.8 [39].
Table 3.7 Specifications of APEV80-12(16) Motor.
Table 3.8 AEV100-D540D540200L2 motor controller Specification.
Input Voltage range from 250-720 Weight / kg 28 battery (VDC)
Motor Control Input Range 18-36 Capacity Rating 180
Max Output Current (A) 800 Peak Capacity (KVA) 250
Protect IP67 Flow cooling > = 15L/min
Cooling water Water + Ethylene Max Coolant Inlet 65
3.3.2.1 Calculation of Power Battery Parameters
According to [2], the essential criteria of an energy storage system are safety, dependability, high efficiency, maximum speed, acceleration time, operating distance requirements, and acceleration time Battery pack capacity (Ah), C-rate (capacity of a battery in an hour), peak and continuous charge and discharge power capacities (kW), maximum and minimum operating voltage (V), maximum and minimum operating current (A), operation temperature (C), allowable SOC operating range (%), internal resistance, state of charge (SOC), depth of discharge (DOD), state of health (SOH), battery management system (BMS), and thermal management system are all important considerations The electric bus must manage high power and high energy capacity while remaining within space, weight, and cost constraints.
In [31], the rated power required by the motor according to the maximum driving speed of the car can be calculated as:
Follow the [7] [40], the work done per second is defined as power The watt is the power measurement unit (symbol W) In mathematical form: energy = power × time (3.12)
However, a joule is a relatively small unit of energy, and it is more common to reference other energy storage units such as watt-hours.
One watt-hour (Wh) is defined as follows:
Capacity, measured in ampere-hours, is a typical quantity associated with battery energy storage (Ah) The ampere is the unit of current I (symbol A) The coulomb is the standard SI unit for charging Q (symbol C).
Q = It or charge = current × time (3.14)
Again, the coulomb is a small unit, and the ampere-hour is more commonly referenced:
The capacity in ampere-hours can be related to the energy in watt-hours by multiplying the capacity by the battery voltage V: energy = capacity × voltage (3.16)
In [33], specific energy by volume:
The volume of each battery cell (m 3 ) is calculated by the formula:
The voltage of the battery system will determine the maximum electrical capacity that the battery system can provide continuously The power P is calculated according to the formula:
We assume that we want the maximum distance the car can travel on a single charge d (km) Then we can calculate the function the amount of energy required by the battery system to cover the distance d:
Number of battery cells connected in series NC:
Energy of a series of cells Ebs:
Estimated calculation design for electric bus is based on the need of driving range per day with average energy consumption 85 kWh/km.
The maximum energy storage for a pack of electric battery is 180kWh, the capacity is 280Ah.
According to [41], the stops of bus routes, which are shown schematically The bus network is shown as a series of lines All buses start and end their trips at the depot, which is linked to the terminal and is represented by Terminal A The depot has no say in the matter and is always stocked with chargers for overnight charging.
Each line's fleet size and frequencies are provided We put up a series of breaks and recharging stations As seen in Figure 3.3, several stations, such as stop 2 and stop | S|-1, are shared by both directions Stops 3 and |S|-2, on the other hand, are only used in one direction.
Figure 3.3 A bus route model of circular bus line
The network's elements, along with their definitions and characteristics for 3 SORT, are discussed below. a Bus cycle
The bus cycle for a specific route is defined by the sequence in which stations are visited, beginning at the departure point and ending at the arrival point Several bus cycles depict the regular activities of the bus Because of differences in travel demand and traffic congestion, the energy consumption between two stops might fluctuate during the day However, we presume that these changes have no effect on our point estimate.
We can observe that a bus cycle displays both circular and back-and-forth bus routes This may be done by allowing stations to be visited in either or both directions A bus cycle displays the whole trip of a bus from one terminal to another We use the term terminal to refer to a certain type of charging station. Terminus is a geographical term that refers to the place at which a bus journey comes to an end When a bus travels a circular route, each stop is visited once On a back-and-forth route, however, a station is only visited once or twice.
According to the Bus route 109, 32, 53 [32] represent to SORT 1 to 3 respectively, we can dentify the information of 3 SORT for Electric Bus route show in Table 3.9 below:
Time to complete a route (min) 45 80 87
Time to seperate a route (min) 40 9 22
Total of route per day 48 192 72
15 routes, 10 routes, 8 routes, Total for a bus per day 142.2 km in 233.5 km in 275 km in
This network's batteries have a modularized design and may be customized in a number of ways As a result, we assumed that all operating buses had homogeneous
33 batteries Because the depot contains a charging station, we assume that the batteries are fully charged at the start of each day When connected to a rapid charge station, a bus employs a constant power-constant voltage charging mechanism.
Batteries are charged at fast-feeding stations during the rather short bus stay duration As a result, we anticipate that the state of charge may be increased to 90% of the battery's capacity When the battery's capacity decreases to 80% of its initial nominal capacity, it has reached the end of its usable life At this point, the battery has to be replaced. c Charging stations
In [42], we take into account three different types of charging stations:
SIMULATION AND RESULT
Overall about ADVISOR software
Follow the [45], the National Renewable Energy Laboratory created Advanced Vehicle Simulator (ADVISOR) for the first time in November 1994 With the help of the contracts for the development of hybrid electric vehicle propulsion systems with Ford, General Motors, and DaimlerChrysler, it was created as an analysis tool to aid the US Department of Energy (DOE) in the development of technologies for hybrid electric vehicles (HEV) Its main function is to highlight how hybrid and electric vehicle components interact at the system level and how that affects the performance and fuel efficiency of the vehicle.
The Matlab/Simulink environment was used to develop ADVISOR While Simulink can be used to graphically represent complex systems using block diagrams, MATLAB offers an intuitive matrix-based programming environment for performing calculations.
In [45] [46], three main Graphical User Interface (GUI) displays are used by ADVISOR to lead the user through the simulation process The user can iteratively assess the effects of vehicle specifications and drive cycle requirements on the performance, fuel efficiency, and emissions of the vehicle using the GUIs The MATLAB workspace's raw input and output data can be interacted with more easily thanks to the GUIs To define the linkages between components, Simulink block diagrams are used to graphically represent the vehicle model When the simulation is complete, the model reads the input data from the MATLAB workspace and sends the results to the workspace so that they can be seen in the results window.
Figure 4.1 Structure of ADVISOR 4.1.2 Advantages of ADVISOR in simulating on vehicles
It was shown in [47] that the advantages of ADVISOR is:
• Estimate the fuel economy of vehicles that have not yet been built
• Learn about how conventional, hybrid or electric vehicles use (and lose) energy throughout their drivetrains
• Compare relative tailpipe emissions produced on several cycles
• Evaluate an energy management strategy for your hybrid vehicle’s fuel converter
• Optimize the gear ratios in your transmission to minimize fuel use or maximize performance.
In ADVISOR, the models include: largely empirical, relying on input/output relationships between drivetrain components that have been measured in the lab, and quasi-static, using information gathered during steady state tests (for instance, constant torque and speed) and correcting it for momentary effects like the rotational inertia of the drivetrain components.
In [47], to model current or potential vehicles, ADVISOR uses fundamental physics and measured component performance The ability to predict the performance of yet-to-be-built vehicles is where its true power lies It provides an answer to the hypothetical question, "What if we built a car with certain characteristics?" Typically, ADVISOR forecasts fuel consumption, exhaust emissions, acceleration capabilities, and gradability This includes two steps:
− Use component and overall vehicle data to define a vehicle using measured or estimated values.
− Prescribe the vehicle with a speed versus time trace and the required road grade.
The use of ADVISOR will enable them to respond to queries like:
− Was the car able to keep up with the speed trace?
− How much energy—electrical or otherwise—was needed for the attempt?
− How does a cycle's worth of charging affect the battery’s state of charge?
− What were the maximum powers the drivetrain's components could deliver?
− What was the piston engine's output in terms of speeds and torques?
− How effective on average was the transmission?
Configuration parameter on ADVISOR
4.2.1 How to set up the parameters
Figure 4.2 Vehicle component signal variables
The default files that are available to upload variables, and vehicle component information, such as energy storage system, powertrain control, transmission, and wheels, are uploaded by ADVISOR when the user selects a particular powertrain. Users have the option to use or modify the simulation to fit the vehicle by changing options The components that are available in the chosen powertrain will change as a result The input signal variables for a vehicle are detailed in Table 4.1 below; each variable has a different option for various vehicle types.
Table 4.1 Input information of a vehicle
Internal combustion engine model in Simulink with look-up tables ic si Spark ignition ci Compressed ignition
Fuel cell model in Simulink
Fuel net Net power vs Fuel consumption lookup model converter fcell polar Polarization curve-based model gctool Links to GCTOOL
Internal combustion engine model with neural network emissions model via s- ic_nn function ci Compression ignition
Storage nimh Nickel metal hydride
Internal Resistance Battery Model. Simulink battery model consisting of a voltage source and an internal resistor to model the battery pb Lead-acid
Rint li Lithium ion nimh Nickel metal hydride cap Ultra capacitor nicad Nickel cadmium NiZn Nickel zinc fund fund Fundamental lead acid battery model nnet nnet Neural network battery model.
Conventional man Manual transmission conv auto Automatic transmission cvt Continuously variable transmission
Control man Manual transmission par auto Automatic transmission cvt Continuously variable transmission ser Series
Ev ev man Manual transmission
Powertrain control for the japanese prius prius_jpn
Planetary gear continuously variable pg transmission insight Insight man Manual transmission
Fuel cell fc man Manual transmission man man Manual transmission auto auto Automatic transmission
Transmission cvt cvt Continuously variable pgcvt pgcvt Planetary gear continuously variable transmission
Crr Crr Constant coefficient of rolling resistance model
J2452 J2452 Model using SAE J2452 rolling resistance parameters Const Const Constant power accessory load models
Accessory Var Spd Variable accessory models (using configurable subsystems) Saber Saber cosimulation on accessory loads
Sinda Sinda/fluint co-simulation model initialization files
Sinda Sinda/fluint co-simulation model initialization files
4.2.2 Load and save vehicle configuration
To load or save a specific vehicle configuration, click on the button “loading vehicle” at the top of the image or click the “Save” button at the bottom of the picture The file will be saved in the format 'filename_in.m A saved vehicle can be accessed by pressing the “load” button.
In the lower left part of the figure, there is a selection panel and axes with the ability to view information about components such as the performance map, emissions map, fuel usage map, etc These are graphs along with the corresponding maximum torque in the appropriate modes To view the contents of a specific vehicle or modify the vehicle's information with a file ending in "m-file" we can see the option
To view a vehicle's system in the electric vehicle powertrain, we select the electric vehicle's powertrain in the "Load File" option then select the "Drivetrain Config" option, a window will appear, then we Select the vehicle to view and select
“View/Edit M-file” to view or change the information of that vehicle.
4.2.4 Establish the parameters of the Electric Bus model.
4.2.4.1 Set up the drivetrain system
Because there is no available E-Bus model, we have created a new one including modifying the parameters of the motor, energy store system, vehicle, and transmission As a first step, we operated ADVISOR and then chose “Load file”, and picked “Electric_Bus_in” which was created by basing on “EV_default_in”, then click Done to complete.
To show the code in the Matlab environment, we went for Electric_Bus.in created based on EV_defaults.in, then clicked on View/Edit M-File displaying a window showing the content of Electric_Bus.in as figure below:
Figure 4.5 The code of Electric_Bus.in
The window displays components that we need to modify such as the electric motor, reduction box, and battery system which are represented by MC_PM200, TX_1SPD_BUS, and ESS_LI7_SORT3, respectively.
Next, we selected the drivetrain system, because we have been simulating E-Bus using an electric powertrain system, in “Drivetrain Config” we chose the EV powertrain as below figure.
Figure 4.6 Select the powertrain system
In “Vehicle” we go for “VEH_Electric_Bus” which has been modified with the given parameters of the model shown below.
For the motor model, because there is no PMSM model that meets the design requirements in ADVISOR, we conducted the secondary development of the motor model using software and established a new PMSM model by modifying the M file. The figure also presents a diagram showing the relationship between motor speed and torque on the under-left corner that we modified similarly to the motor of the model To be more specific, we based on an available PMSM model, for a start we clicked on “Motor”, then find an appropriate model, and next select “View/Edit M- file” leading to the Matlab workspace where we can change parameters that suits our selected motor.
To modify the parameters of the motor to suit our E-Bus model, we selected a type of PMSM that is available, then click on Motor → View/Edit M-file and a window were appearing and displayed the Matlab environment where we could change some parameters of the motor to match to the given motor.
Figure 4.9 The window displays the parameter of the motor (1)
Figure 4.10 The window displays the parameter of the motor (2)
Both the figures above show a variety of parameters of the motor needed to change, such as torque, speed, max current, and so on For example, to set up the torque and speed, we just modify the scale of the mc_map_trq and mc_map_spd which is shown in Figure:(1) Furthermore, the maximum current and minimum voltage of the motor is demonstrated through mc_max_crrnt and mc_min_volts arranged respectively.
After we established the parameters of the mechanical components as well as the electric motor, we continued to modify the figure for energy storage which was based on different types of drive cycles However, In ADVISOR there are no available driving cycles that we would rather do some simulation, so we took into account choosing the drive cycle for the bus that is Standardize On-road Test cycles (SORTs) In this part, we are going to show how to create driving cycles, then put the designed specification of the battery system into the software to run the simulation As a first step, we will click on the “Continue” button to move next stage.
Figure 4.12 Simulation configuration setting interface
In the setting interface where we picked “CYC_SKELETON” to carry out modifications Similarly, by modifying the parameters of motor and mechanical components, we also selected “View/Edit M-file” leading to the Matlab workspace where we would change matrixes to match given data in SORTs, which are shown below.
The loop settings of typical Chinese cities were chosen as the criteria for the cycle computation of operating circumstances in "SORT - Standardised On-Road Tests Cycles" Table 6 [10] displays the statistical features of cycle of public transportation data from typical cities:
Table 4.2 Characteristics of the cycle of public transport
Acceleration [m/s 2 ] 1.03 1.03 0.77 Trapeze 2 v-const [km/h]/length [m] 30/200 40/220 50/600
After clicking on View/Edit M file, the screen will appear as a window showing the code of the “CYC_Skeleton” driving cycle in the Matlab environment There are two main values that we need to change, which are time and velocity These values are dislayed in cyc_mph with 2 columns, time on the left side and velocity on the other side The below figure showed that.
Figure 4.14 CYC_SKELETON driving cycle
As mentioned way, we have created 3 SORTs shown below:
Simulation Result
Figure 4.18 Parameter running on the bench
The number of battery packs, motor power model, wheel rolling resistance coefficient, and wind resistance coefficient were chosen in ADVISOR based on the nine orthogonal trials According to the calculation findings in the Chepter 3, the depth of discharge _ess was set at 100%, and the number of operating condition cycles was chosen to make the battery's SOC 30% The speed range was adjusted to 109.8 km/h The acceleration of the vehicle from 0 to 60 km/h in 10.2s are given in Figures 4.13 The next paragraphs describe the application and a full explanation of the simulation findings.
Figure 4.19 Available torque out of the motor
The first diagram shows the velocity of the SORT 2–Mixed, while the second chart depicts the available output torque following the driving cycle time It is clear that the torque of the motor when accelerating from 0 to 20 km/h is higher than the other two because the acceleration time to reach the desired speed of 20 km/h is less.Furthermore, after reaching the desired speeds of 20, 40, and 50 km/h respectively,there may be a force of inertia to maintain those desired speeds, and the amount of torque required to accelerate will gradually decrease close to zero, however, when the vehicle begins to slow down to 0 km/h, the amount of torque will be negative because then the regenerative brake works and recovers energy for the battery system.
Figure 4.20 Current output of the battery
The graph shows us that when the motor is operating at a standstill, how much speed should be accelerated to the corresponding current required to pull the vehicle to work, when the desired speed is reached, the current will decrease to a moderate level that speed and the part that is negative is the part that recharges the battery.
Figure 4.21 Force achieved by the vehicle
Look at the cycle when the car accelerates from 0 to the desired speed to how much, then how much force is needed for the car to operate, when decelerating, how much resistance is to return the car to the initial state, when The higher the vehicle speed, the less traction the vehicle will have As for the negative force, because the vehicle is under force, a brake force is applied to the vehicle to reach 0 km/h.
Figure 4.22 The actual power loss for the energy storage system
Looking at the second graph, it is clear that when the electric bus applies braking, the vehicle will recover energy thanks to the regenerative braking system, while the battery will provide a small amount of energy to allow the electric motor to decelerate more efficiently This is to account for the small protrusion in the second graph.
Figure 4.23 Available power in the motor
Available power in a motor refers to the amount of power that can be delivered to the load by converting electrical energy into mechanical energy As can be seen clearly from the second graph, the power will change with time, and the speed when reaching the desired value, the power will remain constant and the motor after passing through the mechanical parts, efficiency will remain at about 87–90% this extends to the graph will have a negative part due to the power loss of the electric motor.
Figure 4.24 Average temperature of the battery module
The graph shows the temperature of the battery system after it has been in use for a while It starts out with a battery temperature of 20°C, but after some time, it rises to 38°C, which is also the temperature at which the battery cooling system kicks in. This system is in charge of assisting the battery system in keeping the temperature where the battery performs best.
Figure 4.25 Average temperature of motor and controller
The second graph displays the electric motor's operating temperature range It is easy to see that after operating for more than 400 seconds, the electric motor reaches its maximum operating temperature at 45 degrees Celsius, after which the temperature is maintained constant.
Figure 4.26 Power lost by the motor/controller
The graph shows us the power loss of the electric motor, the amount of power loss gradually increases until the vehicle reaches the desired speed, and the amount of power will gradually decrease to a stable level and maintain at that speed In special point, the power loss close to the zero, then rapidly increase It mean when then vehicle deceleration, the electric motor and vehicle are not interactive together duration short time, so there are no power loss at this time After that, the vehicle tend to drive the electric motor, the power loss increase.
Figure 4.27 State of charge history
This graph depicts the condition of the battery after completing multiple driving cycles corresponding only one route in SORT 2 The remaining battery is about87% after 88 mitnutes the vehicle running.
CONCLUSION
Electric Bus Model
China is presently leading the world trend in terms of the quantity and technology of electric buses, followed by Europe, and many other areas are progressively shifting to using electric buses instead of traditional motor vehicles According to market studies, electric buses will be a popular mode of public transportation worldwide in the future.
The fundamental criteria of the electric bus are guaranteeing traction to satisfy acceleration, climbing capabilities, and reaching the intended maximum speed of
110 km/h The electric motor drive system, with a capacity of 200 kW and a top speed of 3500 Nm, assures that the design is acceptable for Vietnamese traffic. Lithium-phosphate battery technology guarantees the vehicle works at the right capacity and operational range, such as route characteristics, passenger count, traffic density, and driving style Furthermore, the charging station helps to optimize the distance and quantity of batteries used, lowering the vehicle's cost.
Through simulation trials, the main aims of this project were to propose new ideas for the power system design of pure electric buses and to reduce the testing costs of the whole shuttle bus development of Vietnam's public transportation system The vehicle's core attributes were determined by simulating a pure electric bus After that, the vehicle power system design scheme with the best power performance was simulated and tested To validate the computed and selected parameters, a driving cycle of three SORTs was set up and tested in ADVISOR, with the following results:
− The fundamental features of the bus, as well as the expected performance indicators, were specified.
− Each power system module's model was created using the ADVISOR software's secondary development The battery and motor parameters are computed and entered into the simulation, with the results compared to the prior computation.
− The simulated routes provide comparable results, but the running circumstances for each route change, with just one type of battery utilized for each route, thus while the simulation only produces relative results, the battery used for SORT 1 is too redundant, while SORT 2, SORT 3 produce acceptable results.
Suggestion for Future Work
Despite the favorable study findings, the simulation model has numerous areas for further development, including:
− SORT 1's battery system has been redesigned to be suited for road conditions and vehicle operation.
− The charging system for electric buses need improvement More study is required to minimize the time and cost of charging the electric bus.
− The driving cycle parameters of 3 SORT are simply European standard specifications, which are impractical for the Vietnamese traffic system As a consequence, selecting the driving cycle parameters appropriate for bus routes in Vietnam will be a new approach for developing the topic, resulting in more trustworthy and accurate simulation results.
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T m is tractive effort of vehicle is resistance force of vehicle is rolling resistance force of vehicle is gravitational force (gradient force) of vehicle is gradient resistance is total mass of vehicle (kg) is vehicle acceleration (m/s 2 ) is rolling resistance force of vehicle is rolling resistance coefficient is gradient resistance is total mass of vehicle (kg) is aerodynamic drag force of vehicle is density of air (kilogram per meter cube) is front area of vvehicle is airodynamics drag coefficient is velocity of vehicle is velocity of the wind is gradient resistance is total mass of vehicle (kg) is slope angle (deg) is the gear ratio of the transmission defined as i g = N in /N out (N in - input rotating speed, N out - output rotating speed). is the gear ratio of the final drive. is the efficiency of the driveline from the power plant to the drive wheels. is the torque output from the power plant.
T m is the motor torque (Nm)
N m is motor speed (rpm) i g is gear ratio of transmission i 0 is gear ratio of final drive η t is the efficiency of the whole driveline from motor to the driven wheel r d is the radius of the drive wheel
N p is the transmission rotating speed (RPM), which is equal to the engine speed in a vehicle with a manual transmission and the turbine speed of a torque converter in a vehicle with an automatic transmission
N p max is the maximum speed of the electric motor.
M is the total mass of the vehicle in kg δ is the rotational inertia factor t a is the expected acceleration time in second v b is the vehicle speed corresponding to the motor-base speed in m/s v f is the final speed of the vehicle during acceleration speed in m/s g is the acceleration of gravitational constant in 9.8 m/s 2 f r is the rolling resistance coefficient ρ a is density of air (kilogram per meter cube) kg/m 3
P t is the tractive power in W