Electric Vehicle Modelling using Lithium-ion Battery

Electric Vehicle Modelling using Lithium-ion Battery

 

Aim-

            1)To model an Electric Vehicle using an Induction Motor and Lithium-Ion Battery from powertrain block set

            2)To check the performance of the system configuration, model parameter on areas like

• Motor Speed
• Motor Torque
• State of Charge
• Battery Voltage/Current

            3)To check whether the vehicle speed track the give reference speed

System-Level Configuration

Electric Vehicle Model

1)The electric vehicle model is represented by using MATLAB/Simulink, this model is a complete representation of an Electric Vehicle which is

been build using powertrain block sets.

2)This model has vehicle dynamics and electrical system; the vehicle dynamics contains subsystem relates to the vehicle body and tires whereas

the electrical system contains a subsystem related to motor and battery pack.

3)This subsystem contains various other components, let's understand each and every component in detail. 

Vehicle Dynamics

1)Vehicle Dynamics is nothing but the study of the vehicle in motion and how the vehicle behaves in motion.

2)The Vehicle Dynamics consist of two main subsystems which are

1. Vehicle Body
2. Wheels

 

1. Vehicle Body

• In this model vehicle body(1DOF) longitudinal block is implemented. This Block helps us to determine the vehicle inertia and drag load.

• There are mainly two forces that are acting on the axel of the wheels which are longitudinal forces and normal forces.
• These forces act on the rear and front of the wheels, the longitudinal forces on rear and front is given by (FwF, FwR)

         Whereas the normal forces are given by (FzF, FzR). This force is connected to the respective axle of the wheels.

  

• The Vehicle body consists of Grade and Wind input ports which can be used to simulate slope and wind drag but this port

          are been grounded to minimize the complexity of the model.

• The xdot output port is a longitudinal force in the x-axis which acts as the velocity/speed of the vehicle in m/s.
• Parameters for the vehicle body

1. No of Wheels on the Front/Rear = 2
2. Mass of the Vehicle = 1500(kg)
3. Frontal area = 4m²
4. CG height above axle = 0.35m
5. Drag coefficient = 0.3

      

1. Wheels & Brakes

• The Wheels used in this vehicle are longitudinal wheels which have brakes of disk type
• Disk brakes have great stopping power and cause less wear and tear and provide précises braking. This block implements the

     Longitudinal behavior of actual wheels.

• This vehicle is rear wheeled drive hence the axle torque is connected to the rear of the wheels and the axle of the front wheel is

        Grounded.

                     

• The longitudinal forces of the tires are set to magic formula constant The magic formula is a separate form of a characteristic function of stiffness, shape, peak, and curvature. (BCDE)

• Magic Formula is given as (Fx=f (K, Fz) =FzDsin (Ctan−1[ {Bκ−E[Bκ−tan−1(Bκ)] } ])
• The Brake input command for the front and rear wheels are connected commonly as one input port.
• Omega is the angular velocity of the wheels in the y-axis; hence this force is considered as torque input to the wheels.
• Parameters for wheels

1. Wheels inertia = 0.8kg*m²
2. Wheel radius = 0.3m
3. Tire Pressure = 220000
4. Brake pad radius = 0.117m

 

 

Torque Differential

• The Torque Differential block is connected between the motor shaft and the axle of the wheels
• The Block consist of an open differential block and a torsional compliance
• The open differential block is basically a set of planetary gear systems. It matches the drive shaft gear to the crown gear.

         and couple the transmission driveshaft to the wheel axle

• The block uses a coordinate system that produces a positive tire and vehicle motion

      

• Input for the open differential is drive shaft torque which accepts input from the motor drive shaft and axle torque which are

         connected to the axle of the wheels.

• On the other side Torsional compliance is basically a spring-damper which is a shaft that connect between the open differential and

          axle wheels

• Parameter for Torque Differential

1. Drive Shaft Ratio = 3.4
2. Axle 1 inertia = 0.3 kg*m^2
3. Carrier inertia = 0.25 kg*m^2
4. Torsional stiffness = 5000 N*m/rad
5. Torsional damping = 10 N*m*s/rad

 

Electrical System

1)The Electrical System is the most important system in the whole drive cycle

2)The Electrical System is subdivided by

1. Motor (Induction Motor)
2. Battery (Lithium-ion Battery)

     

1. Induction Motor & Induction Motor controller

• This vehicle uses a three-phase induction motor as the main driving source. The induction motor also called as asynchronous motor

          It is an AC motor that works on the principle of electromagnetic induction.

• Most of the electric cars use IM as their man drive because as they offer high power/torque density and speed range and

          compact size.

• Induction motor performance in field weakening constant power region. But IM has low-speed performance efficiency, heat loss which lead

         to low power factor and efficiency.

• Hence to control the speed and torque of the motor we need to use an IM controller
• The IM controller blocks implemented a torque-based field-oriented controller with an outer speed loop control
• The controller also implements equation for speed control, torque determination regulator
• Some basic formula that the blocks implements are-

 

                   To calculate speed, frequency and poles                              Formula Required to calculate losses in the motor

                                ɳ_{sync = 120f/p}                                                                           Stator Copper Losses

                           ɳ_{sync = Synchronous speed}                                                             P_{sc =} 3I²R_s

                                   _{f       = frequency}                                                                     Rotor Copper Losses

                                   _{p      = poles}                                                                               P_RC= 3I²Rr

                                                                                                                                  Mechanical Power required

                                                                                                                                      P_{mech =} P_RC(1-S/S)

                               Motor Slip calculation

                      s = (ɳ_{sync -} ɳ_m) ɳ_sync * 100

 

                      ɳ_m = Mechanical shaft speed

 

                      To calculate Torque and Speed

                                T = P/ω_m

                                _{T = Torque(N/m)}

                                _{P =} Power in Kw

                               ω_{m = rad/min}

• The corresponding phases (A, B) is connected to the motor controller, the speed of the motor is constantly regulated by its controller

         closed-loop speed control (SpdFdk port).

• The vehicle speed in(m/s) is converted to motor speed in(rad) by the help of unit conversion and signal specification block. Taking a product of
• motor speed and acceleration a torque command is generated.
• The lookup table takes input as vehspd in rad which is then scaled by accelerator command and the product of two is implemented as a torque command

                     

                                      Torque Command Data

• The resultant motor torque signal is obtained from the bus selector.

 

• Parameters for Induction Motor/Controller

1. Motor Type = 3phase Induction motor
2. No of poles = 2
3. Stator resistance =1.77Ὠ
4. Rotor resistance =1.34Ὠ
5. Inductance = 0.368H
6. Frequency = 60hz
7. Line to Line Voltage = 460v
8. Torque at rated current = 12.646
9. Rated Slip = 0.017
10. Inverter efficiency = 98%

 

 

1. Lithium-ion Battery

• The battery is the energy source of any system. The battery used in the system is a Datasheet Battery which implements a model for the lithium-ion battery.

• The question arises that why most of the EV uses lithium-ion cells as a source, like any other battery. Because battery like a lead-acid battery which

         required constant maintenance and monitoring, hydrogen cells which are quite bulky and expensive also capacitor banks are used as

         a battery pack but they have a high discharge rate and drain quickly.

• Hence the Lithium-ion battery eliminates all such disadvantages and requires fewer maintenances and operational cost are less
• Longevity- The average lithium-ion battery life span for large capacity is more than 8 years.
• Safety-Reduce the risk of accidents by eliminating exposures to flammable fuels. Able to withstand even in the high temperature without explosions.

• Environmental Impact-Lithium ion battery provides significant environmental benefits over fossil fuels. With the steady increase in the electric vehicle,
• we can see an immediate impact on the reduction in carbon emission.
• Hence knowing all such advantages of lithium-ion manufacturers prefer using lithium cells as their main source of energy.

 

 

• The battery pack is packed with 30 numbers of cells in series and 2 numbers of cells in parallel each.
• Rated capacity of the battery (Ah) = 100
• Output Voltage = 12V
• The Battery rated capacity is 100Ah and rated voltage is 12 the battery provides 1200kwh considering its charging/discharging.

Charging of battery: If the applied Current is 10 Amperes, then it would be 100Ah/10A= 10 hrs. approximately.

Discharging: Battery Ah X Battery Volt / Applied load. Say, 100 Ah X 12V/ 100 Watts = 12 hrs. (with 40% loss at the max = 12 x 40 /100 = 4.8 hrs.)

the backup will last up to 4.8 hrs.

• Formula to calculate SOC =

SOC(t) = SOC (t-1) + ∫ I/C_{Bat. dt}

Where

               SOC(t)=state of charge at time t

               SOC(t-1) =Initial state of charge

               I = charge/discharge current(A)

               t = time(H)

              C_Bat = Battery capacity(A)

• The BattCurr and the BattVolt are connected to the motor controller respectively, the batt soc can be determined by the bus selector soc is scaled to 100 by using a gain block.

 

• Parameter for Battery

1. Battery Type = Lithium ion Battery
2. BattChargeMax = 100Ah
3. No cells in series =30
4. No of cells in parallel =2
5. Output Battery Voltage = 12v

 

Driver

• The driver block is basically a controller for the vehicle, it controls the acceleration, acceleration, and braking of the vehicle.
• The block is implemented with a PID controller which is basically the main controller in the whole drive cycle.
• The PID controller works as closed-loop speed control, it takes the input as a reference speed and corrects the error generated by

     the vehicle speeds.

• PID controller is tuned for the adequate acceleration and deacceleration command, it is done by limiting its output to upper and lower saturation.

• Separating the output of the PID to accelerate and deacceleration command we use a saturation block for each command, for acc command we use an upper saturation
• value and for the deaccelerate command, we use a lower saturation value.

 

     

• Tuning its proportional, derivative and integral values we should be able to track the reference speed
• The below table gives us an idea for the manual tuning of the controller.

    

 

Result

• Taking all the above factors into consideration we now run the simulation
• The reference speed here is Artemis Motorway (130Kmph)

 

• The simulation was run for about 1068sec and we have obtained the result shown above
• There are 6 individual graphs showing the result for motor and the battery
• In this result, we see that a max torque of about 400Nm was obtained and a max speed of the motor was about 1500rpm at 130kmph
• The graph of the battery soc shows a linear and a slow discharge rate, we also observe a peak of charging spike at about 950sec as a cause by the regenerative braking of the vehicle.

• The result for the Vehicle speed and reference speed is shown below

  

• We can see that the vehicle speed tracks the reference speeds Artemis Motorway thanks to the PID controller, the manual tuning of the PID controller help to track the ref speeds.

 

 

Conclusion

• The Efficiency of the Electric Vehicle is more compare to normal IC vehicle or HEV Vehicle
• Also, the run time cost of the vehicle is very low. e.g.-

                                Full Range = 130km

                                Total consumption of electricity at full charge = 16.5units

                                Electricity usage per km = 16.5/130 = 0.12units

                                Cost of 1-unit electricity = 4.5Rs

                                Total cost of running for 1 km = 0.12*4.5 = 0.54p

                                Total cost of running for 130km =15.6Rs

• The power losses are comparatively less than a conventional vehicle as they use a complex gear system
• But to use the EV at the full potential there is a need to increase a public charging station
• The Manufacturing of electric vehicles is domestic, for instance, come at a high cost, production of battery is are largely expensive due to material like cobalt hence there is a need to find an alternate for such materials.

• There is hence a need for adoption of the electric vehicle especially for India as it could save up to $300bn in oil imports and 1 gigaton of CO₂ emission.