Project-1: Modelling an electric Car with Li-ion battery

Aim –

1. To model an electric car vehicle using an Induction Motor & Lithium Ion battery from Powertrain Blockset.
2. To check the performance of the system configuration, model parameters on areas like – Motor speed, Motor Torque, State of Charge, Battery voltage & current.
3. To check whether the vehicle speed track at the given reference speed.

Introduction -

                                                                                    

Electric vehicle is a vehicle, which uses one or more electric motors for propulsion. Depending on the type of the vehicle motion may be provided by rotary motor or by linear motor (in tracked vehicle). The electricity stored in battery powered by electric motor & battery can be charged by plugging it in grid, like our phone. According to the degree of electricity used, electric vehicle is divided into 3 categories –BEV, PHEV & HEV.

Battery Electric Vehicles (BEV) –

 BEVs are fully electric vehicles with rechargeable batteries with no engine. It stores power in battery pack & this power is used to run the vehicle & other peripherals. BEVs are charged by electricity from external source. BEVs don’t emit any hazardous emissions. Some most famous examples of this types of cars are – BMW i3, Tesla Model 3, Kia Soul, Toyota Rav4 etc.

Plug-In Hybrid Electric Vehicles (PHEV) –

These types of vehicles are propelled by motor as well as gasoline engine. Battery is charged with regenerative braking & it can be charged with external source. PHEVs can go from 10-40 miles before assistance of engine. Examples of PHEVs – Chevy Volt, Audi A3 E-Tron, BMW i8, Toyota Prius etc.

Hybrid Electric Vehicle (HEVs) –

HEVs are powered with both gasoline & electricity. Battery can be charged with regenerative power only. Motor supplies power from starting, engine takes care of high speed & heavy load. Controller is used to ensure best economy. HEVs are – Honda Civic Hybrid, Toyota Prius Hybrid, Toyota Camry Hybrid.

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 built using Powertrain Blockset.
2. This model has vehicle dynamics & electrical system; the vehicle dynamics contains subsystem relates to the vehicle body & tires whereas the electrical system contains a subsystem related to motor & battery pack.
3. This subsystem contains various other components which we will understand further.

Vehicle Dynamics –

                                                

The vehicle dynamics is nothing but the study of the vehicle in motion & how the vehicle behaves in motion.

The vehicle Dynamics consist of 2 main subsystems which are –

1. Wheels -
2. Vehicle Body –

                                                      

In this model Vehicle Body (1DOF) longitudinal block is implemented. This block helps us to determine the vehicle inertia & drag load.

There are mainly 2 forces that are acting on the axle of the wheels which are longitudinal forces & normal forces.

These forces act on the rear & front of the wheels, the longitudinal forces on the rear & 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 & Wind input ports which can be used to simulate Slope & Wind Drag but this port is been grounded to minimize the complexity of the model.

The X-Dot output port is a longitudinal force in the x-axis which acts as the velocity/speed of the vehicle in m/s.

• The No. of wheels on the front/Rear = 2.
• Mass of the vehicle = 1500 (Kg).
• Frontal area = 4 m
• CG Height above the axle = 0.35 m.
• Drag Coefficient = 0.32.

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 & tear & provide precise braking. This block implements the longitudinal behaviour of the actual wheels.

This vehicle is rear wheeled drive hence the axle torque is connected to the rear of the wheels & 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 & curvature (BCDE).

Magic formula is given as (F_x = f (k, F_z) = F_zDsin (Ctan-1[{B_k-E [B_k – tan -1(B_k)]}])

The brake input command for the front & rear wheels are connected commonly as one input port.

Omega is the angular velocity of the wheels in the y-axis; hence this form is considered as torque input to the wheels.

Parameters for wheels –

1. Wheels Inertia = 0.8 Kg*m²
2. Wheels Radius = 0.3 m.
3. Tire pressure = 220000
4. Brake Pad Radius = 0.117 m.
5. Torque Differential –

The torque differential block is connected between the motor shaft & axle of the wheels.

The block consists of an open differential block & 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& couple the transmission driveshaft to the wheel axle.

The block uses a coordinate system that produces a positive tire & wheel motion.

Input for the open differential drive shaft torque which accepts input from the motor drive shaft & 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 & axle wheels.

Parameter for Torque Differential –

1. Drive Shaft Ratio – 3.4
2. Axle 1 Inertia – 0.3 Kg*m².
3. Carrier Inertia – 0.25 Kg*m².
4. Torsional Stiffness – 5000 N*m/rad.
5. Torsional Damping - 10 N*m*s/rad.

1. Electrical System –

                                                                        

The electrical system is the most important system in the whole drive cycle.

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 is also called asynchronous motor.

It is an AC motor which works on the principle of electromagnetic Induction.

Most of the electric cars use IM as the main drive because they offer high power/torque density & speed range & 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 & efficiency.

Hence to control speed & torque of the motor we need to use an Induction Motor Controller.

The IM controller block implemented a torque-based-field-oriented-controller with an outer speed loop controller.

The controller also implements equation for speed control, torque determination regulator.

Some of the basic formulas that the block implements -

To Calculate Speed, Frequency & Poles –

ἡ_sync = 120f/p.

ἡ_sync = Synchronous Speed.

f = Frequency.

p = Poles.

Formula Required to calculate losses in the motor –

Stator Copper Losses – P_sc = 3I²R_s.

Rotor Copper Losses – P_Rc = 3I²R_R.

Motor Slip Calculation – (ἡ_sync - ἡ_m) ἡ_sync*100

ἡ_m = Mechanical Shaft Speed.

Mechanical Power Required – P_mech. = P_RC (1-S/S)

To calculate Torque & Speed,

T = P/ὠ_m.

T = Torque (N/m).

P = Power in Kw.

ὠ_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 is (m/s) is converted to motor speed in (rad) by the help of unit conversion & signal specification block. Taking a product of motor speed & acceleration a torque command is generated.

The lookup table takes input as vehSpd which is then scaled by accelerator command and then the product of 2 s implemented as a torque command.

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

                                                                                            

Parameters of Induction Motor Controller –

1.Motor Type = 3 –Phase IM.

1. No. of Poles = 2
2. Stator Resistance = 1.77 Ὠ.
3. Rotor Resistance = 1.34 Ὠ.
4. Inductance = 0.368 H.
5. Frequency = 60 Hz.
6. Line to Line Voltage = 460 V.
7. Torque at Rated Current = 12.646
8. Rated Slip = 0.017
9. Inverter Efficiency = 98%.

 Lithium Ion Battery –

                                                         

The battery pack is packed with 30 Nos. of cells in series and 2 Nos. of cells in parallel each.

Rated capacity of the battery (Ah) = 100

Output Voltage = 12 V.

The battery rated capacity is 100 Ah & rated voltage is 12 the battery provides 1200 Kwh considering its charging/discharging.

Charging of the battery – if applied current is 10 Amps. Then it would be 100 Ah/10A = 10 Hrs. Approx.

Discharging – Battery Ah X Battery Volt/Applied Load. Say 100 Ah. X 10V/100 Watts = 12 Hrs. (With 40 % loss at the max = 12 X 40 /100 =4.8 Hrs.)

 The battery is the energy source of any system. the battery used in the system is the datasheet battery which implements the model for the Lithium-Ion Battery. The reason behind popularity of these cells batteries in EVs low discharge rates compared to capacitor banks also less expensive & required less maintenance and constant monitoring than Hydrogen cells. Lithium Ion battery eliminates all these disadvantages and requires fewer operational costs.

Lithium Ion battery has average life span for more than 8 years. Safety reduce the risk of accidents by eliminating exposure to flammable fuels. Able to withstand even in the high temp. without high temperatures.

Also, Lithium Ion batteries provide significant environmental benefits over fossil fuels. With steady increase in the electric vehicle we can see the 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.

Formula to calculate SoC –

SOC (t) = SOC (t-1) + _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.

The BattCurr and the BattVolt are connected to the motor controller respectively. the BattSoC can be determined by the Bus Selector & the SoC is scaled to 100 by using a gain block.

Parameters for Battery –

Battery type = Lithium Ion Battery.

Battery Charge Max. = 100 Ah.

No. of Cells in Series = 30

No. of Cells in Parallel = 2

Output Battery voltage = 12.

Driver - 

                                           

The Driver Block is basically the controller for the vehicle. It controls the acceleration, Deceleration & 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 a Closed-Loop Control, it takes the input as a reference speed & corrects the error generated by the vehicle speed.

PID controller is tuned for the adequate acceleration & Deceleration command. It is done by limiting its output to upper and lower saturation.

Value and for the deaccelerate command, we use a lower saturation value.

Tuning its proportional, derivative & integral values we should be able to track the reference speed.

The table given below shows us the idea of the manual tuning of the controller –

Result –

Taking all the above factors into consideration we now run the simulation.

The simulation was run for about 1068 Sec. nd we have obtained a result shown above.

There are 6 individual graphs showing the results for motor & battery.                     

In this result we see that a maximum torque of about 320 Nm was obtained and max. speed of motor was about 1100 RPM at 44 Kmph.

The graph of the battery SoC shows a linear and a slow discharge rate as a cause by the regenerative braking of the vehicle.

We can see that the vehicle speed tracks the reference speeds FTP 75 with the help of PID controller. The manual tuning of the PID controller help to track ref. speeds.

Conclusion –

The efficiency of the electric vehicle is more compared to normal IC vehicle as they use a complex gear system.

The power losses are comparatively less than a conventional vehicle as they use a complex gear system.

But to use the EV at full potential there is a need to establish public charging stations.

The manufacture of electrical vehicles is domestic, for instance, come at high cost, production of battery is expensive due to material like cobalt, hence there is a need to find an alternate for such materials.

Hence there is need for adoption of electric vehicles especially for India as it could save upto $ 300 Billion in oil imports nd 1 Gigaton of CO₂emissions.