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

Nowadays, the trend of reducing energy consumption and environmental impact has led to the electrification of vehicle for future transportation. The serious issue of global warming, also known as the greenhouse effect, urban pollution, and the depletion of fossil fuels have increased tensions worldwide. Although the Internal Combustion Engine (ICE) technology is being matured over the past 100 years, it will mainly rely on improving the fuel economy and reduce emissions. Powered by battery, Electric Vehicles (EV) have been proposed by many as one of the above solution as they are highly efficient, silent, produce zero emission, and can be regulated by the power grid operator . However, the main challenges to solve in EV are battery-related issues; the high initial cost, limited driving range, and long charging time of its battery.  The battery must contain sufficient energy to drive certain range and provide enough power during accelerations. In order to estimate and optimize the energy consumption of EV, we need to model an EV. It is important to have a good model of EV to prevent wrong conclusions.

 

 

In this simulation we are designing a Electric Vehicle having following specifications: -

 

 

BATTERY PACK
BATTERY PACK	UNIT	SPECIFICATIONS
Type		Lithium-ion
Voltage	V	60
Capacity	Ah	630
DC MOTOR
Field Type		Permanent Magnet
Rated Voltage V	V	60
Motor Rating	kW	20
MOTOR CONTROLLER
Type		PWM H-Bridge
Controlled PWM Voltage	V	60
PWM Frequency	Hz	5000
VEHICLE BODY
Weight of the Vehicle Body	Kg	940
Frontal Area	m^2	2.11
Drag Co-efficient		0.337
Rolling Radius	m	0.3
Co-efficient of Rolling Resistance		0.015
Air Density	kg/m^3	1.18

 

 

 

System Level Configuration:

To model the EV in SIMULINK, we need to model the individual components of an EV such as the motor, controller, power converters, wheels, and batteries. All of these components are available as blocks from the simscape and powertrain blocksets. The various components of the EV will be modelled and explained in the sections below:

 

Vehicle Body 

To model the body of the EV, we need to insert the vehicle body block shown in the image below:

 

This block has 6 ports which represent various aspects of the modelling of the vehicle body:

• H - This stands for hub and allows us to connect the hubs of the wheels of the vehicle to the body.
• V - This stands for velocity and outputs the velocity of the vehicle.
• W - This represents wind velocity and allows us to model a headwind (against the front of the vehicle) acting on the velocity by giving a speed for it. 
• NR - This represents the normal force on the rear wheels of the vehicle.
• NF - This represents the normal force on the front wheels of the vehicle. 
• beta - This represents the grade (incline) of the surface that the vehicle travels on, as an angle to the horizontal. 

 

Double-clicking the vehicle body block opens the block parameters shown below:

Main Tab

                 

 

From the "Main" tab, here, we can model the basic parameters of the vehicle such as mass, number of wheels per axle and even gravitational acceleration. For our model, we are using a mass of 800kg, 2 wheels per axle (total of 4 wheels), and a gravitational acceleration of 9.81 metres per second squared. 

 

Drag Tab

                                 

 

From the "Drag" tab, we can model the frontal area, drag coefficient, and the air density. I have used a frontal area, drag coefficient, and air density of 3, 0.3, and 1.18 respectively.

Wind Velocity & Slope

From the "W" and "beta" ports on the vehicle body block, I have used a "PS-Constant" block to model the effect of the wind velocity and the slope.

                             

For the wind velocity, I have used a constant value of 5.

                             

For the road incline, I have used a constant value of 0.

 

Velocity Subsystem

From the "V" port on the vehicle body bock, I have created a subsystem. This is because by default, this port will output the vehicle speed in miles per hour. For personal preference, I have created the subsystem to get the output speed in kilometres per hour. This system consists of a PS-Simulink converter block, a gain block, and a zero-order hold block. The gain block uses a factor of 1.6 to convert the speed from miles per hour to kilometres per hour. The PS-Simulink converter block is used to convert the physical signal of speed to a SIMULINK signal to be displayed on the scope block.

This subsystem is shown below:

 

Tires

In this model, I have used the "Magic Formula" tires. There are various tire blocks that can be used, but the advantage of the magic formula ones is that they enable us to model the longitudinal behavior of tires on a highway. This block is shown below:

                               

This block has 4 ports which represent various factors that can be modelled:

• N - This port represents the normal force on the tire and the downward direction is considered positive.
• S- This port represents the slip acting on the tire.
• A - This port represents the axle and is the mechanical rotational conserving port for the wheel axle.
• H - This port represents the hub and is the mechanical translational conserving port for the wheel hub.

 

Double-clicking the magic formula tire block, opens the block parameters window shown below:

 

Main

                                 

In the "Main" tab, we can model parameters such as tire nominal vertical load, and various coefficients. All values are kept as default.  

 

Geometry

                              

In the "Geometry" tab, we can model the rolling radius of the tire.

 

Dynamics

                         

In the "Dynamics" tab, we can model parameters such as the tire inertia and initial velocity. 

 

Rolling Resistance

                                                  

In the "Rolling Resistance" tab, we can model the effect of rolling resistance more closely. In this model, I have turned on the effect of rolling resistance, and have used a constant rolling resistance coefficient. 

 

Gear

In this section, I have modelled the transmission of the EV. To simplify the transmission system of the EV model, I have used a "Simple Gear" block which uses a fixed gear ratio with no inertial effects. This block is shown below:

                  

Double-clicking this block, opens the block parameters where we can model additional parameters of the gear.

 

Main

                          

 

In the "Main" tab, we can model the follower to base teeth ratio and the direction of rotation of the output shaft. These settings were kept as default.

 

Meshing Losses

                                       

In the "Meshing Losses" tab, we can model the frictional effects on the gear. I have used a constant efficiency friction model with an efficiency of 0.86 and a follower power threshold of 0.001.

 

Side Shaft

The side shaft block is used to create inertial effects on the simple gear. This block only has one mechanical rotational conserving port and the positive direction of the block is from the port to the reference point (simple gear block). The side shaft block is shown below:

                                          

 

Double-clicking the side shaft block, opens the side shaft block parameters shown below:

Parameters

                                   

In the "Parameters" tab, we can model the inertia of the side shaft. The default value of 0.01 is used.

 

 

Vehicle Body Subsystem

 

                          

The full vehicle body system is shown in the image above with all the aforementioned blocks connected together. Four magic tire block are used to represent a four-wheeled vehicle. This system is then converted to a subsystem shown in the image below:

 

                                          

 

 

Motor

For our EV model, I am using a DC motor block which is shown below:

                                 

 

The left side of the motor represents the electrical part of the motor, whereas the right side represents the mechanical part. The mechanical part has 2 ports labelled C and R. C refers to the casing of the motor and R represents the rotation of the motor which produces the torque. The electrical part has 2 ends labelled with a positive and negative sign which represent the positive and negative terminals of the motor. Double-clicking the motor block opens the block parameters:

Electrical Torque

                                            

Under the "Electrical Torque" tab, we can model the electrical torque characteristics of the DC motor such as no-load speed, and rated DC supply voltage. I have used the values and settings shown in the image above.

 

Mechanical

                                              

 

Under the "Mechanical" tab, we can model the mechanical torque characteristics such as rotor inertia and initial rotor speed. I have used the default values as shown in the image above.

After setting the DC motor block parameters, make the connections as given in the image below:

                                   

 

1) H-Bridge Motor Driver

 The H - Bridge with Thermal Port block is used to drive a motor. The H bridge two output ports

Positive Port 

Negative Port 

This port is directly connected to the motor that has to be controller. There is also a REV port.When the reverse threshold voltage is lower than the REV port voltage,the polariy of the motor is reversed, and if the BRK port voltage is greater than the value of breaking threshold voltage, it indicates that the vehicle is in braking condition.

The following image shows the H-Bridge Motor Driver block from Powertrain block set.

 

                   

                             

 

We changed the Input Thresholds as per our requirements

 

                                              

                                           

 

2) Controlled PWM Voltage Source

The PWM signal is used or controlling the speed of the traction motor. This block is used for providing a controlled PWM voltage output.

The Duty cycle is given by,

100*(Vref-Vmin/Vmax-Vmin)

Where,

Vref - is the reference voltage across the ref+ and ref- ports.

Vmin - denotes the minimum reference voltage.

Vmax - denotes the minimum reference voltage.

The following image shows the Controlled PWM Voltage Source block from Powertrain blockset.

                                        

                                        

                                          

3) Temperature sensor

This block and its parameters are shown below, this block measure temperature in a thermal network. There is no heat flow through the sensor.

                                    

                                                   

4) Current Sensor

                               

This block is used to measure the flow current through of circuit.

 

5) Controlled voltage Source

                             

The controlled voltage source block is used to give a constant voltage output. It has two electrical conserving ports and a physical signal port. The output from the controlled voltage source is fed to the controlled PWM voltage source.

Electrical Reference

The electrical reference block is used to create a grounding effect for electrical circuits. Any model that uses electrical or electronics components will need to have atleast one electrical reference block in it. The electrical reference block is shown below:

 

                              

In this EV model, we are using this block for 2 occasions. The first is for to create an electrical ground between the controlled voltage source, controlled PWM voltage and the H-Bridge blocks. The second is for the battery system which will be modelled afterwards,

 

 

Solver Configuration

The solver configuration block is used to solve any necessary equations in a model and in my case, I have used them in the connection to the 'REV' port of the H-Bridge block. The solver configuration block is shown below:

 

                               

 

The image below shows the connections that can be made with the components discussed till this point. 

                           

 

Battery System

The battery system is an essential part of the EV model as it will provide the electrical power required to power the DC motor. The components of the battery system are explained below:

 

Battery

The battery block used is a simple one and considers only the basic parameters. The battery block is shown below:

                                 

 

Double-clicking the battery block, opens the block parameters which is shown in the image below:

                                        

As we can see, the battery block parameters include the nominal voltage, the internal resistance and the battery charge capacity. I have used a nominal voltage of 400V, an internal resistance of 0.2 Ohms and an infinite battery charge capacity. 

 

 

Controlled Current Source

The controlled current source block is a part of the battery system used in the EV model. Similar to the controlled voltage source, this block will represent an ideal current source that is powerful enough to maintain the specified current regardless of the voltage across it. The controlled current source block is shown below:

                            

 

Current Sensor

The current sensor block represents an ideal current sensor and is used to convert the current measured in an electrical circuit to a physical signal that is proportional to the current. This block is used to measure the current between the battery circuit (controlled current source) and the DC motor. The current sensor block is shown below:

                                   

The positive and negative terminals represent the terminals across which the current sensor is inserted in to the circuit. The third port outputs the physical signal and in my model, it will send the signal to the controlled current source. 

                                    

 

From the image above, we can see that the current sensor is embedded in between the electrical side of the DC motor and the H-Bridge. The current sensor can be connected from its physical signal port to the remaining components in the battery system including an electrical reference block. This is shown in the image below:

 

                                        

 

 

SOC & Current

SOC stands for state of charge and it is a measurement of the available charge in a battery. When a battery is fully charged, it is considered to have a 100% charge and conversely 0% charge if fully discharged. In this EV model, I want to measure the current and the SOC of the battery as the simulation is run. For this, I have used a scope block which shows the output signal we wish to measure as a plot against time. 2 scopes have been used, one for the current and the other for the SOC. In order for this to be measured, we need to use a 'PS - Simulink converter' block. This is because the current signal is a physical one and we are measuring it as a logic signal in the SIMULINK workspace. 

The PS-Simulink converter block is shown below:

                                      

 

The scope block is shown below:

                                            

 

SOC Subsystem

To measure the state of charge of the battery, a subsystem was created of various blocks. The first block is the 'Rate Transition' block and it is used to handle data transfer between different rates and tasks. Next, a 'Gain' block is used in order to multiply or divide the signal coming from the rate transition block. In this case, the gain block will divide the current signal with the ampere rating of the battery which has been taken as 80Ah multiplied by 3600 (seconds in an hour). This is shown in the gain block parameters below:

                                    

Then, a 'Discrete - Time Integrator' block is used to perform a discrete integration of the current signal with respect to the time. A constant block is used to represent the initial SOC of the battery. Assuming that the battery is always fully charged when performing a simulation, I have altered the constant block with a value of 1 representing 100%. Next, a 'sum' block is used to perform addition and subtraction operations. The signal from the 'discrete time integrator' block will be subtracted from the constant block representing 100% charge. These components are connected as shown below:

 

                             

These blocks are then made in to a subsystem called 'SOC Estimate' and linked with the battery circuit using the PS-Simulink converter block. A scope block is used at the junction of the PS-Simulink converter block to plot the output signal of the current from the battery. Another scope is used to plot the output signal of the SOC from the SOC subsystem. This is shown in the image below:

 

                                           

 

 

Drive Control

In order to control the vehicle, we need another system that decides how the vehicle will operate. This means that data needs to be input in to this model as commands for how we desire the vehicle to operate. In addition, we need blocks that control how the vehicle will operate as a response to its instantaneous state. This system is explained below:

 

Drive Cycle

A drive cycle is a data set that contains velocity and time data for the purpose of modelling the motion of a vehicle. The drive cycle will be a plot of the velocity against the time and it is made to resemble typical driving conditions that a consumer may experience themselves in. For instance, they can model highway driving situations, driving in urban areas, or driving with full power etc. Drive cycles are used by automotive companies for various testing procedures such as mileage, pollution tests, and acceleration and top speed tests. There are various different drive cycles that are industry standard e.g. Urban Dynamometer Driving Schedule (UDDS), FTP 75. 

In my EV model, a drive cycle is used as the reference velocity data for the longitudinal driver block to send acceleration or deceleration commands according to the drive cycle. There are 3 ways of implementing a drive cycle. One method is to create or own drive cycle with a spreadsheet of velocity data in one column and time data in another column. Another method is to use a signal builder block and create signals that represent the velocities at which the vehicle should travel and the durations for which those velocities are to be maintained. The last method is to use the industry standard drive cycles which are in - built in to the SIMULINK library. In my case, I have used an industry standard 'WOT' drive cycle. This drive cycle stands for 'Wide Open Throttle' and it models the situation where the vehicle is made to accelerate at full power and maintained at a particular speed and made to decelerate back to rest. 

By default, the drive cycle block is set to the FTP75 drive cycle shown below:

                        

 

This can be modified by opening the block parameters shown below:

                                                    

 

When the 'WOT' drive cycle is chosen, some extra parameters are made available for modification which are shown below:

                                       

 

As we can see, with the 'WOT' drive cycle, we can modify the start time, time to start deceleration, and the entire duration of the drive cycle. I have used a start time of 3 seconds meaning that the vehicle will begin acceleration after 3 seconds of starting simulation. I have used a nominal reference speed of 5 m/s and this refers to the maximum speed the vehicle should achieve. I have set the deceleration to begin at t = 5 seconds and the whole cycle is set for a duration of 10 seconds. The input and output velocity units are both set to m/s. 

The plot below shows the custom WOT drive cycle I have created. 

                                    

 

 

Sum Block

The "Sum" block is used as part of a feedback system. This system will require data from the drive cycle (command signals) and data from the vehicle body (actual speed) as well. The aim of this speed control system is to have the actual vehicle speed to match the command speed data from the drive cycle as closely as possible. The feedback system is essential to this control method because it will relay the actual speed data back for a comparison with the drive cycle data. Any difference in the data between the two is considered as an error and the sum block is used to find the difference.

This block is shown below:

                                      

 

Double-clicking the sum block opens the block parameters as shown below:

                                               

In order to find the difference between the drive cycle data and the actual speed from the vehicle block, the list of signs need to be changed to "+-". 

PID Controller

The PID controller block is essential for the speed control of the EV model. The PID controller block takes the error data between the drive cycle data and the actual speed of the vehicle (from the sum block) and works to minimize this error. The PID controller block is shown below:

 

                                            

 

Double-clicking the block opens the block parameters shown below:

 

                                        

In this model, I have used the continuous-time domain PID controller. All other parameters are left as default.

 

Saturation Block

In order to set the acceleration and brake commands, I have used the saturation block. This block is used when we want to set limits for signals. This block is shown below:

                                          

In the case of the accelerator command, I have set the limits between 0 and 1 by opening the saturation block parameters as shown below:

                                             

 

Another saturation block was used for the deceleration/brake commands which is shown below:

                                    

 

To create the deceleration commands, I have used a different set of limits between -1 and 0. This is shown in the image below:

                                        

These limits ensure that there is no crossover with the acceleration commands.

 

Transfer Function 

The transfer function block is used when we want to insert a transfer function. A transfer function is defined as the ratio of the Laplace transform of the output of a system to the input of a system. The transfer function block is shown below:

 

                                                 

Double-clicking the block opens the block parameters as shown below:

                                                          

 

From the block parameters, we can modify the transfer function by changing the numerator and denominator coefficients. I have used the default coefficients.

For the deceleration command, I have used another transfer function block with a slightly different transfer function. This is shown in the image below:

                                        

 

The transfer function block was modified by changing the coefficient of the denominator as shown in the image below:

 

                                                 

 

Absolute Block

An absolute block is also implemented for the deceleration command which takes the absolute value from the deceleration saturation block. This block is shown below:

                                           

 

With the aforementioned blocks, the control system can be made as shown in the image below:

                            

 

The accelerator and brake commands can be connected to the power converter as shown in the image below:

                                               

 

 

Speed Measurement

In order to measure the speed of the EV model, I needed to use the scope block once again. I modified the scope block to have 2 input ports where one port takes the output velocity signal from the vehicle subsystem block and the other port takes the output signal from the drive cycle to the reference velocity port on the longitudinal driver block. This has been done so that the scope can show us the plots of the reference velocity and the actual velocity of the vehicle to see how they compare with each other. 

 

Distance Measurement

I have used the scope block and mathematical operator blocks to measure the distance travelled by the vehicle according to the drive cycle data. The area under a velocity time graph tells us the distance travelled by an object and so in my model. This means that the integral of the velocity with respect to time, gives us the distance travelled. So, I have implemented the integrator block to integrate the velocity signal that is output from the vehicle subsystem. 

The integrator block is shown below:

                                             

From the integrator block, I needed to use the 'Divide' block along with a 'Constant' block having a value of 3600 in order to convert the divide the integrated speed signal which is in kilometres per hour by 3600. This will give us the distance travelled in kilometres. 

The constant block with a value of 3600:

                                       

 

The 'Divide' block:

                                     

Finally, a 'Display' block is used to show the distance travelled as the simulation is run. The display block is shown below:

                             

 

If these blocks have been added to the workspace, they can be connected as shown in the image below:

 

                                      

 

From the drive cycle block, a connection is given to the speed scope block to plot the drive cycle data during the simulation. From the speed scope block, a connection is sent back to the control system to the sum block negative port for the feedback control to occur.

 

 

Results

Without Modified Coefficients

After a simulation time of 10 seconds, the following default PID values were used:

• `K_p = 1`
• `K_i = 1`
• `K_d = 0`

 

The distance and speed plot shown below was obtained:

                         

                                       

From these results, we can see that the vehicle only begins its acceleration at t = 3.4 seconds as opposed to the commanded t = 3 seconds from the drive cycle. At t = 4 seconds, the vehicle speed has increased to 0.2 m/s whereas the commanded speed from the drive cycle is 5 m/s at the same time period. By t = 5 seconds, the vehicle is meant to start its deceleration back to rest, but the vehicle is still in its acceleration phase as the speed increases to 0.8 m/s at the same time period. After t = 5 seconds, the vehicle's acceleration appears to be linear and the vehicle speed reaches its peak value of 3.1 m/s at t = 9 seconds. Immediately after, the vehicle begins deceleration and the vehicle speed drops to 3 m/s at t = 10 seconds.

For the default PID values, there appears to be a delayed response time in the actual vehicle speed. There is no overshoot and there is very minimal steady state error.

First Modification

For the same simulation time, the proportional and integral constants in the PID controller block were modified to the following:

• `K_p = 800`
• `K_i = 300`
• `K_d = 0`

For these parameters, the following speed-time plot was obtained:

                                

From these results, we can see the plot of the drive cycle data and the actual vehicle speed. In the actual speed of the vehicle, there is a slight delay in the acceleration of the vehicle wherein the vehicle only starts accelerating at t = 3.3 seconds instead of t = 3 seconds as seen in the drive cycle. At t = 4 seconds, the vehicle reaches 0.3 m/s which is much lower than the commanded speed of 5 m/s. By t = 5 seconds, the vehicle achieves a speed of 0.8 m/s whereas the drive cycle is still at 5 m/s and is about to begin its deceleration back to 0 m/s. The actual speed of the vehicle has a delayed response time as it is still in its acceleration stage and has not reached its peak speed value either. By t = 8 seconds, the vehicle achieves its peak speed of 2.6 m/s which is only half of the commanded peak speed. The peak speed was commanded to be maintained for 2 seconds, but the actual peak speed was not maintained and immediately begins to decrease after t = 8 seconds. At t = 9 and t = 10 seconds, the actual speed of the vehicle dropped to 2.5 m/s and 2.2 m/s respectively. 

For the selected PID vales, there is a slightly quicker response time. However, compared to the default PID values, the peak speed of the vehicle was 0.5 m/s lesser in this attempt. Once again, there was no overshoot and the steady state error was minimal.

Second Modification

For the same simulation time, the following PID values were used:

• `K_i = 550`
• `K_p = 800`
•  `K_d = 0`

For these parameters, the following speed-plot was obtained:

                                  

As we can see, for this attempt, the proportional constant was decreased and the integral constant was increased. The derivative constant was left as 0 as there is no overshoot in the results. From the speed-time plot, we can see that the response time of the vehicle is unchanged. Once again, the vehicle only begins its acceleration at t = 3.4 seconds just like the previous attempts. The vehicle acceleration behavior is also unchanged in that the vehicle reaches the same speeds at the same time periods as before. The vehicle reaches 0.8 m/s by t = 5 seconds and has a linear acceleration before reaching its peak speed of 3 m/s at t = 8.8 seconds. This peak speed is only maintained for 0.3 seconds before the vehicle begins its deceleration.

For these PID values, the results in the plot were shifted upwards causing the peak speed to be higher than the previous attempt. However, despite having a higher peak speed in this attempt, the peak speed was achieved quicker in the previous attempt by almost 1 second. Once again, there was no overshoot and the steady state error was minimal.

Third Modification

For the same simulation time, the following PID vales were used:

• `K_i = 550`
• `K_p = 800`
• `K_d = 0`

For these PID values, the following speed-time plot was obtained:

                                           

From the speed-time plot shown above, we can see that the vehicle's starting acceleration time is unchanged starting at t = 3.4 seconds once again. The vehicle reaches a speed of 0.2 m/s by t = 4 seconds and the acceleration continues in the same linear behaviour as seen in the previous attempts. While the drive cycle reference begins its deceleration back to rest at t = 5 seconds, the actual speed of the vehicle is still in its acceleration phase. The vehicle continues to accelerate and reaches a peak speed of 3.3 m/s at t = 9.2 seconds. Immediately after, the vehicle begins its deceleration phase and decelerates to 3.2 m/s at t = 10 seconds. 

In this attempt, the overall speed behavior of the vehicle is unchanged. However, the peak speed was the highest compared to all other simulation attempts. There is still a delayed response time in the acceleration of the vehicle and the vehicle fails to achieve the commanded peak speed of 5 m/s. The vehicle also fails to maintain the actual peak speed for the commanded 2 seconds of time.

Conclusion

The Matlab model of an Electric Vehicle has been successfully made by choosing Suitable blocks from powertrain block set. We understand how to make the model of Electric Vehicle by using powertrain blockset. 

•  The designed Electric Vehicle model for a suitable FTP75 drive cycle travels for a distance of 17.82Km for the simulation time of 2474 secs.
•  The designed Electric Vehicle has a SOC of about 72% after a successful run of 17.82Km.