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

• Predict the engine torque and fuel consumption that a vehicle requires to achieve desired speed and acceleration for a given gear shift reference.

• Produce realistic velocity and shift references for closed loop acceleration and braking commands for vehicle control and plant models.

• Study, tune, and optimize vehicle control, system performance, and system robustness over multiple drive cycles.

• Drive cycles from predefined sources. By default, the block includes the FTP-75 drive cycle. 

• .mat, .xls, .xlsx, or .txt files can also be implemented through the block.

For the Drive Cycle the following modes are choosen as shown below:

ii) Multi-port Switch:

This block is used to determine which of several inputs to the block passes to the output. The block bases this decision on the value of the first input. The first input is the control input and the remaining inputs are the data inputs. The value of the control input determines which data input passes to the output.

In this porject as there are 4 types of velocity reference used so that's why 4 data ports are required as shown below:

2. PID Controller Subsystem:

Proportional-Integral-Derivative (PID) control is the most common control algorithm used in industry and has been universally accepted in industrial control. The popularity of PID controllers can be attributed partly to their robust performance in a wide range of operating conditions and partly to their functional simplicity, which allows engineers to operate them in a simple, straightforward manner. The basic idea behind a PID controller is to read a sensor, then compute the desired actuator output by calculating proportional, integral, and derivative responses and summing those three components to compute the output. 

                             Block Diagram of a PID Controller

The three major response of the PID Controller are discussed below:

• Proportional Response: The proportional component depends only on the difference between the set point and the process variable. This difference is referred to as the Error term. The proportional gain (K_c) determines the ratio of output response to the error signal. For instance, if the error term has a magnitude of 10, a proportional gain of 5 would produce a proportional response of 50. In general, increasing the proportional gain will increase the speed of the control system response. However, if the proportional gain is too large, the process variable will begin to oscillate. If K_c is increased further, the oscillations will become larger and the system will become unstable and may even oscillate out of control.
• Integral Response: The integral component sums the error term over time. The result is that even a small error term will cause the integral component to increase slowly. The integral response will continually increase over time unless the error is zero, so the effect is to drive the Steady-State error to zero. Steady-State error is the final difference between the process variable and set point. A phenomenon called integral windup results when integral action saturates a controller without the controller driving the error signal toward zero.
• Derivative Response: The derivative component causes the output to decrease if the process variable is increasing rapidly. The derivative response is proportional to the rate of change of the process variable. Increasing the derivative time (T_d) parameter will cause the control system to react more strongly to changes in the error term and will increase the speed of the overall control system response. Most practical control systems use very small derivative time (T_d), because the Derivative Response is highly sensitive to noise in the process variable signal. If the sensor feedback signal is noisy or if the control loop rate is too slow, the derivative response can make the control system unstable.

The Corresponding MATLAB Model of the PID Controller is shown below:

The MATLAB PID Controller block performs the same function described above; the values of the PID gain is implemented after linearizing the plant with a step response output and correspondingly track the error input to the PID block, the valus of the PID gains are hown below:

i) Saturation Block:

The Saturation block produces an output signal that is the value of the input signal bounded to the upper and lower saturation values. The upper and lower limits are specified by the parameters Upper Limit and Lower Limit in the Command Block.

3. Motor and Its Controller Subsystem:

A Motor and its Controller are a device or group of devices that can coordinate in a predetermined manner the performance of an Electric Motor. A motor controller might include a manual or automatic means for starting and stopping the motor, selecting forward or reverse rotation, selecting and regulating the speed, regulating or limiting the torque, and protecting against overloads and electric faults. Motor controllers may use electromechanical switching, or may use power electronics devices to regulate the speed and direction of a motor.

This subsystem consists of blocks which are configured as follows:

i) Controlled PWM Voltage:

This block is responsible for the creation of the Pulse Width Modulated(PWM) signal across the PWM and REF ports. The output voltage is zero when the pulse is low, and is equal to the Output voltage amplitude parameter when high. At time zero, the pulse is initialized as high unless the duty cycle is set to zero or the Pulse delay time is greater than zero. 

For the Electrical Input ports variant of the block, the demanded duty cycle is:

In this project, the Simulation Mode is choosen as Averaged where the ouput signal will be constant with value equal to the averaged PWM signal. The PWM frequency is choosen as 6kHz with an output voltage amplitude of 300V respectively, as shown in the below figure:

ii) H-Bridge:

H Bridge is a simple electronic circuit which enables us to apply voltage to load in either direction. It is commonly used in robotics application to control DC Motors. By using H Bridge we can run DC Motor in clockwise or anticlockwise directions.  This circuit is also used to produce alternating waveforms in inverters.

In MATLAB, the H-Bridge block performs the same function highlighted above which is ultimately driven by the Contolled PWM Voltage Block in Averaged Mode as per the project requirement. In Averaged mode, the PWM port voltage divided by the PWM signal amplitude parameter defines the ratio of the on-time to the PWM period. Using this ratio and assumptions about the load, the block applies an average voltage to the load that achieves the correct average load current. The Simulation mode parameter value must be the same for the Controlled PWM Voltage and H-Bridge blocks. If the REV port voltage is greater than the Reverse threshold voltage, then the output voltage polarity is reversed. If the BRK port voltage is greater than the Braking threshold voltage, then the output terminals are short circuited via one bridge arm in series with the parallel combination of a second bridge arm and a freewheeling diode.

For Averaged Simulation Mode, the load current characteristics is set to Smoothed rather than Discontinuous. As per the requirement, the thermal port of the H-Bridge is also enabled so as to monitor the temperature variation of the converter w.r.to the vehicle velocity output.

The choice of the corresponding value of the H-Bridge parameters along with the Simualtion Mode is shown in the figure below:

iii) DC Motor(Permanent Magne Type):

This block constitute the the electrical and torque characteristics of a DC motor. The assumption of this block is that there is no electromagnetic energy is lost, and hence the back-emf and torque constants have the same numerical value when in SI units. Motor parameters can either be specified directly, or derived from no-load speed and stall torque. When a positive current flows from the electrical + to - ports, a positive torque acts from the mechanical C to R ports. Motor torque direction can be changed by altering the sign of the back-emf or torque constants.

The type of Motor choosen is the Permanent Magnet Type so that it resemblance the BLDC type of Motor which is most commonly used in the Electric Vehicle. In this project, the Thermal Port of the DC Motor block is used to simulate the effects of copper resistance losses that convert electrical power to heat. 

Here the 'C' port represents the casing of the Motor which needs to be grounded using the Mechanical Rotational Reference Frame whereas the 'R' port consitutes the Rotor of the Motor which is connected to the Gear system of the vehicle dynamics. The value of the parameters considered for DC Motor block is shown in figure below:

iv) Controlled Voltage Source:

The block represents an ideal voltage source that is powerful enough to maintain the specified voltage at its output regardless of the current passing through it. The output voltage is V = Vs, where Vs is the numerical value presented at the physical signal port.

Two quantities of the volatage source block is required; one one is required for to drive the Controlled PWM Volatge source and another is required to drive the Braking command of the H-Bridge. The respective volatge of this block is controlled as per the acceleration command(to control the PWM voltage source) and the De-acceleration command(to control the Braking voltage of the H-Bridge) of the Longitudinal Driver.

v) Current Sensor:

The block represents an ideal current sensor, that is, a device that converts current measured in any electrical branch into a physical signal proportional to the current. Connections '+ ve' and '- ve' are conserving electrical ports through which the sensor is inserted into the circuit. Connection 'I' is a physical signal port that outputs current value.

The positive and the negative part of the block is connected betwee the H-Bridge and the DC Motor whereas the physical port 'I' is connected to the Controlled Current Source of the Battery MAnagement system of the E-Rickhaw Model.

vi) Temperature Sensor:

This block measures temperature in a thermal network. There is no heat flow through the sensor. The physical signal port T reports the temperature difference across the sensor. The measurement is positive when the temperature at port A is greater than the temperature at port B.

Here ther are two temperature sensors used; one is for the measurement of the temperature in the H-Bridge while the other for the DC-Motor. The output of the Sensor is taken from the physical port 'T'  which is connected to the Scope in order to analyse the temperature profile of both the Motor and its Converter Block.

4. Vehicle Dynamic Subsystem:

The goals of vehicle dynamics are twofold: First, they make vehicles safer by intervening to provide support in problematic driving situations. Second, vehicle dynamics control systems can be adjusted to implement the individual DNA of an OEM.  Because vehicle dynamics control systems influence vehicle movement, several of the systems have an important role to play in achieving the goal of autonomous driving. For example, the ESC deploys the braking action in autonomous vehicles. Vehicle dynamics are undergoing continuous development to further improve vehicle safety and comfort. As a result, ESC now encompasses a variety of additional support functions, significantly increasing the effort needed for validation during development.

This subsystem consists of blocks which are configured as follows:

i) Vehicle Body:

This block represents a two-axle vehicle body in longitudinal motion. The block accounts for body mass, aerodynamic drag, road incline, and weight distribution between axles due to acceleration and road profile. This block gives the option of having the same or a different number of wheels on each axle with Optional inclusion of pitch and suspension dynamics or additional variable mass and inertia. The vehicle body block does not move vertically relative to the ground.

This block consists of an all total of 6 connection port; out of which 'H' is the Mechanical Translational Conserving port associated with the horizontal motion of the vehicle body and its connected to the 'H' port of the wheel hub of the tire through which the resulting traction motion of the tires will get generated. 'V' is the physical output port which is used to examine and monitor the vehicle velocity curve, 'NF' and 'NR' are also physical output ports but they represent fron and rear normal wheel forces and due to this reason they are connected to the 'N' of the tires through the forces will get act on the wheel for rotation, 'W' and 'beta' are physical signal input ports corresponding to headwind speed and road inclination angle.

The value of the parameters given to the vehicle body is shown below:

ii) Tire(Magic Formula):

The Tire (Magic Formula) block models a tire with longitudinal behavior given by the Magic Formula [1], an empirical equation based on four fitting coefficients. The block can model tire dynamics under constant or variable pavement conditions. The longitudinal direction of the tire is the same as its direction of motion as it rolls on pavement and to increase the fidelity of the tire model, the properties can be specified such as tire compliance, inertia, and rolling resistance. However, these properties increase the complexity of the tire model and can slow down simulation. Consider ignoring tire compliance and inertia if simulating the model in real time or if preparing the model for hardware-in-the-loop (HIL) simulation.

Same as vehicle body, this block aslo consists of 4 connection port; out of which 'A' is the mechanical rotational conserving port for the wheel axle and it is connected to the Gear arrangement of the vehicle. 'H' is the mechanical translational conserving port for the wheel hub through which the thrust is developed by the tires of the vehicle and it is connected to the 'H' port of the vehicle body for initiation of the horizontal motion. 'N' is the physical signal input port that applies the normal force acting on the tire and it is connected to the 'NR' and 'NF' of the vehicle body.

The values of the parameters assigned to the tires are shown below:

iii) Simple Gear:

This block represents a fixed-ratio gear or gear box. No inertia or compliance is modeled in this block. You can optionally include gear meshing and viscous bearing losses. 

Connections B (base) and F (follower) are mechanical rotational conserving ports which are connected to the Shaft Input of the DC Motor and the 'A' port of the wheel and axle respectively. The relation between base and follower rotation directions with the Output shaft rotates parameter.

The value choosen for the parameters of the Simple Gear is shown below:

iv) Inertia:

The block represents an ideal mechanical rotational inertia. The block positive direction is from its port to the reference point which means that the inertia torque is positive if the inertia is accelerated in the positive direction.

The value of the Inertia is choosen to be 4kg*m2. 

5. Battery Management Subsystem:

The BMS will also control the recharging of the battery by redirecting the recovered energy (i.e.- from Regenerative Braking) back into the battery pack (typically composed of a number of battery modules, each composed of a number of cells). Battery thermal management systems can be either passive or active, and the cooling medium can either be air, liquid, or some form of phase change. Air cooling is advantageous in its simplicity. Such systems can be passive, relying only on the convection of the surrounding air, or active, utilizing fans for airflow. Commercially, the Honda Insight and Toyota Prius both utilize active air cooling of their battery systems. 

The major disadvantage of air cooling is its inefficiency. Large amounts of power must be used to operate the cooling mechanism, far more than active liquid cooling. The additional components of the cooling mechanism also add weight to the BMS, reducing the efficiency of batteries used for transportation. Liquid cooling has a higher natural cooling potential than air cooling as liquid coolants tend to have higher thermal conductivities than air. The batteries can either be directly submerged in the coolant or coolant can flow through the BMS without directly contacting the battery. Indirect cooling has the potential to create large thermal gradients across the BMS due to the increased length of the cooling channels. This can be reduced by pumping the coolant faster through the system, creating a tradeoff between pumping speed and thermal consistency.

The configuration of the Subsystem is shown below:

i) Battery:

This block implements a generic dynamic model that represents most popular types of rechargeable batteries with the following assumptions:

• The internal resistance is assumed to be constant during the charge and discharge cycles and does not vary with the amplitude of the current.

• The parameters of the model are derived from the discharge characteristics. The discharging and charging characteristics are assumed to be the same.

• The capacity of the battery does not change with the amplitude of the current (there is no Peukert effect).

• The self-discharge of the battery is not represented. It can be represented by adding a large resistance in parallel with the battery terminals.

The equivalent circuit of the Battery Block is shown below:

When the battery gets charge then there is a exponential voltage drop, and the width of the drop is depends upon the Battery Type. Since the battery is rechargable so a considerable amount of charge can be extracted from the battery until the voltage drops below the battery nominal voltage. 

As per the project requirement, the Nominal Voltage of the Battery is set as 300V with initial SOC of 100%.

The positive terminal of the battery is connected to the Controlled Current Source Block where the current is controlled as per the voltage of the DC-motor.  

The value of the parameters set for the Battery is given as a figure below:

ii) Controlled Current Source:

This block is responsible converting the Simulink input signal into an equivalent current source. The generated current is driven by the input signal of the block. The block is initialized as a AC current source type and the simulation is started in the steady state condition, so therefore the block input must be connected to a signal starting as a sinusoidal or DC waveform corresponding to the initial values.

The positive and the negative terminals of the block is connected across the Battery and the physical port 'S' is connected to the physical output port 'I' of the Current Sensor of the DC Motor Subsystem. It is arranged in a fashion that the current drawn by the DC Motor is coming form the Generic Battery.

6. SOC Estimation Subsystem:

The following subsystem is configured as shown below:

i) Rate Transition:

The Rate Transition block transfers data from the output of a block operating at one rate to the input of a block operating at a different rate. Use the block parameters to trade data integrity and deterministic transfer for faster response or lower memory requirements. The behaviour of the Rate Transition block depends on the following criteria:

• Sample times of the ports to which the block connects.
• Priorities of the tasks for the source and destination sample times.
• Whether the model specifies a fixed- or variable-step solver.
• Setting of model configuration parameters.

As per the project requirement, the Initial Conditions of the output is kept at zero and the output port sample time is specified with a magnitude of -1. 

ii) Discrete Time Integrator:

This block is used to create a purely discrete model. This block helps to define the following scenario:

• initial conditions on the block dialog box or as input to the block
• an input gain (K) value
• output the block state
• upper and lower limits on the integral

According to the project, the Inetgrator method is choosen as Forward Euler Method with a gain value of 1.0 with no initial conditions and with a sample time of -1.

The parameters of the block so choosen are shown below:

iii) Gain:

The Gain block multiplies the input by a constant value (gain) and the input and the gain can each be a scalar, vector, or matrix. The value of the gain is specified in the gain parameter section of the block. The Mutiplication parameter lets the user to specify element-wise or matrix multiplication. For matrix multiplication, this parameter also allows to indicate the order of the multiplicands. 

The Gain value is shown in the figure below:

7. Distance Calculation Subsystem:

The configuration of the subsystem is shown below:

i) Zero-Order Hold:

This block is used to hold the magnitude of the input for the sample period specified by the user. If the input is a vector, the block holds all elements of the vector for the same sample period. the user have to specify the sample time parameter which is by default set to -1. The Zero-Order Hold block is a bus-capable block. The input can be a virtual or nonvirtual bus signal. No block-specific restrictions exist. All signals in a nonvirtual bus input to a Zero-Order Hold block must have the same sample time, even if the elements of the associated bus object specify inherited sample times.

ii) Integrator:

This block produces the output of the integral of its input signal with respect to time. The selected solver computes the output of the Integrator block at the current time step, using the current input value and the value of the state at the previous time step. To support this computational model, the Integrator block saves its output at the current time step for use by the solver to compute its output at the next time step. The block also provides the solver with an initial condition for use in computing the block's initial state at the beginning of a simulation. The default value of the initial condition is 0. Use the block parameter dialog box to specify another value for the initial condition or create an initial value input port on the block.

8. Energy Calculation Subsystem:

The subsystem configuration is shown below:

In this subsystem the amount of energy calculated is constantly examined. The energy is derived from the following forces:

• Rolling Resistance Force(Frr): This force is responsible resisting the motion of a body rolling on a surface. In the broad sense, specific "rolling resistance" (for vehicles) is the force per unit vehicle weight required to move the vehicle on level ground at a constant slow speed where aerodynamic drag (air resistance) is insignificant and also where there are no traction (motor) forces or brakes applied. In other words, the vehicle would be coasting if it were not for the force to maintain constant speed.

        The governing equation for the rolling resistance force is given by:

         Frr = `muunderset(rr)`*, Current m * g;

         where; `muunderset(rr)` is the Rolling Resistance Co-efficient(Dimensionless)

                     'm' is the Mass of the vehicle

                     'g' is the acceleration due to gravity.

         As per the project requirement; `muunderset(rr)`is taken as 0.015, Mass of the vehicle is taken as 1500kg and acceleration due to gravity is 9.81 m/sec2.

• Aerodynamic Drag Force(Fad): This force is offered by the resistance of the incoming air to the movement of the body. Its main goals are reducing drag and wind noise, minimizing noise emission, and preventing undesired lift forces and other causes of aerodynamic instability at high speeds. 

        The governing equation of the Aerodynamic Drag force is given by:

        Fad = 0.5* `rho` * `Cunderset(d)` * `v^2` * A;

        where; `rho` is the Air Density.

        `Cunderset(d)` is the drag coefficient 

         'v' is the velocity of the vehicle

         'A' is the frontal area of the vehicle.

         According to the project; `rho` is taken as 1.18 kg/m3, `Cunderset(d)` is taken as 0.4, 'v' is the ultimate vehicle velocity which is coming as an output and 'A' is the taken as 3m2.

In this project, it is assumed that the vehicle is moving in the level ground and so that's why the gradient is taken as zero which ultimately makes the Hill Climbing Force equal to zero.

After calculating the forces, the respective power is then computed by multiplying the Force with respective velocity points of the vehicle which is coming out as an output from the Vehicle Dynamics subsystem. After that the Integration of this power w.r.to the Time will give the ultimate energy usage by the vehicle for a given driving cycle source.

The Energy calculation is very vital from the perspective of the size of the Vehicle Battery. The Dynamic Performance and the Charging Time of the battery can be optimise by knowing the average energy consumption and the range of the vehicle. 

RESULTS AND DISCUSSION:

As per the project requirement, the performance characteristics of the Electric Car Model is analysed w.r.to Three different Drive Cycle Source; the three drive cycles are FTP75, WOT and a custom drive cycle which is following a constant speed of 45kmph i.e 12 mpsec for a total distance of 100km. Corresponding to each cycle, all the performance parameters like vehicle velocity, SOC, Voltage and Current drawn by the Motor etc. are examined and a profile has been established in the following section.

Case 1: The Drive Cycle Source is FTP75:

The FTP-75 (Federal Test Procedure) has been used for emission certification and fuel economy testing of light-duty vehicles in the United States. The test is often referred to as simply ‘FTP’ (this should not be confused with the FTP test for heavy-duty engines). The "city" driving program of the EPA Federal Test Procedure is identical to the UDDS plus the first 505 seconds of an additional UDDS cycle.

The velocity profile of this Drive Cycle has the following charateristics:

• Distance travelled: 17.77 km (11.04 miles)
• Duration: 1874 seconds
• Average speed: 34.1 km/h (21.2 mph)

                                                                     A Typical FTP75 Drive Cycle.

Before going into the velocity comparison of the actual velocity w.r.to the reference velocity, it is very much important to understand the contribution of the PID controller in the plant response and due to this reason a Comparison is layed out in the form of Before Tunning and After Tunning of the PID controller in order to understand the role its play on the response of the system output.

BEFORE TUNNING:

For this Drive Cycle Source, the corresponding vehicle velocity in comparison with the reference velocity of the Drive Cycle is coming as follows:

                                                       Upper Part(Peak) of the Curve

                                                      Lower portion of the Curve.

Form the above two scenarios we can see that there is a considerable amount of deflection occuring in the velocity response if the PID controller is not tuned properly, this can become a dangerous scenario in real time situation where even a small protion of deviation of the actual velocity from the reference drive cycle can lead to accidental or hazardous situation. So, in order to eliminate this problem perfect tunning of PID controller is mandatory.

AFTER TUNNING:

After proper tunning of the PID controller, these errors will get reduced to large extent as shown below:

Thus, from the above figure it is quite clear that the error in the velocity output is get reduced to a great extent.

The corresponding temperature profile of both the PMDC Motor and its Converter, of the vehicle is shown below:

From the figure we can clearly see that; from the time the vehicle started following the reference velocity the temperature of the Motor and its converter started rising linearly because of the continuous operation of the Motor and its converter for supplying the torque in order to generate the vehicle velocity constantly upto a time of around 1400sec, after that the reference speed is becoming zero so thats why the Motor and the Converter temperature becomes constant for upto 2000 sec and then again the temperature starts to rise because of the variation in the reference speed profile. 

The SOC Estimation curve is coming as follows:

Here from the figure we can see that, the state of charge of the battery is decreasing whenever the vehicle accelerates and the peaks in the curve is due to the regenerative braking condition under which the battery is getting recharge due to the opposite power flow occuring because of the de-acceleration of the vehicle. From the curve it can be seen, that after the completion of the cycle the amount of charge left in the battery is 91.81% so approximately 9% of charge is depleted by the Battery for completing the above cycle.  

The Nature of the Current drawn by the Motor is coming as follows:

                                                                                                                               Current Curve of the PMDC Motor.

The above two curves can be justify from the fact that, when the vehicle is accelerating then the current is increasing from the initial value due to the increase in the threshold of the Motor operation. However, when the vehicle is de-accelerating then the Regenerative Braking condition of the Motor is satisfying and due to this the Current is moving to the negative axis because of the opposite direction of rotation of the Motor which clearly justifies the regenerative phenomena of the Motor when the vehicle is de-accelerating.  

The Distance Profile of the Vehicle is shown in the figure below:

This is the Distance Profile covered by the vehicle while following the reference velocity of the Drive Cycle Source. The Total Distance Covered by the vehicle in km after the end of the cycle is also measured using the 'Display Block' of the MATLAB as shown below:

The Energy Consumption profile of the vehicle is shown below:

This is the Energy Consumption Profile covered by the vehicle while following the reference velocity of the Drive Cycle Source. The Total Energy Consumed by the vehicle in kWhr after the end of the cycle is also measured using the 'Display Block' of the MATLAB as shown below:

Case 2: The Drive Cycle Source is WOT:

Under the Wide Open Throttle(WOT) condition; the engine speed shows a sudden increase due to the high engine torque production associated with the WOT conditions, and to the absence of a load connected to the engine. The acoustic emission of the engine contains information related to this speed increase and thus to the engine torque production. The methodology unveils the information contained in the engine acoustic emission to estimate the torque produced under WOT operating conditions. This estimation can be performed without the need of coupling the engine to a brake, and does not require installing any additional sensor.

                                                                                                           WOT Drive Cycle.

 For this Drive Cycle Source, the corresponding vehicle velocity in comparison with the reference velocity of the Drive Cycle is coming as follows:

From the above graph it is seen that, the sharp rise of the rerference velocity can't be achievable due to internal circuit constraints of the vehicle and that is why it is increasing linearly from 10 sec and takes another 15 sec to completely reach the desirable speed value. Again during de-acceleration, the vehicle speed takes around another 15sec to comes back to zero position from the maximum value due to the vehicle inertia. 

The corresponding temperature profile of both the PMDC Motor and its Converter, of the vehicle is shown below:

From the nature of the curve we can clearly understand that, during acceleration of the vehicle the corresponding temperature of both the Motor and the Converter gets increased from 298.15 degK to around 301 degK(for Converter) and 288.05 degK to 299 degK(for the Motor) beacuse of the rise in torque demand from the Motor. Again during the constant maximum speed driving, the temperature of both the Motor and its converter gets increases slighlty around 0.4degK which is basically due to the constant running operation of the Motor and the Converter. And also during de-acceleration of the vehicle the temperature rises sharply of the Motor and its Controller due to the Regenerative Braking Phenomena and ultimately settles at the maximum temperature. For the entire process of the cycle there is a temperature rise of 10-11degK for the Converter and a 20-22degK rise for the Motor respectively.

The SOC Estimation curve is coming as follows:

For the above curve it can be seen that, during the acceleration of the vehicle the charge of the Generic Battery depletes from 100% to 99.18% in a span of 53sec i.e from the moment of acceleration of the vehicle to the constant maximum speed drive for upto around 50sec, after that during de-acceleration as the Motor will rotate in the Reverse direction due to the Regenerative Braking so the power will flow into the Battery and that's why it recovers some charges and ultimately gets settles at 99.54%. As the duration of the WOT drive cycle is less comapred to other ones so thats why very less amount of charge gets depleted.

The Nature of the Current drawn by the Motor is coming as follows:

                                                                                                                          Current Curve of the PMDC Motor.

The above two curve correponds to the Voltage and the Current of the PMDC motor where the nature is coming exactly the same as discussed in the previous FTP75 drive cycle.

The Distance Profile of the Vehicle is shown in the figure below:

This is the Distance Profile covered by the vehicle while following the reference velocity of the Drive Cycle Source. The Total Distance Covered by the vehicle in km after the end of the cycle is also measured using the 'Display Block' of the MATLAB as shown below:

The Energy Consumption profile of the vehicle is shown below:

This is the Energy Consumption Profile covered by the vehicle while following the reference velocity of the Drive Cycle Source. The Total Energy Consumed by the vehicle in kWhr after the end of the cycle is also measured using the 'Display Block' of the MATLAB as shown below:

Case 3: Custom Drive Cycle of Constant Velocity of 45kmph for 100km:

Here a constant 45kmph i.e 12.5 mpsec of velocity is given to the system as reference for 8000sec in order to achieve the 100km Distance.

For this Drive Cycle Source, the corresponding vehicle velocity in comparison with the reference velocity of the Drive Cycle is coming as follows:

Here a constant speed profile is maintained by the vehicle velocity as per the reference velocity, after an initial spike which is due to the sudden jump in the vehicle speed from 0 to 12.5mpsec.

 The corresponding temperature profile of both the PMDC Motor and its Converter, of the vehicle is shown below:

As the velocity is maintained constant at 12.5mpsec for 8000sec in order to cover a total distance of 100km, so the temperature of the Motor and its Converter will also rise linearly beyond 370degK for the Motor and 317degK for its Converter. 

The SOC Estimation curve is coming as follows:

Here the SOC of the battery will decrease linearly to 66%, which is around 34% charge depletion from the Battery. 

The Nature of the Current drawn by the Motor is coming as follows:

                                                                                                                       Current Curve of the PMDC Motor.

It is quite evident from the two figure that as there is no Regenerative Braking happening so both the Motor Current and the Voltage are contant and in positive axis for the entire cycle.

The Distance Profile of the Vehicle is shown in the figure below:

 This is the Distance Profile covered by the vehicle while following the reference velocity of the Drive Cycle Source. The Total Distance Covered by the vehicle in km after the end of the cycle is also measured using the 'Display Block' of the MATLAB as shown below:

 Here the Distance is rising linearly upto 100km.

The Energy Consumption profile of the vehicle is shown below:

This is the Energy Consumption Profile covered by the vehicle while following the reference velocity of the Drive Cycle Source. The Total Energy Consumed by the vehicle in kWhr after the end of the cycle is also measured using the 'Display Block' of the MATLAB as shown below:

CONCLUSION:

So the performance charateristics of the MATLAB Electric Car Model is successfully implemented by taking various drive cycle source and examining the results thoroughly with detailed analysis and discussion. All necessary results for each drive cycle is represented along with detailed description of the Model blocks with parameters. 

REFERENCES:

1. https://www.mathworks.com/help/autoblks/ref/drivecyclesource.html

2. https://www.energy.gov/eere/electricvehicles/electric-vehicle-basics

3. https://en.wikipedia.org/wiki/Electric_vehicle

4. https://www.energy.gov/eere/electricvehicles/electric-vehicle-benefits

5. https://www.twi-global.com/technical-knowledge/faqs/what-is-an-ev

The Model is attached below:

https://drive.google.com/file/d/1XdCKHtozClkMiFe5lp9DdBoPd1Gc3L8H/view?usp=sharing