Week-11 Challenge: Braking

1. For a defined driving cycle, calculate the energy required for braking.

Drive cycle is a test cycle for a vehicle with various input conditions. This drive cycle test the emission, fuel efficiency, battery power efficiency, range of EV vehicle with various input throttle and various hill climbing angles.

The driving cycle taken into consideration is FTP_Drive_cycle. Which stands for US EPA Federal Test Procedure. This drive cycle total driving time is 2477 sec for simplicity total driving time taken in this example is 130 sec. in this driving time speed is in mile per hour. This converted into meter per second.

The equation for Braking power is,

Mt = Total weight of vehicle

V = Vehicle speed in m/s

t = Deceleration time

From the drive cycle 10 breaking point were obtained. The total weight of vehicle is 1400 kg.

The energy required for braking data is given below,

Therefore, the total energy required for braking is 13.22 KW.

The Excel sheet file of the drive cycle and braking data is provided below.

https://docs.google.com/spreadsheets/d/16_QzsBkcNost_BTaPAQwgRg0aLJAHPPh/edit?usp=sharing&ouid=108387349640963561095&rtpof=true&sd=true

2. Why electric motor can’t develop braking torque at high speed similar to starting? How electric and mechanical brakes are coordinated?

Electric Motor Braking:

• The electric motor braking is also known as Regenerative Braking, which is an energy recovery mechanism that slows down a moving vehicle or object by converting its kinetic energy into a form that can be either used immediately or stored until needed.
• When we press the brake pedal, we cut off the power supply to the motor and now the motor will be in rotation due to its inertia.
• As this rotation is happening inside the magnetic field a Back Emf is generated which produces a negative Torque and that is used as the brakes to reduce the vehicle speed. Also, the current flows in reverse direction, using a Bi-directional Inverter we can store the current back into the battery.
• This process of Braking by the effect of negative Torque produced and where the motor acts as a generator in producing the current out of the motor's rotation and storing it back into the battery is called Regenerative braking.

From the above figure we can see the speed and torque behavior of an electric motor.

• During the initial low speed, the Torque is high which is the constant Torque region. As speed builds up, after the Critical speed point the torque gradually decreases which is known as constant Power region.
• So, during high speeds the motor will be at constant power region and while braking, due to high speed of the motor the negative Torque produced will be less. But while starting the motor, the speed will be very less and at this stage the motor will be operating in constant Torque region and this is the reason for High accelerating torque during the start of motor.
• From this we can say that the Braking torque produced at High-speed motor operations will be lesser than the starting Torque of an Electric motor. Also, there are other reasons like Battery Limitations due to which we cannot get High braking torque.
• The rate of discharge is always higher than the rate of charging due to the battery's chemical compositions.

Co-ordination of Electric and Mechanical brakes:

• Motor of electric vehicle is able to be used to brake regeneratively, so braking energy can be recycled. Braking stability of electric vehicles with electro-hydraulic hybrid braking system can be influenced by braking force distribution between hydraulic braking force and regenerative braking force. Electric cars have regenerative braking and this does substantially reduce the need for hydraulic braking.
• But there are some limitations like, the maximum deceleration with the engine alone is far smaller than with brake assistance. So, you still need an ordinary Frictional brake system to make the car stop instantly if required.
• When the regenerative capacity is less than the actual braking required, mechanical brakes are applied at those times.

• When the brake pedal is pressed the control signal is sent to both the Hydraulic cylinder and power converters for producing both Frictional Braking and Regenerative braking.
• There are two ways of applying the combination of brakes and they are classified as,
  • Series - The Regenerative braking and Frictional braking are applied one after another.
  • Parallel - The Regenerative braking and Frictional braking are applied at the same time
• The series braking and parallel braking is chosen based on two parameters, one is Driver's comfort and other one is based on the Efficiency.
• This parallel combined braking Technology is further developed as EDIB, which is Electric Driven Intelligent Braking.

• The above figure shows the Electric driven intelligent braking system, where we see that both the Regenerative Brakes and the Frictional brakes are applied at the same time.
• After breaking the speed reduces from higher speed values and at this moment the percentage of composition of the combined braking changes. after brake the speed is reduced to low speeds. Here Torque will be high and the motor will be operating at constant Torque region.
• Now at this point the percentage of Frictional brake application is reduced and Regenerative Braking is Increased because at this point more Negative Torque can be generated and thus higher electric power generated out of this braking can also be feedback to the battery.
• Thus, using this technology in Breaking an electric driven vehicle certainly increases the stopping power and contribute to higher efficiency figures.

3. Make a MATLAB program which plots contour of given motor speed, torque and efficiency values. Attach the code as a .m file attach a screenshot of all the plots.

A contour plot is a plot which represents heights in Two-dimensions figure.

A MATLAB program is done to plot the contour of the Electric DC Motor's efficiency at given speed and torque ranges of the motor. The losses that happen is taken into consideration while calculating the efficiency and they are,

• Copper Loss
• Iron Loss
• Windage Loss
• Constant motor Loss

• Copper Loss:

Copper loss is given by - ((I)^2 * R), where I - Current; R – Resistance

As the Torque is proportional to the current,

((I)^2 * R) = KC * (T)^2

where Kc - Copper loss constant that takes care of the Resistance in Brushes and Magnetic Flux Effects.

• Iron Loss:

Iron Losses are simply due to the Magnetic Losses that is given by

Iron Loss - (Ki * w)

were, Ki - Iron loss constant; w - speed of the motor.

Ki depends on the effect of magnetic field. The Magnetic field changes with change in the speed values and at various speeds the Back Emf changes accordingly.

• Windage Loss:

The Windage loss is based on the Size & Shape of the motor and the amount of windage that the motor experiences and is given by,

Windage Loss - (Kw * (w)^3)

were, Kw - Windage loss constant; w - speed of the motor.

• Constant motor Loss:

In all the motor there are some constant losses happening and is given as C.

The Total Loss = copper Loss + Iron Loss + Windage Loss + Constant Motor Loss.

Output Power = Input Power - The Total Losses.

Finally, the Efficiency of the DC Motor is given by,

Efficiency = Output Power / Input Power.

MATLAB Program for plots contour of given motor speed, torque and efficiency values.

clear all

close all

clc

%Definig the speed and Torque range of the Motor as arrays

speed = linspace (0,1000);

torque = linspace (0,250);

%Motor loss constant

Kc = 0.2; %copper loss constant

Ki = 0.008; %Iron loss constant

Kw = 0.00001; %windage loss constant

C = 20; %constant motor loss

%creating 2-D Array for speed and toque

[W,T] = meshgrid(speed,torque);

output_power = (W.*T);

%calculation of losses

copper_loss = Kc*(T.^2);

iron_losses = (W).*Ki;

windage_losses = (W.^3)*Kw;

%calculation of power and efficiency

input_power = output_power + copper_loss + iron_losses + windage_losses + C;

efficiency = output_power./input_power;

%mapping the contourz of the efficiency

V = [0.70,0.75,0.80,0.85,0.90,0.91,0.92,0.93];

%plotting the Contour for speed, torque and efficiency

box off

grid off

contourf(W,T,efficiency,V);

colorbar

xlabel('Motor speed (RPM)');

ylabel('Torque (Nm)');

zlabel('Efficiency');

title('Contour of given motor speed, torque and efficiency');

The above figure shows the contour plot and the X axis is speed in RPM, Y axis is Torque in Nm and the height (i.e.) Z axis is Efficiency.

The color bar is used to know the efficiency based on the color of shading in the plot ranging from 0.75 to 0.93. The contour plot represents the operational condition of the Permanent Magnet DC Motor.

The efficiency of the Motor is High at Lower values of speed & Torque at 0.93. As Speed and Torque Increases the efficiency of the motor goes down up to 0.75 value of efficiency. Thus, the contour plot is made using a MATLAB program for an electric motor with given speed, Torque and efficiency values.