Week-11 Challenge: Braking

Study of Induction Motor Braking and its Efficiency

Aim:

* To calculate the total energy required for Braking in a Drive cycle.

* To study the characteristics of electric motor braking.

* To plot the contour of given motor speed, torque and efficiency values.

QUESTIONS:

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

Drive cycle:

* Drive cycle is a test cycle for a vehicle with various input conditions which will be done for all the newly produced and about to lauch vehicles.

* This Drive cycle is done to Test the Emmision , fuel efficiency , with various input of throttle and various hill climbing angles in case of an IC engine

* In case of an Electric vehicle the test is done with various input of throttle and various hill climbing angles to analyze Power efficiency , Range of the vehicle and the State of charge that is left after running the test in the battery.

* There are many defined Drive cycles and in this part we have taken the " The Highway Fuel Economy Driving Schedule (HWFET) " as our reference Drive cycle.

* Using this drive cycle we are intrested in calculating the braking energy required to complete one cycle

Link To Open Drive Cycle Excel Data:

https://drive.google.com/file/d/1C4Mbcm_PVhW6EuWTXPUe7QXxTSBK5QyB/view?usp=sharinghttps://drive.google.com/file/d/1C4Mbcm_PVhW6EuWTXPUe7QXxTSBK5QyB/view?usp=sharing

Braking Energy:

* To accelerate a vehicle we need some Energy to accelerate, like the same to brake the vehicle we need some energy to brake.

* In acceleration the velocity changes from initial to final velocity value. While Braking the velocity changes from Final value to initial value or 0.

* So, in this case of Braking, the Kinetic Energy is given by,

Braking Energy = 1/2 * M * (Vf - Vi)^2

where M - Mass of the vehicle ; Vi - Initial velocity ; Vf - Final velocity

* To calculate the Braking energy required in a defined driving cycle, we are using this formula in the above mentioned HWFET Drive cycle.

* The mass of the vehicle is assumed to be 1000 kg and the Total time period of this HWFET Drive cycle is 766 Seconds.

* From the drive cycle data file, wherever the Deceleration occurs we can say that the Braking occurs and in those parts.

* We are using the above formula to find the baraking energy in those parts and adding all the deceleration part throughout the drive cycle, we can get the Total Braking Enrgy required for one cycle.

* A MATLAB program is used to calculate the Braking Energy required for the HWFET Drive cycle.

Matlab codes to calculate Braking energy:

clear all
close all
clc
% Mass of the vehicle
M = 1000;
% Total Time period of the cycle
T = 766;
% Drive cycle data
A = readmatrix('highway drive cycle.xlsx');
% Time of Drive cycle in seconds
time = A(:,1);
% velocity in mph
velocity = A(:,2);
% converting velocity from mph to m/s 
v = velocity.*0.4470;
% Creating same length vectors for values storage and plotting
deceleration = zeros(1,T);
Braking_energy = zeros(1,T);
for i = 1:(length(v) - 1)
    if v(i) > v(i+1)
        decreased_velocity(i) = v(i+1) - v(i);
        difference_in_time(i) = time(i+1) - time(i);
        deceleration(i) = decreased_velocity(i) / difference_in_time(i);
        Braking_energy(i) = 0.5*M*((v(i))^2 - (v(i+1))^2) / 3600;
        
    end
end

% Plotting the Drive cycle and the the Braking energy
figure
subplot(3,1,1)
plot(time,velocity,'linewidth',2)
xlabel('Time period of the cycle (Sec)');
ylabel('Velocity (Miles per Hour)');
title('The Highway Fuel Economy Drive cycle(HWFET)');

subplot(3,1,2)
plot(time,deceleration,'linewidth',2,'color','r')
xlabel('Time period of the cycle (Sec)');
ylabel('Deceleration (m/s^2)');
title('Deceleration in the Drive cycle');

subplot(3,1,3)
plot(time,Braking_energy,'linewidth',2,'color','b')
xlabel('Time period of the cycle (Sec)');
ylabel('Braking energy (w.h)');
title('The Braking energy required throughout the Drive cycle');

fprintf('The Total Braking Energy Required For HWFET Drive cycle is %3f W.h',sum(Braking_energy))

* The above program calculates the energy required for braking.

* The mass of the vehicle is given as a input and the excel file containing the HWFET Drive cycle data is read into the program.

* From the drive cycle data file the velocity and time values are extracted to a array.

* Using a For Loop the part where deceleration occurs in the entire cycle is found and in those parts the Braking energy formula is applied.

* Then all the braking energy values found is added to get the Total Braing Energy required for one cycle of HWFET Drive cycle.

* Finally the plotting is done for input drive cycle data with deceleration and Braking energy requiered.

Result:

* The Result plot can be used to visualize the above codes, the 1st subplot is made to plot the Drive cycle curve with Time vs Speed.

* The 2nd subplot shows the Deceleration parts with respect to the Time values.

* The 3rd subplot shows the Instantaneous Braking energy which is requierd at that particular Time period.

* The Total braking energy required for one cycle of HWFET Drive cycle is 323.5 Watt.Hour.

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.

Speed and Torque Characteristics of a DC Motor:

* From the above figure we can see the speed and torque behaviour of a 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.

Combination 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

* Yes 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 regenative capacity is less than the actual braking required, mechanical brakes are applied at those times.

Brake control Strategy:

* 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,

1. Series - The Regenerative braking and Frictional braking are applied one after another.

2. 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.

EDIB Braking Technology

* 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 braking the speed reduces from higher speed values and at this moment the % of composition of the combined braking changes.

* So after brake application 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 % of Frictional brake application is reduced and Regenative 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 fed back to the battery.

* Thus using this technology in Braking an electric driven vehicle certainly increases the stopping power and also contributes 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.

Contour plot:

* 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 happens is taken into consideration while calculating the efficiency and they are,

1. Copper Loss

2. Iron Loss

3. Windage Loss

4. Contant motor Loss

1. 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.

2. Iron Loss:

* Iron Losses are simply due to the Magnetic Losses that is happening, and is given by

Iron Loss - (Ki * w) where, 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.

3. 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) where, Kw - Windage loss constant ; w - speed of the motor.

4. Contant 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 to plot the contour of Motors speed , torque , efficiency values.

clear all
close all
clc

% The Torque and Velocity Range of the motor
Torque = linspace(0,250);
Velocity = linspace(0,1000);

% copper Loss constant
kc = 0.2;
% Iron loss constant
ki = 0.008;
% windage loss constant
kw = 0.00001;
% constant motor loss
c = 20;

% Creating 2D Array for torque & velocity
[W,T] = meshgrid(Velocity,Torque);
output_power = (W.*T);

% Loss calculations
copper_losses = kc*(T.^2);
Iron_losses = (W).*ki;
Windage_losses = (W.^3)*kw;

% Power and Efficiency calculations
Input_power = output_power + copper_losses + Iron_losses + Windage_losses + c;
Efficiency = output_power./Input_power

% Efficieny curves values range
V = [0.70,0.75,0.80,0.85,0.875,0.90,0.91,0.92,0.93]

% 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 program plots the contour for a Given speed, torque and efficiency values of a DC motor.

Result:

* 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 upto 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.