Week-11 Challenge: Braking
Objective -
- For a defined driving cycle, calculate the energy required for braking.
- Why electric motor can’t develop braking torque at high speed similar to starting? How electric and mechanical brakes are coordinated?
- 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.
Braking :
Braking is the process of controlling the velocity of an object by inhibiting its motion. An object in motion possesses kinetic energy and to bring the object to a stop this kinetic energy must be removed. Removing the kinetic energy can be accomplished by dissipating the energy to the atmosphere through friction or by converting it into another form of energy. The most common type of braking is a mechanical brake which inhibits motion through friction brake pads. A mechanical brake applies a friction force to convert the kinetic energy of the vehicle into thermal energy which then dissipates into the atmosphere. Braking systems which don't use friction are referred to as Regenerative Braking System (RBS). In RBS, the kinetic energy is converted into other forms of useful energy, which can be stored for later use, increasing fuel efficiency.
As with any system, the process of braking must follow the principal of conservation of energy. Energy cannot be created or destroyed but only converted from one form to another,
∑EIN=∑EOUT∑EIN=∑EOUT
The energy present in an object in motion is given by the following equation:
EKINETIC=mv22EKINETIC=mv22
where,
m- mass of the object in Kilogram(Kg),
v - velocity of the object in meters per second(m/s),
EKINETICEKINETIC - Kinetic energy in Joules(J)
From this above equation, and assuming the mass of the object is constant, it is clear the in order to remove the kinetic energy from the system, the velocity must be brought to zero.
Braking Energy Calculation :
For Calculating the Energy required for Braking, Drivecycle data is prepared in the Excel sheet, which Drive cycle data includes Time and Speed.
After Preparing Drivecycle data, Import the Drivecycle data in MATLAB file by using 'Import Data' option in MATLAB
After Importing the Drive Cycle Data, Create a Program to Calculate the energy required for Braking for the above Imported Drivecycle.
MATLAB Program for Calculating the Braking energy :
Mass=1000;%Mass of Vehicle in Kg
Time = Drivecycle(:,1);%Time in sec
Vel = Drivecycle(:,2);% Velocity in m/s
for i = 1:(length(Drivecycle)-1)
if Vel(i)>Vel(i+1)
E(i) = 0.5*Mass*(Vel(i)-Vel(i+1))^2;
end
end
fprintf('Total Braking energy is %d',sum(E))
fprintf('\nAverage Braking energy is %d',mean(E))
figure(1)
subplot(2,1,1)
plot(Time,Vel,'linewidth',3,'color','r')
xlabel('Time(sec)')
ylabel('Velocity(m/s)')
title('Drivecycle')
hold on
subplot(2,1,2)
plot(E,'linewidth',3,'color','g')
xlabel('Time(s)')
ylabel('Energy(J)')
title('Brakingenergy')Explanation for above Program :
Step-1 : Assume Mass of the Vehicle is 1000 Kg, and assume Time and Velocity value from the Imported drive cycle data.
Step-2 : For Deceleration Initial Velocity[Vel(i)] is greater than Final Velocity[Vel(i+1)], for that using 'if condition' to check [Vel(i)]>[Vel(i+1)] and the condition satisfies which calculate the Braking enrgy. Braking Energy Formula is
E=m⋅(vi−vf)22E=m⋅(vi-vf)22
where,
m- Mass of the Vehicle(kg),
vivi- Initial Velocity(m/s),
vfvf - Final Velocity(m/s),
E - Braking Energy (J)
Step-3 : Calculate the Braking Energy for the length of Drive cycle using 'for loop' condition.
Step-4 : After Calculating all Braking Energy for given Drive cycle, find Total Braking energy using 'sum(E)' command and Average Braking energy by using 'mean(E)' command.
Step-5 : Plot the results using 'plot' command and use 'xlabel','ylabel','title command for proper identification in the Plot window.
Step-6 : Using 'subplot' command to display two plot results in a single window.
Step-7 : Finally Click the 'Run' button to get the Output results.
Results :
Fig 1
Fig 2
Fig 3
The above Fig-1 Plot window refers Drivecycle and energy required for Braking for given Drive Cycle, Fig-2 shows that assinged and calculated values stored in Workspace and Fig-3 shows that the Total Braking energy(J) and Average Braking energy(J) required for Braking for a given Drive Cycle.
Why electric motor can’t develop braking torque at high speed similar to starting? How electric and mechanical brakes are coordinated?
The electric motor can't develop braking torque at high speed similiar to starting because once the electric supply is pulled off from the motor,it acts as a generator and due to the flux weakening effect of the electric generator,the generator produces low torque as expected.
Regerative Braking:
Regenerative braking 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. In this mechanism, the electric traction motor uses the vehicle's momentum to recover energy that would otherwise be lost to the brake discs as heat. This contrasts with conventional braking systems, where the excess kinetic energy is converted to unwanted and wasted heat due to friction in the brakes, or with dynamic brakes, where the energy is recovered by using electric motors as generators but is immediately dissipated as heat in resistors. In addition to improving the overall efficiency of the vehicle, regeneration can significantly extend the life of the braking system as the mechanical parts will not wear out very quickly.
The most common form of regenerative brake involves an electric motor functioning as an electric generator. In electric railways, the electricity generated is fed back into the traction power supply. In battery electric and hybrid electric vehicles, the energy is stored chemically in a battery, electrically in a bank of capacitors, or mechanically in a rotating flywheel. Hydraulic hybrid vehicles use hydraulic motors to store energy in the form of compressed air. In a hydrogen fuel cell powered vehicle, the electrical energy generated by the motor is used to break waste water down into oxygen and hydrogen which is recycled back into the fuel cell for later reuse.
The most common form of regenerative brake involves using an electric motor as an electric generator. The working of the regenerative braking system depends upon the working principle of an electric motor, which is an important component of the system. The electric motor gets activated when some electric current is passed through it. But, when some external force is applied to activate the motor (during the braking), then it behaves as a generator and generates electricity. This means that whenever the motor runs in one direction, the electric energy gets converted into mechanical energy, which is then used to accelerate the vehicle, and whenever the motor runs in the opposite direction, it performs functions of a generator, which then converts mechanical energy into electrical energy, which makes it possible to utilize the rotational force of the driving axle to turn the electric motors, which results in regenerating electric energy for storage in the battery and simultaneously reducing the speed of the car with the regenerative resistance of the electric motors. This electricity is then used for recharging the battery.
Coordination of Electric and Mechanical Brake :
In an electric Motor, the Total Brake distribution is in two aspects which are Electrical Brake which is called Regenerative Brake, and Mechanical Brake or Classical Brake with a hydraulic cylindrical system. Brake Force distribution must be uniform, If the Regenerative braking power requirement is more than the charging limit of the battery or more than the regenerative capacity of the machine we must apply Mechanical brakes as well. In a practical case, the combination of these two is applied. So usually it is a combined response of Mechanical brake and Regenerative brake. The reason for how this braking force is combined, that particular phenomena are called Brake Control Strategies. There are two Brake Control Strategies, which are Series - In case of Series, we apply Mechanical brake and Regenerative electric brake one after another. We can apply only one brake strategy at a time either apply Regeneratively or apply Mechanical brake. The Series Brake Control Strategy has a further classification, that is based on whether we want the comfort of driver or Brake behavior compared to energy efficiency. Parallel - In the case of Parallel, we apply both brakes simultaneously. This Particular Parallel braking is going to happen both at a time. Electric Driven Intelligent Brake (EDIB) is a combination of Hydraulic brake or Mechanical brake along with a Regenerative brake. It is a Parallel braking technique. The Control criteria such that at low speed use regenerative braking higher and at high speed or during the initial braking period we actually combine the both.
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.
To plot contour line for a given Motor. A Motor have various types of losses happening inside. The various types of losses are:
Copper Losses - I2RI2R , where R is the Armature resistance and we say that Torque is proportional to Current, this copper loss can be consider as .where is to take care of resistance of brushes and also take care of ux and its effect.
Copper losses = kc⋅T2kc⋅T2
Iron Losses - Iron Losses are nothing but Magnetic losses, which is denoted as , where factor is based on the Magnetic eld effect. For Permanent Magnets have constant Magnetic eld and this Iron losses is based on the value of and this are going to change according to the Speed. At Various Speed have different value of Back EMF and that is going to affect the Iron Losses.
Iron Losses = ki⋅ωki⋅ω
Windage Losses - This is a Mechanical or friction of Windage losses. This is based on size of shape of Motor and the amount of windage losses that the motor is going to experience.
Windage Losses = kw⋅ω3kw⋅ω3
Constant Losses - This is denoted as C.
Total Losses - The Total Losses are considering the above four losses and denoted as,
Total Losses = kc⋅T2+ki⋅ω+kw⋅ω3+Ckc⋅T2+ki⋅ω+kw⋅ω3+C
All Motors are model as per the above equation of losses. This above equation is not only applicable for Permanent Magnet DC Motor, but other motors as well like induction motor.
MATLAB program for calculating the losses of the EV motor:
clear all
close all
clc
w = linspace(0,1000);
T = linspace(0,250);
% motor constants
kc = 0.2; % for copper loss
ki = 0.008; % for iron loss
kw = 0.00001; % for windage loss
conL = 20; % for constant motor losses
% making mesh
[X,Y] = meshgrid(w,T);
OutputPower = (X.*Y); % Torque x Speed = Power
B = (Y.^2)*kc; % copper loss
C = (X.^3)*kw; % winding loss
D = X*ki; % Iron loss
InputPower = OutputPower + B + C + D + conL;
Z = OutputPower./InputPower;
% Set the efficiencies for which the contours will be plottted
V = [0.70 , 0.75 , 0.80 , 0.82 , 0.85 , 0.87 , 0.89 , 0.90 , 0.92];
box off
grid off
contour(X,Y,Z,V);
xlabel('Speed(rad/s)')
ylabel('Torque(N.m)')
hold on
V = [8000,10000];
contour(X,Y,OutputPower,V);
Result -
