Week-11 Challenge: Braking

Generally, the braking system for a car is based on hydraulic braking technology. However, this traditional braking methodology causes a lot of energy wastage since it produces unwanted heat during braking. Thus, the invention of regenerative braking in electric cars has overcome these disadvantages moreover it helps in saving energy and provides higher efficiency for the car.

 

In a regenerative mode, the motor act as a generator, it transfers the kinetic to electrical energy to restore the batteries or capacitors. Meanwhile, the brake controller monitors the speed of the wheels and calculates the torque required plus the excessive energy from the rotational force that can be converted into electricity and fed back into the batteries during the regenerative mode. The merits of regenerative braking over traditional braking are energy conservation, wear reduction, fuel consumption, and more efficient braking

 

When the motor is at rest it has to operate from a standstill position to start moving, high torque is required in order to bring the motor in motion. Whereas while braking, the motor is already operating at speed, the maximum operating limit is already reached by the motor operation and thus further higher torque could not be obtained while braking. Also, the discharge rate of a battery during accelerating is 2 times that of the charging rate of the battery during regenerative braking.

 

clear all
close all
clc

% Speed Array
omega = linspace(0, 300, 100);

% Torque Array
T = linspace(0, 2000, 100);

% Meshgrid
[X,Y] = meshgrid(T, omega);

% Loss Coefficients
cu = 0.17;                              % Copper coefficient
fe = 0.006;                             % Iron coefficient
win = 0.000015;                         % Windage coefficient

% Losses
cu_loss = cu*(Y.^2);                  % Copper Losses
fe_loss = fe*(X.^2);                  % Iron Losses
win_loss = win*(X.^3);                % Windage Losses
cond_loss = 18;                       % Conduction Losses% Output Power
P_out = (X.*Y);      

% Input Power
P_in = P_out +  (cu_loss) + (fe_loss) + (win_loss) + (cond_loss);

% Efficiency
eta = ((P_out)./(P_in));

% Efficiency values for contour
W = linspace(0.75, 0.95, 10);

% Contour Plot

contour(X,Y,eta,W)
xlabel('Angular Speed, rad/s')
ylabel('Torque, Nm')
title('Speed, Torque and Efficiency characteristics of Motor')

Code Explanation:

In the MATLAB script, I begin with the clear all, close all, and clc commands. Then, I create arrays for the speed and the torque of the motor using the ‘linspace’ command.  For the speed, I am taking a range of values from 0 to 2000 radians per second whereas for the torque, I am taking a range of values from 0 to 300Nm.

These arrays are then used to create 2D grid coordinates using the ‘mesh grid’ command(X,Y). These coordinates will help in the creation of the contour plot. In order to find the efficiency of the motor, we need to consider the various losses that occur in the motor’s operation.

The main losses that occur are:

• Copper losses
• Iron losses
• Windage losses
• Conduction losses

These various losses are dependent on the speed and the torque of the motor. They each also have a characteristic constant of proportionality which are all assumed for the following calculations and represented as 'K'. In each calculation, the speed and the torque are represented respectively as: `omega and `T`

• Copper losses = `K_(cu)*omega^2`
• Iron losses = `K_(fe)*T^2`
• Windage losses = `K_w*T^3`
• Conduction losses are assumed to be 18 Joules. 

We also need to calculate the efficiency of the motor using the data we currently have. Since efficiency is defined as the ratio of the output power to the input power, we can calculate the efficiency of the motor by determining the input and output power of the motor. The output power of the motor can be calculated by multiplying the angular speed with the torque.

`P_(out) = T*omega`

 Then, we can calculate the input power supplied to the motor by adding the output power to the energy losses.

`P_i = P_(out) + Cu_(loss) + Fe_(loss) + W_(loss) + Cond_(loss)`

Since efficiency is defined as the ratio of the output power to the input power, we can calculate the efficiency of the motor by:

`eta = P_(out) /(P_i + Cu_(loss) + Fe_(loss) + W_(loss) + Cond_(loss))`

As you can see, the calculations for the output power are performed with the values from the mesh grid and not the individual variables of speed and torque. 

Plotting of the contour is done with the 'contour' command. In addition, an array for the efficiency values we want to plot for is created called 'W' and is assigned for values ranging from an efficiency level of 0.75 to 0.95. This array is used in the creation of the contour. Axis labels and a title are also made for better readability. 

Output:

The image below shows the contour plot that is achieved when the code is executed:

From this contour plot, we can see that the highest level of efficiency arises in the innermost contour plot and this efficiency decreases as the contours increase in size from the innermost contour. The innermost contour shows that any point on the contour will have an efficiency of 0.9054. The second, third, and fourth innermost contour display efficiencies of 0.88, 0.86, and 0.84 respectively anywhere on their respective contour plots.