Week-6 Challenge: EV Drivetrain

Aim:

1. Which types of power converter circuits are employed in electric and hybrid electric vehicles?
2. An Electric Vehicle's powertrain with a 72V battery pack is shown in the diagram below. The duty ratio for acceleration operation is 'd1' and for the braking operation the duty ratio is 'd2'. What is EV steady-state speed if the duty cycle is 70%?
3. Develop a mathematical model of a DC Motor for the below equation using Simulink.
4. Refer to the blog below topic: 

  Induction Versus DC brushless motors by Wally Rippel, Tesla

            Explain in brief about author’s perspective. 

Procedure:

1. Which types of power converter circuits are employed in an electric and hybrid electric vehicle?

Power Converter:

Power Conversion is the process of converting electric energy from one form to another. A power converter is an electrical or electro-mechanical device for converting electrical energy. A power converter can convert alternating current (AC) into direct current (DC) and vice versa.

The power converter can be as simple as a transformer or it can be a far more complex system, such as a resonant converter. Power conversion systems often incorporate redundancy and voltage regulation.

Types of Power Converters:

There are four types of converters for Electric and Hybrid Electric Vehicles.

AC-DC(Rectifier):

A rectifier is an electrical device that converts alternating current (AC), which periodically reverses direction, to direct current (DC), which flows in only one direction. The process is known as rectification since it "straightens" the direction of the current.

Physically, rectifiers take several forms, including vacuum tube diodes, wet chemical cells, mercury-arc valves, stacks of copper and selenium oxide plates, semiconductor diodes, silicon-controlled rectifiers, and other silicon-based semiconductor switches.

Uses:

• Rectifiers have many uses but are often found serving as components of DC power supplies and high-voltage direct-current power transmission systems.
• Rectification may serve in roles other than to generate direct current for use as a source of power. As noted, detectors of radio signals serve as rectifiers.
• In gas heating systems flame rectification is used to detect the presence of a flame.
• Depending on the type of alternating current supply and the arrangement of the rectifier circuit, the output voltage may require additional smoothing to produce a uniform steady voltage.
• Many applications of rectifiers, such as power supplies for radio, television, and computer equipment, require a steady constant DC voltage.
• In these applications the output of the rectifier is smoothed by an electronic filter, which may be a capacitor, choke, or set of capacitors, chokes, and resistors, possibly followed by a voltage regulator to produce a steady voltage.

More complex circuitry that performs the opposite function, that is converting DC to AC, is called an inverter.

DC-AC (Inverter):

A power inverter, or inverter, is a power electronic device or circuitry that changes direct current (DC) to alternating current (AC). The resulting AC frequency obtained depends on the particular device employed. Inverters do the opposite of “converters” which were originally large electromechanical devices converting AC to DC.

The input voltage, output voltage and frequency, and overall power handling depend on the specific device or circuitry design. The inverter does not produce any power; the power is provided by the DC source.

A power inverter can be entirely electronic or maybe a combination of mechanical effects (such as a rotary apparatus) and electronic circuitry. Static inverters do not use moving parts in the conversion process.

Power inverters are primarily used in electrical power applications where high currents and voltages are present; circuits that perform the same function for electronic signals, which usually have very low currents and voltages, are called oscillators.

DC-DC:

A DC-to-DC converter is an electronic circuit or electromechanical device that converts a direct current (DC) source from one voltage level to another. It is a type of electric power converter. Power levels range from very low (small batteries) to very high (high-voltage power transmission).

Uses:

• DC-to-DC converters are used in portable electronic devices such as cellular phones and laptop computers, which are supplied with power from batteries primarily.
• Such electronic devices often contain several sub-circuits, each with its own voltage level requirement different from that supplied by the battery or an external supply (sometimes higher or lower than the supply voltage).
• The battery voltage declines as its stored energy are drained. Switched DC to DC converters offer a method to increase the voltage from a partially lowered battery voltage thereby saving space instead of using multiple batteries to accomplish the same thing.

Most DC-to-DC converter circuits also regulate the output voltage. Some exceptions include high-efficiency LED power sources, a kind of DC to DC converter that regulates the current through the LEDs, and simple charge pumps that double or triple the output voltage.

DC-to-DC converters designed to maximize the energy harvest for photovoltaic systems and wind turbines are called power optimizers.

Electronic conversions:

• Practical electronic converters use switching techniques.
• Switched-mode DC-to-DC converters convert one DC voltage level to another, which may be higher or lower by temporarily storing the input energy and then releasing that energy to the output at a different voltage.
• The storage may be in either magnetic field storage components (inductors, transformers) or electric field storage components (capacitors).
• This conversion method can increase or decrease voltage. Switching conversion is often more power-efficient (typical efficiency is 75% to 98%) than linear voltage regulation, which dissipates unwanted power as heat.
• Fast semiconductor device rise and fall times are required for efficiency.
• However, these fast transitions combine with layout parasitic effects to make circuit design challenges.

Step-down:

A converter where the output voltage is lower than the input voltage (such as a buck converter).

Step-up:

A converter that outputs a voltage higher than the input voltage (such as a boost converter).

Continuous current mode:

Current and thus the magnetic field in the inductive energy storage never reaches zero.

Discontinuous current mode:

Current and thus the magnetic field in the inductive energy storage may reach or cross zero.

Noise:

Unwanted electrical and electromagnetic signal noise, typically switching artifacts.

AC-AC:

A solid-state AC-to-AC converter converts an AC waveform to another AC waveform, where the output voltage and frequency can be set arbitrarily.

AC to AC converters is used for converting the AC waveforms with one particular frequency and magnitude to AC waveform with another frequency at another magnitude. This conversion is mainly required in the case of speed controlling of machines, for low frequency and variable voltage magnitude applications as well. We know that different types of loads work with different types of power supplies like single-phase, three-phase supply, and the supplies can be differentiated based on the voltage and frequency range.

Current Source Inverter Converter:

In this type of inverter, one or two series inductors are used between one or both limbs of the connection between the rectifier and inverter. The rectifier used here is a phase-controlled switching device like Thyristor Bridge.

2. An Electric Vehicle's powertrain with a 72V battery pack is shown in the diagram below. The duty ratio for acceleration operation is 'd1' and for the braking operation the duty ratio is 'd2'.

The other parameters of the electric vehicle are given below,

Motor and Controller Parameters:

Rated Armature voltage= 72 V

Rated armature current= 400 A

R_a= 0.5Ω, KΦ= 0.7 Volt second

Chopper Switching frequency= 400 Hz

What is EV steady-state speed if the duty cycle is 70%?

Given,

Rated Armature Voltage,  =72 V

Rated Armature Current, = 400 A

`KΦ`= 0.7

The Duty Cycle (dc) is given as 70% - 0.7

The Average Voltage is given by the product of the battery voltage and the duty cycle.

`V_o=V×dc=72×0.7=50.4` V

The Average voltage is 50.4 V.

The Vehicle Characteristics are given in the form of the equation

`T_v=24.7+0.0051ω^2"_______(1)"`

The derived formula for the motor speed characteristics

`T= (V×KΦ)/R_a -((KΦ)^2/R_a ×ω)`

By substituting the Values,

`T= (50.4×0.7)/0.5-((0.7)^2/0.5×ω)`

`T=70.56-0.98ω" _________(2)"`

Compare the Equations 1 and 2, we get

`0.0051ω^2+0.98ω-45.89=0`

By using the Quadratic Equation Formula we get

`x=(-b±sqrt(b^2-4ac))/(2a)`

`ω=(-0.98±sqrt(0.98^2-4(0.0051×(-45.89))))/(2(0.0051))`

 `ω=(-0.98±1.377)/0.0102`

We get two solutions for this angular speed

`ω=38.92 rad⁄sec` or `ω=-231.078 rad⁄sec`

We can consider only the positive value considering the positive value.

• To visualize the Speed Vs Torque we can write a code based on the inputs given in the question.

% Input
V_a= 72;     % Rated Armature Voltage in Volts
I_a= 400;    % Rated Armature Current in Amps
R_a= 0.5;    % Rated Armature Resistance in Ohms
K_Phi= 0.7;  % Proportionality Constant
d_c= 0.7;    % Duty Cycle 

• Now, give a speed array values in the given range.

speed = linspace(0,300,301);

• Create a for-loop such that it runs for the duration of speed.
• Vehicle Torque and Motor Torque formulas are taken from above.
• Write the equation stating the steady-state condition.

% For the vehicle and Motor torque
for i=1:length(speed)
    T_v(i)= 24.7+(0.0051*speed(i)^2);
    T_m(i)= (((K_Phi*V_a)/R_a)-(((K_Phi^2)/R_a)*speed(i)));
end

% Motor Torque by using the equation 70.56-0.98*w 
Motor_Torque = 70.56-0.98.*speed;

• Now, write a code to plot the graph.

%Plotting of Graphs
figure()
plot(T_v, speed)
hold on
plot (T_m, speed)
hold on 
plot (Motor_Torque, speed)
xlabel('Angular Speed (rad/sec)');
ylabel('Torque (N-m)');
legend('Vehicle Torque','Motor Torque','Motor Torque at steady state');
saveas(gcf,'speed vs torque.png');

• Save the file and run it.

Code:

clear;clc;

% Speed Torque Characteristics of DC motor

% Input
V_a= 72;     % Rated Armature Voltage in Volts
I_a= 400;    % Rated Armature Current in Amps
R_a= 0.5;    % Rated Armature Resistance in Ohms
K_Phi= 0.7;  % Proportionality Constant
d_c= 0.7;    % Duty Cycle 

speed = linspace(0,300,301);

% For the vehicle and Motor torque
for i=1:length(speed)
    T_v(i)= 24.7+(0.0051*speed(i)^2);
    T_m(i)= (((K_Phi*V_a)/R_a)-(((K_Phi^2)/R_a)*speed(i)));
end

% Motor Torque by using the equation 70.56-0.98*w 
Motor_Torque = 70.56-0.98.*speed;
%Plotting of Graphs
figure()
plot(T_v, speed)
hold on
plot (T_m, speed)
hold on 
plot (Motor_Torque, speed)
xlabel('Angular Speed (rad/sec)');
ylabel('Torque (N-m)');
legend('Vehicle Torque','Motor Torque','Motor Torque at steady state');
saveas(gcf,'speed vs torque.png');

3. Develop a mathematical model of a DC Motor for the below equation using Simulink.

`ω= V/(KΦ)-(R_a/(KΦ)^2 ×T)`

• Initially, a Code is written in MATLAB to provide inputs for the Simulink blocks such that every time the user changes the inputs the Block Plots also changes.
• We take input values of Speed Constant, Voltage Supply, and Rated armature resistance.

%Inputs
angular_speed = linspace(0,300,100);    % Motor Speed in rad/sec
E_b= 1;                                 % Back EMF  
speed= angular_speed*(60/2*pi);         % Motor Speed in RPM
W= input('Enter the Speed Constant of Motor value: ');
V= input('Enter the Voltage Supply value: ');
R_a= input('Enter the Rated Armature Resistance value: ');

• Value is equated such that it is converted to RPM.

K_PHI= (E_b/W)*(60/(2*pi));  % Calculating the K-Phi value and converting it to RPM.

• Torque Characteristics equation is written to calculate.

%Torque Characteristics 
T= (((V*K_PHI)/R_a)-((((K_PHI)^2)/R_a).*angular_speed));

• Next, write a code to plot the graphs.

%Plotting of graphs
figure()
plot(speed,T)
title('Torque Speed Characteristics of DC Motor');
xlabel('Speed (RPM)');
ylabel('Torque (N-m)');
saveas(gcf,'torque vs Speed graph.png');

• Save the file and run it.
• Now, open the Simulink workbench, use the Constants, Ramp, Divide, Square, and Subtract and use the formula mentioned above.

• Now save the file and run it and once the simulation is done, the scope is used to check the plot.

Code:

clear;clc;

% Torque-Speed Characteristics of DC motor

%Inputs
angular_speed = linspace(0,300,100);    % Motor Speed in rad/sec
E_b= 1;                                 % Back EMF  
speed= angular_speed*(60/2*pi);         % Motor Speed in RPM
W= input('Enter the Speed Constant of Motor value: ');
V= input('Enter the Voltage Supply value: ');
R_a= input('Enter the Rated Armature Resistance value: ');

K_PHI= (E_b/W)*(60/(2*pi));  % Calculating the K-Phi value and converting it to RPM.

%Torque Characteristics 
T= (((V*K_PHI)/R_a)-((((K_PHI)^2)/R_a).*angular_speed));

%Plotting of graphs
figure()
plot(speed,T)
title('Torque Speed Characteristics of DC Motor');
xlabel('Speed (RPM)');
ylabel('Torque (N-m)');
saveas(gcf,'torque vs Speed graph.png');

4. Refer to the blog below topic: 

Induction Versus DC brushless motors by Wally Rippel, Tesla

            According to the blog ‘Induction vs DC Brushless motors by Wally Rippel, Tesla’, the writer states the changes in the world years ago and the latest technological trends that are happening. He then explains about the DC Brushless motors and Induction motors.

DC Brushless Machines:

According to him, the rotor has two or more permanent magnets that generate a DC magnetic field. This magnetic field will enter the stator core which interacts with the currents flowing in the windings to produce an interaction between rotor and stator. It needs a proper flow of current into the rotor and stator if it’s not connected properly the current will not generate and the torque decreases. During the Electric and mechanical conversion when the rotor is rotating, the magnitude and polarity of the stator current will continuously vary such that the torque remains constant and optimal efficiency is achieved.

Induction Motor:

The 3-phase induction motor was invented by Nikola Tesla sometime before 1889. The stators for the 3-phase induction motor and the DC brushless motor are virtually identical. Both have three sets of distributed windings that are inserted within the stator core. The essential difference between the two machines is with the rotor.

Unlike the DC brushless rotor, the induction rotor has no magnets. They have just stacked steel laminations with buried peripheral conductors that form a shorted structure. Currents flowing in the stator windings produce a rotating magnetic field that enters the rotor. The frequency of this magnetic field as seen by the rotor is equal to the difference between the applied electrical frequency and the rotational frequency of the rotor itself. An induced voltage exists across the shorted structure that is proportionate to this speed difference between the rotor and electrical frequency. The currents are produced within the rotor conductors that are approximately proportionate to the voltage, hence there’s a speed difference. Finally, these currents interact with the original magnetic field to produce forces.

When a 3-phase induction motor is connected to utility type 3-phase power, torque is produced at the outset. The motor has the ability to start under load. No inverter is needed. The fact that induction motors are directly compatible with conventional utility power is the main reason for their success. In contrast, a brushless DC motor produces no starting torque when directly connected to fixed frequency utility power. They really need the aid of an inverter whose phase is maintained in step with the angular position of the rotor.

Differences:

He then explained that there were only a few brushless drives in the past but now most of the Hybrid Electric Vehicles use it. There’s a difference between brushless and inverter controls is the control. The Dc brushless requires a position sensor but an induction motor requires only a speed sensor.

Less rotor heat is generated in DC brushless drive and Rotor cooling is easier and peak point efficiency is generally higher.

DC brushless drive operates at a power factor of one, whereas the induction drive power factor is 85%.

With the increase in the size of the DC Brushless machine, magnetic losses increase and the part-load efficiency decreases, whereas the induction drives, as the machine size increases, losses don’t grow. During high-performance tasks, induction drives are suitable.

Finally, we can know that the writer says that the DC brushless will dominate the Hybrid Electric Vehicle Markets but the Induction drive will maintain dominance in the High performance in the pure electric vehicles. As of now, there is no winner out of the two as each has its own pros and cons and excels at its own forte.

Result:

Steady State Speed vs Torque Graph:

Workspace:

The Mathematical model for the equation is created in the Simulink block and the plot is shown below.

Command Prompt:

Torque vs Speed Graph:

Workspace:

References:

Many articles helped to gain knowledge on the problems faced most of them are from google.