Week-9 Challenge: Induction Motor-2

1.Discuss about the equivalent circuit network of induction motor MATLAB model.

Description

The above figure shows the circuit of induction motor, in which the voltage is applied to the motor based on the phase. Stator and Rotor are the main pans of Induction motor Current flows to the stator resistance which is less than the rotor resistance. Slip occurs if the force on the shaft is more and which obeys the condition like ws > Wr_ In the equivalent circuit RI represents, the resistance of the stator winding and Xl the stator leakage reactance (flux that does not link with

the air gap and rotor). Magnetising reactance required to cross the air gap is represented by Xm and core losses (hysteresis and eddy current) by Rc An ideal transformer of NI and N2 turns respectively represents the air gap. For the rotor side, the induced emf is affected by the slip (as the rotor gains speed, slip reduces and less emf is induced). The rotor resistance and reactance are represented by R2 and X2; with X2 being dependant on the frequency of the inductor rotor emfs.

The Simplified Induction Motor block represents the electrical and torque characteristics of an induction motor powered by an ideal AC supply. The following figure shows the equivalent circuit model of the Simplified Induction Motor block.

In the figure:

• R1 is the stator resistance.
• R2 is the rotor resistance with respect to the stator.
• L1 is the stator inductance.
• L2 is the rotor inductance with respect to the stator.
• Lm is magnetizing inductance.
• S is the rotor slip.
• V and I are the sinusoidal supply voltage and current phasors.

Rotor slip (S) is defined in terms of the mechanical rotational speed ωm, the number of pole pairs p, and the electrical supply frequency ω by:

This means that the slip is one when starting, and zero when running synchronously with the supply frequency.

For an n-phase induction motor the torque-speed relationship is given by:

where:

• Vrms is the line-neutral supply voltage for a star-configuration induction motor, and the line-to-line voltage for a delta-configuration induction motor.
• n is the number of phases.

You can parameterize this block in terms of the preceding equivalent circuit model parameters or in terms of the motor ratings the block uses to derive these parameters.This block produces a positive torque acting from the mechanical C to R ports.

Assumptions and Limitations

• The block does not model the starting mechanism for a single-phase induction motor.
• When you parameterize the block by motor ratings, the block derives the equivalent circuit model parameters by assuming that the effect of the magnetizing inductance Lm is negligible, and the magnetizing inductance is not included in the simulated component.

2.3 phase, 50 Hz induction motor, represented by equivalent circuit constants X1 = X2 = 0.1 ohm and R1 = R2 = 0.2 ohm is operated at half of rated voltage and frequency. Calculate the ratio of starting torque at half voltage & frequency to rated values.

V = Voltage per phase

nph = Number of phase

P = Number of poles

R1 = Stator Resistance

R2 = Rotor Resistance

X1 = Stator Inductance

X2 = Rotor Inductance

Xm = Magnetizing Inductance

Given:

50 Hz

X1 = X2 = 0.1 ohm

R1 = R2 = 0.2 ohm

V = V/2 (calculating for half rated voltage and frequency)

Wms = 2 * pi * Ns

Ns = (120 * Freq) / P

NOTE: Since R1,R2,X1,X2 are the constant values it will never be changed once the motor is manufactured in the factory but the value of the voltage and the poles can be changed according to the needs of the power of the motor.

Formula:

Starting torque for Rated Voltage & Frequency

T = (3 * (V^2) * R2) / (Wms * ((R1+R2)^2 + (X1+X2)^2))

T = (3 * (V^2 * 0.2) / ((2*3.14*120*freq/ P) * ((0.4)^2)+((0.2)^2)

Ts = (7.956e-5) * (V^2) * P

Starting torque for half Rated Voltage & Frequency

T = (3 * (V/2)^2) * R2) / (Wms * ((R1+R2)^2 + (X1+X2)^2))

T = (3 * (V/2)^2 * 0.2) / ((2*3.14*120*freq) /2P) * ((0.4)^2 + (0.2)^2))

Ts = (3.978e-5) * (V^2) * P

The ratio of starting torque at half voltage & frequency to rated values, divide equation (2) to (1)

Ts = 0.5

3.Make a MATLAB script file which will plot speed torque characteristics for frequency control method.

clear all
close all
clc

% voltage per phase
V = 230/sqrt(3);
% number of phase 
N = 3;
% number of poles
p = 4;
% stator resistance
R1 = 0.095;
% rotor resistance
R2 = 0.23;
% stator inductance
X1 = 0.680;
% rotor inductance
X2 = 0.672;
% magnetizing inductance
Xm = 18.7;
% calculate stator thevnin equivalent
Zleq = 1i*Xm*(R1+1i*X1)/(R1+1i*(X1+Xm));
Rleq = real(Zleq);
Xleq = imag(Zleq);
Vleq = abs(V*1i*Xm/(R1+1i*(X1+Xm)));
% variable frequency
f=linspace(10,50,5)
for i=1:5
    w = (4*pi*f(i))/p;
    wms = (120*f(i))/p;
    for n=1:200
        s(n) = n/200; %slip
        rpm(n) = wms*(1-s(n));%rpm
        I2 = abs(Vleq/(Zleq+1i*X2+R2/s(n)));%I2
        Tmech(n)= N*I2^2*R2/(s(n)*w);
    end

%plotting the torque v/s rpm
plot(rpm,Tmech);
hold on
grid on
title(\'torque-speed characteristics of the induction motor\');
xlabel(\'RPM\');
ylabel(\'TORQUE (N-m)\');
legend(\'10 Hz\',\'20 Hz\',\'30 Hz\',\'40 Hz\',\'50 Hz\');

end

Output:

4.Explain in brief about operation of BLDC motor.

What is a Brushless Motor

A brushless DC motor (also known as a BLDC motor or BL motor) is an electronically commuted DC motor which does not have brushes. The controller provides pulses of current to the motor windings which control the speed and torque of the synchronous motor.

These types of motors are highly efficient in producing a large amount of torque over a vast speed range. In brushless motors, permanent magnets rotate around a fixed armature and overcome the problem of connecting current to the armature. Commutation with electronics has a large scope of capabilities and flexibility. They are known for smooth operation and holding torque when stationary.

Hall Sensors

Hall sensor provides the information to synchronize stator armature excitation with rotor position. Since the commutation of BLDC motor is controlled electronically, the stator windings should be energized in sequence in order to rotate the motor. Before energizing a particular stator winding, acknowledgment of rotor position is necessary. So the Hall Effect sensor embedded in stator senses the rotor position.

Most BLDC motors incorporate three Hall sensors which are embedded into the stator. Each sensor generates Low and High signals whenever the rotor poles pass near to it. The exact commutation sequence to the stator winding can be determined based on the combination of these three sensor’s response.

Working Principle and Operation of BLDC Motor

BLDC motor works on the principle similar to that of a conventional DC motor, i.e., the Lorentz force law which states that whenever a current carrying conductor placed in a magnetic field it experiences a force. As a consequence of reaction force, the magnet will experience an equal and opposite force. In case BLDC motor, the current carrying conductor is stationary while the permanent magnet moves.

When the stator coils are electrically switched by a supply source, it becomes electromagnet and starts producing the uniform field in the air gap. Though the source of supply is DC, switching makes to generate an AC voltage waveform with trapezoidal shape. Due to the force of interaction between electromagnet stator and permanent magnet rotor, the rotor continues to rotate.

Consider the figure below in which motor stator is excited based on different switching states. With the switching of windings as High and Low signals, corresponding winding energized as North and South poles. The permanent magnet rotor with North and South poles align with stator poles causing motor to rotate.

Observe that motor produces torque because of the development of attraction forces (when North-South or South-North alignment) and repulsion forces (when North-North or South-South alignment). By this way motor moves in a clockwise direction.

Here, one might get a question that how we know which stator coil should be energized and when to do. This is because; the motor continuous rotation depends on the switching sequence around the coils. As discussed above that Hall sensors give shaft position feedback to the electronic controller unit.

Based on this signal from sensor, the controller decides particular coils to energize. Hall-effect sensors generate Low and High level signals whenever rotor poles pass near to it. These signals determine the position of the shaft.

Brushless DC Motor Drive

As described above that the electronic controller circuit energizes appropriate motor winding by turning transistor or other solid state switches to rotate the motor continuously. The figure below shows the simple BLDC motor drive circuit which consists of MOSFET bridge (also called as inverter bridge), electronic controller, hall effect sensor and BLDC motor.

Here, Hall-effect sensors are used for position and speed feedback. The electronic controller can be a microcontroller unit or microprocessor or DSP processor or FPGA unit or any other controller. This controller receives these signals, processes them and sends the control signals to the MOSFET driver circuit.

In addition to the switching for a rated speed of the motor, additional electronic circuitry changes the motor speed based on required application. These speed control units are generally implemented with PID controllers to have precise control. It is also possible to produce four-quadrant operation from the motor whilst maintaining good efficiency throughout the speed variations using modern drives.

Advantages of Brushless DC Motor

1.Brushless motors are more efficient as its velocity is determined by the frequency at which current is supplied, not the voltage.

2.As brushes are absent, the mechanical energy loss due to friction is less which enhanced efficiency.

3.BLDC motor can operate at high-speed under any condition.

4.There is no sparking and much less noise during operation.

5.More electromagnets could be used on the stator for more precise control.

6.BLDC motors accelerate and decelerate easily as they are having low rotor inertia.

7.It is high performance motor that provides large torque per cubic inch over a vast sped rang.

8.BLDC motors do not have brushes which make it more reliable, high life expectancies, and maintenance free operation.

9.There is no ionizing sparks from the commutator, and electromagnetic interference is also get reduced.

10.Such motors cooled by conduction and no air flow are required for inside cooling.

Disadvantages of Brushless DC Motors

1.BLDC motor cost more than a brushed DC motor.

2.The limited high power could be supplied to BLDC motor, otherwise, too much heat weakens the magnets and the insulation of winding may get damaged.

Applications of Brushless DC Motors (BLDC)

Brushless DC Motors (BLDC) are used for a wide variety of application requirements such as varying loads, constant loads and positioning applications in the fields of industrial control, automotive, aviation, automation systems, health care equipments etc. Some specific applications of BLDC motors are

• Computer hard drives and DVD/CD players
• Electric vehicles, hybrid vehicles, and electric bicycles
• Industrial robots, CNC machine tools, and simple belt driven systems
• Washing machines, compressors and dryers
• Fans, pumps and blowers