CALCULATION OF STARTING TORQUE OF AN INDUCTION MOTOR

AIM:

1. To Study the equivalent circuit of induction motor.

2. Calculating the ratio of starting torque at half voltage & frequency to rated values.

3. Plotting the speed-torque characteristics for frequency control method using matlab.

4. To Study the operation of BLDC motor.

KEYWORDS: Induction motor, BLDC motor, 3-phase, Space vector, RMS, VFD

SOFTWARE: Matlab, Simulink

OBJECTIVE:

1. To study the parameters involved in the induction motor circuit and working method.

2. Using rotor and stator resistance and inductance, calculate the the ratio of starting torque at half voltage & frequency to rated values.

3. Plotting the speed-torque characteristics for frequency control method using matlab with reference of torque equation.

4. To Study the operation of BLDC motor.

INTRODUCTION:

Study 1:-

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 parts 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 R1 represents, the resistance of the stator winding and X1 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 N1 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.

Study 2:-

Given:

Freq = 50;

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

R1 & R2 = 0.2;

X1 & X2 = 0.1; (X ∝ Freq)

Wms = 2 * pi * Ns;

Ns = (120 * Freq) / P ;

Formula:

( i ) Starting torque for Rated Voltage & Frequency

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

T = (3 * (V/2)^2 * 0.2) / ((2*3.142*120*Freq / P) * ((0.4)^2 + (0.1)^2))

Ts = (7.956e-5) * (V^2) * P ------------------- ( 1 )

( ii ) 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*3.142*120*Freq / 2P) * ((0.4)^2 + (0.1)^2))

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

Calculating the ratio of Starting torque, divide equation (2) to (1)

Ts = 0.5

Study 3:-

Code Explanation:

1. Collecting the datas required for the Torque - Speed characteristics of induction motor.

2. The formula for Torque - Speed characteristics is given by

3. It can be calculated for different frequency amd result is obtained.

% Calculating Voltage per phase
V1 = 230/sqrt(3);
% Number of phase
nph = 3;
% Number of poles
poles = 4;
% Stator Resistance (R1) & Rotor Resistance (R2)
R1 = 0.095;
R2 = 0.23;
% Stator Inductance (X1) & Rotor Inductance (X2)
X1 = 0.680;
X2 = 0.672;
% Magnetizing Inductance
Xm = 18.7;
% Variable Frequency
n1 = [10:10:50];
for fz = n1
% Calculating Ws wrt Frequency    
omegas = (4*pi*fz)/poles;
ns = (120*fz)/poles;
Zleq = 1i * Xm * (R1+1i*(X1))/(R1+1i*(X1+Xm));
Rleq = real(Zleq);
Xleq = imag(Zleq);
Vleq = abs(V1 * 1i * Xm / (R1+1i*(X1+Xm)));
for n = 1:200
    % Calculating Torque - Speed
    S(n) = n/200;
    rpm(n) = ns * (1-S(n));
    I2 = abs(Vleq / (Zleq+(1i*X2)+(R2/S(n))));
    Tmech(n) = nph*(I2^2)* R2 / (S(n)*omegas);
end
hold on
% Plotting Torque vs RPM
plot(rpm,Tmech)
title('Torque-Speed Characteristics of Induction Motor')
xlabel('rpm')
ylabel('Torque (N-m)')
legend('10 Hz' , '20 Hz' , '30 Hz' , '40 Hz' , '50 Hz')
grid on
end
figure
% Plotting Slip vs RPM
plot(rpm,S)
title('Slip vs. Speed')
xlabel('RPM')
ylabel('Slip')
grid on

OUTPUT:

Study 4:-

Theory:

A brushless DC motor (known as BLDC) is a permanent magnet synchronous electric motor which is driven by direct current (DC) electricity and it accomplishes electronically controlled commutation system (commutation is the process of producing rotational torque in the motor by changing phase currents through it at appropriate times) instead of a mechanically commutation system. BLDC motors are also referred as trapezoidal permanent magnet motors. Unlike conventional brushed type DC motor, wherein the brushes make the mechanical contact with commutator on the rotor so as to form an electric path between a DC electric source and rotor armature windings, BLDC motor employs electrical commutation with permanent magnet rotor and a stator with a sequence of coils. In this motor, permanent magnet (or field poles) rotates and current carrying conductors are fixed.

Construction:

The construction of this motor has many similarities of three phase induction motor as well as conventional DC motor. This motor has stator and rotor parts as like all other motors. Stator of a BLDC motor made up of stacked steel laminations to carry the windings. These windings are placed in slots which are axially cut along the inner periphery of the stator. It can be arranged in either star or delta. However, most BLDC motors have three phase star connected stator. Each winding is constructed with numerous interconnected coils, where one or more coils are placed in each slot. In order to form an even number of poles, each of these windings is distributed over the stator periphery. The stator must be chosen with the correct rating of the voltage depending on the power supply capability. For robotics, automotive and small actuating applications, 48 V or less voltage BLDC motors are preferred. For industrial application and automation system, 100 V or higher rating motors are used.

Working principle and Operation:

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 above 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. The motor continuous rotation depends on the switching sequence around the coils. 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.