Explanation about Equivalent circuit network
AIM :
1. To discuss about Equivalent circuit network of Induction motor MATLAB model.
2. To Calculate the ratio of starting torque at half voltage & frequency to rated values by using given Parameters.
3. To Make a MATLAB script file which will plot speed torque characteristics for frequency control method.
4. To explain about operation of Brushless DC Motor.
STUDY - 1:
Equivalent Circuit network of Induction Motor :
Three phase Induction motor is acts as a Generalized Transformer, because three phase AC supply is given to Stator winding of Induction motor, Rotating magnetic field is develop and due to rotating magnetic field resultant flux will produce and due to resultant flux EMF is induced in the rotor winding and it produces the current. Electromagnetic Induction takes place in the three-phase Induction motor, so electromagnetic induction may acts as a Generalized Transformer.
Equivalent circuit of Induction motor enables the Performance Characteristics which are evaluated for steady state conditions. A Induction motor is based on the induction of voltage and current. The Voltage and current is induced in the rotor circuit from the stator circuit for the operation.
Equivalent circuit of any machine shows the various parameter of machine such as its ohmic losses and also other losses.
The losses are modeled by just inductor and resistor. The Copper losses are occured in the windings so winding resistance is taken into an account. Also,the winding has the inductance for which there is a Voltage drop occur due to inductive reactance and also term called Power factor comes into the picture.
Fig : Equivalent Circuit Network of Induction Motor
Physical phenomena are actually converted with some assumptions to a circuit network. The above fig is Network of Induction Motor and this is called per phase Equivalent Circuit.
In Equivalent Circuit, R1 and L1 represents the resistance and Inductance of Stator Winding and X1 the stator leakage reactance(flux that does not link with air gap and rotor). V and I is supply Voltage and Current which is flowing through Stator. Stator Current(I) is divided into two parts, Magnetising Current(Im) and Rotor Current(I2).
I = Im + I2
There is an Air gap between the Stator and rotor, Magnetising reactance required to cross the air gap is represented by Xm. Magnetisng Current(Im) is produces the effect in such a way that, There is a Magnetic field establish.
The rotor resistance and reactance are represented by R2 and X2, with X2 being dependant on the frequency of the inductor rotor emfs.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).
Rotor behaviour is goverened by a parameter called slip, which is represented by [R2(1-s)/s]. Rotor power having the rotor copper losses and remaining power is available to the shaft. Power to the shaft that analysis the Torque-Speed relation. From the Equivalent Circuit of Induction Motor, next step is to derive Speed and Torque relation. where
Synchronous speed(Ns) is based on the supply frequency and no.of.poles of the motor.
Ns = (120*f) / p
For the Equivalent Circuit model, slip(s) is defined as
s = 1 - (pωm/f)
where,
p - no.of.pole pairs,
ωm - motor speed,
f - Electrical supply frequency,
Slip can also be expressed as,
s = ( ωs - ωm) / ωs
where, The difference between the Stator speed(ωs) and actual rotor speed(ωm) is known as slip(s). Slip can be expressed either a fraction or percentage.
Torque-Speed relation of Induction motor is,
Where,
n - number of phases,
X1 - Stator Inductance,
X2 - Rotor Inductance.
STUDY - 2 :
Given :
3 Phase 50 Hz Induction motor represented by equivalent circuit constatnt,
X1 = X2 = 0.1 ohm,
R1 = R2 = 0.2 ohm,
To Find :
To Calculate the ratio of starting torque at half voltage & frequency to rated values by using given Parameters.
Solution :
Torque-Speed relation of Induction motor is,
`T = [(n*R2)/(s*ωs)]*[V^2/((R1+(R2)/(s))^2+(X1+X2)^2)]`
Motor reaches Starting torque and Steady state speed will occurs and it transfers 100% efficient as there is no related slip in stable region. Slip reaches maximum value to 1. So Torque- Speed relation of Induction Motor equation becomes,
`T = [(n*R2)/(ωs)]*[V^2/((R1+R2)^2+(X1+X2)^2)]`
where,
Synchronous Speed for Full rated frequency,
N1 = (120*f) / p
N1 = (120*50)/p
N1 = 6000/p
So,
ωs1 = (2*π*N1) / 60
ωs1 = (2*3.14*6000)/(60*p)
ωs1 = 628/p
Synchronous Speed for Half rated frequency,
N2 = (120*(f/2)) / p
N2 = (120*25)/p
N2 = 3000/p
So,
ωs2 = (2*π*N2) / 60
ωs2 = (2*3.14*3000)/(60*p)
ωs2 = 314/p
Case(i) - Starting Torque at Rated Voltage & Frequency,
`T1 = [(n*R2)/(ωs1)]*[V^2/((R1+R2)^2+(X1+X2)^2)]`
`T1 = [(3*0.2)/(ωs1)]*[V^2/((0.2+0.2)^2+(0.1+0.1)^2)]`
`T1 = [(0.6)/(ωs1)]*[V^2/(0.16+0.04)]`
`T1 = [(0.6)/(ωs1)]*[V^2/0.2]`
`T1 = 3*(V^2/(ωs1))`
sub ωs1 value in above eqn, we get
`T1 = 3*(V^2 /(628/p))`
`T1 = (3*V^2*p)/628`
`T1 = (4.77*10^-3)*(V^2*p)`........................eqn(1)
Case(ii) - Starting Torque at half-Rated Voltage & Frequency,
`T2 = [(n*R2)/(ωs2)]*[(V/2)^2/((R1+R2)^2+(X1+X2)^2)]`
`T2 = [(3*0.2)/(ωs2)]*[(V/2)^2/((0.2+0.2)^2+(0.1+0.1)^2)]`
`T2 = [(0.6)/(ωs2)]*[(V/2)^2/(0.16+0.04)]`
`T2 = [(0.6)/(ωs2)]*[(V^2/4)/0.2]`
`T2 = [(0.6)/(ωs2)]*[V^2/0.8]`
`T2 = 0.75*(V^2/(ωs2))`
sub ωs2 value in above eqn, we get
`T2 = 0.75*((V^2*P)/314)`
`T2 = (2.38*10^-3)*(V^2*P)`........................eqn(2)
By Dividing eqn(2) by eqn(1), we get The ratio of starting torque at half voltage & frequency to rated values
`(T2)/(T1) = ((2.38*10^-3)*(V^2*P))/((4.77*10^-3)*(V^2*p))`
`(T2)/(T1) = 0.5`
Result :
The ratio of starting torque at half voltage & frequency to rated value is 0.5.
STUDY - 3 :
MATLAB script file to plot speed torque characteristics for frequency control method :
clear all
close all
clc
V1 = 230/sqrt(3);
nph = 3;
poles = 4;
fe = [10:10:50];
R1 = 0.095;
R2 = 0.23;
X1 = 0.680;
X2 = 0.672;
Xm = 18.7;
for i=1:length(fe)
%Calculate the Synchronous Speed
omegas(i) = 4*pi*fe(i)/poles;
ns(i) = 120*fe(i)/poles;
% Claculate the Stator Equivalent circuit
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
s(n)= n/200;
rpm(n) = ns(i)*(1-s(n));
I2 = abs(Vleq/(Zleq + 1i*X2 + R2/s(n)));
Tmech(n) = nph*I2^2*R2/(s(n)*omegas(i));
end
plot(rpm,Tmech)
hold on
xlabel("Speed(rad/s)");
ylabel("Torque(Nm)");
legend("10Hz","20Hz","30Hz","40Hz","50Hz");
title("Torque-Speed Characteristics of Induction Motor");
grid on
endExplanation for above MATLAB Program :
Step-1 : 12kw Motor has taken and in delta connection 230V is applied,for per phase Voltage V=230/sqrt(3) is given.
Step-2 : No.of.phases are 3 and No.of.poles are 4 and Fundamental frequency of the Motor is fe=50Hz. Frequency value is given in array.
Step-3 :R1,R2,X1,X2 & Xm are calculated from No load and Block rotor test. These are Motor Parameters considering as Input Parameters. Input Parameters are Fundamental Motor Design Parameters and These are per phase values.
Step-4 : Using "for loop" Calculating Synchronous speed, for Variuos Frequency.
Ns = (120*fe)/p
ωs = (2*pi*Ns)/60 = (4*pi*fe)/p
Step-5 : Stator Equivalent circuit is calculated Zleq,Rleq,Xleq&Vleq.
Step-6 : Using another "for loop" to run the loop for 200 times to Calculate the Mechanical Torque.
"Tmech(i) = nph*I2^2*R2/(s(n)*omegas(i))"
The above "Tmech" Equation is Similar to Speed-Torque Characteristic relation of Induction Motor.
"T = [(n*R2)/(s*ωs)]*[V^2/((R1+(R2)/(s))^2+(X1+X2)^2)]"
This Torque Equation is Solved in MATLAB code based on Equivalent Circuit analysis and simplified into "Tmech" equation and used in MATLAB Program.
Step-7 : "I2" is a rotor Current and Motor "rpm" which is also calculated.
Step-8 : Using "plot" command to plot the Output results.
Step-9 : "xlabel","ylabel","legend","title","grid on" command is used for proper Identification of Output results.
Step-10 : Run the MATLAB code to display the output results.
Result :
The above plot shows the Speed-Torque Characteristics of Induction Motor for Various Frequency range. By increasing the frequency range from 10Hz to 50Hz Speed is also increased and Maximum Torque is reduced. By Keeping Same Voltage and Varying Frequency, we get better Torque This is the relation of Induction Motor Speed-Torque Characteristics with frequency Variation.
STUDY - 4 :
Brushless DC Motor :
Brushless DC motor may be described as electronically commuted motor which do not have brushes. These types of motors are highly efficient in producing 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 large scope of capabilities and flexibility and brushless motor do not produce sparking or friction noises within it.. They are known for smooth operation, and holding torque when stationary.
Construction :
A commutator-brushes arrangement helps in achieving unidirectional torque in a typical dc motor. Obviously, commutator and brush arrangement is eliminated in a brushless dc motor. Here, an integrated inverter/switching circuit is used to achieve unidirectional torque. That is why these motors are, sometimes, also referred as 'electronically commutated motors'.
Just like any other electric motor, a BLDC motor also consists of two main parts a stator and a rotor. Permanent magnets are mounted on the rotor of a BLDC motor, and the stator is wound for a specific number of poles. Also, a control circuit is connected to the stator winding. Most of the times, the inverter/control circuit or controller is integrated into the stator assembly. This is the basic constructional difference between a brushless motor and a typical dc motor.
A typical controller provides a three-phase frequency-controlled supply to the stator winding. The supply is controlled by logical control circuits and energizes specific stator poles at a specific point of time. This can be understood from the below animations about working of BLDC motors.
Types of Brushless DC Motor :
Basically, BLDC are of two types, one is outer rotor motor and other is inner rotor motor. The basic difference between the two are only in designing, their working principles are same.
Inner Rotor Design :
In an inner rotor design, the rotor is located in the centre of the motor and the stator winding surround the rotor. As the rotor is located in the core, rotor magnets do not insulate heat inside and heat get dissipated easily. Due to this reason, inner rotor designed motor produces a large amount of torque and validly used.
Outer Rotor Design :
In outer rotor design, the rotor surrounds the winding which is located in the core of the motor. The magnets in the rotor trap the heat of the motor inside and do not allow to dissipate from the motor. Such type of designed motor operates at lower rated current and has low cogging torque.
Working Principle and Operation of BLDC Motor :
This type of motor have Rotor with Permanent magnets and in Stator has electromagnets exicted by windings and coils. Both Stator and Rotor are composed elctromagnet to increase the magnetic field and higher mechanical power density by unit of weight of the motor. The Torque of the brushless motor is due to the magnetic interaction impose by the electromagnets on the permanent magnets. There is a presize sequence of excitation of the electromagnets which imposes to the permanent magnets in angular movement, which is always in the same direction and it is as constant as possible under the same excitation. Obviously the sequence is cyclical and rotor continous its rotation interelates power. Repeating the sequence from time to time. To be more specific the sequence of excitation of the electromagnet inside the stator in such that the magnets of the rotor is attracted to the electromagnets without ever reaching them.
When electricity flows into coil A, the opposite poles of the rotor and stator are attracted to each other. When the rotor is getting close to the coil A, the electricity flows in the coil B and When the rotor is getting close to the coil B, the electricity flows in the coil C. Later in the coil A the electricity will flow again but with opposite polarity.
This process is repeated continously inside the engine ensuring a constant rotation of the rotor. In the case rotor follows the magnetic flux generated in exact sequence in the coils of the stator. In the case of more coils always more multiples of two it make sense to use the sequence the uses them all. To increase the magnetic flux to which the permanent magnets are subjected and turning off only the opposite electromagnets. This simple force site increase the torque that is the power that the motor can supply without substantially modifying its design criteria. The greater the number of coils, the smoother is the rotation of the rotor. Which will thus have a constant Torque. Electronic controller has sensor to detect the precision of the rotor magnets and thus decide to which coil to energize by following the right excitation sequence.The Modern brushless motor use Hall effect sensor.
Advantage of BLDC Motor :
BLDC Motor can operate at high speed under any condition. More electromagnets could be used on the stator for more precise control. Brushless motor is noisless and it is reliable and it provide low energy cost and maintenance free. It can also used in flammable environments.
Disadvantage of BLDC Motor :
BLDC motor cost more than a brushed DC motor. The limited high power could be supplied to BLDC motor, otherwise too much heat weakens the magnet and the insulation of winding may get damaged.
Application of BLDC Motor :
BLDC motors fulfill many requirements that a brushed DC motor does. But as they require a complicated control circuit and due to cost considerations, they haven’t yet completely replaced brushed DC motors, especially in low-cost applications. Despite this, there are many applications where BLDC motors dominate –
- Consumer electronics – computer hard drives, small cooling fans, cd/dvd players, etc. and also in modern appliances where quiet operation is desired – such as washing machines, air conditioners, etc.
- Electric Vehicles – many electric vehicles including electric and hybrid cars, electric bikes use BLDC motors.
- They have a wide range of applications in many other areas including robotics, industrial, motion control systems, etc.