Induction Motor Characteristic-II

TARGET-

1. Discuss about the equivalent circuit network of induction motor MATLAB model.
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.
3. Make a MATLAB script file which will plot speed torque characteristics for frequency control method.
4. Explain in brief about operation of BLDC motor.

SOLUTION-

1. Induction Motor Matlab Model>

• Library:

• Powertrain Blockset / Propulsion / Electric Motors

Model Description> The Induction Motor block implements a three-phase induction motor. The block uses the three-phase input voltages to regulate the individual phase currents, allowing control of the motor torque or speed.

Three-Phase sinosoidal Model Electrical System> The block implements equations that are expressed in a stationary rotor reference (qd) frame. The d-axis aligns with the a-axis. All quantities in the rotor reference frame are referred to the stator.

Working> An Induction Motor is a well-known device which works on the principle of transformer. So it is also called the rotating transformer. That is, when an EMF is supplied to its stator, then as a result of electromagnetic induction, a voltage is induced in its rotor. So an Induction motor is said to be a transformer with rotating secondary. Here, primary of transformer resembles stator winding of an induction motor and secondary resembles rotor.

Equivalent Circuit> The equivalent circuit of any machine shows the various parameter of the machine such as its Ohmic losses and also other losses.The losses are modeled just by inductor and resistor. The copper losses are occurred in the windings so the winding resistance is taken into account. Also, the winding has inductance for which there is a voltage drop due to inductive reactance and also a term called power factor comes into the picture. There are two types of equivalent circuits in case of a three-phase induction motor- Circuit 1>

The induction motor always runs below the synchronous or full load speed and the relative difference between the synchronous speed and speed of rotation is known as slip which is denoted by s. Slip(s)=(Ns-N)/Ns Synchronous speed(Ns)=120f/P

Ws)=2*π*Ns Where f is the supply frequency & P is the no of pole.

Where, R₁ is the winding resistance of the stator.
X₁ is the inductance of the stator winding.
R_c is the core loss component.
X_M is the magnetizing reactance of the winding.
R₂/s is the power of the rotor, which includes output mechanical power and copper loss of rotor.

Circuit 2> If we draw the circuit with referred to the stator then the circuit will look like- Where, R₂’ is the rotor winding resistance with referred to stator winding.
X₂’ is the rotor winding inductance with referred to stator winding.
R₂(1 – s) / s is the resistance which shows the power which is converted to mechanical power output or useful power. The power dissipated in that resistor is the useful power output or shaft power.

Now,

Zeq=(R1+R'2(1-s)/s)+j(X1+X'2)

Is=V1/Zeq

Putting the value of Zeq we get,

Is=V1/[(R1+R'2(1-s)/s)+j(X1+X'2)] Is=lIsl=V1/[(R1+R'2(1-s)/s)^2+j(X1+X'2)^2]

P=V1IsCosΦ2 =(V1^2)(R'2(1-s)/s)/[(R1+R'2(1-s)/s)^2+(X1+X'2)^2]

Torque equation is given by,

T=P/Ws

T=(V1^2)(R'2/s)/Ws[(R1+R'2/s)^2+(X1+X'2)^2]

The above equation is the torque equation of an induction motor.

2. For an induction motor Torque calculation, the parameters are following>

R1=Stator resistance

R2=Rotor resistance

X1=Stator inductance

X2=Rotor inductance

V1=Voltage Applied

Ns=Synchronous Speed

Ws=Angular speed

P=Number of poles

f=Supplied frequency

Ph=No of phase

Given values of these parameters are> R1=R2=0.2 ohm

X1=X2=0.1 ohm

V1=V/2 (half of the rated voltage)

f'= f/2 (half of the rated frequency)

Formula>

Ws=2*π*Ns

Ns= 120*f/P

At half of the rated frequency>

Ns=120 *f/2P

=1/2*(120*f/P)

Now 120*f/P=2*Ns=Ns'

or, Ws=2*π*Ns'

=2*π*2*Ns

or Ws'=Ws/2=2*π*Ns

Starting torque at rated voltage and frequency>

T=Ph*(V1^2)(R2)/Ws[(R1+R2)^2+(X1+X'2)^2]

=3*(V^2)(0.2)/Ws[(0.4^2)+(0.2^2)]

Tr=3*(V^2)/Ws..........(i)

Starting torque at half of the rated voltage and frequency>

T=Ph*(V1^2)(R2)/Ws[(R1+R2)^2+(X1+X'2)^2]

=3*(V/2)^2(0.2)/(Ws/2)[(0.4^2)+(0.2^2)]

Thr=3*(V^2)/2*Ws.......(ii)

Comparing equation (i) and (ii) we get>

(Thr/Tr)=[3*(V^2)/2*Ws]/[3*(V^2)/Ws]

=1/2

=0.5

Therefore the ratio of starting torque at half voltage & frequency to rated values will be 0.5.

3.MATLAB Script>

EXPLANATION>

Here in this matlab script file all the parameters for speed and torque equation is provided. After that 5 variable frequency is provided with a fixed interval. Then for calculatiing Angular speed and synchronous speed a function is defined which will varry the frequency by continously increasing its value of 1 unit. Then slip is also varried in the range of 1 to 200. After that all the inputs are given in the Speed and Torque equations. By which we can plot the Characteristic curve of Speed vs Torque.

MATLAB Simulation>

EXPLANATION>

Torque Speed Characteristic is the curve plotted between the torque and the speed of the induction motor. As we can see the nature of the curve is like that as the speed is increasing the torue is also increasing upto a perticular point and after that as the speed is incresing further but the torque is reducing and become zero at max speed, the point is called the breakdown or peak torque point. Moreover in the variation of frequency as the frequency is increasing the speed is increasing but the maximum torque is reducing.

4.DESCRIPTION>

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 of speed and torque of the motor.

These types of motors are highly efficient(85% to 90%) 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.

WORKING>

In brushes motors, there are permanent magnets on the outside and a spinning armature which contains electromagnet is inside. These electromagnets create a magnetic field in the armature when the power is switched on and help to rotate the armature.

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.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.

Continuous rotation of motor 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> The Control unit is implemented by microelectronic has several high-tech choices. This may be implemented using a micro-controller, a dedicated micro-controller, a hard-wired microelectronic unit, a PLC, or similar another unit.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. PWM (Pulse Width Modulation) wave can be used to control the speed of the motor. Here the average voltage is given or the average current flowing through the motor will change depending on the ON and OFF time of the pulses controlling the speed of the motor i.e. The duty cycle of the wave controls its speed. On changing the duty cycle (ON time), we can change the speed. By interchanging output ports, it will effectively change the direction of the motor.

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.

TYPES OF BLDC MOTOR>

Basically BLDC motors are two types .Those are (i) Inner Rotor Motor (ii) Outer Rotor Motor The operation is same for both two types but the basic difference is in there design.

(i) Inner Rotor Motor>> 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.

(ii) Outer Rotor Motor>> 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.

ADVANTAGES>

• Better speed versus torque characteristics
• High dynamic response
• High efficiency
• Long operating life due to a lack of electrical and friction losses
• Noiseless operation
• Higher speed ranges

APPLICATIONS>

• 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.
• Computer hard drives and DVD/CD players.