· By : ALOK TRIPATHI email: [email protected] Page 1 Introduction of Induction Motor Drives: Three phase induction motors are more commonly employed in adjustable speed drives

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By: ALOK TRIPATHI email: [email protected] Page 1

Introduction of Induction Motor Drives:

Three phase induction motors are more commonly employed in adjustable speed drives than three phase synchronous motor.

Three phase induction motors are of two types

[1] Squirrel cage Induction Motor (SCIM) [2] Slip ring or Wound Rotor Induction Motor (WRIM)

Basic Principle of Operation:

When 3-Phase supply is connected to three phase stator winding, rotating magnetic field is produced.

The speed of this rotating field, called synchronous speed, is given by equation….

Where: Ns = Synchronous Speed, f1 = Supply frequency, P = No. of Poles

Rotor cannot attain synchronous speed. It runs at a speed Nr, less than Ns, where

Nr = Rotor Speed in rpm. s = (Ns-Nr)/Ns = Slip

Rotor parameters are affected by slip. Rotor frequency f2 = sf1, Rotor induced emf V2 = sV1.

As we change the frequency the slip is also changed.

Analysis Performance and Torque Equation:

Per phase equivalent circuit of a three phase induction motor is shown in figure.

From fig (a) the value of current I2 will be

If we refer the rotor values to the stator

Then X2 will be replaced by sX2.

From equation it is clear that resistance

r2 is changed to r2/s.

Fig (b) is the modified circuit.

From fig (b) the current I2 will be

Power transferred from stator to rotor Rotor ohmic losses = 3I22r2

through air gap is given as ………

So developed power in rotor (Pm) = Pg – Ohmic losses

= [3I22r2/s] – [3I2

2r2] = 3I2

2 r2 [(1-s)/s]

Developed mechanical power = Te .wm

Both powers will be equal So. Pm = Te .wm

Te = Pm / wm = 3I22 r2 [(1-s)/s] x [1/ws(1-s)] = 3I2

2 r2 /[s.ws]

Te = Pg / ws

UNIT-V

Content

Control of A.C. Drives: Introduction, basic Principle of Operation, Squirrel-cage Rotor Design, Speed Control of Induction

Motors, stator Voltage Control, Variable Frequency control, Rotor Resistance Control, Slip Power Recovery Scheme,

Synchronous Motor Drives

Ns = 120 f1/P

Nr = Ns (1-s)

I2 = V2 / [r2 + jX2]

I2 = V2 / [r2 + jsX2]

I2 = (V2/s) / [(r2/s) + jX2]

I2 = V1/ [(r2/s) + jX2]

I2 = V1/ [(r1 + r2/s) + j(X1 + X2)]

Magnitude will be

I2 = V1 / [(r1 + r2/s)2 + (X1 + X2)

2]

1/2

Pg = 3I22r2/s

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This expression is called as Torque

Equation…………………………..

Torque Slip & Torque Speed Characteristics:

For Small Value of slip (0< s <0.05) the torque and slip has almost linear characteristics. Speed has its maximum value.

For high value of slip (0.05< s < 1) the characteristics become non-linear.

When s=1, the torque value is called as starting torque.

When s= 0, the rotor rotates at synchronous speed.

Speed Control of Three phase Induction motors

Stator Voltage Control Variable frequency Control Rotor resistance Control Slip-Energy Recovery Scheme

Stator Voltage Control: The torque equation is given as...

From this expression it is clear that torque (Te) is proportional

to the square of the stator supply voltage. A reduction in the

Supply voltage will reduce the motor torque and therefore

the speed of the drive.

Torque Slip & Torque Speed Characteristics:

From above characteristics it is clear that for a constant torque as we reduce the voltage the speed decreases.

3 V12 r2

Te =

ws [(r1 +r2/s)2 + (X1 + X2)

2] s

3 V12 r2

Te =

ws [(r1 +r2/s) 2 + (X1 + X2)

2] s

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Block Diagram:

Variable Frequency Control: By changing the supply frequency, motor synchronous speed can be changed and thus torque

and speed of a three phase induction motor can be controlled.

For a three phase induction motor per phase supply voltage is given by...

With constant supply voltage, if the supply frequency is increased, the synchronous speed and therefore motor speed increases.

But with increase in frequencies, flux and torque decreases. Induction motor performance at constant voltage and increased frequency

can be obtained by neglecting Xm and r1 from the equivalent circuit.

Synchronous Speed ws = 4πf1/P = 2w1/P rad/sec, and s= w2/w1 = f2/f1.

Where f2 and w2 are the rotor frequencies in Hz and rad/sec respectively.

Now the torque expression is given as (r1 is neglected and s is replaced by w2/w1)

Tem. w12 = Constant

Therefore Tem. w12 is always constant. As the operating frequency is increased, maximum torque is reduced to keep Tem. w1

2 remains

constant.

Characteristics:

From characteristics it is clear that as we increase the frequency the starting torque decreases. As we decrease the frequency the

starting torque increases.

V1 = √2 .π.f1N1φKw1

I2 = V1 / [(r2/s)2 + (X1 + X2)

2]

1/2

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Block Diagram:

Static Rotor Resistance Control: In a slip ring induction motor, a three phase variable resistor R2 can be inserted in the rotor

circuit. By varying the rotor circuit resistance R2, the motor torque can be controlled. The starting torque and starting current can also

be varied by controlling the circuit resistance.

This method of speed control is used when speed drop is required for a short time, as for example in overhead cranes, in load

equalization etc.

Circuit:

The three phase resistor of fig (a) may be replaced by a three phase diode rectifier, chopper and one resistor R. When chopper is ON,

Vdc = Vd = 0 and resistor R gets short circuited. When Chopper is OFF Vdc = Vd and Resistance in the rotor circuit is R.

So effective external resistance is

Characteristics:

From above characteristics it is clear that as we increase the resistance starting torque increases but for constant torque or load

torque or almost linear torque condition shows that the speed decreases.

Re = TOFF . R / T = [T_TON].R/T

Re= (1_ α) R

Where α = duty cycle = TON / T

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Slip Power Recovery Schemes: In Chopper method of speed control for SRIM, the slip power is dissipated in the external

resistance and it leads to poor efficiency of the drive. Instead of wasting the slip power in the rotor circuit resistance it can be

conveniently converted by various schemes for the speed control of SRIM.

Two important slip-power recovery schemes are…

[1] Static Kramer Drive [2] Scherbius Drive

Static Kramer Drive

Circuit:

Working: The circuit diagram for static Kramer drive is shown in above figure. It consists of a three phase bridge rectifier and a three

phase thyristor bridge inverter. The output of thyristor based bridge inverter is fed to the transformer. And the output of this

transformer is fed to supply system. The three phase supply system is connected with the stator of motor. And the rotor is connected

with diode bridge rectifier. The output of rotor at slip frequency is converted to a DC output and then converted to an AC output (three

phase) at line frequency using the bridge inverter with a delay in firing angle. Firing angle varies between 90o to 180

o. The output

voltage is low for the low values of slip, so to improve this voltage we use a step up transformer to increase the voltage up to its rated

value.

The output voltage of the diode rectifier will be (neglect the stator and rotor voltage drop) …

Where ‘n’ is stator to rotor turns ratio of motor.

The output voltage of thyristor bridge inverter will be

Where ‘m’ is source side to converter side turn ratio.

From the expression it is clear that the inverter output voltage depends upon α, and α varies from 90o to 180o. So the inverter output

voltage will always be negative.

From the circuit it is clear that the sum of output voltage of rectifier

and inverter will be zero if we neglect the voltage drop at

Ld. (By using KVL)

From above equation it is clear that the variation of delay angle

allows power flow and speed control. In this case the speed is only

subsynchronous speed. ( less than synchronous speed)

The power flow is from rotor circuit to supply, Static Kramer drive offers constant torque drive.

Scherbius Drive

Working: In super synchronous speed control, the additional power is fed into the rotor circuit at slip frequency. The circuit diagram,

as shown in figure, allows both sub synchronous and super synchronous speed control. It consists of one WRIM, two phase controlled

bridges, smoothing inductor and a transformer as shown in figure.

For super synchronous speed control bridge 1 is made to work as line commutated inverter with firing angle more than 90o and bridge

2 as a rectifier with firing angle less than 90o. The power flow is now from the supply to transformer, bridge 2, bridge 1 and to rotor

circuit.

Vd = 3 6 s V / [n.π]

Vdc = 3 6 s V Cosα / [m.π]

Vd + Vdc =0

Vd = _ Vdc

3 6 s V / [n.π] = _3 6 s V Cosα / [m.π]

s = _ n Cosα / m

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Methods 1 and 2 are applicable for both SCIMs and WRIMs, whereas method 3 and 4 can be used for WRIM only.

Circuit:

SYNCHRONOUS MOTOR DRIVES

Synchronous motors have two windings, one on the stator and other is on the rotor. Stator field is excited by 3Phase AC supply while

DC excitation is supplied to the field winding. The magnetic field created by the armature current rotates at the same speed as that

created by the field current on the rotor. It rotates at synchronous speed. So it always has zero slip. For the speed controls of

synchronous motors, both inverters and cycloconverters are employed. The various types of Synchronous motors are

[1] Cylindrical Rotor Motors [2] Salient Pole Motors

[3] Reluctance Motors [4] Permanent Magnet Motors

Cylindrical Rotor Motors:

The round rotor or cylindrical rotor synchronous motor has a uniform air gap between a slotted stator and rotor. This motor has its

rotor in cylindrical form. The rotor field winding van be excited with direct current supplied through slip rings and brushes from a

static phase controlled rectifier or from a DC generator.

Cylindrical Rotor (fig.a) Circuit Diagram per phase (fig.b)

Where Ef = excitation voltage or field voltage, Vt = terminal voltage

Ra = armature resistance, Xa = Synchronous Reactance per phase

The per phase equivalent circuit for a cylindrical rotor synchronous motor is given in fig (b).

The phase difference between terminal voltage (Vt) and excitation voltage (Ef) is δ. Where δ = power angle, load angle or torque angle

The torque is given as

So the Torque versus load angle characteristics for a cylindrical rotor synchronous motor is given in fig (c).

Te = Ef.Vt.Sinδ / [ωs.Xs]

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Fig.c

Power factor of a synchronous motor depends on the field current. The variation of armature current with respect to field current for

different loads on the synchronous motor is shown in fig (d). As the shape of curves resemble the letter V, these are called V-Curves

of a synchronous motor.

For low values of field current synchronous motor operates at a lagging power factor. As the field current is increased it would start

operating at unity power factor. If the field current is still increased beyond the unity power factor point, synchronous motor begins to

operate at a leading power factor.

SALIENT POLE MOTORS

The armature winding on the stator of a salient pole motor is similar to that of a cylindrical rotor motor. In this type of motor air gap

is not uniform. For analysis purposes, its armature current is resolved into two components, called direct axis current Id and

quadrature current axis Iq.

Developed Torque is given by…

Where δ = power angle

Xd = d-axis synchronous reactance

Xq = q-axis synchronous reactance

The first and second components of torque equation are called respectively the electromagnetic torque and the reluctance torque. The

construction of salient pole rotor is shown in fig (a) and the torque-power angle characteristics s shown in fig (b)

RELUCTANCE MOTORS

A salient pole synchronous motor connected to a voltage source runs at synchronous speed. If its field current is switched off, it

continues running at synchronous speed as a reluctance motor. Thus a machine designed to operate as a reluctance motor is similar to

a salient pole motor with no field winding on the rotor. Three phase armature winding produces rotating magnetic field in the air

gap. This rotating flux induces a field in the rotor which tends to align itself with the armature field, thus producing a reluctance

torque at synchronous speed.

Reluctance motors are used for low power drive where constant speed operation is required and where more than one motor is

needed for the job so that number of motors can run in synchronism.

The expression of reluctance torque is given as …………………….

Variation of reluctance torque with load angle is shown as below

𝑇𝑒 = 𝐸𝑓𝑉𝑡

𝑋𝑑𝑆𝑖𝑛𝛿 +

𝑉𝑡2

2 1

𝑋𝑞−

1

𝑋𝑑 𝑆𝑖𝑛2𝛿

1

𝜔𝑠

𝑇𝑒 = 𝑉𝑡2

2 1

𝑋𝑞−

1

𝑋𝑑 𝑆𝑖𝑛2𝛿

1

𝜔𝑠

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PERMANENT MAGNET MOTORS

A permanent magnet synchronous motor (PMSM) is similar to a salient pole synchronous motor without the field winding on the

poles. In PMSM, the required field flux is produced by permanent magnets mounted on it. In these motors, the excitation emf Ef

cannot be varied. All the equations governing the performance of a salient pole synchronous motor are also capable to PMSM with

excitation emf Ef taken as constant.

For the same frame size, PMSM has higher pull out torque and more efficiency as compared to salient pole motor.

These motors are used in ROBOTS and MACHINE TOOLS.

Documents

· By : ALOK TRIPATHI email: [email protected] Page 1 Introduction of Induction Motor Drives: Three phase induction motors are more commonly employed in adjustable speed drives