What Are The Harmonics In Synchronous Machines

Harmonics Harmonics In Synchronous Machines

Harmonics: When the uniformly sinusoidally distributed air gap flux is cut by either the stationary or rotating armature sinusoidal emf is induced in the alternator. Hence the nature of the waveform of induced emf and current is sinusoidal. But when the alternator is loaded waveform will not continue to be sinusoidal or becomes non-sinusoidal. Such non-sinusoidal wave form is called complex wave form.

By using Fourier series representation it is possible to represent complex non-sinusoidal waveform in terms of series of sinusoidal components called harmonics, whose frequencies are integral multiples of fundamental wave. The fundamental wave form is one which is having the frequency same as that of complex wave.The waveform, which is of the frequency twice that of the fundamental is called second harmonic. The one which is having the frequency three times that of the fundamental is called third harmonic and soon. These harmonic components can be represented as follows.

Fundamental: e1 = Em1 Sin ( t ± θ1)
2nd Hermonic e2 = Em2 Sin (2 t ± θ2)
3rd Harmonic e3 = Em3 Sin (3 t ± θ3)
5th Harmonic e5 = Em5 Sin (5 t ± θ5) etc.
In case of alternators as the field system and the stator coils are symmetrical the induced emf will also be symmetrical and hence the generated emf in an alternator will not contain any even harmonics.

Slot Harmonics: As the armature or stator of an alternator is slotted, some harmonics are induced into the emf which is called slot harmonics. The presence of slot in the stator makes the air gap reluctance at the surface of the stator non uniform. Since in case of alternators the poles are moving or there is a relative motion between the stator and rotor, the slots and the teeth alternately occupy any point in the air gap. Due to this the reluctance or the air gap will be continuously varying. Due to this variation of reluctance ripples will be formed in the air gap between the rotor and stator slots and teeth. This ripple formed in the air gap will induce ripple emf called slot harmonics.

Minimization Techniques of Harmonics: To minimize the harmonics in the induced waveforms following methods are employed:
1. Distribution of stator winding.
2. Short Chording
3. Fractional slot winding
4. Skewing
5. Larger air gap length.

Effect of Harmonics on induced emf:

The harmonics will affect both pitch factor and distribution factor and hence the induced emf. In a well designed alternator the air gap flux density distribution will be symmetrical and hence can be represented in Fourier series as follows.

The RMS value of the resultant voltage induced can be given as

Eph2 =  [(E1)2+ ....+ …………… (En)2]

**(A)2 Means A Square 

Effect of Harmonics of pitch and distribution Factor:

The pitch factor is given by Kp = cos /2, where is the chording angle.
For any harmonic say nth harmonic the pitch factor is given by Kpn = cos n α/2
The distribution factor is given by Kd = (sin mβ /2) / (m sin β/2)

For any harmonic say nth harmonic the distribution factor is given by 
Kdn = (sin mn β/2)/(m sin nβ/2)

This is the detailed info about Harmonics In Synchronous Machines,Minimization Methods of Harmonics.Effect of Harmonics on induced emf.

EMF Equation Of Alternator / 3 Phase AC Generator EMF Equation

EMF Equation of an Alternator

We know Synchronous Machines generates E.M.F.the amount of EMF generated can be calculated using below simple derivation.

Consider following
Φ= flux per pole in wb
P = Number of poles
Ns = Synchronous speed in rpm
f = frequency of induced emf in Hz
Z = total number of stator conductors
Zph = conductors per phase connected in series
Tph = Number of turns per phase
Assuming concentrated winding, considering one conductor placed in a slot
According to Faraday's Law electromagnetic induction,
The average value of emf induced per conductor in one revolution 
eavg = dΦ /dt
eavg = Change of Flux in one revolution/ Time taken for one revolution

Change of Flux in one revolution = p x Φ
Time taken for one revolution = 60/Ns seconds.
Hence eavg = (p x  Φ  ) / ( 60/Ns) = p x   Φ x Ns / 60
We know f = PNs /120
hence PNs /60 = 2f
Hence eavg = 2   Φ f volts
Hence average emf per turn = 2 x 2 Φ f volts = 4Φf volts
If there are Tph, number of turns per phase connected in series, then average emf induced in Tph turns is
Eph,avg = Tph x eavg = 4 f   Φ Tph volts

Hence RMS value of emf induced E = 1.11 x Eph, avg
= 1.11 x 4  Φ f Tph volts
= 4.44 f  Φ Tph volts

Eph,avg= 4.44 f  Φ Tph volts

This is the general emf equation for the machine having concentrated and full pitched winding.In practice, alternators will have short pitched winding and hence coil span will not be  180o(degrees), but on or two slots short than the full pitch.

***If we assume effect of 
Kd= Distribution factor
Kc or KP = Cos α/2

Eph,avg= 4.44Kc  Kd f  Φ Tph volts
This is the actual available voltage equation of an alternator per phase.If alternator or AC Generator is Star Connected as usually the case, then the Line Voltage is √3 times the phase voltage.

Tags:derive the emf equation of an alternator,emf equation of synchronous machine,emf equation of induction motor,emf equation of synchronous generator,emf equation of alternator pdf,emf equation of an alternator wikipedia

Blocked Rotor Test On Induction Motor

Blocked Rotor Test On Induction Motor

This test is also called as Locked Rotor test or short circuit test.In the previous articles we had discussions on construction of induction motor,working of induction motor.We know induction motor is functionally similar to transformer.Like short circuit test on transformer blocked rotor test on induction motor is conducted.
Quick Point: Blocked rotor test on induction motor is to find out stator copper loss, rotor copper loss without friction and windage losses. 
In this test, the rotor is blocked by a belt-pulley mechanism,so it is not allowed to rotate.So rotor speed will be zero (N= 0).So slip (s) =1 and RL' = R2' (1-s)/s is zero.If the induction motor whichever is using for this test is slip ring induction motor then the winding are short circuited at the slip rings. 

Procedure of  Blocked Rotor Test of Induction Motor

1.First block the rotor of induction motor by pulley-belt mechanism.
2.Apply 10 to 15 % of rated voltage to stator of induction motor.(Because if we apply even more than 30% rated voltage rotor will be short circuited.)
3.Now, slowly increase the voltage in the stator winding so that current reaches to its rated value. At this point, note down the readings of the voltmeter, wattmeter and ammeter to know the values of voltage, power and current.
4.Now the applied voltage Vsc, the input power Wsc and a short circuit current Isc are measured.

As RL' = 0, the equivalent circuit is exactly similar to that of a transformer and hence the calculations are similar to that of short circuit test on a transformer.
                     Vsc = Short circuit reduced voltage (line value)
                     Isc = Short circuit current (line value)
                     Wsc = Short circuit input power
       Now      Wsc = √3Vsc Isc cosΦsc ----------- Line values
cosΦsc=Wsc/√3Vsc Isc ( This gives us short circuit power factor of a motor.)
        Now the equivalent circuit is as shown in above figure.
        where Isc = Per phase value
R1e = Wsc/3(Isc)²
This is equivalent resistance referred to stator.
                       Z1e = Vsc (per phase)/ Isc (per phase) = Equivalent impedance referred to stator.

X1e = 1e-1e  =  equivalent reactance reffered to stator.
During this test, the stator carries rated current hence the stator copper loss is also dominant. Similarly the rotor also carries short circuit current to produce dominant rotor copper loss. As the voltage is reduced, the iron loss which is proportional to voltage is negligibly small. The motor is at standstill hence mechanical loss i.e. friction and windage loss is absent. Hence we can write,

Wsc = Stator copper loss + Rotor copper loss

But it is necessary to obtain short circuit current when normal voltage is applied to the motor. This is practically not possible. But the reduced voltage test results can be used to find current ISN which is short circuit current if normal voltage is applied.
If             VL = Normal rated voltage (line value)
                Vsc = Reduced short circuit voltage (line voltage)
then  ISN = (VL * ISC) / Vsc
where       Isc = Short circuit current at reduced voltage
Thus,        ISN = Short circuit current at normal voltage
Now power input is proportional to square of the current.
So   WSN = Short circuit input power at normal voltage
This cab be obtained as,
But at normal voltage core loss can not be negligible hence,
WSN = Wsc (ISN / ISC
       WSN = Core loss + Stator and rotor copper loss

Differences Between Synchronous and Induction Motor

Differences Between Synchronous and Induction Motor

We have two major types of AC motors.They are synchronous and induction motor,synchronous motor runs at synchronous speed where induction motor runs at less than synchronous speed.In this article we are going to discuss on comparisons between synchronous and induction motor. There are so many differences between synchronous motor and induction motor like excitation,speed control.etc.Most important points are listed below.

Synchronous Motor Induction Motor
Construction is complicated. Construction is simpler , particularly in
case of cage rotor.
Not self starting.(why read here) Self starting.
Separate DC source is required for rotor
Rotor gets excited by the induced e.m.f
so separate source is not necessary.
The speed is always synchronous irrespective
of the load.
The speed is always less than synchronous
but never synchronous.
Speed control is not possible. Speed control is possible though difficult.
As load increases, load angle increases,keeping
speed constant at synchronous.
As load increases , the speed keeps on
By changing excitation , the motor p.f can be
changed from lagging and leading.
It always operates at lagging p.f and p.f
control is not possible.
It can be used as synchronous condenser for p.f
It can not be used as synchronous condenser.
Motor is sensitive to sudden load changes and
hunting results.
Phenomenon of hunting is absent.
Motor is costly and requires frequent maintenance. Motor is cheap, especially cage rotors and
maintenance free.

Read Here: Differences B/W Induction Motor & Transformer
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V-Curves and Inverted V-Curves

 V-Curves and Inverted V-Curves of Synchronous Motor

A synchronous motor is a double-excited machine, its armature winding is energized from an a.c source and its field winding from d.c source.Synchronous motor operates at unity power factor when field current is enough to set up the air-gap flux, as demanded by constant applied voltage.This field current, which causes unity power factor operation of the synchronous motor, is called normal excitation or normal field current.

If the the motor is under excited i.e, current is less than normal excitation,there will be some deficiency in flux to compensate that winding draws a magnetizing current from the a.c source and as a result of it, the motor operates at a lagging power factor.In other case, in over excited i.e, field current more than normal excitation machine operates at leading power factor.In the below figure you can observe leading and lagging variations.
In synchronous motors  performance characteristics obtained by v-curves and inverted v-curves. Synchronous machines have parabolic type characteristics.If excitation is varied from very low (under excitation) to very high (over excitation) value, then current Ia decreases, becomes minimum at unity p.f. and then again increases.But initial lagging current becomes unity and then becomes leading in nature.V-curves and inverted V-curves are used to analyze motor efficiency with no-load and with load.

What are V and inverted V curves ?

  • V-curve is a graph between Ia Vs If.
  • Inverted V curve are drawn between cosΦ Vs If.
In the above two cases If (field current) taken on x-axis.We can control the field excitation of synchronous motor by increasing/decreasing the field current.

Experiment to Obtain V-Curves and Inverted V-Curves 

If graph of armature current drawn by the motor (Ia) against field current (If) is plotted, then its shape looks like alphabet V. If the power factor (cos Φ) is plotted against field current (If), then the shape of the graph looks like an inverted V.
v and inverted v curves of synchronous motor circuit diagram
  • Connect stator of motor to 3 phase supply as shown in the above figure through watt meters and ammeter.
  • In this experiment two watt meter method is used to measure input power of motor.Ammeter reads the line current which is same as armature (stator) current. Voltmeter is reads line voltage.
  • A rheostat in a potential divider arrangement is used in the field circuit to control the excitation.By changing its value note down the voltage,armature current,watt meter readings(W1&W2) in a table like below.

 Now IL = Ia, per phase value can be determined, from the stator winding connections. 
       IL  = Iaph for stator connection
       IL/√3 = Iaph for delta connection
       The power factor can be obtained as
From above values make a final table like this,

The graph can be plotted from this result table.
1) Ia Vs If  → V-curve
2) cosΦ Vs If  → Inverted V-curve
This is the entire procedure can be repeated for various load conditions to obtain of V-curves and Inverted V-curves of any synchronous motor.

Tags: v and inverted v curves of synchronous motor wikipedia,v and inverted v curves of 3 phase synchronous motor

Starting Methods of Synchronous Motor

In the previous article we came to know that synchronous motors are not self starting so to make them start automatically we should add some tweaks.We should rotate rotor near to the speed of synchronous speed,so it attains synchronous speed.We have some fine methods to start the synchronous motor.They are,
1. Using pony motors.
2. Using small d.c. motor.
3. As a slip ring induction motor.
4. Using damper winding.

1. Pony Motor Method / Induction Motor

Pony motors are small motors mostly induction motors,which are used to run the rotor near to the synchronous speed. Once the rotor attains the synchronous speed, the d.c. excitation to the rotor is switched on.Pony motors are connected to the shaft of synchronous motor only up to it attains synchronous speed.Once the synchronism is established pony motor is decoupled. The motor then continues to rotate as synchronous motor.

In the below figure we tried to show you pony motor connection to synchronous motor.This is not exact arrangement what we use in industries.
Methods of Starting Synchronous Motor

2. Using Small D.C. Machine

This is also similar to pony motor method with some advantages.Mostly this method employed for large synchronous motors.For synchronous motor a dc machine will be connected.This dc machine is used as a d.c. motor to rotate the synchronous motor at a synchronous speed.. Once motor starts running as a synchronous motor, the same d.c. machine acts as a d.c. generator to supply dc to the rotor of syn. motor.This have some advantages like low power usage and easy starting.

3.Using Damper Winding

This is the most used method of starting synchronous motor.In addition to the normal field winding an additional winding consisting of copper bars placed in the slots in the pole faces.Ends of the copper bars are short circuited with the help of end rings.This winding is called damper winding.This damper winding acts as a squirrel cage rotor of an induction motor.
Methods of Starting Synchronous Motor
First synchronous motor runs as induction motor due to the damper winding at sub synchronous speed.Then d.c. supply is given to the field winding. At some instant motor gets pulled into synchronism and starts rotating at a synchronous speed.As rotor rotates at synchronous speed, the relative motion between damper winding and the rotating magnetic field is zero. Hence when motor is running as synchronous motor, there can not be any induced e.m.f. in the damper winding. So damper winding is active only at start, to run the motor as an induction motor at start. 

4. Slip Ring Induction Motor

In this method an external rheostat then can be introduced in series with the rotor circuit. So when stator is excited, the motor starts as a slip ring induction motor and due to resistance added in the rotor provides high starting torque.
Methods of Starting Synchronous Motor
The resistance is then gradually cut off, as motor gathers speed. When motor attains speed near synchronous. d.c. excitation is provided to the rotor, then motors gets pulled into synchronism ans starts rotating at synchronous speed. The damper winding is shorted by shorting the slip rings. The initial resistance added in the rotor not only provides high starting torque but also limits high inrush of starting current. Hence it acts as a motor resistance starter.

Why Synchronous Motor Is Not Self Starting?

Everyone is saying synchronous motors are not self starting but why here we going to discuss if you don't have time to read this whole article to know why synchronous motor is not self starting ANSWER IS INERTIA OF ROTOR.Let us have a detailed information on this topic.
To get a clear idea about this question consider a rotating magnetic field as equivalent to physical rotation of two stator poles N1 and S1 as shown in the figure.Assume any instant like that two poles are in line with stator magnetic axis [A-B].At this instant, rotor poles are arbitrarily positioned as shown in the figure.
Read This : Synchronous Motor Working
When DC supply is given to stationary rotor unlike poles will try to attract each other.Because of this action rotor will be subjected to an instantaneous torque in anticlockwise direction.As we connected power supply to stator,stator poles will rotate at speed of  Ns  r.p.m.

Due to inertia of rotor it is unable to rotate in the direction of  anticlockwise torque, to which is driving force or stator rotating field.Just in that instant the stator poles change their positions. Consider an instant half a period latter where stator poles are exactly reversed but due to inertia rotor is unable to rotate from its initial position.Shown in figure (b).

At this instant, due to the unlike poles trying to attract each other, the rotor will be subjected to a torque in clockwise direction. This will tend to rotate rotor in the direction of rotating magnetic field.But before this happen, stator poles again change their position reversing the direction of the torque exerted on the rotor.

Key Point : Hence the average torque on the rotor is zero.So synchronous motor will not start it self .

Shaded Pole Induction Motors-Working & Construction

Shaded Pole Induction Motors

We know that 'single phase induction motors are not self-starting' .To make them self starting we use capacitors,shaded poles etc.In this article we going to see shaded pole induction motors-working, construction.Shaded pole induction motors are very popular for low ratings about 0.05 HP (~ 40 W) because of its extremely simple construction and high performance. 

Shaded pole induction motor consists of salient poles(projected poles) on stator and a squirrel cage rotor.Poles are shaded i.e. each pole carries a copper band on one of its unequally divided part called shading ban.You can observe 4 pole shaded poles in below figure.
Shaded Pole Induction Motors-Working & Construction

Construction of Shaded Pole Induction Motor

Shaded Pole Induction Motors-Working & Construction


The stator of shaded pole induction motors are also similar to normal motor's stator construction. Usually 2 to 4 salient poles are used. A coil is wounded on it and part of each pole is wrapped by a copper coil.These poles are shaded by copper band or ring which is inductive in nature. The poles are divided into two unequal halves. The smaller portion carries the copper band and is called as shaded portion of the pole.The slot is approximately one third distance from the edge of the pole. 

Speed of motor depends on number of poles for example at 50Hz supply 2 pole stator gives a synchronous speed of 3000 rpm where a 4 poled stator speed will be 1500rpm.


Squirrel cage type rotor is used in shaded pole induction motors.Rotor bars are skewed in 60 degrees to obtain efficient starting torque and for limiting the torque dip during run up.Air gap length will be around  0.25 to 0.5 mm between stator and rotor.It doenst have any extra make ups like commutator, brushes, collector rings etc.This is very cheap in cost, rugged in construction and reliable. Absence of centrifugal switch eliminates the possibility of motor failure due to faulty centrifugal switch mechanisms.
Shaded Pole Induction Motors-Working & Construction

Working of Shaded Pole Induction Motor

The working operation of  shaded pole motor can be easily understood.Our main aim is to produce rotating magnetic field with single phase AC supply this is possible with shaded poles.How ? lets see

Alternating flux is produced by input ac supply.We can observe waveform of the flux in below figure.The distribution of this flux in the pole area is greatly influenced by the role of copper shading band.Now assume our ac supply as sine wave as shown in 1.
Shaded Pole Induction Motors-Working & Construction
  • During the portion OA
In OA portion  the alternating-current cycle [1], the flux begins to increase and an e.m.f. is induced in the shading coil. The resulting current in the shading coil will be in such a direction (Lenz’s law) so as to oppose the change in flux. Thus the flux in the shaded portion of the pole is weakened while that in the unshaded portion is strengthened as shown in figure 2.
  • During the portion AB
During the portion AB of the alternating-current cycle, the flux has reached almost maximum value and is not changing. Consequently, the flux distribution across the pole is uniform [Fig 3] since no current is flowing in the shading coil. 
  • During the portion BC
As the flux decreases (portion BC of the alternating current cycle), current is induced in the shading coil so as to oppose the decrease in current. Thus the flux in the shaded portion of the pole is strengthened while that in the unshaded portion is weakened as shown in Fig 4.

The effect of the shading coil is to cause the field flux to shift across the pole face from the unshaded to the shaded portion. This shifting flux is like a rotating weak field moving in the direction from unshaded portion to the shaded portion of the pole.The rotor is of the squirrel-cage type and is under the influence of this moving field. Consequently, a small starting torque is developed. As soon as this torque starts to revolve the rotor, additional torque is produced by single-phase induction-motor action. The motor accelerates to a speed slightly below the synchronous speed and runs as a single-phase induction motor.

Advantages & Applications of Shaded Pole Induction Motor

  • Cheap
  • These motors are commonly used in
  • Small fans
  • Advertising displays
  • Film projectors
  • Record players
  • Gramophones
  • Hair dryers
  • Photo copying machines etc.
  • Low starting torque, low power factor and low efficiency, copper losses are high due to presence of copper band.[ Disadvantage :-( ]