Post on 09-Feb-2022
Module II
Performance of an alternator KTUNOTES.IN
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Rotating Magnetic Field
Performance of an alternator
When balanced 3-phase currents flow in balanced 3-phase windings, a rotating magnetic field is produced.
2-pole 3-phase stator winding
Three windings are displaced by 120o along the air-gap periphery.
Each phase spread over 60o
(called phase-spread σ=60o)
Coil aa′ represents phase a winding
Positive currents are to be flowing as indicated by crosses in coil-sides a′ , b′ , c′
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Performance of an alternator
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Space phasor representation
Performance of an alternator
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Space phasor representation
Performance of an alternator
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Space phasor representation
A constant-amplitude rotating m.m.f. or rotating field is produced in the air-gap of a three-phase machines at synchronous speed
Performance of an alternator
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Armature Resistance
Armature reaction
Armature leakage reactance
Synchronous reactance
Causes of voltage drop in alternators
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Electrical machine works based on Faraday's law.
Machine requires a magnetic field and armature
Faraday's law - an emf induced in the armature.
Load connected with armature, current flowing in the
armature
As soon as current starts flowing through the armature
conductor there is one reverse effect of this current on the
main field flux of the alternator
This reverse effect is referred as armature reaction in
So, the effect of armature (stator) flux on the flux produced
by the rotor field poles is called armature reaction.
Armature reaction in alternators
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It is the interaction between field pole and the
armature pole
The armature reaction in synchronous machine
affects the main field flux and vary differently for
different power factors.
Armature reaction
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Armature reaction is discussed three conditions
unity power factor
zero power factor lagging
zero power factor leading.
Unity power factor
Armature current and induced emf - same phase.
EMF induced in the armature - due to changing
main field flux, linked with the armature
Armature reaction
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Field is excited by DC- the main field flux is constant
in respect to field magnets
it would be alternating in respect of armature
main field flux of the alternator
emf E across the armature is proportional to
Armature flux φa is proportional to armature current
Armature reaction - Unity power factor
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Armature flux φa is proportional to armature current
Armature flux φa is in phase with armature current I.
At unity power factor I and E are in same phase.
Φa is phase with E.
Φa is in phase with E and Φf is in quadrature with E
φa is in quadrature with main field flux φf
two fluxes are perpendicular to each other,
The armature reaction of alternator at unity power
factor is purely distorting or cross-magnetizing type.
Armature reaction - Unity power factor
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Hence, at ωt = 0, E is maximum and φf is zero.
At ωt = 90°, E is zero and φf has maximum value.
At ωt = 180°, E is maximum and φf zero.
At ωt = 270°, E is zero and φf has negative maximum
value.
Armature reaction - at Lagging Zero Power Factor
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Here, φf got maximum value 90° before E.
Hence φf leads E by 90°.
Now, armature current I is proportional to armature
flux φa, and I lags E by 90°.
Hence, φa lags E by 90°.
φa and φf act directly opposite to each other.
Thus, armature reaction of alternator at lagging zero
power factor is purely demagnetizing type. That
means, armature flux directly weakens main field
flux.
Armature reaction - at Lagging Zero Power Factor
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At leading pf, Ia leads emf E by an angle 90°.
φf leads, emf E by 90°, φa is proportional to Ia.
Hence, φa is in phase with Ia.
φa also leads E, by 90° as Ia leads E by 90°.
As in this case both armature flux and field flux lead
induced emf E by 90°
Armature reaction - at Leading Zero Power factor
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φf and φa are in same direction.
Hence, the resultant flux is simply arithmetic sum of
field flux and armature flux.
Hence, at last it can be said that, armature reaction
of alternator due to a purely leading electrical power
factor is totally magnetizing type.
Armature reaction - at Leading Zero Power factor
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Armature reaction flux is constant in magnitude and
rotates at synchronous speed.
The armature reaction is cross magnetizing when the
generator supplies a load at unity power factor.
When the generator supplies a load at leading
power factor the armature reaction is partly de
magnetizing & partly cross-magnetizing.
Nature of Armature reaction
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When the load current flows through the armature
winding, it build up the local flux, which cuts the
winding and counter emf is generated. This effect
produces armature reactance which is equal to 2πfL,
where L is in H. This armature reactance is called
leakage reactance
Synchronous Reactance and Impedance
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The combination of leakage reactance with armature
reactance is synchronous reactance
Synchronous Impedance
Synchronous Reactance and Impedance
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Equivalent circuit of syn. Generator is
Phasor Diagram
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The per phase model of a synchronous machine
Open and short circuit test data can be used to
determine synchronous reactance
In short circuit condition
Determination of synchronous reactance
Armature resistance is often neglected,
stf JXVE
0V , t scA II
0V when , t sc
f
sI
EX
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The voltage regulation of an alternator is defined as the change in its terminal voltage when full load is removed, keeping field excitation and speed constant, divided by the rated terminal voltage.
So if Vph = Rated terminal voltage
Eph = No load induced e.m.f.
the voltage regulation is defined as,
Voltage regulation
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The Open-Circuit Test
1. Generator is rotated at the rated speed.
2. Field current is increased from 0 to maximum.
Voltage regulation - EMF
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Voltage regulation-EMF method
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Voltage regulation- EMF method
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Voltage regulation- EMF method
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The Open-Circuit Test
Voltage regulation - EMF method
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Voltage regulation EMF method
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MMF method (Ampere turns method)
Tests: Conduct tests
OCC (upto 125% of rated voltage)
SCC (for rated current)
Voltage regulation
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MMF method (Ampere turns method)
Voltage regulation- MMF method
1. By suitable tests plot OCC and SCC 2. From the OCC find the field current If1 to produce rated voltage, V. KTUNOTES.IN
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3. From SCC find the magnitude of field current If2 to
produce the required armature current.
4. Draw If2 at angle (90+Φ) from If1, where Φ is the
phase angle of current from voltage. If current is
leading, take the angle of If2 as (90-Φ).
5. Find the resultant field current, If and mark its
magnitude on the field current axis.
6. From OCC. find the voltage corresponding to If, which
will be E0.
Voltage regulation - MMF method
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Voltage regulation - MMF method
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Tests:
Conduct tests to find
1. OCC (upto 125% of rated voltage)
2. SCC (for rated current)
3. ZPF (for rated current and rated voltage)
4. Armature Resistance (if required)
Voltage regulation- ZPF method
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Voltage regulation- ZPF method
1. plot OCC and SCC
2. Draw tangent to OCC (air gap line)
3. Conduct ZPF test (using purely
inductive load at rated current and
rated voltage) at full load for
rated voltage and fix the point B.
4. Draw the line BH with length equal
to field current required to produce
full load current at short circuit.
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5. Draw HD parallel to the air gap line so as to touch the OCC.
6. Draw DE parallel to voltage axis. Now, DE represents
voltage drop IXL and BE represents the field current
required to overcome the effect of armature reaction.
Triangle BDE is called Potier triangle and XL is the
Potier reactance
7. Find E from V, IXL and Φ. Consider Ra also if required.
The expression to use is
8. Find field current corresponding to E.
Voltage regulation- ZPF method
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8. Find field current corresponding to E.
9. Draw FG with magnitude equal to BE at angle (90+Ψ)
from field current axis, where Ψ is the phase angle
of current from voltage vector E (internal phase
angle).
10. The resultant field current is given by OG. Mark this
length on field current axis.
11. From OCC find the corresponding E0.
Voltage regulation- ZPF method
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ASA method
Tests: Conduct tests to find
1. OCC (upto 125% of rated voltage)
2. SCC (for rated current)
3. ZPF (for rated current and rated voltage)
4. Armature Resistance (if required)
Voltage regulation- ASA method
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Voltage regulation- ASA method Steps:
1. Follow steps 1 to 7 as in ZPF method.
2. Find If1 corresponding to terminal
voltage V using air gap line (OF1 in
figure).
3. Draw If2 with length equal to field
current required to circulate rated current
during short circuit condition at an angle
(90+Φ) from If1. The resultant of If1 and
If2 gives If (OF2 in figure).
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4. Extend OF2 upto F so that F2F accounts for the
additional field current accounting for the effect of
saturation. F2F is found for voltage E as shown.
5. Project total field current OF to the field current axis
and find corresponding voltage E0 using OCC.
Voltage regulation- ASA method
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Load Characteristics of Synchronous Generator
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Load Characteristics of Synchronous Generator
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Load Characteristics of Synchronous Generator
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Load Characteristics of Synchronous Generator
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While If and N constant, V changes with IL in the
armature and the relationship between the Vand IL of
an alternator is known as its load characteristics.
Load Characteristics of Synchronous Generator
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In salient pole machines the air gap is not uniform
Minimum along the polar axis and maximum along the inter
polar axis.
So, in a salient-pole machine, the two mmfs do not act on the
same magnetic circuit.
Consequently the methods for finding out the regulation of
cylindrical rotor machines when applied to salient pole
machines give incorrect results .
In case of salient pole machines regulation is found out by
applying Blondel’s two reaction theory.
REGULATION OF SALIENT POLE SYNCHRONOUS MACHINE
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According to this theory two axes are recognized in the
machine theory
1. Along the polar axis called the direct axis or d-axis
2. Component acting at right angles to the pole axis called the
quadrature axis or q-axis
BLONDELS TWO REACTION THEORY
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The direct axis component is magnetising or demagnetising.
Quadrature component axis is cross magnetising.
Fig shows the stator m.m.f. wave and the flux distribution in
the air gap along direct axis and quadrature axis of the pole.
BLONDELS TWO REACTION THEORY
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The field winding wound on salient poles produces the m.m.f.
wave (Ff) which is nearly sinusoidal and it always acts along
the direct axis.
m.m.f. Ff always acts along the direct axis.
Due to this m.m.f, emf (Ef ) is produced and it lags Ff by 90o .
Armature carries current Ia, produces its own m.m.f. wave FAR.
This Ia and FAR resolved in two components, one acting along
d-axis and other along quadrature axis.
These components are denoted as, Fd & Fq and Id & Iq
BLONDELS TWO REACTION THEORY
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The positions of FAR, Fd and Fq in space are shown in the Fig.
The instant chosen to show these positions is such that the
current in phase R is maximum positive and is lagging Ff by
angle Ψ.
BLONDELS TWO REACTION THEORY
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The phasor diagram corresponding to the positions considered is shown in the Fig. The Ia lags Ef by angle Ψ.
BLONDELS TWO REACTION THEORY
• Fd is produced by Id which is at 90o to Ef
• Fq is produced by Iq in phase with Ef .
• Flux components of ΦAR are Φd and Φq
• It can be seen that the reactance offered to
flux along direct axis is less than the
reactance offered to flux along quadrature
axis.
• Due to this, the flux ΦAR is no longer along
FAR or Ia.
• Depending upon the reluctances offered
along the direct and quadrature axis, the
flux ΦAR lags behind Ia.
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Φd = Pd Fd where Pd = permeance along the direct axis
Permeance is the reciprocal of reluctance
But Fd = m.m.f. = Kar Id in phase with Id
The m.m.f. is always proportional to current. While Kar is the
armature reaction coefficient.
... Φd = Pd Kar Id
Similarly Φq = Pq Kar Iq
As the reluctance along direct axis is less than that along
quadrature axis, the permeance Pd along direct axis is more than
that along quadrature axis, (Pd Pq ).
The phasor diagram corresponding to the positions considered is shown in the Fig. 3. The Ia lags Ef by angle Ψ.
BLONDELS TWO REACTION THEORY
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Let Ed and Eq be the induced e.m.f.s due to the fluxes Φd and Φq
Ed lags Φd by 90o while Eq lags Φq by 90o .
where Ke = e.m.f. constant of armature winding
The resultant e.m.f. is the phasor sum of Ef, Ed and Eq.
The phasor diagram corresponding to the positions considered is shown in the Fig. 3. The Ia lags Ef by angle Ψ.
BLONDELS TWO REACTION THEORY
Substituting expressions for Φd and Φq
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Now Xard = Equivalent reactance corresponding to the d-axis
component of armature reaction = Ke Pd Kar
Xarq = Equivalent reactance corresponding to the q-axis
component of armature reaction = Ke Pq Kar
For a realistic alternator we know that the voltage equation is,
where Vt = terminal voltage
XL = leakage reactance
BLONDELS TWO REACTION THEORY
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Substituting in expression for ĒR ,
Xd = d-axis synchronous reactance
= XL +Xard
Xq = q-axis synchronous reactance
= XL + Xarq
BLONDELS TWO REACTION THEORY
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In the phasor diagram shown in Fig. the angles Ψ and δ are not
known, through Vt, Ia and Φ values are known. Hence the
location of Ef is also unknown.
Determination of Ψ
BLONDELS TWO REACTION THEORY
Id = Ia sinΨ
Iq = Ia cosΨ
cosΨ = Iq/Ia
Ia Ra has two components
Id Rd = drop due to Ra in phase with Id
Iq Ra = drop due to Ra in phase with Iq
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Detail phasor diagram
The Id Xd and Iq Ra can be drawn leading Id and Iq by 90o
respectively.
BLONDELS TWO REACTION THEORY
Id = Ia sinΨ
Iq = Ia cosΨ
cosΨ = Iq/Ia
Ia Ra has two components
Id Ra = drop due to Ra in phase with Id
Iq Ra = drop due to Ra in phase with Iq
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cosΨ = Iq/Ia
Thus point C can be located. Hence the direction of Ef is also known.
Now triangle ODC is also right angle triangle,
BLONDELS TWO REACTION THEORY
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Now triangle ODC is also right angle triangle,
δ = Ψ - Φ for lagging p.f.
BLONDELS TWO REACTION THEORY
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PROCEDURE:
1. Connections are made as per the circuit diagram.
2. Initially set field regulator, 3-ɸ variac at minimum position and TPST switch open.
3. The DC motor is started slowly by sliding starter handle and it is run at a speed slightly less than the synchronous speed of the alternator.
4. Close the TPST switch.
5. With field winding left open, a positive sequence balanced voltages of reduced magnitude (around 25% of rated Value) and of rated frequency are impressed across the armature terminals.
Slip Test
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6. The prime mover (DC motor) speed is adjusted till ammeter and voltmeters pointers swing slowly between maximum and minimum positions.
7. Under this condition , readings of maximum and minimum values of both ammeter and voltmeter are recorded
Slip Test
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