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RGPV EX 503 Unit IV notes on electrical Machines II
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1
Prof MD Dutt HOD Ex Department SRCT Bhopal
READING MATERIAL FOR B.E STUDENTS
OF RGPV AFFILIATED ENGINEERING COLLEGES
SUBJECT ELECTRICAL MACHINES II
Professor MD Dutt
Addl General Manager (Retd)
BHARAT HEAVY ELECTRICALS LIMITED
Professor(Ex) of EX Department
Bansal Institute of Science and Technology
KOKTA ANANAD NAGAR BHOPAL
Presently Head of The Department ( EX)
Shri Ram College Of Technology
Thuakheda BHOPAL
Sub Code EX 503 Subject Electrical Machines II
UNIT IV Synchronous Machines II
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Prof MD Dutt HOD Ex Department SRCT Bhopal
RGPV Syllabus
EX503 ELECTRICAL MACHINES II
UNIT IV SYNCHRONOUS MACHINES II
Salient pole machine, two reaction theory equivalent circuit model and phasor
diagram. Determination of Xd and Xq by slip test, SCR and its significance,
Regulation of salient pole alternator, power angle equation and characteristics,
synchronizing of alternator with infinite bus bar, parallel operation and load
sharing, synchronizing current, synchronizing power and synchronizing coefficient
, synchroscope and phase sequence indicator, effect of varying excitation and
mechanical torque
INDEX
S No Topic Page
1 Salient pole machine, two reaction theory equivalent circuit
model and phasor diagram
3,4,5
2 Determination of Xd and Xq by slip test, SCR and its
significance
6,7,8
3 Regulation of salient pole alternator 9,10
4 Power angle equation and characteristics 11,12
5 Synchronizing of alternator with infinite bus bar 13,14,15
6 Parallel operation and load sharing 15
7 synchronizing current, synchronizing power and
synchronizing coefficient
16,17
8 Synchroscope and phase sequence indicator 17,18
9 Effect of varying excitation and mechanical torque 18,19,20,26
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Prof MD Dutt HOD Ex Department SRCT Bhopal
SALIENT POLE MACHINE, TWO REACTION THEORY, EQUIVALENT
CIRCUIT MODEL AND PHASOR DIAGRAM
Salient pole machines have the non uniform air gap. In case of cylindrical
rotor machines the air gap is uniform. The protruding or projected pole
structure of the rotor of salient pole machine makes the air gap highly non
uniform. The axis of symmetry of north magnetic poles is negative d axis.
The axis of symmetry half way between adjacent north and south poles is
quadrature axis or q axis.
TWO REACTION THEORY:- The theory proposes to resolve the armature m.m.f
into two components, with one located along the axis of rotor salient pole, It
is known as direct axis or d axis component. The other component is located
perpendicular to the axis of the rotor salient pole, It is known as the
quadrature axis or q axis. The d axis component of armature m.m.f Fa is
denoted Fd and the q axis component by Fq. The component Fq results in a
cross magnetizing effect. If Ψ is the angle between armature current Ia and
excitation voltage Ef, the amplitude of Fa of armature m.m.f is than
Fd = Fa sinΨ , Fq = Fa cos Ψ
The armature current produces stator magnetic motive force Fs the m.m.f
lags behind Ia by 90º. The m.m.f Fs produces magnetic field Bs along the
direction of Fa. The Fs stator m.m.f is resolved into two components namely
Fd and Fq.
If Φd = direct axis flux and Φq = quadrature axis flux
Rd = direct axis reluctance path
x path, Rq = q axis reluctance path
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Prof MD Dutt HOD Ex Department SRCT Bhopal
Than Φd = Fd/ Rq Φq = Fq/Rq
Since Rd < Rq The direct axis component of mmf Fd produces more flux
than the quadrature axis component of m.m.f Fq. The direct and quadrature
axis stator fluxes produces voltages in stator windings by armature reaction
Ead = direct axis component of armature reaction voltage
Eaq = quadrature axis component of armature reaction voltage
Since each armature reaction voltage is directly proportional to its stator
current and lags behind by 90º. Therefore the armature reaction voltages can
be written as
Ead = - JXad Id
Eaq = -j Xaq Iq
The value of Xaq is always less than Xad since the e.m.f induced by a given
m.m.f acting on direct axis due to its higher reluctance. The total voltage
E’ = Ef +Ead + Eaq
E’ = Ef –jXad Id– jXaq Iq
Xad = armature reaction reactance in the direct axis per phase
Xaq = armature reaction reactance in the quadrature axis per phase
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Prof MD Dutt HOD Ex Department SRCT Bhopal
Since the emf induced by a given m.m.f acting on direct axis is smaller than
for the quadrature axis due to its higher reluctance The total voltage induced
in the stator is sum of e.m.f’s induced by the field excitation.
E’ = Ef +Ead + Eaq
E’ = Ef –jXad Id– jXaq Iq
The voltage E’ is equal to terminal voltage V plus the voltage drop in
resistance and leakage reactance of the armature.
E’ = V +Ia Ra + jXlIa
Ia is split into two components
Ia = Id +Iq
Ef = V +IaRa +jXadId +jXaqIq +jXlIa
Ef = V Ra ( Id + Iq) +jXad Id +jXaqIq +jXl( Id +Iq)
Ef = V + Ra (Id+Iq) +j(Xl+Xad) Id +j (Xl+Xaq) Iq
Xd = Xl+Xad
Xq = Xl+Xaq
We get Ef = V +IaRa + JXd Id + jXqIq
Phasor Diagram:- The complete Phasor diagram of a salient pole generator based
on the two axis theory is drawn here below with lagging power factor.
PHASOR DIAGRAM
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Prof MD Dutt HOD Ex Department SRCT Bhopal
Simplified Phasor diagram of salient pole synchronous generator at lagging power
factor. In the above diagram angle Ψ =Φ+δ is not known for given values of
V. Ia and Φ, The components Id and Iq of the armature current are usually
not given. These component currents depend upon δ which is to be
determined.
Iq = Ia _Id
Ef = V +RaIa +jXdId +JXq(Ia_Id)
Ef = V +RaIa +jXqIa +j(Xd-Xq)Id
We have
Id = Iasin Ψ and Iq = Ia cosΨ
In the following Phasor diagram drawn below BC is drawn at 90º to Ia and CD is
drawn perpendicular to Ef In Triangle BCD ∟BCD =Ψ
cosΨ =CD/BC = XqIq/BC , BC = XqIq/cosΨ = Xq ( Iacos Ψ) = XqIa
cos Ψ
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Prof MD Dutt HOD Ex Department SRCT Bhopal
Thus the line BC represents the Phasor JXqIa and its end point M such that the
direction of Ef. Now BC is extended to point M such that the distance BM =
XdIa or CM =(Xd-Xq)Ia. The line MN is drawn perpendicular to Ef making
the angle Ψ at point M, which makes CN = (Xd-Xq)Ia sin Ψ = (Xd_Xq)Id.
The point N is the end point of Ef, from triangle OCK
Tan Ψ +CK/OK = KB+BC = VsinΦ +XqIq
OL +LK VcosΦ +RaIa
Ψ = Tan ¯¹ VsinΦ +XqIq
VcosΦ +RaIa
Ψ = δ +Φ or δ = Ψ – Φ
Once δ is known , Id and Iq can be easily found. The magnitude of excitation
voltage Ef can be determined either from the Phasor diagram or from the
following equation
IEfI =Vcosδ + RaIq + Ra Id
Determination of δ If the armature resistance is neglected the equation becomes
Tanδ = XqIa cosΦ
V + XqIa sinΦ
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Prof MD Dutt HOD Ex Department SRCT Bhopal
DETERMINATION OF Xd and Xq BY SLIP TEST,
In a simple no load test or slip test, a small voltage at rated frequency of rated
value is applied to the stator winding. The field winding is kept open circuited. The
rotor is driven by an auxiliary motor at a speed slightly less or more than
synchronous speed. Note the direction of rotation it should be same as that the
rotating field of stator . a small voltage reading V2 is indicated by the voltmeter
across the open field winding terminals shows that the direction of rotation of rotor
is proper. Since the rotor is rotating at speed ήr close to ήs there will be small slip
between the rotating magnetic field produced by the armature mmf and the field
poles is equal to slip speed ήs – ήr . Since stator m.m.f moves slowly past the
actual field poles, There will be an instant when the peak of armature mmf wave is
in line with axis of actual salient field poles. This axis is along the d axis. In this
position, the armature flux linkage with field winding is maximum and the rate of
change of this flux linkage is zero. Therefore the induced voltage across the field
winding is zero. The d axis can therefore be located on the oscillogram. From the
figure Xd = ab/cd , also the ratio of armature terminal voltage per phase to the
corresponding current per phase to the armature current gives Xd
Also, the ratio of armature terminal voltage per phase to the corresponding current
per phase gives Xd.
After one quarter of slip cycle the peak armature wave is in line with q axis. In this
position, the reluctance offered by long air gap is maximum as shown in figure b .
a large magnetizing current is needed to establish the same air gap flux. This
maximum current Imax is measured from the line ammeter A. Also in this position,
the armature flux linking the field winding is zero, and the arte of change of this
flux linkage is maximum. Consequently the field winding is zero, and the rate of
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Prof MD Dutt HOD Ex Department SRCT Bhopal
change of flux linkage is maximum. Consequently, the induced voltage across the
field winding is maximum. Thus q axis can also be located on the oscillogram.
From this
Xq = a’b’/c’d’.
Also the ratio of armature terminal voltage per phase to the corresponding
armature current per phase given Xq.
The slip test is generally used to find out ratio Xd/Xq . the direct axis synchronous
reactance Xd is determined from open and short circuit test as in the case of
cylindrical rotor machine. Knowing Xd from O.C and S.C test and ratio Xd/ Xq
from slip test we can find out Xq.
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Prof MD Dutt HOD Ex Department SRCT Bhopal
SCR AND ITS SIGNIFICANCE
The short circuit ratio (SCR) of synchronous machine is defined as the ratio of the
field current required to generate rated voltage on open circuit to the field current
required to circulate rated armature current on short circuit.
The short circuit ratio SCR can be calculated from the open circuit characteristics
(O.C.C) at rated speed and short circuit characteristics of three phase synchronous
machine.
SCR = If for rated O.C Voltage = Oa
If for rated S,C Current Od
Since triangle Oab and Odc are similar
SCR = Oa = ab
Od de
The direct axis synchronous reactance Xd is defined as the ratio of open circuit
voltage for given current to the armature short circuit current for the same field
current
XdΩ = ac
ab
The per unit value of Xd is given by
Xdpu = XdΩ
Base impedance
But base impedance = Per phase rated voltage
Per phase rated armature current
= Vrated = ac Ω
Ia rated de
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Prof MD Dutt HOD Ex Department SRCT Bhopal
Therefore Xd pu = ac · de = de
ab ac ab
SCR = ab = 1 = 1
de ( de/ab) Xd pu
The SCR is equal to the reciprocal of per unit value of the direct axis synchronous
reactance.
SIGNEFICANCE OF SCR
The SCR is an important factor for the synchronous machine. It affects the
operating characteristics, Physical size and cost of the machine. With a low value
of S.C.R a synchronous generator has a large variation in terminal voltage with a
change in load. That is the machine is very sensitive to load variations. In order to
keep the terminal voltage constant, field current is to be varied over a wide range.
The synchronizing power is small if the SCR small. Since the synchronizing power
keeps the machine in synchronism, a low SCR is less stable when operating in
parallel with other generators. But the armature current under shrt circuit
conditions is small for a low SCR.
A synchronous machine with high value of SCR has better voltage regulation and
improved steady state stability limit but the short circuit fault current in the
armature is high.
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Prof MD Dutt HOD Ex Department SRCT Bhopal
REGULATION OF ALTERNATOR
Draw the Phasor diagram OB = V to represent 100% voltage at full load. The
current Phasor I = OA is drawn at angle Cos¯¹θ, the lagging P.F behind V, The
resistance voltage drop IR is drawn parallel to I. The leakage reactance drop Ix is
drawn oerpendicular to I. The Phasor sum of
V,Ir = IXs ( OD=E)
Therefore OD = V volts
From OCC the field current required to get V volts is say Io, draw OM
perpendicular to Phasor E to represent excitation required to induce emf E. The
field current equivalent to full load armature reaction on short circuit is MN and is
parallel to current Phasor I. Take a point S on MN such that MS= KMN, where K
is the ratio of cross reaction to the direct axis reaction per ampere turn.
Suppose K = 0.5 in that case it will be at mid point of MN. Join OS and draw a
perpendicular NG on OS produced. The OG is required excitation, OY is the
Phasor sum of OM & MH. Measure OG in amps, from OCC find out the voltage
fro OG amps The EMF induce is Ex
Therefore the % regulation = Ex-Vo X100
Vo
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Prof MD Dutt HOD Ex Department SRCT Bhopal
POWER ANGLE EQUATION AND CHARACTERISTICS,
The resistance Ra of the armature has negligible effect on the relationship between
the power out put of a synchronous machine and its torque angle δ. It may
therefore may be neglected. The power diagram of lagging P.F for salient pole
alternator neglecting Ra is drawn
Complex power output per phase SiΦ = V Ia۰
Taking Ef as the reference Phasor
V = V∟-δ = Vcosδ – jVsinδ
Iq +jId =Ia۰
erThrehT SiΦ = V Ia ۰
= ( V cosδ -jsinδ) ( Iq+jId) Equation I
XqIq = CD = AM = Vsinδ
Therefore Iq = Vsinδ /Xq
XdId = AC= MD=OD-OM = Ef –Vcosδ
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Prof MD Dutt HOD Ex Department SRCT Bhopal
Id = (Ef- V cosδ)/Xd
SiΦ = (Vcosδ – jVsinδ) (Vsinδ /Xq) + j(Ef- V cosδ)/Xd
Substituting the values of Iq and Id in the equation I we get
SiΦ = (Vcosδ – jVsinδ) [(Vsinδ /Xq) + j(Ef- V cosδ)/Xd]
= [V²cosδsinδ/Xq + VEfsinδ/Xd -V²cosδsinδ/Xd] + j [VEfcosδ/Xd -V²cos²δ/Xd
- V²sin²δ/Xq]
= [VEfsinδ/Xd +(V²/2)[ (1/Xq-1/Xd)sin2δ] +j [ (VEf cos /Xd) –
(V²/2XdXq)(Xd+Xq) – (Xd-Xq) Cos2δ]
Also S1Φ = P1Φ + j Q1Φ
P1Φ = [VEfsinδ/Xd +(V²/2)[ (1/Xq-1/Xd)sin2δ] real power in watts for single
phase
P3Φ = 3 P1Φ =3 [VEfsinδ/Xd +(V²/2)[ (1/Xq-1/Xd)sin2δ]
The reactive power
Q1Φ =[ (VEf cos /Xd) – (V²/2XdXq)(Xd+Xq) – (Xd-Xq) Cos2δ]
Q3 Φ = 3 Q1Φ = 3[ (VEf cos /Xd) – (V²/2XdXq)(Xd+Xq) – (Xd-Xq) Cos2δ]
The real power is the same as that obtained in the case of cylindrical rotor
machine. The reactive power depends upon the saliency defined by the quantity [
1/Xq-1/Xd]. The saliency disappears when Xd= Xq That is for cylindrical
rotor)Also this term disappears even when there is no field current ( Ef=0). The
equation for active power and reactive power is applicable for the generator and for
the synchronous motor. The torque angle δ is positive for generator and negative
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Prof MD Dutt HOD Ex Department SRCT Bhopal
for motor. P- Q curve i.e verses δ curves for salient pole machine is as shown
below.
The electromagnetic torque or torque developed for a 3 phase synchronous
machines is given by
Tem = 3P1Φ/ώm = 3 [ Efsinδ + (Xd – Xq)sin2δ ]
2Пήs Xd 2Xd Xq
The resulting torque so developed has two components , The first term represents
Texc due to field excitation
Texc = 3 Efsinδ
2Пήs Xd
The second term is the reluctance torque Trel = 3 [(Xd – Xq) ]sin2δ
2Пήs 2Xd Xq
The reluctance torque is independent of excitation and exists only if the machine is
connected to a system receiving reactive power from the synchronous machine
operating in parallel with terminal voltage V.
The reluctance torque is due to the saliency of field poles which tend to align the
direct axis with that of the armature mmf. It is to be noted that if there is no field
current Ef=0, the first term
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Prof MD Dutt HOD Ex Department SRCT Bhopal
VEf sinδ/ Xd becomes zero, and the machine still has some power generation.
However it is impractical to operate the synchronous machine without field
excitation on a power system, because it would supply only about 25% or less of
its real power rating. Also it will absorb an excessive amount of reactive power.
The maximum reluctance torque occurs at δ =45º.
The power angle ( P –δ) curve for a salient pole machine is shown . It is to be
noted that peak power or steady state limit occurs at a value of δ less than 90º,
The value δmax depends on the relative magnitude of V, Ef and saliency.
SYNCHRONISING OF ALTERNATOR WITH INFINITE BUS BAR.
In a power system more than one alternator operate in parallel. The machines may
be located at different places. The machines, connected to the same bus but
separated by transmission lines of low reactance’s. The capacity of system is so
large that its voltage and frequency may be taken as constant. The connection or
disconnection of single machine or a small load on such system would not effect
the voltage and frequency. The system behaves like a large generator having
virtually zero internal impedance and infinite rotation inertia. Such a system of
constant voltage and constant frequency regardless of load is called infinite bus bar
system.
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Prof MD Dutt HOD Ex Department SRCT Bhopal
The characteristics of infinite bus bars are as follows:-
a) The terminal voltage remains constant, because incoming machine is too
small to increase or decrease it.
b) The frequency remains constant, because the rotational inertia is too large to
enable the incoming machine to alter the speed of the system.
c) The synchronous impedance is very small since the system has large number
of alternators in parallel.
In an isolated operation, the change of excitation changes the terminal voltage,
the power factor depends on the load only. When an alternator is working in
parallel with an infinite bus and its excitation is change, The P.F of the machine
changes. However change in excitation does not change the terminal voltage.
Which is held constant by the system.
AN ALTERNATOR CONNECTED TO AN INFINITE BUS HAS THE
FOLLOWING OPERATING CHARACTERISTIC
1) The terminal voltage and frequency of generator are controlled by system to
whom it is connected.
2) The governor set point of the alternator control the real power supplied to
infinite bus
3) The field current in the alternator controls the reactive power supplied by the
alternator to the infinite bus. Increasing field current in the alternator
operating in parallel with an infinite bus increases the reactive power output
of the alternator.
OBTAINING INFINITE BUS
a) Proof of voltage remaining constant
V= terminal voltage, E = induced EMF in each generator, Zs =
Synchronous impedance, n=no off generators in parallel.
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Prof MD Dutt HOD Ex Department SRCT Bhopal
V=E-IZseq, Zseq= Zs/n
When n is very large Zseq 0, Izseq = 0
Therefore V = E constant.
b) Proof of frequency remaining constant
Let J = Moment Inertia of each alternator
Total moment of inertia = J1 +j2+j3 +……….. Jnd = nf
Acceleration of alternator = accelerating torque / moment of inertia
τa = τa
∑j nj
If n is very large so n j will also be large
Therefore acceleration = 0 and thus the speed is constant.
SYCHRONISING POWER, PARALLEL OPERATION AND LOAD
SHARING OPERATION ON INFINITE BUS
SYCHRONISING POWER:- When a synchronous machine is
synchronized to infinite bus bars has a inherent tendency to remain in
synchronism. Consider a synchronous machine is transferring steady
state power P o at a steady load angle δ o, Suppose due to transient
disturbances, the rotor of generator accelerates, so that the load angle
increases to dδ. The operating point of the machine shifts to a new
constant power line and the load on the machine increase to P o +dδ.
Since Te steady power input remains unchanged this additional load
decreases the speed of the machine and brings it back to synchronism.
Similarly, if due to transient disturbances the rotor of the machine
retards, so that the load angle decreases, the operating point of the
machine shifts to a new constant power line and the load ion the machine
decreases to P o –dδ. Since the steady power remains same, the reduction
in load accelerates the rotor, consequently the machine again comes in
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Prof MD Dutt HOD Ex Department SRCT Bhopal
synchronism. It is seen that the effectiveness of this correcting action
depends on the change in power transfer for a given change of load angle.
A measure of effectiveness is given by Synchronizing power coefficient.
It is defined as rate at which the synchronous power P varies with load
angle. It is also called stiffness factor, rigidity factor or stability factor
and is denoted by Psyn
Psyn = ∆ dP/dδ
In a salient pole machine
P= VEfsinδ/Xs +(V²/2)[ (1/Xq-1/Xd)]sin2δ
Psyn = VEfcosδ/Xs +V²[ (1/Xq-1/Xd)]cos2δ
PARALLEL OPERATION
Electric power system are interconnected for economy and reliable operations.
Interconnection of ac power system requires synchronous generator’s to operate in
parallel with each other. In a generating stations two or more generators are
connected in parallel. In an interconnected system forming a grid the alternators
are located at different places. They are connected in parallel by means of
transformers and transmission lines.
An arrangement of generators for parallel operation enable a plant engineer to
adjust the machines for optimum efficiency and greater reliability. As the load
increases beyond the generating capacity of the connected units, Additional
generators’ are paralleled to carry the load. Similarly as the load demand falls off
one or more of the machines are generally taken off the line to allow the units to
operate at a higher efficiency.
ADVANTAGES
1. Several alternators can supply a bigger load than single alternator.
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Prof MD Dutt HOD Ex Department SRCT Bhopal
2. During light load, one or more alternators may be shut down, and
those remaining operates at or near full load, and thus more
efficiency.
3. When one machine is taken out of service for maintenance and
inspection, the remaining machines maintain the continuity of supply.
4. If there is a breakdown of a generator, there is no interruption of
power supply.
5. In order to meet the increasing future demand of load more machines
can be added without disturbing the original machines.
6. The operating cost and cost of energy generated are reduced when
several generator’s operate in Parallel.
CONDITION FOR PARALLEL OPERATION
Most of the synchronous machines will operate in parallel with other synchronous
machine and process of connecting one machine in parallel with another machine
or infinite bus bar system is known as synchronizing. Those machines already
carrying load are known as running machines, while alternators which is to be
connected in parallel with the system is known as incoming machine. Before the
incoming machine is to be connected to the system , the following conditions are to
be satisfied.
i) The phase sequence of the bus bar voltage and the incoming
machine voltage must be same.
ii) The bus bar voltages and the incoming machines voltage must
be in phase.
iii) The terminal voltage of incoming machine should be equal to
that of the alternator with which it is to be run parallel or with
bus bar voltage
iv) The frequency of the generated voltage of the incoming
machine must be equal to the frequency of voltage of bus bar.
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Prof MD Dutt HOD Ex Department SRCT Bhopal
SYNCHRNOUS MACHINES LOAD SHARING OPERATION ON INFINITE
BUS BAR
Consider two alternators are running in parallel . The frequency load
characteristics of two machines is shown below.
W1 = full load rating of machine 1
W2 = full load rating of machine 2
P1 = Power shared by machine 1
P2 = Power shared by machine 2
P = Total power supplied by two machines
fo1 = No load frequency of Machine 1
fo2 =No load frequency of Machine 2
fl1 = Full load frequency of machine 1
fl2 = Full load frequency of machine 2
f = common operating frequency when both the machines are
running in parallel.
MACHINE 1
Drop in frequency from no load to full load = fo1 -- fl1
Drop in frequency per unit rating = fo1 -- fl1
W1
Drop in frequency for a load P1
fl =P1 fo1 -- fl1
W1
Operating frequency = No load frequency – drop in frequency
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Prof MD Dutt HOD Ex Department SRCT Bhopal
f = fo1 -- P1 fo1 -- fl1
W1
MACHINE 2
Similarly for alternator 2 , the operating frequency is
f = fo2 -- P2 fo2 -- fl2
W2
fo1 -- P1 fo1 -- fl1 = fo2 -- P2 fo2 -- fl2
W1 W2
We also know that P = P1+ P2
The above equation is used to determine P1 and P2 and f.
EFFECT OF SYNCHRONIZING CURRENT , HUNTING OF ALTERNATOR
Effect of synchronizing current
Consider a synchronous machine with terminal voltage Vt. Operating at rotor angle
δ, drawing armature current Ia and having excitation emf Ef. A sudden
disturbances causes its rotor angle to increase (δ +∆δ). As we have seen above it
develops synchronizing power Ps which counters the change. The synchronizing
power arise from synchronizing emf Es and synchronizing current Is. As the
terminal voltage is constant the armature equation before after change are
׀ ׀ ( ) = ( )
E s = E f ( ) - E f∟-δ = change in Ef
I s = I a , -I a Change in I a
= E f ( ) - E f∟-δ = - j (I a -I a)Xs
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Prof MD Dutt HOD Ex Department SRCT Bhopal
E s = - jI s Xs where E s is synchronizing emf, and I s = synchronizing current.
I s = E s/- jI s Xs
HUNTING OF ALTERNATOR
A steady state operation of alternator is a condition of equilibrium in running
conditions. With the sudden increase in the load the speed drops and similarly with
decrease of load the speed increases. This type of changes causes hunting of
alternators. The main reasons for hunting are as follows;-
a) Sudden change of load
b) Faults occurring in the system which the generator supplies.
c) Sudden change in field current.
d) Cyclic variation of load.
EFFECTS OF HUNTING
1) It can lead to loss of synchronism
2) It can cause variations of the supply voltages
3) It increases the possibility of resonance
4) Large mechanical stresses may develop in the rotor shaft.
5) The machine losses increases and the temperature of the machine rises.
Out of these effects , the first one is the most important and it is to be
avoided.
The hunting of alternator causes the circulating current also. It always
preferred that the alternator should not operate on hunting condition.
If the hunting prevails in the machine the electrical power fed to the mains
and shaft oscillates, which in turn causes shaft fatigue.
REDUCTION OF HUNTING
Following are some of the technique used to reduce hunting
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Prof MD Dutt HOD Ex Department SRCT Bhopal
a) Use of Damper Winding
b) Use of Fly Wheel
c) By designing synchronous machine.
DAMPER WINDING :- Additional damping is provided in the salient pole
synchronous machine by means of damper bars located in the main pole of the
machine and short circuited through round rings at both ends. These bars acts like a
squirrel cage induction motor. These damper windings are used in synchronous
motors for the starting purpose.
USE OF FLY WHEEL:- The prime mover is provided with a large and heavy fly
wheel. This increases the inertia of the prime mover and helps in maintaining the
rotor speed. The Large Hydro generators having big diameter compare to core
length also works as fly wheel.
DESIGN:- By designing synchronous machines with suitable synchronizing power
coefficients.
SYNCHROSCOPES AND PHASE SEQUENCE INDICATORS
The phase sequence of the generator is checked carefully at the time of installation.
By means of synchroscope the voltage from one phase of incoming machine with
that of the corresponding phase of the three phase system is compared. The
position of the pointer of synchroscope indicates the phase difference between the
voltages of incoming machine and the infinite bus. When the frequencies are equal,
the pointer is stationary. When the frequencies differ, the pointer rotates in one
direction or the other direction. The direction of motion of the pointer shows
whether the incoming machine is running too fast or too slow, that is whether the
frequency of incoming machine is higher or lower than that of infinite bus bar. The
speed of rotation of the pointer is equal to the difference between the frequencies
of incoming machine and infinite bus. The frequency and phase position are
controlled by adjusting the prime mover input to the incoming machine. When the
indicator moves very slowly ( that is the condition when frequencies are almost
same) and passes through the zero phase point ( vertical u position), the circuit
breakers is closed and the incoming alternator is connected to the bus. It is to be
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Prof MD Dutt HOD Ex Department SRCT Bhopal
noted that synchroscope checks relationship only with one phase. It gives no
information for the PH sequence.
The procedure is used for synchronizing synchronous motors with bus bars. When
the motor reaches synchronous speed, the d.c field is excited and if the load is not
excessive, The motor pulls in synchronism with the bus.
PHASE SEQUENCE INDICATORS
The phase sequence indicator is a device used to compare the phase sequence of
three phase generators or motors. One type of phase sequence indicator is tiny
three phase induction motor having and aluminum disc mounted for free rotation
on a cushioned glass hard bearing and having field winding placed at 120º
geometrical degree intervals about the rotor axis. One terminal of each winding is
extended beyond the case to a distinctly colored conductors and to altered test clip
for attachment to one conductor of the system or machine.
The flexible cable withstands severe handling and is meant for suspending the
phase sequence meter from the live wires or terminals with test clips. The cables
are anchored in the sealed housing. It can be used to correlate the motor or
generator conductor or terminal markings with the phase sequence of applied or
generated voltage. This type phase sequence meter avoids reversal of a generator
phase rotation when being paralleled, which would avoid short circuits. The three
leads of the Phase sequence indicators are colored RED, YELLOW and BLUE.
The RED colored wire is for phase A and Yellow for B and blue for C Phases. The
rotor in the instrument can be observed through the three ports at which it turns so
that we can note the direction in which it is rotating. The rotor can be started by
means of a momentary switch, it stops when we release the switch. It is necessary
to determine the phase sequence of line and alternator’s before synchronizing. This
can be easily checked by using Phase Sequence Indicators./
EFFECT OF VARYING EXCITATION AND MECHANICAL TORQUE
From the power curves for salient pole machines drawn in relation with δ. The
torque angle is positive for generator and negative for motor. The electromagnetic
torque or torque developed for a 3 phase synchronous machine is given by
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Prof MD Dutt HOD Ex Department SRCT Bhopal
τem = 3P1Φ/ώm = 3 [ V Efsinδ + (Xd – Xq)sin2δ ]
2Пήs Xd 2Xd Xq
It is be noted that the resulting torque has two components, the first term represents
the torque τexc due to field excitation
τexc = 3 V Efsinδ
2ПήsXd
The second term is known as reluctance torque
τrel = 3 [(Xd – Xq) ]sin2δ
2Пήs 2Xd Xq
The reluctance torque is independent of excitation and exists only if the machine is
connected to a system receiving reactive power from other synchronous machines
operating in parallel with the terminal voltage V.
The reluctance torque is due to the saliency of the field poles which tend to align
the direct axis with that of the armature m.m.f.
It is to be noted that if there is no field current or no field excitation
Ef = 0
The term V Efsinδ becomes zero, and the machine still has some power
Xd generation capability
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Prof MD Dutt HOD Ex Department SRCT Bhopal
However, it is impractical to operate a synchronous generator without field
excitation on a power system., because it would supply only 25% or less of its real
power rating. Also it would absorb an excessive amount of reactive power.
If an attempt is made to cause the machine to act as a generator or motor no field
current ( V supplied by the bus to which the machine is connected) , the poles shift
relative to the stator field, thus increasing the reluctance of the flux path as the
torque increase, For this reason the torque given by the following equation is called
the reluctance torque.
τrel = 3 [(Xd – Xq) ]sin2δ
2Пήs 2Xd Xq
The maximum value of this reluctance torque occurs at δ =45º It is to be noted that
peak power or steady state limit occurs at a value of δ less than 90º. The value of
δmax depends on the relative magnitude of V,Ef and saliency.
In general the value of δ decides whether the machine is overexcite generator or
motor supplies reactive power to the bus bars, and an under excited generator or
motor consumes or absorbs reactive power from bus bars.
The power angle ( P -- δ) curve for a salient pole machine drawn is as follows