Prof. Tejas H. Panchal Electrical Engineering Department · Parallel Operation of Alternators • The process of switching of an alternator to another alternator or with a common

Alternators

Prof. Tejas H. Panchal

Electrical Engineering Department

Zero Power Factor Method

• This method is also called potier method. In the operation of any alternator, thearmature resistance drop and armature leakage reactance drop IXL are actually e.m.f.quantities while the armature reaction is basically m.m.f. quantity. In the synchronousimpedance method all the quantities are treated as e.m.f. quantities as against this inM.M.F. method all are treated as m.m.f. quantities.

• This method is based on the separation of armature leakage reactance andarmature reaction effects. The armature leakage reactance XL is calledPotier reactance in this method, hence method is also called potierreactance method.

• To determine armature leakage reactance and armature reaction m.m.f.separately, two tests are performed on the given alternator. The two testsare, 1. Open circuit test 2. Zero power factor test

Zero Power Factor Method (Cont….)

1. Open circuit test:

Experimental setup for ZPF method


1. Open circuit test:

• The steps to perform open circuit test are,

1. The switch S is kept open.

2. The alternator is driven by its prime mover at its synchronous speed and same is

maintained constant throughout the test.

3. The excitation is varied with the help of potential divider, from zero upto rated value

in definite number of steps. The open circuit e.m.f. is measured with the help of

voltmeter. The readings are tabulated.

4. A graph of If and (Voc) i.e. field current and open circuit voltage per phase is plotted

to some scale. This is open circuit characteristics.


2. Zero power factor test:

• To conduct zero power factor test, the switch S is kept closed. Due to this, a purely

inductive load gets connected to an alternator through an ammeter. A purely inductive

load has power factor of cos i.e. zero lagging hence the test is called zero power factor

test.

• The machine speed is maintained constant at its synchronous value. The load current

delivered by an alternator to purely inductive load is maintained constant at its rated

full load value by varying excitation and by adjusting variable inductance of the

inductive load.

• Note that, due to purely inductive load, an alternator will always operate at zero p.f.

lagging.


• In this test, there is no need to obtain number of points to obtain the curve. Only two

points are enough to construct a curve called zero power factor saturation curve.

• This is the graph of terminal voltage against excitation when delivering full load zero

power factor current.

• One point for this curve is zero terminal voltage (short circuit condition) and the field

current required to deliver full load short circuit armature current. While other point is

the field current required to obtain rated terminal voltage while delivering rated full

load armature current.

• With the help of these two points the zero p.f. saturation curve can be obtained as,



1. Plot open circuit characteristics on graph as shown in the Fig.

2. Plot the excitation corresponding to zero terminal voltage i.e. short circuit full loadzero p.f. armature current. This point is shown as A in the Fig. which is on the x-axis.Another point is the rated voltage when alternator is delivering full load current atzero p.f. lagging. This point is P as shown in the Fig.

3. Draw the tangent to O.C.C. through origin which is line OB as shown dotted in theFig. This is called air line.

4. Draw the horizontal line PQ parallel and equal to OA.

5. From point Q draw the line parallel to the air line which intersects O.C.C. at point R.Join RQ and join PR. The triangle PQR is called potier triangle.

6. From point R, drop a perpendicular on PQ to meet at point S.


7. Through point A, draw line parallel to PR meeting O.C.C. at point B. From B, drawperpendicular on OA to meet it at point C. Triangles OAB and PQR are similartriangles.

8. The perpendicular RS gives the voltage drop due to the armature leakage reactancei.e. IXL.

9. The length PS gives field current necessary to overcome demagnetizing effect ofarmature reaction at full load.

10. The length SQ represents field current required to induce an e.m.f. for balancingleakage reactance drop RS.


• In numerical, first determine full load current and rated phase voltage from the rating.

• From Potier triangle determine leakage reactance drop IXL i.e. voltage correspondingto RS.

• Determine filed current AB required to overcome demagnetizing effect of armaturereaction i.e. length PS.

• Determine IaRa drop. Then determine E using the formula

• From O.C.C. determine field current OA required for E.

• Determine total field current OB.

• From O.C.C. determine e.m.f. E0 corresponding to this total

field current OB.

2 2( cos ) ( sin I )a a a LE V I R V X

O A

B

90+φ

Operation of a Salient Pole Synchronous Machine

• Cylindrical rotor SM has uniform airgap, so its reactance remains same. HenceCylindrical rotor SM possesses one axis of symmetry (direct axis)

• Non salient SM has non-uniform airgap, so its reactance varies with rotor position.Hence, it possesses two axis of geometric symmetry

1. filed pole axis called direct or d-axis

2. axis passing through center of the interpolar space called quadrature axis or q-axis

• On d-axis two mmf acts, field mmf and armature mmf

• On q-axis only one mmf acts i.e. armature mmf because field mmf has nocomponent on q-axis

Operation of a Salient Pole Synchronous Machine (Cont.…)


• The magnetic reluctance is low along the poles and high between thepoles

• According to two reaction theory

1. Armature current Ia can be resolved into two components

Id perpendicular to E0 and Iq along E0

2. Armature reactance has two components i.e. d-axis arm. react. Xad

associated with id and q-axis arm. react. Xaq associated with iq


• If we include armature leakage reactance Xl which is same on both axis,we get

• Reluctance on the q-axis is higher because of the larger air-gap, so

d ad l q aq lX X X and X X X

aq ad q d d qX X or X X or X X

Phasor Diagram for a Salient Pole Synchronous Machine

• If Ra is neglected the Phasor diagram becomes as shown in fig.

• Here V is the terminal voltage/phase and E0 is the e.m.f. per phase towhich generator is excited.

0 a a d d q q a d qE V I R j I X j I X and I I I

Phasor Diagram for a Salient Pole Synchronous Machine(Cont.…)

Phasor Diagram for a Salient Pole Synchronous Machine(Cont.…)

Phasor Diagram for a Salient Pole Synchronous Machine (Cont.…)

• The angle 𝛿 between E0 and V is called the power angle.

cos( ) sin( )q a d aI I and I I

0

0

cos

cos sin( ) [ sin( )]

cos (sin cos cos sin ) __(1)

sin

cos( )

sin (cos cos sin sin ) __(2)

d d

a d d a

a d

q q

a q

a q

E V I X

V I X I I

E V I X

Also V I X

I X

V I X

Power Developed by Salient Pole Synchronous Generator

• If we neglect arm. resistance Ra (and hence Cu loss), then power developed(Pd) byan alternator is equal to the power output(Pout)

• The per phase power output of the alternator is

0

0

cos __(1)

cos cos sin

cos

cos

sinsin

out d a

a q d

d d

d

d

q q q

q

P P VI

Now I I I

Also E V I X

E VI

X

Vand V I X I

X

Power Developed by Salient Pole Synchronous Generator (Cont.…)

0

20

2

0

2

0

cos [ cos sin ]

,

cossincos sin

sin cos sin cossin

( ) sin 2sin

2

( )sin sin 2

2

d a q d

q d

d

q d

d q d

d q

d d q

d q

d

d d q

P VI V I I

Putting the values of I and I

E VVP V

X X

E VV

X X X

V X XE V

X X X

V X XE VP p

X X X

__(2)er phase

Power Developed by Salient Pole Synchronous Generator (Cont.…)

• The total power developed would be three times the above power.

1. If there is no saliency, Xd = Xq

• This is the power developed by cylindrical rotor machine.

2. The second term in eq.(2) above introduces the effect of salient poles. It representsthe reluctance power i.e. power due to saliency.

0 sind

d

E VP per phase

X

Parallel Operation of Alternators

• The process of switching of an alternator to another alternator or with a commonbus bar without any interruption is called synchronization.

• Alternatively it can also be defined as the process of connecting the two alternatorsin parallel without any interruption.

• The syn. machine which is to be synchronized is normally called an incomingmachine.

• If any alternator is connected to a bus bar which has many other alternators alreadyconnected, no matter what power it is supplying then alternator is said to beconnected to infinite bus bar.

• An infinite bus bar is one whose frequency and phase e.m.f. remains unaffected bychanges in condition of any one machine connected to it. Thus they are nothing butconstant frequency and constant voltage bus bars.

Parallel Operation of Alternators (Cont…)

Parallel Operation of Alternators (Cont…)

• In case of alternator, stator carries arm. winding which is having small resistance.

• Under stationary conditions e.m.f. induced in stator winding is zero. So if such analternator at stationary condition is connected to bus bar, there is always danger ofshort circuit.

• So it is not a practice to connect a stationary alternator to live bus bars.

Necessary Conditions for Synchronization

• To have effective synchronization without any interruption there are certainconditions to be fulfilled. These conditions are

1. The terminal voltage of the incoming machine must be same as that of bus barvoltage.

2. The frequency must be same as that of the incoming machine as well as that of thebus bar. This necessitates that speed must be properly adjusted (f = PN/120).

3. With respect to the external load, the phase of alternator voltage must be identicalwith that of the bus bar voltage. Alternately we can say that phase sequence for thetwo voltages must be same.

• The above conditions can be satisfied by using a voltmeter, synchronizing lamps orsynchroscope.

• The use of voltmeter will satisfy the first condition.

• By using synchronizing lamps conditions (2) and (3) will be satisfied.

Synchronization of Three Phase Alternators

• In synchronizing three phase alternators, three lamps are connected as shown inFig. 1 so that it can be used to indicate whether the incoming machine is runningslow or fast.

• Consider two alternators A and B to be synchronized. The alternator A is alreadyrunning at synchronous speed and its excitation is so adjusted that it builds up therated voltage.

• The alternator A is connected to the bus bars of constant voltage and frequency. Thealternator B is to be connected to bus bar i.e. it is to be synchronized with alternatorA.

• The process of synchronization can be explained as:

Synchronization of Three Phase Alternators

Fig. 1

Synchronization of Three Phase Alternators (Cont.…)

• Step 1: Start the prime mover of machine. Adjust its speed to a synchronous speedof machine B. This will rotate the rotor of alternator B at synchronous speed.

• Step 2: The switch S4 is then closed. By adjusting the rheostat Rx the excitation tothe field is adjusted so that induced e.m.f. of B is equal to the induced e.m.f. of A.This can be verified by voltmeter.

• Step 3: To satisfy remaining conditions, three lamp pairs are used which are L1, L2

and L3 as shown in Fig 2. These are connected in such a way that pair L1 is straightconnected while the pairs L2 and L3 are cross connected.

• Now two supplies are supplying lamp pairs, ERYB i.e. voltage supply of bus barswhile ER’Y’B’ i.e. supply generated by alternator B. The switch S3 is still open.


Fig. 2


• Let the three bus bar voltages be represented by phasors OR, OY, OB rotating atangular speed of ω1 rad/sec. The incoming alternator voltage are represented byOR’, OY’ OB’ rotating at angular speed ω2 rad/sec.

• The phasor ERR’, joining the tips R and R’ is voltage across lamp pair L1. Similarly

EYB’ and EBY

’ are voltage across lamps L2 and L3 respectively.

• If there is difference between the two frequencies due to difference in speeds of thetwo alternators, the lamps will become dark and bright in a sequence. This sequencetells whether incoming alternator frequency is less or greater than machine A.

• The sequence L1, L2, L3 tells that machine B is faster as the voltage star R’Y’B’ willappear to rotate anticlockwise w.r.t. bus bar voltage RYB at a speed correspondingto difference between their frequencies shown in Fig. 3.


Machine B is Faster

Machine B is Slower

Fig. 3


• The sequence L3, L2, L1 tells that the machine B is slower because voltage starR’Y’B’ will appear to rotate clockwise w.r.t. bus bar voltage RYB. The prime moverspeed can be adjusted accordingly to match the frequencies.

• The synchronization is done at the moment when Lamp L1 is in the middle of darkperiod. If the lamps pair becoming dark and bright simultaneously, it indicatesincorrect phase sequence which can be corrected by interchanging any two leadseither of the incoming machine or of bus bars.

• In this method when lamp L1 is dark the other two lamp pairs L2 and L3 equallybright. So this method of synchronization is called “Lamps bright and dark” method.

Synchronization by Synchroscope

• It can be seen that the previous method is not accurate since it requires correct senseof judgement of the operator. Hence to avoid the personal judgement, the machinesare synchronized by accurate device known as synchroscope.

• It consists of a rotating pointer which indicates the exact moment of closing thesynchronizing switch. If the pointer rotates in anticlockwise direction, it indicates thatincoming machine is running slow whereas clockwise rotation of pointer indicatesthat incoming machine is running faster.

• The rotation of pointer is proportional to the difference in the two frequencies. Thepointer should rotate at a very low speed in the direction of arrow marked ‘Fast’ asshown in the Fig. 4.

Synchronization by Synchroscope (Cont.…)

Fig. 4

Synchronization by Synchroscope (Cont.…)

• When the rotating pointer reaches the vertical position at slow speed, the switch mustbe closed. The pointer will oscillate about some mean position instead of rotating ifdifference in frequencies is large. In such cases the speed of incoming machine isadjusted properly.

• The connections for synchroscope are shown in Fig. 4. Any two bus bars lines areconnected to its terminals while its other terminals are connected to correspondinglines of incoming machine.

• The phase sequence from bus bars and from machine must be same. It can be checkedwith the help of phase sequence indicator.

• The voltmeter is used to check the equality of voltage of bus bars and incomingmachine. The synchronization procedure is already explained before.

• Note : The use of lamps and synchroscope together is a best method of synchronization.

Synchronizing Current

• After proper synchronization of the alternators, they will run in synchronism. Asynchronizing torque will be developed if any of the alternator drops out ofsynchronism and will bring it back to the synchronism.

• Consider the two alternators shown in the Fig. 5 which are in exact synchronism. Dueto this they are having same terminal p.d. and with reference to their local circuit theyare in exact phase opposition. So there will not be any circulating current in the localcircuit. The e.m.f. E1 of alternator 1 is in exact phase opposition to that of alternator E2 .

Fig. 5

Synchronizing Current (Cont….)

• With respect to external load, the e.m.f.s of the two alternators are in the samedirection although they are in phase opposition with reference to local circuit. Therewill be no resultant voltage in the local circuit.

• Now assume that speed of alternator 2 is changed such that its e.m.f. E2 falls by anangle α. But E1 and E2 are equal in magnitude. The resultant voltage in this case willcause a current in the local circuit which is called synchronizing current. Thiscirculating current is given by,

• Where Zs = synchronous impedance of phase windings of both the machines

• The phase angle of ISY is given by an angle θ which can be computed astanθ = Xs/Ra where Xs is synchronous reactance and Ra is armature resistance. Thisangle is almost 90o.

rSY

s

EI

Z


Fig. 6


• Thus ISY lags Er by almost 90o and approximately in phase with E1. This current isgenerating current with respect to alternator 1 since it is in the same direction as that ofe.m.f. of alternator 1 while it will be motoring current for alternator 2 as it is in theopposite direction as that of e.m.f. of alternator 2. This current ISY will produce asynchronizing torque which will try to retard alternator 1 whereas accelerate thealternator 2.

• Now assuming that E2 has advanced in phase as shown in Fig. 6(b). The synchronizingcurrent ISY in this case will be generating current for machine 2 and motoring currentfor machine 1. This will again produce torque which will try to accelerate alternator 1and try to retard alternator 2.

• Note : Hence if synchronism between the two machines is lost then synchronizingcurrent will flow in the local circuit which will produce a synchronizing torque.

• This torque will tend to accelerate the lagging machine while will try to retard theleading machine. In case of machines which are loaded this current is superimposed onthe load current.

Synchronizing Power

• In Fig. 5, machine 1 is generating and machine 2 is motoring. The power supplied by

machine 1 is called synchronizing power.

• The power output of alternator 1 supplies power input to alternator 2 and copper

losses in the local path formed by armatures of two alternators.

• Power output of alternator 1 = E1 ISY cosΦ1 = E1 ISY

• This power is approximately equal to E1 ISY as Φ1 is small and is almost in phase with

E1. This power is called synchronizing power. Similarly power input to alternator 2 is

E2 ISY cosΦ2 which is equal to E2 ISY as Φ2 is also small.

• E1 ISY = E2 ISY + Cu losses in the local circuit

Synchronizing Power (Cont….)

• Let E1 = E2 = E

• Let the magnitude of resultant e.m.f. be Er which is given by,

• The electrical angle α is expressed in radians.

• Synchronizing current

Assuming Ra of both machines negligible

• Xs = synchronous impedance of each machine

1802 cos

2

2 cos 90 2 sin 2 ( )2 2 2

rE E

E E E E is small

. 2 2

r rSY

s s s

E E EI

syn impedance Z X X

Synchronizing Power (Cont….)

• Synchronizing power supplied by machine 1 is

• Total synchronizing power for three phase

• The above expression is valid for two alternators connected in parallel and operating

at no load.

1

2

2 2

SY SY

s s

P E I

E EE per phase

X X

23

2SY

s

EP

X

Alternators connected to infinite bus bars

• When an alternator is connected to infinite bus bars, the equation of PSY is valid but the

impedance of only that alternator is considered.

• Total synchronizing power for three phase = 3 PSY

2

rSY

s s

SY

s

E EI

Z X

EP

X

Synchronizing Torque

• Let TSY be the synchronizing torque per phase in newton-meter(N-m)

1. When there are two alternators in parallel

2. When alternator is connected to infinite bus bars

Ns is syn. speed in rpm

22 / 2

60 2 / 60 2 / 60

3

s SY sSY SY SY

s s

SY

N P E XP T T N m

N N

Total torque due to three phases T

22 /

60 2 / 60 2 / 60

3

s SY sSY SY SY

s s

SY

N P E XP T T N m

N N

Total torque due to three phases T

Short Circuit Ratio of an Alternator

• The short circuit ratio of an alternator is defined as the ratio of the field current

requited to generate rated voltage on open circuit to the field current required to

circulate rated armature current on short circuit.

• It can be calculated from open-circuit characteristic (O.C.C.) at rated speed and short

circuit characteristic (S.C.C.) of alternator.

• From Fig.

• The direct-axis synchronous reactance Xd is defined as the ratio of open-circuit

voltage for a given field current to the armature short-circuit current for the same field

current.

• Since triangles Oab and Ode are similar,

(1. .

__. .

)f

f

I for rated O C voltage OaSCR

I for rated S C current Od

__(2)Oa ab

SCROd de

Short Circuit Ratio of an Alternator (Cont...)

Field Current If


• From Fig. for a field current equal to Oa, the direct-axis syn. reactance in ohms is

• The per-unit value of Xd is given by

• But base impedance

__(3)d

acX

ab

__(4)d

d pu

XX

base impedance

__(5)

rated

a rated

d pu

per phase rated voltage

per phase rated armature current

V ac

I de

ac de deX

ab ac ab


• From eq. (2) and (5)

• Eq. 6 shows that the short-circuit ratio(SCR) is equal to the reciprocal of the per-unitvalue of the direct axis synchronous reactance.

• In a saturated magnetic circuit, value of Xd depends upon the degree of saturation. Itis to be noted that SCR is single valued because it pertains to the rated voltage onO.C.C. and rated armature current on S.C.C.

1 1__(6)

/ d pu

abSCR

de de ab X


• Effect of SCR on Machine Performance:

• SCR affects the operating characteristic, physical size and cost of the machine.

1. Voltage regulation: A low value for SCR means that synchronous reactance has alarge value. Thus machine has greater changes in voltage under fluctuations of load.That means the inherent voltage regulation of the machine is poor.

2. Stability: Maximum power output of synchronous machine is inverselyproportional to Xd and directly proportional to SCR. A machine with low value ofSCR has lower stability limit.

3. Parallel operation: Synchronizing power is responsible for keeping the machinesin synchronism.

• If SCR is low ⇒ Xd is high ⇒ synchronizing power is low ⇒machines are difficultto operate in parallel.

1

d pu

SCRX


4. Short circuit current:

• If SCR is low ⇒ Xd is high ⇒ short circuit current is low ⇒ cost of controlequipment is reduced.

Synchronous inductance

SCR may be increased by increasing length of air-gap. With increased air-gap length,the field mmf is to be increased for the same excitation emf.

To increase field mmf either field current If or number of field turns Tf is to beincreased. This requires greater height of field poles. So, overall diameter of machineincreases. Thus, a large SCR will increase size, weight and cost of the machine.

1

d pu

SCRX

1

relutance of air gap

1air-gap reluctance or air-gap length

s

s

L

SCRL


• Above discussion indicates that the performance is better with high value of SCR, butfrom economic consideration, it is advisable to design the machine with low value ofshort circuit ratio.

• The present trend is to design the synchronous machine with low value of SCR. Theuse of low values of SCR results in a cheaper machine.

• Typical values of SCR are:

• Cylindrical rotor machines 0.5 to 0.9

• Salient-pole machines 1 to 1.5

Documents

Prof. Tejas H. Panchal Electrical Engineering Department · Parallel Operation of Alternators • The process of switching of an alternator to another alternator or with a common