Apaper Aresented at the 157th Meeting of theA merican Institute of,Eectrica1Engineers,Aew York, October 25th Sor. PresidentSteini,nets in the COhir.

PARALLEL RUNNING OF ALTERNATORS.

BY ERNEST J. BERG.

In the following article an endeavor will be made to show theprinciples govering parallel operation of alternators, driven bysteam engines or turbines. The laws of parallel running whengenerators are driven by electric motors depend so much uponthe action of the mnotors that this part of the subject is omittedand reserved for another paper.

Consider two alternators intended for parallel operation,and let:

e induced E. M. F.Z,7

Z2 'r22- 02 = the initernal imnpedance of the differentarmiatures.

Y1 and Y2 = the corresponding admittances.Z = r-j x the impedance of the external load.YB= joint admittance of the armature circuits.

Z= corresponding impedanee.Zo -total impedance in the circuit.We h-ave tben:

Z2 Z121- Jf =¾ -+

2.

Y - Y2jj22- z2 jZ, 2 5

75-3

754 BERG ON PARALLEL RUNNING '[Oct. 25,S ~~~~~~~1

Z3=_3

zo Z3 + z

Total current 1 = "z3 Z

Voltage across load = I1 = eZ

Drop in armatuires e - +Z

Currenlt in armatnre N6. 1 = (e - e+Z) Y

Current in armature No. 2 (e - z< z ,)Z3+\- t7

73 +

Volt-amperes of one armature e2 Y2(1-

Power of: each armature is the real part of the e-xpression forvolt-a mperes.

This is expresse( as:

Pie2 (Pr-gl

[+ }j2) (,r + X1)-and

P2 2 (p r2-q 2)(f2 + n2) (r.2 + 2

where:V = M2 + nr2- n x

q= inAr-n r

en ,, ( ,+ r= 2+±B2+B

G2 A- B2 +

1901.3 OF ALTERNATORS. 755

G gl +q2

B-Y + bi

Y- g2 + j&2

Neglecting the resistances of the armatures as compared withthe reactances, we get the following expressions:

e X2 r (Xl + X2)Z2 (XI + X2)2 + X2

p e2 x (x1+X2)22 (X1 + X2)2 + X12 22+ 2 x X1 X2 (X1 + X2)

In other words, tlhe alternators divide the load inversely, astheir armature reaction.With a non-indtuctive external circuit, these questions be-

come:

P, - power of one armature 2 e2 x2(x1+ 2)r(Xi -H X2) + XI x2

P2 = power of otlher armature = e r X1 (Xl + r2)power~ ~~~~~ (I+ 2)2+X,1 X22

which with close approximation can be written:

2PI le aX2

r (xl+ x2)=_ e2 01 ',

r (XI +x2)

Therefore two machines of saine induced E. M. F. and arma-ture reaction running in phase will share the load evTenly. Ifone has twice as high armature reaction as the other, it will takeone half of the load, etc. Thus since machines of identical regu-lation have practically armature reactions inversely proportionalto their size, it is possible to run such mnachines from the sameengines at proper share of the total load. Should, however, twomachines of the same size and different armature reaction runfrom the same eingine, the distribution of power will not be inaccordance with the rating.

756 BERG ON PARALLEL RUNNING [Oct. 25,

To balance the load it is then necessary to add reactance inone armature or to mechanically offset one armature in regard tothe other, or, finally, to run them at such field excitation as willcause considerable cross-current, which effect will be discussedlater.

In tlle discussion given above it was assuied that the ma-chines were running strictly in phase, wbieh would practicallylimit the case to alternators clutched together. If, however,they are rigidly connected together,, but out of phase, the cur-rent which is due to the resultant of the two E. rI. F.'s has a dif-ferent phase displacement from the E. M. F. of one machine thanit lhas from that of the other, that is, the energy correspondingis different in the two miachines, or the one supplies more powerthan the other.The relation of currents to E. M. F.' s can also be changed by

changing the excitation,Assume m'achines of the same armature reaction which, before

beintg throwin in parallel, have unequal E. M. F."S. After beingconnected together their terminal voltages inust be the same,therefore a cross-curreint must flow between them which, in thehigher excited alternator, is lagging, and in the other leading;which eurrents, in conjunction with the field excitation, give aresultant field of same magnitude in the two, but displaced inphase. In the hiigher excited machine it will bring the resultantfield more in phase with the energy current, thus giving a resultequivalent to an armature of lower reactance; in the lower ex-cited machine a result same as higher arnmature reaction. It istherefore possible to change the load by change of field excita-tion by sacrifice of current, since this method involves wattlesscurrents between the generators.

In view of the above discussion, it is thus evident that thequestion of distribution of power between alternators is quitesimple, if they are running at absolutely the same speed at allloads; that is, if the enginies regulate so closely as to permit theclutch to be opened and the armatures still retain the same posi-tions. In reality, however, engines cannot be made to governso closely, but one will teind to hold up the speed somewhatbetter than the other. That being the case, it is safe to say thatas a rule the engines will not tend to give the same power atexactly the same speed.

Referring back to the equations and discussions we find, there-

1901.] o0 ALT7ERNA TORS. 757

fore, that with the same armature reaction and induced E. M. F.)if different power is given each machine, the armatures must beoffset a certain and fixed degree, which means that by even themost ininute difference in speed regulationi the armatures areforced to change their relative positions, whicil obviously is acause for " hunting."The relative power given by each machine depends upon the

respective powers of the engines at identical speeds.From the above discussion it is apparent that a definite tend-

ency for "hunting" exists, and that this hunting is mnanifest ina mechanical pulsation in the speed of the armatures, and a trans-fer of power fromn one unit to another.A most superficial investigation will show that this flow of

power is mnuch greater than that corresponding to the storedenergy of the artnature fly-wheel, etc., at the relatively smalldifferences in speed, and that pulsating power actually has to besupplied by the engines. Therefore, and since power cannot beobtained fromn an engine without corresponding steam, theflow of stearmi must be periodic to sustain an accumnulated huint-ing.The remiiedy is therefore to be found by preventinig such

periodic flow of steam, which can be accomplished by properdash-pot arrangements at the governor. Otlher remedies also sug-gest themselves, the favorite being to make a short-eircuited*winding in and around the field of alternators. The object of suchwinding obviously is to establish a load when these oscillationsoccur, which load tends to stop the acceleration and retardationof the armnatuire. The disadvantages of this method are thatlosses of no small magnitude not only are introduced when themachines hunt, bu't also when they are running at steady speed,which losses are eaused by induced currents in this short-cir-nuited winding, due to pulsations of flux ineidental to modernconstruction of iron-clad armatures.

Schenectady. October 14th. 1901.