CHAPTER XVI 


REACTION MACHINES 

147. In the usual treatment of synchronous machines and 
induction machines, the assumption is made that the reactance, 
x, of the machine is a constant. While this is more or less 
approximately the case in many alternators, in others, especially 
in machines of large armature reaction, the reactance, x, is 
variable, and is different in the different positions of the armature 
coils in the magnetic circuit. This variation of the reactance 
causes phenomena which do not find their explanation by the 
theoretical calculations made under the assumption of constant 
reactance. 

It is known that synchronous motors or converters of large 
and variable reactance keep in synchronism, and are able to do 
a considerable amount of work, and even carry under circum- 
stances full load, if the field-exciting circuit is broken, and thereby 
the counter e.m.f., E,, reduced to zero, and sometimes even if 
the field circuit is reversed and the counter e.m.f., £.',. made 
negative. 

Inversely, under certain conditions of load, the current and 
the e.m.f. of a generator do not disappear if the generator field 
circuit is broken, or even reversed to a small negative value, in 
which tatter case the current is against the e.m.f., Ea, of the 
generator. 

Furthermore, a shuttle armature without any winding (Fig. 
120) will in an alternating magnetic field revolve when once 
brought up to synchronism, and do considerable work as a motor. 

These phenomena are not due to remanent magnetism nor 
to the magnetizing effect of eddy currents, because they exist 
also in machines with laminated fields, and exist if the alternator 
is brought up to synchronism by external means and the rema- 
nent magnetism of the field poles destroyed beforehand by 
application of an alternating current. 

These phenomena can uol be explained under the assump- 
tion of a constant synchronous reactance: because in ilu- oast 
al no-field excitation, the e.m.f. or counter e.m.f. of the machine 


REACTION MACHINES 


2fil 


let 
mi 

mi 


H MVO, ;md the only cm. I', existing in tlic- al tern (it in1 is the e.m.f. 
of self-induction; that is, the e.m.f. induced by the alternating 
current upon itself. If, however, the synchronous reactance is 
constant, (he counter e.m.f. of self-induction is in quadrature 
with the current and wattless; that is, can neither produce nor 
consume energy. 

In the synchronous motor running without field excitation, 
always a large lag of the current behind the impressed e.m.f. 
exists; and an alternating-current generator will yield an e.m.f. 
without field excitation only when closed by an external circuit 
of large negative reactance; that is, a circuit in which the current 
the e.m.f., as a condenser, or an overexcited synchronous 

iotor, etc. 

14S. The usual explanation of the operation of the synchronous 
machine without field excitation is self-excitation by reactive 
armature currents. In a synchronous motor a lagging, in a 
generator a leading armature current magnetizes the field, and in 
such a case, even without any direct-current field excitation, there 
is a field excitation and thus a magnetic field flux, produced by the 
m.m.f. of the reactive component of the armature current*. In 
the polyphase machine, this is constant in intensity and direc- 
tion, in the single-phase machine constant in direction, hut pul- 
sating in intensity, and the intensity pulsation can be reduced 
by a short-circuit winding around the field structure, as more 
fully discussed under "Synchronous Machines." 

Thus a machine as shown diagram mat ically in Fig. 124, with 
a polyphase (three-phase) current impressed on the rotating 
armature, A, and no winding on the field poles, starts, runs up 
to synchronous and does considerable work as synchronous 
motor, and underload may even give a fairly good (lagging) power- 
factor. With a single-phase current impressed upon the arma- 
ture, A, it does not start, but when brought up to synchronism, 
continues to run as synchronous motor. Driven by mechanical 
power, with a leading current load it is a generator. 

However, the operation of such machines depends on the 
existence of a polar field structure, that is a strucinre having a 
low reluctance in (he direction of the field poles, P — P, and a 
high reluctance in quadrature position thereto. Or, in other 
words, the armature reactance with the coil facing the field poles 

high, and low in the quadrature position thereto. 

In a structure with uniform magnetic reluctance, in which 


263 


ELECTRICAL APPARATUS 


therefore the armature reactance does oof vary with the posi- 
tion of the armature in the field, us shown in Fig. 125, such ■ H 
excitation hy reactive armature currents does not occur, and 
direct-current field excitation is always necessary (except in the 
so-called "hysteresis motor"). 

Vectorially this is shown in Figs. 124 and 125 by the relalivc 
position of the magnetic flux, *, the voltage, E, in quadrature to 
*, and the m.m.f. of the current, /. In Fig. 125, where / and 
4> coincide, I and E are in quadrature, that is, the power zero. 
Due In the polar structure in Fig. 124, /and * do not coincide, 


thus / is not in quadrature to E, but contains a positive 01 a 
negative energy component, making the machine motor or 
generator. 

As the voltage, E, is produced by the current, /, it is an e.m.f. 
of self-induction, and self-excitation of the synchronous machine 
by armature reaction can be explained by the fact that the 
counter e.m.f. of self-induction is not wattless or in quadrature 
with the current, but contains an energy component; that if, 
that the reactance is of the form X = h + jx, where x is the watt- 
less component of reactance and h the energy component of 
reactance, and k is positive if the reactance consumes power — 
in winch case the counter e.m.f. of self-induction lags more than 
90° behind the current — while h is negative if the reactance 
produces power — in which case the counter e.m.f. of self-induction 
lags less than 90° behind the current. 

149. A case of this nature occurs in the effect of hysteresis, 
from a different point of view. In "Theory and Calcuation of Al- 
ternating Current" it was shown, thai -magnetic hysteresis distorts 
the current wave in such a way that the equivalent sine wave, 


REACTION MACHINES 263 

that is, the sine wave of equal effective strength and equal power 
with the distorted wave, is in advance of the wave of magnetism 
by what is called the angle of hysteretic advanee of phase a. 
the e.m.f. generated by the magnetism, or counter e.m.f. 
nf self-induction lag* 90° behind the magnetism, it lags 90° + a 
heh;nd the current ; that is, the self-induction in a circuit contain- 
ing iron is not in quadrature with the current and thereby 
wattless, but lags more than 90° and thereby consumes power, so 
that the reactance has to be represented by X = k + jx, where 
h is what has been called the "effective hysteretic resistance." 

A similar phenomenon takes place in alternators of variable 
reactance, or, what is the same, variable magnetic reluctance. 

Operation of synchronous machines without field excitation 
is most conveniently treated by resolving the synchronous 
reactance, 3"u, in its two components, the armature reaction and the 
true armature reactance, and once more resolving the armature 
reaction into a magnetizing and a distorting component, and 

msidering only the former, in its effect, on the field. The true 
armature self-inductance then is usually assumed as constant. 
Or, both armature reactance and self-inductance, are resolved 
into the two quadrature components, in line and in quadrature 
with the field poles, as shown in Chapters XXI and XXIV of 
"Alternating-Current Phenomena," 5th edition. 

160. However, while a machine comprising a stationary single- 
phase "field coil," A, and a shuttle-shaped rotor, R, shown 
diagrammatically as bipolar in Fig. 120, might still be interpreted 
in this matter, a machine as shown diagrammatically in Fig. 
127, as four-polar machine, hardly allows this interpretation. 
In Fig. 127, during each complete revolution of the rotor, !<', 
it four times closes and opens the magnetic circuit of the single- 
phase alternating coil, A, and twice during the revolution, the 
magnetism in the rotor, n", reverses. 

A machine, in which induction takes place by making and 
breaking (opening and closing) of the magnetic circuit, or in 
general, by the periodic variation of the reluctance of the 
magnetic circuit, is called a reaction machine. 

Typical forms of such reaction machines are shown diagram- 
matically in Figs. 126 and 127. Fig. 126 is a bipolar, Fig. 127 
is a four-polar machine. The rotor is shown to the position of 
closed magnetic circuit, but the position of open magnetic i-in-uit 
is shown dotted. 


204 


ELECTRICAL APPARATUS 


Instead of cutting out segments of the rotor, iu Fig. 126, the 
same effect can lie produced, with a cylindrical rotor, by a shorl- 
circuitcd turn, S, as shown in Fig. 128, This gives a periodic 
variation of the effective reluctance, from ft minimum, shown in 
Fig. 128, to a maximum in the position shown in dotted lines in 
Fig. 128. 

This latter structure is the so-called "synchronous-induction 
motor," Chapter VIII, which here appears as a special form of 
I he reaction machine. 

If a direct current is sent through the winding of the machine, 


BIO. 1 2U.— Bipolar n 


Fig. 126 or 127, a pulsating voltage and current is produced in 
this winding. By having two separate windings, and energizing 
the one by a direct current, we get a converter, from direct cur- 
rent in the first, to alternating current in the second winding. 
The maximum voltage in the second winding can not exceed the 
voltage, per turn, in the exciting winding, thus is very limited, 
and so is the current. Higher values are secured by inserting a 
high inductance in series in the direct-current winding. In this 
case, a single winding may be used and the alternating-circuit, 
shunted across the machine terminals, inside of the inductance. 
161. Obviously, if the reactance or reluctance is variable, it 
will perform a complete cycle during the time the armature coil 
moves from one field pole to the next field pole, that is, during 
one-half wave of the main current. That is, in other words, 
the reluctance and reactance vary with twice the frequency of 
the alternating main current. Such a case is shown in Figs. 
129 and 130. The impressed e.m.f., and thus at negligible 
resistance, the counter e.m.f., is represented by the sine MVft, 


REACTION MACHINES 


E, thus the magnetism produced thereby is a sine wave, $, 90° 
ahead of E. The reactance is represented by the sine wave, x, 


,, 

h\ 

*_j _\ 

/p\ ' y^~/\ /"~1 E 

""N / /*" ' / 7v - ■*" N. 

\ / I / / //\ \ 

•^' V\ / \ Wp^X, J/ ' |\ -"*" \*v 

\ /\ " X/i )\ V^^^ \ ? 

a V ^~ > v/ / 1 — r*\ i V 

v\ /\ Ji. \ A : \\ /\ 

\*-J**T \ p -«-— - p' ^V-— - — * N 

i vSv i i v if / "Y^"^ 

\ \ i Ts/i/ / \ \ 

\ \ / ""■-». ^^ \ ^ 

^-^-V- ^oJ 

i 7 

XX 

V 

Fio. 129. — Wave shapes in reaction machine as generator. 


?v 

ft 

'""^ 

/ ^*r~x* E 

N ~X-v Sl. W^ ^V 

I' fa/ii t- 

\ ■**"'' V, // */J^""Vj \ / 

^^^tn/^'A^^^^v 

^ /\ /A ' / \V A 

*» ' \ y~i^ / v / 

\\ / X ' \ // ^N / 

\ \ / / ')/ \\ / I \\/ 

1 ■£*,' > *^ s\' 1 \ /L ' 

» - N^-^' i \ | "'/■-* 

i / IT / 

R / A I 

IV' vj 

e shape in reaction machine a 


varying with the dpuble frequency of E, and shown in Fig. 129 
to reach the maximiim value during the rise of magnetism, in 


266 ELECTRICAL APPARATUS 

Fig. 130 during the decrease of magnetism. The current, /, 
required to produce the magnetism, *, is found from * and x in 
combination with the cycle of molecular magnetic friction of the 
material, and the power, P, is the product, IE. As seen in Fig. 


__ ] t* _ j/> _ ^ >^ 


Fid. 131.— Hysteresis loop of reaction machine as generator. 

129, the positive part of P is larger than the negative part: 
that is, the machine produces electrical energy as generator, 
In Fig. 130 the negative part of P is larger than the positive: 


/^ '- ""5 

t _z 

: U'-z - 

-I / / 41 

7y 

€" J- ; = = 

Fia. 132. — Hysteresis loop of reaction machine as motor. 

that is, the machine consumes, electrical energy and produces 
mechanical energy as synchronous motor. In Figs. 131 and 132 
are given the two hysteretic cycles or looped curves, *, I under 
the two conditions. They show that, due to the variation of 


REACTION MACHINES 267 

reactance, x, in the first case, the hysteretic cycle has been over- 
turned so as to represent, not consumption, but production of 
electrical energy, while in the second case the hysteretic cycle has 
been widened, representing not only the electrical energy consumed 
by molecular magnetic friction, but also the mechanical output. 

152. It is evident that the variation of reluctance must be 
symmetrical with regard to the field poles; that is, that the 
two extreme values of reluctance, maximum and minimum, will 
take place at the moment when the armature coil stands in front 
of the field pole, and at the moment when it stands midway 
between the field poles. 

The effect of this periodic variation of reluctance is a distortion 
of the wave of e.m.f., or of the wave of current, or of both. 
Here again, as before, the distorted wave can be replaced by 
the equivalent sine wave, or sine wave of equal effective intensity 
and equal power. 

The instantaneous value of magnetism produced by the 
armature current — which magnetism generates in the arma- 
ture conductor the e.m.f. of self-induction — is proportional to 
the instantaneous value of the current divided by the instan- 
taneous value of the reluctance. Since the extreme values of 
the reluctance coincide with the symmetrical positions of the 
armature with regard to the field poles — that is, with zero and 
maximum value of the generated e.m.f., E0, of the machine — 
it follows that, if the current is in phase or in quadrature with 
the generated e.m.f., E0, the reluctance wave is symmetrical to 
the current wave, and the wave of magnetism therefore sym- 
metrical to the current wave also. Hence the equivalent sine 
wave of magnetism is of equal phase with the current wave ; that 
is, the e.m.f. of self-induction lags 90° behind the current, or is 
wattless. 

Thus at no-phase displacement, and at 90° phase displace- 
ment, a reaction machine can neither produce electrical power 
nor mechanical power. 

If, however, the current wave differs in phase from the wave 
of e.m.f. by less than 90°, but more than zero degrees, it is un- 
symmetrical with regard to the reluctance wave, and the re- 
luctance will be higher for rising current than for decreasing cur- 
rent, or it will be higher for decreasing than for rising current, 
according to the phase relation of current with regard to generated 
e.m.f., #o. 


268 ELECTRICAL APPARATUS 

In the first, case, if the reluctance is higher for rising, Inner Fat 
decreasing, current, the magnetism, which is proportional to 
current, divided by reluctance, is higher for decreasing than for 
rising current; that is, its equivalent sine wave lugs behind the 
sine wave of current, and the e.m.f. or self-induction will lag 
more than 90° behind the current; that is, it will consume 
electrical power, and thereby deliver mechanical power, and do 
work as a synchronous motor. 

In the second case, if the reluctance is lower for rising, and 
higher for decreasing, current, the magnetism is higher for rising 
than for decreasing current, or the equivalent sine wave of 
magnetism leads the sine wave of the current, and the counter 
e.m.f. of self-induction lags less than 90° behind the current; 
that is, yields electric power as generator, and thereby consumes 
mechanical power. 

In the first ease the reactance will lie represented by X = ft + 
jx, as in the case of hysteresis; while in the second case the 
reactance will be represented by A" = — ft + jx. 

153. The influence of the periodical variation of reactance 
will obviously depend upon the nature of the variation, that is, 
upon the shape of the reactance curve. Since, however, no 
matter what shape the wave has, it can always be resolved in a 
series of sine waves of double frequency, and its higher har- 
monies, in first approximation the assumption can l>e made 
that the reactance or the reluctance varies with double frequency 
of the main current ; that is, is represented in the form: 

x = a + b cos 2 &. 

Let the inductance be represented by: 

L = I + 1' cos 2 ft 
= ((1 +7 cos 2 0); 


■- amplitude of variation of inductance. 


!■ of current behind maximum value 


where 7 
Let: 

fl = angle of lag of zero vah 
of the inductance, L. 

Then, assuming the current as sine wave, or replacing it by 
the equivalent sine wave of effective intensity, /, current: 

i » / v^sin (tf - 8). 


REACTION MACHINES 269 


The magnetism produced by this current is: 

Li 


n 


where n = number of turns. 
Hence, substituted: 


= ll^sin (0.- 0) (1 + 7 cos 2/3), 


n 


or, expanded: 


$ = ^V? /l - A cos 0 sin 0 - (l + *) sin 0 cos /j|, 

when neglecting the term of triple frequency as wattless. 
Thus the e.m.f. generated by this magnetism is: 


e = — n 


dt 

hence, expanded: 

e = -2 tt/ZZ V2 I (l - ?) cos 0 cos 0 + (l + |) sin 0 sin 0 
and the effective value of e.m.f. : 


E = 2wfll yj(l _^2cos20+ (l+|)2sin20 

= 2vfllJ\ + £- 7 cos 20. 
Hence, the apparent power, or the volt-amperes: 


Q = IE = 27r///2^l+£-7Cos20 


*/*^l + 


J£J 


1 + * - 7 cos 2 0 
4 


The instantaneous value of power is: 
p = ei 

= -4tt///2 sin (0 - 0) I (l - ^ cos 0 cos 0 + 

(l + J) sin 0 sin /»} ; 


270 ELECTRICAL APPARATUS 

and, expanded: 

V = -2wfll* {(l + l) sin 2 $ sin2 0 - (l - J) 

sin 2 0cos20 + sin 2/3 (cos 2 6 - |) }• 

Integrated, the effective value of power is: 

P = -7r/LT27sin2 0; 

hence, negative, that is, the machine consumes electrical, and 
produces mechanical, power, as synchronous motor, if 6 > 0, 
that is, with lagging current ; positive, that is, the machine pro- 
duces electrical, and consumes mechanical power, as generator, 
if 6 > 0, that is, with leading current. 
The power-factor is: 

P y sin 2 $ 


V = 


Q „ L '. y2 


2 Jl + -£- - 7 cos 2 6 


hence, a maximum, if: 

dp 


or, expanded: 


de=0> 


2 , 7 

cos 2 0 = - and = {r 
7 2 


The power, P, is a maximum at given current, /, if: 

sin 2 6 = 1 ; 
that is: 

6 = 45°; 

at given e.m.f., E, the power is: 

p fl27 sin 2 0 

4wfl(l +^ - 7 cos 2 6) 
hence, a maximum at : 

to ' 

or, expanded: t 

±y 


cos 2 e = 


•v1 
1+4- 


REACTION MACHINES 271 

154. We have thus, at impressed e.m.f., E, and negligible 
resistance, if we denote the mean value of reactance: 

x - 2 *■//. 
Current: 

/- E 


x yjl +4*- y cos 20 
Volt-amperes: 

«--...-.«■....-- 

xJl + j - 7 cos 2 0 

Power: 

E*y sin 2^ 

2x(l + ?- - 7 cos 2 0) 

Power-factor: 

/et r\ 7 sin 2 0 
V = cos {E, I) = ,-^ ■ — - 

2 Jl + ^ - 7 cos 2 0 

Maximum power at : 

cos 2 0 = y 


72 

1+4 


Maximum power-factor at: 


2 7 

cos 2 0 = - and = '-• 
7 2 

0 > 0 : synchronous motor, with lagging current, 
0 < 0: generator, with leading current. 

Ah an example is shown in Fig. 133, with angle 0 as abscissa*, 
the values of current, power, and power-factor, for the constants, 
E = 110, x = 3, and 7 = 0.8. 

/ = - --41 

Vl.45 - cos 2 6 


p = -2017>in 2 0 
1.45 - cos 2 0 


— » 


, „ 7X 0.447 sin 2 0 

p = cos (E, I) = -/_.:.--=-.--- • 

V 1.45 - cos 2 0 


272 ELECTRICAL APPARATUS 

As seen from Fig. 133, the power-factor, j>, of such a machine 
is very low — does not exceed 40 per cent, in this instance, 

Very similar to the reaction machine in principle and characiei 
of operation are the synchronous induction motor, Chapter IX, 
and the hysteresis motor, Chapter X, either of which is a gen- 
erator above synchronism, and at synchronism can be motor as 

REACTION MACHINE 

p. 

c. 

E -110 
*- 3 

- 

m 

«> 

H 

A 

a 

fcs 

P= vUs-mi* JP 

m 

/ 

\ 

Jp 

... 

/ 

<Z 

s 

^ 

— 

-^ 

-7 

\ 

/P 

U 

i 

10 

«i 

i 

/ 

»i 

>, 

/ 

-*. 

t 

LB* 

- 

\ 

-l-.« 

ra 

s 

\ 

a 

1 

\ 

■1*1 

\ 

I 

\ 

_/ 

-M 

<i 

Ti 

i'.H 

■n 

t 

■■ 

"■;. 

-if 

.if 

LA 

-■JO 

htf 

..v 

KM 

- 71 

... 

well a. 
stator 

166. 
the re 
also d 
it thus 

It h 
in kecj 

: 

Fig. 133. — Load curves of reiirtion machine. 

generator, depending on the relative position b 

ield and rotor. 

The low power-factor and the low weigh! efficSu 
iction machine from extended use for large powe 
K-s the severe wave-shape distortion produced by 

has found a very limited use only in small sizes. 
is, however, the advantage or a high degree of ex 

ing in step, that is, it does not merely keep in synch 
iftfi more or less over a phase angle with respect 

>i ween 

cy bar 
s. Bo 
t, and 

tctnea 

nni-lil 

to the 

REACTION MACHINES " 273 

impressed voltage, but the relative position of the rotor with 
regards to the phase of the impressed voltage is more accurately 
maintained. Where this feature is of importance, as in driving 
a contact-maker, a phase indicator or a rectifying commutator, 
the reaction machine has an advantage, especially in a system 
of fluctuating frequency, and it is used to some extent for such 
purposes. 

This feature of exact step relation is shared also, though to 
a lesser extent, by the synchronous motor with self-excitation 
by lagging currents, and ordinarily small synchronous motors, 
but without field excitation (or with great underexcitation or 
overexcitation) are often used for the same purpose. 

Machines having more or less the characteristics of the reac- 
tion machine have been used to a considerable extent in the 
very early days, for generating constant alternating current for 
series arc lighting by Jablochkoff candles, in the 70's and early 
80's. 

Structurally, the reaction machine is similar to the inductor 
machine, but the essential difference is, that the former operates 
by making and breaking the magnetic circuit, that is, periodically 
changing the magnetic flux, while the inductor machine operates 
by commutating the magnetic flux, that is, periodically changing 
the flux path, but without varying the total value of the magnetic 
flux. 


18