Theory and Calculation of Electrical Apparatus (1917) — part 18 of 21

ft _ ~ + CqX " 4 _ 1 ( 1 S \ f 4 — Co\ ,f 4 \

Sb\i*(S* + co 2 ) ~ co 2 + 5* t Sb X?" J ’

,?/ C0&X4 2 CoX'4 S" 4 1 [Co Co\ -f* S"t\

sb\ 4 *(s 2 +tf) ~ ^Ts~ 2 is s&x? } ;

or approximately:

t > . 1 1

Co 2 + >S 2 ’

jii £0

5(Co 2 +S 2 )

( 112 )

(113)

t" = 0 substituted in equation (112) gives £ = So, the value recorded in equation (108). .

It follows herefrom, that with increasing speed, S, t f and still more t ” 9 decrease rapidly. For S = 0, t' and t" become infinite. That is, at standstill, it is not possible by this method to produce zero commutation current.

The phase angle, 0 2 , of the voltage ratio, T = t' — jt n , is given by:

• a _ t" _ C06X4 2 — coV 4 — SW\ tan Vt-jr- /S6X4 2 - SXU + CoX'V

(114)

rearranged, this gives:

Co sin 62 + S cos 62 _ 6X 4 2 — W . Co sin 62 — S sin 62 X" 4

(115)

and, denoting:

= tan cr, (116)

Co

where o may be called the “speed angle,” it is, substituted in (115):

x , \ b\i“ - ' 4

tan (02 + cr) = \ t / ’

A 4

= constant;

(117)

hence:

0 2 + <r = 7,

(118)

and:

b

1

c-

II

(119)

is a large quantity, hence 7 near 90°. x 4

<7 is also near 90° for all speeds, S , except very slow speeds, since in (116) co is a small quantity.

408

ELECTRICAL APPARATUS

Hence 0 2 is near zero for all except very low speeds.

For very low speeds, c is small, and 0 2 thus large and positive. That is, the voltage, Ei, impressed upon the compensating circuit to get negligible commutation current, must be approxi-

mately in phase with e for all except low speeds. At low speeds, it must lag, the more, the lower the speed. Its absolute value

is very large at low speeds, but decreases rapidly with increasing speed, to very low values.

For instance, let, as before:

it is:

hence:

X4 = 0.304 - 0.248 j, Co = 0.4, b = 10;

tan (0 2 Act) = 5.05,

02 + <r = 79°;

0 2 = 79° - o\

02 = 0 for <T = 79°; hence, by (116), S 0 = 2.02, or double syn- chronism. Above this speed, 0 2 is leading, but very small, since the maximum leading value, for infinite speed, $ = 00 , is given

by o' = 90°, as, 0 2 = -11°. Below the speed, S 0 , 0a is positive, or lagging;

. = 1, it is <r = 68°, 0 2 = -+11°, hence still approximately

m phase;

for S = 0.4, it is v = 45°, 0 2 = 34°; hence is still nearer in phase than in quadrature to e.

The corresponding values of T = t' A t" are, from (112) :

5 = 2 - 02 - ■= 0, T = 0.197, t = 0.197,

5 = 1, 0 2 = +11°, T = 0.747 -f 0.140,7, t = 0.760*

S = 0.4, 0 2 = 34°, T = 3.00 -2.00 j, t = 3.61.

224. The introduction of a phase displacement between the compensating voltage, # 2 , and the total voltage, e, in general is more complicated, and since for all but the lowest speeds the required phase displacement, 0 2 , is small, it is usually sufficient to employ a compensating voltage, e 2 , in phase with e.

In this case, no value of t exists, which makes the commutation current vanish entirely, except at the speed, S 0 .

The problem then is, to determine for any speed, S, that value

SINGLE-PHASE COMMUTATOR MOTORS 409

of the voltage ratio, t, which makes the commutation current, i g a minimum. This value is given by:

din t -*

where i g is given by equation (106).

Since equation (106) contains t only under the square root, the minimum value of i 6 is given also by :

^ = 0 it

where:

K = [l — SX' 4 4 Stb (SX' 4 - coX" 4 )] 2 4 [b " 4 - Stb (coV 4 + SK" a)] 2 .

Carrying out this differentiation, and expanding, gives:

__ Sb~X 4 2 “ 4 4 OoX" 4 _ 1 f - $X' 4 — OoX'^)

1 ~ Sb\S (co 2 + S 2 ) " co 2 4 S 2 l 1 S&X 4 2 I * { J

This is the same value as the real component, f, of the complex voltage ratio, Ti, which caused the commutation current to vanish entirely, and was given by equation (112).

It is, approximately:

1 = co 2 4- £ 2 ' (122)

Substituting (121) into (105) gives the value of the minimum commutation current, i a 0 .

Since the expression is somewhat complicated, it is preferable to introduce trigonometric functions, that is, substitute:

tan & = (123)

A 4

where 5 is the phase angle of X 4 , and therefore:

X 4 = X4 sin 5, . 194. ^

X\ = X 4 cos $,] v J

and also to introduce, as before, the speed angle (116):

.... 8 1

hence:

q = Vc» 2 +S 2 ;

S = q sin <j, Co = q cos a.

( 125 )

410

ELECTRICAL APPARATUS

Substituting these trigonometric values into the expression ( 121 ) of the voltage ratio for minimum commutation current, it is:

JL^ sin (o- — <5) 1 ^2

SHX. - < 127 >

Substituting (117) into (106) and expanding gives a relatively simple value, since most terms eliminate :

Ig — e {[cos 2 (cr — 8) + b\ (sin a sin (a — d) — cos 5)]

• j [ sin (a — 5) cos (cr — «5) — &X 4 (sin a cos (<r — 8) — sin 3)] }

CqZ (1 — C 0 X 4 , (c 0 jS)

(128)

(129)

(130)

and the absolute value:

♦ _ e ( CQS (o' — ^) — 5 X 4 cos O') ,

CoS [ 1 — C0X4] V Co 2 + £ 2 or, resubstituting for 0 - and <5:

. e {S\ /f 4 — co (X 4 2 6 — X 4 ') }

C 0 Z [1 - C0X4] (Co 2 + S>) '

From (129) and (130) follows, that i 0Q = 0, or the commutation current vanishes, if :

cos (or — 8) — frX 4 cos a = 0, (131)

or:

S" 4 - co (X 4 2 6 - X' 4 ) = 0.

This gives, substituting, X" 4 = a/x 4 2 — X' 4 2 > and expanding:

X 4

co 2 + S 2

{&X 4 C 0 2 ± S Vs 2 - Co 2 ( 6 2 X 4 2 — 1)17

COS (o' — ($) =

6X4C0

-v/co 2 + S 2

From (131) follows:

cos (<r — 5) = Z)X 4 cos cr.

Since cos (<r — 5) must be less than one, this means:

b \ 4 cos o- < 1 , or:

1

(132)

X 4 <

or:

or, inversely:

b cos o'

V Co 2 + £ 2 '

c 0 6

5 > Co V^X? - 1.

X 4 <

(133)

SINGLE-PHASE COMMUTATOR MOTORS 411

That is:

The commutation current, i g , can be made to vanish at any speed, S , at given impedance factor, X 4 , by choosing the phase angle of the impedance of the short-circuited coil, 8 , or the resist- ance component, X', provided that X 4 is sufficiently small, or the speed, S, sufficiently high, to conform with equations (133).

From (132) follows as the minimum value of speed, S } at which the commutation current can be made to vanish, at given X 4 :

Si - co vVx 4 2 - 1,

V. - i;

x "‘ ■ yfis-p-

For high values of speed, S, it is, approximately:

COS (<r — 8) = 0,

a - 8 = 90°,

• S. tan cr — — ,

Co

hence: cr = 90°

8 = 0 ’

and:

hence:

X' 4 = X 4

That is, the short-circuited coil under the brush contains no inductive reactance, hence:

At low and medium speeds, some inductive reactance in the short-circuited coils is advantageous, but for high speeds it is objectionable for good commutation.

225 . As an example are shown, in Figs. 189 and 192, the char- acteristic curves of series-repulsion motors, for the constants:

Impressed voltage:

Exciting impedance, main field: Exciting impedance, cross field: Self-inductive impedance, main field:

Self-inductive impedance, cross field:

e = 500 volts,

Z = 0.25 + 3 j ohms, Z'= 0.25 +2.5 j ohms,

Z 0 = 0.1 + 0.3 j ohms,

Z 2 = 0.025 + 0.075 j ohms,

KILOV

SINGLE-PHASE COMMUTATOR MOTORS 413

Self-inductive impedance arma-

fcu f e : Zi = 0.025 + 0.075 j ohms,

Self-inductive impedance, brush short-circuit: jZ 4 = 7.5 _j. 10 j ohms,

Reduction factor, main field: Co = 0.4,

brush short-circuit c 4 = 0.04;

that is, the same constants as used in the repulsion motor Fig. 188.

Curves are plotted for the voltage ratios:

t = 0 : inductively compensated series motor, Fig. 189. t = 0.2 : series repulsion motor, high-speed, Fig. 190. t = 0.5: series repulsion motor, medium-speed, Fig. 191.

^ = 1 - 0 : repulsion motor with secondary excitation, low-speed, Fig. 192.

It is, from above constants :

Zi = Zi 4- co 2 (Zo + Z )

= 0.08 + 0.60 j.

A, - —

A s

= 0.202 - 0.010 j.

= 0.835 - 0.014 j.

• Z2

M z ,

= 0.031 - 0.007 j.

q + z 4

= 0.179 + 0.087 j.

414

ELECTRICAL APPARATUS

Hence, substituting into the preceding equations:

(90) ZK = Z»- jScoZ - \ iCo Z (c 0 - jS ) +

= (0.160 + 0.975 5) + j (0.590 - 0.187 S),

(92) ^ = {jSXi (co ~ jS) + Xa}

= Ik + JR K " °- 031 + °- 035 5 _ °- 179 8 *>

-j(- 0.007 + 0.072 s + 0.087 S 2 )},

(91) h = h (0.969 + 0.007 j) + et (0.010 - 0.096 j)

(93)

T e (0.072+0.035^) +/Se<{ (0.016 — 0.072(S) —j 0.045+0. 035 /S) }

U ~ ZK

etc.

226 . As seen, these four curves are very similar to each other and to those of the repulsion motor, with the exception of the

commutation current, i 0 , and commutation factor, k = ~?*

The commutation factor of the compensated series motor, that is, the ratio of current change in the armature coil while leaving the brushes, to total armature current, is constant in the series motor, at all speeds. In the series repulsion motors, the commutation factor, k, starts with the same value at standstill, as the series motor, but decreases with increasing speed, thus giving a superior commutation to that of the series motor, reaches a minimum, and then increases again. Beyond the minimum commutation factor, the efficiency, power-factor, torque and out- put of the motor first slowly, then rapidly decrease, due to the rapid increase of the commutation losses. These higher values, however, are of little practical value, since the commutation is bad.

The higher the voltage ratio, t, that is, the more voltage is impressed upon the compensating circuit, and the less upon the armature circuit, the lower is the speed at which the commuta- tion factor is a minimum, and the commutation so good or perfect. That is, with t = 1, or the repulsion motor with secondary ex- citation, the commutation is best at 70 per cent, of synchronism, and gets poor above synchronism. With t = 0.5, or a series repulsion motor with half the voltage on the compensating, half on the armature circuit, the commutation is best just above syn- chronism, with the motor constants chosen in this instance, and

SINGLE-PHASE COMMUTATOR MOTORS 415

gets poor at speeds above 150 per cent, of synchronism. With t = 0.2, or only 20 per cent, of the voltage on the compensating circuit, the commutation gets perfect at double synchronism.

Best commutation thus is secured by shifting the supply vol- tage with increasing speed from the compensating to the arma- ture circuit.

t > 1, or a reverse voltage, —e h impressed upon the armature circuit, so still further improves the commutation at very low speeds.

For high values of t , however, the power-factor of the motor falls off somewhat.

The impedance of the short-circuited armature coils, chosen in the preceding example :

Z 4 = 7.5 + 10.7,

corresponds to fairly high resistance and inductive reactance in the commutator leads, as frequently used in such motors.

227. As a further example are shown in Fig. 193 and Fig. 194 curves of a motor with low-resistance and low-reactance com- mutator leads, and high number of armature turns, that is, low reduction factor of field to armature circuit, of the constants:

Z\ = 4 + 2 j;

hence:

X 4 - 0.373 + 0.267 j,

and:

Co = 0.3,

c 4 = 0.03,

the other constants being the same as before.

Fig. 193 shows, with the speed as abscissae, the current, torque, power output, power-factor, efficiency and commutation current, i g , under such a condition of operation, that at low speeds t = 1.0, that is, the motor is a repulsion motor with secondary excita- tion, and above the speed at which t = 1.0 gives best commuta- tion (90 per cent, of synchronism in this example), t is gradually decreased, so as to maintain i g a minimum, that is, to maintain best commutation.

As seen, at 10 per cent, above synchronism, i g drops below i, that is, the commutation of the motor becomes superior to that of a good direct-current motor.

Fig. 194 then shows the commutation factors, h = +> of the

%

ELECTRICAL APPARATUS

e =500 VOLTS 700

Z = 0.25 4-3 j OHMS Zi= 0.025 4- 0.075 j ohms Z'= 0.25 +-2.5 j ohms Z2=0.0254-0.075joHMS 650 Zo=0.1 + 0.3 J Ohms Z.4 = 0-4 + 0.2j ohms 600 Co =0.3 <?4 = 0.03

MMia—iiBaai

0.6 0.8 1.0 1.2 1.4

SPEED

Fig. 193.

!9I

■i&CSSgSSS

■IpH

ill

IM— I

Z » 0.25

• Z'-*0.25 + 2.5 j ohms _ Z 0 “"0.1 +0.3iOHMS

” Zi ! °0.025+0.075ioHM8

• Za»0.025+0.075iOHM8 z 4 =4“ 2 j 0HM8

• Co- 0.3

<*4-0.03

'Ca-1.2

0.80 1.00 1.20 1.40 1.60

SPEED % OF SYNCHRONISM

Fig. 194.

SINGLE-PHASE COMMUTATOR MOTORS 417

at motors, all under the assumption of the same constants:

Z = 0.25 4 3 j,

Z' = 0.25 4 2.5j,

Zo = 0.1 4 0.3 j,

Z 2 = 0.025 4 0.075 j,

Zi = 0.025 4' 0.075 j,

£* = 4 4 2j,

Co = 0.3, c 4 = 0.03.

re I gives the commutation factor of the motor as induct- ompensated series motor (t = 0), as constant, k = 3.82,

, the current change at leaving the brushes is 3.82 times tin current. Such condition, under continued operation, give destructive sparking.

re II shows the series repulsion motor, with 20 per cent, of Itage on the compensating winding, t = 0.2; and re III with half the voltage on the compensating winding,

.

re IY corresponds to t = 1, or all the voltage on the com- ing winding, and the armature circuit closed upon itself: on motor with secondary excitation.

re V corresponds to t = 2, or full voltage in reverse direction sed upon the armature, double voltage on the compen- winding.

re VI gives the minimum commutation factor, as derived ying t with the speed, in the manner discussed "before, further comparison are given, for the same motor nts:

re VII, the plain repulsion, motor, showing its good com- on below synchronism, and poor commutation above onism; and

re VIII, an overcompensated series motor, that is, con-

ly compensated series motor, in which the compensating g contains 20 per cent, more ampere-turns than the arma- 0 giving 20 per cent, overcompensation.

3 een, overcompensation does not appreciably improve Ltation at low speeds, and spoils it at higher speeds.

194 also gives the- two components of the compensating E 2 , which are required to give perfect commutation, or. mmutation current;

418

ELECTRICAL APPARATUS

b'

t' 0 = — = component in phase with e, giving quadrature

B

flux:

e fr

t” o = — - = component in quadrature with e, giving flux in 6

phase with e.

228. In direct-current motors, overcompensation greatly improves commutation, and so is used in the form of a com- pensating winding, commutating pole or interpole. In such direct-current motors, the reverse field of the interpole produces a current in the short-circuited armature coil, by its rotation, in the same direction as the armature current in the coil after leaving the brushes, and by proper proportioning of the com- mutating field, the commutation current, i 0) thus can be made to vanish, that is, perfect commutation produced.

In alternating-current motors, to make the commutation current vanish and so produce perfect commutation, the current in the short-circuited coil must not only be equal to the arma- ture current in intensity, but also in phase, that is, the commu- tating field must not only have the proper intensity, but also the proper phase.

In paragraph 223 we have seen that the commutating field has the proper phase to make i 0 vanish, if produced by a voltage impressed upon the compensating winding:

E 2 = Te,

which for all except very low speeds is very nearly in phase with e. The magnetic flux produced by this voltage, or the com- mutating flux, so is nearly in quadrature with e, and therefore approximately in quadrature with the current in the motor, at such speeds where the current, i, is nearly in phase with e. The commutating flux produced by conductive overcompensa- tion, however, is in phase with the current, i 7 hence is of a wrong phase properly to commutate.

That is, in the alternating-current commutator motor, the commutating flux should be approximately in quadrature with the main flux or main current, and so can not be produced by the main current by overcompensation, but is produced by the combined magnetizing action of the main current and a sec- ondary current produced thereby, since in a transformer the re- sultant flux lags approximately 90° behind the primary current,

SINGLE-PHASE COMMUTATOR MOTORS 419

The same results we can get directly by investigating the com- mutation current of the overcompensated series motor. This motor is characterized by:

1 . 6 = E 1 -|- CoEq -f- C 2 E 2 ',

where c 2 = 1 + q = reduction factor of compensating circuit to armature.

2. 1 0 — col, 1 2 — c 2 I, I\ = /.

Substituting into the fundamental equations of the single- phase commutator motor gives the results:

r _ X 4 (c 0 — jSqA)

U ZK e,

where :

ZK = (Z a + Z 5 + jScoZ ) + jS\ 4 (c 0 Z - jSqZr To make I g vanish, it must therefore be :

or approximately:

. c 0 x

or, with the numerical values of the preceding instance:

0.046 - 0.295 j q = 5

That is, the overcompensating component, g, must be approxi- mately in quadrature with the current, /, hence can not be pro- duced by this current under the conditions considered here; and overcompensation, while it may under certain conditions improve the commutation, can as a rule not give perfect commutation in a series alternating-current motor.

229. The preceding study of commutation is based on the assumption of the short-circuit current under the brush as alternating current. This, however, is strictly the case only at standstill, as already discussed in the paragraphs on the repul- sion motor. At speed, an exponential term, due to the abrupt

420

ELECTRICAL APPARATUS

change of current in the armature coil when passing under the brush, superimposes upon the e.m.f. generated in the short- circuited coil, and so on the short-circuit current under the brush, and modifies it the more, the higher the speed, that is, the quicker the current change. This exponential term of e.m.f. generated in the armature coil short-circuited by the commutator brush, is the so-called “e.m.f. of self-induction of commutation.” It exists in direct-current motors as well as in alternating-current motors, and is controlled by overcompensation, that is, by a commutating field in phase with the main field, and approxi- mately proportional to the armature current.

The investigation of the exponential term of generated e.m.f. and of short-circuit current, the change of the commutation current and commutation factor brought about thereby and the study of the commutating field required to control this exponential term leads into the theory of transient phenomena, that is, phenomena temporarily occurring during and immedi- ately after a change of circuit condition. 1

The general conclusions are:

The control of the e.m.f. of self-induction of commutation of the single-phase commutator motor requires a commutating field, that is, a field in quadrature position in space to the main field, approximately proportional to the armature current and in phase with the armature current, hence approximately in phase with the main field.

Since the commutating field required to control, in the arma- ture coil under the commutator brush, the e.m.f. of alternation of the main field, is approximately in quadrature behind the main field — and usually larger than the field controlling the e.m.f. of self-induction of commutation — it follows that the total commutating field, or the quadrature flux required to give best commutation, must be ahead of the values derived in paragraphs 221 to 224.

As the field required by the e.m.f. of alternation in the short- circuited coil was found to lag for speeds below the speed of best commutation, and to lead above this speed, from the position in quadrature behind the main field, the total commutating field must lead this field controlling the e.m.f. of alternation, and it follows:

1 See “Theory and Calculations of Transient Electric Phenomena and Oscillations/' Sections I and II.

SINGLE-PHASE COMMUTATOR MOTORS

421

Choosing the e.m.f., E 2 , impressed upon the compensating winding in phase with, and its magnetic flux, therefore in quad- rature (approximately), behind the main field, gives a com- mutation in the repulsion and the series repulsion motor which is better than that calculated from paragraphs 221 to 224, for all speeds up to the speed of best commutation, but becomes in- ferior for speeds above this. Hence the commutation of the repulsion motor and of the series repulsion motor, when con- sidering the self-induction of commutation, is superior to the calculated values below, inferior above the critical speed, that is, the speed of minimum commutation current. The com- mutation of the overcompensated series motor is superior to the values calculated in the preceding, though not of the same magnitude as in the motors with quadrature commutating flux.

It also follows that an increase of the inductive reactance of the armature coil increases the exponential and decreases the alter- nating term of e.m.f. and therewith the current in the short- circuited coil, and therefore requires a commutating flux earlier in phase than that required by an armature coil of lower reac- tance, hence improves the commutation of the series repulsion and the repulsion motor at low speeds, and spoils it at high speeds, as seen from the phase angles of the commutating flux calculated in paragraphs 221 to 224.

Causing the armature current to lag, by inserting external inductive reactance into the armature circuit, has the same effect as leading commutating flux: it improves commutation at low, impairs it at high speeds. In consequence hereof the com- mutation of the repulsion motor with secondary excitation — in which the inductive reactance of the main field circuit is in the armature circuit — is usually superior, at moderate speeds, to that of the repulsion motor with primary excitation, except at very low speeds, where the angle of lag of the armature cur- rent is very large.

CHAPTER XXI

REGULATING POLE CONVERTERS

230 . With a sine wave of alternating voltage, and the com- mutator brushes set at the magnetic neutral, that is, at right angles to the resultant magnetic flux, the direct voltage of a syn- chronous converter is constant at constant impressed alternating voltage. It equals the maximum value of the alternating voltage between two diametrically opposite points of the commutator, or “ diametrical voltage,” and the diametrical voltage is twice the voltage between alternating lead and neutral, or star or Y voltage of the polyphase system.

A change of the direct voltage, at constant impressed alter- nating voltage (or inversely), can be produced:

Either by changing the position angle between the commuta- tor brushes and the resultant magnetic flux, so that the direct voltage between the brushes is not the maximum diametrical alternating voltage but only a part thereof.

Or by changing the maximum diametrical alternating voltage, at .constant effective impressed voltage, by wave-shape distortion by the superposition of higher harmonics.

In the former case, only a reduction of the direct voltage be- low the normal value can be produced, while in the latter case an increase as well as a reduction can be produced, an increase if the higher harmonics are in phase, and a reduction if the higher harmonics are in opposition to the fundamental wave of the dia- metrical or Y voltage.

A. Variable Ratio by a Change of the Position Angle between Commutator Brushes and Resultant Magnetic Flux

231 . Let, in the commutating machine shown diagrammatic- ally in Fig. 195, the potential difference, or alternating voltage between one point, a, of the armature winding and the neutral, 0 (that is, the F voltage, or half the diametrical voltage) be repre- sented by the sine wave, Fig. 197. This potential difference is a maximum, e, when a stands at the magnetic neutral, at A or B.

REGULATING POLE CONVERTERS

423

If, therefore, the brushes are located at the magnetic neutral, A and B, the -voltage between the brushes is the potential differ- ence between A and B, or twice the maximum Y voltage, 2 e, as indicated in Fig. 197. If now the brushes are shifted by an angle, r, to position C and D , Fig. 196, the direct voltage between

Fig. 195. — Diagram, of Fig. 196. — E.m.f. variation commutating machine by shifting the brushes, with brushes in the mag- netic neutral.

the brushes is the potential difference between C and D, or 2 e cos r with a sine wave. Thus, by shifting the brushes from the position A y B y at right angles with the magnetic flux, to the posi- tion E , F } in line with the magnetic flux, any direct voltage be-

B

Fig. 197. — Sine wave of e.m.f.

tween 2 e and 0 can be produced, with the same wave of alter- nating volage, a.

As seen, this variation of direct yoltage between its maximum value and zero, at constant impressed alternating voltage, is in-

424

ELECTRICAL APPARATUS

dependent of the wave shape, and thus can be produced whether the alternating voltage is a sine wave or any other wave.

It is obvious that, instead of shifting the brushes on the com- mutator, the magnetic field poles may be shifted, in the opposite direction, by the same angle, as shown in Fig. 198, A, B, C .

Instead of mechanically shifting the field poles, they can be shifted electrically, by having each field pole consist of a number of sections, and successively reversing the polarity of these sec- tions, as shown in Fig. 199, A , B } C, Z>.

Fig. 198. — E.m.f. variation by mechanically shifting the poles.

Instead of having a large number of field pole sections, obvi- ously two sections are sufficient, and the same gradual change can be brought about by not merely reversing the sections but reducing the excitation down to zero and bringing it up again in opposite direction, as shown in Fig. 200, A, B, C, D, E.

Fig. 199. — E.m.f. variation by electrically shifting the poles.

In this case, when reducing one section in polarity, the other section must be increased by approximately the same amount, to maintain the same alternating voltage.

When changing the direct voltage by mechanically shifting the brushes, as soon as the brushes come under the field pole faces, self-inductive sparking on the commutator would result if the iron of the field poles were not kept away from the brush

REGULATING POLE CONVERTERS

425

position by having a slot in the field poles, as indicated in dotted line in Fig. 196 and Fig. 198, B. With the arrangement in Figs. 196 and 198, this is not feasible mechanically, and these arrange-

Fig. 200. — E.m.f. variation by shifting-flux distribution.

ments are, therefore, unsuitable. It is feasible, however, as shown in Figs. 199 and 200, that is, when shifting the resultant magnetic flux electrically, to leave a commutating space between

Fig. 201. — Variable ratio or split-pole converter.

the polar projections of the field at the brushes, as shown in Fig. 200, and thus secure as good commutation, as in any other com- mutating machine.

426

ELECTRICAL APPARATUS

Such a variable-ratio converter, then, comprises an armature A , Fig. 201, with the brushes, B , B', in fixed position and field poles, P, P', separated by interpolar spaces, C, C', of such width as required for commutation. Each field pole consists of two parts, P and Pi, usually of different relative size, separated by a narrow space, DD', and provided with independent windings. By vary- ing, then, the relative excitation of the two polar sections, P and Pi, an effective shift of the resultant field flux and a corresponding change of the direct voltage is produced.

As this method of voltage variation does not depend upon the wave shape, by the design of the field pole faces and the pitch of the armature winding the alternating voltage wave can be made as near a sine wave as desired. Usually not much atten- tion is paid hereto, as experience shows that the usual distributed winding of the commutating machine gives a sufficiently close approach to sine shape.

Armature Reaction and Commutation

232. With the brushes in quadrature position to the resultant magnetic flux, and at normal voltage ratio, the direct-current generator armature reaction of the converter equals the syn- chronous-motor armature reaction of the power component of the alternating current, and at unity power-factor the converter thus has no resultant armature reaction, while with a lagging or leading current it has the magnetizing or demagnetizing re- action of the wattless component of the current.

If by a shift of the resultant flux from quadrature position with the brushes, by angle, r, the direct voltage is reduced by factor cos r, the direct current and therewith the direct-current

armature reaction are increased, by factor, > as by the law

of conservation of energy the direct-current output must equal the alternating-current input (neglecting losses). The direct- current armature reaction, ^F, therefore ceases to be equal to the armature, reaction of the alternating energy current, £Fo 7 but is

greater by factor, — — : b J 'cos r

cos r

The alternating-current armature reaction, SF 0 , at no phase dis- placement, is in quadrature position with the magnetic flux.

REGULATING POLE CONVERTERS

427

The direct-current armature reaction, £F, however, appears in the position of the brushes, or shifted against quadrature position by angle r; that is, the direct-current armature reaction is not in opposition to the alternating-current armature reaction, but differs therefrom by angle r, and so can be resolved into two components, a component in opposition to the alternating-cur- rent armature reaction, $ 0 , that is, in quadrature position with the resultant magnetic flux:

CP" = CP cos r = 9r 0 ,

that is, equal and opposite to the alternating-current armature reaction, and thus neutralizing the same; and a component in quadrature position with the alternating-current armature reac- tion, fro, or in phase with the resultant magnetic flux, that is, magnetizing or demagnetizing:

& — $ sin t — $ o tan r;

that is, in the variable-ratio converter the alternating-current armature reaction at unity power-factor is neutralized by a component of the direct-current armature reaction, but a result- ant armature reaction, CP', remains, in the direction of the resultant magnetic field, that is, shifted by angle (90 — r) against the position of brushes. This armature reaction is magnetizing or demagnetizing, depending on the direction of the shift of the field, r.

It can be resolved into two components, one at right angles with the brushes :

CP'i = cos r = ^ o sin r, and one, in line with the brushes:

tf'o = CP' sin r = CP sin 2 r = CF 0 sin r tan t,

as shown diagrammatieally in Figs. 202 and 203.

There exists thus a resultant armature reaction in the direc- tion of the brushes, and thus harmful for commutation, just as in the direct-current generator, except that this armature reac- tion in the direction of the brushes is only = 2F sin 2 t, that is, sin 2 r of the value of that of a direct-current generator.

The value of CF' 2 can also be derived directly, as the difference between the direct-current armature reaction, CF, and the com-

REGULATING POLE CONVERTERS

4 29

ponent of the alternating-current armature reaction, in the direc- tion of the brushes, tfo cost, that is:

& 2 = $ - COS r = S' (1 - cos 2 r) = SF sin 2 r = sin r tan r.

233. The shift of the resultant magnetic flux, by angle r, gives a component of the m.nnf. of field excitation, 3" f = sin r, (where = m.m.f. of field excitation), in the direction of the commutator brushes, and either in the direction of armature reaction, thus interfering with commutation, or in opposition to the armature reaction, thus improving commutation.

If the magnetic flux is shifted in the direction of armature rotation, that is, that section of the field pole weakened toward which the armature moves, as in Fig. 202, the component SF", of field excitation at the brushes is in the same direction as the armature reaction, fy' 2 , thus adds itself thereto and impairs the commutation, and such a converter is hardly operative. In this case the component of armature reaction, Sr', in the direction of the field flux is magnetizing.

If the magnetic flux is shifted in opposite direction to the armature reaction, that is, that section of the field pole weakened which the armature conductor leaves, as in Fig. 203, the com- ponent, ST"/, of field excitation at the brushes is in opposite direc- tion to the armature reaction, 9r' 2 , therefore reverses it, if suffi- ciently large, and gives a commutating or reversing flux, <3> r , that is, improves commutation so that this arrangement is used in such converters. In this case, however, the component of arma- ture reaction, in the direction of the field flux is demagnet- izing, and with increasing load the field excitation has to be in- creased by 9r r to maintain constant flux. Such a converter thus requires compounding, as by a series field, to take care of the demagnetizing armature reaction.

If the alternating current is not in phase with the field, but lags or leads, the armature reaction of the lagging or leading component of current superimposes upon the resultant armature reaction, IF', and increases it — with lagging current in Fig. 202, leading current in Fig. 203 — or decreases it — with lagging cur- rent in Fig. 203, leading current in Fig. 202 — and with lag cf the alternating current, by phase angle, 6 = r, under the conditions of Fig. 203, the total resultant armature reaction vanishes, that is, the lagging component of synchronous-motor armature reaction compensates for the component of the direct-current reaction,

430

ELECTRICAL APPARATUS

which is not compensated by the armature reaction of the power component of the alternating current. It is interesting to note that in this case, in regard to heating, output based thereon, etc., the converter equals that of one of normal voltage ratio.

B. Variable Ratio by Change of Wave Shape of the Y Voltage

234 . If in the converter shown diagrammatically in Fig. 204 the magnetic flux disposition and the pitch of the armature winding are such that the potential difference between the point,

a , of the armature and the neutral 0, or the Y voltage, is a sine wave, Fig. 205 A, then the voltage ratio is normal. Assume, however, that the voltage curve, a , differs from sine shape by the superposition of some higher harmonics: the third harmonic in Figs. 205 B and C; the fifth harmonic in Figs. 205 D and E. If, then, these higher harmonics are in phase with the fundamental, that is, their maxima coincide, as in Figs. 205 B and D, they increase the maximum of the

Fig. 204. — Variable ratio con- alternating voltage, and thereby the ofthe y y e C mi! ginK shape direct voltage; and if thesehar monies

are in opposition to the funda- mental, as in Figs. 205 C and E, they decrease the maximum alternating and thereby the direct' voltage, without appreciably affecting the effective value of the alternating voltage. For in- stance, a higher harmonic of 30 per cent, of the fundamental increases or decreases - the direct voltage by 30 per cent., but varies the effective alternating voltage only by VT + 0.3 2 = 1.044, or 4.4 per cent.

The superposition of higher harmonics thus offers a means of increasing as well as decreasing the direct voltage, at constant alternating voltage, and without shifting the angle between the brush position and resultant magnetic flux.

Since, however, the terminal voltage of the converter does not only depend on the generated e.m.f. of the converter, but also on that of the generator, and is a resultant of the two e.m.fs. in approximately inverse proportion to the impedances from the converter terminals to the two respective generated e.m.fs., for

REGULATING POLE CONVERTERS

431

varying the converter ratio only such higher harmonics can be used which may exist in the Y voltage without appearing in the converter terminal voltage or supply voltage.

In general, in an n-phase system an nth harmonic existing in the star or Y voltage does not appear in the ring or delta voltage,

Fig. 205. — Superposition of harmonics to change the e.m.f. ratio.

as the ring voltage is the combination of two star voltages dis- 180

placed in phase by degrees for the fundamental, and thus by

n

180°, or in opposition, for the nth harmonic.

Thus, in a three-phase system, the third harmonic can be in- troduced into the Y voltage of the converter, as in Figs. 205 B and C, without affecting or appearing in the delta voltage, so can be used for varying the direct-current voltage, while the fifth harmonic can not be used in this way, but would reappear and

432

ELECTRICAL APPARATUS

cause a short-circuit current in the supply voltage, hence should be made sufficiently small to be harmless.

235 . The third harmonic thus can be used for varying the direct voltage in the three-phase converter diagrammatically shown in Fig. 206 A, and also in the six-phase converter with

Fig. 206. — Transformer connections for varying the e.m.f. ratio by super- position of the third harmonic.

double-delta connection, as shown in Fig. 206 B, or double-7 connection, as shown in Fig. 206 C, since this consists of two separ rate three-phase triangles of voltage supply, and neither of. them contains the third harmonic. In such a six-phase converter with double- 7 connection, Fig. 206 G, the two neutrals, however,

REGULATING POLE CONVERTERS 433

must not be connected together, as the third harmonic voltage exists between the neutrals. In the six-phase converter with diametrical connections, the third harmonic of the Y voltage ap- pears in the terminal voltage, as the diametrical voltage is twice the Y voltage. In such a converter, if the primaries of the sup-

ply transformers are connected in delta, as in Fig. 206 D, the third harmonic is short-circuited in the primary voltage triangle, and thus produces excessive currents, which cause heating and interfere with the voltage regulation, therefore, this arrangement

Fig. 20 8. — Core-type transformer.

is not permissible. If, however, the primaries are connected in Y, as in Fig. 206 E, and either three separate single-phase trans- formers, or a three-phase transformer with three independent magnetic circuits, is used, as in Fig. 207, the triple-frequency voltages in the primary are in phase with each other between

434

ELECTRICAL APPARATUS

the line and the neutral, and thus, with isolated neutral, can not produce any current. With a three-phase transformer as shown in Fig. 208, that is, in which the magnetic circuit of the third harmonic is open, triple-frequency currents can exist in the sec- ondary and this arrangement therefore is not satisfactory.

In two-phase converters, higher harmonics can be used for regulation only if the transformers are connected in such a man- ner that the regulating harmonic, which appears in the converter terminal voltage, does not appear in the transformer terminals, that is, by the connection analogous to Figs. 206 E and 207.

Since the direct-voltage regulation of a three-phase or six- phase converter of this type is produced by the third harmonic,

Fig. 209 . — Y e.m.f. wave.