Theory and Calculation of Electrical Apparatus (1917) — part 10 of 21

if ii is positive or inductive load, from equation (9) follows that the terminal voltage, e h drops with increasing load; while

if ii is negative or anti-inductive load, the terminal voltage, ei t rises with increasing load, ultimately reaches a maximum and then decreases again.

From equation (9) follows, that by changing the impedances, the amount of compounding can be varied. For instance, at non-inductive load, or in equation (10) by increasing the re- sistance, r 4 , the voltage, increases faster with the load.

That is, the overcompounding of the machine can be increased by inserting resistance in the rotor circuit.

124 . As an example is shown, in Fig. 65, in full line, with the total current, I = y/i* + id, as abscissae, the voltage regulation of such a machine, or the terminal voltage, Ci, with a four- cycle synchronous motor as exciter of a 60-cycle synchronous- induction generator driven at 64-cycles speed.

1. For non-inductive load, or h = i. (Curve I.)

2. For inductive load of 80 per cent, power-factor; or

1 1 = I (0.8 — 0.6 j). • (Curve II.)

3. For anti-inductive load of 80 per cent, power-factor; or h = I (0.8+ 0.6 j)- ' (Curve III.)

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ELECTRICAL APPARATUS

For the constants:

e 0 = 2000 volts.

Zi = 0.1 + 0.3 j.

Z 2 — 1 + 0.5 j.

Then :

Z z = 1.6 + 1.3 j and Z 4 = 1.4 + 0.7.7. Hence, substituting in equation (9) :

e\ = VI X 10 s - (0.7e + 1.6?i) 2 + 1.4 i - 1.3 n;

Z 0 = 0.5 + 0.5 j. a = 0.067.

£ = 1, that is, the same number of turns in stator and rotor

2S0Q

2GOO

2400

2200

2000

1800

1G00

1400

1200

-90 - 80 -70 - 60 - 50 -40 -30 -20 -10 0 10 20 30 40 50 60 70 80 90

Fig. 66. — Synchronous induction generator, voltage regulation with power-

factor of load.

thus, for non-inductive load, ii = 0:

«i = VI X 10 6 - 0.49 i- + 1.4 i; for inductive load of 80 per cent, power-factor = 0.6 1;i = 0.8 1 :

Ci = VI x 10 6 - 2.31 P + 0.34 J;

and for anti-inductive load of 80 per cent, power-factor i\ — —0.6 I; i — 0.8 7:

ei = V4 X 10 6 - 0.1 6~P + 1.9 I.

Comparing the curves of this example with those of the same machine driven as frequency converter with exciter generator,

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S YNCHRONO US 1ND UCTION GENERA TOR 21 1

and shown in dotted lines in the same chart (Fig. 65), it is seen that the voltage is maintained at load far better, and especially at inductive load the machine gives almost perfect regulation of voltage, with the constants assumed here.

To show the variation of voltage with a change of power- factor, at the same output in current, in Fig. 66, the terminal voltage, ex, is plotted with the phase angle as abscissae, from wattless anti-inductive load, or 90° lead, to wattless inductive load, or 90° lag, for constant current output of 400 amp. As seen, at wattless load both machines give the same voltage but for energy load the type (6) gives with the same excitation a higher voltage, or inversely, for the same voltage the type (a) requires a higher excitation. It is, however, seen that with the same current output, but a change of power-factor, the voltage of type (a) is far more constant in the range of inductive load, while that of type (6) is more constant on anti-inductive load, and on inductive load very greatly varies with a change of power-factor.

CHAPTER XIV

PHASE CONVERSION AND SINGLE-PHASE GENERATION

125. Any polyphase system can, by means of two stationary transformers, be converted into any . other polyphase system, and in such conversion, a balanced polyphase system remains balanced, while an unbalanced system converts into a polyphase system of the same balance factor. 1

• In the conversion between single-phase system and polyphase system, a, storage of energy thus must take place, as the balance factor of the single-phase system is zero or negative, while that of the balanced polyphase system is unity. For such energy storage may be used capacity, or inductance, or momentum or a combination thereof :

Energy storage by capacity, that is, in the dielectric field, required per kilovolt-ampere at 60 cycles about 2000 c.c. of space, at a cost of about $10. Inductance, that is, energy storage by the magnetic field, requires about 1000 c.c. per kilo- volt-ampere at 60 cycles, at a cost of $1, while energy storage by momentum, as kinetic mechanical energy, assuming iron moving at 30 meter-seconds, stores 1 kva. at 60 cycles by about 3 c.c., at a cost of 0.2c., thus is by far the cheapest and least bulky method of energy storage. Where large amounts of energy have to be stored, for a very short time, mechanical momentum thus is usually the most efficient and cheapest method.

However, size and cost of condensers is practically the same for large as for small capacities, while the size and cost of induc- tance decreases with increasing, and increases with decreasing kilovolt-ampere capacity. Furthermore, the use of mechanical momentum means moving machinery, requiring more or less attention, thus becomes less suitable, for smaller values of power. Hence, for smaller amounts of stored energy, inductance and capacity may become more economical than momentum, and for very small amounts of energy, the condenser may be the cheapest device. The above figures thus give only the approxi-

1 “ Theory and Calculation of Alternating-current^ Phenomena/ ’ 5th edition, Chapter XXXII.

PHASE CONVERSION

213

mate magnitude for medium values of energy, and then apply only to the active energy-storing structure, under the assumption, that during every energy cycle (or half cycle of alternating cur- rent and voltage), the entire energy is returned and stored again. While this is the case with capacity and inductance, when using momentum for energy storage, as flywheel capacity, the energy storage and return is accomplished by a periodic speed variation, thus only a part of the energy restored, and furthermore, only a part of the structural material (the flywheel, or the rotor of the machine) is moving. Thus assuming that only a quarter of the mass of the mechanical structure (motor, etc.) is revolving, and that the energy storage takes place by a pulsation of speed of 1 per cent., then 1 kva. at 60 cycles would require 600 c.c. of material, at 40c.

Obviously, at the limits of dielectric or magnetic field strength, or at the limits of mechanical speeds, very much larger amounts of energy per bulk could be stored. Thus for instance, at the limits of steam-turbine rotor speeds, about 400 meter-seconds, in a very heavy material as tungsten, 1 c.c. of material would store about 200 kva. of 60-cycle energy, and the above figures thus represent only average values under average conditions.

126. Phase conversion is of industrial importance in changing from single-phase to polyphase, and in changing from polyphase to single-phase.

Conversion from single-phase to polyphase has been of con- siderable importance in former times, when alternating-current generating systems were single-phase, and alternating-current motors required polyphase for their operation. With the prac- tically universal introduction of three-phase electric power generation, polyphase supply is practically always available for stationary electric motors, at least motors of larger size, and conversion from single-phase to polyphase thus is of importance mainly :

(a) To supply small amounts of polyphase current, for the starting of smaller induction motors operated on single-phase distribution circuits, 2300 volts primary, or 110/220 volts secondary, that is, in those cases, in which the required amount of power is not sufficient to justify bringing the third phase to the motor: with larger motors, all the three phases are brought to the motor installation, thus polyphase supply used.

(b) For induction-motor railway installations, to avoid the

214

ELECTRICAL APPARATUS

com ation and inconvenience incident to the use of two trolley wires. In this case, as large amounts of polyphase power are required, and economy in weight is important, momentum is enerally used for energy storage, that is an induction machine is employed as phase converter, and then is used either in series or in shunt to the motor.

For the small amounts of power required by use (a), generally inductance or capacity are employed; and even then usually the conversion is made not to polyphase, but to monocyclic, as the latter is far more economical in apparatus.

Conversion from polyphase to single-phase obviously means the problem of deriving single-phase power from a balanced polyphase system. A single-phase load can be taken from any phase of a polyphase system, but such a load, when consider- able, unbalances the polyphase system, that is, makes the vol- tages of the phases unequal and lowers the generator capacity. The problem thus is, to balance the voltages and the reaction of the load on the generating system.

This problem has become of considerable importance in the last years, for the purpose of taking large single-phase loads, for electric railway, furnace work, etc., from a three-phase supply system as a central station or transmission line. For this pur- pose, usually synchronous phase converters with synchronous phase balancers are used.

As illustration may thus be considered in the following the monocyclic device, the induction phase converter, and the synchronous phase converter and balancer.

Monocyclic Devices

127 . The name “monocyclic” is applied to a polyphase sys- tem of voltages (whether symmetrical or unsymmetrical), in which the flow of energy is essentially single-phase.

For instance* if, as shown diagrammatically in Fig. 67, we connect, between single-phase mains, AB , two pairs of non-in- ductive resistances, r, and inductive reactances, x (or in general, two pairs of impedances of different inductance factors), such that r = x, consuming the voltages Ex and E 2 respectively, then the voltage eo = CD is in quadrature with, and equal to, the voltage e = AB f and the two voltages, e and eo, constitute a monocyclic -system of quarter-phase voltages: e gives the energy

PHASE CONVERSION

215

axis of the monocyclic system, and e Q the quadrature or wattless axis. That is, from the axis, e, power can be drawn, within the limits of the power-generating system back of the supply voltage. If, however, an attempt is made to draw power from the monocyclic quadrature voltage, e 0 , this voltage collapses.

If then the two voltages, e and e 0 , are impressed upon a quarter- phase induction motor, this motor will not take power equally from both phases, e and e 0 , but takes power essentially only from phase, e. In starting, and at heavy load, a small amount of power is taken also from the quadrature voltage, e 0 , but at light- load, power may be returned into this voltage, so that in general the average power of e 0 approximates zero, that is, the voltage, Co, is wattless.

A monocyclic system thus may be defined as a system of poly- phase voltages, in which one of the power axis, the main axis or energy axis, is constant potential, and the other power axis, the auxiliary or quadrature axis, is of dropping characteristic and therefore of limited power. Or it may be defined as a poly- phase system of voltage, in which the power available in the one power axis of the system is practically unlimited compared with that of the other power axis.

A monocyclic system thus is a system of polyphase voltage, which at balanced polyphase load becomes unbalanced, that is, in which an unbalancing of voltage or phase relation occurs when all phases are loaded with equal loads of equal inductance factors.

In some respect, all methods of conversion from single-phase to polyphase might be considered as monocyclic, in so far as the quadrature phase produced by the transforming device is limited by the capacity of the transforming device, while the main phase is limited only by the available power of the generating system. However, where the power available in the quadrature phase produced by the phase converter is sufficiently large not to constitute a limitation of power in the polyphase device sup- plied by it, or in other words, where the quadrature phase- pro- duced by the phase converter gives essentially a constant-poten- t al voltage under the condition of the use of the device, then the system is not considered as monocyclic, but is essentially polyphase.

In the days before the general introduction of three-phase power generation, about 20 years ago, monocyclic systems were

216

ELECTRICAL APPARATUS

extensively used, and monocyclic generators built. These were single-phase alternating-current generators, having a small quadrature phase of high inductance, which combined with the main phase gives three-phase? or quarter-phase voltages. The auxiliary phase was of such high reactance as to limit the quadra- ture power and thus make the flow of energy essentially single- phase, that is, monocyclic. The purpose hereof was to permit the use of a small quadrature coil on the generator, and thereby to preserve the whole generator capacity for the single-phase main voltage, without danger of overloading the quadrature phase in case of a high motor load on the system. The general introduction of the three-phase system superseded the mono- cyclic generator, and monocyclic devices are today used only for local production of polyphase voltages from single-phase supply, for the starting of small single-phase induction motors, etc. The advantage of the monocyclic feature then consists in limiting the output and thereby the size of the device, and making it thereby economically feasible with the use of the rather expen- sive energy-storing devices of inductance (and capacity) used in this case.

The simplest and most generally used monocyclic device con- sists of two impedances, Z i and Z 2 , of different inductance factors (resistance and inductance, or inductance and capacity), con- nected across the single-phase mains, A and B. The common connection, C, between the two impedances, Zi and Z 2 , then is dis- placed in phase from the single-phase supply voltage, A and B , and gives with the same a system of out-of-phase voltages, AC y CB and AB , or a — more or less unsymmetrical — three-phase triangle. Or, between this common connection, C, and the middle, D, of an autotransformer connected between the single- phase mains, AB , a quadrature voltage, CD, is produced.

This “monocyclic triangle” ACB y in its application as single- phase induction motor-starting device, is discussed in Chapter V.

Two such monocyclic triangles combined give the monocyclic square, Fig. 67.

128 . Let then, in the monocyclic square shown diagrammatic- ally in Fig. 67:

F] = < 7 i — jbx = admittance AC and DB;

F 2 = <72 — jb 2 = admittance CB and AD;

and let :

Yq = g 0 — jb 0 = admittance of the load on

PHASE CONVERSION

217

the monocyclic quadrature voltage, E 0 — CD, and current, J 0 . Denoting then :

E — e = supply voltage, AB, and / = supply current, and Ei, Ei = voltages, h, J 2 = currents in the two sides of the monocyclic square.

It is then, counting voltages and currents in the direction indicated by the arrows in Fig. 67 :

hence:

and:

substituting:

into (3) gives:

Ei + Ei — e>

E 2 — Ei ~ E oj

v E + E 0 ] Ei = — o — ’

l = 1 1 + 1 2, /o = h - h;

U EoYo, h = EiYi, ■

h = EiYi)

I =EiYi + EtYi, EoYo = EiYi - EiYi)

( 1 )

( 2 )

(3)

(4)

(5)

substituting (2) into (5) gives:

xt _ * (Ji - Yi) .

• J ° Y 1 + Yi + 2Y 0 ’

substituting (6) into (2) gives:

Ei = Ei =

e(Yi + Y 0 )

Y 1 + Y 1 + 2Y 0 ’ e (Yi + Y 0 )

Yx +Yi + 2 7o’

( 6 )

( 7 )

218

ELECTRICAL APPARATUS

substituting (7) and (6) into (4) and (5) gives the currents:

r = e JAh ~ IA 1

•° Y 1 +Y 2 + 2Y 0 ’

t = g (W + yor 2 + 2r,y 2 )

• Y 1 + y 2 + 2 Y 0

T _ eY 1 (Y i +F 0 )

• l Y 1 +Y 2 + 2Yo r _ eY,(Y 1 + Y 0 )

• 2 Yj + Y 2 + 2Yo

129. For a combination of equal resistance and reactance:

Fig. 67. — Resistance-inductance monocyclic square, topographical regular tion characteristic.

and a load:

Yx = a,

F 2 = —ja;

Yq = a(p -jq);

equations (6) and (8) give:

E o = lo =

I =

£ (1 + j)

1 - j + 2 (p - jg)’

ea (p - jg) (1 + j)

1 - j + 2 (p - jgj’

[(P ~ jg) (1 ~ j) - 2 j] 1 - j + 2 (p — jq)

1

1,

PHASE CONVERSION

219

Fig. 67 shows the voltage diagram, and Fig. 68 the regulation, that is, the values of eo and i, with io as abscissae, for:

e = 100 volts, a = 0.1 V2 mho.

Fig. 68. — Resistance-inductance monocyclic square, regulation curve.

For: q = 0, that is, non-inductive load, the voltage diagram is a curve shown by circles in Fig. 67, for 0, 2, 4, 6, 8 and 10 amp. load, the latter being the maximum or short-circuit value.

For q = p, or a load of 45° load, the voltage diagram is the straight line shown by crosses in Fig. 67. That is, in this case, the monocyclic voltage, e 0) is in quadrature with the supply voltage,

220

ELECTRICAL APPARATUS

e, at all loads, while for non-inductive load the monocyclic voltage, e 0} not only shrinks with increasing load, but also shifts in phase, from quadrature position, and the diagram is in the latter case shown for 4 amp. load by the dotted lines in Fig. 67.

In Fig. 68 the drawn lines correspond to non-inductive load. The regulation for 45° lagging load is shown by dotted lines in Fig. 68.

e'o shows the quadrature component of the monocyclic voltage, e 0 , at non-inductive load. That is, the component of e 0 , which is in phase with e , and therefore could be neutralized by inserting into 6q a part of the voltage, e, by transformation.

As seen in Fig. 68, the supply current is a maximum of 20 amp. at no-load, and decreases with increasing load, to 10 amp. at short-circuit load.

The apparent efficiency of the device, that is, the ratio of the volt-ampere output:

Qo = e Q i 0

to the volt-ampere input:

Q = ei

is given by the curve, 7, in Fig. 68.

As seen, the apparent efficiency is very low, reaching a maxi- mum of 14 per cent. only.

If the monocyclic square is produced by capacity and induc- tance, the extreme case of dropping of voltage, eo, with increase of current, i 0 , is reached in that the circuit of the voltage, e 0 , becomes a constant-current circuit, and this case is more fully discussed in Chapter XIV of u Theory and Calculation of Electric Circuits” as a constant-potential constant-current transforming device.

Induction Phase Converter

130 . The magnetic field of a single-phase induction motor at or near synchronism is a uniform rotating field, or nearly so, deviating from uniform intensity and uniform rotation only by the impedance drop of the primary winding. Thus, in any coil displaced in position from the single-phase primary coil of the induction machine, a voltage is induced w T hich is displaced in phase from the supply voltage by the same angle as the coil is displaced in position from the coil energized by the supply vol- tage. An induction machine running at or near synchronism thus can be used as phase converter, receiving single-phase sup-

PHASE CONVERSION

221

ply voltage, E 0 , and current, 1 0 , in one coil, and producing a voltage of displaced phase, E 2 , and current of displaced phase, I 2 , in another coil displaced in position.

Thus if a quarter-phase motor shown diagrammatically in Fig. 69A is operated by a single-phase voltage, E 0 , supplied to the one

z 0 z, z, z 0

Fig. 69. — Induction phase converter diagram.

phase, in the other phase a quadrature voltage, E 2 , is produced and quadrature current can be derived from this phase.

The induction machine, Fig. 69 A, is essentially a transformer, giving two transformations in series: from the primary supply circuit, Eolo, to the secondary circuit or rotor, EJi, and from the rotor circuit,’ Eili, as primary circuit, to the other stator circuit

222

ELECTRICAL APPARATUS

or second phase, E 2 I 2 , as secondary circuit. It thus can be repre- sented diagrammatically by the double transformer Fig. 695.

The only difference between Fig. 69A and 695 is, that in Fig. 69A the synchronous rotation of the circuit, EJi, carries the cur- rent, Ji, 90° in space to the second transformer, and thereby pro- duces a 90° time displacement. That is, primary current and voltage of the second transformer of Fig. 695 are identical in intensity with the secondary currents and voltage of the first transformer, but lag behind them by a quarter period in space and thus also in time. The momentum of the rotor takes care of the energy storage during this quarter period.

As the double transformer, Fig. 695, can be represented by the double divided circuit, Fig. 69C, 1 Fig. 69C thus represents the induction phase converter, Fig. 69 A, in everything except that it does not show the quarter-period lag.

As the equations derived from Fig. 69(7 are rather complicated, the induction converter can, with sufficient approximation for most purposes, be represented either by the diagram Fig. 695, or by the diagram Fig. 69 E. Fig. 695 gives the exciting current of the first transformer too large, but that of the second trans- former to.o small, so that the two errors largely compensate. The reverse is the case in Fig. 695, and the correct value, cor- responding to Fig. 69(7, thus lies between the limits 695 and 695. The error made by either assumption, 695 or 695, thus must be smaller than the difference between these two assumptions.

131. Let:

F 0 = g 0 — jbo = primary exciting admittance of the induc- tion machine,

Z 0 = r 0 + jx 0 = primary, and thus also tertiary self-induc- tive impedance,

Z 1 = ri + jx 1 = secondary self-inductive impedance, all at full frequency, and reduced to the same number of turns.

Let:

F 2 = p 2 — j6 2 == admittance of the load on the second phase; denoting further:

Z = Zo + Zi f

^‘Theory and Calculation of Alternating-current Phenomena,” 5th edition, page 204. *

PHASE CONVERSION 223

it is, then, choosing the diagrammatic representation, Fig. 69 D:

1 0 ~ EqYq = 1 2 + E 2 Y 0 = hj

Eo = E% + 2 Z ( 1 2 + E^Yq), 1 2 = E2Y2)

substituting (11) into *(10) and transposing, gives:

T? .

1 + 2Z(Y 0 + Y 2 y

if the diagram, Fig. 69Z£, is used, it is:

rp Eo

• 2 1 + 2Z(Yo + Y2[1 + Y 0 Z])’

which differs very little from (12).

And, substituting (11) and (12) into (9):

h = #2 (7 0 + Yt) + EoY 0,

__ 7 2 +2 7 0 +2Z7 0 (7o+7 2 ) •

‘° l + 22(7 0 + 7 2 ) ~

(9)

(10)

(ID

( 12 )

(13)

(14)

Equations (11), (12) and (13) give for any value of load, 7 2 , on the quadrature phase, the values of voltage, # 2 , and current, / 2 , of this phase, and the supply current, / 0 , at supply voltage, # 0 .

It must be understood, however, that the actual quadrature voltage is not # 2 , but is jE 2) carried a quarter phase forward by the rotation, as discussed before.

132. As instance, consider a phase converter operating at con- stant supply voltage:

Eo = e 0 = 100 volts;

of the constants :

Y 0 = 0.01 - O.tj,

Z 0 = Zi = 0.05 + 0.15 j;

thus:

Z = 0.1 + 0.3 j;

and let:

Yi - a (p - jq)

= a (0.8 — 0.6 j),

that is, a load of 80 per cent, power-factor, which corresponds about to the average power-factor of an induction motor.

224

ELECTRICAL APPARATUS

It is, then, substituted into (11) to (13):

100

(1.062 + 0.52 -a) + j (0.36 a - 0.028)’

T (80 - 60 j) a

U (1.062 + 0.52 a) + j(0.36a - 0.028)'

for:

a = 0, or no-load, this gives :

62 ^ 94.1,

H = 0 ,

10 = 19.5;

for:

a = 00 ; or short-circuit, this gives:

62 = 0,

i 2 = 159,

11 = 169.

The voltage diagram is shown in Tig. 70, and the load char- acteristics or regulation curves in Fig. 71.

As seen: the voltage, e 2 , is already at no-load lower than the supply voltage, e 0 , due to the drop of voltage of the exciting cur- rent in the self-inductive impedance of the phase converter.

In Fig. 70 are marked by circles the values of voltage, e 2 , for every 20 per cent, of the short-circuit current.

Fig. 71 gives the quadrature component of the voltage, e 2 , as e r/ 2 , and the apparent efficiency, or ratio of volt-ampere output to volt-ampere input :

__ 62^2 ^ eo'io

and the primary supply current, io-

It is interesting to compare the voltage diagram and especially the load and regulation curves of the induction phase converter, Figs. 70 and 71, with those of the monocyclic square, Figs. 67 and 68.

As seen, in the phase converter, the supply current at no-load is small, is a mere induction-machine exciting current, and in- creases with the load and approximately proportional thereto.

The no-load input of both devices is practically the same, but the voltage regulation of the phase converter is very much better: the voltage drops to zero at 159 amp. output, while that of the

PHASE CONVERSION

225

226

ELECTRICAL APPARATUS

monocyclic square reaches zero already at 10 amp. output. This illustrates the monocyclic character of the latter, that is, the limi- tation of the output of the quadrature voltage.

As the result hereof, the phase converter reaches fairly good apparent efficiencies, 54 per cent., and reaches these already at moderate loads.

• The quadrature component, e" 2 , of the voltage, e 0 , is much smaller with the phase converter, and, being in phase with the supply voltage, e 0 , can be eliminated, and rigid quadrature relation of 6 2 with eo maintained, by transformation of a voltage — e" 2 from the single-phase supply into the secondary. Furthermore, as e" 2 is approximately proportional to i 0 — except at very low loads — -it could be supplied without regulation, by a series transformer, that is, by connecting the primary of a transformer in series with the supply circuit, i 0 , the secondary in series with e 2 . Thereby e 2 would be maintained in almost perfect quadrature relation to e 0 at all important loads.

Thus the phase converter is an energy-transforming device, while the monocyclic square, as the name implies, is a device for producing an essentially wattless quadrature voltage.

133. A very important use of the induction phase converter is in series with the polyphase induction motor for which it sup- plies the quadrature phase.

In this case, the phase, e 0 , io of the phase converter is connected in series to one phase, eVo, of the induction motor driving the electric car or polyphase locomotive, into the circuit of the single- phase supply voltage, e = e Q + e'o, and the second phase of the phase converter, e 2 , i 2 , is connected to the second phase of the induction motor.

This arrangement still materially improves the polyphase regu- lation: the induction motor receives the voltages:

e f o = e — eo,

and:

e' 2 — e 2 .

At no-load, e 2 is a maximum. With increasing load, e 2 = e' 2 drops, and hereby also drops the other phase voltage of the in- duction motor, e'o. This, however, raises the voltage, e 0 = e — e'o, on the primary phase of the phase converter, and hereby raises the secondary phase voltage, e 2 = e' 2 , thus maintains the

PHASE CONVERSION

227-

two voltages e' 0 and e' 2 impressed upon the induction motor much more nearly equal, than would be the case with the use of the phase converter in shunt to the induction motor.

Series connection of the induction phase converter, to the in- duction motor supplied by it, thus automatically tends to regu- late for equality of the two-phase voltages, e' 0 and e' 2 , of the induc- tion motor. Quadrature position of these two-phase voltages can be closely maintained by a series transformer between i 0 and i 2 , as stated above.

It is thereby possible to secure practically full polyphase motor output from an induction motor operated from single-phase sup- ply through a series-phase converter, while with parallel connec- tion of the phase converter, the dropping quadrature voltage more or less decreases the induction motor output. For this reason, for uses where maximum output, and especially maximum torque at low speed and in acceleration is required, as in rail- roading, the use of the phase converter in series connections to the motor is indicated.

Synchronous Phase Converter and Single-phase Generation

134. While a small amount of single-phase power can be taken from a three-phase or in general a polyphase system without dis- turbing the system, a large amount of single-phase power results in unbalancing of the three-phase voltages and impairment of the generator output.

With balanced load, the impedance voltages, e* = iz, of a three- phase system are balanced three-phase voltages, and their effect can be eliminated by inserting a three-phase voltage into the system by three-phase potential regulator or by increasing the generator field excitation. The impedance voltages of a single- phase load, however, are single-phase voltages, and thus, com- bined with the three-phase system voltage, give an unbalanced three-phase system. That is, in general, the loaded phase drops in voltage, and one of the unloaded phases rises, the other also drops, and this the more, the greater the impedance in the circuit between the generated three-phase voltage and the single-phase load. Large single-phase load taken from a three-phase trans- mission line — as for instance by a supply station of a single-phase electric railway — thus may cause an unbalancing of the trans- mission-line voltage sufficient to make it useless.

A single-phase system of voltage, e , may be considered as com- bination of two balanced three-phase systems of opposite phase

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ELECTRICAL APPARATUS

, e ee ee 2 , e et 2 ee

rotation: 2 > y. -y and y y> y where e = Vl

-i + i_/3, 2

The unbalancing of voltage caused by a single-phase load of impedance voltage, e = iz , thus is the same as that caused by two three-phase impedance voltages, e/2, of which the one has the same, the other the opposite phase rotation as the three-phase supply system. The former can be neutralized by raising the supply voltage by e/2, by potential regulator or generator excita- tion. This means, regulating the voltage for the average drop. It leaves, however, the system unbalanced by the impedance voltage, e/2, of reverse-phase rotation. The latter thus can be compensated, and the unbalancing eliminated, by inserting into the three-phase system a set of three-phase voltages, e/2, of re- verse-phase rotation. Such a system can be produced by a three- phase potential regulator by interchanging two of the phases. Thus, if A, B, C are the three three-phase supply voltages, im- pressed upon the primary or shunt coils a, b, c of a three-phase potential regulator, and 1, 2, 3 are the three secondary or series coils of the regulator, then the voltages induced in 1, 3, 2 are three-phase of reverse-phase rotation to A, B, C, and can be in- serted into the system for balancing the unbalancing due to single-phase load, in the resultant voltage: A + 1, B + 3, C + 2. It is obviously necessary to have the potential regulator turned into such position, that the secondary voltages 1, 3, 2 have the proper phase relation. This may require a wider range of turn- ing than is provided in the potential regulator for controlling balanced voltage drop.

It thus is possible to restore the voltage balance of a three- phase system, which is unbalanced by a single-phase load of im- pedance voltage, e’ , by means of two balanced three-phase poten- tial regulators of voltage range, e'/2, connected so that the one gives the same, the other the reverse phase rotation of the main three-phase system.

Such an apparatus producing a balanced polyphase system of reversed phase rotation, for inserting in series into a polyphase system to restore the balance on single-phase load, is called a phase balancer, and in the present case, a stationary induction phase balancer.

A synchronous machine of opposite phase rotation to the main system voltages, and connected in series thereto, would then be a synchronous phase balancer .

PHASE CONVERSION

229

The purpose of the phase balancer, thus, is the elimination of the voltage unbalancing due to single-phase load, and its capacity must be that of the single-phase impedance volt-amperes. It obviously can not equalize the load on the phases, but the flow of power of the system remains unbalanced by the single-phase load.

135. The capacity of large synchronous generators is essentially determined by the heating of the armature coils. Increased load on one phase, therefore, is not neutralized by lesser load on the other phases, in its limitation of output by heating of the arma- ture coils of the generators.

The most serious effect of unbalanced load on the generator is that due to the pulsating armature reaction. With balanced polyphase load, the armature reaction is constant in intensity and in direction, with regards to the field. With single-phase load, however, the armature reaction is pulsating between zero and twice its average value, thus may cause a double-frequency pulsation of magnetic flux, which, extending through the field circuit, may give rise to losses and heating by eddy currents in the iron, etc. With the slow-speed multipolar engine-driven alternators of old, due to the large number of poles and low per- ipheral speed, the ampere-turns armature reaction per pole amounted to a few thousand only, thus were not sufficient to cause serious pulsation in the magnetic-field circuit. With the large high-speed turbo-alternators of today, of very few poles, and to a somewhat lesser extent also with the larger high-speed machines driven by high-head waterwheels, the armature reac- tion per pole amounts to very many thousands of ampere-turns. Section and length of the field magnetic circuit are very large. Even a moderate pulsation of armature reaction, due to the un- balancing of the flow of power by single-phase load, then, may cause very large losses in the field structure, and by the resultant heating seriously reduce the output of the machine.

It then becomes necessary either to balance the load between the phases, and so produce the constant armature reaction of balanced polyphase load, or to eliminate the fluctuation of the armature reaction. The latter is done by the use of an effective squirrel-cage short-circuit winding in the pole faces. The double- frequency pulsation of armature reaction induces double-fre- quency currents in the squirrel cage — just as in the single-phase induction motor — and these induced currents demagnetize, when

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ELECTRICAL APPARATUS

the armature reaction is above, and magnetize when it is below the average value, and thereby reduce the fluctuation, that is, approximate a constant armature reaction of constant direction with regards to 4 the field — that is, a uniformly rotating magnetic field with regards to the armature.

However, for this purpose, the m.m.f. of the currents induced in the squirrel-cage winding must equal that of the armature winding, that is, the total copper cross-section of the squirrel cage must be of the same magnitude as the total copper cross-section of the armature winding. A small squirrel cage, such as is suffi- cient for starting of synchronous motors and for anti-hunting purposes, thus is not sufficient in high armature-reaction machines to take care of unbalanced single-phase load.

A disadvantage of the squirrel-cage field winding, however, is, that it increases the momentary short-circuit current of the generator, and retards its dying out, therefore increases the danger of self-destruction of the machine at short-circuit. In the first moment after short-circuit, the field poles still carry full magnetic flux — as the field can not die out instantly. No flux passes through the armature — except the small flux required to produce the resistance drop, ir. Thus practically the total field flux must be shunted along the air gap, through the narrow sec- tion between field coils and armature coils. As the squirrel-cage winding practically bars the flux to cross it, it thereby further reduces the available flux section and so increases the flux density and with it the momentary short-circuit current, which gives the m.m.f. of this flux.

It must also be considered that the reduction of generator out- put resulting from unequal heating of the armature coils due to unequal load on the phases is not eliminated by a squirrel-cage winding, but rather additional heat produced by the currents in the squirrel-cage conductors.

136. A synchronous machine, just as an induction machine, may be generator, producing electric power, or motor, receiving electric power, or phase converter, receiving electric power in some phase, the motor phase, and generating electric power in some other phase, the generator phase. In the phase converter, the total resultant armature reaction is zero, and the armature reaction pulsates with double frequency between equal positive and negative values. Such phase converter thus can be used to produce polyphase power from a single-phase supply. Th$ in-

PHASE CONVERSION

231

duction phase converter has been discussed in the preceding, and the synchronous phase converter has similar characteristics, but as a rule a better regulation, that is, gives a better constancy of voltage, and can be made to operate without producing lagging currents, by exciting the fields sufficiently high.

However, a phase converter alone can not distribute single- phase load so as to give a balanced polyphase system. When transferring power from the motor phase to the generator phase, the terminal voltage of the motor phase equals the induced vol- tage plus the impedance drop in the machine, that of the gen- erator phase equals induced voltage minus the impedance drop, and the voltage of the motor phase thus must be higher than that of the generator phase by twice the impedance voltage of the phase converter (vectorially combined).

Therefore, in converting single-phase to polyphase by phase converter, the polyphase system produced can not be balanced in voltage, but the quadrature phase produced by the converter is less than the main phase supplied to it, and drops off the more, the greater the load.