down will become thermal. Observation the liquid until the test voltage is well Dr.

is well Dr. Dakin and Dr. Berberich have

of the samples indicate that this is true. above the operating voltage. When ioniza- offered an interesting discussion on the
The dielectric constant of pressboard in- tion first occurs, it is associated with air- mechanisms of failure associated with the
creases as moisture is added. insulated parts such as bushings. pressboard samples. The further reduction
With reference to the discussion of Mr. Referring to Mr. Bridegam's discussion, in the 60-cycle, 1-minute strength with
Curdts, the Ro.25/R . ratio was used be- we have found no simple relation between increased power factor, discussed earlier in
cause it showed greater differences with power factor and temperature. Data ob- this closure, evidently is caused by thermal
different moisture content. If the usual tained but not shown in the paper indicate failure although the reduction in strength
RoI/R, ratio had been used it would have that temperature correction is a function occurring at low power factors is probably
become unity at a lower moisture content of the moisture content. This problem is due to some other mechanism.
and no difference could have been detected further complicated in a transformer by the Dakin and Berberich's remarks about
between samples of a higher moisture mixing of various kinds of insulation. the extension of the results of the tests on
content. The time constant of the measur- Another complication in units that have pressboard to power-factor measurements
ing circuit must be considered, of course. just been taken out of service is the differ- on assembled transformners are quite true.
The time of the final reading is dependent ences in temperature within the transformer. The stress on the pressboard insulation is
somewhat on the time that can be justified It is necessary in practice to arrive at an usually small in transformers and direct
for the test. average temperature value. Correction application of the data in Figures 3, 4 or
Reversed polarity d-c measurements on curves based on experience usually give 5 of the paper to the interpretation of
transformers were made with rather inter- values close enough for practical purposes. measurements on completed transformers
esting results from a theoretical viewpoint, The capacitance of a transformer is, as may give quite pessimistic results.
but no practical significance was found in Mr. Bridegam states, a function of the Fundamental differences between liquid-
the detection of moisture in these tests. moisture content. However, in our in- immersed and dry-type equipment are
Our statement about ionization potentials vestigation on pressboard samples and on pointed out by Dakin and Berberich.
of liquid-filled transformers that was ques- completed transformers the capacitance The differences are important and require
tioned by Mr. Curdts was based on our was not found to be nearly as sensitive to different types of testing and interpretation
investigation on new power transformers moisture as power factor or insulation re- of results.
and using instruments with voltages ranging sistance. At low values of power factor We believe that the principal application
up to 13.8 kv. Based on our experience a 100-per-cent change in power factor of the high-voltage testing equipment dis-
in design and with radio-influence testing, corresponded to 20-per-cent change in cussed by Mr. Curdts is with dry-type ap-
we would not expect any ionization under capacitance. paratus.

important as indicating the effectiveness

Simpliried Measurement Subtransient or of damper windings in suppressing tran-
sient voltages in stator and rotor windings
and Negative Sequence Reactances in
when unsymmetrical faults occur on the
power system.
The subtransient reactance of a syn-
Salient-Pole Synchronous Machines chronous generator is that reactance
which, coupled vectorially with the rela-
tively negligible resistance, determines
F. K. DALTON A. W. W. CAMERON the initial symmetrical value of current
MEMBER AIEE ASSOCIATE MEMBER AIEE that will flow in the stator winding upon
sudden application of a short circuit at its
terminals when the machine is running at
Synopsis: The principles and practical sudden fault conditions becomes ever normal rated voltage and without load.
results of a greatly simplified and much more important with the increasing ex- The short-circuit current may be resolved
improved method of measuring subtransient tension and complication in intercon- into direct-axis and quadrature-axis com-
and negative sequence reactances of gener-
ators are explained. This method is based nected power networks and studies of ponents. The subtransient reactance also
upon the acceptance of methods now stability of such systems. To determine is resolved into similar components each
approved in an AIEE Standard' and a the operating characteristics of synchro- applying to determine the value of the re-
Westinghouse reference book' for measure- nous generators and thus to be able to pre- spective component in initial short cir-
ment respectively of direct-axis and quadra- cuit or fault current. The components of
ture-axis subtransient reactances of salient- dict their behavior, actual test measure-
pole synchronous generators, and is subject ments on such generators must be taken this reactance are known respectively as
to the same reasoning regarding the merits and certain constants extracted to be used
of testing with stationary rotor and with later where they apply in a synthesis of
stator currents of lower than rated or calculated performance for given operat-
saturated values. This is a radical modi- Paper 52-168, recommended by the AIEE Rotating
fication of these methods; it avoids many ing conditions. These constants are Machinery Committee and approved by the AIEE
serious mechanical and electrical difficulties, known as the synchronous machine quan- Technical Program Committee for presentation at
the AIEE Summer General Meeting, Minneapolis,
delays, and consequently some expense tities, some of which are chiefly of in- Minn., June 23-27, 1952. Manuscript submitted
usually experienced in field testing and gives terest for transient system conditions. February 6, 1952; made available for printing
consistent and reliable results. No special April 21, 1952.
test equipment is required. The method of Specifications and contracts for large F. K. DALTON and A. W. W. CAMERON are with
making the test is described fully and the synchronous generators state calculated The Hydro-Electric Power Commission of Ontario,
equations to be used in calculating the con- values for the direct-axis and quadrature-
Toronto, Ontario, Canada.
stants are given. The authors are deeply indebted to the Canadian
axis subtransient reactances Xd" and General Electric Company, the Canadian West-
Xqff and for negative sequence reactance inghouse Company, and the English Electric Com-
pany for their interest and valued assistance in
THE necessity of analyzing and pre- X2. The calculated ratio of these sub- running these special tests on their new synchronous
dicting the behavior of synchronous transient reactances, that is, Xq"l/Xd"f generators and motors, thus proving the merits of
these test methods by measurement on actual
machines in normal operation and under also is stated, this value being considered machines of different designs and ratings.

752 Dalton, Cameron-Measurement of Negative Sequence Reactance OCTOBER 1 952

the direct-axis and quadrature-axis sub- Figure 1. (A) The displaced sine
transient reactances. wave of subtransient reactance be-
Negative sequence reactance may be tween stator terminals. One cycle
taken as the arithmetical average of the per pole span
direct-axis and quadrature-axis sub- M=amplitude of wave; K=dis-
transient reactances, usually calculated placement or offset of wave1
between stator terminal and neutral. A, B, C=any set of three values
spaced 120 degrees apart
Measurement of Subtransient (B) The fully rectified sine wave of
Reactances induced rotor current, rms values.
One half-cycle per pole span
The AIEE Test Code for Synchronous P=maximum possible value; X,
Machines' approves several special tests xil
Y, Z=values corresponding to wli II
for finding the various individual syn- positions of A, B, and C, but not
chronous machine quantities. Attention necessarily in the same order.
here is drawn to method 3, section 1.865 The highest of the three values (B)
for determining the direct-axis subtransi- must be designated X for insertion
ent reactance of a 3-phase generator by in the equation to calculate the
measurement of applied single-phase sta- maximum possible value P
< x <

tor impedance voltage and stator current, 0 60 120 180 240 300 360 60
with the rotor stationary in one special DEGREES
position in relation to the phase windings
of the stator; namely, in that position up to 40 to 50 per cent of rated stator from terminal to neutral were taken as
where a given stator current induces the currents, and in a few cases used full rated one-half of the measured values.
maximum alternating current in the rotor current. In later acceptance tests of a 23,500-
winding when it is short-circuited across These tests, with the rotor in special kva 60-cycle machine at another generat-
the collector rings. Actually, impedance positions, may be convenient and satis- ing station, the time necessary to un-
is measured, but the resistance component factory for very small machines but when couple and recouple the turbine and to
is considered as being so small that it be- large vertical generators driven by water make the tests described could not be
comes negligible and the results are taken turbines are to be tested in this way, it spared so subtransient reactance tests had
as measurement of subtransient reactance may be necessary to uncouple the turbine to be waived in this case. This informa-
only. One-half of the reactance thus from the generator and then to move the tion has now been obtained, however, by
measured is the direct-axis subtransient rotor several times through small angles the new method of test.
reactance of the generator from stator ter- to find the particular two positions de-
minal to neutral, in ohms. sired. Such small movements of the New 3-Reading Method of
This test code does not suggest a sta- large rotors introduce considerable dif- Measurement
tionary-rotor method of determining ficulty, not only in starting the motion
quadrature-axis subtransient reactance of but also in preventing the rotor from As the uncoupling and recoupling of the
generators, but the Westinghouse Trans- gliding too far. Furthermore, very many turbine require much labor and many
mission and Distribution Reference Book2 movements and measurements may be hours to complete, and since the movement
recommends a method, the same as the necessary to be certain that maximum of the rotor by small angles to special posi-
test code method 31 for the direct-axis and minimum rotor current positions have tions is difficult and needs several riggers
subtransient reactance, except that for been found. and considerable tackle, the following
the quadrature-axis measurement the When these tests were made on a 22,- simplified method of test has been de-
rotor is placed in a position where there is 500-kva 60-cycle generator after installa- veloped to circumvent these problems and
no induced current in its windings, no tion, the previously mentioned methods has been applied in several instances, on
matter what value of stator current be were modified by marking off one pole generators rated from 100 kva to 50,000
used. One-half of the reactance measured span on the stator frame and taking a kva, with great facility and success.
in this case is the quadrature-axis sub- series of readings for several rotor posi- The procedure is as follows. The tur-
transient reactance from terminal to tions within this span of movement. The bine is not uncoupled and the rotor is
neutral, in ohms. subtransient reactances between terminals stationary in any position whatsoever.
Sherwin H. WNright3 discusses the sta- for these positions were plotted, and the With the rotor winding short-circuited,
tionary-rotor tests for measurement of points appeared to be following a sine preferably through a current transformer
both subtransient reactances, and em- wave displaced from the zero line by con- or ammeter across the collector rings, and
phasizes the necessity of using low stator siderably more than its amplitude, see with the lead disconnected from any one
current to avoid rotor heating. He states Figure 1(A). Thus, there were two com- stator terminal, single-phase voltage is
that for salient-pole machines with damp- ponents-a constant offset or displace- applied to the remaining two terminals.
ers the direct-axis subtransient reactance ment K and a sine wave of amplitude M Stator voltage and current are read and
measured at rated current is very nearly having one cycle per pole span. The recorded, and also rotor current, though
the saturated value of Xd", and that the maximum and minimum values, namely, not necessary in this test. Single-phase
quadrature-axis subtransient reactance the quadrature-axis and direct-axis sub- voltage then is applied in turn to each of
measured at low-current values equals transient reactances, between terminals, the other two possible pairs of stator ter-
approximately the saturated value of were determined from the plotted results. minals, the respective third terminal being
Xq". In testing generators by the new Their ratio gave the important quantity open, and voltage and currents read again
method of measurement, the authors used X,"/Xd'. The subtransient reactances in each case, as before.

OCTOBIER 1 952 Dalton, Cameron-MIeasurement of Negative Sequence Reactance 753

 Figure 2. The 2. Quadrature-axis subtransient reactance
/ATIox7 subtransient re- Xq" =(K+M)/2
/ X actances of a 3. Negative-sequence reactance X2 = K/2
/ small synchro- 4. Ratio-
nous generator
/ / showing the Quadrature-axis subtransient reactance
/ / effects of intro- Direct-axis subtransient reactance
/ / ducing damper _Xq" K+M
windings and of Xd" K-Al
n interconL --:ting
the damper cages When per-unit values of subtransient
4 12 -2 , between poles and negative-sequence reactances are
0~
ND=no damper
desired, their respective values in ohms,
as previously calculated, will be multi-
o0 r windings in-
plied by rated-stator amperes per phase
ir
10 -o0
staled; NC= and then divided by rated-stator volts
ddmper wind- from terminal to neutral.
// ings installed in
/ pole faces but The series of tests may be repeated
not connected with the rotor turned to any new position
o 8_
z / /A"
/
, q /
/ between poles;
FC = damper
by its turbine. Readings again may be
taken in any order and would give the
/ / / cages fully con- same values of K and M thus serving as a
z 6 / / L-/ nected between check on the first series. In fact, the
/ 71 poles series of tests may be repeated as often as
o 2
desired, with different positions of the
rotor, the limitation, however, being the
heating of the damper windings which
4 /
will necessitate spacing of readings in time
to prevent overheating.
2 / // The method of test described herein
greatly simplifies the measurement of
subtransient reactances, for it is not
necessary to uncouple the turbine from
FC NC ND the generator nor to move the rotor
through small angles to special positions
by improvised means at the generating
The results of these measurements give If desired, the phase position 0 of stations. The position of the rotor poles
three values of stator voltage-current measurement B, in degrees from the zero in relation to stator phases is not impor-
ratios, that is, subtransient reactances be- value of the sine wave (where increasing tant in this test. Rotor currents do not
tween stator terminals, corresponding to positively), can be detennined by enter the calculation and, therefore, need
three different positions of the rotor. not be measured unless desired as further
These ratios may be designated as quan- tan 0= 3(B -K) information. The test readily may be re-
tities A, B, and C. They may be meas- C-A peated with different rotor positions,
ured or lettered in any order desired with- The rotor position in relation to stator turned by turbine, and the results will
out even keeping track of the sequence, phases can thus be found. serve as a check on previous tests.
and from these results, on the basis of the The phase angles of readings A and C In the calculations, vector phase rela-
variation being a sine wave, as previously will be 0-120 degrees and 0+120 de- tions disappear and only scalar quantities
explained and now quite well proved, the grees, in this order or vice versa, accord- are used. As readings may be taken in
desired quantities readily may be cal- ing to the values associated with A, B, any sequence and introduced into the
culated by the following equations: and C. equations in any order, the tracing and re-
The constant offset or displacement It should be noted that for any given cording of phases during the tests are not
component K value of tan 0 there are two angles, in op- required. Check tests are made very
K=(A+B+C)/3 posite quadrants and differing by 180 de- easily. From all viewpoints, this appears
grees, that satisfy. Care would be neces- to be a thoroughly practical method of
The amplitude M of the sine wave com- sary, therefore, in choosing the proper test which has already given satisfactory
ponent, measured from its offset zero quadrant for 0. Determination of the results and been recommended by manu-
line values of angles, however, is quite un- facturers of large synchronous machines.
necessary in the calculations of sub-
M= IB
( K)2+ (C-A)2 transient or negative sequence reactances, Maximum Induced Rotor Current
the angles merely indicating the rotor
The determination of the value of M is position, which is not important when this In connection with subtransient react-
very much simplified if, for a given rotor method of test is used. ance measurements, it may be desirable
position, any two of the three ratios A, B, Reactances, from terminal to neutral, sometimes to know the maximum possible
C be equal. In such case, Al is the arith- in ohms, will be as follows current that can be induced in the rotor
metic difference between K and the third, 1. Direct-axis subtransient reactance windings with rated stator current flow-
or unequal ratio. Xd" = (K- M)/2 ing. If, in the foregoing tests, the induced
754 Dalton, Cameron-Measurement of Negative Sequence Reactance OCTOBER 1 952
rotor currents be read and compared with X2, and P of introducing damper bars in a
stator currents for the three rotor posi- machine which previously had no damp- SLUBTRAINS IENTT
tions A, B, and C, the maximum possible REACTANCE \
ers, and then testing with these bars non-
value of induced rotor current for rated connected between poles and when fully
SINE\
stator current can be calculated easily. connected, see Figure 2. W AV E
Whereas the plotted results of sub-
transient reactances for a series of rotor Nonconnected Dampers. Commencing ,' 5000 H.P. MOTOR

positions across one pole span gives a dis- with no damper bars, at the right of the
placed sine wave, the plotted values of in- graph, the introduction of nonconnected
duced rotor current, corresponding to damper windings caused the values of K,
rated stator current or any other one M, Xd, Xa,, X2, and P to be reduced in SUBT RANSI ENT /
chosen value, will give a fully rectified practically the same proportions-about REACTANCE/, IN
sine wave having one-half cycle per pole 25-per-cent reduction. Consequently, the /o WAVE-s

span, the maximum value occurring with important ratio Xq"/Xd" remained nearly
that rotor position which gives direct-axis constant. This then would be interpreted
subtransient reactance, and the zero value that the introduction of nonconnected
dampers in a generator does not improve ~~~800 H.P. MOTOR
corresponding to the position which gives
quadrature-axis subtransient reactance, this ratio-a very disappointing thought
for this would mean that such a damper Figure 3. Variations, from pure sine wave,
see Figure 1(B). of the actual wave forms of subtransient react-
The procedure is as follows. Let the arrangement has no value in suppressing ance of synchronous machines determined by
three induced rotor currents, rms values, transient voltages in stator and rotor test. Damper windings not connected be-
each corrected to correspond to rated windings on the occasion of an unsym- tween poles
stator current, be X, Y, and Z, X being metrical short circuit at the terminals of
the highest value. The maximum pos- the machine or on the system to which it
is connected. These tests, however, have ured with various rotor positions across a
sible rms value of induced rotor current
P then may be calculated by the follow- been possible on only one machine so pole span, gave a displaced sine wave,
far. see Figure 1(A). With fully connected
ing equation.
Fully Connected Dampers. When
damper windings, the amplitude M of
this wave is very low so it is difficult to de-
p= X2+(y-Z)1 the nonconnected damper winding is now
termine its form accurately by actual
fully connected, that is, interconnected tests. With nonconnected damper wind-
There are, however, two special cases between poles, further interesting infor-
mation is obtained. The values of both ings, however, the wave is of much higher
1. If there be two equal high values, that is, K and MlI are further reduced but by ap-
amplitude and tests on several small
if either Y or Z be equal to X, the third machines have verified the sine form ab-
reading will be zero. In this case proximately equal amounts in this case.
The value of Xq" now becomes about 60 solutely.
P = (2X)/\,/3 On some larger synchronous motors
per cent of its nonconnected value whereas
with nonconnected damper windings
2. If Y equal Z, the second term in the Xd" remains practically constant. Thus
equation then becomes zero and P =X. the ratio Xq"/Xd" is much reduced and slight departure from the sine form has
been observed, see Figure 3. This has
As with measurements of subtransient may approach quite close to unity. This
been noticed in calculations, by small
reactances, the rotor in any other position change, therefore, shows an advantage to variations in values of M for different
should give the same value of P, the be gained by interconnection of damper
rotor positions. The values of K, the off-
maximum possible induced current in the windings. set of the wave, does not appear to vary
short-circuited rotor. The value of P, however, does not ap- appreciably.
Note that the highest value of cor- pear to change with the interconnection of Further studies are being made with a
rected rotor current must be in the posi- dampers. As this maximum occurs with view to determining the cause of these
tion of term X in the equation. If there the rotor position that gives direct-axis minor variations. At the present time it
be two equal high values, this is the first subtransient reactance, it would be ex- is thought that they may be associated
special case previously mentioned. pected that nonconnected dampers would with certain stator slot positions in rela-
have the effect observed on the rotor cur- tion to damper bars.
Special Features Investigated rent but that interconnection would not
make any further change. THE POSSIBLE RANGE OF STATOR
While the foregoing simplified methods The opportunity to test a machine CURRENT
of measuring subtransient reactances and without damper windings and then with
It has been customary to use 40 to 50
maximum induced rotor current have these two connections of dampers is un-
per cent of rated stator current in meas-
been applied to synchronous generators usual, and such a series of tests seldom
would be possible on large generators uring subtransient reactances with sta-
and motors of a variety of ratings to tionary rotor, the limitation in current
prove the merits of the methods them- where nonconnected damper windiiigs
usually are installed in the pole faces be-
being the possible overheating of the
selves and also the ease of applying them, damper windings when too high a current
several interesting opportunities were fore rotor windings are put on poles.
is used. Some tests, however, have been
found to obtain some rather special in- made by the authors with lower currents,
formation by these simple tests. THE SINE WAVE OF SUBTRANSIENT
REACTANCE over a range from very low values up to
THE APPLICATION OF DAMPER WINDINGS half rated values. This matter is being
It was explained in the theory of this studied by tests to further simplify the
These tests were made for the purpose simplified method of test that plotted making of measurement by using the low-
of determining the effect upon Xd", Xq", values of subtransient reactance, meas- est reliable values of stator currents.

OCTOBER 195)9 Dalton, Cameron Mleasurement of Negative Sequence Reactance 755

TESTS WITH DIRECT CURRENT IN ROTOR difficult to perform in the field. The ac- that stator currents be kept below rated
WINDING tual position of the rotor in relation to values to avoid overheating in the rotor.
It was suggested that the use of direct stator phases is quite unimportant. Read- Tests will be brief but currents must be
current in rotor windings could simulate ings may be taken in any sequence and held steady to insure consistent read-
operating conditions. Several tests were introduced into the equations in any ings.
made but the direct currents were mis- order. Vector phase relations disappear An effort has been made to present the
leading and gave false results, bringing and only scalar quantities are used. principles of these methods by the most
values of Xd' and Xq." to zero when rotor Check tests can be made easily by turn- simple equations supported by actual test
currents corresponding to values for the ing the rotor, by its turbine, and letting results on synchronous machines of vari-
no-load normal-voltage condition of the it stop in any new positions. Actual ap- ous ratings.
machine were reached. This suggestion, plications of the method have produced It is hoped that the advantages in these
therefore, has been discarded as not very satisfactory results on salient-pole new methods will be appreciated by engi-
simulating operating conditions. generators over a wide range of rating. neers who design synchronous machines
The maximum possible value of induced and also by those who study system con-
Conclusions rotor current, with rated stator current, ditions and that the simplification here
may be obtained readily from rotor cur- introduced will permit reliable informa-
The simplified methods of measuring rent measurements taken at the same tion to be obtained on actual machines
subtransient reactances, negative se- time as those for determining subtransient much more easily than heretofore.
quence reactances, and maximum pos- reactances.
sible induced currents in short-circuited Having experienced the difficulties en- References
rotor windings of synchronous machines countered in field testing where it was
are submitted here for the first time. necessary to uncouple the turbines and to 1. TEST CODE FOR SYNCHRONOUS MACHINES.
AIEE Standard Number 503, June 1945.
These new test methods are extremely shift the rotors of large generators
2. ELECTRICAL TRANSMISSION AND DISTRIBUT10N
simple and remarkably flexible, especially through small angles, the authors feel REFERENCE BOOK. Westinghouse Electric Corpo-
for large generators. It is not necessary that these new test methods, avoiding ration (East Pittsburgh, Pa.), fourth edition, 1950.
to uncouple the turbine or to move the these problems, will be appreciated fully 3. DETERMINATION OF SYNCHRONOUS MACHINE
by others who have had similar experi- CONSTANTS BY TEST, Sherwin H. Wright. Elec-
rotor through small angles to special trical Ezgineering (AIEE Transactions), volume 50,
positions, both of which operations are ences. The chief caution to be heeded is number 4, December 1931, pages 1331-51.

2. MEASUREMENT OF THIE SUBTRANSIENT IMPED-

Discussion reactance if the direct-axis subtransient re-
actance also is known. These methods of ANCES OF SYNCHRONOUS MACH1INES, Gordon F.
Tracy, William F. Tice. ElecIrical Engineering
C. Concordia (General Electric Company, obtaining negative-sequence reactance are (AIEE Transactions), volume 64, February 1945,
Schenectady, N. Y.): The authors are to be given in the Test Code and I am referring pages 70-76.
complimented on the development of an in- particularly to the ordinary measurement of 3. OVERVOLTAGES CAUSED BY UNBALANCED
a sudden single-phase short circuit and to the SHORT CIRCUITS-EFFECT OF AMORTISSEUR WIND-
genious and simple method of test for sub- INGS, Edith Clarke, C. N. Weygandt, C. Concordia.
transient reactance by means of measure- corresponding method of measuring sus- Electrical Engineering (AIEE Transactions), vol-
ments with the machine under test at stand- tained line-to-line short-circuit current and ume 57, August 1938, pages 453-68.
still. Their method is definitely a consider- voltage measured from the open-phase ter-
able improvement not only over the stand- minal to the short-circuited terminals. In
still method in the AIEE Test Code1 but this case the negative-sequence reactance is A. D. Avtzine and V. W. Ruskin (Canadian-
also over the somewhat similar method equal to the ratio of the voltage so measured Brazilian Services Limited, Toronto, On-
outlined by Tracy and Tice2 in 1945. This to the square root of 3 times the sustained tario, Canada): The method of measure-
latter method, like the one under discussion, short-circuit current. ment of subtransient and negative-phase
also avoided the mechanical difficulties as- As an example of the possible variation of sequence reactances in synchronous ma-
sociated with small angular movements of subtransient reactance with current, it may chines presented by the authors may be
the rotor, but involved making field meas- be of interest to refer to a paper by Clark, termed a logical continuation or per-
urements to obtain the rotor angle. Thus Weygant and Concordia.3 Conclusion 7 of fection of the "locked line-to-line test" of
it is neither as simple nor as straightfor- this reference states: "The ratio Xq"lXd" S. H. Wright.1 The chief difference be-
ward the new method. may be determined by test from single- tween the two is that the first takes one set
It should be pointed out, however, that phase static impedance measurements. The of readings and derives the constants by
both of these methods, as well as the corre- ratio should either be measured at a current calculation, while the second takes a number
sponding method 3 of section 1.864 of the equal to the expected rms displaced single- of readings and determines the constants
AIEE Test Code,' suffer from the defect phase short-circuit current or several points from the highest and lowest values or ratios
that they correspond to unsaturated con- taken in order to extrapolate to this cur- of voltages and currents. The new method
ditions. If it is thought to use the quadra- rent." is much handier to use since it does not re-
ture-axis subtransient reactance in connec- Figure 15 of the reference shows a curve quire turning of the rotor in locating the
tion with the direct-axis subtransient react- of Xq"/Xd " (determined by line-to-line static direct and quadrature axes of the machine.
ance in order to determine open phase
tests) as a function of armature current up The new method gives unsaturated values
overvoltages during line-to-line short cir- to an armature current of about 3.6 times of the constants. It is based on the follow-
cuits, it must be remembered that during normal. There is a variation in Xq"IXd" ing assumptions or premises:
the short circuit the machine also will have a from 2.0 at zero current to 1.5 at 3.6 times
normal current. It was possible to test at 1. The subtransient reactance varies sinu-
d-c component of field flux which may af- soidally with the rotor position.
fect the ratio of quadrature-axis to direct- these high currents because the machine was
small. It would appear from this figure 2. The armature windings are distributed
axis subtransient reactance. Therefore it is uniformly.
desirable to have a method which involves that an extrapolation to the probable short-
circuit current, from test currents below 3. The expressions determining the react-
use of the machine during the proper satura- ances are given in terms of rms values
tion conditions. In connection with this, 1.0 per unit would be rather unreliable.
all of the methods of obtaining the negative-
(measurements).
sequence reactance are directly applicable
REFERENCES The paper gives no numerical examples
to determining quadrature-axis subtransient 1. See reference 1 of the paper. which would demonstrate the efficacy of the

756 Dalton, Cameron-MAeasurement of Negative Sequence Reactance OCTOBER 1 952

new method and would compare the values Comparison of test results on several versy, to determine quite accurately the re-
based on the old and new modes of measure- similar generators of varied rating, produced lation between reactances measured by the
ment. Such information would have much by one manufacturer, shows very close agree- different methods of test now in use.
interest since it would indicate both the possi- ment in the values of constants which apply The authors wish to thank Mr. Concordia
bilities and limitations of the new method. in actual test and which therefore may be for his interest in their paper and his valu-
If the proposed method proves itself to be used for computation in future production able contribution of information in the dis-
adequately accurate, it may be found to be and design. To calculate reactances for cussion he has submitted.
desirable to include it, as an alternative, in saturated values of current, on running Regarding the discussion by A. D. Avt-
AIEE Test Code Number 5032 if and when tests, the values obtained by this new zine and V. W. Ruskin, the authors have
this Code is revised. Since the method gives method, with stationary rotor and with 50 proved in factory tests, by applying both
unsaturated values, it might be advanta- per cent of rated current in the stator, may the old and new stationary-rotor methods
geous to supplement it by a multiplier or mul- be multiplied by the following approximate of measuring subtransient reactances to each
tipliers which would permit estimation of the comparison constants: of several relatively small machines, that the
saturation effects. values of the desired synchronous machine
The authors found that the ratio of 1. Direct-axis subtransient reactance: 0.87 quantities obtained will be the same when
Xq'/1Xd" did not change on introduction of 2. Negative sequence reactance: 0.92 measured by either of these methods. As
nonconnected damper windings (for a given 3. Quadrature-axis subtransient the new method is an expansion of earlier
value or values of armature current). This reactance: 0.96 methods it was logically expected that this
does not mean that nonconnected damper The constant for direct-axis subtransient would be so.
windings have no value insofar as perform- reactance Xd" was derived by comparison of Numerical examples have not been given
ance of synchronous machines is concerned. the oscillographic results of sudden short- because actual test results are regarded as
Damper windings (even incomplete) achieve circuit tests, at rated voltage, with measure- confidential by the respective manufactur-
a valuable reduction in the values of Xd'", ers. The illustrations are based upon these
ments made by this new stationary-rotor
Xq " and hence X2, although the ratio of method, at half of rated stator current. tests.
XQ"/Xd" may stay nearly constant. A re- The constant for negative-sequence re-
Factory tests were made on several ma-
duction in X2 in turn tends to cut down un- chines with each rotor in a series of positions,
balances in voltage and wave distortion. actance X2 is the ratio of measurements by confirming the original conclusion that the
In regard to the negative-phase sequence the standard running test at half rated cur- subtransient reactance varies practically
reactance, it is known that (Colloquium on rent, described by Mr. Concordia, to the re- sinusoidally with the rotor position. The
Power-Circuit Analysis, held at Massachu- sults of stationary-rotor tests at the same slight variations found in some machines
setts Institute of Technology in June 1929) value of stator current. See section 1.883 are, in the opinion of several design engi-
of AIEE Standard 503. neers, so small as to be considered insig-
X2= 1/2(Xd'+Xa") From the running tests for the reactances nificant-especially unimportant in com-
"if there is large external series reactance." just given, the "running" value of quadra- parison with certain assumptions made in
On short circuit, apparently ture-axis subtransient reactance Xq" was designing generators.
calculated on the basis that X2 is the arith- In the machines tested by the authors, the
metical average of Xd" and Xe", Xd" and armature windings were distributed uni-
X2 = V\Xd "XQ" X, being readily measurable quantities. The formly, or understood to be essentially so.
The two values approach each other when value of Xq" thus obtained was compared All measurements of stator impedance volt-
the difference between Xd" and Xq" is with the value from stationary-rotor tests, ages, stator currents, and induced rotor cur-
small. at half of rated stator current, to obtain the rents are in rms values.
comparison constant for quadrature-axis The significance of the reduction in sub-
REFERENCES subtransient reactance. transient and negative-sequence reactances
1. See reference 3 of the paper. In regard to the values of comparison con- by introduction of damper windings, even
2. See reference 1 of the paper. stants, however, Sherman H. Wright has though the ratio of subtransient reactances
stated that the quadrature-axis subtransient be unchanged, is recognized by the authors.
reactance XQ", at low current values equals The damper windings also have anti-hunting
F. K. Dalton and A. W. W. Cameron: Re- approximately the saturated value, that is, a values which alone may justify their in-
garding Mr. Concordia's discussion, the comparison constant of 1.0. On this basis, sertion in the pole faces, whether the cages
authors are aware of the controversy re- and with the comparison constant of 0.87 as be interconnected or not.
garding the merits of various methods of found for direct-axis subtransient reactance, The calculation of X2 by the two different
subtransient reactances of generators and the corresponding constant for negative- equations submitted gives practically the
have been careful to explain, in the Synop- sequence reactance would be 0.94 instead of same value where Xq"/Xd" is 1.3 or lower
sis of this paper, that this new method is 0.92 representing only a slightly higher Hence either equation, but preferably the
subject to the same reasoning as other negative-sequence reactance at saturated more simple one, is used.
methods of test with stationary rotor and values of stator current. Considering the The Chairman of the AIEE Test Code
with stator currents of lower than saturated characteristics of the machines that the Committee on Rotating Machinery has al-
values. However, this simple method has authors tested. however, it does not appear ready recommended to the Test Code
facilitated greatly the obtaining of informa- possible for the constant to be higher than Subcommittee on Synchronous Machines
tion, and the authors have continued the 0.92. It may even be slightly lower than that this new method be incorporated when
study by measurement of more large gen- this value. the Test Code is revised.
erators, up to 50,000 kva, to determine the The authors have found considerable con- Mr. Avtzine and Mr. Ruskin suggest the
probable values of comparison constants sistency between respective comparison use of "multipliers" to estimate the values
whereby, according to the design of machine, constants determined for large machines of of subtransient reactances that would apply
test results obtained by this new method similar design, and believe that for station- with saturated values of stator current.
may be corrected to apply very closely in ary-rotor tests at half of rated stator cur- The authors, however, have made tests al-
giving the results that would be obtained rent reliable comparison constants may be ready to try to determine such multipliers,
with saturated values of current on running derived and applied for various designs. or comparison constants, and have given
tests. With the range of current that the By making similar tests on machines of some values, with explanation, in their
authors used on these tests, it is apparent their own production, manufacturers will be closure to Mr. Concordia's discussion of this
that values of both subtransient reactances able to determine for themselves the most paper.
reduce slightly as stator currents are in- suitable values of comparison constants to The authors are glad to have these points
creased, the direct-axis component reducing use for their own designs of generator. brought forward and thank Mr. Avtzine
more rapidly than the quadrature-axis com- Thus, this simple method of test may be ex- and Mr. Ruskin for their interest and dis-
ponent. panded, in the light of the existing contro- cussion.

OCTOIBER 1952 Dalton, Cameron-lIeasurement of NVegative Sequence Reactance 757