Fault ectiZerRectiIer au t C. C. HERSKIND FELLOW AIEE
Currents-Il urrents~
A. SCHMIDT, JR. MEMBER AIEE
C. E. RETTIG
NONMEMBER AIEE
connected to the d-c windings of one phase of the rectifier transformer conduct
current alternately so that the fault currents in the a-c winding are the same as
in a 3-phase short circuit. Under sustamed
conditions each tube conducts
current for 180 degrees.
A NUMBER of modes of circuit action J may be obtained during faults on power rectifiers because of the variety of fault conditions and circuit parameters. Analyses of some of these have been treated in a previous paper.' This paper presents a further extension of this work with analyses of a number of idealized cases. An analysis is presented for the transient tranien fault falt current urrnt duing d-c sort short urig dc circuit and a procedure is outlined for analyzing the fault currents during arcback with both a-c and d-c feed. The objective of these studies is the development of a comprehensive procedure for the analysis of the circuit action and the determination of fault currents in rectifier circuits during d-c short circuits and arc-back. A complete treatment of the fault currents obtained in the widely used 6-phase double-Y circuit is particularly desired. The results of fault current calculations and tests on a 200-kw 300-volt scaled ignitron rectifier equipment are compared. The wave forms and magnitudes of the fault currents obtained under various test conditions are shown by oscillographic records. Data are presented showing the nature of the rectifier arc-drop at fault current levels. Some of the factors which influence the arc-drop are discussed. Methods for representing the effect of arc-drop in fault current calculations are proposed. Types of Faults
Rectifier faults are of two general types, namely, d-c short circuit and arcback. Three idealized cases may be defined for each tvpe as illustrated in Figures 1 and 2: Case 1-primary impedance only Case 2-secondary impedance only
Case 3-both primary and secondary impedancesavrcealei Arc-Back Case 1-a-c feed only Case 2-d-c feed only Case 3-both a-c and d-c feed
D-C Short Circuit
During d-c short circuit, the circuit action is determnined by the relative magnitude and location of the various
impedances in the rectifier unit and the short-circuit path. Three idealized cases are obtained with equivalent circuits and wave forms as shown in Figure 1. These three cases do not cover all the possible conditions which may be obtained as additional cases may be defined for d-c short circuits with impedance in the fault path and for other rectifier circuits.
CASE 1-D-C SHORT CIRCUIT WITH PRIMARY IMPEDANCE ONLY In this case, it is assumed that the rectifier transformer d-c windings are perfectly interwound so that all the reactance may be considered to be located in
pattern and action, and the analytical , ..
commidttee and apoed byEthetoi AIBE technical program committee for presentaat the winter general meeting, New ~~~~~~tion AIEE
simplifying assumptions are necessary. These result in a number of idealized cases.
c. c. HERSKIND, A. SCHMIDT, JR. and C. E. RETTIG are all with the power electronics division of the General Electric Cumpany, Schenectady, N. Y.''
treatment which applies. In order to permit mathematical analysis, certain
1949, VOLUME 68
und esuaineconditin the and c each anode carries a half cycle of current whose crest value is
D-C Short Circuit
the a-c windings and supply line as shown in Figure 1. The tw-o tubes which are Rectifier faults may be classified on the sicigage$=0 h wthn
basis of the nature of the fault, the circuit
STEADY-STATE CONDITIONS
power converter
York, N. Y., January 31-February 4, 1949. Manuscript submitted November 17, 1948; made avail-
= V2 E,/Z
(1)
The d-c short-circuit current is equal to
the sum of the anode currents, and its average valueis
I
2
=3X-XiA 7
(2)
The sustained d-c short circuit current may also be expressed n therform
2V/2 VA Ids -. XEZ
(3)
TRANSIENT CONDITIONS Under transient conditions, immediately following the start of the short circuit, the fault-current waves in the transformer windings are displaced, and the current in the short circuit exceeds its sustained value. If it is assumed that the anodes are free to conduct at all times and that the fault is a bolted short circuit, the fault currents may be readily determined graphically by a procedure based on a single-phase analysis.
A graphic analysis of the current on d-c short circuit for a 6-phase double-Y rectifier is shown in Figure 3. In this analysis, the current in each pair of anodes is determined as for a single-phase circuit. The short circuit is assumed to occur at the beginning of the positive voltage wave on phase R,, that is, at angles on the other two phases differ from
this value by their phase displacements of 60 and 120 degrees. The short-circuit current is obtained
by adding the anode current waves which are indicated by the shaded areas. The osrcinsoni o ermn cosrcinsonifoadeem t
Herskind, Schmidt, Rettig Rectifier Fault Currents-II
243
of impedance on the primary side of the transfonner permits a determination of the fault current on the basis of six singleEQUIVALENT
CIRCUIT
r4~-I ar X
Lik kjttX 1 I
I Ip I I I I I
,
g
$
phase circuits where the applied voltages have the phase relations determined by the transforner connection. In this case each tube acts independently; and under sustained conditions, the tube conduction period increases toward a value of 360 as the circuit resistance is reduced degrees to zero.
STEADY-STATE CONDITIONS
DIRECT CURRENT
A . /IiWAVE l
FORMS
ANODE
0I2 O -3CYCLES
0)
3
I
2 3 -360'-i Igoe+ I6
0
O
CASE
PRIMARY IMPEDANCE ONLY
CASE 2
N
CASE 3
SECONDARY IMPEDANCE
BOTH PRIMARY AND
ONLY
SECONDARY IMPEDANCE
Figure 1. D-c short circuit-idealized conditions factor R/X = 0.3. The maximum value of the fully displaced current wave, which would be attained with zero resistance, is also shown. Its value is twice the crest value of the sustained fault current. The crest value of the instantaneous current depends upon the switching angle and the circuit reactance as expressed by the R/X ratio. Analyses show that the effect of switching angle is small and may be disregarded as it usually causes less than 5 per cent variation in crest current. However, the transient component due to reactance may cause the maximum in-
In contrast to Case 1, with its sinusoidal
steady-state currents, the circuit arrange-
F\ ment . / in. Case 2 causes the currents through the impedances to be discontinuous so that the transient is repeated each cycle. Therefore, the crest value of sustained anode current is the same as the maximum instantaneous value for Case 1 as given by -Es i
das=Kp z(5)
stantaneous current to range in value from 1 to 2 times the sustained crest current. The maximum short circuit current may be expressed by the relation 7d (4) 3 The value of the transient factor K, for various R/X ratios- is given in Figure 5.
CASE 2-D-C SHORT CIRCUIT WITH
SECONDARY IMPEDANCE ONLY The 6-phase star circuit shown in Figure 1 represents an idealized case having inductance and resistance that may be lumped in the anode leads. The absence
The crest value of the short-circuit current is larger than the maximum obtained in the transient state in Case 1 because of the longer conducting interval. The crest short circuit current is given by i d,=K8X2
J
o
(6) .
m
4.
The average value of the short-circuit current may be determined for an idealized case with no resistance by the equation VA
=2V\2-
Ids
+
i 4 $ g
g
$+
S
(7)
It should be noted that this value is ir times the value obtained for Case 1 as given by equation 3. When resistance is present the sustained short circuit current will have a lower value. This is shown in Figure 5.
TRANSIENT CONDITIONS DC FEED BACK CURRENT
DC FEED BACK CURRENT
!1 /1I
CURRENT IN
NORMAL ANODES
O
!,I
/1
URRENT IN NORMAL
t//R \;/ /\ 0V \i 2 CYCLES
CURRENT IN FAULTY ANOD)E
CASE A4C FEED ONLY
244
,
2.
3
Conduction During First Cycle. If the circuit occurs at the instant the voltage on phase is going through zero, conduction takes place initially in phases 5,6, /and 1. Sixty degrees later phase 2 starts conducting, and the remaining phases enter in sequence.
Ashort
\ ANODES
CU1/ LV /r\ dA \2 / A \!1 O\
~~~~~~Neglecting
resistance the currents in \ CUR?ENT IN FAULTY ANODE \i/ j.. phase 1 and all succeeding phases are fully .. displaced. However, the shortcurrent does not reach its maxiCASE 2 CASE 3 . mum . value until phase 6starts conducting DC FEED ONLY BNOTH AC a DC FEED . a.second time and steady-state conditions. Figure 2. Arc-back-idealized conditions are reached. ....
8 \-/
~~~~circuit
Herskiznd, Schmidt, Rettig- Rectifier Fault Currents-II
AJEE TRANSACTIONS
Figure 1 shows a sketch of the shortcircuit current and the current in phase 1 that would exist in this case with a small R/X ratio. Effect of Interphzase Transformer. Neglecting the interphase transformer and treating the 6-phase star circuit yields results which apply with sufficient accuracy to the 6-phase double-Y circuit. Introducing the interphase transformer causes no change in the short-circuit current. Some redistribution of current among the anodes is caused, but the maximum change is less than 2.0 per cent of the crest value of anode current.
CASE 3-D-C SHORT CIRCUIT WITH
Arc-Back
BOTH PRIMARY AND SECONDARY IMPEDANCE
This is the general case which is usually encountered in practice. Its circuit action combines the effects obtained in the first two cases. With reactance and resistance in both primary and secondary windings of the rectifier transformer, the crest value of the anode current is still represented by the displacement factor Kp. X and R in this case are the sum of the components in the primarv and secondary windings. The short-circuit current has a peak value which falls between the two extremes represented by Kp and K, in Figure 4. The exact value has not been determined, but it is dependent upon the 4
MAXIMUM VALUE
I 0
90
I
180
270
During arc-back, the circuit action is determined primarily by the sources of voltage producing the fault current. Three idealized cases may be defined with equivalent circuits and wave forms as shown in Figure 2.
CASE 1-ARC-BACK WITH A-C FEED ONLY In this case, the current flow in the f anode S establshed b faulty and it is assumed that there is no ply other source of voltage. The equivalent circuit is shown in Figure 2. A 3-phase rectifier is assumed as it represents one commutating group of the rectifier. During arc-back, a reverse current flows in the faulty anode which is equal to the sum of the forward currents in the two
SUSTAINED VALUE ]
V
(9)
ZC
Values of the reverse current and forward current factors as a function of the R/X ratio are given in Figure 6. These factors give the crest value of current obtained during the first cycle when arcback occurs at the end of conduction. It is assumed that the arc-drop is represented as an equivalent resistance in determining the R/X ratio. 2-RC-BACK WITH D C FEED CASE ,
ONLY
This is an idealized case where all the current in the faulty anode flows in the d-c system. The equivalent circuit is a single loop containing an alternating and a direct voltage in series. The current consists of an alternating component of constant magnitude and a direct compo-
nent which increases exponentially with
Figure 4 (below). Transient factors for determining
oCURRENT l 7 \I
360
Kf \2Es
Figure 3 (left). Graphic analysis of transient current on d-c short circuit with primary impedance only
iDIRECT
\
I
ot,
~
t
i'
normal anodes. k / R/X'O 0In the treatment presented in the origi-
TRANSNT VALUE 2k f
ratios Rp/RS, Xp/XS and the total resist- nal paper,' this case was referred to as ance to total reactance ratio R/X. The arc-back in a wye and sustained values of trend may be expressed as follows: For a current were given. Further studies indigiven XpIXS ratio, the value falls upon the cate that the first cycle values are generupper curve when the R/X ratio is equal ally more important than sustained values to zero, but approaches rapidly the lower in system studies.5 curve as the R/X ratio increases. The first cycle crest values of the reThe ratios Xp/XS and RS/Rp determine verse current in the faulty anode and the the rapidity with which the value ap- forward current in the normal anodes may proaches the lower curve. The larger be determined by equations 8 and 9. these ratios, the more rapidly the value Crest reverse current in faulty anode is approaches the lower curve. For practical ratios of these quantities itar = K V/2Es (8) where no reactance is intentionally added Ze in the anode leads, the lower curve apCrest forward current in normal anodes plies for usual R/X ratios. is
crest
anode current and d-c short-circuit current
values of
~~~~~~~~~~~~~~~~~~~~3.02
J
0.5
0
I0-
R4X RATI
1949, VOLUME 68
HIerskind, Schmidt, Rettig-RecttfiZer Fault Currents-Il
245
time until it is limited by resistance. Such a condition may be realized in practice if all the normal anodes of the rectifier are prevented from firing at the time of fault or may be approximated if a number of rectifiers are paralleled on the same d-c bus. The reverse current in the faulty anode is given by the equation _, Rd /E -(-ti)I Ed' eLd 1± x =t EL
R3
F
Z3
Rd -1d ) sin (o -Oi)j (10) [sin (cat - 03)-eE s
The idealized conditions are not closely
approximated in practice and useful
re-
sults of adequate accuracy may be obtamed by an approximate expression based on the following assumptions: First, it is assumed that the arc-back occurs at the zero point of the a-c voltage wave when hi =0O. This is justified on the basis that the majorty of arc-backs occur at the end of conduction which is usually within a few degrees of the zero point of the voltage wave. Second, it is assumed that the resistance of the fault path is low in comparison with the inductance so that 0= 90. The approximate value of the reverse current is given by the simplified equation -e\[Ed'VE1[s +L
idr =LR3
3t-t
Z3
V12Es [I Z3
(11)
cos t]
CASE 3-ARC-BACK WITH BOTH A-C AND
D-C FEED This is the case usually encountered in practice and combines the action of the first two cases. In order to simplify the analysis, the action is considered on the
24 C basis of a single wye. During arc-back, 2l2 the current in the faulty anode is a combination of a-c feed from the two normal a0_ anodes of the wye and d-c feed from a 8 single d-c source representing all other 6 - - .. anodes and parallel sources. Currents feeding into an arc-back from 14 - K a counter electromotive force load and from the normal anodes in a faulted wye , 12 - - - are additive components of the current in i.the faulted phase. Each of these compo, 08.06 nents is smaller than the value obtained in Rd l either Case 1 or Case 2, but their sum ~~~~~~~~~~~~~~~~~~~~~00.6 04 yields an arc-back current larger than 02 either component considered separately. 0 A method is described in the following 0 analysisforobtainingtheexacttheoretical 0.2 08I Q4 0.6 L RATIO R/X values of currents in the faulty anode, the Figure 6. Factors for determining reverse and normal anodes, and the d-c feed. . . . . . forward current during arc-back with a-c feed
Corcuit Analysis.
The
equivalent circuit
only
for this case is shown in Figure 2. Paralleled converting equipment, counter electromotive force load, and the normal wye of the 6-phase double-Y rectifier are reduced to an equivalent voltage source Ed', resistance Rd, and inductance Ld. The action of individual phases is considered only in the faulted wye. The phases in this wye are designated in their normal conducting sequence. R1 is the faulty phase and R2 and R3 are the normal phases in the faulted wye. L, and R, are the commutating inductance and resist-
ance per phase. Arc-drop is treated as an equivalent resistance whose value is included in R,. Circuit action during the first cycle following a commutation arc-back is shown in Figure 7. For purposes of defining circuit action, the cycle of operation is divided into four intervals. The divisions correspond to the instants at which a phase either starts or stops conducting. The current in phase 1 and the feed-back
R2
Figure 5 (below). Average value of
sustained d-c shortcircuit current with
secondary impedance only Figure 7 (right). CircuitIaction during arcback with a-c and d-c feed
PHASE
R3
0
VOLTAGES
V
INTERVALS
I1
IC.-
1
I 2
y
2 -j-
-
/
3
w
-
z
-
-
CUR-ENT
-
0mv
I
0
~
~
RX AI PER UNIT 8ASE.a/2E
246
l
ANODE
31
)
3
0.8~~~~~~~~~~~~~~~~~ a.
R,
4
2
3
22 L___\_I
-
I
$
0AC RTFIERD CURN
0
Herskind, Schmidt, Rettig-Rectifier Fault Currents-IIl.
.
AIEE TRANSACTIONS
/0
l ( |n AC SUPPLY
C
CIRCUIT
0~~ 40
-%
ARC-DROP 0
3C ARC- DROP (AVG VOLTS)
O
/
O a0
~
~
~
o,/ O Q
^
/ __
~
I
~
|
/
|
i
It460V
_
~
~
|
~ ~V AC BREAKER
*
/'
BUS.4 '
X
2 0
283V
,__o_L_._I I_ I_I_____
AT 45-C RISE - 460/283 V L TO N. -IMPED. Z 5.97% AT 480/283 V AND 75 C - COMM. REACT. Xc r .060 OHMS L TO N. -LOAD LOSSES: P, g 3707 WATTS AT RATED WINDING H s / . CURRENT Idn a 667 AMPS
DC
/
ITASE
-
'TRANSF.
R8 /R8 1
5
10 -
15
RS
20 DC BREAKER
(
(I
/ /-
.Le 4R-.004
so
ARC-DROP AVG VOLTS) 40
211-110 /
PO
,
*
R.40t 0D0
I
x
TOR
Figure 8 (left, above). Arcdrop of sealed ignitron under fault current conditions
/
Figur
A
0
,I
drop
20
30
40
!
FORWARD CURRENT AT NORMAL LOADS
current are continuous, and the intervals are determined by conduction in the two normal phases as follows: Interval l-conduction in phase 2. Interval 2-conduction in both phases 2 and 3. Interval Interval 3-conduction In phase 3. Intervl4-coductin nither Interval 4-onduction in neither normal phase.
~ 3-odcin*npae3
During interval 1, the circuit action proceeds as follows: A current will start flowing from anode 2 to anode 1 with values as determined in Case 1. Upon this current will be superimposed a current from the d-c source,
whose value is determined from equation 1. The a-c voltage which applies in this equation is the average voltage of phases 1 and 2. The culrrent from the d-c source divides equally between phases 1 and 2, one-half its numerical value being added to the current in phase 1 and subtracted from the current in phase 2. The end of interval 1 is reached when the voltage of phase 3 equals the voltage
1949, VOLUME 68
9 (left, below) Arcpumped gnitron
of
fault current conditions ~~~~~~~~~~~~under u
CURRENT PER TUBE (AVG KILOAMPERESI O FORWARD CURRENT -FAULT TESTS ON RECTIFIER UNIT * REVERSE CURRENT-FAULT TESTS ON RECTIFIER UNIT FORWARO CURRENT-PULSE TESTS SNSINGLE TUBE * REVERSE CURRENT- PULSE TESTS ON SINGLE TUBE
O
\-
/*X/ :C -/ors
/
c
Figure 10 (right). Power circuit during fault tests on 6anode 200-KW 300-volt rectifier
I
at the terminals of the rectifier as given by did, ed = d-Adldr-d dt ed
DR
r
-d
12
.
where dr IS the feed-back current during interval 1. A later later time time may interval may apply if if 1. A
phase control iS used. During interval 2 alla-c threevoles anodes apare andethelne cDucting, conducting, and the net a-c voltage appearing in the d-c circuit is zero. The current from the d-c source divides equally between anodes 1, 2, and 3, onethird of its numerical value adding to the current in anode 1 and subtracting from the currents in anodes 2 and 3. The value of the d-c current is determined for the series circuit including Ed', Ld, Rd, and one-third of Lc and R, with the initial value as determined at the end of interval
1.
236-I18
OUTPUT VOLTS
ANODE CABLES
1Q20
/
AT 45- C RISE-
-LOAD LOSSES'346 WATTS AT RATED CURRENT -RESISTANCE .00316 OHMS ACROSS FULL COIL
-RESISTANCEr .003 OHMS PER PHASE TUBES (ARC DROP)
(AVG. KILOAMPERES)
O FORWARa CURRENT -PULSE TESTS ON SINGLE TUBE * REVERSE CURRENT- PULSE TESTS ON SINGLE TUBE FORWARD CURRENT AT NORMAL LOADS
loo
COIL
INTERPHASE TRANSFORMER IISO/-180 CYCLES -78 .KVA
R4
RECTIFIER
CURRENT
RESISTANCE AC WIND. Rp .0241 OHMS PER COIL DC WIND. OHMS PER
R5'.00632
/4-Rz0025Ll 0
BASE)
~~~~~~~~~~~~ ~~RECTIFIER TRANSfORMER -60 CYCLE -230 KVA CONT.
J/R RECT TRANSF. / >-AC WINDING
H1
0
UNIT VALUES ON 230 KVA lPER R .0031
BUS
) 'H
R R2
0
LINE
.0250
/
-i
iR /.0015
/
SUPPLY
-0$-------
- o
CONSTANTS
The a-c components of current in the three transformer phases follow the values resulting from a complete 3-phase short circuit. The transient components maintain continuity between intervals 1
/
RECTIFIER -EQUIV.
RESISTANCE
.0015 OHMS PER TUBE
LOAD CIRCUIT CABLE LEADS - RESISTANCE a .0034 OHMS 4 - INDUCTANCE 79.5 X 10-6 HENRYS ODC MOTOR (EQUIVALENT MACHINE) -RESISTANCE OF ARMATURE CIRCUIT8.0170 INDUCTANCE OF ARMATURE CIRCUIT' 46 X 10 HENRYS
\<
-VOLTAGE
Ed'
'280
OHMS
VOLTS OPEN CIRCUIT
and 2 and decay with the exponential
(R/L,:)t.
Interval 2 ends when the current in phase 2 reaches zero. Calculation of the
currents in anodes 1 and 3 and in the d-c at this time
determines the initial 3 is similar to that in interval I in that there are two conducting anodes. The average voltage of anodes 1 and 3 during this interval is opposed to the voltage of the d-c source and usually reverses the rate of rise of cathode current. source
codtin fo. nevl33. for interval ~~~~~~~~~~~~~~~~~~~~~conditions The action in interval
The transition from interval 3 to inter-
val 4 is determined when the current in phase 3 goes to zero. The same current is then carried by the faulty anode and the
d- srce interval Because the a-c on phase to the voltageduring I is 4.opposed d-c voltage during most of this interval, the fault current is decreased. Interval 4ed hntevlaeo hs xed 2exceeds 4endswhenthe voltage ofrphase the voltage at the rectifier terminals, at which time intervals 1 to 4 will be repeated with new initial conditions. Appendix II gives the equations which intervals.
.S'mstained Fault Current. The value of
sustained fault current may be determined by carrying out the circuit analysis for a sufficient number of cycles. It may also be found by trial, assuming values of id and t at the start of interval 1 and determining the resulting currents throughout the sequence. At cot= 360 degrees the current should have the vaLlue assumed at
Herskind, Schmidt, Rettig- Rectifier Fault Currents-II
247
A
>
L
.
_
J
,
E
fF\ / L 7480A
A more precise approximation results by assuming that on the average two anodes are conducting throughout the cycle and that the resulting impedance to d-c feed includes one-half the transformer impedance. A further assumption is that net a-c voltage in the d-c feed circuit is one-half of Es. This permits calculation of the d-c feed as described in Case 2. Since two anodes are assumed to be conducting, half this value is added to the current in the faulty anode resulting from arc-back in a wye and is subtracted from the current in the normal anodes.
/Athe
6370A m
A
,
0
Figure 11. (Test 5) Fault current during d-c short circuit (inductance in the short), 6-anode 200-kw 300-volt rectifier "A' to "F" inclusive-anode currents current G -cathode -cdthode current
the start of interval 1, and anode 2 should be ready to start conducting.
factors
Modifying Circuist Acton. The
c utah foregoing ane-balysisafree descrfibes tthree tion arc-back in a free rectifier with
alenoes Ahe nircumbactiof fartictarsly initial action. Phase of Arc-Back-While arc-back commonly occurs at the end of commutation, it may occur at a later time during interval
1 or during intervals 2 or 3. The initial peak of reverse current is re.duced in such cases. (Compare tests 43 and 45, Fignres 17 and 18.) Interphase Transformer-The interphase transformer acts as a large inductance to reverse current from the d-c load until saturation occurs. At the time of a commutation arc-back, the interphase transformer flux may have reached 0.1 to 0.5 times its saturation value, depending upon the design of the interphase transformer and the amount of phase control used. Phase Control-Phase control may delay the entry of a normal anode and thereby reduice its contribution to the arc-back.
Approximate Solution. While the foregoing analysis for the case of arc-back
with a-c and d-c feed constitutes an exact method of procedure, its use is likely to prove cumbersome and approximations of reasonable accuracy are well worth con-
There may be considerable variation in the arc-drop voltage across a rectifier on successive trials at the same fault current value.
(Figure
Tests 30 and 31
248
16)
show
the arc-drop voltage in a pumped ignitron at pulse currents of approximately 25,000 amperes crest. In test 30, the arc-drop voltage wave has a rounded crest at 87 volts. Test 31 shows a sudden rise in
4920A
EA
A \I
G
74
Figure 13. (Test 29) Fault current during arcback with a-c feed only, 6-anode 200-kw 300-volt rectifier operating with only three tubes (one wye)
"A"-anode I current '-anodle number ~~~~~~~~~~~~~"B' (faulty anode) number 23 current 'C"-anode number
"D--anode-to-cathode voltage in faulty tube
voltage from 70 to 152 volts near the crest
high arc-drop voltages of short duration.
of the wave approximately doubling value. In many value its of cases, the crest
ignitron are shown byduring test 23 pulse-current This test (Figure 15). tests
the arc-drop voltage does not have ticular
significance
insofar
as
par-
its influence
Arc-drop measurements on a sealed
shows form
a
triangular arc-drop voltage wave
starting
from
a
high
value at the
the magnitude of fault current is concerned, since the break in the arc-drop
beginning of the conduction period and dropping regularly to approximately zero
Average values of the arc-drop voltage would appear to be more representative of the effect of arc-drop as they are a measure of both the volt-seconds appearing across the tube and the energy dissipated in the arc during the fault. Average values do not give undue weighting to
be as significant as its average value in determining the current obtained during faults. The nature of the arc phenomena at fault current levels is not accurately known. In the case of the pumped ignitron, the sharp rise in voltage would ap-
on
voltage wave does not occur until the fault current has reached its crest value.
at its end. Again in this case the initial value of the arc-drop would not appear to
pear to be the result of arc starvation. Observations show that this voltage occurs at a quite definite current level. WNbhen fault currents in excess of this critical value flow through the tube, the rise in voltage occurs before the current crest, . . a c the a considerable increase in the ~~causing value of for averaged arc-drop voltage a small increase in fault current. In the case of the sealed ignitron, observations show that when the tube is passing currents of fault magnitude, a considerable part of the cathode current is collected on the walls of the tube. The shorter arcpath which results may account for the reduction in arc-drop in the latter part of the conducting period. Average arc-drop values for a sealed ignitron rectifier tube of the type used in units ranging in size from 200 to 500 kw for 250- and 600-volt applications are shown in Figure 8. Typical arc-drops for a pumped ignitron of the. type used in p
495A
A
A
4000A
A
3720A / OA
D E F
4
5430A
> _
7
J,,,OA 7700A
sideraticon.
The simplest approximation consists of determining upper limits for fault current values. Thus the current in the normal anodes cannot exceed the value for arcback in a wye and the current in the d-c source generally cannot exceed the value for d-c feed only. The current in the faulty anode cannot exceed the sum of these values.
_ c
*29
Arc-Drop
*5 -
A
G|
| i
Figure 12. (Test 9) Fault current during d-c short circuit (bolted short), 6-anode 200-kw 300-volt rectifier "A ' to "F" inclusive-anode currents "G' -cdthode current
Herskind, Schmidt, Rettig-Rectifier
Fazult Currents-Il
AJEE TRANSACTIONS
units ranging in size from 1,000 to 2,500 kw for 250- and 600-volt applications are shown in Figure 9. Two dashed lines representing equivalent resistance are shown in each figure. The lower value of resistance in each figure would be applicable to an equivalent circuit containing a battery and
A
A _Go
D-C SHORT CIRCUIT The total impedance of the circuit is determined as follows:
G
"B"-circuit-breaker voltage
'C' -anode-to-cdthode voltdge (drc-drop) D'-anode current E' -ignitor-to-cathode voltdge
_
3X2832 = 1.042 230X 1,000
3E2 r . . d-c winding = s~___ VA
ARC-BACK WITH D-C FEED ONLY In calculating the fault current in this case, case, theth total ohmic resistance of the d-c
the totalterminedebysadding by adding the
fault path is determined
resistances of the various elements.
Rectifier transformer
0.00324
I)-c cable=
0.003 0.0034 0.0170
(3,707/230 X 1,000) 1.042= Interphase = Anode cabletransformer = D-c motor=
RD=
0.0168 0.0016
0.0450
The tube arc-drop is not included as the
Anode Cables R -0.003/1.042=0.00288 -
B
2
I
F
Zc = 0.0860
F
Sustained Direct Current ~~~ 230,000 ~~~~~VA Ids=0.9XE=.9X 283X0. 0860 =48,500 ampere (average value) (3)
070A,
IXi
A / k<'C
747O.,8026OA-
_
Ratio R/X=0.0250/0.0825=0.304 Kp =1. 41 (Figure 4)
Transient Direct Current 7r l idSl-4lX-XIdS=12,500 amperes
3
||\|
value) ~~~~~~~~~~~~(crest
25,OA
Figure 14. (Test 32) Fault current during arc back in double-)' circuit with no external d-ed -nd 0-w30vl etfe
"4A", "B'", "D', "E", and "F' 'currents in normal anodes
"C"-current in Faulty dnode 'G'"-anode-to-cathode voltage in faulty tube
The ohmic value of commutating impedance is calculated from the total per unit value as determined for the case of d-c short circuit.
Z,c= z_-1 042X0.0860=0.0895 ohm VA -
F
(4)
R-BcARC-BACK WITHACFEDOL A-C FEED ONLY
* 32 -
1949, VOLUME 68
Ohms
Supply line 0.0031X1.042=
Total
X/1042-0060/1042 00575
X
Total
'Vb
F
#23 Figure 1 5. (Test 23) Arc-drop on sealed ignitron during current pulse
(9)
Zc
Total Xc= 0.0250+0.0575=0.0825 Total R =0 0031 +0.0176+0.00288+ 0.00144 = 0.0250
2400!A
E
E
1.20
A
A
Crest Forward Current
Crs F r r iaf / Kf E =6,040 amperes
osOOA
on
amperes (8) ~~~~~~~~~~~~~~~~~~~~7,020
Using other values as given in Figure
6430 A
4970 A
=
I
I
.. > Normal ohms
~~0.0895
ze
/\
R = 0.0015/1.042 = 0.00144
3,707+346 R 2P VA230 X 1,000 X= VZ\2 R2 =0.0570 ==Xp+±/2Xs
VN
z
Rectifier Tubes
Rectifier Transformer
Z,=0.0597 (on 230-kva base)
D
Crest Reverse Current \2E -2X283 = 1.57X
"A '-60-cycle timing wdve
Extensive fault-current tests were made on a 6-phase 200-kw 300-volt sealed ignitron rectifier. The complete circuit of the rectifier unit and the associated a-c supply and d-c load systems during these tests, together with the circuit constants, are shown in Figure 10. Oscillographic records of fault currents are shown by six tests included in the illustrations. The fault current calculations are as follows:
C
K7 54i7=
= .7 57 Kf=1.35, (Figure 5) I=13,(iue5
D
resistance. The higher value of equivalent resistance is an approximation accounting
Calculated and Test Results
r
8
resistance.
for the total arc-drop. This approximation simplifies analytical treatment and is of commensurate accuracy with the determination of other circuit parameters.
Using the R/X ratio determined for d-c short circuit
Z\A
20
Figure
16. (Tests 30 and 31) Arc-drop on pumped ignitron during current pulse 'A'"-6-cycle timing wave
"B"-gsrid-to-cathode voltage
"C"-grid current "D' '-node-to-cathode voltage (arc-drop)
current "E"-anode "F"-ignitor-to-cathode
Herskind, Schmidt, Rettig-Rectifier Fault Currents-Il
voltage 249
4620A
car-back was simulated by a switch. The total inductance in the fault path is determined from the reactances of the various elements.
Test 32 (Figure 14) shows the fault current during arc-back in a double wye circuit with no external d-c load. This record shows the effect of the current contribution of the anodes of the normal wye. Test 45 (Figure 18) shows the fault current during arc-back with both a-c and d-c feed w t a feed when the arc-back occurs at the end of conduction. Calculated and test values are as follows:
A
5 __ 5
W
4100A Henrys
Supply line 0.025 X 1.042/377=
69 1 X 10-6
Rectifier transformer
0.0575X 1.042/377=
159.0
62?OA
15.88
Interphase transformer=
D-c cables=
IOOOA
79.5
D-c motor= Total
46.0 _-
Li=
369.4 X 10-6
The total reactance and impedance are X3= wL3= 377 X 369.4 X 10-6=0.139 ohm
-3
Fo
_
Go
G *43---.
_t
/ 2 vz t_~~~G
Calculated,
back with both a-c and d-c feed (arc-back approximately 120 degrees after end oF conduction) 6-anode 200-kw 300-volt rectifier
=XV2+R32=0.146 ohm
"A"-anodenumber1
The ratio R3/X3=0.324.
vau.ftecreti
,1--anou
Substitut*ng Ed' 280 R3 0.045
ae number
V2E,
N_2 X 283
Za
0.146
a
0
0
Co ut) =2 cos = cot 3r, 1 _ e =34c= 0.950, and (1- 0.995 and (1coS )-= 2 5w, = c,,t =2 1ot) =52~~ Cos wt)
The approximate currents in the faulty anode at the end of the first, third, and fifth half cycles are 7,680, 8,790, and 8,960 amperes, respectively.
ARC-BACK FEED
WITH
BOTH
A-C AND
D-C
If we assume that on the average, two phases are conducting and that the average a-c voltage in the circuit is one-half E., then Total Li =255.4 X 10- I henries Xi=1wL = 0.096 ohm R= 0.0335 ohm
RI/X, = 0.348 ohm
Z =0.101 ohm
From equation 11 Ed 280 R1-- 0.0335 -=8,400 amperes
\/E8 VWX283 - 2X010=o 1,980 amperes
* The approximate currents in the d-c is,tid soure a theendoftefrst hir ann fifth half cycles are respectively 7,280, 9,960, and 10,340 amperes.
source~~ atteedo'h ~
250
....
8,680
12,300
7,030
____________________
The effect of the time taken for satura-
tion of the interphase transformer was not
considered in the calculation. This results in too high a calculated value for the
first half cycle.
The approximate current in the faulty anode is obtained by adding half these values to the value derived from Case 1. This results in an ultimate peak value of 7,020+ 10,380/2 = 12,210 amperes. COMPARISON OF TEST AND CALCULATE£D
=2,740 amperes
cor, 1
2
_t] (II)_-Cos
6
cycle....
....
_
Z3
Reverse current in faulty anode, At end of lst half cycle ..... 10,660.... At end of 3rd half 12,000
end of 5th half cycle.... 12,200 12,900 currentAt Maximum d-c feed back.... 6,230 .... current
B -a-c circuit breaker volts pole number 2 TheThaprxmt approximate value of thcurnt n ""aoe nubr2current anoe number 2 current (alty equation C-anode (faulty anode) the faulty anode is given by the equation l."dcici.,ekrot volts thefaultyanodeisgi eD-d-c circuit breaker -Rs Wt 3 current anode number 'Et' Ed' V \/2Es [Ed' E dr= l+ -1 X3 d-anodenumber3r idr "G"-cathode current R3 Z3 __
V/2E,
Test,
Amperes Amperes
Figure 1 7. (Test 43) Fault current during arc-
Summary A comprehensive procedure for the
analysis of fault currents in power rectifiers has been developed and some of the more usual cases have been analyzed for the 6-phase double-Y circuit. However,
Test 9 (Figure 12) shows the fault currents during d-c short circuit with a bolted short. Calculated and test values are as
further analyses are still required to cover all the conditions which may he encountered in practice and provide a ready
follows:
means
Calculated,
Average sustained current. 8,500.
Crest transient current ........12,500....
Test,
for
determining fault currents.
Appendix
7,700
io000
I.
Symbols
i =instantaneous current, also crest value of sinusoidal component of current i' =crest value of instantaneous current including transient component current ~~~~~~~~~~~~I=avreragevalue of crrn First subscript: a-anode (phase) culrrent (Figure 12). d-d-c bus current Test 29 (Figure 13) shows the fault cur1, 2, 3-phase 1, 2, 3 rent during arc-back with a-c feed only Second subscript: with the rectifier operating on only three s-d-c short circuit tubes. Calculated and test values are as f-forward (normal) direction of flow r-reverse direction of flow follows: 1, 2, and so forth-start of intervals 1 and 2 e =instantaneous voltage Calculated, Test, Es= open-circuit, secondary voltage of Amperes rectifier transformer in rms crest reverse current . Amperes ......7,020 ..7,440 ..Ed' =counter electromotive-force volts compoC:rest forward current . 040.6,370 .....6, neat of d-c load voltage ...... Asicwauedtshrtefuly L¢, Rc, Zc= VC 2 ~line-to-neutral commutating inductance, resistance A switch was used to short the faulty tube in making the arc-back test. Norand impedance of rectifier Ld, Rd=circuit inductance resistance of d-c alacdo a sue nmkn h malarcdropwasassued n maingthe elementsand external to rectifier calculations, giving a calculated value Lp, Rp= inductance and resistance on priwhich is too low. mary side of rectifier
Test 5 (Figure 11) shows the fault current during d-c short circuit with inductance in the short. The average sustained ' current is 7,480 amperes and is only slightly below that obtained on test 9
=arag vaueor
Herskindl, Schmidlt, Rettig-Rectizfier Fault Currents-II
AIEE TRANSACTIONS
RsLs,
= inductance
4430A
and resistance on
secondary side of rectifier transformer
Figure 18. (Test 45) Fault current during arc-
back with both a-c and d-c feed (arc-back at
_A
Note
Li, R,, ZiLl=Ld+±/2Lc, RI=Rd+'/2Rc, Z1 =R
Y
2L
C L2, R2L2=Ld+-5/3Lc, R2=Rd+±/3Rr L3, R3, Z3L3aLd+Lc, R3=Rd+Rc,
Z3 = V\R32+ ,,2L32 tl, t2, and so forth=time at beginning of intervals 1 and 2
2
L
Go
/G'-cathode current
' f
Appendix 11. Currents during Arc-back with A-C and D-C Feed
t2) Ea' 1-E- f-2(tL2 'Id
Interval I1- tl to t2 Interval 1 - t1 to t2
'Interval 3- t3 to t4 ~-\/
in(ctl
RI(t-tl e-E--(tj i+
X/2E1[Si~~ (wt±~-
2Z\L2E
dls Ll1
Eii
RI(t L
[
l
L1(t4) (14)
t
I
R(17)
(1-tI)
Lc
x
idId3)e
Re
C (18)
V2ES
-\1Esx 2Zd
1rd Od3) +]dI6l
RI
(19)
Lsn il=I[sinI,=ct_okogt3-trJ
c(t2-'-O)
Re-(te
t2)
c
X xR
r
sin cot+
3
\s((tt-)t4) Od3
(15)
+ id+
~~~3
R3=Rd+RC L3+Ld=LC Z3+± R32+W2L32 0d3=tan
H. L. Kellogg. ELECTRICAL ENGINEERING (AIEE TRANSACTIONS), volume 64, April 1945, pages
145-50.
R3
1
Discussion A. J. Maslin: (Westinghouse Electric Corporation, Sharon, Pa.): The treatment of short circuits and arc-backs presented in
the paper by Herskind, Schmidt, and Rettig is an interesting addition to the published information on these subjects. In particular, the approximate solution for arcback with a-c and d-c feed is most welcome, for it permits an estimate of the fault currents for this most important case, without laborious point-by-point computation of the current values in individual branches of the circuit. Everyone concerned with the design, application, or use of rectifier equipment will wholeheartedly endorse the authors' statement: "A complete
1949, VOLUME 68
MERCURY
Marti, Harold Winograd.
AND
McGraw-Hill Book
ANODE-CIRCUIT-BREAKER DESIGN
AND PER4. }eFORMANCE CRITERIA, E. W. Boehne, W. A. Atwood. ELECTRICAL ENGINEERING (AIEE TRANSACTIONS), volume 64, June 1945, pages 337-45.
(20)
the fault currents obtained in the widely used 6-phase double-Y circuit is particularly desired." Generally, short circuits are relatively rare in comparison with arc-backs, and result in lower maximum fault currents in individual rectifying devices and transformer windings. As explained in the paper, all actual installation will have the a-c circuit impedance divided between th.e a-c winding and the d-c winding circuits. Because of the characteristics of rectifier transformers, the ratio Xp/XS will usually be of the order of ten or more, hence the assumption that all impedance is located in the a-c winding circuit is usually completely justified. Short-circuit currents determined on this basis will be in error by being slightly too small.
treatment of
OF
Company, New York, N. Y., 1930.
5.
/1
PRINCIPLES
3. MERCURY ARC RECTIFIER (book), Othmar K.
Wt4+3-Od3lE+id4C 3 --c(1-12) Rsinsn3d3I+I4EL35. I
R3
McGraw-Hill Book Company, New York, N. Y., 1927.
/
11-tdl JE Le 3 J
13
Prince, F. B. Vodges. THEIR CIRCUITS (book), D. C. ARC-RECTIFIERS
Z3
27r
R2=R±ER L2=Ld±-L 3
2.
Eid'g[l-e DJ( 4)]+ i2E5
_7r.
=tan-'1L
1. RECTIFIER FAULT CURRENTS, C. C. Herskind,
Interval 4 t4 to tl
1-c3
dl
References
t3)
RIi)sin (wt3
RL,Rd+-~Rc Ll=Ld+-Lc 2 ~ ~~~~~~~~2 Z= R12+w2L12
t8
-Rl,RI,2Z [sin (wt-Odl)-e 1( X r
sin
Interval*2-t2 to t3
sin
____i V3 e (
cos(t3-O) ]+dd+(ilI-
1-d= R
/iflK 7r---O"1l-l-*E sinlwtl0drdd + ld
+id
Cos
TO)]±i+(i li-))X
Zc
-t2)
R--(t-t2)11
=-21-I3[cos(t-O)-e
LC
Rr(1- 1) (13) ELe
id -. '[
R2
V2E,
(tI-0 )j-
2 sin Re
CotX
"F-d-c voltage
41290A
id+(X22+-id2)E L(t
sin
2 ' C -anode number 2 current (faulty anode) "D"'-d-c circuit breaker volts "E"-anode number 3 current
703 A
1230C
i2 I[sin(,wt -o) -,LeL
-v/3
rectifer
"A"-anode number 1 current B" -a-c circuit breaker voltage pole number
8680A
Phase 2 voltage zero is the time reference for defining circuit action during arc-back with a-c and d-c feed. f3=switching angle (angle after voltage zero at which fault occurs). 9 = tani- IR
end of conduction) 6-anode 200-kw 300-volt
J
B
CALCULATION oF THE BACKFIRING PEENOMENON H. Forssell. Technical AchieveResearch, Vasteras (Sweden),
RECTIFIERS,
ments of ASEA 1946, pages 58-64.
factors, mentioned but briefly in theOther paper, are the inductance and resistance which are always present in the d-c circuit. Both of these operate to reduce the shortcircuit current, usually to an extent more than sufficient to offset the error introduced by assuming all a-c circuit impedance located on the a-c winding side of the transformer. In the extreme case where the d-c circuit inductance is sufficient to completely smooth the direct current, the anode currents, instead of being sinusoidal with a
crest value given by equation 1 of the paper, are approximately trapezoidal with a crest value only 87 per cent as great. For most double-way circuits the location of the a-c circuit impedance is of no consequence. The short-circuit current is the same whether the impedance is a}l on the
Ilerskind, Schmidt, Rettig-Rectifier Fault Currents-II
251
33
The arc-back is initiated at the inhave the same potential in Figure 1 of this discussion) afid (c,wt=0 to1\s the third anode begins to carry current at the instant its potential becomes positive (wt =90 degrees in Figure 1 of this discus_i _ 30 sion). The data cited are for the assumption that the arc is equivalent to a resistance in Forssell's Figure 2). An explanat \(ac=0 tion of the basis of the values in Figure 6 of 2.0 _. ./ .the paper would be appreciated. A L > W use of a direct voltage in series with The 1.5 - 4 s/ inductance and resistance to simulate the \ / X \ actin oftheload he wyeof of the load, and. of of the.second wye of e _ t _ L-S I.o action is a very useful the 6-phase double-Y circuit, stant two anodes
ITY3.0
./
2/0
an
J T2---si5
-g
_
-i
II
1.0 -
- )\ -
-
-
IS 8O
0
\ -
7
artifiCe.
z
, X I!
-
X ,r / )
- -
360
I t
It was suggested but not developed in a previous paper.3 A discussion,4 howo0lT ever, presented a detailed comparison of ixc - XrEs test values of arc-back current in a double-Y circuit with calculated values for a single \ t ttt twye_ with both a-c and d-c feed. The equa-
540
720
Figure 1. Arc-back, a-c feed only a-c winding side, all on the d-c winding side, or divided between them.' In spite of the great progress made in reducing the frequency of occurrence of arcbacks, they remain the most common rectifier fault. They are also the most severe, and are best isolated by high-speed anode-
circuit switchgear. Because of this, experimental and analytical determinations of arc-back currents continue to receive a great deal of attention. One of the simpler analytical treatments covers arc-back in a wye with a-c feed only, as presented in the paper. The values of paper, K, and Kf given in Figure 6 of the . , r 11. however, appear to be rather high.r Figure of of this discussion was wa calculated fro thidicsso caclae from equations which assume the arc to be equivalent to a resistance, and permit consideration of time of occurrence of the fault and amount of phase control. It applies to an arc-back occurring at no load, at the time wt=0, for a controlled rectifier operating
with zero retard. The values of K, and Kf from Figure 6 of the paper and Figure 1 of this discussion, as well as values of K, taken from Figure 2 of a paper by H. Forssell,2 are compared in Table I. It should be noted that Forssell's Figure 2 applies to arc-back in a wye with a-c feed only, at no load, and for an uncontrolled
rectifier.
252
scon
cate that the first crest of arc-back current is about 90 per cent of that calculated on the basis of both a-c and d-c feed; while the second and subsequent crests are about 15 per cent greater than calculated on the
basis of
a-c feed only, this increase being due to the contribution of the other wye.
REFERENCES
RECTIFIER York, CIRCUIT, A. J. Maslin. Electronics (New YN. .), volume 9, December 1936, page 28. 1. THE THREE-PHASE FULL WAVE
2. CALCULATION ENON IN
OF THE BACKFIRING PHENOMRECTIFIERS, Harry Forssell. Technical of ASEA Research, March 1946,
Achievements
page 58.
3.
RECTIFIER FAULT CURRENTS, C. C.
Herskind,
H. L. Kellogg. ELECTRICAL ENGINEERING (AIEE TRANSACTIONS), volume 64, April 1945, pages
145-50.
4. Discussion, R. D. Evans, A. J. Maslin, Loc. Cit., pages 441-42. 5.
ARC-BACKS
IN
CIRCUITS-ARTI-
RECTIFIER
ARC-BACK TESTS, R. D. Evans, A. J. Maslin. ELECTRICAL ENGINEERING (AIEE TRANSACTIONS),
tions used in this comparison permit taking tions-used-inJthis permit
FICIAL
they yield highly satisfactory results, are very laborious to make. The approximate solution demonstrated in the paper is therefore most welcome. Whenever arc-back currents are calculated by these methods, the influence of switchgear must be given careful consideration. With high-speed switchgear, either cathode or anode, the crest calculated current will not be realized because the opening switch will intioduce an important voltage drop into the d-c feed circuit, or the anode circuit itself, early enough to effect some degree of current limitation. A number of arc-back tests5 on 600-volt 6-phase double-Y rectifiers, feeding regenerative loads through high-speed cathode circuit breakers, indi-
C. C. Herskind, A. Schmidt, Jr., and C. C. Rettig In his discussion, Maslin has compared values of Kr and KM in Figure 6 of values thepaper calculated by paper wilth values calclae by himself and also by Forssell in another paper. The differences noted by Maslin may be explained as follows:
account of the load being carried, the time of occurrence of arc-back, and the amount of phase control. These calculations, while
'
2 of Figure 1 of 6 of Dis- ForsR/X Paper cussion sell 0
0.1
0.4 0.5
0.6
Kf Figure
Figure 1 of
6 of DisPaper cussion
...2.40.. .2.30 ... 2.35 ... 1.98 .... 1.86 ...
i
.2.00. 2.00... 1.70
0.333 .152
.7... 1. 148
43
1.45.1.36... 1.25 ... 1.35 .1.23. 1.16 .1.30 ... 1.07
.
himself
1. We have assumed a free rectifier, with conduction beginning as soon as the anode becomes positive. The per unit base for Kr and Kfis \/2Es/Z. 2. 2.cMashin has assumed phase control which prevents conduction from starting for 30 degrees after the anode becomes positive to thecontrol with respect transformer such phase does notneutral. affect R~~~~~~~~~~~hile normal operation of the rectifier, it does serve to reduce the a-c feed are-back.
during
Table I Kr Figure Figure
volume 64, June 1945, pages 303-11.
1.12 ...1..
18
3. Forssell uses a base of N12E,/X in stead of V2Es/Z. When this change in base is made, Forssell's curve agrees closely with ours. There is a slight difference at R/X =0, in the plotted curves. The calculated value of K,at this pointis 2.366. 23 is by o The treatment of fault currents means complete. Among the cases that merit consideration are: 1. Contribution of normal wye in arc back of double-Yrectifier.
2. Effect of impedance in d-c fault. 3.
Circuits other than double-Y.
H-erskind, Schmidt, Rettig-Rectifier Fault Currents-II
AIFE TRANSACTIONS
