1180 IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 24, NO. 6 , NOVEMBERIDECEMBER 1988

A Comparison of ANSI-Based and Dynamically Rigorous Short-circuit Current Calculation

Procedures

Abstract-Standards and procedures used in the application of power circuit breakers are correlated according to short-circuit current, both as prescribed by the empirically based ANSI standards and using a dynamically rigorous procedure. The correlation is made in order to determine the degree of accuracy of the simplified empirical ANSI calculation procedure, which is composed of short-circuit calculation techniques of the predigital computer era. With use of today’s computer capabilities, a great degree of accuracy is possible in determining the limits of these standards and methods. A brief qualitative comparison of the procedures promulgated in the two methods is presented. Their correlation is further tested by carrying out a short-circuit calculation on a specific industrial system design. The study results are tabulated and reviewed to identify their unique characteristics. The broad conclusion suggests that the ANSI short-circuit current values are higher and hence more conservative than the more dynamic rigorously calculated values.

INTRODUCTION N the postwar period of 1945-1965, the international I electrical equipment market was dominated by U.S.

manufacturers. As a consequence, the American National Standards Institute (ANSI) standards became the de facto world standard. Canadian industry standards, with minor modifications, have been generally patterned after the ANSI standards, which are “consensus” standards. This implies a consensus of those substantially concerned with a standard’s scope and provision.

The last two decades have witnessed a gradual reduction of participation by large U.S. electrical manufacturers in the electrical equipment world markets. Whether this develop- ment was caused by weakness in the U.S. market, lagging U.S. technology, a strong dollar, or aggressive foreign competition; U.S. engineers have been getting increasingly involved in the application of foreign power circuit breakers in U.S. and Canadian power systems. Such applications are no longer limited to U.S. industrials operating on foreign soil, but increasingly include applications within the U.S. and Canada.

Uncertainties about the proper correlation between foreign- rated equipments and U .S. calculation standards have created

Paper PID 88-4, approved by the Petroleum and Chemical Industry Committee of the IEEE Industry Applications Society for presentation at the 1987 Petroleum and Chemical Industry Committee Technical Conference, Calgary, AB, Canada, September 14- 16. Manuscript released for publication April 5, 1988.

J . R. Dunk-Jacobs is with Industrial Power Systems, Inc., 14080 S.W. Maverick Court, Beaverton, OR 97005.

B. P. Lam and R. P. Stratford are with Power Technologies, Inc., 1482 Erie Boulevard, Schenectady, NY 12301-1482.

IEEE Log Number 8822916.

many questions which can be addressed only by standard- making bodies. The American National Standards Institute (ANSI), Verein Deutscher Electrotechniker (VDE)-the Ger- man equivalent to IEEE-and International Electrotechnical Commission (IEC) committees are among those that have worked diligently and have made considerable progress toward an internationally acceptable standard for the applica- tion of power circuit breakers. The engineering, commercial, and political complexities of such work, however, become immediately apparent when considering that such standards must encompass voltage, frequency, continuous current, temperature rise, surge performance, capacitor switching, etc.

For U.S. equipment and applictions, the ANSI standards prevail. To assure that the breaker short-circuit current rating is properly matched with the duty, it is essential that the ANSI- instructed test procedure (ANSI C37-09-1979) be followed carefully in order to demonstrate the breaker’s ability to meet its claimed ratings (ANSI C37.06-1979). Furthermore, an ANSI-directed short-circuit calculation procedure (ANSI C37.010-1979 or C37.13-1981) must be executed to deter- mine the duty. The proper application of an interrupter simply requires that any and all specific ratings or capabilities (i.e., first-cycle or close-and-latch and interrupting, etc.) exceed the comparable short-circuit duties (first-cycle, three-cycle, etc.).

For foreign equipment in U.S. market applications, the application procedure has more recently become less complex for the reason that some foreign equipments have also been assigned an ANSI rating. If this rating has not been identified, two solutions are possible. First, require the foreign manufac- turers to assign the necessary ANSI ratings and capabilities by subjecting their breakers to ANSI-instructed test procedures. Alternatively, modify the results of computer program calcu- lations to obtain the short-circuit duties that compare directly with foreign ratings. To implement this alternative, U.S. industry must be in possession of and keep up-to-date information on foreign rating procedures.

In the prevailing absence of one internationally recognized standard, the original intent of the authors was to attempt to make a detailed comparison of most major world standards, such as those of the ANSI, IEC, VDE, and a British procedure. When it became apparent that the VDE and IEC standards were in states of major revision, and probable consolidation, these standards were excluded from the scope of this paper.

The authors’ inquiries into the presence of a British standard

0093-9994/88/1100-1180$01.00 O 1988 IEEE

DUNKI-JACOBS et al. : ANSI-BASED AND DYNAMICALLY RIGOROUS SC CURRENT CALCULATION I181

resulted in the realization that no consensus standard appears to exist in Great Britain. In regard to the calculation of the short-circuit duty, the Central Electricity Generating Board (CEGB) and a number of industrials have sponsored a calculation procedure, developed by a British university, which is based on an algorithm in their computer analysis of the short-circuit current phenomenon. This algorithm uses an iterative approach in modeling the short-circuit behavior of dynamic machines as a function of time and the effect of the network on the time constants of the machines. Hence the individual contributions of synchronous and induction ma- chines could be calculated and summed at each time interval. A corresponding British interrupter testing procedure or standard, fundamental to the establishment of an interrupting rating, has not been identified. For these reasons, this paper’s concern is limited to the application of ANSI and U.S. rated interrupters.

SHORT-CIRCUIT CALCULATION TECHNIQUES

When the significance of assigning short-circuit interrupting ratings was recognized in the United States in the early 1940’s (ASA C37.6-1941 I ) , the computing techniques and tools were relatively crude. The dc network analyzer was claimed to speed fault-current calculations in an August 3, 1959 article of Electrical World. Its successor, the ac network analyzer, allowed the representation of both rt-sistance and reactance components of network.

ASA Standard C37.5-1953 introduced the “total current basis of rating” and offered a simple “general” method of calculating a symmetrical fault-current magnitude. The multi- plier to be used to determine the total asymmetrical interrupt- ing current was a simple 1 .O for the generally used eight-cycle breakers if the fault level was less than 500 MVA. This simplicity was also reflected in the representation of genera- tors and motors for momentary and interrupting duty studies. A major change became effective in 1964, when the “symmet- rical current basis of rating” was introduced; C37.5-1953 was given the designation C37.05-1964. A new standard, C37.010 (the application guide), was formalized from Section 3 of

To achieve the desired degree of accuracy in the calculation of short-circuit current magnitudes in a complex system while utilizing only simple calculation procedures and tools, an empirical methodology was selected. The early as well as current ANSI standards are based essentially on empirical procedures. The current ANSI standards (C37.06-1979 and C37.010-1979) of course rely on greatly refined empirical procedures and the availability of sophisticated computers and digital calculation techniques.

The results of the ANSI calculating procedures are com- pared with a dynamically rigorous program that models the machines using the differential equations for flux and other equations to ensure the most accurate representation of the dynamic forces present. These models require extensive input data as well as sophisticated computers with mass storage capabilities. The analytical software required to model the

C37.5-1953.

’ American Standards Association (ASA), predecessor of ANSI.

current sources is equally sophisticated. Its output is a time- dependent continuous short-circuit current which allows the identification of the current magnitude at any point in time for comparison with the breaker’s pxformance characteristics.

The outputs from the ANSI-directed procedure and those of the dynamic program offer the opportunity to compare the empirically calculated ANSI valL.es with what is happening in real time.

REPRESENTATIVE SYSTEM FOR A U .S. BASED INDUSTRIAL PLANT

In recognition that design philosophies and standard voltage levels vary across international borders, the representative system is based on U.S. system design practices. The repre- sentative system of Fig. 1 is not intended to be typical. Instead, the intent is to include various s t ort-circuit sources, such as a utility tie, synchronous generators, as well as synchronous motors and induction motors of qarious horsepower, voltage, and speed ratings. Since ANSI s andards and the dynamically rigorous procedure represent tt ese sources differently, the resulting calculated fault Contributions can be clearly identi- fied and compared.

The data pertaining to static circuit elements, common to both representations and expressed in actual ohms, are shown in Fig. 1. The representation of the short-circuit sources differs considerably in the two cdculation procedures. Tables 1-111 present all detailed data, f r im which can be derived the dynamic and empirical equ ivah t circuits. These data are considered to be typical for U.S. designed equipments.

It should be noted that the eflect of voltage regulators are not considered in either the AN31 procedure or the dynamic calculation procedure. The excii er field and armature short- circuit time constants delay the cffect of such regulators well beyond the timeframe of interest in short-circuit studies.

GENERAL REVIEW OF ANSI SH ~RT-CIRCUIT CALCULATIONS

The empirical short-circuit calculation procedure prescribed by ANSI C37.010-1979 (high vcltage) and C37.13-1981 (low voltage) treats all types of shon-circuit current sources as a voltage behind an equivalent impedance. As shown in Table IV, these impedances are used with or without a multiplier, to make the empirical solution confirm more accurately with the actually anticipated short-circuit current magnitudes.

The short-circuit impedance nctwork constructed in compli- ance with ANSI standards utilizcs the data shown in Tables I and 11. These data are applicable to the system shown in Fig. 1.

ANSI C37.010 recognizes two calculation procedures:

the complex, or R + j X network reduction is used to calculate the current value, while the separate R and X reduction is used to ca1cula:e the X / R ratio; and the separate R, separate X network reduction, which yields more conservative results. Also, contributions from adjacent buses may not always correlate well. However, this calculation procedure makes possible much simpler computing al Zorithms.

Both ANSI calculation procedures yield symmetrical cur- rent values. To compare these values with corresponding

1182

k V A 23529 9357 hp k V 13.8 4.16 k V POLES 2 2 POLES PF 0.850 0.800 PF RI 0.003 0.007 k V A

Xd 1.484 1.335 Ra X'd 0.154 0.137 Xd T'do 5.115 3.569 X'd X"d 0.102 0.096 T d o T d o 0.023 0.021 X"d x q 1.399 1.259 T d o X'q 0.396 0.485 x q X"q 0.099 0.090 X'q XI 0.114 0.107 x"q x2 0.097 0.088 XI

Conn. WYE WYE T d T'd3 0.532 0.362 T d T d 0.015 0.015 T"q r q 0.015 0.015 T23 Ta3 0.194 0.106 In (A) SCR 0.730 0.830 F fl

If 200 136

R2 @25C ( I -n ) 0.003 0.003 A

Rf (DC Ohms) 1.010 1.469 Rf (105C)

BUS # 2 11.12 BUS #

IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 24, NO. 6, NOVEMBERIDECEMBER 1988

GEN #I 23.529 MVA .85 PF 3600 RPM ' 2o MVA INTERRUFTING CAPABILITY (MAX. SYM. RMS)

36KA 58KA JCYCLE

'5 @ 13.8 KV 750 MVA

AS #2 GEN #2 9.375 MVA 0.8 PF 3600 RPM

I I

& V

1000 HP (25-40 HP)

50HP 0 ANSI EQUIV. 7

- x

0.W63 t J 0.0088

1 100 k P T 4 - m ~ B h o w

5-75 HP 5-40 HP 4-POLE &POLE

1

r' 0.007 + I)

6OOO HP 6-POLE

S M M HP 4-POLE

( 4 2-POLE 6-POLE &POLE 6-POLE

T - -

300 HP 4-POLE

2-500 HP IO-POLE

Fig. 1. One-line diagram of representative industrial power system. Note: Cable impedances are in s2 at 75°C; transformer impedances are in percent; all 13.8-, 4.16-, and 2.4-kV breakers are 5-cycle breakers (3-cycle contact parting time) and are rated on symmetrical current basis.

TABLE I SYNCHRONOUS MACHINE DATA ON MACHINE BASE

Svnchronous Generator Data I / Synchronous Motor Data

6000 13.20

6 0.80 5800

253.7 0.0065 2.8060 0.3760 4.2640 0.2300 0.5722 1.4290 1.4290 0.2060 0.1540 0.5710 0.3500 0.0210 0.0890

140.0 454.0

0.1680

3000 4.00

6 0.80 2890

417.0 0.0081 1.5690 0.3630 3.1460 0.2330 9.0195 1.0010 1.0010 0.2930 0.1 160 0.7280 0.0125 0.0140 0.0860

60.0 139.0

0.6860

2000 4.00

4 0.80 1940

280.0 0.0106 1.9260 0.2820 2.9260 0.1760 0.0135 1.1400 1.1400 0.2370 0.0970 0.4290 0.0084 0.0106 0.051 1

40.0 96.5

0.9840

2000 2.30

6 0.80 1949

489.0 0.0102 3.0270 0.3850 3.9860 0.2010 0.0159 1.8460 1.8460 0.2400 0.1050 0.5070 0.0083 0.0094 0.0568

33.5 106.0

0.9200

4 12 I 1 8

500 2.30

10 1 .oo 392 98.4

0.0171 1.3200 0.3470 1.1970 0.1970 0.0220 0.8740 0.8740 0.2210 0.1080 0.3150 0.0125 0.0150 0.0325

23.5 35.5

2.6200

9

150 0.460

12 0.80 154

193.0 0.0179 1.4970 0.3170 1.2300 0.1960 0.2604 0.9490 0.9490 0.2170 0.1130 0.2600 0.1610 0.0085 0.0310

13.4 26.6

4.2301)

15

DUNKI-JACOBS et a/. : ANSI-BASED A N D DYNAMICALLY RIGOROUS SC CURRENT CALCULATION

Bus

3 12 I I 8 8 9

15 17 17 16 19 20

1183

HP Poles kV kVA Xlr X / R ' R(o/ l ) jX(o/ l )

5000 4 13.2 4275 ,166 26.32 0.0135 0.3553 2000 6 4.0 1767 ,185 15.66 0.0618 0.96hO 1000 6 4.0 877.8 ,172 10.63 0.1693 1.7996 1000 6 2.3 877.8 ,172 10.63 0.1693 1.79"6 1000 2 2.3 834.6 ,178 20.00 0.0979 1.95X7 300 4 2.3 277.7 ,155 8.35 0.6141 5.121~1 IO0 4 .46 92.4 . I70 8.00 2.1121 16.89"O 75 4 .46 70.8 ,157 7.00 2.9094 20.36:;7 40 4 .48 41.4 ,166 5.00 7.3650 36.82'15

<SO .48 1000 .I67 6.00 0.2783 1.6700 <25 - .48 200 .I67 4.00 2.0875 8.3500 <IO - ,208 I50 ,167 3.00 3.5207 10.56!0

-

-

TABLE I1 INDUCTION MOTOR DATA FOR ANSI CALCULATIONS

APPLICABLE STANDARD C37.010- 1979 C37.13-1981

First Cycle Interrupting First Cycle

TABLE KI INDUCTION MOTOR DATA FOR DYNAMIC CALCULATIONS (MACHINE BASE)

/Bus HP Poles I kV kVA A 1 R , ' R, I X , X, X, ' X, 1

8 1000 8 1000

300 2.3 .46 .46 .46

4275. 187. 1767. 256. 877.8 127. 877.8 220. 834.6 214. 277.7 69.7

92.4 116. 70.8 88.9 41.4 52.0

.0059 ,0106 .O I59 .o 1 59 .0085 ,0185 ,0267 ,0246 .0279

.0042 ,135 .075 ,166 4.161 ,0112 .I40 . IO9 ,185 3.820 ,0125 ,140 ,082 .I72 3.860 ,0125 ,140 ,082 ,172 3.860 ,0078 .I41 ,087 ,178 6.204 ,0103 ,082 ,134 ,155 2.919 .0126 ,099 ,175 ,170 3.738 ,0114 ,105 ,205 .I57 3.734 I- ,0156 .099 ,179 ,166 2.396

- ,0690 ,1148 ,0175 .0175 .0469 .0036 .oooo .oooo .oooo

For calculation of various time constants and X / R ratio per NEMA Standard MG1-1.58 (1980).

TABLE IV REACTANCE MULTIPLIERS FOR A N S I CALCULATIONS

]BREAKER TYPE I HV Breakers (> 600 V) I LV Breakers I

Utility Supply

In-plant Generation ( I )

Synchronous Motors (2)

Induction Motors (3) > 1000 hp

250-1000 hp - 2 Pole 50-1000 hp - others < 50 hp

x s

X"d

X"d

Xlr Xlr

1.2 Xlr neglect

x s

X"d

1.5 X"d

1.5 Xlr 1.5 Xlr 3.0 Xlr neglect

x s

X d

X d

Xlr Xlr

1.67 Xlr (4) 1.67 Xlr

Note: Use Xd" on generator kVA base. If not known, use 15 percent for < 6 pole and 20 percent for > 6 pcle on motor hp = kVA if 0.80 PF, and hp = 0.8 kVA if 1.0 PF. Suggested motor impedances taken from IAS-Transactions, M;rch/April 1982. If not known, use 16.7 percent on motor hp = kVA if < 100 hp; hp = 0.9 kVA if IO00 hp, and hp = 0.95 kVA for all others. Suggested motor impedances taken from [ l ] . Calculation uses 1.2 multiplier, judged to be more appropriate for this size group.

breaker ratings or capabilities, various multiplying factors need to be considered.

If the X / R ratio of the separately derived fault reactance and resistance of the interrupting network is equal to or less than 15, then the calculated symmetrical current can be used directly to verify the symmetrically rated breaker interrupting capability at the prevailing operating voltage, regardless of the breaker operating time (8, 5, 3, or 2 cycles).

This apparent simplicity breaks down if the X / R ratio is greater than 15, a value not uncommon in medium-voltage (2.4-13.8 kV) systems. The empirical nature of the ANSI standards then requires a modification of the calculated interrupting duty, based on the operating speed of the breaker and the particular standard to which the breaker was manufac- tured.

The calculated symmetrical duty also needs to be modified, depending upon the nature of the short-circuit contribution in terms of remote or local contribL tions and the type of breaker in place. To account for the effect of local or remote contributions, the concept of the "no AC decrement" (NACD) factor was introduced. 'This factor identifies the local or remote curves in ANSI (C37.C110-1979 to use for symmetri- cally rated breakers, or C37.5-1979 for total-rated breakers.

The ANSI standards procedu-e for the verification of the "close-and-latch" rating of the breaker is not without com- plexities either. The standards p aescribe the construction of a first-cycle duty network that a ,lows the calculation of the symmetrical duty, which is to be multiplied by 1.6. If this value exceeds the breaker's close-and-latch rating, the stand- ards recognize the application of a multiplication factor less

I184 IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 24, NO. 6. NOVEMBERIDECEMBER 1988

0 r , Y

d

than 1.6, which can be expected only when the fault X / R ratio is much less than 25. This clause simply recognizes that a higher network resistance forces a faster decay of the short- circuit current.

Low-voltage breakers and fuses are assigned a first-cycle symmetrical interrupting current rating because of their extremely fast interrupting time, generally about one cycle or less. For these devices, the interrupting rating must exceed the calculated first-cycle symmetrical duty at t = 0.5 cycle as prescribed by ANSI C37.13-1981. This quasi-simplicity pre- vails when the calculated system fault power factor is greater than 0.15, which corresponds to an X/R ratio of 6.6 (ANSI test value) or less in the case of a low-voltage power circuit breaker, or a molded-case breaker with a symmetrical interrupting rating of 20 kA or higher. For lower rated molded-case breakers or differing short-circuit X/R ratios, a myriad of multiplying factors needs to be considered to modify the symmetrical interrupting rating. The inquisitive reader is referred to the NEMA-AB 1 standard for molded-case break- ers; NEMA standard SG2-1 for power fuses, and ANSI standards C 19.3-1973 through C19.7-1973 for low-voltage controllers and combination starters.

These complexities may become overwhelming to the uninitiated and/or those who only occasionally need be concerned with the proper application of power circuit breakers.

The refinements necessary to bring the ANSI empirical procedures in closer harmony with the reality of the short- circuit phenomenon thus create complexities in the selection and verification of the short-circuit ratings of high-voltage breakers (indoor oiless or outdoor type), low-voltage breakers (power breakers or molded-case breakers), fuses (high- and low-voltage types), and combination starters.

From a user's viewpoint-especially for those who were privileged to use the old and simple ASA C37.5-1953 "total" rated structure-working with the present ANSI short-circuit standard is too laborious and too vexing.

No wonder-and fortunately-digital computer programs are presently heavily relied upon to help assure that the correct procedures are being followed! As a consequence, this development places a great responsibility on the developers of the software packages being offered to perform these studies.

p,_

Two questions now arise: 1) Are such programs rigorously complying with the ANSI standards? and 2) Are the calcu- lated short-circuit current values based on the ANSI-directed empirical procedures indeed accurate, in fact, somewhat conservative?

The answer to the first question should be ascertained by a detailed study of the algorithms used in the available pro- grams; the software developer's brochures should be con- sulted regarding any claims made of being in compliance with ANSI standards. The answer to the second question is more complex, and should be left to those who are experts at short- circuit current complexities and breaker short-circuit perform- ance.

Recognizing that ANSI standards permit two calculation procedures-as noted previously-computer programs can be written in compliance with either one. This paper reports on the results of short-circuit studies, based on both procedures, on the power system as shown in Fig. 1 . The difference between these procedures are identified for the case o f t = 0.5 cycles only (Table V). The study results suggest that the separate R, separate X procedure produces up to 7 percent higher ac-plus-dc short-circuit current magnitudes. Note that the differential in ac components is due only to the use of different computer programs and computers.

In this paper an attempt is made to compare an ANSI- directed empirical short-circuit calculation procedure with the dynamically rigorous short-circuit procedure, which should produce the most accurate results. The ANSI-directed empiri- cal procedure was performed using a short-circuit program offered by a major electrical manufacturer. The dynamically rigorous calculation was performed using the machine net- work transient electrical (MNTIE) program developed by an electrical consulting firm.

DYNAMIC SHORT-CIRCUIT CALCULA I ION PROCEDURk

The availability of powerful computers, capable of execut- ing sophisticated algorithms and storing mass data banks, opened the opportunity for analytical engineers to optimize known techniques to the dynamic simulation of electrical power systems. Even the extreme of complex analysis, as involved in power system stability studies, was gradually reduced to simply inputing the appropriate detailed data of the

ea Network R.L,C elements with nonlineorit ies

eC ( d i f f eqs 1

Machine model 2 Pork 's -%-

l d i f f equations . v q vo;bo,ae __ eq ';j;;;e e b I n d 8 q axes

of f luxes and i n e r t i a )

- e o transf. B o ;;Jt ~

J 4 1 -

i d l a

i q d . g , o i b tronsf.

' 0 iC

DUNIC-JACOBS et ol. : ANSI-BASED AND DYNAMICALLY RIGOROUS SC CURRENT CALCULATION

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22

1185

138.00 13.800 13.800 13.800 13.800 13.800 13.800 2.400 2.400 4.160 4.160 4.160 4.160 0.480 0.480 0.480 0.480 0.480 0.480 0.208 0.208 0.208

TABLE V COMPARISON OF ANSI STANDARD CALCULATION METHOD, COMPLEX ( R + J X ) , AND SEPARATE R AND JX REDUCTIONS:

T = 8.33 MS (112 CYCLE)

6.420 28.547 24.469 25.123 25.981 25.981 26.631 33.883 22.287 47.327 35.211 35.763 25.070 14.086 25.104 22.624 15.825 17.434 3.551

11.103 3.759 4.198

8.410 18.68 46.580 6.10 32.820 6.64 34.720 7.35 32.700 5.98 32.700 5.98 39.060 7.37 50.120 1.69 25.390 4.27 75.620 3.55 57.120 1.97 58.080 1.42 28.670 1.19

0.06 0.28 0.03 2.21 0.30 0.51 0.03 0.24 0.02

3 4 5

ANSI (Complex)

- 5 SYM -

- - - -

5 SYM 5 SYM

5 SYM 5 SYM

LV MCB LV MCB LV MCB LV MCB LV MCB LV MCB

- -

Assym AC

Fact Mult- M-RMS

- 750 MVA -

- - - -

150 MVA Fus1:s

250 MVA 250 MVA

15 1 - r 22 IrA 22 1rA 22 IrA 22 IrA 15 1-A

-

-

-

1.150 1.540 1.270 1.300 1.200 1.200 1.380 1.450 1.110 1.550 1.590 1.600 1.130 1.200 1.300 1.290 1.110 1.100 1.340 1.140 1.290 1.000

AC+DC M-RMS - 7.086

43.903 30.776 32.343 30.854 30.854 36.380 49.286 24.350 73.026 56.014 57.267 28.333 16.850 32.511 29.152 17.220 19.132 4.726

12.602 4.834 4.197 -

6.184 28.468 24.243 24.902 25.660 25.660 26.442 33.835 21.933 47.235 35.174 35.741 24.971 14.077 25.034 22.617 15.483 17.381 3.533

11.100 3.750 4.197

+ ANSI (Separate R & X) ~

A S S p Mult- Fact

1.310 1.632 1.341 1.382 1.259 1.259 1.467 1.479 1.139 1.598 1.622 1.624

-

1.144

_I

M-RMS AC jRC t D C M-RMS 1 Corre ~

12 13

Breaker Ratings @ Bus kV

10 :.l

Type I cli'ss

Interr. M-RMS

- 39.13 -

- - - -

- 41.19 41.19 - ~-

atching A-RMS

- 58 - - - - -

- 58 58 -

Note: Correlation for 2.4 kV to 138 kV = (column 8/column 5) - 1.0. Correlation for 480 V and below = (column 7/column 4) - 1.0.

kc phase B 4

1 ' T h r e e P h a s e F a u l t c u r r e n t a t BUS 2

I I

Fig. 3. Phase currents of fault at bus 2. Note relationship o f phase with maximum offset (A) and other two phases (B and C). Oscillations in current values are result o f motor contributions adding and subtracting from total as machines come into and go out of step with system.

power system and its dynamic components. The short-circuit analysis is only one application of the power system dynamic simulation techniques.

In essence, a dynamic analysis allows the calculation of the changing behavior of interacting rotating machines on a very small time step basis. (A time step of 0.0001 s was used in these simulations .) This procedure offers the opportunity to track the behavior of a multitude of rotating machines as influenced by their varying electrical and mechanical charac- teristics. As a result, short-circuit currents can be determined to a degree of accuracy limited only by the accuracy of the system's static and dynamic elements as well as the assumed process operating conditions.

Generally, most dynamic prclgrams model all synchronous machines by their appropriate subtransient, transient, and synchronous impedances as well as their corresponding time constants. For this particular apdication, field flux linkges are modeled using differential equations so that dc offset and harmonic effects will be accoun:ed for. Fig. 2 shows the block diagram of the machine reprmentation. For the induction machines, the field voltages ar: zero. For induction motors, their initial steady-state operating points are found using the equivalent circuits for the field flux linkages. During dynamic simulations, the motor flux linkages are modeled using differential equations similar to those used to represent synchronous machines.

1186 IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 24. NO. 6, NOVEMBERIDECEMBER 1988

kA 8 0 i/- Phase B

Fig. 4. Phase currents of fault at bus 11.

The optional inclusion of voltage regulators and excitation systems is not likely to affect the 0.5-cycle results or even the 3-cycle results. However, for longer fault clearing times, or in the case of static excitation systems, their inclusion may become significant. The special t = 30 cycles case is included strictly to determine the performance of generator-overcurrent voltage-restraint (or controlled) relays.

Auxiliary plotting programs can be called upon to plot the instantaneous short-circuit current at each fault location, such as shown in Figs. 3 and 4 (see Appendix) for the 13.8 kV, bus no. 2, and the 4.16 kV, bus no. 11. Usually, only the phase that carries the highest fault current in the three phases is of interest. The instantaneous asymmetrical rms and the symmet- rical rms, or the dc value of the short-circuit current at t = 0.5 cycle, t = 3 cycles, or any instant of time can be directly taken from the oscillographic traces. There is no need to modify a calculated symmetrical current value as required by the empirical ANSI calculation procedure.

The dynamic simulations put heavy demand not only on computing resources, but also on accurate data resources. Clearly, the use of approximated input data could produce only approximated short-circuit results. Fortunately, mass computer storage capabilities accept a broad range of data from which the actual machine constants can be closely approximated. Nevertheless, the need for quantity and accu- racy of machine data is much greater. On new or recent installations, accurate and extensive data are generally availa- ble for medium voltage (2.3-13.2 kV) machines. It is unlikely, however, that all competitively priced low-voltage machines are delivered with an extensive list of machine characteristics. The data problem becomes more acute on older systems where design data were never received or where records were lost or destroyed.

In any event, the present-day power engineer is in a much

better position, having access to an extensive database and dynamic simulation programs. The engineer of yesteryear was uncertain and concerned about both his data and the empirical calculation resources available for interpreting his study results.

BASIS FOR COMPARISON OF EMPIRICAL AND DYNAMIC PROCEDURES

To determine the differences between the results of those studies available to the power engineers of yesteryear and today, this paper will subject a representative system (Fig. 1) to the ANSI empirical and a rigorous dynamic calculation procedures. The comparison will be made with two objectives in mind:

1) to determine the correlation based on the total bus fault on each bus (Tables VI-VIII) (in this comparison, the effect of differing fault-source contributions is not traceable); and

2) to determine the correlation based on the individual fault-source contributions to arbitrarily selected buses, operating at 13.8 kV, 4.16 kV (with generation), and 2.4 kV (without generation) (see the Appendix, Figs. 5-23).

The comparison applicable to 2.4- 13.8 kV breakers must be based on the ANSI C37.010 calculated values at

t = 0.5 cycle (8.33 ms) as required by ANSI to verify the close-and-latch capability of these breakers (Table VI); t = 3 cycles (50 ms) as required by ANSI to verify the interrupting rate of these breakers (Table VII); t = 30 cycles (500 ms) generally considered to be a useful benchmark for setting time-overcurrent relays, as applied on buses operating at 2.4-13.8 kV (Table VIII).

The comparison of low-voltage breakers (less than 600 V) must be based on the ANSI C37.13 calculated values at t =

0.5 cycle but differs from the preceding calculation for t = 0.5 cycle because it must include all low-voltage motors, even those less than 50 hp.

To facilitate the comparison, or correlation, column 9 in Tables VI-VI11 presents a correlation factor. Because 2.4- and 13.8-kV breakers are rated in terms of total asymmetrical amperes, it is essential that the correlation factor be defined differently as follows. For 2.4-13.8-kV buses:

column 8 percent correlation factor = 100

For low-voltage buses:

percent correlation factor = 100 (- - 1) . (2) column 4

Note: The low-voltage factor is applicable to t = 0.5 cycle (Table VI) only because these breakers are rated to operate in 0.5 cycles. The correlation factors for I = 3 cycles and t = 30 cycles are therefore irrelevant.

Based on the preceding definitions, a positive correlation factor indicates that the empirically derived values are higher than the dynamically calculated results, suggesting that the

DUNKI-JACOBS el al.: ANSI-BASED AND DYNAMICALLY RIGOROUS SC CURRENT CALCULATION

1 2

F a u l t e BUS

1187

3 4 5

D y n a m i c Progress

TABLE VI

DYNAMIC CALCULATION PROCEDURES: T = 8.33 MS (1/2 CYCLE) COMPARISON OF THREE-PHASE SHORT-CIRCUIT CURRENTS ON PHASE WITH MAXIMUM DC OFFSET USING EMPERICAL AND

C l a s s

II_ - 750 MV4 - - - - - 150 MV4 FUSES

250 MV4 250 MV4

15 kA 22 kA 22 kA 22 kA 22 kA 15 kA

- -

6 7 8 I 9 1 1 0 11 12 13

Interr kA-RM

- 39.13 - -

- - -

- 41.19 41.19 -

14.70 4.38 1.23

-5.78 2.54

-2.24

ANSI ( S e p a r a t e R X ) I I B r e a k e r R a t i n g s @ Bus kV

LV MCB LV MCB LV MCB

C+DC A-RMS

6.393 30.070 23.390 24.009 24.872 24.872 25.490 30.413 20.417 46.580 35.370 36.250 23.891 12.795 21.522 18.288 12.804 15.649

2.676 9.448 3.270 3.984

% C o r r e . N o t e 1

12.07 12.00 31.31 31.13 34.29 34.29 26.43 12.75 16.24

1.93 -2.94 -2.60 26.10

-18.77 13.74

1.49 12.70 10.11

-13.37 -8.85 -2.79 -2.25

A s p Mult- F a c t

1.000 1.096 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.026 1.070 1.070 1.000 N . A . N . A . N . A . N . A . N . A . N . A . N . A . N . A . N . A .

AC kA-RMS

6.393 27.234 23.390 24.009 24.872 24.872 25.490 30.413 20.417 45.420 33.042 33.886 23.891 12.795 21.522 18.288 12.804 15.649

2.676 9.448 3.270 3.984

1 2 3 4 5 6 7 8 9 10 11

138.00 13.800 13.800 13.800 13.800 13.800 13.800

2.400 2.400 4.160 4.160

AC+DC 1 % . /Type kA-RMS C o r r e

AC kA-RMS

- 6.104

23.267 21.431 21.794 22.952 22.952 22.566 29.295 20.764 40.133 28.469 28.318 23.777 17.514 22.326 20.908 13.797 16.702

3.508 11.784

3.657 4.294 -

AC+DC kA-RMS -

8.545 41.213 33.228 34.401 34.479 34.479 37.157 48.012 28.565 70.617 52.093 52.050 34.168 24.260 33.732 31.542 19.095 22.782

5.459 16.408

5.453 5.295

A s W Mult- F a c t

1.310 1.632 1 .341 1.382 1.259 1.259 1.467 1.479 1.139 1.598 1.622 1.624 1.144

_I

-

AC kA-RMS -

6.420 28.547 24.469 25.123 25.981 25.981 26.631 33.883 22.287 47.327 35.211 35.763 25.070 14.086 25.104 22.624 15.825 17.434

3 .551 11.103

3.750 4.198

N o t e 1

5.980 34.018 25.387 26.616 25.730 25.730 29.520 38.039 19.617 58.105 43.626

38.00 3.800 3.800 3.800 3.800 3.800 3.800 2.400 2.400

10 4.160 11 4.160

7.08 - 9.65 15 SYM

58.080 11.59 5 SYM 12 14.1601 43.673

15 23.616 13.202 15.495

4.183 11.417

4.045 3.098

0.480 0.480 0.480 0.480 0.208 0.208 0.208

Note: Correlation for 2.4-138 kV = (column 8/column 5) - 1.0. Correlation for 480 V and below =: (column 7/column 4 ) - 1 .o.

TABLE VI1 COMPARISON OF THREE-PHASE SHORT-CIRCUIT CURRENTS ON PHASE WITH MAXIMUM DC OFFSET L SING EMPERICAL AND

DYNAMIC CALCULATION PROCEDURES: T = 50 MS (3 CYCLES)

6 7 8 1 9 10 11 12 13

ANSI ( S e p a r a t e R h X) B r e a k e r R a t i n g s @ B u s kV

AC kA-RMS

C l a s s Interr.1 Latching ! kA-RMS kA-RMS AC+DC kA-RMS

__I

5.704 26.848 17.812 18.308 18.521 18.521 20.161 26.972 17.564 45.697 36.443 37.221 18.945 15.753 18.922 18.019 11.361 14.211

3.089 10.366

3.354 4.076 -

T y p e

- 5 SYM 5 SYM 5 SYM 5 SYM 5 SYM 5 SYM 5 SVM 5 SYM FUSES 5 SYM 5 sYM 5 SYM 5 SYM

0.594 18.276

2.720 3.571 1.828 1.828 7.284 9.629 0.377

29.791 27.649

- 750 MV4 - - -

- 150 MV4

- 250 MV4 250 MV4 - ~.

5.673 19.763 17.603 17.956 18.431 18.431 18.794 25.194 17.561 34.651 23.740 23.750 18.940 15.747 18.813 17.884 11.342 14.211

3.019 10.353

3.353 4.076 -

41:19 1 41.19 112 14 .160 128.660

Note: Correlation = (column 8/column 5) - 1.0. 480-V values are current benchmarks only.

1188

2

Bus

IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 24, NO. 6, NOVEMBERIDECEMBER 1988

3 4 5

Dynamic Progress

TABLE VI11 COMPARISON OF THREE-PHASE SHORT-CIRCUIT CURRENTS ON PHASE WITH MAXIMUM DC OFFSET USING EMPERICAL AND

kV

138.00 13.800 13.800 13.800 13.800 13.800 13.800 2.400 2.400 4.160 4.160 4.160 4.160 0.480 0.480 0.480 0.480 0.480 0.480 0.208 0.208 0.208

DYNAMIC CALCULATION PROCEDURES: T = 500 MS (30 CYCLES)

DC AC M-INST kA-RMS

0.041 4.654 1.125 11.041 0.050 8.744 0.015 7.238 0.015 7.742 0.015 7.742 0.044 7.579 0.166 23.945 0.032 15.262 0.222 17.664 0.281 16.593 0.331 15.860 0.011 13.520 0.003 15.156 0.089 17.754 0.004 16.614 0.002 10.343 0.013 13.028 0.001 2.830 0.002 9.950 0.000 2.902 0.001 3.863

- a u l t e c u s

1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 7

Note: Correlation = (column B/column 5) - 1.0.

11038 A RES

0 5 0 6 A RMS

AC+DC kA-RMS

4.654 11.111

7.238 7.742 7.742 7.579

23.946 15.262 17.665 16.596 15.864 13.529 15.156 17.754 16.614 10.343 13.028 2.830 9.950 2.902 3.863

__.

a. 744

Fig. 5. Maximum phase current for fault at bus 2. Current values at 3 cycles and 30 cycles are in symmetrical amperes rms.

6 7 8

ANSI

A S P Mult-

0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000

AC AC+DC kA-RMS kA-RMS

6.203 20.672 18.231 18.631 19.286 19.268 19.626 23.831 16.797 35.556 24.628 24.628 19.072 12.590 18.152 18.152 10.881 13.782 2.667 9.400 3.265 3.977

6.203 20.672 18.231 18.631 19.286 19.268 19.626 23.831 16.797 35.556 24.628 24.628 19.072 12.590 18.152 18.152 10.881 13.172 2.667 9.400 3.264 3.977

9

% Corre. Note 1

33.28 86.05 108.49 157.40 149.10 148.87 158.95 -0.48 10.05

101.27 48.39 55.24 40.97

-16.93 2.24 9.25 5.20 1.10

-5.76 -5.52 12.47 2.95

Contribution From Gen $ 1 to Fault at Bus 2

5582 A RETS

12 1 I .I 24

1/2 Cycle

J 2 3 3 6 2 :.5 Sec.

Fig. 6. Fault current contribution from generator I . High X / R ratio of 73 accounts for large dc offset.

DUNKI-JACOBS el al.: ANSI-BASED AND DYNAMICALLY RIGOROUS SC CURRENT CALCULATION

- I,

- 10

- c 0.5 Seconds-

1189

v kA I 2829 A 1/2Cycle

Contribution from 6000 HP Syn. Motor to Fault at BUS 2

0.5 sec.

Fig. 8. Fault current contribution from 6000-hp synchronous motor. Note that there are only 27 cycles of current within 0.5 s because of slowdown of motor.

Contributl Jn from 5000 FIP Inl. Motor to Fault at BUS 2

Fig. 9. Fault current contribution f r tm 5000-hp induction motor. Note lengthening of cycle time as motor slows down.

Contribution from 2.4 kV Bus to Fault at BUS 2

+ O . 4

0.5 Sec.

I I

Fig. 10. Fault current contribution frcm bus 5 . Oscillations occur as result of motor si Jwdown.

1190 IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 24, NO. 6, NOVEMBERIDECEMBER 1988

I Y l/2 Cycle 10372 A

Contribution from Bus 7 to Fault at BUS 2 1

30 506- A

Contribution From BUS 5 or Bus 6 to Fault at BUS 8 I

I I I I

Fig. 1 1 . Fault current contribution from bus 7. Oscillations are caused by Fig. 13. Fault current contribution from bus 5 . Contribution from bus 6 is out-of-step contribution from machins on buses 1 1 and 12. same.

3 cycle 25174 A RMS

30 cycle

Fault Current at BUS 8

l/2 cycle '1'76079 A I 0.5 Sec. A

Contribution From Bus 9 to Fault at Bus 8

3 Cycle 392 A REIS 0.5 I

I I

Fig. 14. Fault current contribution from bus 9, which includes one induction Fig. 12. Maximum phase current for fault at bus 8. Current values at 3

cycles and 30 cycles are in symmetrical amperes rms. motor and two synchronous motors. Contribution from one synchronous motor is represented on this curve.

DUNKI-JACOBS et al. : ANSI-BASED AND DYNAMICALLY RIGOROUS SC CURRENT CALCULATION 1191

3 C y c l e 1 3 6 5 A PJlS

C o n t r i b u t i o n From 6 P o l e 200 HP Syn. Plotor t o F a u l t a t B U S 8

1/2 C y c l e 5218 A

0 . 5 S e c . h

Fig. 15. Fault current contribution from 2000-hp six-pole synchronous motor. Note that there are only 27 cycles in 0.5 s.

423 A IFis Contrlbution From 6 Pole 1000 HP Ind. m t o r to Fault a t BUS 8

U 0 .5 S e c .

1/2 Cycle 2173 A

Fig. 16. Fault current contribution from 1000-hp six-pole induction motor. Notice slowdown of machine in lengthening of cycle time.

Contrlbution From 2 Pole

y 0.5 Sec.

1/2 Cycle 2130 A

Fig. 17. Fault current contribution from 1000-hp two-pole induction motor.

3740 A RMS

F a u l t C u r r e n t a t BUS 11

0 . 5 S e c . -b

Fig. 18. Maximum phase current for fault at bus 11. Current values at 3 cycles and 30 cycles are in symmetrical amperes rms.

-1/2 q c l e 45282 A

C o n t r i b u t i o n rrom n u s 1 0 t o F a u l t a t Bus 11 b

Fig. 19. Fault current cmtribution from bus 10.

t C o n t r i t u t l o n From Gen # 2 t o F a u l t a t

0 . 5 s e c . - ~~

Fig. 20. Fault current contribution fr4m generator 2. Note that dc offset is less for this generator as X / R ratio is 40.

1192 IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 24, NO. 6, NOVEMBERIDECEMBER 1988

kA

c

C o n t r i b u t i o n From 200 H P Syn Motor t O F a u l t a t BUS 11

1/2 3515 A

0 . 5 set.-,

Fig. 21. Fault current contribution from 1000-hp four-pole synchronous motor. Note that only 27 cycles occur in 0.5 s because of slowdown of motor.

30 C y c l e I O A R M S -

C o n t r i b u t i o n From T h r e e 1 0 0 0 EP I n d . Motors t o F a u l t a t BUS 11

1/2 C y c l e 3660 A

0 . 5 Sec.

Fig. 22. Fault current contribution from 1000-hp six-pole induction motor. Notice slowdown of motors.

1910 A

C o n t r i b u t i o n From

B u s 11 Bus 1 3 t o F a u l t a t

c I 0 . 5 Sec. c

Fault current contribution from bus 13 includes contributions from

- Fig. 23.

induction and synchronous motors at 480-V buses.

ANSI objective of yielding a conservative estimate of short- circuit current has been reached. A negative correlation factor obviously suggests the opposite.

CORRELATION OF EMPIRICAL AND DYNAMIC PROCEDURES

It should be noted that the following discussion pertains to the correlation of an empirical ANSI-directed procedure and a dynamic simulation procedure. Although both computations are performed using computer programs considered to be reliable, it should not be inferred that the dynamic study output would be absolutely accurate. Thus the result comparison is pre: snted in relative terms, recognizing that a dynamic analysis is potentially more accurate than an empirical analysis.

There is a wealth of data to be evaluated, especially by those skilled and particularly interested in the intricacies of the short-circuit phenomenon. These readers are invited to extend their evaluations beyond those presented by the authors.

A comparison of the half-cycle current calculations in Table VI indicates that for all in-plant buses, the correlation factors

DUNKI-JACOBS et a/.: ANSI-BASED AND DYNAMICALLY RIGOROUS SC CURRENT CALCULATION 1193

for total fault currents are

between -5.2 and 13.0 percent for 13.8-kV buses; between - 16.1 and 11.6 percent for 2.4- and 4.16-kV

between - 19.6 and 14.7 percent for 480- and 208-V

The correlation factors of between - 20 and 15 percent can be considered well within the accuracy requirements of most studies.

A comparison of the three-cycle current print-out data for in-plant buses suggests that the correlation factors for the total fault currents shown in Table VI1 are

buses;

buses.

between 12.0 and 34.3 percent for 13.8-kV buses; between -2.9 and 26.1 percent for 2.4- and 4.16-kV

between - 18.8 and 13.7 percent for 480- and 208-V buses;

buses.

While it is not unexpected that for longer calculation times the discrepancies between the respective output data may increase, the magnitude of these factors appears to assume considerable proportions.

A comparison of the 30-cycle relay current calculations in Table VI11 reveals significant divergence at medium-voltage levels (up to 159 percent). The reverse is true at low voltage levels ( - 16.9 to 12.5 percent).

It is well-known that the accuracy of any calculation which models a response to an event decreases as the timeframe of the calculation increases. However, such radical divergence between two methods should attract attention. The difference may be largely attributed to the fact that the empirical procedure utilizes transient parameters for 30-cycle relaying current calculations while the dynamic method calculates the motor and generator impedances as a function of time. These findings strongly suggest that, for ANSI-directed calculations, generator short-circuit decrement curves must be applied when calculating 30-cycle relaying current for faults closed to the generators.

CONCLUSION

An empirical short-circuit current study of a representative industrial system was made in accordance with ANSI Stand- ards. A second, comparable study was made using a dynami- cally rigorous short-circuit program. Both programs are commercially accessible or available from reputable suppliers. As anticipated, the ANSI-directed calculations yield high- voltage short-circuit current duty levels in excess of those produced by the dynamic analysis.

At medium-voltage levels (2.4- 13.8 kV), the correlation between these values is particularly favorable at t = 0.5 cycle, where the maximum deviation is less than 17 percent. At t = 3 cycles, the deviation reaches a maximum of about 34 percent. This trend is reversed at low-voltage levels (208-480 V), in which the maximum deviation starts out at 20 percent at t = 0.5 cycle, reduces to 19 percent at t = 3 cycles, and then to 17 percent at t = 30 cycles.

Where generators are operating at medium-voltage buses,

the generally accepted practice of constructing a generator short-circuit decrement curve, inl:luding the effect of voltage regulators, should be relied upon to determine the 30-cycle fault currents.

In those cases where the c;ilculated short-circuit duty approaches or slightly exceeds 1 he specific breaker rating, relief from the short-circuit bottlcneck appears to be possible by resorting to a dynamic analysis. ANSI Standard C37.010- 1979, paragraph 5.1, permits the use of more complex calculations, which are acknowledged to yield improved accuracy.

This paper's discussion is based solely on two programs, selected for their availability and reputation. It is recognized that a number of equally outstanc ing programs-both empiri- cal and dynamic-may be commercially available. Vendors of these programs could test the relative accuracy of their programs by conducting simil: r studies of the identical representative power system and utilizing the extensive input data given in this paper.

The sequel to this paper would be one comparing the ANSI- directed short-circuit study with the German VDE and the IEC standards. These latter standards were in a state of imminent major revisions at the time this paper was in preparation.

The continuing review and research on the analytical procedures produced a further optimization, which resulted in somewhat higher short-circuit niagnitudes appearing in the tables of this paper as compared o those listed in the original conference paper. Also, recentl:! developed information on capacitor short-circuit contributi m s has been added to this version.

APPENLNIX

This Appendix lists the traces of the short-circuit currents of selected buses and current contributions of branches connected to the 13.8-kV bus 2, 4.16-kV biis 11, and the 2.4-kV bus 8. The current values for the 0 . 5 , 3-, and 30-cycle times are listed. The 0.5-cycle values are the peak values of currents while the 3- and 30-cycle values are rms values. Comments are included in the captions of Figs. 3-23 to explain any unusual characteristics shown on the traces.

Contribution of Capacitor Banks to Short-circuit Duty

Questions concerning the contribution of power-factor improvement capacitors to a faulted bus sometimes arise. An example of the very short disctarge time of a capacitor is shown here. The equation for a capacitor discharge current is given as

where RC is the time constant of the circuit, or the time to reach 0.368 of the initial value cf current. As an example of such time, if a IO-Mvar capacitor bank is connected to a 13.8- kV bus, and there is a fault 100 R away through a 500-kcmil cable, then the time constant is

C= 140 pF R = 0.006 Q RC= 0.84 ps.

1194 IEEE TRANSACTIONS

The inductance of the circuit will add some small amount of time to the capacitor discharge, but the time constants are so small that the capacitor will be discharged long before the first half-cycle peaks. The same analysis is applicable for capaci- tors at motor terminals.

ACKNOWLEDGMENT

The authors gratefully acknowledge assistance provided by W. C. Huening, F. J. Shields, and C. St. Pierre of General

ON INDUSTRY APPLICATIONS, VOL. 24, NO. 6, NOVEMBERIDECEMBER 1988

mission svstems and sut

Baldwin P. Lam (S’75-M’75) received the B.S. and M.Eng. degrees in electric power engineering from Rensselaer Polytechnic Institute, Troy, NY, in June 1975.

He has been with Power Technologies, Inc., in Schenectady, NY, since 1975, and is presently working as a Senior Engineer in the Utility System Performance Unit of the Consulting Services De- partment. His concentration has been in the analyses of power system planning and operational prob- lems. He has conducted analytical studies of trans-

istations for U.S. and foreign utilities and industries. Electric Company, Schenectady, NY, as well as by C. E. Davis of Electrical Systems Analysis, Inc., Oregon City, OR.

REFERENCES

He has i s 0 developed computer programs for shErt-term load forecasting, Optimal thermal-unit commitment, hydrothermal power coordination, trans- mission-system expansion planning, transmission-system reliability analysis, and optimal reactive power control. He has coauthored a number of technical papers and articles on power system economic operation and reliability.

[ l] W. C. Huening, Jr., “Calculating short-circuit currents with contribu- Mr. Lam is a member Of the IEEE Power Engineering Society. tions from induction motors,” IEEE Trum. Ind. Appl., vol. IA-18, pp. 85-92, MarJApr. 1982.

J. R. Dunki-Jacobs (M’56-SM’58-F’82) joined the General Electric Company in 1954. In his 30- year career as a Power Systems Engineer in Schenectady, NY, he gained broad experience in the design and implementation of extensive indus- trial power systems. He developed a nationally recognized expertise in the areas of conceptual design, stability, grounding, and system protection. Upon his retirement in 1984, he began his second career by establishing Industrial Power Systems, Inc., specializing as a Consultant and Lecturer on

industrial power system design. In 1985 he moved his operations from Schenectady to Beaverton, OR.

Mr. Dunki-Jacobs has been active in the IEEE by authoring and coauthoring papers for professional societies and journals. He received a number of IEEE paper awards, among them the Best Paper Award from the IEEE Industrial Applications Society in 1978.

Ray P. Stratford (M’51-SM’58-F’82) joined the general electric (GE) Company after graduation from Stanford University, Palo Alto, CA, in 1950. After assignments in several product departments, he joined Industrial Sales in 1954 as an Application Engineer, specializing in industrial power systems. In 1955 he worked in electrochemical applications and was associated with the introduction of semi- conductor rectifiers to this industry. In 1963, he joined the Metal Industry Engineering Section and acted a Project Manager for several large ferrous

and nonferrous mill projects. In 1974 he joined the Industrial Power Systems Engineering Operation at General Electric. In 1985 he retired from GE and joined Power Technologies, Incorporated, as a Senior Consultant, where he consults and does studies for industrial clients.

Mr. Stratford has been active in the IEEE and at present is co-chairing the task force on the revision of IEEE-5 19 harmonic standard. He has written over 30 technical papers and received the IEEE-IAS Best Paper Award in 1981. He is a Registered Professional Engineer in the State of New York.