Analysis of Factors Influencing Shield Wire Fault Current Requirements on Electric Power Transmission Systems

572

IEEE Transactions on Power Apparatus and Systems, Vol. PAS-102, No. 3, March 1983

MINIMUM SHTFIT WIRE SIZE - FAULT CURRENT CONSIDERATIONS

S. R. LanIert, Senior Menber, IEEE Power Technologies, Inc. Schenectady, N. Y.

Abstract - This paper presents results showing the effect of various system parameters on shield wire fault current requirements. The effect of tower footing resistances, generator excitation systems, dc offsets and fault location are shown. Current splitting between shield wires in one span is examined, and shield wire capabilities are presented.

1. 61 km 16.1 km V.-

1

160 km

Station A

Station B

INIRDUCTION

Fig. 1. Example Systel,m

When ground faults occur on a system, the 60 Hz fault current returns fram the fault point via SWs (shield wires) as well as earth. Current distribution between the SWs and earth depends on the tranasission line characteristics as well as the TFRs (tower footing resistances) adjacent to the fault and along the line. The fault current is a function of system impedances, generator excitation characteristics, fault location, TFRs and the X/R ratio at the fault point.

SW currents are highest in the spans adjacent to the fault location. In subsequent spans, SW currents decrease as one moves away fram the fault location because more and more current is shunted through towers-to-ground. Therefore, unless otherwise noted, the SW currents presented in this analysis are the currents in the first span adjacent- to the faulted tower. Although the SW and fault currents are phasors, it is the phasor magnitude which is important, and only the magnitudes are reported.

When fault current levels are low, minimum SW size is usually dictated by lightning considerations rather than 60 Hz fault current. However, when fault levels exceed about 20 kA, SW current can exceed current carrying capabilities. When this occurs, larger conductor sizes are necessary to prevent SW damage and possible burndown.

EFFECT OF TFR AND FAULT LOCATION ON SW CURRENT

The purpose of this paper is to analyze the effect of various system parameters on SW current magnitudes, and to present information which can be used to more accurately predict the expected SW currents. This information can then be used to select SWs capable of withstanding the current during faults.

SW current, like the fault current, varies as a function of the fault location along the line (Figure 2). The effect of TFR varies depending on whether the fault is located close to or remote from the station. However, as will be discussed, care must be taken to carefully consider possible TFR combinations around the fault location before making a judgment as to their effect on SW current. I

I

I

SW Capability

CALCULATION PROCEDURE

Size

To determine the effect of various parameters on SW current, a mathematical analysis was used to simulate the system. Using an ABCD coefficients approach, the phase conductors, shield wires, earth effects, sources, station grounds and tower footing resistances as well as faults were all represented.

For the examples a 500 kV line was investigated (Appendix B). Ihe single line diagram indicating the line, equivalent system and fault locations is shown on Figure 1. The equivalent at Station A represents a strong generating station while Station B reflects the remainder of the system.

Faults were assumed to be single line-to-ground and to occur at a tower. While mid-span flashovers are possible, they are extremely rare and were not considered.

82 SM 341-6 A paper recommended and approved by the IEEE Transmission and Distribution Committee of the

IEEE Power Engineering Society for presentation at the IEEE PES 1982 Summer Meeting, San Francisco, California, July 18-23, 1982. Manuscript submitted February 27, 1982; made available for printing April 14, 1982.

4-J

- A

0)

-B

SI

-C =I

80 km

Station A

Fig. 2.

Shield Wire Requirement

Faults Close to

a

Station B

vs.

capability

Station

Figure 3 shows the currents around a faulted tower located 1.61 km froan Station A. Similar results would be obtained for a fault at the first tower away frcan the station. Twenty ohm TFRs and 7#8 AW (Alumoweld) SWs were simulated. The currents are given in percent on a total fault current basis. As shown, each SW on the station side carries about 46 percent of the total fault current. As the TFR increases in magnitude, more fault current will return through the SWs than through the tower and earth. Figure 4 shows the effect of TFR on SW currents for three SW types - 3/8 inch EHS, 7#8 AW

0018-9510/83/0002-0572$01.00 ( 1983 IEEE

573

46% C

Faults Remote Fram Station

4%

As the fault point moves out along the line and away frcm the station, SW current tends to split more evenly between the station and remote side of the faulted tower. Figure 5 illustrates this effect for 7#8 AW SWs and 20 ohm TFRs. The conditions are identical to those shown on Figure 3 except that the fault is now located 16.1 km frcm the station. Similar results would be obtained for faults located in the middle of the line. Comparing the results for the close-in fault (1.61 km) and the remote fault (16.1 km) shows that the highest SW current, as a percent of total fault current, is significantly reduced - frcm 46 percent to 26 percent. These results seem to imply that a significant reduction in SW current carrying requirements for SWs out on the line is possible.

*-

46%

-88%

4%

>S

12%

n,g. ut

Fig. 3. Fault 1.6 km from Station A

and Minorca ACSR. The values indicated are the highest current which occurred in any SW as a percent of total fault current. The fault was located 1.61 km fran the station. The results illustrated on Figure 3 are included on Figure 4. On Figure 3 the highest SW current is 46 percent of the total fault current. This 46 percent value is plotted on the 7#8 AW SW curve opposite the 20 ohm TFR value.

However, for the preceding cases the TFR was assumed to be a uniform 20 ohms all along the line. Now consider the case where all the TFRs are 20 ohms except for one or two towers having low TFRs. For example, if two towers having 3 ohm TFRs immediately preceded the faulted tower on the station side, the SW currents would be as shown on Figure 6. 26%

20% 26%

50

81%

20%

hE

19%

Mirnorca ACSR 40

14

0 CL 05

20

Fig. 5. Fault 16.1 km from Station A 1

10

100

Tower Footing Resistance (0)

Fig. 4.

Shield Wire Current as a Function of TFR

The calculations show that the highest SW current for this condition has now risen to 37 percent of the total fault current. This is not a trivial case because it is possible for there to be a few low TFRs out along a line which predominately consists of high TFRs. As the ratio between the high and low TFRs increases, the SW current on the span between the faulted tower and the the towers having low TFRs will increase.

The results shown on Figure 3 and 4 illustrate three important points. 1) For faults close to a station, most of the SW current is carried in the SWs on the station side of the fault. 2) For ACSR and AW the shield wire current is higher than for EHS. This effect is more pronounced with lower TFRs. 3) For TFRs higher than about 15 to 20 ohms, most of the fault current is carried in the SWs.

The preceding results indicate the desirability of lowering high TFRs close to the station. Lowering the TFR fram 20 ohms to 3 ohms, for example, reduces the 3/8 inch EHS SW requirements by about 30 percent. This could well make a difference in SW size requirements near a

station.

Conversely, what are the SW currents when the TFRs are low? Figure 7 illustrates this condition for 3 ohm TFRs. As before the fault is at 16.1 km and 7#8 AW SWs were simulated. The highest SW current is now 24 percent of the fault current as opposed to 34 percent for the same configuration when the fault was 1.61 km away fram the station (see Figure 4). Would the last case (low TFRs along the line) be influenced by a few towers having high TFRs?

No, the SW current would have to travel a few more spans before being shunted by low TFRs, but the highest current in the spans adjacent to the faulted tower would be essentially no different than that shown in Figure 7.

574 11%

37%

37%

81%

result in the SW current exceeding its capability and a resultant SW burndown. But because there are so few cases of SW failure attributable to this effect, there is little reason to believe that large resistances differences are cormmon. However, because there could undoubtedly be other effects which would contribute to a other than a 50/50 split, it seems prudent to use a 55/45 split to account for any other unknown effects.

11%

The current carrying capability of a SW is influenced by the magnitude and duration of the SW current. The preceding sections have discussed what portion of the fault current can be expected to be carried by the SW. This section discusses the effect of various parameters on the fault current magnitude and duration.

4%

Fig. 6.

Faulted Tower (Higher TFR) Preceded by Towers Having Low TIs

The results indicate that some benefit can be derived from the more even SW current split between With spans immediately adjacent to the faulted tower. low TFRs along the line the highest SW current is on the order of 25 to 30 percent. With high TFRs along the line, coupled with the possibility of an occasional low TFR scattered along the line, the highest SW current could be expected to be on the order of 35 to 45 percent of the total fault current.

24%

81%

20%

%%½S

19%

Tower

of the fault the effect of fault clearing it dictates the Additionally,

Fault Clearing Time EHV systems the fault clearing time can range few cycles, for primary clearing time, to as 15 to 20 cycles, for backup clearing time. It considered prudent to base the required SW

On

fram

a much as

is capability

on

the backup clearing time.

(Low TFR) Preceded by

Having Low TFR Is

Subsequent to fault occurrence, generator reactance changes with time. In the first few cycles the generator subtransient following the fault, reactance, X"d, accurately reflects the generator reactance. After a number of cycles have passed (dependent on the machine time constant), the transient reactance, X'd, can be used to represent the generator. Historically, the SW has been rated for backup clearing times and the X'd value has been used to determine the fault current. There is some error in this approach because the effective current applied to the SW should reflect the higher fault current present during the first few cycles. However, if the machine time constant is low the error is small. Fast Excitation Systems

12%

Faulted

Ihe fault current is a function clearing time, system reactance and generation excitation. Of these the time is the most significant because characteristic effect of the other two. any dc offset is also important.

System Reactance

20% 24%

Fig. 7.

FAULT CURRENTS

19%

\

Towers

CURRENT SPLIT BEIWEEN SWS IN A SPAN

The SW currents shown on the preceding figures indicate that the current being carried on one span essentially splits evenly between the two SWs. The tower resistances between the faulted conductor and the two SWs were set equal, while the tower gecmetry was accurately represented (see Appendix B). Therefore, the results indicate that tower geonetry and geanetric nonsymetry due to fault location do not influence the current split in the two SWs.

What would happen, however, if the resistances between the SWs and the faulted phase were substantially different? In the extreme case, one SW could be well isolated fran the tower (perhaps due to corrosion). In that event the remaining SW would have to carry all the current. This event would likely

The increasing use of fast generation excitation systems results in additional complications. With older excitation systems the fault current did indeed track the change in generator reactance. This was true because although the machine reactance changed with time, the voltage behind the generator reactance did not change very rapidly. With fast exciters, however, the generator voltage does increase rather rapidly with time and, in fact, does contribute appreciably to the effective fault current. This effect is illustrated in Figure 8. Figure 8 shows the results of a dynamic simulation Two fault current curves are following a fault. shown - the lower one indicates the fault current when fast exciters are not usedr while the upper curve shows the influence of fast exciters on the fault current. The

results

indicate

that

the

fast

exciters

do

significantly increase the fault current and hence the current flowing in the SWs. The

proper

approach

for

determining the effective

SW current would be to run dynamic simulations of the system following a fault and accurately define the

575 1.8

1.7

I rms -

Fast Exciters

Fault Initiation

/

1.6

-

K

I

ac, rms

1.5.

---1-.onventional Exciters

K 1. 4-

_

_

_

1.3

Time

30 Cycles

1.0_2

Fig. 8. Effect of Fast Exciters

fault current as a function of time. However, based on I2R analysis of the fault current, it appears reasonable, as an approximation, to simply calculate the fault current using X'd to represent the generator reactances. This approximation should result in an effective current relatively close to the actual value.

100

10 Time (cycles)

1

Fig. 9.

Effect of DC on SW Current

an

DC Current Contribution

Fault currents can contain an appreciable amount of dc offset. The magnitude of the offset is most likely to be high near generating stations, however, with very low resistance SWs the *effect could be The appreciable for quite a distance along the line. dc contribution is a function of the X/R ratio as well as the point on the voltage wave at which the fault was initiated.

Previous results indicated that for faults near a station most of the 60 Hz fault current flows in the SWs. Although not rigorously analyzed, based' on resistance.considerations around the fault and station, it also seems reasonable to assume that most of the dc will' also flow in the SWs. Thberefore, the curves shown on Figure 9 indicate the effective SW current (current applied to SW heating) as a function of X/R ratio and fault duration. The derivation for the data presented may be found in Appendix.A. It should be noted that the data-is based on the assumption that the fault was initiated at, the worst'possible time - the time which results in the largest dc offset. The results indicate,' for example,' that for a fault clearing time of 10 cycles and an X/R of 20, the ac, rms fault current should be multiplied by 1.15 to determine the heating -current effectively applied to the SWs. This current is actually the true rms current reflecting..the SW heating contribution frdm the ac and the dc' currents.

Summary It is suggested that SW requirements be determined based on backup clearing times. If fast exciters are not used in the system, then the X'd value may be used to determine the fault current, although the higher fault current during the first few cycles should be taken into' account. If fast exciters are used, then accurate dynamic simulations should be used to determine the fault current. Alternatively, the X"d reactance value could be used to approximate the results. It is further suggested that the effect of dc offset be considered for faults near stations.

SW CURRENT CARRYING CAPABILITY

As current flows through SWs, the I2R losses cause the SW material to heat. Above a certain temperature, dependent on the material, the conductor will sustain damage and/or lose mechanical strength.'. Therefore, the purpose of capability calculations is to determine for a given current the maximum fault duration beyond which the conductor will be damaged or lose mechanical capability.

Specifically, SW capability is a function of a number of material characteristics including resistivity, mass,' specific heat,¢ density and temperature It is also a function of coefficient of resistance. the initial and final operating temperatures. Ihe characteristic equation describing' SW current carrying capability isl: I

=

{JA2Ds/pct l/t

ln[l +

O

(0

0.)]} /2

(1)

where

I is the rms current in Amps P is the resistivity in ohm-cm J is a constant - 4.185 Joules/calorie A is the conductor area in cm2 s is the specific heat in calories/gmvOC D is the density in gn/cc is the temperature coeff. of resistance in /PC # is the final temperature OC

00 is the initial temperature OC

1) 2) 3) 4)

In particular the assumptions are: The conductor is infinitely long.' The amount of radiated heat is negligible. The specific heat is constant over the temperature range. The

resistivity is

a

function of temperature.

To reflect the effect -of specific heat as a function of temperature would complicate the equation. However, it 'is known that if specific heat as a

576

function of temperature were included, the conductor would have a slightly higher capability than that predicted by Equation 1. Therefore, the predicted capabilities inherently contain some conservatism.

Equation 1 has been evaluated for selected AW, EHS and ACSR SW types, and the'results are shown on Figure 10. Table 1 suggests parameters to be used' for evaluating the expression, and these values were used to generate data presented on Figure 10. TABLE 1

A~W

8.53x10-6 15 .9xlO-6 0.0036 0.0035 400. 400. 40. 40. 6.66 7.86 0.118 0.118

P (ohm-cm) a (/OC)

0 (OC) go (OC) D (gm/cc) s (cal/grrC)

40

a'

L

.

- -

6

T = _

--

1o

1 1

l

l

0.01

_77

REFERENCES

1. Kesselring, The Elements of Switchgear Design, 1932. 2. L. F. Roehmann and E. Hazan, "Short-Time Annealing Characteristics of Electrical Conductors,". IEEE Transactions on Power Apparatus and Systems, Vol. PAS-69, pp. 1061-1068, Dec, 1963. 3. "Current Carrying Capacity of Skywires," Ontario Hydro Research Quarterly, Fourth Quarter, 1965.

~~IZ

For the circuit shown on Figure lA, can be described by: L

i(t) a VV2 .1..0

10

Fast generator excitation systems, as well as dc contributions, can substantially increase SW currents and requi red capability.

APPENDIX A EFFECr OF DC COMPONENT

l-1

0.1 5

L~~~-4

_i:S

--

Assuming a 55/45 percent split between the two SW currents in one span is prudent.

A

t

1( A_ _ 1141-

a'

2.87xlO-6 0.0040 200. 40. 2.70 0.210

AST_

2- CGuinea

U4

ACSR

EHS

For faults remote fran a station, the highest SW current is on the order of 40 percent of the total even for the more critical cases. Required SW capabilities out along the line may be significantly reduced fran that necessary near a station. Thus, it may be econamical to utilize two different SW sizes on one line.

15 20

seconds cycles

[sin (t + $) - sin(/)eat]

where a =

VIV

Fault Duration

Fig. 10.

SW Fault Current Capability

The parameters presented in Table 1 are based on experimental data presented in Reference 3 and on conductor manufacturer's literature. The EHS data is essentially that normally used for steel. The data suggested for AW represents -parameters reflecting a combination of aluminum and steel. The ACSR data is based on-aluminum since the steel core apparently plays little part in the heating phenomenon.

For ENS SWs a temperature rise of 3600C over a 400C ambient was chosen because above about 4000C the conductor galvanization is subject to melting. Based work presented in Reference '3, on the maximum temperature allowed for AW and ACSR was set at 4000C and 2000C. These values were selected' because the conductors begin to lose significant strength when heated above the selected levels.

Z

R + jwL

+i

Fiqure 1A The rms

current is:

value (the effective heating value) of the

irms - [ Vt i2 dt11/2 When , = f71/2 the fully offset dc represented and the integral result is:

'rms

ac,rms

2

Close to a station most of the fault current is carried in the SW's on the station side span. With low TFR's (3 ohms), each SW carries about 30-40 percent of the total fault current. With higher TFR's (20-100 ohms), each SW carries about 45-48 percent.

=

Vm sin ut

e2 -t

CONCLUSIONS

the current

condition

rut + Tr f2w -4

-eat

(

sin

is

2 t

a cost

wt)

=I k ac,rms The value "k" has been evaluated for a and T, and the results are given in

the paper.

various values of the main body of

577 APPENDIX B SYS[EM DATA The source impedances used for the analysis were:

Station A Station B

0.4 Percent infinite bus

For the transmission line, individual towers and transmission line spans were represented in the vicinity of the fault. Tle number of represented towers varied depending on the TFR. -For low TERs only towers one to two.miles away fram the- fault location were rigorously simulated.i With high TFRs many more towers had to be represented in order to obtain .a satisfactory representation. The number of towers actually used was determined by increasing the number represented until further additions-had no effect on the SW current adjacent to the faulted tower. For the transnission each conductor, phase and ground, were individually represented 'in a span. A typical 500 kV, horizontal tower configuration was used which. consisting of three Cardinal ACSR conductors per phase (457 inm bundle, spacing). At the tower the. phase spacing-was 9.76m, and the pbase conductor height. was 27.9m. Shield wires were located at a height of 37.4m with a spacing of -21.3m. .Tfhel earth resistivity represented was 100 ohm-i. For 3/8 ENS SW's, the characteristic series and shunt matrices are shown on Table 1B. ' The individual- conductors are numbered, to correspond with the-numbering shown on Figure lB. SW 5



RTFR

Figure 1B Tower and Fault Representation

CONDUCTOR

CDNDUCIOR

-jO .25838

1

-jO .06034 - jO .25837

2

-jO.03240 -jO.06034 -jO.25838

3

-jO.05750 -jO.05653 -jO.04236 -jO.45184

4

-jO.04236 -jO.05653 -jO.05750 -jO.08282 -jO.45184

5

578 Discussions Donald T. Jones (Copperweld Bimetallics Group, Pittsburgh, PA): The capability of a shield wire to carry fault currents safely is becoming increasingly important as fault current magnitudes increase. The author, therefore, is to be commended for undertaking his study and sharing his findings in this paper. The values of fault current vs. fault duration for EHS steel obtained by the use of equation (I) in the paper do not, in the opinion of the discusser, seem to agree with the values shown in Figure 10. It appears that the calculated values are appreciably lower than Figure 10 indicates. The author's comments regarding this apparent difference between equation (1) values and Figure 10 values for steel will be appreciated. Also, reference (3) of this paper provides fault current data resulting from tests performed on steel, aluminum-clad steel and ACSR shield wires. The test values for the aluminum-clad steel agree fairly closely with those values shown in Figure 10 of the paper. However, the values provided for the EHS steel in reference (3) are significantly lower than those shown in Figure 10. This difference would seem to confirm the discrepancy between the values calculated by equation (1) and the plotted values of Figure 10. The author's comments would also be welcomed on this point. Manuscript received August 12, 1982.

G. B. Niles (Baltimore Gas and Electric Company, Baltimore, MD): The author has done. a fine job of relating several parameters to consider for shield wire size and fault current aspects. My first question deals with Figure 3 of the paper and the illustration of 0% fault current going to ground through the structure. It is true that small amounts of fault current do go to ground especially near stations, but in making a similar computation as the author did and trying to use all of his parameters as possible, then the 0% current to the structure base was not realized. The input and results are given in Table A and this shows that the minimum percentage going into the structure for a 20 ohm tower is about 41/2%. The computer program used was part of an EPRI research program.1 There was also disagreement with percent flowing to generating station A vs. flowing to station B via the overhead shield wires. Using Rudenberg's method2 then there also is shown to be a small percentage going to the structure base and not 0% as indicated by the author in Figure 3. The case of Figure 5 was also duplicated but the results are very similar to the author's results. In Figure 8 there is no value given for the fault current values. Is this a general case that is true in all situations or was this case particular for only one system? Would the author elaborate on the quantitative aspect of significant strength loss when shield wires are heated above 2000 or 400° (ACSR, AW). The reason for this is that many shield wires are never subjected to their ultimate strength in operation and many times can afford to have some loss of strength incorporated into the design. This loss of strength can be as much as 30/40% depending upon the ultimate strength of the conductor and the original design. Would the author comment on his coice of 40°C ambient temperature for the shield wires as this appears unrealistic for most considerations. In the author's Appendix B dealing with system data he lists the RI and R2 terms from .1 to 1 ohms in connection with low footing resistance and high footing resistance. The author's comments on why they chose this particular variation would be useful. Does the author have a basis for the values of the resistance values of Rl and R2 based on any actual tests?

Results TFR Case 20 ohm 10 ohm 3 ohm

Sta. Impedance (ohms) .300 + j .010 .100 + j .010

RI andR2 = .20 + j .001 ohm Self-Impedance Phase Conductors .079 + j .667 ohms/km Self-Impedance 3/8" AW (twc) .812 + j .667 ohms/km Source Terminal Voltage 500 kV

To Sta. B 7532 8193 8197

km from Sta. A

1) Transmission Line Grounding, Palo Alto, CA, EPRI Project RP 1494-1 Final Report, prepared by Safe Engineering Services Ltd.

August 1982. 2) R. Rudenberg, Transient Performance of Electric Power Systems, Cambridge, MA, The MIT Press, 1967, pp. 355-366. Manuscript received August 17, 1982.

S. R. Lambert: The interest and effort expended by the two discussers is sincerely appreciated. Regarding Mr. Niles' comments, the current through the tower (Figure 3) is not identically zero. Obviously there is some flow, however, the physics of the problem certainly indicates it to be small for close in faults. Notwithstanding the difference between the results in the paper and that of Mr. Niles, a few percent is not significant to the conclusions especially considering all the possible unknowns existing in the field. The results shown on Figure 8 can indeed be considered general, assuming that fast excitation systems are used. Such results not only have an impact on shield wire selection but also on other station equipment, switchgear in particular. Regarding Mr. Niles' comment on raising the acceptable upper shield wire temperature limit and accepting a loss of strength, the approach could result in disastrous consequences if not carefully considered. Because some conductors lose strength rapidly while others demonstrate a more gradual degradation, caution should be observed before attempting such an approach. Furthermore, EHS shield wire galvanization melts at about 4000C, occurring rather as a step function. More detailed information may be found in Reference 3 of the paper. The 40°C may be excessive for some applications but not for others. This is ultimately a decision to be made by the engineer. Regarding Mr. Niles' last comment on contact resistance, the values were selected based on the opinion of the author and others knowledgeable in the field. No actual test data is available. Mr. Jones' comment is most appreciated, and he is correct. When the paper was being prepared, EHS data was computed with conductor areas taken from Table 3.3.11 of the "Red Bookl." Unfortunately, the conductor area column (Table 3.3.11) is in error. The correct area may be calculated by multiplying the number of strands by the strand area obtained from the strand diameter column in the same table. (Note that the strand diameter for ½2 inch EHS is 0.165 inches not 0.105 inches.) These results yield the data shown in a corrected Figure 10 below. 30 ^ 40 30

-~~~i I

Guinea

.,,

20

-Minorca,-

111711Y6A

11]

~~~~7#6AW

LI

V

L

A

II

_ inc

1.

EH

10

1

iI

Lu8 ______

-

/

f~~~ T

inch 3/j inc 1: EHS3

5

0.1

EFault Duration

Eq. Source Impedance (ohms) .800 + j 10.0 1.6 + j 20.1

To Sta. A 16481 15165 12988

REFERENCES

0.01

TABLE A

To Structure 1145 1922 4304

NOTE: Fault current in amperes - magnitude only 1.6 with tower spacing 322m.

4i

Input Gen A Gen B

Total Fault 25111 25245 25413

10

15 20

1.0 secads

cycles

Figure 10

REFERENCE 1. Transmission Line Reference Book, 345 kV and Above, Electric Power Research Institute, 1975. Manuscript received September 16, 1982.