IEEE Transactions on Electrical Insulation Vol. EI-22 No.4, August 1987

CABLE LIFE EXPECTANCY CALCULATION -

A PRACTICAL APPROACH

Z. Z. Bajbor

Stone and Webster Engineering Corp.Cherry Hill, New Jersey

ABSTRACT

Cable life expectancy calculations can yield much betterresults if based on actual, rather than rated or extreme,load and environmental conditions. Activation energy at 60%retained relative elongation and realistically assessedservice conditions should, inlife with sufficient built-inculation with fluctuating currpresented.

INTRODUCTION

The Arrhenius technique remains the major, if not theexclusive, methodology for demonstrating long-term per-formance of safety-related cables used in nuclear powerplants. In principle, the Arrhenius equation is appli-cable only to single discrete chemical or physical re-

actions. In the late 1940's T. W. Dakin pioneered ap-plication of the Arrhenius equation as a tool to meas-ure electrical insulation deterioration, which is a

complex chemical process [1,2]. Today it remains pre-ferred and recommended by relevant standards and regu-latory guides in the nuclear industry.

In application to electrical cables, the Arrheniustreatment of aging data is found to result in consist-ently shorter life expectancy than observed in real ca-

ble life, mostly because the rated conductor tempera-ture is used in the calculations as continuous insula-tion temperature.

The purpose of this paper is to demonstrate thatArrhenius methodology, despite its technical limita-tions, and even if most rigorously implemented, can, inmost cases, yield satisfactory results in cable quali-fication. The key is to account for actual, ratherthan rated or extreme, environmental conditions. Thetemperature to which cable insulation is to be exposedshould be based on actual load rather than rated am-

pacity. Also, a fluctuating rather than constant am-

bient temperature should be taken into account.

SAMPLE CALCULATION

A practical approach in cable qualification is illus-trated by the following sample life expectancy calcula-tion for a 5 kV power cable, for which simple appli-cation of the Arrhenius equation yields unsatisfactoryresults.

most cases, result in a 40-yearsafety margin. A sample cal-^ent load and temperature is

Postulated Input Data

Cable primary insulation: crosslinked polyethylenerated 90°C; Activation energy: E60=1.13 eV at 60% re-tained relative elongation [3,5]; E50=1.17 eV at 50%retained relative elongation [3], calculated from pres-ented Arrhenius-type plots; Oven aging prior to success-ful accident test: 504 h at 150°C; Cable data andservice conditions: 5 kV, 4/0 AWG triplexed cablerouted in conduits in air; load profile: Daily fluc-tuations in the load: 224 A for 65% of the time, 200 Afor 35%. The ambient temperature profile: 500C for45%, 400C for 40%, and 300C for 15% of the time inseasonal fluctuations.

CalcuZations

The Arrhenius equation, when applied straightforwardfor a 900C continuous conductor temperature, yields thefollowing life expectancy

L = taging exp[E60(/Tcond-l/Taging) kB]

= 84339 h = 9.6 y

Because such a result is far from acceptable, the lifeexpectancy is recalculated for the actual, rather thanrated, cable service conditions.

The allowable ampacity for a 4/0 triplexed cable rout-ed in a conduit is 280 A, based on a 900C conductor tem-perature and a 400C air ambient temperature [6].

The following equation can be used to recalculate cop-per conductor cable parameters based on rated conditions(subscript 1) to those based on actual cable service con-ditions (subscript 2) [6].

0)018-9367/87/0800-0485$01 .00CD 1987 IEEE

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IEEE Transactions on Electrical Insulation Vol. EI-22 No.4, August 1987

-2- -Ta2 - DT2 234.5 + Tl12

- l Tvcl - Tal - DT1 234. 5 + 1c2Table 2

(2)Calculated Results

(3)

where I is the ampacity [A], T. the conductor tempera-

ture [OC], Ta the ambient temperature [OC], and DT thedielectric loss temperature rise [OC]. For low-voltagecables, DT=O; for medium voltage cables, see Reference

[6].

Table 1 presents an array of data based on Eq. (3)where conductor temperature Tc2 is found for the con-

sidered cable load 12 and the fluctuating ambient tem-

perature Ta2:

Table 1

I =280; T -=40; DT1=.32 Tcl-90

E60=1.13; E50=1.17;

TiC(C)81.2674.4570.1763.6159.0952.76

Ti(0K)354.42347.61343.33336.77332.25325.92

to=168hr; To=1500Cp.

0. 29250.15750. 26000.14000.09750.0525

P .0160

0.000717380.000187190.000193170.000049360.000020240.00000507

; pi= * 0000l poip=0.00117231

Life L60 t o/IP =504/0.00117231o 0160

=499920 h =49.0 y

Life Ls,o=t /fP =504/0.000932880 01,rj=540262 h =61.6 y

I2

224200224200224200

Ta2

50.0050.0040.0040.0030.0030.00

DT2

0.320.320.320.320.320.32

81.2674.4570. 1763.6159.0952.76

Having determined conductor temperature at two loadlevels and the three fluctuating ambient temperatures,the cable life expectancy can be calculated from theArrhenius equation as follows:

Poi E0 1

= exp[ (4)Pi K7 (T T

L = to/Epoi (5)

Where Ti is the incremental fluctuating conductor tem-

perature [K], Ti=-12; pi the fraction of time the cableservice is at Ti, it should account for combination ofconditions listed in the input data, e.g. 0.65x0.45=0.2925, 0.35xO.45=0.1575, etc.; To the aging tempera-ture [K] for time to; to the time [hr] of aging at TO;poi the fraction of 1-h exposure at To per 1-h serviceat Ti; L the life expectancy [h]; E. the activationenergy [eV] for cable insulation at the postulated end-point; and k is the Boltzmann constant.

The results of the calculations based on Eqs. (4) and(5) are presented in Table 2.

Incremental values for Poi5o are not listed in Table2, they have been obtained by the identical procedurewith activation energy ESO being applied.

DISCUSSION

Since the cable life calculation by the above present-ed method yields significantly better results, it isappropriate to review safety margins involved.

Instead of accumulating a safety margin by an assumedcontinuous rated conductor temperature, the safety mar-

gin in the presented method is controlled by rationalselection of the applied acitvation energy.

The slope of an Arrhenius plot, and equivalently theactivation energy, depends on the adopted endpointcriterion (retained relative elongation if elongationis elected as a measure of material aging). A lowerelongation endpoint (or allowed more thermal degrada-tion to be accrued by the material) results in higheractivation energy and in longer life calculated fromthe Arrhenius equation. Data from any standard insula-tion aging test provide sufficient input to calculateactivation energy at any selected endpoint.

The mechanism of cable breakdown due to the agingprocess is portrayed as physical cracking of the insula-tion, followed by moisture penetration. There is a widerange of opinions as to what level of retained elonga-tion the cable can withstand bending without insulationcracking. On the conservative side of that range, the50% retained relative elongation is considered as an

endpoint which could be reached before serious crackingdevelops [3]. If that endpoint is adopted as a criter-ion for establishing cable life, then a safety margincan be secured by applying in cable life calculation an

activation energy corresponding to less thermal degrad-ation than 50% loss of elongation.

In the presented sample calculation, the 50% endpointcriterion (E50=1.17) yields L50=61.6 y life; at 60% re-

tained elongation (E60=1. 13) the calculated life is

L60=49.0 y. The difference L50-L60=12.6 y represents a

safety margin in the calculated cable life of L50=49.0Y.

Additional conservatism in cable life expectancy is

built in all those cases when applied activation energy

is established by the standard oven heating test where

insulation dumbbells or specimens of stripped insulationtubes are aged. T. H. Ling in his work on acceleratedaging [4] shows that oven aging is considerably more

severe in comparison to current load aging (and to in-

service aging) due to two major factors: (1) "jacket-on" condition provides protection against insulationexposure to air and oxygen; and (2) only the inner sur-

face of cable insulation is exposed to the conductortemperature while the outer portion of the insulation

remains at lower temperature.

12I2or=T2Il

1a2 - D12 234. 5 + Tcl-l Tal - DT, 234. 5 + Tc2

486

Eajbor: Cable life expectancy calculation: A practical approach

SUMMARY

Two prerequisites are required for successful appli-cation of the foregoing method of cable life calcul-ation:

Credibly established activation energy for insulationmaterial at an endpoint which would secure sufficientsafety margin.

Realistically assessed cable service condition.

While proven experimental methods for activation en-ergy measurement provide consistent, repetitive results,there is no prescribed or agreed-upon criterion by whichactivation energy is to be established. There is anurgent demand for rational endpoint criteria adoptionby the insulation aging standards.

In the sample calculation, the maximum continuouscurrent load is postulated to be 224/280=80% of theallowable ampacity, and this is a typical margin appli-cable in power circuits design. In most cases involv-ing nuclear power plants, even larger cable load mar-gins are applied, and such broad margins can contributevery effectively to life expectancy extension.

As could be expected, and as is illustrated in Table2 [Poi=f(Ti)], the higher service temperatures contri-bute substantially more to cable deterioration thanthe low temperatures. To achieve better results incable life calculation, it could be worthwhile to spe-cify cable service at high ambient and high load in de-tail by several temperature and load increments. Ser-vice at low ambient and low load could be covered byfewer increments since their contribution is less onoverall results.

REFERENCES

[1] T. W. Dakin, "Electrical Insulation DeteriorationTreated as a Chemical Rate Phenomenon", AIEETrans., Vol. 67, pp. 113-118, 1948.

[2] L. J. Berberich and T. W. Dakin, "GuidingPrinciples in the Thermal Evaluation of Elec-trical Insulation", AIEE Trans., Vol. 75, pp.752-761, August 1956.

[3] E. E. McIlveen, V. L. Garrison and G. T.Dobrowolski, "Class IE Cables for Nuclear PowerGenerating Stations", IEEE Trans., PAS, Vol.PAS-93, pp. 1121-1132, 1974.

[4] T. H. Ling, "The Significance of AcceleratedAging Testing of Rubber Insulation", AnacondaWire and Cable Co., Marion, IN, 12th AnnualWire and Cable Symposium, Asbury Park, NJ,December 1963.

[5] S. P. Carfagno and R. J. Gibson, "A Review ofEquipment Aging Theory and Technology", Elec-tric Power Research Institute, Report EPRINP-1558, September 1980.

[6] "Power Cable Ampacities, Vol. 1 - Copper Con-ductors", IPCEA Pub., pp. 46-426, 1962.

Manuscript was received on 20 June 1985, in finaZform 1 October 1986.

CONCLUSION

The method presented for cable life expectancy cal-culations is limited in that it can be applied only ona case-by-case basis. It is, however, a practical toolto demonstrate, in a verifiable way, adequate cable lifeexpectancy in most cases when a simplified calculationproduces an unacceptably short life.

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