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Sizing of power cables for circuit breaker controlled feeders(part 1)

The following three criteria apply for the sizing of cables for circuit breaker controlled feeders:

I. Short circuit current withstand capacity

This criteria is applied to determine the minimum cross section area of the cable, so that cable canwithstand the short circuit current.

Failure to check the conductor size f or short-circuit heating could result in permanent damage to the cableinsulation and could also result into f ire. In addition to the thermal stresses, the cable may also besubjected to signif icant mechanical stresses.

II. Continuous current carrying capacity

This criteria is applied so that cross section of the cable can carry the required load current continuously atthe designed ambient temperature and laying condition.

III. Start ing and running voltage drops in cable

This criteria is applied to make sure that the cross sectional area of the cable is suf f icient to keep thevoltage drop (due to impedance of cable conductor) within the specif ied limit so that the equipment which isbeing supplied power through that cable gets at least the minimum required voltage at its power supplyinput terminal during starting and running condition both.

1. Criteria-1 Short circuit capacity

The maximum temperature reached under short circuit depends on both the magnitude and duration of theshort circuit current. The quantity I2t represents the energy input by a f ault that acts to heat up the cableconductor. This can be related to conductor size by the f ormula:

A = Minimum required cross section area in mm2t = Operating time of disconnecting device in secondsIsc = RMS Short Circuit current Value in AmpereC = Constant equal to 0.0297 f or copper & 0.0125 f or aluminumT2 = Final temp. ° C (max. short circuit temperature)T1 = Init ial temp. ° C (max. cable operating temperature – normal conditions)T0 = 234.5° C f or copper and 228.1° C f or aluminum

Equation-1 can be simplif ied to obtain the expression f or minimum conductor size as given below inequation-2:

Now K can be def ined as a Constant whose value depends upon the conductor material, its insulation andboundary conditions of init ial and f inal temperature because during short circuit conditions, the temperatureof the conductor rises rapidly. The short circuit capacity is limited by the maximum temperature capability ofthe insulation. The value of K hence is as given in Table 2.

Boundary conditions of init ial and f inal temperature f or dif f erent insulation is as given under in Table 1below.

Table 1

Insulation material Final temperature T2 Init ial temperature T1

PVC 160° C 70° C

Butyl Rubber 220° C 85° C

XLPE / EPR 250° C 90° C

Table 2

Material → Copper Aluminum

Insulation → PVC Butyl Rubber XLPE / EPR PVC Butyl Rubber XLPE / EPR

(K) 1 Second CurrentRating in Amp/mm2

115 134 143 76 89 94

(K) 3 Second CurrentRating in Amp/mm2

66 77 83 44 51 54

In the f inal equation-2 we have determined the value of constant K. Now the value of t is to be determined.The f ault current (ISC) in the above equation varies with t ime. However, calculating the exact value of thef ault current and sizing the power cable based on that can be complicated. To simplif y the process thecable can be sized based on the interrupting capability of the circuit breakers/f uses that protect them.

This approach assumes that the available f ault current is the maximum capability of the breaker/f use andalso accounts f or the cable impedances in reducing the f ault levels.

The f ault clearing time (tc) of the breakers/f uses per ANSI/IEEE C37.010, C37.013, and UL 489 are:

For medium voltage system (4.16 kV) breakers, use 5-8 cycles

For starters with current limiting f uses, use ½ cycle

For low voltage breakers with intermediate/short t ime delay, use 10 cycles

For low voltage breakers with instantaneous trips, use 1 cycle

Alternatively let us consider that f eeder is f or any large motor which is being f ed f rom LV 415V or 400Vswitchgear having a circuit breaker with separate multif unction motor protection relay (For this calculation itis assumed to be SIEMENS made 7SJ61).

The instantaneous protection f eature of this relay will be turned ON as and when any f ault occurs.

However, the selected cable shall have the capacity to withstand the maximum f ault current f or a f initeduration (that is f ault clearing time of the circuit breaker).

The minimum f aults withstand duration necessary (f or the instantaneous setting) f or cable is calculated asunder:

Si. No. Parameters Time in ms Source/Back up

1 Relay sensing/pickup time 20 SIEMENS 7SJ61 technical data

2 Tolerance/Delay time 10 SIEMENS 7SJ61 technical data

3 Breaker operating time 40 L&T make C-Power breaker have typical openingtime of 40 ms and closing time of 60ms)

4 Relay overshoot 20 GEC handbook “Network Protection & automationGuide”

5 Saf ety Margin 30

TOTAL TIME IN MILI SECONDS 120

Theref ore the cable selected f or a circuit breaker controlled motor f eeder in 415V or 400V switchgear shallbe suitable to withstand the maximum rated f ault current of 50kA f or at least 120msec. However takingallowance of 40 Mili seconds in the opening time of circuit breaker due to aging, f requent number ofoperation, increase in contact resistance of circuit breaker and f inally to cover the variation due f rommanuf acturer to manuf acturer.

Hence the cable selected f or a circuit breaker controlled motor f eeder in 415V or 400V switchgear shall besuitable to withstand the maximum rated f ault current of 50kA f or at least (120+40) 160msec. Manyconsultants recommend f or use operating time of disconnecting device as 200msec also. Value of “t” morethan 160 seconds is a conservative design.

A = (Isc x √t)/K = (50000 x √0.16)/94 = 212.766mm2

Next standard cable size: = 240 mm2

Although it may appear that selection of minimum cross sectional area of cable conductor as 240 mm2 isonly just large enough f or the duty, the actual f ault current in the motor circuit is generally less than theswitchboard f ault withstand rating of 50kA, hence the selection of cable of cross sectional area 240 mm2in practice of f ers suf f icient design margin.

The minimum cross sectional area of cable required f or 415V or 400V switchgear motor f eeder f rom f aultwithstand point of view shall be 240mm2.

We have considered f or circuit breaker controlled motor f eeder and analyzed the duration ofshort circuit/f ault withstanding time in seconds f or the same. Exactly the Same holds true f orCircuit breaker controlled (Please see the below f igure) outgoing transf ormer f eeder.

However operating time of disconnecting device is slightly dif f erent f or circuit breaker controlled incomerand tie f eeders. Duration of f ault withstanding/operating time of disconnecting device f or incomer and tief eeder is 1 and 0.5 second respectively. This is because of additional presence of inverse def inite minimumtime delay protection relays along with instantaneous protection. The inverse def inite t ime delay protectionhas time settings greater than 0.5 f or incomer f eeders and about 0.5 f or t ie f eeders.

For all dif f erent type of f eeders the operating time of disconnecting device is indicated in f igure below:

Typ ical value o f t (fault c le aring time ). All the co nne cting cab le s has to b e s ize d fo r sho rt c ircuit d uratio n(t) ind icate d in the d iag ram ab o ve

The f inal cable size shall be selected considering the other two criteria that is continuous current carryingcapacity & voltage drop criteria which would be continued in part-2 and part-3.