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 can withstand the short circuit current.

Failure to check the conductor size for short-circuit heating could result in permanent damage to the cable insulation and could also result into fire. In addition to the thermal stresses, the cable may also be subjected to significant 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 at the designed ambient temperature and laying condition.

III. Starting and running voltage drops in cable

This criteria is applied to make sure that the cross sectional area of the cable is sufficient to keep the voltage drop (due to impedance of cable conductor) within the specified limit so that the equipment which is being supplied power through that cable gets at least the minimum required voltage at its power supply input 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 the short circuit current. The quantity I2t represents the energy input by a fault that acts to heat up the cable conductor. This can be related to conductor size by the formula:

A = Minimum required cross section area in mm2
t = Operating time of disconnecting device in seconds
Isc = RMS Short Circuit current Value in Ampere
C = Constant equal to 0.0297 for copper & 0.0125 for aluminum
T2 = Final temp. ° C (max. short circuit temperature)
T1 = Initial temp. ° C (max. cable operating temperature – normal conditions)
T0 = 234.5° C for copper and 228.1° C for aluminum

Equation-1 can be simplified to obtain the expression for minimum conductor size as given below in equation-2:

 


Now K can be defined as a Constant whose value depends upon the conductor material, its insulation and boundary conditions of initial and final temperature because during short circuit conditions, the temperature of the conductor rises rapidly. The short circuit capacity is limited by the maximum temperature capability of the insulation. The value of K hence is as given in Table 2.
Boundary conditions of initial and final temperature for different insulation is as given under in Table 1 below.

Table 1

Insulation material	Final temperature T2	Initial 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 Current Rating in Amp/mm2	115	134	143	76	89	94
(K) 3 Second Current Rating in Amp/mm2	66	77	83	44	51	54

In the final equation-2 we have determined the value of constant K. Now the value of t is to be determined. The fault current (ISC) in the above equation varies with time. However, calculating the exact value of the fault current and sizing the power cable based on that can be complicated. To simplify the process the cable can be sized based on the interrupting capability of the circuit breakers/fuses that protect them.

This approach assumes that the available fault current is the maximum capability of the breaker/fuse and also accounts for the cable impedances in reducing the fault levels.

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