*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 T_{2} | Initial temperature T_{1} |

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/mm ^{2} | 115 | 134 | 143 | 76 | 89 | 94 |

(K) 3 Second Current Rating in Amp/mm ^{2} | 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.

- For medium voltage system (4.16 kV) breakers, use 5-8 cycles
- For starters with current limiting fuses, use ½ cycle
- For low voltage breakers with intermediate/short time delay, use 10 cycles
- For low voltage breakers with instantaneous trips, use 1 cycle

Alternatively let us consider that feeder is for any large motor which is being fed from LV 415V or 400V switchgear having a circuit breaker with separate multifunction motor protection relay (For this calculation it is assumed to be SIEMENS made 7SJ61).

The instantaneous protection feature of this relay will be turned ON as and when any fault occurs. However, the selected cable shall have the capacity to withstand the maximum fault current for a finite duration (that is fault clearing time of the circuit breaker).

The minimum faults withstand duration necessary (for the instantaneous setting) for cable is calculated as under:

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 opening time of 40 ms and closing time of 60ms) |

4 | Relay overshoot | 20 | GEC handbook “Network Protection & automation Guide” |

5 | Safety Margin | 30 | |

TOTAL TIME IN MILI SECONDS | 120 |

Therefore the cable selected for a circuit breaker controlled motor feeder in 415V or 400V switchgear shall be suitable to withstand the maximum rated fault current of 50kA for at least 120msec. However taking allowance of 40 Mili seconds in the opening time of circuit breaker due to aging, frequent number of operation, increase in contact resistance of circuit breaker and finally to cover the variation due from manufacturer to manufacturer.

Hence the cable selected for a circuit breaker controlled motor feeder in 415V or 400V switchgear shall be suitable to withstand the maximum rated fault current of **50kA** for at least (120+40) 160msec. Many consultants recommend for use operating time of disconnecting device as 200msec also. Value of “**t**” more than 160 seconds is a conservative design.

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

^{2}**Next standard cable size: = 240 mm ^{2}**

Although it may appear that selection of minimum cross sectional area of cable conductor as 240 mm^{2} is only just large enough for the duty, the actual fault current in the motor circuit is generally less than the switchboard fault withstand rating of 50kA, hence the selection of cable of cross sectional area 240 mm2 in practice offers sufficient design margin.

The minimum cross sectional area of cable required for 415V or 400V switchgear motor feeder from fault withstand point of view shall be 240mm^{2}.

We have considered for circuit breaker controlled motor feeder and analyzed the duration of short circuit/fault withstanding time in seconds for the same. Exactly the Same holds true for Circuit breaker controlled (Please see the below figure) outgoing transformer feeder.

However operating time of disconnecting device is slightly different for circuit breaker controlled incomer and tie feeders. Duration of fault withstanding/operating time of disconnecting device for incomer and tie feeder is 1 and 0.5 second respectively. This is because of additional presence of inverse definite minimum time delay protection relays along with instantaneous protection. The inverse definite time delay protection has time settings greater than 0.5 for incomer feeders and about 0.5 for tie feeders.

For all different type of feeders the operating time of disconnecting device is indicated in figure below:

The final cable size shall be selected considering the other two criteria that is continuous current carrying capacity & voltage drop criteria which would be continued in * part-2* and

*.*

**part-3**