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

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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.

The fault clearing time (tc) of the breakers/fuses 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 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 = 212.766mm2

Next standard cable size: = 240 mm2

Although it may appear that selection of minimum cross sectional area of cable conductor as 240 mm2 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 240mm2.

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.

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#### Asif Eqbal

Bachelor of Engineering in Electrical & Electronics engineering, from Manipal University, (Karnataka), India in 2006. Presently involved in the design of EHV outdoor substation and coal fired thermal power plants for more than seven years. Motto of joining EEP as a contributor is to share my little engineering experience and help the budding engineers in bridging the conspicuous gap between academics and Industrial practice. “If you have knowledge, let others light their candles with it, so that people who are genuinely interested in helping one another develop new capacities for action; it is about creating timeless learning processes".

1. Azley
Aug 16, 2017

Thanks for the info!

2. RR
Nov 04, 2015

Dear asif
why do we need to have circuit breakers on both side of cable can have a load break switch on the load other side(load side).

3. GINA MOODY
Oct 01, 2015

Dear Sir,
Iam Eng. Gina from Fox for international Trading.

Item no
Line Description QTY UNIT
1 SIEMENS CIRCUIT BREAKER 250A
MODEL: 3VF4212-2MM41-0AA0
4-POLE, 400 VAC
200-250 A
ICU/ICS= 70KA 2 EA

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4. Ashfaq
Dec 06, 2014

Good

5. Tareq
Oct 24, 2014

Thanks

6. Rahul
Sep 05, 2014

If we are having 300 mm2 cable size from the formula
A= I SC x √t / k for a LT Incomer then can we use two runs of 150 mm2 for the same incomer instead of one run of 300 mm2 cable.
Can you please clear this point with electrical design aspect.(with consideration of short circuit level and without short circuit level ) Explain the same for HT cable sizing.

7. krishna
Sep 03, 2014

dr sir pls help me in finding the cable size n breaker rating respetive of single phase n three phse load. if it a induction motor syn motor n slip ring….considering ther starting current n efficiency

8. sumedha
Jul 23, 2014

really a great job.
I do have many confusions with LV switch gear designing .
wish if some one could post on LV switch gear designing.

9. Senthilnathan
Mar 11, 2014

Dear sir
Got the answer for my long days queries. Fault clearing time is 0.16 sec. 0.25 sec is presence of relays.
Really superb sir…
Thank you so much…

10. deepakdj18
Nov 18, 2013

Thanks asif for such lovely information……..

11. ianguisq
Sep 11, 2012

Mr. Asif some observation, the area is not in [mm2] it is [cmil]

12. rp_amarlapudi
Jul 05, 2012

Dear Asif Eqbal good job keep it up i just down loaded ur material after studying i will reply u give ur mail

13. Sufi Shah Hamid Jalali
May 18, 2012

Thank you Asif for such hard and honest work. Much appreciated. Thank you all the authors for great job.

14. harsha
May 18, 2012

Good work Asif, it is working for us like a barrier between theory and practicals

May 14, 2012

Nice job.

16. hpardeshi
May 12, 2012

Very good knowledge sharing.

17. douglas
May 12, 2012

Hi, so far so good and great tutorials. More than that am grateful for the weekly subscriptions through mail. Its amazing you sent me articles coinciding on what am doing in the industry.
Thanks but I’d Like to know if you have an article on Change Over switch i.e, the one that uses contractors and phase failures circuits.
Thanks, I think it maybe an article of interest to many.

18. Asif Eqbal
May 12, 2012

Thanks everybody for feedback. Let this series gets completed in part-2 and 3 for ampacity deration and voltage drop, than definitely fuse and MCCB will be covered. Thanks

19. Shailesh Kumar
May 12, 2012

yes, sizing is nicely explained. try to give explanation on let-through energy for fuse & MCCB cases for group users. !

20. Sutirtha Chakraborty
May 11, 2012

Nice Article Asif. Now we are waiting for the cable sizing for SFU / MCB / MCCB operated feeders.

21. ivan.kurniawan
May 11, 2012

thanks a ton for sharing, Asif….

Best Regards