*Continued from article Sizing of power cables for circuit breaker controlled feeders (part 1)*

## 2. Criteria-2 Continuous current capacity (Ampacity)

This criterion is applied so that cross section of the cable can carry the required load current continuously at the designed ambient temperature and laying condition. Ampacity is defined as the current in amperes a conductor can carry continuously under the conditions of surrounding medium in which the cables are installed. An ampacity study is the calculation of the temperature rise of the conductor in a cable system under steady-state conditions.

Cable ampacity, if required to be calculated than it is calculated as per the following equation givenin IEEE -399, section 13.

*This equation is based on Neher-McGrath method where,*

**Tc’**– allowable conductor temperature (ºC)**Ta’**– ambient temperature (either soil or air) (ºC)**∆Td**– temperature rise of conductor due to dielectric heating (ºC)**∆Tint**– temperature rise of the conductor due to interference heating from adjacent cables (ºC)**Rac**– electrical ac resistance of conductor including skin effect, proximity and temperature effects (µ_/ft)**R’ca**– effective total thermal resistance of path between conductor and surrounding ambient to include the effects of load factor, shield/sheath losses, metallic conduit losses, effects of multiple conductors in the same duct etc (thermal- Ωft, ºC-cm/W).

*From the above equation it is clear that the rated current carrying capacity of a conductor is dependent on the following factors:*

- Ambient temperature (air or ground)
- Grouping and proximity to other loaded cables, heatsources etc.
- Method of installation (aboveground or below ground)
- Thermal conductivity of the medium in which the cable is installed
- Thermal conductivity of the cable constituents

However please note that while sizing a power cable we never calculate the ampacity. The above equation is used to analyze the cable ampacities of unique installations. Standard ampacity tables are available for a variety of cable types and cable installation methods and can be used for determining the current carrying capacity of a cable for a particular application.

These standards provide tabulated ampacity data in manufacturers catalog for cables installed in air, in ductbank, directly buried or in trays for a particular set ofconditions clearly defined.

It is because of this reason that we need to give the reference of manufacturers catalog from where the ampacity values are picked up.

Now once the current carrying capacity of a cable is found from standard catalog; we convert that rated capacity (Ampacity) into actual laying condition. The standard current ratings for cables are modified by the application of suitable multiplying factors to account for the actual installation conditions. Hence we define one more term here called ampacity deration factor.

Ampacity duration factor is defined as the product of various factors which accounts for the fraction decrease in the ampacity of the conductor. Those factors and physical condition deriving them are as follows:

- K1= Variation in ambient air temperature for cables laid in air / ground temperature for cables laid underground.
- K2 = Cable laying arrangement.
- K3 = Depth of laying for cables laid direct in ground.
- K4 = Variation in thermal resistivity of soil.

K = K1 x K2 x K3 x K4

Now from where do we get these multiplying factors to find the overall ampacity deration factor? Againwe get these values from manufacturers catalog because manufacturer of the cable is in best position to conduct thepractical experiments and test on the cables and find the percentage/fractional decrease in current carrying capacity of the cable in various conditions.

For better understanding of the ampacity deration factor the following pictorial representation is provided below.

Table for ampacity deration factor along with pictorial representation is provided below.

### Rating factors for variation in ambient air temperature:

Air Temperature – °C | 20 | 25 | 30 | 35 | 40 | 45 | 50 | 55 | |

Rating Factors | Conductor Temp. 90°C | 1.81 | 1.41 | 1.10 | 1.05 | 1.00 | 0.95 | 0.89 | 0.84 |

### Rating factors for variation in ground temperature:

Ground Temperature – °C | 20 | 25 | 30 | 35 | 40 | 45 | 50 | |

Rating Factors | Conductor Temp. 90°C | 1.12 | 1.08 | 1.04 | 0.96 | 0.91 | 0.87 | 0.82 |

### Rating factors for multicore cables laid on open racks in air:

No. of rocks | No of cables per rack | ||||

1 | 2 | 3 | 6 | 9 | |

1 | 1.00 | 0.98 | 0.96 | 0.93 | 0.92 |

2 | 1.00 | 0.95 | 0.93 | 0.90 | 0.89 |

3 | 1.00 | 0.94 | 0.92 | 0.89 | 0.88 |

6 | 1.00 | 0.93 | 0.90 | 0.87 | 0.86 |

No. of rocks | No of cables per rack | ||||

1 | 2 | 3 | 6 | 9 | |

1 | 1.00 | 0.84 | 0.80 | 0.75 | 0.73 |

2 | 1.00 | 0.80 | 0.76 | 0.71 | 0.69 |

3 | 1.00 | 0.78 | 0.74 | 0.70 | 0.68 |

6 | 1.00 | 0.76 | 0.72 | 0.68 | 0.66 |

### Rating factors for single core cable in trefoil circuits laid on open racks in air:

No. of rocks | No of circuits per rack | ||

1 | 2 | 3 | |

1 | 1.00 | 0.98 | 0.96 |

2 | 1.00 | 0.95 | 0.93 |

3 | 1.00 | 0.94 | 0.92 |

6 | 1.00 | 0.93 | 0.90 |

### Rating factors for groups of multicore cables laid direct in ground, in horizontal formation:

Spacing | No. of cables in group | ||||

2 | 3 | 4 | 6 | 8 | |

Cables touching | 0.79 | 0.69 | 0.62 | 0.54 | 0.50 |

15 cm | 0.82 | 0.75 | 0.69 | 0.61 | 0.57 |

30 cm | 0.87 | 0.79 | 0.74 | 0.69 | 0.66 |

45 cm | 0.90 | 0.83 | 0.79 | 0.75 | 0.72 |

60 cm | 0.91 | 0.86 | 0.82 | 0.78 | 0.76 |

### Rating factors for grouping of multicore cables laid direct in ground in tier formation:

Spacing | No. of cables | ||

4 | 6 | 8 | |

Cables touching | 0.60 | 0.51 | 0.45 |

15 cm | 0.67 | 0.57 | 0.51 |

30 cm | 0.73 | 0.63 | 0.57 |

45 cm | 0.76 | 0.67 | 0.59 |

60 cm | 0.78 | 0.69 | 0.61 |

### Rating factors for grouping of single core cable laid in trefoil circuits laid direct in ground in horizontal formation:

Spacing | No. of circuits in group | ||||

2 | 3 | 4 | 6 | 8 | |

Cables touching | 0.78 | 0.68 | 0.61 | 0.53 | 0.48 |

15 cm | 0.81 | 0.71 | 0.65 | 0.58 | 0.54 |

30 cm | 0.85 | 0.77 | 0.72 | 0.66 | 0.62 |

45 cm | 0.88 | 0.81 | 0.76 | 0.71 | 0.67 |

60 cm | 0.90 | 0.83 | 0.79 | 0.76 | 0.72 |

### Rating factors for depth of laying for Cables laid direct in the ground:

* Voltage | Depth of laying | 75 | 90 | 105 | 120 | 150 | 180 and above |

1.1 kV | Rating factor up to 25 sq. mm. | 1.00 | 0.99 | 0.98 | 0.97 | 0.96 | 0.95 |

Rating factor above 25 sq. mm and up to 300 sq. mm | 1.00 | 0.98 | 0.97 | 0.96 | 0.94 | 0.93 | |

Rating factor above 300 sq. mm. | 1.00 | 0.97 | 0.96 | 0.95 | 0.92 | 0.91 |

### Rating factors for variation in thermal resistivity of soil:

*(multicore cables laid direct in ground)*

Nominal area of conductor in sq. mm | Rating factors for value of Thermal Resistivity of Soil in °C cm / Watt | |||||

100 | 120 | 150 | 200 | 250 | 300 | |

25 | 1.14 | 1.08 | 1.00 | 0.91 | 0.84 | 0.78 |

35 | 1.15 | 1.08 | 1.00 | 0.91 | 0.84 | 0.77 |

50 | 1.15 | 1.08 | 1.00 | 0.91 | 0.84 | 0.77 |

70 | 1.15 | 1.08 | 1.00 | 0.90 | 0.83 | 0.76 |

### Rating factors for variation in thermal resistivity of soil, three single core cables laid direct in the ground:

*(three cables in trefoil touching)*

Nominal area of conductor in sq. mm | Rating factors for value of Thermal Resistivity of Soil in °C cm / Watt | |||||

100 | 120 | 150 | 200 | 250 | 300 | |

25 | 1.19 | 1.09 | 1.00 | 0.88 | 0.80 | 0.74 |

35 | 1.20 | 1.09 | 1.00 | 0.88 | 0.80 | 0.74 |

50 | 1.20 | 1.09 | 1.00 | 0.88 | 0.80 | 0.74 |

Now let us apply the ampacity criteria for sizing the cable of a motor. The minimum required size as per criteria-1 is already determined in part-1 of this article.

No. | Input Required | Source of Input |

1 | Rated kW of Load (Here we assume it as 160kW Motor) | Mechanical/Process Load list |

2 | Motor Data (PF and efficiency, Here we are considering PF of 0.85 and motor efficiency of 95%) | From Motor Data sheet submitted by manufacturer |

3 | Type of Cable to be used (Here we are considering Aluminium, XLPE, 3 core cable) | Project technical specification (For insulation and conductor material) |

4 | Electrical design ambient temperature (We are considering electrical design ambient temperature of 50C) | Project technical specification |

5 | Laying condition | From Electrical cable route layout |

6 | Cable ampacity and deration factors | From reputed cable manufacturers catalog |

Rated Load current for 160kW motor = 160 x 1000/ (1.732 x 415 x 0.85 x motor efficiency)

Rated load current for motor = 275.66 Ampere

Now assuming that cable is laid in open racks in air the applicable ampacity deration factor will be:

**K = K1 X K2** *(K3 and K4 will not be applicable in this case)*

**K1 = 0.89**

**K2 = 0.70** *(assuming 3 Nos. of cable rack with number of cables/rack to be 6 and cables are laid touching each other)*

K = 0.89 x 0.70 = 0.623

Now K x Cable Ampacity should be greater than or equal to the required load current.

Aluminum, XLPE, 3C x 300 Sq mm cable has ampacity in air = 461 Amperes (From Manufactures catalog)

Applying ampacity deration factor = **461 * 0.623 = 287.203 Amperes** which is greater than required load current of 275.6 Amperes.

**Hence cable size selected on the basis of continuous current requirement is single run of 3C x 300 Sq mm, Aluminum, XLPE.**

### Conclusion:

A motor rated 160kW controlled by air circuit breaker fed from main PCC of fault rating 50kA and connected through Aluminum XLPE cable requires a cable size of 3C x 240 Sq mm minimum because of short circuit rating, however selected size because of continuous current requirement is 3c x 300 Sq mm.

*The third and final criteria of voltage drop will be discussed in part-3 of this article.*

Thanks for the articles! Very useful!

Btw why do you use 3 cable rack and 6 cable/rack at the calculating stage of K the factor? Is it just because for the example?

Is it possible to just add one separated cable rack for the 3c x 300 Sq cable?

Thank you in advance!

Hello, I have some questions about Neher-MCgrath Method. Do you know if I can learn about it in a book? Can you recomend a book to learn about neher mcgrath?

Thank you.

Hi,

I like the explanation & looking forward for part 3 ie voltage drop calculation regarding.

Find 3rd part here, it’s being published quite a long time ago:

https://electrical-engineering-portal.com/sizing-of-power-cables-for-circuit-breaker-controlled-feeders-part-3

Good job Asif…. it is a step-by-step comprehensive explanation. I recommend the readers to down load excell calculation sheet made by jignesh.parmar.

Regards.

Good suggestion Ivan! 3rd part of Asif’s technical article is on the way, it will be published in the matter of days.

I must say I’m quite surprised with depth of explanation in all three parts of article. Goog job Asif!