**Cable size and Voltage drop calculation for LT / LV (Low tension/Low voltage)**

__Purpose__

The purpose of this document is lay to down the guidelines and design procedure for performing the LV cable size and voltage drop calculation.

Relevant IS standards:-

- IS:694/1990 for PVC cable
- IS:1554 part-1/ 1998 for heavy duty PVC cable
- IS: 7098 part-1 /1988 for XLPE cable

__Procedure__

**The cable size is selected base on the four following consideration:-**

**Cable Derating Amp should be higher than Full Load Current of Load.****Cable voltage drop should be less than Defined voltage drop .****No of Run of Cable ≥= (Full Load current / Cable Derating Current).****Cable Short Circuit Capacity should be higher than System S.C Capacity.**

**Steps for cable **__size & voltage drop calculation__–

__size & voltage drop calculation__–

Following steps are to be followed to conclude proper techno-economical cable size and voltage drop for a consumer.

__Step-1:- Cable Size According To Load Current__

- Calculate load current for a consumer using following formulas

** I _{L} = KW / (∛ * V * pf )**

Where ,

I_{L} *= Load current of the electrical consumer (in Amp)*

KW = Output KW nameplate Rating of the load .In case of a battery charger maximum load considering normal load + boost charging to be considered.

V = Line to line voltage in case of 3 ph ac line to phase in case of 1 ph AC / DC voltage in case of Dc ( in KV and name plate voltage rating of the consumer, not the switchgear bus voltage) in KV.

Pf = Power factor in case of AC voltage at rated load

- Compare the cable size as per short circuit and according to load current select the higher cable size.

__Step-2 Effective current carrying capacity (D Rating factor / Rating factor)__

The current carrying capacity of a cable corresponds t the maximum current that it can carry under specified conditions without the conductors exceeding the permissible limit of steady state temperature for the type of insulation concerned. Derating factor or correction factor(C) shall be applied every where the installation condition differ from those for which values of current carrying capacity are defined derating factors generally considered are as follows:

a) In ground Installation (Direct Burial)

C =Cs * Cg * Cd *Ct

Where,

Cs = Rating factor for variation in ground temperature

Cg= Rating factor for Group of cables

Cd= Rating factor for Depth of laying

Ct=Rating for thermal resistivity) Above ground installation

b) Above Ground Installation

** C = Ca * Cg**

Where,

Ca= Rating factor for variation in ambient air temperature

Cg= Rating factor for Grouping cables

C) Values of different derating factors for calculating ‘C’ shall be taken as per manufacture catalogs. The value of C thus calculated is multiplied by the cables continuous current obtained from the standard tables and gives the derated current capacity of cables.

D) In case cables laid partially in air and large size in ground, take the derating factor from ground calculation.

Total load current after derating Factor (Purpose for select the cable from manufacture data sheet for voltage drop calculation)

** I = I˪/C**

__Step-3 Verification of cable size according to permissible voltage drop during steady state operating conditions and motor start up.__

For **Three Phase **circuits

Voltage drop can be computed using the formula

**%Vd = ∛ * I * L (Rac *Cos???? + X * Sin????)* 100 / (N * V *1000)**

**Vd = ∛ * I * L (Rac *Cos???? + X * Sin????) / (N * 1000)**

For **Single Phase** Circuit

**Vd = 2 * I * L (Rac *Cos???? + X * Sin????)* 100 / 1000**

Where,

Vd = Voltage drop percentage

**????** = Power factor angles as considered to calculate I

L = Line current in Amps

V = System voltage in Volts

Rac = Ac conductor resistance at maximum rated conductor temperature in KM ohms per KM (70 deg C for PVC, 90 deg C for XLPE

X = Reactance in ohms per km at rated frequency

L = Cable length in Km

N = Number of runs (for star delta feeder, minimum no of runs is 2)

**Indian Electricity Rules specify maximum voltage variation from the declared voltage at consumer’s supply point as +65 for LV and MV +6%, -9% for HV and + 10%, 12.5% for EHV systems.**

**Rating factor:-**

__Rating factor for variation in ambient temperature for cable laid in air__

Air in Temp in C | 25 | 30 | 35 | 40 | 45 | 50 | 55 | 60 |

MV cable XLPE insulated | 1.16 | 1.11 | 1.06 | 1.00 | 0.094 | 0.88 | 0.81 | 0.74 |

__ __

__Rating factor for variation in ground temperature for cable laid in direct ground__

Ground Temp in C | 15 | 20 | 25 | 30 | 35 | 40 | 45 | 50 |

MV cable XLPE insulated | 1.12 | 1.08 | 1.04 | 1.00 | 0.96 | 0.91 | 0.87 | 0.82 |

__ __

__Rating factor for Depth of laying for cable lay in direct in ground__

Depth of laying in mm | 750 | 1050 | 1200 | 1500 | 1800 | 2000 | 2500 | 3000 & above |

MV cable XLPE insulated | 1.00 | 0.99 | 0.97 | 0.95 | 0.94 | 0.93 | 0.87 | 0.90 |

Group rating factors for circuits of three core cables lay direct in ground

No of cables in Group | Spacing between cable centre in mm | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |

MV cable XLPE insulated
Source: OMAN Cables |
Touching | 1 | 0.8 | 0.68 | 0.62 | 0.58 | 0.55 | 0.52 | 0.50 | 0.48 | 0.46 | 0.45 | 0.44 |

150 | 1 | 0.84 | 0.74 | 0.69 | 0.65 | 0.62 | 0.59 | 0.57 | 0.55 | 0.54 | 0.53 | 0.52 | |

300 | 1 | 0.87 | 0.79 | 0.75 | 0.72 | 0.69 | 0.67 | 0.66 | 0.65 | 0.64 | 0.63 | 0.62 | |

450 | 1 | 0.90 | 0.83 | 0.80 | 0.77 | 0.75 | 0.73 | 0.72 | 0.71 | 0.70 | 0.70 | 0.69 | |

600 | 1 | 0.91 | 0.86 | 0.83 | 0.80 | 0.78 | 0.77 | 0.75 | 0.75 | 0.74 | 0.74 | 0.73 |

Soil Correction Factor of Soil (When Thermal Resistance of Soil is not known)

Nature of Soil | Ct |

Very Wet Soil | 1.21 |

Wet Soil | 1.13 |

Damp Soil | 1.05 |

Dry Soil | 1 |

Very Dry Soil | 0.86 |

__ let’s take Quick Example__

__let’s take Quick Example__

Q- Which cable size use for 3 phase motor for buried / underground cable?

__Data Available/ Require__

- Motor Rating 100 HP ,
- Temperature is approximate 45 C,
- Distance 300 mtr ,
- Depth of laying depth in 750 mm,
- Number of cable per trench is 1,
- Soil resistivity (Mostly provided by Civil department) 1,
- Demand factor is 1,
- System short circuit capacity 6 ka.
- power factor is 0.8.

__Calculations :-__

Load current ( **I˪** )= ?

Motor 100 Hp = 74.6 KW (1 HP=0.746 kw)

** ** I˪= 122.5 A

Total derating factor (C) = ?

According to above detail:

Ground temperature correction factor (Cs) = 0.91

Cable depth correction factor (Cd) = 1

Cable distance correction factor (Touching)(Ct) = 1

Soil correction factor (Cg) = 1

Derating factor (C )= Cs * Cg *Ct * Ct

** C = 0.91**

Total load current after derating Factor = 122.5/ 0.91=134.61 amp

Select the cable size (Cable Manufacture data sheet : Havells )) for voltage drop.

__Selection of cable – Case #1__

Let’s select 3 core 70 Sq.mm cable for single run,

Current capacity of 70 Sq.mm cable is 135 Amp,

Resistance =0 .532 Ω/Km and

Reactance = 0.076 mho/Km

Total derating current of 70 Sq.mm cable = 135 · 0.91 = 122.85 Amp.

Voltage drop of cable =

(1.732 * 122.5 * 100 (0.532 *0.8 + 0.076 * 0.6) *100) / (1 *415* 1000) = 2.24%

__To decide 70 Sq.mm cable, cable selection condition should be checked.__

- Cable derating Amp (122.85 Amp) is higher than full load current of load (122.5 Amp)= O.K
- Cable voltage drop (2.24%) is lower than defined voltage drop (5%) = O.K
- Number of cable runs (1) ≥ (122.5A / 135A = 0.78) = O.K
- Cable short circuit capacity (5.32KA) is higher than system short circuit capacity at that point (6.0KA) = Not OK

** “70 Sq.mm cable not satisfied all four condition and so it is advisable not to use.”**

__Selection of cable – Case #2__

Let’s select 3 core 95 Sq.mm cable for single run,

Current capacity of 95 Sq.mm cable is 165 Amp,

Resistance =0 .384 Ω/Km and

Reactance = 0.076 mho/Km

Voltage drop of cable =

(1.732 * 122.5 * 100 (0.384 *0.8 + 0.076 * 0.6) *100) / (1 *415* 1000) = 1.8%

__ To decide 95 Sq.mm cable, cable selection condition should be checked.__

- Cable derating Amp (150.15 Amp) is higher than full load current of load (122.5 Amp)= O.K
- Cable voltage drop (1.8%) is less than defined voltage drop (5%) = O.K
- Number of cable runs (1) ≥ (122.5A / 165A = 0.74) = O.K
- Cable short circuit capacity (7.22KA) is higher than system short circuit capacity at that point (6.0KA) = O.K

** “95 Sq.mm cable satisfied all four condition and so it is advisable to use.”**

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