Cable Size Calculation for LT & HT Motors

How to calculate the Cable size for LT & HT Motors?

Selecting the right cable size for the motor is an important parameter for the Industry whether it’s during Installation and Commissioning or during running condition. It is a very important aspect for Safety, Cost minimization and reduction of undesired losses. An undersized cable can burn during motor operation causing risk to human life, machine, infrastructure, loss of production and replacement cost.

Whereas an oversized conductor will incur unnecessary cost not only for the long run cables but also for cable termination materials used along with them i.e. lugs, glands, jointing kit (in case any fault occur in the future) and oversized cable tray. The cost of labor for laying of higher size cable will also be higher compared to respective lower size cable. Considering all these vital points it’s important to make an proper cable size calculation for our motor.

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Before we go in details, let’s clear the main difference between LT & HT Motors.

What is the difference between LT and HT Motors?

Well, as the word LT (Low Tension i.e. Low Voltage) and HT (High Tension i.e. High Voltage) or low torque and high torque respectively describe the whole story itself.

its also depends on the availability of supply voltage,i.e. in USA and EU,

LT Motors ranges = 230V – 415V

HT Motors ranges = 3.3 kV, 6.6kV – 11kV

while keep in mind that LT motors need more current than HT motors.

in other regions, they classified LT Motor under 1kV & HT Motor Over 1kV.

Now we have to discuss the main topic that’s how to calculate the cable size for motors?

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Cable Size Calculation of 125 Kw LT Motor

Motor KW = 125

Pf = 0.8, Efficiency = 94%

System Voltage, V₁ = 415

Cable length  = 200 m

Load Current = P / (1.732 x V x Pf x Eff)       —>     (P = √3 x Vx I CosΦ = for three phase circuits)

                      = 125000 / (1.732 x 415 x 0.8 x 0.94)

                       ~ 230 A

This is the full load current cable needs to cater in Ideal condition. But in practical situation, there are several derating factors which need to be considered.

The current rating given for the cables is defined for ambient temp of 40* C. If the ambient temp is greater than that, cable current carrying capacity derates.

Suppose our cable is in Air laid on cable tray,

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Air Temperature in Deg.		20°	25°	30°	35°	40°	45°	50°	55°
	Normal PVC	1.32	1.25	1.16	1.09	1.00	0.90	0.80	0.80
De-Rating factors	HR PVC	1.22	1.17	1.12	1.06	1.00	0.94	0.87	0.80
	XLPE	1.20	1.16	1.11	1.06	1.00	0.95	0.88	0.82

Rating factors related to variation in ambient air temperature

Temperature Correction Factor, K₁ when cable is in the Air = 0.88 (for 50* Amb temp & XLPE cable)

Grouping of cables also derates cable’s current carrying capacity. If many cables are grouped together, they will all heat up. The heat won’t be able to dissipate properly hence it will warm up the cable itself and those in its contact. This will raise the temperature further. Hence we have to derate the current carrying capacity of the cable according to the grouping factor.

Let’s go for worst case scenario, i.e. 3 trays parallel to each other having 9 cables each touching to each other.

No. of Racks	No. of Cables per Rack					No. of Cables per Rack
	1	2	3	6	9	1	2	3	6	9
1	1.00	0.98	0.96	0.93	0.92	1.00	0.84	0.80	0.75	0.73
2	1.00	0.95	0.93	0.90	0.89	1.00	0.80	0.76	0.71	0.69
3	1.00	0.94	0.92	0.89	0.88	1.00	0.78	0.74	0.70	0.68
6	1.00	0.93	0.90	0.87	0.86	1.00	0.76	0.72	0.65	0.66

Table: Cable Grouping Factor (No of Tray Factor), K2 = 0.68 (for 3 trays having 9 cable each)

Total derating factor = K₁ x K₂

                                    =  0.88×0.68 = 0.5984

Let’s select 1.1 KV, 3 core, 240 Sq.mm, Aluminum, XLPE, Armored cable for single run

Click to enlarge the table

Technical Details For 1.1 KV, 3 Core, Aluminum/Copper Conductor, XLPE Insulated, Armored Cables

Current capacity of 240 Sq.mm XLPE Armored aluminum cable in Air is 402 Amp

Total derating current of 240 Sq.mm Cable = 402×0.5984 = 240.55 Amp

Resistance = 0.162 Ω / Km and
Reactance = 0.072 Ω / Km

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Estimated Voltage Drops in PVC/XLPE Aluminum Cables For A.C. System
	(Voltage drop – Volts/Km/Amps)
Nominal Area of Conductor (Sq. mm)	P.V.C. Cable		XLPE Cable
	Single Phase	Three Phase	Single Phase	Three System
1.5	43.44	37.62	46.34	40.13
2.5	29.04	25.15	30.98	26.83
4	17.78	15.40	18.98	16.44
6	11.06	9.58	11.80	10.22
10	7.40	6.41	7.88	6.82
16	4.58	3.97	4.90	4.24
25	2.89	2.50	3.08	2.67
35	2.10	1.80	2.23	1.94
50	1.55	1.30	1.65	1.44
70	1.10	0.94	1.15	1.00
95	0.79	0.68	0.83	0.70
120	0.63	0.55	0.66	0.56
150	0.52	0.46	0.55	0.48
185	0.42	0.37	0.44	0.40
240	0.34	0.30	0.35	0.30
300	0.28	0.26	0.30	0.26
400	0.24	0.22	0.24	0.22
500	0.23	0.20	0.23	0.20
630	0.20	0.18	0.21	0.18
800	0.19	–	0.20	–
1000	0.18	–	0.18	–

Voltage drop, V₂ = 0.3 Volts/Km/Amp    (as per Havell’s brochure)

                           = 0.3 x 230 x (200 / 1000)

                           = 13 V

Terminal voltage at Motor, V₂ = 415 -13 = 402 V

% Drop = (V₂ – V₁) / (V₁)

             = (415 – 402) x 100 / (415)

             = 3.13%

To decide 240 Sq.mm cable, cable selection condition should be checked

1. Cable derating Amp (240.55 Amp)is higher than full load current of load (230 Amp) = OK
2. Cable voltage Drop (3.13%)is less than defined voltage drop (10%) = OK
3. Cable short circuit capacity (22.56 KA) is higher than system short circuit capacity at that point ( X KA) = OK

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240 Sq.mm cable satisfied all three condition, so it is advisable to use 3 Core 240 Sq.mm cable.

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Cable Size Calculation for 350 KW HT Motor

In case of LV system cable can be selected on the basis of its current carrying capacity and voltage drop but in case of MV/HV system cable short circuit capacity is an important/deciding factor. So in case of HT motor, the cable short circuit capacity alone is enough to determine the cable size as rest two parameters will automatically follow.

Consider the below example:

Motor KW = 350

Pf = 0.8, Efficiency = 94%

System Voltage, V₁ = 6.6 KV

Cable length = 200 m

Load Current = P / (1.732 x V x Pf x Eff)

                      = 350000 / (1.732 x 6600 x 0.8 x 0.94)

                      = 41 A

Suppose Short circuit level/Fault level for H.T. system, I_sh (for duration t=1sec) = 26.2 KA

With Aluminum conductor, XLPE insulated cable =

= 278.72 Sq.mm

Hence nearest higher size 300 sq mm is required.

We can see from the below table also that the short circuit capacity of 300sqmm cable is 28 KA which is more than our fault level.

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Click image to enlarge

(6.6KV UNEARTHED / 11KV EARTHED GRADE)

Technical Details For 6.6 KV, 3 Core, Aluminum/Copper Conductor, XLPE Insulated, Armored Cables

We can see that this will automatically satisfy other two conditions also.

Let’s select 6.6 KV, 3 core, 300 Sq.mm, Aluminum, XLPE, Armored cable for single run

Temperature Correction Factor, K₁ when cable is in the Air = 0.88 (for 50* Amb temp & XLPE cable)

Cable Grouping Factor (No of Tray Factor), K₂ = 0.68 (for 3 trays having 9 cable each)

Total derating factor = K₁ x K₂   = 0.88 x 0.68 = 0.5984

Current capacity of 300 Sq.mm XLPE Armored aluminum cable in Air is 450 Amp

Total derating current of 300 Sq.mm Cable = 450×0.5984 = 269.28 Amp

Resistance   = 0.130 Ω / Km and

Reactance    = 0.0999 Ω / Km

Voltage drop = 0.26 Volts / Km / Amp    (as per Havell’s brochure)

                      = 0.26 x 200 x 41 / 1000

                      = 2.132 V

Terminal voltage at Motor, V₂ = 6600 – 2.132 = 6597.868 V

% Drop          = (V₁ – V₂) / (V₁)

                      = (6600 – 6597.8) x 100 / (6600)

                      = 0.032%

To decide 300 Sq.mm cable, cable selection condition should be checked

1. Cable derating Amp (269.28 Amp) is higher than full load current of load (41 Amp) = OK
2. Cable voltage Drop (0.032%)is less than defined voltage drop (5%) = OK
3. Cable short circuit capacity (28.20 KA) is higher than system short circuit capacity at that point (26.2 KA) = OK

300 Sq.mm cable satisfied all three condition, so it is advisable to use 3 Core 300 Sq.mm cable.

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