Calculating Maximum Power Cable length

 

Calculating Maximum Power Cable length

We calculate maximum power cable length on single phase AC supply:-

 

Lmax = (1000 X V X VD) / (2 X I X (Rcos ᶿ + Xsinᶿ ))

 

Where

 

Lmax = Maximum power cable length (m)

V = Maximum Permissible Voltage Supply (V)

VD = Voltage drop (%)

I = Starting Current (A)

R = Power Cable Resistance (Ω/m)

Cos ᶿ = Power Factor

X = Conductor inductive reactance (Ω/m)

ᶿ = Phase angle of load (°)

We already learned how to calculate Power Cable Resistance in article Power Cable Size &  Calculation of Voltage Drop.

  

Let we assume:-

 

Power factor (Cos ᶿ) = 1

Phase angle of load (ᶿ) = 90°

 

Lmax = (1000 X V X VD) / (2 X I X (R X 1 + Xsin90°))

 

We know that sin90° = 0, i.e.

 

Lmax = (1000 X V X VD) / (2 X I X (R + 0))

 

And we get final result-

 

Lmax = (1000 X V X VD) / (2 X I X R)

 

 

We calculate maximum power cable length on Three phase AC supply:-

 

Lmax = (1000 X V X VD) / (√3 X I X (Rcos ᶿ + Xsinᶿ))

 

Where

 

Lmax = Maximum power cable length (m)

V = Maximum Permissible Voltage Supply (V)

VD = Voltage drop (%)

I = Starting Current (A)

R = Power Cable Resistance (Ω/km)

Cos ᶿ = Power Factor

X = Conductor inductive reactance (Ω/km)

ᶿ = Phase angle of load (°)

 

Let we assume:-

 

Power factor (Cos ᶿ) = 1

Phase angle of load (ᶿ) = 90°

 

Same theory applicable here then we get result:-

 

Lmax = (1000 X V X VD) / (√3 X I X R)

 

 

We calculate maximum power cable length on DC supply:-

 

Lmax = (1000 X Vdc X VD) / (2 X I X R)

 

Lmax = Maximum power cable length (m)

Vdc = Voltage Supply (V)

VD = Voltage drop (%)

I = Starting Current (A)

R = Power Cable Resistance (Ω/km)

 

Example1:-

 

V = 230V

I = 25A

R = 5.9

Cos ᶿ = 1

ᶿ = 90°

Phase = 1ph

VD = 5%

Lmax = ?

 

Solution:-

 

We use formula:-

 

Lmax = (1000 X V X VD) / (2 X I X R)

 

Putting all value in formula:-

 

Lmax = (230 X 1000 X 5%) / (2 X 25 X 5.9)

 

Lmax = 11500 / 295

 

Lmax = 38.98m

 

We can use upto 38.98m of cable length in this parameter.

 

Example2:-

 

V = 440V

I = 120A

R = 0.495

Cos ᶿ = 1

ᶿ = 90°

Phase = 3ph

VD = 5%

Lmax = ?

 

Solution:-

 

We use formula:-

 

Lmax = (1000 X V X VD) / (√3 X I X R)

 

Putting all value in formula:-

 

Lmax = (1000 X 440 X 5%) / (√3 X 120 X 0.495)

 

Lmax = 22000 / 102.88

 

Lmax = 213.84m

 

We can use upto 213.84m of cable length in this parameter.

Power Cable Size

 

How to Calculate Power Cable Size?

 

Solution:-

 

Installed Current Ratings:

Ic = Ib x Kd

Where

Ic is the installed current rating.

Ib is the base current rating.

Kd are the product of all the derating factors.

Kd = Kamb x Kg

Where

Kamb is ambient temperature derating factor (assumed 0.94).

Kamb is grouping derating factor (assumed 0.85).

 

For Example:-

Base Current = 42A

Ambient temperature derating factor= 0.94

Grouping derating factor = 0.85

Installed current rating = ?

Answer:-

Ic = Ib x Kd

Where

Kd = Kamb x Kg

i.e.

Ic = Ib x Kamb x Kg

Ic = 42 x 0.94 x 0.85

Ic = 33.558A

Cable selection & coordination with protective devices:-

Ii <= Ip <= Ic

Where

Ii is full load current (A)

Ip is protective current rating (A)

Ic is the installed current rating (A)

 

 Now We Calculate Voltage Drop:-

We have two types of power supply: -

1.    AC Supply

2.    DC Supply

 Voltage Drop for AC Supply

 

Calculate Voltage drop for single phase DC supply:-

Vdp = (2 X I X Rc X L) / 1000

 

Where

I is the current in A.

Rc is the DC resistance of cable (ohm/m)

L is the cable length (m)

Now we will select cable size as per calculated resistance of cable in power cable datasheet which is highlighted in sky color and also will be checked install current rating. Always installed current rating must be less than cable current which are highlighted in yellow color. 

Otherwise we change resistance and calculate cable size again.

 

CU, PVC insulated, armoured cables			Al, PVC insulated, armoured cables
Resistance (Ohm/km)	Size (Sq. mm)	Current (A)	Resistance (Ohm/km)	Size (Sq. mm)	Current (A)
14.500	1.5	17	21.720	1.5	13
8.870	2.5	24	14.520	2.5	18
5.520	4	30	8.890	4	23
3.690	6	39	5.530	6	30
2.190	10	57	3.700	10	40
1.380	16	66	2.290	16	51
0.870	25	90	1.440	25	70
0.627	35	110	1.040	35	86
0.463	X50	135	0.770	X50	105
0.321	70	165	0.532	70	130
0.231	95	200	0.384	95	155
0.184	120	230	0.304	120	180
0.149	150	265	0.250	150	205
0.120	185	305	0.200	185	240
0.091	240	355	0.150	240	280
0.074	300	400	0.120	300	315
0.059	400	455	0.090	400	375
0.045	500	520	0.075	500	425
0.036	630	675	0.061	630	480

 

Al, XLPE insulated, armoured cables			CU, XLPE insulated, armoured cables
Resistance	Cable Size 3C	Current	Resistance	Size	Current
	X1.5			1.5
	X2.5			2.5
9.480	X4	31	5.900	4	40
5.900	X6	40	3.940	6	51
3.940	X10	53	2.340	10	70
2.440	X16	70	1.470	16	90
1.540	X25	95	0.930	25	122
1.110	X35	117	0.670	35	148
0.820	X50	140	0.495	X50	181
0.567	X70	176	0.343	70	230
0.410	X95	221	0.247	95	284
0.325	X120	258	0.196	120	330
0.265	X150	294	0.159	150	375
0.211	X185	339	0.127	185	434
0.162	X240	402	0.097	240	515
0.130	X300	461	0.077	300	588
0.102	X400	542	0.060	400	677
0.081	X500	624	0.048	500	750
0.065	X630	723	0.039	630	875

Table only for your reference.