Cable Sizing for High Voltage Motor

Cable Sizing for High Voltage Motor
Minimum Size of Cable required to withstand short-circuit :

Minimum Cross Section Area of HV Cable = (If x √t)/k

Where,
Maximum Fault level at 6600 V - 457 MVA (Assumed)
If = 40 kA at 6.6kV
k = Material Constant = 0.094 (for aluminium cables)
t = Fault withstand time in sec. = 0.25 sec (Assumed)
Minimum Cross Section Area of HV Cable = (40 x √0.25)/0.094 = 212.76 mm2
Next available standard size is 240 mm2

Hence, minimum cross sectional area for HV cables is 240 sq. mm

Now, we have to check three parameters :
a)Able to withstand continuous current rating
b)Voltage Drop (During Normal Running Condition)
c)Voltage Drop (During Starting Condition)

a)Able to withstand continuous current rating :

Rating = 210 kW
Power Factor = 0.88
Efficiency = 93%

Rated current = 210 / (√3 x 6.6x 0.88 x 0.93) = 22.44 Amp

Required current rating of cable, after adjusting for derating factor (Derating factor is explained at bottom)
= 22.4/ 0.579 = 38.76 Amp

Continuous current rating of 3Cx240 sq mm, 6.35/11kV A2XFY cables is 326 Amp (Data is available from cable manufacturer catalogue) which is higher than the required current rating. Hence, we can use 1 Run of 3Cx240 sqmm A2XFY cable. Now, this cable size shall be checked for voltage drop during normal running and motor starting conditions as per following.

b)Voltage Drop (During Normal Running Condition) :

% V. D = (√3 x I x ( RcosØ + XsinØ ) /V sys )xL x 100/1000

Where,
L : Length of Cable in meters = 385 m (assumed)
cosØ : Power Factor of motor = 0.88 (assumed)
I : Rated Current = 22.44Amp
V sys : Rated Voltage = 6600 volts
R : Cable Resistance =0.162 Ω/km (Data from Cable manufacturer)
X : Cable Reactance = 0.072 Ω/km (Data from Cable manufacturer)

Substituting these values in above equation
% V.D = (√3 x 22.44 x (0.162 x 0.88 + 0.072 x 0.47/6600 ) x L x 100/1000
= 0.039
Thus, Voltage Drop is lower than 3% limit (%VD must be within at least 5%).

c)Voltage Drop (During Starting Condition) :

% V. D = (√3 x Ist x ( RcosØst + XsinØst ) /V sys )xL x 100/1000

Where,
L : Length of Cable in meters = 385
cosØst :Power Factor of motor during starting = 0.2 (assumed)
Ist : 5 x Rated Current = 5x22.44 = 112.2 Amp (normally startingcurrent for HT motor is 5 times)
V sys : Rated Voltage = 6600 volts
Substituting these values in above equation

% V.D = (√3 x 112.2 x ( 0.162 x 0.2 + 0.072 x 0.98) /6600 )x 385 x 100/1000
= 0.11 %

Thus, Voltage Drop is lower than 15% limit (practice)
Hence for 6.6kV, 210kW motor, 1 Run of 6.35/11kV, 3Cx240sq mm A2XFY cable shall be used.