Calculate Size of Capacitor Bank

Electrical Load of

(1) 2 No’s of 120KW, 415V motor, 90% Efficiency, 0.8 P.F.
(2) 2 No’s of 150KW, 415V motor, 90% Efficiency, 0.8 P.F.
(3) 100KW, 415V Lighting Load. The targeted P.F. Of system is 0.98

Calculate Size of Discharge Resister for discharging of Capacitor Bank Discharge rate of capacitor is 55v in less than 1 minute. Also calculate reduction in KVAR Rating of capacitor if Capacitor bank is operated at frequency of 30Hz instead of 50Hz and if operating voltage is 390V instead of 415V

Calculation:

For Connection (1):

Total Load KW for Connection (1) =KW / Efficiency=(120×2) / 0.9=266.67KW
Total Load KVAR1= KW×([(√1-(Old P.F.)^2) / Old P.F.] - [(√1-(New P.F.)^2 / New P.F])

Total Load KVAR1=266.67×([(√1-(0.8)^2) / 0.8] - [(√1-(0.98)^2) / 0.98])

Total Load KVAR1=145.98 KVAR

OR

Total Load KVAR1= KW×(tanϕ1- tanϕ2) =266.67×(tan 36.87 - tan 11.48)

= 266.67×(0.75 - 0.203)

= 145.98KVAR

For Connection (2):

Total Load KW for Connection (2) =KW / Efficiency=(150×2) / 0.9=333.33KW
Total Load KVAR2= KW×([(√1-(Old P.F.)∧2) / Old P.F.] - [(√1-(New P.F.)∧2 / New P.F])

Total Load KVAR2=333.33×([(√1-(0.8)∧2) / 0.8] - [(√1-(0.98)∧2) / 0.98])

Total Load KVAR2=182.33 KVAR

Total Load KVAR2= KW×(tanϕ1- tanϕ2) =333.33×(tan 36.87 - tan 11.48)

= 333.33×(0.75 - 0.203)

= 182.33KVAR

For Connection (3):

Total Load KW for Connection (3) = KW = 100KW
Total Load KVAR3= KW×([(√1-(Old P.F.)∧2) / Old P.F.] - [(√1-(New P.F.)∧2 / New P.F])

Total Load KVAR3=100×([(√1-(0.8)∧2) / 0.8] - [(√1-(0.98)∧2) / 0.98])

Total Load KVAR3=54.7 KVAR

Total Load KVAR3= KW×(tanϕ1- tanϕ2) =100×(tan 36.87 - tan 11.48)

= 100×(0.75 - 0.203)

=54.7KVAR

Total KVAR=KVAR1+ KVAR2+KVAR3
Total KVAR=145.98+182.33+54.7
Total KVAR=383.01 KVAR

Size of Capacitor Bank

Size of Capacitor Bank=383.01 KVAR
Leading KVAR supplied by each Phase= KVAR/No of Phase
Leading KVAR supplied by each Phase =383.01/3

=127.67KVAR per Phase

Capacitor Charging Current (Ic) = (KVAR per Phase×1000)/Volt

Capacitor Charging Current (Ic )= (127.67×1000)/(415/√3)

Capacitor Charging Current (Ic) = 532.84 Amp

Capacitance of Capacitor = (Ic)/ 2πfVc

C = 532.842 ÷ (2×3.14×50×(415/√3))

= 7070.4 µF

Protection of Capacitor Bank

Size of HRC Fuse for Capacitor Bank Protection:

Size of the fuse = 165% to 200% of Capacitor Charging current.
Size of the fuse= 2×532.84 Amp
Size of the fuse= 1065.68 Amp

Size of Circuit Breaker for Capacitor Protection:

Size of the Circuit Breaker =135% to 150% of Capacitor Charging current.

Size of the Circuit Breaker=1.5×532.84 Amp

Size of the Circuit Breaker=799.26 Amp

Thermal relay setting between 1.3 and 1.5 of Capacitor Charging current.
Thermal relay setting of C.B. = 1.5×532.84 Amp
Thermal relay setting of C.B= 799.26 Amp

Magnetic relay setting between 5 and 10 of Capacitor Charging current.
Magnetic relay setting of C.B. = 10×532.84 Amp
Magnetic relay setting of C.B.= 5328.4 Amp

Sizing of cables for capacitor Connection:

Capacitors can withstand a permanent over current of 30% + tolerance of 10% on capacitor Current.
Cables size for Capacitor Connection= (1.3 + 1.1) x nominal capacitor Current
Cables size for Capacitor Connection = 2.4 × nominal capacitor Current
Cables size for Capacitor Connection= 2.4 × 532.84 Amp
Cables size for Capacitor Connection= 1278.816 Amp

Maximum size of discharge Resistor for Capacitor:
Capacitors will be discharge by discharging resistors.
After the capacitor is disconnected from the source of supply, discharge resistors are required for discharging each unit within 3 min to 75 V or less from initial nominal peak voltage (according to IEC-standard 60831). Discharge resistors have to be connected directly to the capacitors. There shall be no switch, fuse cut-out or any other isolating device between the capacitor unit and the discharge resistors.
Max. Discharge resistance Value (Star Connection) = Ct / Cn x Log (Un x√2/ Dv).
Max. Discharge resistance Value (Delta Connection) = Ct / 1/3×Cn×log(Un×√2/ Dv)

Where

Ct =Capacitor Discharge Time (sec)
Cn=Capacitance Farad
Un = Line Voltage
Dv=Capacitor Discharge voltage

Maximum Discharge resistance = 90/((7070.4/1000000) × log( 415×√2 /55)

Maximum Discharge resistance = 12.38 KΩ

Effect of Decreasing Voltage & Frequency on Rating of Capacitor:

The KVAR of capacitor will not be same if voltage applied to the capacitor and frequency changes
Reduction in KVAR size of Capacitor when operating 50 Hz unit at 40 Hz

Actual KVAR = Rated KVAR ×(Operating Frequency / Rated Frequency)
Actual KVAR = Rated KVAR ×(30/50)

Actual KVAR = 60% of Rated KVAR
Hence 383.01 KVAR Capacitor works as 60% × 383.01KVAR = 229.8KVAR

Reduction in KVAR size of Capacitor when operating 415V unit at 390V

Actual KVAR = Rated KVAR x (Operating voltage / Rated voltage)^2
Actual KVAR = Rated KVAR x (390/415)^2
Actual KVAR=88.3% of Rated KVAR
Hence 383.01 KVAR Capacitor works as 88.3% × 383.01KVAR = 338.19KVAR

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