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What the capacitor Current formula?, For 1 KVAr how amps
its required? for using the KVAr for boosting the PF Design
Calculation.( Eg: for 30 KVAr required how many KW?)
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Answer Posted / muhammad umar
Calculate Size of Capacitor Bank / Annual Saving & Payback Period
APRIL 1, 2014 9 COMMENTS
Calculate Size of Capacitor Bank Annual Saving in Bills and Payback Period for Capacitor Bank.
Electrical Load of (1) 2 No’s of 18.5KW,415V motor ,90% efficiency,0.82 Power Factor ,(2) 2 No’s of 7.5KW,415V motor ,90% efficiency,0.82 Power Factor,(3) 10KW ,415V Lighting Load. The Targeted Power Factor for System is 0.98.
Electrical Load is connected 24 Hours, Electricity Charge is 100Rs/KVA and 10Rs/KW.
Calculate size of Discharge Resistor for discharging of capacitor Bank. Discharge rate of Capacitor is 50v in less than 1 minute.
Also Calculate reduction in KVAR rating of Capacitor if Capacitor Bank is operated at frequency of 40Hz instead of 50Hz and If Operating Voltage 400V instead of 415V.
Capacitor is connected in star Connection, Capacitor voltage 415V, Capacitor Cost is 60Rs/Kvar. Annual Deprecation Cost of Capacitor is 12%.
Calculation:
For Connection (1):
Total Load KW for Connection(1) =Kw / Efficiency=(18.5×2) / 90%=41.1KW
Total Load KVA (old) for Connection(1)= KW /Old Power Factor= 41.1 /0.82=50.1 KVA
Total Load KVA (new) for Connection(1)= KW /New Power Factor= 41.1 /0.98= 41.9KVA
Total Load KVAR= KWX([(√1-(old p.f)2) / old p.f]- [(√1-(New p.f)2) / New p.f])
Total Load KVAR1=41.1x([(√1-(0.82)2) / 0.82]- [(√1-(0.98)2) / 0.98])
Total Load KVAR1=20.35 KVAR
OR
tanǾ1=Arcos(0.82)=0.69
tanǾ2=Arcos(0.98)=0.20
Total Load KVAR1= KWX (tanǾ1- tanǾ2) =41.1(0.69-0.20)=20.35KVAR
For Connection (2):
Total Load KW for Connection(2) =Kw / Efficiency=(7.5×2) / 90%=16.66KW
Total Load KVA (old) for Connection(1)= KW /Old Power Factor= 16.66 /0.83=20.08 KVA
Total Load KVA (new) for Connection(1)= KW /New Power Factor= 16.66 /0.98= 17.01KVA
Total Load KVAR2= KWX([(√1-(old p.f)2) / old p.f]- [(√1-(New p.f)2) / New p.f])
Total Load KVAR2=20.35x([(√1-(0.83)2) / 0.83]- [(√1-(0.98)2) / 0.98])
Total Load KVAR2=7.82 KVAR
For Connection (3):
Total Load KW for Connection(3) =Kw =10KW
Total Load KVA (old) for Connection(1)= KW /Old Power Factor= 10/0.85=11.76 KVA
Total Load KVA (new) for Connection(1)= KW /New Power Factor= 10 /0.98= 10.20KVA
Total Load KVAR3= KWX([(√1-(old p.f)2) / old p.f]- [(√1-(New p.f)2) / New p.f])
Total Load KVAR3=20.35x([(√1-(0.85)2) / 0.85]- [(√1-(0.98)2) / 0.98])
Total Load KVAR1=4.17 KVAR
Total KVAR=KVAR1+ KVAR2+KVAR3
Total KVAR=20.35+7.82+4.17
Total KVAR=32 Kvar
Size of Capacitor Bank:
Site of Capacitor Bank=32 Kvar.
Leading KVAR supplied by each Phase= Kvar/No of Phase
Leading KVAR supplied by each Phase =32/3=10.8Kvar/Phase
Capacitor Charging Current (Ic)= (Kvar/Phase x1000)/Volt
Capacitor Charging Current (Ic)= (10.8×1000)/(415/√3)
Capacitor Charging Current (Ic)=44.9Amp
Capacitance of Capacitor = Capacitor Charging Current (Ic)/ Xc
Xc=2 x 3.14 x f x v=2×3.14x50x(415/√3)=75362
Capacitance of Capacitor=44.9/75362= 5.96µF
Required 3 No’s of 10.8 Kvar Capacitors and
Total Size of Capacitor Bank is 32Kvar
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=2×44.9Amp
Size of the fuse=90Amp
Size of Circuit Breaker for Capacitor Protection:
Size of the Circuit Breaker =135% to 150% of Capacitor Charging current.
Size of the Circuit Breaker=1.5×44.9Amp
Size of the Circuit Breaker=67Amp
Thermal relay setting between 1.3 and 1.5of Capacitor Charging current.
Thermal relay setting of C.B=1.5×44.9 Amp
Thermal relay setting of C.B=67 Amp
Magnetic relay setting between 5 and 10 of Capacitor Charging current.
Magnetic relay setting of C.B=10×44.9Amp
Magnetic relay setting of C.B=449Amp
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 x1.1 x nominal capacitor Current
Cables size for Capacitor Connection = 1.43 x nominal capacitor Current
Cables size for Capacitor Connection=1.43×44.9Amp
Cables size for Capacitor Connection=64 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 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 / 1/3xCn x Log (Un x√2/ Dv)
Where Ct =Capacitor Discharge Time (sec)
Cn=Capacitance Farad.
Un = Line Voltage
Dv=Capacitor Discharge voltage.
Maximum Discharge resistance =60 / ((5.96/1000000)x log ( 415x√2 /50)
Maximum Discharge resistance=4087 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
Reduced in Kvar size of Capacitor when operating 50 Hz unit at 40 Hz
Actual KVAR = Rated KVAR x(Operating Frequency / Rated Frequency)
Actual KVAR = Rated KVAR x(40/50)
Actual KVAR = 80% of Rated KVAR
Hence 32 Kvar Capacitor works as 80%x32Kvar= 26.6Kvar
Reduced in Kvar size of Capacitor when operating 415V unit at 400V
Actual KVAR = Rated KVAR x(Operating voltage / Rated voltage)^2
Actual KVAR = Rated KVAR x(400/415)^2
Actual KVAR=93% of Rated KVAR
Hence 32 Kvar Capacitor works as 93%x32Kvar= 23.0Kvar
Annual Saving and Pay Back Period
Before Power Factor Correction:
Total electrical load KVA (old)= KVA1+KVA2+KVA3
Total electrical load= 50.1+20.08+11.76
Total electrical load=82 KVA
Total electrical Load KW=kW1+KW2+KW3
Total electrical Load KW=37+15+10
Total electrical Load KW =62kw
Load Current=KVA/V=80×1000/(415/1.732)
Load Current=114.1 Amp
KVA Demand Charge=KVA X Charge
KVA Demand Charge=82x60Rs
KVA Demand Charge=8198 Rs
Annual Unit Consumption=KWx Daily usesx365
Annual Unit Consumption=62x24x365 =543120 Kwh
Annual charges =543120×10=5431200 Rs
Total Annual Cost= 8198+5431200
Total Annual Cost before Power Factor Correction= 5439398 Rs
After Power Factor Correction:
Total electrical load KVA (new)= KVA1+KVA2+KVA3
Total electrical load= 41.95+17.01+10.20
Total electrical load=69 KVA
Total electrical Load KW=kW1+KW2+KW3
Total electrical Load KW=37+15+10
Total electrical Load KW =62kw
Load Current=KVA/V=69×1000/(415/1.732)
Load Current=96.2 Amp
KVA Demand Charge=KVA X Charge
KVA Demand Charge=69x60Rs =6916 Rs————-(1)
Annual Unit Consumption=KWx Daily usesx365
Annual Unit Consumption=62x24x365 =543120 Kwh
Annual charges =543120×10=5431200 Rs—————–(2)
Capital Cost of capacitor= Kvar x Capacitor cost/Kvar = 82 x 60= 4919 Rs—(3)
Annual Interest and Deprecation Cost =4919 x 12%=590 Rs—–(4)
Total Annual Cost= 6916+5431200+4919+590
Total Annual Cost After Power Factor Correction =5438706 Rs
Pay Back Period:
Total Annual Cost before Power Factor Correction= 5439398 Rs
Total Annual Cost After Power Factor Correction =5438706 Rs
Annual Saving= 5439398-5438706 Rs
Annual Saving= 692 Rs
Payback Period= Capital Cost of Capacitor / Annual Saving
Payback Period= 4912 / 692
Payback Period = 7.1 Years
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