Engineering
Three-phase AC power (kW, kVA, kVAR) & Power Factor capacitor sizing
Calculate balanced 3-phase Apparent Power (kVA), Real Power (kW = SQRT(3)*V*I*PF/1000), and capacitor bank kVAR required to raise lagging Power Factor.
Never forget SQRT(3) in 3-phase power—and size PF correction capacitors in kVAR!
For balanced sinusoidal three-phase conditions, apparent power is sqrt(3)*line-to-line RMS voltage*line RMS current. Real power multiplies that by displacement power factor. The supplied 480 V, 100 A and 0.8 give 83.14 kVA and 66.51 kW.
For a lagging inductive load at unchanged real power, the ideal compensation estimate is P*(tan(acos(PF1))-tan(acos(PF2))). This exercise requires 0<PF1<=PF2<=1. It does not cover leading loads, distortion power factor or unbalanced systems. Tariff penalties vary; no universal penalty threshold is assumed.
| 3-Phase Feeder Metric (480 V_LL, 100 A, PF = 0.80 -> 0.95) | Formula | Result |
|---|---|---|
| Apparent Power (S in kVA) | SQRT(3) * 480 * 100 / 1000 | 83.14 kVA |
| Real Working Power (P in kW) | SQRT(3) * 480 * 100 * 0.80 / 1000 | 66.51 kW |
| Capacitor Bank to Reach 0.95 PF | kW * (TAN(ACOS(0.80)) - TAN(ACOS(0.95))) | 28.02 kVAR |
Balanced 3-phase Real Power (kW)
A2=LineVoltage_V (480), B2=LineCurrent_A (100), C2=CurrentPF (0.80).
=IF(OR(COUNT(A2:C2)<>3,A2<=0,B2<0,C2<=0,C2>1),"Invalid inputs",ROUND(SQRT(3) * A2 * B2 * C2 / 1000, 2))Capacitor bank kVAR needed to correct Power Factor from PF1 to PF2
D2 holds Target Power Factor (0.95); TAN(ACOS(PF)) gives Q/P reactive-to-real ratio.
This estimates reactive power only, not capacitance, wiring or an installable bank specification. Equipment selection requires voltage/frequency, harmonics, resonance, switching and protection assessment. Unity target is a mathematical endpoint, not a universal installation recommendation.
=IF(OR(COUNT(A2:D2)<>4,A2<=0,B2<0,C2<=0,C2>1,D2<C2,D2>1),"Invalid inputs",LET(kw, SQRT(3) * A2 * B2 * C2 / 1000, ROUND(kw * (TAN(ACOS(C2)) - TAN(ACOS(D2))), 2)))Try the example
Use the original values or change them to test your understanding.