Electrical Formulas

AC Single-Phase

All quantities r.m.s. values:

V = I Z

Total or apparent power in VA = VI= I²Z = V²/Z

Active power in watts, W =VIcos ϕ

Reactive power in VAr = VIsin ϕ

AC Three-Phase

(Assuming Balanced Symmetrical Waveform)

All quantities r.m.s values:

V_l = Line-to-line voltage

V_p = Phase voltage (line-to-neutral)

I_l = line current (wye)

I_p = Phase current (delta)

In a WYE connected circuit, V_p = V_l /√3, V_l =√3Vp, I_l = I_p

In a DELTA connected circuit: I_p = I_l /√3, I_l =√3 I_p V_l =V_p

Total of apparent power in VA = _3 V_l I_l

Active power in watts ,W = _3 V_l I_l cos ϕ

Reactive power in VAr = √3 V_l I_l sin ϕ

Power factor (pf) = cos ϕ

                        = Active power / Apparent power

                        = W / VAr

Three-Phase Induction Motors

All quantities r.m.s values:

kW_mech = horsepower x 0.746

kW_elec = √3 V_l I_l cos ϕ at rated speed and load

where V_l = supply voltage I_l = rated full load current

cos ϕ = rated full load power factor

Efficiency, = (kW_mech / kW_elec) x 100 per cent

Phase current I_p = I_l for wye connection

I_p = I_l / √3 for delta connection

Loads (phase values)

Resistance R, measured in Ohms (no energy storage)

Inductive reactance, XL = ωL = 2ΠƒL Ohms (stores energy)

Where ƒ = frequency (Hz), L = Inductance (H)

Capacitative reactance, XC = 1/ (ωC) = 1/(2ΠƒC)

Where ƒ = frequency (Hz), C = Capacitance (F)

Impedance

Impedance is the algebraic sum of the separate load

values thus:

Z = √(R² + X_L²) or √(R² + X_C²)

If R, X_L and X_C are present in series in the same circuit

then X_L and X_C may be summated, treating X_C as negative,

thus

Z = √(R² + (X_L - X_C)²)

Electrical Formulae

Ohms Law

Amperes = Volts/Ohms  or ohms =Volts/Amperes

or Volts = Amperes x Ohms

Power in DC Circuits

Horsepower = ( Volts x Amperes )/746

Watts = Volts x Amperes

Kilowatts =  (Volts x Amperes)/1,000

Kilowatts-Hours = (Volts x Amperes x Hours)/1,000

Power in AC Circuits

Kilovolt-Amperes (KVA):

kVA (1Ø) = (Volts x Amperes)/1,000

kVA (3Ø) = (Volts x Amperes x 1.73)/1,000

Kilowatts (Kw)

kW (1Ø) = (Volts x Amperes x Power Factor)/1,000

kW (3Ø) = (Volts x Amperes x Power Factor x 1.73)/1,000

Power Factor = Kilowatts/(Kilovolts x Amperes)

Other Useful Formulae

Three-Phase (3Ø) Circuits

HP = (E x I x 3 x Eff x PF)/746

Motor Amps = (HP x 746)/(E x √3 x Eff x PF)

Motor Amps = (kVA x 1000)/(√3 x E)

Motor Amps = (kW x 1000)/(√3 x E x PF)

Power Factor = (kW x 1000)/(E x I x √3)

Kilowatt Hours = (E x I x Hours x √3 x PF)/1000

Power (Watts) = E x I x √3 x PF