PE Power reference

Core circuits and the formulas you'll reach for most on the PE Power exam.

Circuit diagrams

Series R–L circuit (AC source)

Three-phase wye (Y) connection

Resistive voltage divider

One-line: source · transformer · bus · load

Three-phase power

Real power

P = \sqrt{3}\,V_{LL} I_L \cos\theta

Reactive power

Q = \sqrt{3}\,V_{LL} I_L \sin\theta

Apparent power

S = \sqrt{3}\,V_{LL} I_L = \sqrt{P^2 + Q^2}

Power factor

pf = \cos\theta = \dfrac{P}{S}

Per-unit system

Base current

I_{base} = \dfrac{S_{base}}{\sqrt{3}\,V_{LL,base}}

Base impedance

Z_{base} = \dfrac{V_{LL,base}^2}{S_{base}}

Change of base

Z_{pu}^{new} = Z_{pu}^{old}\left(\dfrac{V_{old}}{V_{new}}\right)^2\dfrac{S_{new}}{S_{old}}

Rotating machines

Synchronous speed

n_s = \dfrac{120 f}{P}

Slip

s = \dfrac{n_s - n_r}{n_s}

Rotor frequency

f_r = s\,f

Transmission & faults

Approx. voltage drop

V_{drop} \approx I\,(R\cos\theta + X\sin\theta)

Surge impedance loading

SIL = \dfrac{V_{LL}^2}{Z_c}

Per-unit fault current

I_f = \dfrac{V_{pu}}{X_{pu}}

Power electronics

Full-wave avg. output

V_{dc} = \dfrac{2 V_m}{\pi}

Half-wave avg. output

V_{dc} = \dfrac{V_m}{\pi}

RMS of sinusoid

V_{rms} = \dfrac{V_m}{\sqrt{2}}