《single_and_three_phase_circuits》.pdf

The HK Polytechnic University Phasor, Single and Three Phase Circuits ✬ ✩ 1 Phasors • Power systems mostly operate in the sinusoidal steady state (SSS). • Currents and voltages are represented as phasors as it is difficult to carry out calculation using time domain waveform e.g. multiplication, division, etc. • Consider a sinusoidal waveform : x(t) = Xmax cos(ωt + θ) which has a maximum value Xmax and a phase angle θ when referenced to cos(ωt). 1 1 T 2 root-mean-square (rms) value : X = x(t) dt T 0 Xmax √ or called effective value = 2 2π where T = is the period of the signal and the fraquency f and the ω 1 2π angular speed ω are f = and ω = 2πf = , respectively. ✫ T T ✪ ✬ ✩ 2 Phasor Representation – Complex Notation • Phasor: represent x(t) as a vector X in the complex plane • Vector X is a phasor Im X = Xejθ (exponential form) X = X/θ (polar form) = X cos θ + jX sin θ (rectangular form) θ