{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Lecture02

# Lecture02 - Electric Power single-phase(1~ systems One...

This preview shows pages 1–4. Sign up to view the full content.

Page 1 Fundamentals of Power Systems Lecture 2 1 Electric Power z single-phase (1~) systems ± One source ± Two energy-carrying wires ± Pulsating instantaneous power (2f) z three-phase (3~) systems ± Three sources, 120° phase shifted Fundamentals of Power Systems Lecture 2 2 φ P V I V I cos Single Phase Power ( ) ( ) ( ) () ( ) ( ) cos cos mm pt vt it V t I t ω ωφ =⋅ = ⋅− Definition: t v, i, p Lagging, for φ > 0 I Z = |Z| ∠ φ V 0 V V I ZZ V I Z == = = ∠− = ∠−

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Page 2 Fundamentals of Power Systems Lecture 2 3 Instantaneous and Average Power ( ) ( ) [ ] β α + + = cos cos cos cos 2 1 trigonometric identity: () [] φ ω + = t I V t p m m 2 cos cos 2 the instantaneous power equation: ( ) t 2 cos the average of over a cycle is zero the average power over one cycle: cos 2 1 m m I V P = Fundamentals of Power Systems Lecture 2 4 Average Power from RMS Values The average power in terms of rms : cos rms rms I V P = 2 0 11 ()d 2 T rms m Vv t t V T == for ( ) ( ) sin m vt V t = Root mean square (rms) of an arbitrarily (periodic) AC waveform delivers the same power to a resistor as the corresponding DC quantity. Notation convention (this lecture, not in general): Voltage and currents given in rms if not stated otherwise. e.g. 208 V -30° means V m = 2·208 = 294 V pk
Page 3 Fundamentals of Power Systems Lecture 2 5 Power Factor () φ cos rms rms I V P = power factor I I sin V I cos I I sin V I cos Lagging Power Factor Leading Power Factor Load behaves like R || j ω L R || 1/j ω C Fundamentals of Power Systems Lecture 2 6 Complex Power γ =∠ = ∠− VV II General case: Positive Angle φ : Lagging PF Negative Angle φ : Leading PF sin cos * I V j I V S I V I V S + =

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 12

Lecture02 - Electric Power single-phase(1~ systems One...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online