Lecture02

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

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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 == = = ∠− = ∠−
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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
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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 + =
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This note was uploaded on 11/10/2011 for the course EEL 3216 taught by Professor Brooks during the Fall '08 term at FSU.

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

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