May 2008
Intermediate to advanced
340 pages
9h 41m
English
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1.6 POWER IN SINGLE-PHASE CIRCUITS
In Section 1.3.3 (Balanced Three-phase Systems), we learned that the single-phase instantaneous power is a function of time and therefore not constant. In this section, we will examine the power concept of a single-phase circuit more thoroughly and we will determine the relations between the voltage and current phasors and the power.
1.6.1 Active and Reactive Power
The sinusoidal expressions for voltage and current of a general single-phase load, as shown in Figure 1.27 (a), are:
Figure 1.27 An inductive load split up into a resistor in parallel with an inductor.
θ the phase shift between the voltage and the current: ϕ positive for a current lagging the voltage and negative for a leading current.
The instantaneous power consumed by the impedance Z, amounts to:
The first term in Equation 1.66 (P[1 + cos(2ωt)]) describes an unidirectional component of the instantaneous power with an average value P, which is called the average power and is also addressed as real or active power. So:
P the active/real/average power [W]
cos(ϕ) the power factor. The cosine ...
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