EEE 3230 POWER SYSTEM ANALYSIS 8 Lecture 8: AC Power Analysis Sezai Taskin, Ph.D. sezai.taskin@cbu.edu.tr

8 AC Power Analysis One of the most important parts of circuit analysis is to calculate either power delivered or power absorbed. Instantaneous Power

8 AC Power Analysis The first term is not a function of time, is constant and depends of the phase difference between voltage and current; and the second term is a sinusoidal function which has a cyclic variation at twice the applied frequency.

8 AC Power Analysis

8 AC Power Analysis The first term is not a function of time, is constant and depends of the phase difference between voltage and current; and the second term is a sinusoidal function which has a cyclic variation at twice the applied frequency.

8 Average Power The instantaneous power changes over time so it is difficult to measure. The average power instead is more convenient to measure The average value is denoted by the capital letter P, it is not a function of time and its dimensions are in watts. Substituting the instantaneous power for a sinusoidal steady state into the average power equation gives

8 Average Power Since the first term is a constant, independent of t, the average value must be that constant itself. The second term is a cosine function whose average value over a period is zero. Thus,

8 Average Power Since the first term is a constant, independent of t, the average value must be that constant itself. The second term is a cosine function whose average value over a period is zero. Thus,

8 Average Power Since the first term is a constant, independent of t, the average value must be that constant itself. The second term is a cosine function whose average value over a period is zero. Thus,

8 Average Power Consider two special cases. When θv = θi the circuit is purely resistive meaning that a resistive load absorbs power at all times And when θv – θi = ±90° the circuit is purely reactive meaning that an inductive or capacitive load absorbs no average power at all

Effective Values or RMS Values 8 Effective Values or RMS Values The RMS value for any periodic function x(t) is given by Let us select the sinusoidal voltage

Apparent Power and Power Factor 8 Apparent Power and Power Factor This expression involves a new term called apparent power It is measured in volt‐amperes [VA] The ratio of the average power to the apparent power is called the power factor (PF) so it is the cosine of the phase difference between voltage and current. For a low power factor (≈0) a load draws more current than for a high power factor (≈1) with the same load so the utility company may charge more to a costumer with a low power factor.

8 Complex Power For the power to become a complex quantity an imaginary term is added, the reactive power. The complex power became important because it contains all the information pertaining to the power delivered to a given load. While P is the actual power dissipated by the load, Q is a measure of the energy exchange between the reactive components of the load and the source.

Power triangle with different reactive powers 8 Power triangle with different reactive powers