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power is a function only of the fundamental frequency quantities In the nonsinusoidal case, the computation of the active power must include contributions from all harmonic components; thus it is the sum of active power at each harmonic Furthermore, because the voltage distortion is generally very low on power systems (less than 5 percent), Eq (56) is a good approximation regardless of how distorted the current is This approximation cannot be applied when computing the apparent and reactive power These two quantities are greatly influenced by the distortion The apparent power S is a measure of the potential impact of the load on the thermal capability of the system It is proportional to the rms of the distorted current, and its computation is straightforward, although slightly more complicated than the sinusoidal case Also, many current probes can now directly report the true rms value of a distorted waveform The reactive power is a type of power that does no real work and is generally associated with reactive elements (inductors and capacitors) For example, the inductance of a load such as a motor causes the load current to lag behind the voltage Power appearing across the inductance sloshes back and forth between the inductance itself and the power system source, producing no net work For this reason it is called imaginary or reactive power since no power is dissipated or expended It is expressed in units of vars In the sinusoidal case, the reactive power is simply defined as Q S sin V1I1 sin 2 V1rms I1rms sin (57)
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which is the portion of power in quadrature with the active power shown in Eq (56) Figure 54 summarizes the relationship between P, Q, and S in sinusoidal condition There is some disagreement among harmonics analysts on how to define Q in the presence of harmonic distortion If it were not for the fact that many utilities measure Q and compute demand billing from the power factor computed by Q, it might be a moot point It is more important to determine P and S; P defines how much active power is being consumed, while S defines the capacity of the power system required to deliver P Q is not actually very useful by itself However, Q1, the traditional reactive power component at fundamental frequency, may be used to size shunt capacitors The reactive power when distortion is present has another interesting peculiarity In fact, it may not be appropriate to call it reactive power The concept of var flow in the power system is deeply ingrained in the minds of most power engineers What many do not realize is that this concept is valid only in the sinusoidal steady state When dis-
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Figure 54 Relationship between
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P, Q, and S in sinusoidal condition P
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tortion is present, the component of S that remains after P is taken out is not conserved that is, it does not sum to zero at a node Power quantities are presumed to flow around the system in a conservative manner This does not imply that P is not conserved or that current is not conserved because the conservation of energy and Kirchoff s current laws are still applicable for any waveform The reactive components actually sum in quadrature (square root of the sum of the squares) This has prompted some analysts to propose that Q be used to denote the reactive components that are conserved and introduce a new quantity for the components that are not Many call this quantity D, for distortion power or, simply, distortion voltamperes It has units of voltamperes, but it may not be strictly appropriate to refer to this quantity as power, because it does not flow through the system as power is assumed to do In this concept, Q consists of the sum of the traditional reactive power values at each frequency D represents all cross products of voltage and current at different frequencies, which yield no average power P, Q, D, and S are related as follows, using the definitions for S and P previously given in Eqs (51) and (55) as a starting point: S Q
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