l&s

(b) Consider next Ihe ease where the load is ntmlinear, while the stjtiree is linear and can be motJeled by a Thevenin-equivalenl sinusoidal voltage source and linear impedance Zfs). Again express the average power P as a sum of average powers, as in part (a). What can you say about the polarities ofthe /s in this case?

(c) The following Fourier series are measured:

16& A balanced three-phase wye-connected load is consiructed using a20 Q resistor in each phase. This load

is connected to a balanced three-phase wye-connected voltage source, whose fundamental vohage component is 380 Vrms line-to-line. In aJdition, each (line-lo-neulral) voltage source produces third and fifth harmonics. Each harmonic has amplitude 20 Vrms, and is in phase with the (line-to-netitrai) Itinda-mental.

(n) The ышше and load neutral points are connected, such that a fotir-wire system is obtained. Find ihe Ftjurier seiies ofthe line currents and the neutral current.

(b) The neutral connection is broken, such lhat a three-wire system is obtained. Find the Fourier series ofthe line currents. Also find the Fourier series oflhe voltage between the source and load neutral points.

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Line-Commutated Rectifiers

Conventional diode peak-iJeteetion rectifiers are inexpensive, reliable, and in widespread tise. Their shortcoraing.s are the high harmonic content of their ac line currents, and their low power factors. In this chapter, the basic operation and ac line current waveforms of several of the most common single-phase and three-phase diode rectitiers are summarized. Also introduced are phase-controlled three-phase rectifiers and inverters, and passive harmonic mitigation techniques. Several ofthe many references in this area are listed at the end of this chapter [1-15].

Rigorous analytical design of line-commutated rectifier and fiiter circuits is unfeasible for all but the simplest of circuits. Typical peak-detection rectifiers are numerically ill-conditioned, because small changes in the dc-side ripple voltage lead to large changes in the ac line current waveforms. Therefore, the discussions of this chapter are confined to mostly qualitative arguments, with the objective of giving the reader some insight into the physical operation of rectifier/filter circuits. Wavefomis, harmonic magnitudes, and power factors are best determined by measurement or computer simulation.

17.1 THE SINGLE-PHASE FULL-WAVE RECTIFIER

A single-phase full-wave rectifier, with uncontrolled tliode rectiliers, is shown in Fig, 17,1. The circuit includes a dc-side Z.-C filter. There are two conventional uses for this circuit. In the traditional full-wave rectifier, the output capacitor is large in value, and the dc otitput voltage v[t) has negligible ripple at the second hartnonic of the ac line frequency. Inductor L is most often small or absent. Additional small inductance may be in series with the ac source vjf). A second conventional use of this circuit is in the low-harmonic rectifiers discussed in the next chapter. In this case, the resistive load is replaced by a dc-dc converter that is controlled such that its power input port obeys Ohms law. For the puфoses of understanding the rectifier waveforms, the converter can be modeled by an effective resistance R, as in the cir-