3: Polyphase Networks
- Page ID
- 54441
\( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)
\( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)
\( \newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\)
( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\)
\( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\)
\( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\)
\( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\)
\( \newcommand{\Span}{\mathrm{span}}\)
\( \newcommand{\id}{\mathrm{id}}\)
\( \newcommand{\Span}{\mathrm{span}}\)
\( \newcommand{\kernel}{\mathrm{null}\,}\)
\( \newcommand{\range}{\mathrm{range}\,}\)
\( \newcommand{\RealPart}{\mathrm{Re}}\)
\( \newcommand{\ImaginaryPart}{\mathrm{Im}}\)
\( \newcommand{\Argument}{\mathrm{Arg}}\)
\( \newcommand{\norm}[1]{\| #1 \|}\)
\( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\)
\( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\AA}{\unicode[.8,0]{x212B}}\)
\( \newcommand{\vectorA}[1]{\vec{#1}} % arrow\)
\( \newcommand{\vectorAt}[1]{\vec{\text{#1}}} % arrow\)
\( \newcommand{\vectorB}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)
\( \newcommand{\vectorC}[1]{\textbf{#1}} \)
\( \newcommand{\vectorD}[1]{\overrightarrow{#1}} \)
\( \newcommand{\vectorDt}[1]{\overrightarrow{\text{#1}}} \)
\( \newcommand{\vectE}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash{\mathbf {#1}}}} \)
\( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)
\( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)
Most electric power applications employ three phases. That is, three separate power carrying circuits, with voltages and currents staggered symmetrically in time are used. Two major reasons for the use of three phase power are economical use of conductors and nearly constant power flow.
Systems with more than one phase are generally termed polyphase. Three phase systems are the most common, but there are situations in which a different number of phases may be used. Two phase systems have a simplicity that makes them useful for teaching vehicles and for certain servomechanisms. This is why two phase machines show up in laboratories and textbooks. Systems with a relatively large number of phases are used for certain specialized applications such as controlled rectifiers for aluminum smelters. Six phase systems have been proposed for very high power transmission applications.
Polyphase systems are qualitatively different from single phase systems. In some sense, polyphase systems are more complex, but often much easier to analyze. This little paradox will become obvious during the discussion of electric machines. It is interesting to note that physical conversion between polyphase systems of different phase number is always possible.
This chapter starts with an elementary discussion of polyphase networks and demonstrates some of their basic features. It ends with a short discussion of per-unit systems and power system representation.
- 3.1: Two Phases
- The two-phase system is the simplest of all polyphase systems to describe.
- 3.6: Polyphase Lines and Single-Phase Equivalents
- By now, one might suspect that a balanced polyphase system may be regarded simply as three single-phase systems, even though the three phases are physically interconnected. This feeling is reinforced by the equivalence between wye and delta connected sources and impedances. One more step is required to show that single phase equivalence is indeed useful, and this concerns situations in which the phases have mutual coupling.
- 3.7: Introduction To Per-Unit Systems
- Strictly speaking, per-unit systems are nothing more than normalizations of voltage, current, impedance and power. These normalizations of system parameters because they provide simplifications in many network calculations. As we will discover, while certain ordinary parameters have very wide ranges of value, the equivalent per-unit parameters fall in a much narrower range. This helps in understanding how certain types of system behave.