3PhaseSystem

# 3PhaseSystem - ECSE 486B Power Laboratory Review of...

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ECSE 486B Power Laboratory Review of Three-Phase Circuits 1 Balanced Three-phase Circuits 1.1 Introduction The use of polyphase circuits, mainly three-phase circuits, is quite common in industry and in electrical energy production and transmission. The preference given to three-phase circuits over single-phase circuits comes from the fact that the instantaneous power is constant and independent of time in balanced three-phase circuits while it is pulsating in single-phase circuits. In addition, for rotating machines, and more speciﬁcally for three-phase induction machines, their operating principle is more simple than that of a single-phase machine. The manufacturing and utilization cost is also less, since the power in a three-phase context is constant. Moreover, the magnetic circuit of a single-phase machine can only be used to a fraction of its full capacity 1 . In this unit, we will look mainly at three-phase circuits because of their practical importance and widespread use. However, be aware that there exist other types of polyphase circuits. For instance, the ﬁrst polyphase circuits were 2-phase circuits with voltages phasors in quadrature with respect to each other ( i.e. 90 out of phase). There exist practical applications which use circuits with up to 36 phases. 1.2 Deﬁnitions and Generalities 1. A three-phase circuit is balanced when the source and the load are both balanced. 2. A three-phase source is balanced when the three generated voltages have the same amplitude and are phase shifted by 120 one with respect to each other. 3. A three-phase load is balanced when the impedances (admittances) of each of the three phases is equal in magnitude and angle. 4. It results that in a balanced three-phase circuit, the three line currents have the same amplitude and are phase shifted by 120 one with respect to each other. A three-phase machine is essentially made up of three windings that are electrically independent. We then have three pairs of wires, that is six wires corresponding to the ends a , a 0 , b , b 0 , c and c 0 (Figure 1). We can represent the three voltages as phasors (Figure 2). For now, the only relationship existing between these phasors is their respective orientation and frequency, which is the same for all three. The way by which these phasors are ordered with respect to a given reference corresponds to the phase sequence. 1.3 Y (Star)-Connection Instead of taking the six wires from the source to the load, we can connect together the points a 0 , b 0 and c 0 , thus forming a common node, n ; this permits a reduction in the number of wires from six to four. A line wire or conductor is one of the wires connected to either points a , b or c , while the neutral conductor is connected to n . Through this connection, the three sources become electrically linked; we represent them by the phasors

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## This note was uploaded on 01/10/2011 for the course ECSE 486 taught by Professor Gezajoos during the Winter '10 term at McGill.

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3PhaseSystem - ECSE 486B Power Laboratory Review of...

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