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Unformatted text preview: 11ECE 320 Energy Conversion and Power Electronics Spring 2009 Instructor: Tim Hogan Chapter 1: Introduction and Three Phase Power 1.1 Review of Basic Circuit AnalysisDefinitions: Node Electrical junction between two or more devices. Loop Closed path formed by tracing through an ordered sequence of nodes without passing through any node more than once. Element Constraints: Ohms Law iRv=Capacitor EquationdtdvCi=Inductor Equation dtdiLv=Connection Constraints: Kirchhoffs Current Law The algebraic sum of currents entering a node is zero at every instant in time. =Nodeki(1.1) Kirchhoffs Voltage Law The algebraic Sum of all voltages around a loop is zero at every instant in time. =Loopkv(1.2) Passive Sign Convention: Whenever the reference direction of current into a two terminal device is in the direction of the reference voltage drop across the device, then the power absorbed (or dissipated) is positive. Figure 1. Circuit element and passive sign convention. +_ vi12( ) ( ) ( )tvtitp=(1.3) When the above convention is used, p(t) > 0 for absorbed power, and p(t) < 0 for delivered power. Time Varying SignalsAlthough a number of exceptions can be found throughout the world, the predominance of electric power follows 60Hz or 50Hz frequencies. North America, part of Japan, and ships at sea use 60Hz while most of the rest of the world uses 50Hz. The historical reasons for these two frequencies stem from the differences in lighting (filaments in vacuum or filaments in a gas atmosphere). The lower frequencies caused an annoying flicker for lights having filaments in a gas atmosphere, and thus a higher frequency was adopted in part of the world that initially used such lighting. While not strictly adhered to within your textbook and these notes, an attempt to use the following conventions has been made. Scalar time varying signals (examples): ( )tvvsinmax=(V) ( ) ( )tvtvcosmax=(V) ( )tv=377sin185(kV) ( ) ( )titi=100cosmax(A) Spatial vectors (bold or arrow overhead or line overhead): For Fror BIf necessary, unit vectors will be used, (for example): zByBxBzyx++=BThese unit vectors should not be confused with phasors below Phasors (phasor representation of a time varying signal): A phasor can be represented as a complex number with real and imaginary components such that a phasor of magnitude (or length) Rthat is at a phase angle of with respect to the xaxis (the Real axis) can be written as ( ) ( )sincosjRReRjyxRj+==+=where Eulers formula ( ) ( )sincosjej+=was used for the last representation. Note that Ris the magnitude andthe phase of the phasor, and 22yxR+=and =xyarctan. The phasor can be shown graphically in Figure 2. 13tRealImaginaryRxyFigure 2. Phasor of magnitude Rand phase ....
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This note was uploaded on 05/30/2009 for the course ECE ECE 320 taught by Professor Timhogan during the Spring '09 term at Michigan State University.
 Spring '09
 TimHogan

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