Lecture 3 T Line AC Model

Lecture 3 T Line AC Model - Lecture3...

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Lecture 3: Transmission AC Model 1 Objective: Introduce AC model ayt th d. CH. 13, CH. 11 7 th d. Hayt 6 ed. CH. 13, CH. 11 7 ed. 1 McGill ECSE 352 Fall 2011 D. Davis

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C Steady State AC Steady State the case of AC steady state behaviour it is In the case of AC steady state behaviour it is common practice to use phasors. hasors present sinusoids as complex Phasors represent sinusoids as complex numbers in polar form (i.e. magnitude and hase where the phase is the angle between phase where the phase is the angle between the complex vector and the real axis). The complex vector and the polar form are related: ܣ ൅ ݆ܤൌ ܣ 2 ൅ܤ 2 ݁ ݆ቂݐܽ݊ െ1 ܤ ܣ ቁቃ McGill ECSE 352 Fall 2011 D. Davis 2
C Steady State AC Steady State Phasors represent a frequency domain model, (the argument of the phase contains frequency information), while the source is often a time domain function. In order to switch between time (sine or cosine function) and frequency (polar form) domains, the llowing method is used. following method is used. To convert from time to frequency (phasor) the sinusoid magnitude is made into the phasor agnitude The phase information of the amplitude as magnitude. The phase information of the amplitude as well as the argument of the cosine is made into the argument of the exponential. McGill ECSE 352 Fall 2011 D. Davis 3

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C Steady State AC Steady State convert back the al art of the hasor To convert back, the real part of the phasor will provide the solution if the source function as a sine nd the aginary art of the was a cosine and the imaginary part of the phasor will provide the solution if the source nction was a ne function was a sine . The derivative in time domain becomes a mplex product in frequency domain complex product in frequency domain. ݀൫݁ ݆߱ݐ ݀ݐ ՞݆߱ McGill ECSE 352 Fall 2011 D. Davis 4
C Steady State AC Steady State e general solution to the AC steady state The general solution to the AC steady state behaviour will take the form: ܸ ݖ,ݐ ൌܸ ݖ ݁ ݆߱ݐ ൌܸ ݁ ߛݖ ݁ This separates the amplitude information Vo om the position (z) and time (t) parameters. ݋ from the position (z) and time (t) parameters. The gamma coefficient is the propagation nstant and is a complex quantity constant and is a complex quantity The time derivative will produce a j ω product hasor otation. in phasor notation. McGill ECSE 352 Fall 2011 D. Davis 5

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C Steady State AC Steady State e position derivative will produce a product The position derivative will produce a product of γ .
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Lecture 3 T Line AC Model - Lecture3...

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