9 Power transmission and transmission losses

9 Power transmission and transmission losses - Lecture 7...

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Lecture 7 Power transfer and transmission losses. From previous lectures we have seen that for a transmission line containing only a series inductance as in Figure 1 the equations for the sending and receiving power are, Figure 1 - Lossless transmission line () 2 2 sin cos cos sr rs ss r s r r VV PP X V Q X V Q X δ == = −+ = Since the line is lossless (R=0) hence the real power loss P loss = 0. 22 0 2c o s 0 loss s r s r loss s r P V V QQ Q X =−= +− Consider now the lossy line of Figure 2 Figure 2 - Lossy transmission line
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Typically R < X, 20% R X . The equation for the sending complex power is () * ** * 2 22 s rs s s r s ss s j r s V V VV SV IV Rj X X V e R j X S R X δ  −− == =  +−  −+ = + Substituting j R jX R X e ψ += + , 1 tan X R = , then 2 2 jj r r s V ee Ve VVe S RX δψ + ++ Then the real power is { } Re s s P S = 2 cos cos r s V P =− + And substituting cos R R X = + , sin X R X = + , and using the trigonometric identity ( ) () () () () cos cos cos sin sin x yx y x y , we can express the last equation as, () () 2 2222 cos sin r s VR
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This note was uploaded on 01/27/2011 for the course ECSE 361 taught by Professor Franciscodgaliana during the Spring '09 term at McGill.

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9 Power transmission and transmission losses - Lecture 7...

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