Having some trouble understanding a-c a) Bus 1 is connected to bus 2 by a short (less than 50 miles) and losslesstransmission line modeled by a complex series impedance Z = jX, where X is theline reactance. (The real transmission line has 3 phases a,b,c, but in the balancedsituation of this question, we decouple the phases and analyze the single phase a).The phasor voltage at bus 1 is V1 = |Vi|e7®1 and the phasor voltage at bus 2 isV2 = |V2|e7®2. We already know the formula for the real power sent by bus 1|Vi||V2|P12 =sin 0(1)XTake |V1| = |V½] = 1.0 per unit. Take X = 0.5 per unit. Sketch a graph of P12versus 0. What is the real power flow P12 on the line in per unit when 0 = 10°?(b) [so called “DC power flow" approximation] Take the same transmission line asin part (a) and make the approximations |V1| = |V2| = 1 and 0 is small so thatsin 0 = 0. Let B = 1/X.Use the approximations to obtain the formula for the real power P12 in terms of Band 0.(c) Use the formula in (b) to compute the power flow P12 when 0 = 10°. Compareyour answer to the answer in part (a).

Part (a): Consider the expression of real power sent by bus 1, P12=V1V2Xsinθ…

'a) Bus 1 is connected to bus 2 by a short (less than 50 miles) and lossless transmission line modeled by a complex series impedance Z = jX, where X is the line reactance. (The real transmission line has 3 phases a,b,c, but in the balanced situation of this question, we decouple the phases and analyze the single phase a). The phasor voltage at bus 1 is Vị = |Vi|e3®i_and the phasor voltage at bus 2 is V2 = |V2|e3®2. We already know the formula for the real power sent by bus 1 |Vi||V2 , P12 sin 0 X (1) Take |V1| = |V2| = 1.0 per unit. Take X = 0.5 per unit. Sketch a graph of P12 versus 0. What is the real power flow P12 on the line in per unit when 0 = 10°? (b) [so called “DC power flow" approximation] Take the same transmission line as in part (a) and make the approximations |V1| = |V2| = 1 and 0 is small so that sin 0 = 0. Let B = 1/X. Use the approximations to obtain the formula for the real power P12 in terms of B %3D and 0. (c) Use the formula in (b) to compute the power flow P12 when 0 = 10°. Compare your answer to the answer in part (a).

'a) Bus 1 is connected to bus 2 by a short (less than 50 miles) and lossless transmission line modeled by a complex series impedance Z = jX, where X is the line reactance. (The real transmission line has 3 phases a,b,c, but in the balanced situation of this question, we decouple the phases and analyze the single phase a). The phasor voltage at bus 1 is Vị = |Vi|e3®i_and the phasor voltage at bus 2 is V2 = |V2|e3®2. We already know the formula for the real power sent by bus 1 |Vi||V2 , P12 sin 0 X (1) Take |V1| = |V2| = 1.0 per unit. Take X = 0.5 per unit. Sketch a graph of P12 versus 0. What is the real power flow P12 on the line in per unit when 0 = 10°? (b) [so called “DC power flow" approximation] Take the same transmission line as in part (a) and make the approximations |V1| = |V2| = 1 and 0 is small so that sin 0 = 0. Let B = 1/X. Use the approximations to obtain the formula for the real power P12 in terms of B %3D and 0. (c) Use the formula in (b) to compute the power flow P12 when 0 = 10°. Compare your answer to the answer in part (a).

Power System Analysis and Design (MindTap Course List)

6th Edition

ISBN:9781305632134

Author:J. Duncan Glover, Thomas Overbye, Mulukutla S. Sarma

Publisher:J. Duncan Glover, Thomas Overbye, Mulukutla S. Sarma

Chapter5: Transmission Lines: Steady-state Operation

Section: Chapter Questions

Problem 5.31P: A 500-kV, 300-km, 6()-Hz, three-phase overhead transmission line, assumed to be lossless, has a...

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