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Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...
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To determine the per unit voltage at bus using the iterative method, we need to use the following equations: The voltage reflection coefficient at the load end of the transmission line: \Gamma_L = \frac{Z_L - Z_0}{Z_L + Z_0} The voltage at bus 2 as a function of the voltage at bus 1 and the voltage reflection coefficient: V_2=V_1 \frac{1+ \Gamma_L}{1 - \Gamma_L} where Z_0 is the characteristic impedance of the transmission line, which is assumed to be known. For this problem, we have: Z_L = 0.01 + j0.05 pu Z_0 = ? To calculate Z_0, we can use the formula: Z_0 = \sqrt{\frac{Z_1} {Z_2}} where Z_1 and Z_2 are the impedances of the sending and receiving ends of the transmission line, respectively. In this case, Z_1 = Z_2= Z_L, so: Z_0 = \sqrt{\frac{Z_L}{Z_L}} = \sqrt{1} = 1 Now we can calculate the voltage reflection coefficient at the load end of the transmission line: \Gamma_L = \frac{Z_L - Z_0}{Z_L + Z_0} = \frac{(0.01 + j0.05)-1} {(0.01 + j0.05) + 1} = -0.475 + j0.095
Transcribed Image Text:To determine the per unit voltage at bus using the iterative method, we need to use the following equations: The voltage reflection coefficient at the load end of the transmission line: \Gamma_L = \frac{Z_L - Z_0}{Z_L + Z_0} The voltage at bus 2 as a function of the voltage at bus 1 and the voltage reflection coefficient: V_2=V_1 \frac{1+ \Gamma_L}{1 - \Gamma_L} where Z_0 is the characteristic impedance of the transmission line, which is assumed to be known. For this problem, we have: Z_L = 0.01 + j0.05 pu Z_0 = ? To calculate Z_0, we can use the formula: Z_0 = \sqrt{\frac{Z_1} {Z_2}} where Z_1 and Z_2 are the impedances of the sending and receiving ends of the transmission line, respectively. In this case, Z_1 = Z_2= Z_L, so: Z_0 = \sqrt{\frac{Z_L}{Z_L}} = \sqrt{1} = 1 Now we can calculate the voltage reflection coefficient at the load end of the transmission line: \Gamma_L = \frac{Z_L - Z_0}{Z_L + Z_0} = \frac{(0.01 + j0.05)-1} {(0.01 + j0.05) + 1} = -0.475 + j0.095
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