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EEE471Ch5

EEE471Ch5 - Transmission Line Steady State Operation...

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Transmission Line Steady State Operation Chapter 5
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2 Modeling and Operation of Transmission Lines Transmission line modeling as a 2-port network at terminals I S I R E S E R Model is valid for: Linear, passive, bilateral networks Special class of circuits where the 4 terminal conditions can be related by 4 parameters, which we refer to as A, B, C, and D.
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3 4 Terminal Networks Positive sequence circuits: balanced, lines transposed, currents balanced, voltages balanced, etc. For this type of circuit: V S = AV R + BI R and AD-BC = 1 I S = CV R + DI R In matrix form: = R R S S I V D C B A I V The relationships above can be in either volts, amps, ohms and Siemens, or per unit. S S = V S I S * and S R = V R I R * in per unit
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4 4 Terminal Networks E R E S I S I R A B C D Each type of passive system element can be represented by a 4 Terminal Network Adjacent 4 Terminal Networks can be combined as shown in Figure 5.4 on Page 239
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5 4 Terminal Networks
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6 A B C D Constants for Transmission Lines We will consistently use : z = r + jωL series impedance in Ω or pu per unit length y = g + jωC Shunt admittance in S or pu per unit length Z = z Total series impedance for line of length Y = y Total shunt admittance for line of length Type of transmission line model depends on length: Short: 0 – 50 miles neglect shunt capacitance Medium: 50 – 150 miles approximate Long: > 150 miles accurate
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7 A B C D Constants for Transmission Lines Short line: A = D = 1 B = Z C = 0 Short line 0 – 50 miles : neglect shunt elements Z = z E S E R I S I R I S = I R E S = E R + Z I R = R R S S I E Z I E 1 0 1 D C B A
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8 A B C D Constants for Transmission Lines Z Y/2 Y/2 I S I R E S E R π Z/2 Y I S I R E S E R Z/2 T Medium length line (50-150 miles) Approximate
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9 ABCD Constants for Medium Length Line Z Y/2 Y/2 I S I R E S E R I’ E S = AE R + BI R I S = CE R + DI R R R R R R R S ZI E ZY I Y E Z E ZI E E + + = + + = + = 2 1 2 ' R R R R S S I Y E I ZY Y ZY E I Y E I + + + + = + = 2 2 2 2 1 ' 2 R R R R S S I ZY YE ZY ZY I Y ZY E I Y E I + + + = + + + = + = 2 1 4 1 2 1 2 2 2 ' 2
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10 ABCD Constants for Medium Length Line Z Y/2 Y/2 I S I R V S V R I’ E S = AE R + BI R I S = CE R + DI R R R R R R R S ZI E ZY I Y E Z E ZI E E + + = + + = + = 2 1 2 ' R R R R S S I Y E I ZY Y ZY E I Y E I + + + + = + = 2 2 2 2 1 ' 2 R R R R S S I ZY YE ZY ZY I Y ZY E I Y E I + + + = + +
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EEE471Ch5 - Transmission Line Steady State Operation...

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