Electrical Power & Machines “Electrical Engineering Dept” Prepared By: Dr. Sahar Abd El Moneim Moussa 1

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CLASSIFICATION OF T.L ACCORDING TO LENGTH According to length, T.L. can be classified as follows: 1- Short T.L. : up to 80 km( 50 miles) 2- Medium T.L. : >80 km <240 km 3- Long T.L. : > 240 km Dr. Sahar Abd El Moneim Moussa3

 Representation of a transmission line by a two port Network Dr. Sahar Abd El Moneim Moussa4

The General equation is : V s = A V R + B I R I S = C V R + D I R In Matrix Form : V S A B V R I S = C D I R Dr. Sahar Abd El Moneim Moussa5

Where, V S = sending- end phase (line –to-neutral) voltage V R = receiving - end phase (line –to-neutral) voltage I s = sending-end phase current. I R = receiving-end phase current. Dr. Sahar Abd El Moneim Moussa6

1- Short OHTL: (up to 80 km)  Equivalent Circuit: Dr. Sahar Abd El Moneim Moussa7

 The General equation is: V s = V R + Z I R I s =I R  In Matrix Form : V S = 1 Z V R I S = 0 1 I R Dr. Sahar Abd El Moneim Moussa8

 The ABCD Parameters of a short T.L: A=D=1, B=Z, C=0 Where, Z = R+ jX L = zL = rL +jxL Ω Z= total series impedance per-phase in ohms. z = series impedance of one conductor in ohms per unit length X L = total inductive reactance of one conductor in ohms. X = inductive reactance of one conductor in ohms per unit length L = length of the line. Dr. Sahar Abd El Moneim Moussa9

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Where, V RNL = magnitude of receiving end voltage at no-load V RFL = magnitude of receiving end voltage at full-load with constant Vs Dr. Sahar Abd El Moneim Moussa11

Example 9: A three-phase, 50 Hz overhead 40 km T.L. has a line voltage of 23 kV at the receiving end, a total impedance of 2.48+j6.57  per phase, and a load of 9 MW with receiving end lagging pf of 0,85. Calculate: a) Line to neutral voltage at the sending end b) Efficiency of the line c) Voltage regulation of the line Dr. Sahar Abd El Moneim Moussa12

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2- Medium OHTL: ( from 80 km to 240 km) The medium OHTL can be represented either by: i.  - equivalent circuit ii. T- equivalent circuit Dr. Sahar Abd El Moneim Moussa15

i-  - Circuit:  Equivalent Circuit: Dr. Sahar Abd El Moneim Moussa16 j X VSVS VRVR ISIS R C/2 I cs I I CR IrIr

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i- T- Circuit:  Equivalent Circuit: Dr. Sahar Abd El Moneim Moussa19

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Example 10 A 50 Hz 200 km, transmission line has 132 kV between the lines at the receiving end and has per phase R=0.1  /km, L=0.828 mH/km And C=  F/km. the line is supplying a load of 30MW at 0.85 lagging pf. Find using approximated  -model: a) A,B,C and D constants of the line b) V and I at the sending end of the line c)  and VR of the line Dr. Sahar Abd El Moneim Moussa23

Solution: Z= R+ j  L= 0.1 x j 2 x  x 50 x x x 200 = 20 + j 52  = 55  69  Y= j  C= j 2 x  x 50 x x x 200 = j 314 x mho= 314x10 -6  90 mho YZ= j (  1) a) A= D= 1 B= Z= 20 + j 52  = 55  69  C= Y = j 314 x mho= 314x10 -6  90 mho Dr. Sahar Abd El Moneim Moussa24

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