Explain medium length lines, Electrical Engineering

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Explain Medium length lines?

Medium length lines cover lines in the range of 50 to 150 miles (80 to 240 km). Due to the increased length of the line, the shunt capacitance of the line is significant and is included in the equivalent circuit model. Therefore, the line model may be represented by a π network, as shown in Figure.

1087_Explain Medium length lines.png

Using Kirchhoff's voltage and current laws, the π circuit gives:

VS = VR + Z I         (1)

I = IR + Y/2 VR      (2)

IS = I + Y/2 VS      (3)

To obtain VS and IS in terms of VR and IR , substitute equation (2) into (1) which gives:

VS = [(1 + ZY) / 2] VR + Z IR                                                    (4)

Substituting equations (4) and (2) into equation (3) and rearranging yields:

IS = [(1 + ZY) / 4] Y VR + [(1 + ZY) / 2] IR        (5)

Comparing equations (4) and (5) with equations gives the 2-port network constants as:

A = [(1 + ZY) / 2], B = Z

C = [(1 + ZY) / 4], D = [(1 + ZY) / 2] = A

Another way of representing a medium length line is by the Τ network shown in Figure. In this case:

VS = VC + Z/2 IS                                              (6)

VC = VR + Z/2 IR   and                          (7)

IS = IR + Y VC                                                   (8)

1583_Explain Medium length lines 2.png

As for the π network, equations (6-8) may be solved and rearranged to obtain VS and IS in terms of VR and IR as:

VS = [(1 + ZY) / 2] VR + [(1 + ZY) / 4] IR                                           (9)

IS = Y VR + [(1 + ZY) / 2] IR                                                                     (10)

This gives the 2-port network constants as:

A = [(1 + ZY) / 2], B = [(1 + ZY) / 4] Z

C = Y, D = [(1 + ZY) / 2] = A


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