#### Electrical Systems

##### Transmission Line Calculation

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The per phase sending and receiving end voltages are:

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The line currents at sending and receiving end are:

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The transmission line can be represented as two port network. The two port network representation make it easier for line voltage and current computation

The sending and receiving end voltage and current are formulated as below.

Vs = AVr + BIr

Is = CVr + DIr

The constants are known as generalized circuit constants, or ABCD constants. The ABCD constants are different for different representation of the line, i.e Short, Medium or Long

The ABCD constants satisfy the relationship

$\phi ={\text{tan}}^{-1}\left(\frac{X}{R}\right)$