(Solved): At the end of a 200 km long transmission line, the phase-to-phase voltage is 380 kV. P2=75 MW active ...

At the end of a 200 km long transmission line, the phase-to-phase voltage is 380 kV. P2=75 MW active power, and Q2=3.5 MVAr (capacitive) reactive power is drawn from this end. The resistance of the line per kilometer; r=0.1 ?/km, reactance; x=0.3 ?/km. Its capacitance is 2.5*10^-6 ?/km.

A) Find the line head conditions using the ABCD parameters with the help of the T equivalent circuit model.
B) Find the line head conditions by performing circuit analysis with the help of the T equivalent circuit model.

 

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ABCD parameters of the \( T \) equivalent circuit model \[ \begin{array}{l} \left|\begin{array}{c} V_{1} \\ I_{1} \end{array}\right|=\left|\begin{array}{cc} 1 & \frac{Z}{2} \\ 0 & 1 \end{array}\right|\left|\begin{array}{ccc} 1 & 0 \\ Y & 1 \end{array}\right| \begin{array}{cc} 1 & \frac{Z}{2} \\ 0 & 1 \end{array}|| \begin{array}{|l} V_{2} \\ I_{2} \end{array} \mid \\ \left|\begin{array}{l} V_{1}^{\prime} \\ I_{1}^{\prime} \end{array}\right|=\left|\begin{array}{cc} 1 & \frac{L}{2} \\ 0 & 1 \end{array}\right| \cdot\left|\begin{array}{|l} V_{2}^{\prime} \\ I_{2}^{\prime} \end{array}\right| \begin{array}{c} V_{1}^{\prime \prime} \\ I_{1}^{\prime \prime} \end{array}|=| \begin{array}{cc} 1 & 0 \\ Y & 1 \end{array}|\cdot| \begin{array}{l} V_{2}^{\prime \prime} \\ I_{2}^{\prime \prime} \end{array}\left|\begin{array}{cc} V_{1}^{\prime \prime \prime} \\ I_{1}^{\prime \prime \prime} \end{array}\right|=\left|\begin{array}{cc} 1 & \frac{L}{2} \\ 0 & 1 \end{array}\right| \cdot\left|\begin{array}{c} V_{2}^{\prime \prime \prime} \\ I_{2}^{\prime \prime} \end{array}\right| \\ \left|\begin{array}{c} V_{1} \\ I_{1} \end{array}\right|=\left|\begin{array}{cc} 1+\frac{Z Y}{2} & Z\left(1+\frac{Z Y}{4}\right) \\ Y & 1+\frac{Z Y}{2} \end{array}\right| \cdot|\cdot| \begin{array}{c} V_{2} \\ I_{2} \end{array} \mid \\ \end{array} \]