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# Modeling of a high-voltage transmission

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FIGURE 3(a) represents a 50 Hz, three-phase, high-voltage, transmission line. For one phase, the relationships between the sending end voltage and current and the receiving end voltage are given by the complex ABCD equations:
where VS is the sending-end voltage, IS the sending-end current and VR is the magnitude of the open-circuit receiving end voltage.

(a) Given the parameter values in TABLE A and if the magnitude of the receiving-end line voltage VRL is measured as 154 kV when feeding a balanced load of 40 MVA at a power factor of 0.9, calculate the value of the sending-end phase voltage VSP and sending-end phase
current ISP.
[N.B. VSL = Ã¢??3 Ãƒ- VSP and the total power in a three-phase load is given by P = Ã¢??3VI cos ?.]
(b) Hence or otherwise calculate the sending-end power and thus the power lost in the cable.
(c) If the line is modelled by the ?-circuit of FIGURE 3(b), see if you can estimate the primary line coefficients R, L, G and C. The line is 50 km long.