In this application, the state-space representation of a three-phase transmission line using modal transformation
techniques is described. A 180 km long 3-phase, 50 Hz, 500 kV single circuit, transposed transmission line
illustrated in Figure 7 is chosen for line energization studies, for illustration. It is assumed that the transmission
line at no load is energized by a sinusoidal voltage source with series inductance LS = 34 mH, when the voltage
wave of phase-A is passing through its peak value. It possible to obtain the state-space response of the system
in phase domain directly; however, there is mutual coupling between current and voltage of three phases, and
because of this, analysis of such a system is difficult. The effect of coupling between the phases can be eliminated
using phase to modal transformation techniques, which requires eigenvalue analysis [15]. By this way a threephase
transmission line can be decoupled into three independent modes and each mode is analyzed as a single
phase line.