An application of complex branch modeling to nonreciprocal power transmission elements

The complex branch modeling technique developed by Bandler and El-Kady is applied to derive exact first-order sensitivity formulas for nonreciprocal power transmission elements. An adjoint model of a cascaded phase-shifting transformer model comprising an ideal transformer in series with an equivalent impedance is developed elegantly. The sensitivity formulas for the turns ratio magnitude and phase angle are obtained and verified numerically for a 6-bus sample system.