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We investigate the interplay of rotor-angle and voltage stability in electricpower systems. To this end, we carry out a local stability analysis of thethird-order model which entails the classical power-swing equations and thevoltage dynamics. We provide necessary and sufficient stability conditions andinvestigate different routes to instability. For the special case of a two-bussystem we analytically derive a global stability map.

Rotor-angle versus voltage instability in the third-order model for synchronous generators