Static bifurcation in flux decay dynamics of a transient/midterm stability model

Abstract

A static bifurcation in the generator flux decay dynamics is shown to occur: (i) when a generator reaches field current limits and the field current limit controller reduces field current to continuous rating levels through disabling the excitation control system; or (ii) when the excitation control system is retained to stabilize dynamics. A test matrix T is derived and exists if static bifurcation in inertial dynamics and loss of causality have not occurred. The test matrix T is thus a test for static bifurcation in generator flux decay dynamics. The static bifurcation in flux decay dynamics is the long sought description of the classic voltage instability problem that occurred on the French system in 1978 because it is shown: (a) to occur before static bifurcation in inertial dynamics or loss of causality; (b) to be the only theoretical description of classic voltage instability that can be shown to result in a continuous reduction of generator internal bus voltage that causes an uncontrollable spread of the stability problem; (c) to occur when generator field current limit controllers disable excitation control systems and reduce field current to continuous ratings; (d) to also occur if field current limit controllers do not disable excitation control systems but reduce field current to continuous rating levels; and (e) to occur on systems with large shunt capacitive supply due to long EHV lines or underground cables as is most often the case for systems experiencing voltage instability.