Counterexample to a Continuation-Based Algorithm for Finding All Power Flow Solutions

Existing literature claims that an algorithm based on continuation is capable of finding all solutions to the power flow equations for all power systems. This claim is demonstrated to be incorrect through the use of a five-bus system counterexample. Existing literature also claims that a similar algorithm is capable of finding all Type-1 solutions (i.e., solutions where the power flow Jacobian has a single eigenvalue with positive real part) to the power flow equations for all systems. This claim is also shown to be incorrect using the five-bus system counterexample.