  In complex power systems, nonlinear load flow equations have multiple
solutions. Under typical load conditions only one solution is stable and
corresponds to a normal operating point, whereas the second solution is not
stable and is never realized in practice. However, in future distribution grids
with high penetration of distributed generators more stable solutions may
appear because of active or reactive power reversal. The systems can operate at
different states, and additional control measures may be required to ensure
that it remains at the appropriate point. This paper focuses on the analysis of
several cases where multiple solution phenomena is observed. A non-iterative
approach for solving load flow equations based on the Gr\"{o}bner basis is
introduced to overcome the convergence and computational efficiency associated
with standard iterative approaches. All the solutions of load flow problems
with their existence boundaries are analyzed for a simple 3-bus model.
Furthermore, the stability of the solutions is analyzed using a derived
aggregated load dynamics model, and suggestions for preventive control are
proposed and discussed. The failure of na\"{i}ve voltage stability criteria is
demonstrated and new voltage stability criteria is proposed. Some of the new
solutions of load flow equations are proved to be stable and/or acceptable to
the EN 50610 voltage fluctuation standard.
