  We present a mixed complementarity problem (MCP) approach for a steady-state
stability analysis of voltage and frequency of electrical grids. We perform a
theoretical analysis providing conditions for the global convergence and local
quadratic convergence of our solution procedure, enabling fast computation
time. Moreover, algebraic equations for power flow, voltage control, and
frequency control are compactly and incrementally formulated as a single MCP
that subsequently is solved by a highly efficient and robust solution method.
Experimental results over large grids demonstrate that our approach is as fast
as the existing Newton method with heuristics while showing more robust
performance.
