  In the steady-state contingency analysis, the traditional Newton-Raphson
method suffers from non-convergence issues when solving post-outage power flow
problems, which hinders the integrity and accuracy of security assessment. In
this paper, we propose a novel robust contingency analysis approach based on
holomorphic embedding (HE). The HE-based simulator guarantees convergence if
the true power flow solution exists, which is desirable because it avoids the
influence of numerical issues and provides a credible security assessment
conclusion. In addition, based on the multi-area characteristics of real-world
power systems, a partitioned HE (PHE) method is proposed with an
interface-based partitioning of HE formulation. The PHE method does not
undermine the numerical robustness of HE and significantly reduces the
computation burden in large-scale contingency analysis. The PHE method is
further enhanced by parallel or distributed computation to become parallel PHE
(P${}^\mathrm{2}$HE). Tests on a 458-bus system, a synthetic 419-bus system and
a large-scale 21447-bus system demonstrate the advantages of the proposed
methods in robustness and efficiency.
