A Robust Holomorphic Embedding-Based Method for Fast Tracing of P-V Curves With Limiting Points

Existing approaches for addressing the continuation power flow problem with limits are mainly iterative and can face the serious drawbacks, e.g., the divergence, slow convergence, and ignoring or mis-computing a limiting point, especially for large systems. This paper thus proposes a new method called Enhanced Holomorphic Embedding combining Arc-length Parametrization (E-HEAP) for high performance in the continuation power flow computation of large power systems. A novelty of E-HEAP lies in an effective treatment of the generator's physical hard limits and operating constraints tailored for the framework of holomorphic embedding. Another novelty is attributed to the calculations of the eigenvalues of companion matrices to locate the first position of a violating hard limit robustly and efficiently. These novelties turn the task of solving a set of nonlinear equations or optimization problems formulated by the majority of the existing methods into a simple linear algebra (or eigenvalue) problem for small-sized companion matrices to locate the potential limiting points. Several numerical examples are presented to explain this new eigenvalue- based approach to find limiting points. Distinguishing features of the proposed new method in capturing all the potential and first limiting points in comparison with an intuitive iterative scheme employed in existing methods are highlighted. The performance of E-HEAP in numerical robustness and efficiency is examined on power systems with 10,000+ buses and compared with existing methods that apply the predictor-corrector and other techniques. Numerical results show that E-HEAP can robustly and efficiently deal with the large power system voltage stability problems and significantly outperform other existing methods in terms of robust convergence, numerical efficiency, and technical soundness.