Batch N‑1 Power Flow Via Perturbation Methods
summary
Argues that perturbation/holomorphic‑embedding methods compute high‑order Taylor coefficients once and reuse a single LU factorization to evaluate many N‑1 line outages in batch, matching Newton‑Raphson solutions while avoiding repeated Jacobian rebuilds. Implements rectangular coordinates, convolutional product‑rule for coefficient recursion, and SIMD/multithreaded kernels; shows 16th order expansions faster than one LU on testcases (IEEE‑14, British grid, Paza 2869) and batched all line outages in roughly 2.5 seconds on a laptop.
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chapters (10)
- 0:00Introduction and motivation
- 6:06Perturbation theory basics
- 13:29Algorithm and implementation
- 17:01Two-bus system example
- 20:12Performance comparison
- 21:39IEEE 14-bus test case
- 24:12British network analysis
- 25:58Complexity and scalability
- 26:41Future research and challenges
- 28:28Q&A session
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