inZORi PF-Δ Phase 3 — N-2 Contingency Robustness

Abstract

Phase 3 extends the inZORi Frozen Elite strategy to handle N-2 contingencies — the simultaneous outage of two transmission lines — the most demanding scenario in standard power system security analysis. Using a 15-generation evolutionary search, a superior genome pool was discovered achieving 71.16% S3 convergence under combined N-1+N-2 stress. An 8-genome Frozen Elite pool with dedicated N-2 specialists was built and validated on IEEE 118-bus at 1.75× stressed load. inZORi achieves +16.14pp over Baseline A, with N-2 recovery in 1.45 steps vs 4.12 steps (2.8× faster). Remarkably, inZORi recovers from N-2 events nearly as fast as N-1 events (1.45 vs 1.49 steps), demonstrating that dedicated N-2 specialists effectively neutralize the additional complexity of double-line outages.

71.16%

inZORi S3 convergence
under N-1 + N-2 stress

55.0%

Baseline A S3 convergence
(warm-start, no N-2 specialist)

+16.14pp

Advantage vs Baseline A
CI95 [70.9%, 71.4%]

2.8×

Faster N-2 recovery
1.45 vs 4.12 steps

Elite genomes in pool
incl. 2 N-2 specialists

Evolutionary generations
for genome discovery

1. Why N-2? Real-World Motivation

The N-1 security criterion (mandatory in Europe under ENTSO-E standards) requires grid stability after any single component failure. However, real blackouts rarely start with a single failure:

Event	Type	Impact
Italy Blackout, 2003	N-2 in Switzerland (two 380kV lines tripped within seconds)	Full European cascade, 56 million people
Northeast US/Canada, 2003	Started N-3 in Ohio, cascaded to N-265	55 million people, $6 billion economic loss
ENTSO-E current policy	N-1 mandatory, N-2 increasingly required for critical corridors	Grid codes being updated

Most AC power flow solvers are validated only under N-1 conditions. No published adaptive solver demonstrates robust N-2 recovery with convergence statistics across multiple seeds. This phase addresses that gap.

2. Genome Pool — 8 Genomes with N-2 Specialists

Evolutionary Search

A (μ+λ) evolutionary strategy with 20 genomes × 15 generations, 4 seeds per evaluation. Convergence at generation 7; top genomes refined through local search into the final pool.

#	Type	Profile
0	G01 best (base)	Top-fitness genome from evolutionary search — normal operation
1	Conservative	Low-risk profile, stable under moderate stress
2	High step_scale	Wider exploration radius for voltage deviation
3	High risk	Aggressive warm-start under high load
4	Moderate lr	Balanced memory / exploration trade-off
5	N-1 specialist	High DC-init tendency, activated on single outage
6	N-2 aggressive	Very high DC-init jump, double outage recovery
7	N-2 max DC-init	Maximum jump chance, worst-case N-2 scenario

Exact genome parameters are proprietary to the inZORi framework.

N-2 Selection Logic

Condition	Genome Selected	Rationale
Normal operation	#0 (G01 best)	Optimal for stable conditions
N-1 event detected	#5 (N-1 specialist)	DC-init retry for single outage
N-2 event detected	#6 or #7	Aggressive DC-init for double outage
Post-N-2 recovery	10-step recovery window	vs 5-step for N-1

3. Results

Fig. 1 — S3 convergence under combined N-1 + N-2 scenario. inZORi: 71.16% vs Baseline A: 55.02% (+16.14pp). CI95 [70.9%, 71.4%] — narrow intervals confirm statistical robustness across 20 seeds.

Fig. 2 — Mean recovery steps after N-1 and N-2 events. inZORi recovers from N-2 in 1.45 steps — nearly identical to N-1 recovery (1.49 steps). Baselines are ~2.8× slower and show no differentiation between N-1 and N-2.

Fig. 3 — inZORi advantage maintained as difficulty increases: DC approx. → Real AC PF → AC PF + N-2. Consistent +15–16pp demonstrates algorithmic robustness, not scenario-specific tuning.

Numerical Summary

Strategy	S3 Conv.	CI95	N-1 rec. (steps)	N-2 rec. (steps)
Baseline A (warm-start)	55.02%	[54.6, 55.4]	3.64	4.12
Baseline B (periodic reset)	55.35%	[55.0, 55.7]	3.34	4.05
inZORi Frozen Elite N-2	71.16%	[70.9, 71.4]	1.49	1.45

Key observation: Baseline A and B perform nearly identically (55.02% vs 55.35%), confirming neither has adaptive mechanism for N-2. inZORi's 2.8× recovery advantage comes entirely from N-2 specialist genomes using aggressive DC-initialization (jump_chance=0.87–0.92).

4. Experimental Setup

Parameter	Value
Network	IEEE 118-bus (pandapower)
Load scaling	1.75× base (stressed)
NR max iterations	5 (strict budget)
N-1 interval	Every 300 steps (S3 only)
N-2 interval	Every 600 steps (S3 only)
N-1 duration	25 steps
N-2 duration	20 steps
Seeds	20
Steps per seed	50,000
N-1 events per seed	~21
N-2 events per seed	~21
Total elapsed	66.8 min (12 workers)

5. Claims & Limitations

CLAIMS: inZORi Frozen Elite with N-2 specialists significantly outperforms warm-start and periodic-reset baselines under combined N-1+N-2 stress on IEEE 118-bus (+16.14pp, CI95 non-overlapping)
CLAIMS: N-2 specialist genomes achieve recovery speed statistically indistinguishable from N-1 recovery (1.45 vs 1.49 steps)
CLAIMS: Consistent advantage across Phases 1→3 as difficulty increases confirms algorithmic robustness, not scenario overfitting
DOES NOT CLAIM: IEEE 118-bus is representative of real TSO networks — results on actual grid topologies may differ
DOES NOT CLAIM: Load profiles are synthetic (seasonal drift) — real ENTSO-E profiles are addressed in Phase 5
DOES NOT CLAIM: N-2 specialists are optimal — they were designed based on domain knowledge; automated N-2 genome evolution is future work

6. Reproducibility

cd inzori/

# Extended evolutionary search (15 generations)
python3 -m problems.zor_pf_real_118.run_extended_evo

# N-2 validation (20 seeds × 50,000 steps)
python3 -m problems.zor_pf_real_118.run_n2_validation
      

inZORi PF-Δ Phase 3: N-2 Contingency Robustness