Solver Benchmarks

GAT's SOCP solver has been validated against the complete PGLib-OPF benchmark suite, demonstrating 100% convergence across 67 test cases ranging from 3 to 78,484 buses.

Summary Statistics

Solver Hierarchy

GAT provides a four-tier solver hierarchy, each suited to different use cases:

Tier 1: Economic Dispatch (ED)

gat opf ed grid.arrow --out dispatch.parquet

• Complexity: O(n log n) merit-order sort
• Speed: < 1ms
• Use case: Quick feasibility checks, generation scheduling
• Limitations: Ignores network constraints entirely

Tier 2: DC-OPF

gat opf dc grid.arrow --out flows.parquet

• Complexity: Linear program (LP)
• Speed: ~10ms for IEEE 118-bus
• Use case: N-1 screening, transmission planning, real-time markets
• Limitations: Linear approximation, real power only, no voltage

Tier 3: SOCP Relaxation

gat opf socp grid.arrow --out solution.parquet

• Complexity: Second-order cone program (SOCP)
• Speed: ~100ms for IEEE 118-bus
• Use case: Production dispatch, tight bounds, voltage-aware
• Backend: Clarabel (pure Rust, no external dependencies)

Tier 4: AC-OPF (NLP)

gat opf ac grid.arrow --out optimal.parquet

• Complexity: Nonlinear program (NLP)
• Speed: ~1s for IEEE 118-bus
• Use case: Final validation, feasibility recovery, full physics
• Backend: IPOPT with analytical Jacobian and Hessian

Complete Results

The following table shows SOCP solver results for all 67 PGLib-OPF test cases:

Small Systems (< 100 buses)

Medium Systems (100-1000 buses)

Large Systems (1000-10000 buses)

Very Large Systems (10000+ buses)

Methodology

Test Environment

• Hardware: AMD Ryzen 9 (12 cores), 64GB RAM
• OS: Ubuntu 22.04 LTS
• Solver: Clarabel 0.9.0 (pure Rust SOCP solver)
• Data Format: Arrow IPC

Objective Gap Calculation

The objective gap is calculated as:

gap = |GAT_objective - PGLib_reference| / PGLib_reference × 100%

Where PGLib_reference is the known optimal objective value from the PGLib-OPF repository.

Notes on Large Gaps

Some cases show larger objective gaps (> 5%). This is typically due to:

1. SOCP relaxation gap: The SOCP relaxation may not be tight for certain network topologies
2. Different constraint handling: GAT may handle certain edge cases differently than reference implementations
3. Numerical precision: Large-scale systems may accumulate numerical errors

For cases requiring tighter solutions, use the AC-OPF solver (Tier 4) with IPOPT.

Running Benchmarks

To reproduce these results:

# Download PGLib test cases
gat dataset fetch pglib

# Run SOCP on all cases
gat benchmark pglib --solver socp --out results.csv

# Run specific case
gat opf socp ~/.gat/datasets/pglib/case118_ieee.m --out solution.parquet