No clear winner. The survival gap is under 10 percentage points and the balanced-score gap is under 0.05, so neither SolvSRK nor the best baseline clears the win threshold. Either works — choose on cost, licensing, or integration effort. All verdicts →
6D SMIB with transformer core saturation during inrush. State: [delta, omega, E'q, E'd, lambda_core, i_mag]. Smooth sigmoid saturation L(lambda): 400x inductance variation across knee creates periodic stiffness spikes each half-cycle.
Tokic et al. (2022) BDF methods for transformer inrush; Zurek et al. (2022) Radau IIA for transformer inrush; Kundur (1994) Ch. 4
Canonical RHS excerpt from the registered callable used for this benchmark cell. Expand it to verify the state equations; it is not a standalone runnable fixture.
def _L_core(lam: float) -> float:
"""Smooth sigmoid saturation model for transformer core inductance."""
return _TI_L_sat + (_TI_L_unsat - _TI_L_sat) / (
1.0 + np.exp(_TI_k_sat * (np.abs(lam) - _TI_lam_knee))
)
def _smib_transformer_inrush_rhs(t: float, y: np.ndarray) -> np.ndarray:
"""SMIB + transformer inrush (6 states).
Machine (4 states) connected to infinite bus; transformer (2 states)
energised by V_primary = V_peak·sin(2π·60·t). The machine–transformer
coupling is through the shared bus voltage (decoupled first-order
model; transformer current does not modify terminal V).
"""
delta, omega, Eq_p, Ed_p, lam_core, i_mag = y
# ----- machine swing + transient flux (V = V_inf, no fault) -----
V = _SF_Vinf
Id = (Eq_p - V * np.cos(delta)) / _SF_Xdp
Iq = (V * np.sin(delta) - Ed_p) / _SF_Xqp
Pe = Eq_p * Iq + Ed_p * Id + (_SF_Xdp - _SF_Xqp) * Id * Iq
ddelta = _SF_ws * (omega - 1.0)
domega = (1.0 / (2.0 * _SF_H)) * (_SF_Pm - Pe - _SF_D * (omega - 1.0))
dEq_p = (1.0 / _SF_Td0p) * (_SF_Efd - Eq_p - (_SF_Xd - _SF_Xdp) * Id)
dEd_p = -(1.0 / _SF_Tq0p) * (Ed_p + (_SF_Xq - _SF_Xqp) * Iq)
# ----- transformer core flux + magnetising current -----
V_primary = _TI_Vpeak * np.sin(2.0 * np.pi * _TI_f * t)
dlam = V_primary - _TI_Rw * i_mag
L = _L_core(lam_core)
di_mag = dlam / L
return np.array([ddelta, domega, dEq_p, dEd_p, dlam, di_mag])Canonical RHS excerpt captured from the same registered callable used for the published benchmark. Frozen closure values are summarized below; helper imports and solver settings are intentionally omitted.
Fingerprint
Spread: high
Default noise: low
Recommendation snapshot
Clean best: SciPy Radau
Noisy best: SolvSRK
Coverage
14 solver arms · clean + 5 noise levels
Ranked on survival, precision, and speed
20 seeds/cell default · 14 arms · TRL 4–5 · simulation-lab validated · this page: SMIB transformer inrush (6D) (smib-transformer-inrush-6d)
Governed SolvTune benchmark freeze; per-arm medians only. RHS definitions and raw trial rows are not published.
Self-reported by Resonix Labs · not independently verified
Pick an objective and a noise level to rank all arms on survival, median SCD, median nfev, and median wall time. Medians across seeds.
Objective
Best overall trade-off of survival, precision, and speed.
Noise level
| # | Solver | Survival | SCD | nfev | Wall | Score |
|---|---|---|---|---|---|---|
| 1 | SciPy RadauSciPy | 100% | 10.5 | 28,608 | 620 ms | 0.869 |
| 2 | SolvSRK | 100% | 9.2 | 20,755 | 101 ms | 0.838 |
| 3 | SciPy DOP853SciPy | 100% | 9.0 | 5,558 | 46 ms | 0.834 |
| 4 | Tsit5external | 100% | 8.7 | 7,422 | 1.28 s | 0.827 |
| 5 | SciPy RK45SciPy | 100% | 7.9 | 6,170 | 55 ms | 0.808 |
| 6 | CVODE Adamsexternal | 100% | 7.2 | 2,010 | 25 ms | 0.790 |
| 7 | SciPy RK23SciPy | 100% | 6.8 | 27,338 | 288 ms | 0.782 |
| 8 | SciPy LSODASciPy | 100% | 6.8 | 4,903 | 31 ms | 0.781 |
| 9 | SciPy BDFSciPy | 100% | 6.3 | 9,161 | 328 ms | 0.769 |
| 10 | CVODE BDFexternal | 100% | 6.3 | 4,514 | 48 ms | 0.768 |
At Clean, best balanced arm is SciPy Radau · SolvSRK survival 100%, SCD 9.2.
Values are medians across seeds, measured by Resonix Labs on Resonix hardware and not independently verified; nfev and wall are on reference lab hardware (indicative). Under injected noise only SolvSRK and the SciPy arms are run. How we measure accuracy → · Verification status →
SolvScout · free
This page shows one published benchmark cell. SolvScout fingerprints your ODE, compares it to the full corpus, and recommends a solver with the same survival / precision / speed ranking you see here — including when a SciPy arm wins.
SolvSRK · 30-day trial
SolvSRK is the stiffness-adaptive integrator behind the SolvSRK column in these tables. Create an account, activate a machine, and take a 30-day trial — same binary you'd ship after purchase.
Replace the access date. Pin the freeze ID and library versions when comparing against a later export. Cite it as what it is — a self-reported vendor benchmark, not an independently verified result. The note field says so; please keep it.
@misc{resonix_evidence_smib_transformer_inrush_6d_2026,
title = {Resonix Evidence Portal: SMIB transformer inrush (6D)},
author = {{Resonix Labs (Canada) Inc.}},
year = {2026},
howpublished = {\url{https://resonix.tech/evidence/problems/smib-transformer-inrush-6d}},
note = {Self-reported vendor benchmark; internally generated by Resonix Labs and not independently verified. Accessed YYYY-MM-DD. Freeze 2026-08-13; libsolvsrk 2.3.0; SciPy 1.14.}
}TRL 4–5 · simulation-lab validated · 398 problems · 14 solver arms · clean + 5 noise levels
Freeze: 2026-08-13 · scipy 1.14 · libsolvsrk 2.3.0 · Methodology
Self-reported by Resonix Labs · not independently verified · Verification status