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SMIB transformer inrush (6D)

PARITYS3 · dim 6

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.

Power & energy systems

Problem definition

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.

Show canonical RHS excerpt

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])

Parameters: _SF_D = 2
_SF_Efd = 1
_SF_H = 3.5
_SF_Pm = 0.8
_SF_Td0p = 8
_SF_Tq0p = 1
_SF_Vinf = 1
_SF_Xd = 1.81
_SF_Xdp = 0.3
_SF_Xq = 1.76
_SF_Xqp = 0.65
_SF_ws = 376.991118431
_TI_L_sat = 0.5
_TI_L_unsat = 200
_TI_Rw = 0.005
_TI_Vpeak = 1.414
_TI_f = 60
_TI_k_sat = 10
_TI_lam_knee = 1.2
Initial condition: y(0) = [-0.783775959017, 1, 0.75660879129, -1.70350922899, 0.8, 0]
Horizon: t ∈ [0, 2]

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

Versions & freeze

Methodology →

Freeze: 2026-08-13
libsolvsrk: 2.3.0
SciPy: 1.14
SUNDIALS: CVODE (bundled backend)

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

Results matrix

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 →

Cite this page

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://resonixusa.com/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

Problem definition

Versions & freeze

Results matrix

Cite this page

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