Methodology notes

The physics and linear algebra behind the provenance and integrity checks. Numbered citations refer to the references at the bottom.

Impedance matrix invariants vs fingerprints

The central design principle: enforce invariants — properties no legitimate transformation of the data can break — as hard checks, and treat typical properties as soft provenance fingerprints.

For the series impedance Z = R + jX of a multiconductor line in wire coordinates [1, 5]:

• Reciprocity (Z symmetric) holds for ordinary passive lines in reciprocal media (isotropic conductors and earth — no gyrotropic or otherwise non-reciprocal materials) — hard (E.PROV.NONRECIPROCAL).
• Passivity (R ⪰ 0) holds by the dissipation argument, and survives Kron reduction: elimination of grounded conductors is a Schur complement, and Schur complements of accretive matrices remain accretive [10, 11] — hard (E.PROV.NONPASSIVE).
• Inductive realisability (X ⪰ 0, positive diagonals): the inductance matrix is PSD by the magnetic-energy argument; matrices with both R, X PSD are sectorial, and sectorial matrices are closed under Schur complementation — so X-PSD is also Kron-invariant (W.PROV.X_NOT_PSD, W.PROV.X_NONINDUCTIVE).
• Mutual resistance sign: Carson's earth-return correction [4] makes off-diagonal resistance positive (≈ ω·μ₀/8 = π·f·μ₀/4 ≈ 0.049 Ω/km at 50 Hz), and nearly equal across conductor pairs — a useful fingerprint of geometry-derived data, but only typical: reductions and fitting can perturb it (I.PROV.NEGATIVE_MUTUAL_R, soft).

Sequence-derived matrices and Z₁/Z₀ recovery

A line parameterised from sequence values and transformed back to phase coordinates (TF spec [1], Appendix A.2 / Eq. 148) is perfectly balanced:

Z = Zₛ·I + Zₘ·(J − I),   Zₛ = (Z₀ + 2Z₁)/3,   Zₘ = (Z₀ − Z₁)/3

Geometric (Carson) parameterisations of generic asymmetric untransposed geometries do not produce this, because their phase-pair spacings differ. (Symmetric untransposed arrangements — equilateral spacing, symmetric bundled construction — can be balanced; that is exactly the near_balanced case below.) The classifier inverts the construction — Z₁ = Zₛ − Zₘ, Z₀ = Zₛ + 2Zₘ — and reports the implied sequence parameters (I.PROV.SEQ_DERIVED). The verdict tiers:

The near_balanced tier exists precisely because bundled LV cables (e.g. the adapted ENWL library [6, 7, 8]) are physically near-symmetric — they must not be mistaken for sequence-derived data.

The Maxwell sign pattern

Shunt capacitance in wire coordinates is the Maxwell capacitance matrix C = P⁻¹ (P the potential-coefficient matrix from geometry): positive diagonals, non-positive off-diagonals (coefficients of electrostatic induction), nonnegative row sums (capacitance to ground), symmetric PSD — in fact a Stieltjes matrix [5]. OpenDSS Cmatrix is exactly this form; B = ωC inherits it.

The classic data error is entering the pairwise capacitance cij = −Cij with the wrong sign. Severity calibration:

• PSD / nonnegative diagonals are invariant — Stieltjes (symmetric M-) matrices are closed under Schur complementation (grounded-screen elimination) and under bundling congruences [11] — so violations are warnings (W.PROV.B_SIGN).
• A positive mutual with PSD intact cannot arise from a clean geometry → P⁻¹ → reduction pipeline; it marks fitted, averaged or otherwise processed provenance (I.PROV.B_OFFDIAG, informational). This calibration was validated empirically on the bundled-cable library, where small positive mutuals (+0.0011 vs −0.0114 siblings) occur in PSD matrices.

Kron reduction, grounding and earthing zones

A 4-wire network whose every neutral is solidly grounded admits exact Kron reduction of the neutral; conversely, sparse neutral grounding makes the explicit 4-wire model essential [6, 7]. The checks formalise this:

• wires per voltage level: 3-wire LV is flagged as likely Kron-reduced (LV is physically 4-wire); 3-wire MV is physical and silent.
• neutral continuity graph (lines + closed switches carrying the neutral; transformer windings do not pass it): every section must reach a grounding — perfect grounding, a grounding shunt, or a source that pins the neutral. Floating sections leave the zero-sequence path undefined.
• earthing zones: per galvanic island (transformer windings are galvanic separations) the star-point earthing and the count of downstream neutral electrodes classify the likely earthing system. Downstream neutral electrodes can only exist in multi-earthed systems (TN-C-S/PME/MEN); a source-earthed-only 4-wire zone is genuinely ambiguous between TN-S and TT, because the protective-earth side of installations is not representable in a power-flow data model — the tag states the ambiguity rather than guessing. MV zones use MV vocabulary (solidly/impedance-earthed/isolated).

Voltage reference per galvanic island

Each galvanically isolated island needs at least one voltage reference or its voltages are defined only up to a shift — the nodal admittance matrix is rank-deficient. This is the IEEE 123-bus "bus 610" defect that OpenDSS silently patches with a phantom shunt [2, 12]. A shunt anchors an island only if its admittance has nonzero row sums (Y·1 ≠ 0): a pure delta capacitor bank does not.

OpenDSS default fingerprints

When a .dss file omits a property, OpenDSS substitutes a documented default [9]; after conversion these are indistinguishable from deliberate data except by value. The fingerprint table:

The length check distinguishes scattered exact-1.0 values (default leak) from universal ones (a deliberate length-normalised convention, reported in the convention statement instead) — the adapted ENWL library [8] is the canonical universal case, and its single 1 m source jumper per feeder is the canonical scattered true-positive.

Limit of the method: defaults that PMD resolves at parse time (e.g. basefreq mismatches) leave no trace in the converted data and cannot be fingerprinted downstream.

Regulators and autotransformers

OpenDSS has no first-class regulator branch; modelers encode them either as a near-1:1 wye transformer plus a RegControl (which does not convert), or — per the EPRI autotransformer guidance [9] — as two windings on the same bus (common + ~10 % series winding), kVA rated at the series winding, with a negligible-impedance jumper. Both freeze a control device into a fixed branch; the second bundles three benchmark pitfalls of [2] in one pattern (self-loop topology, deliberate tiny impedance, a rating that reads as 10× overload). Detection (W.PROV.REGULATOR_PATTERN): the self-loop is near-conclusive on its own; the 1:1 form requires corroboration (same-voltage-level endpoints, x_pu < 0.5 %, or a non-unity tap) and is restricted to wye-wye-derived subtypes, since regulators are never delta-coupled — which keeps genuine 1:1 phase-shifting interconnectors silent.

This heuristic concerns imported data where a regulator was hacked into a transformer + shunt. The data model itself has dedicated regulator objects — single_phase_autotransformer (a fixed-tap step voltage regulator with the autotransformer shared-neutral coupling) and open_delta_regulator (monolithic open-delta with the galvanic straight-through of the shared phase) — so a regulator authored natively needs no such pattern-matching. See the OPF reference for their constraints and the conventions for the field set. The from_dss converter does not yet emit these subtypes (regulators arriving from OpenDSS are still detected via the pattern above rather than converted).

Benchmark readiness

Raw utility-derived feeders are power-flow cases, not OPF benchmarks: they ship without costed generation (degenerate objective), without voltage bounds, sometimes without thermal limits [2, 3, 14]. The transmission community closed the analogous gap with curated, well-posed benchmark libraries such as PGLib-OPF [13]; the readiness check exists to bring the same discipline to distribution cases. The readiness check encodes the augmentation recipe of the PSCC study [3] — explicit slack generation (loss-minimisation objective), dispatchable DERs with diverse costs (cost symmetry creates dispatch degeneracy, I.INT.UNIFORM_GEN_COST), voltage envelopes including the sequence/phase-to-neutral bounds whose presence measurably improves NLP robustness [3], and cross-section-derived current ratings.

Beyond the structural augmentation check (I.BENCH.AUGMENTATION), four per-network degeneracy flags catch subtler problems that survive augmentation:

• W.BENCH.GEN_NO_DOF — generators with p_min ≈ p_max on every phase are fixed injections, not decision variables. They add model size without contributing to benchmark difficulty.
• W.BENCH.GEN_ZERO_COST — dispatchable generators with a zero cost vector make the objective flat in their dispatch direction; the optimal solution is primal non-unique and solver-dependent.
• W.BENCH.GEN_DEGENERATE_COST — pairs of dispatchable generators on the same bus or one hop apart with identical cost coefficients allow free power redistribution between them. Benchmarks with this property have multiple optima and produce inconsistent comparisons across solvers.
• I.BENCH.LOAD_ZERO_PNOM — loads with zero real-power setpoint are electrically inert and likely represent missing or placeholder data.

References

1. M. Deakin, A. Pandey, F. Geth, Mathematical Model and Data Model for Up-To-Four-Wire Distribution System OPF, IEEE Task Force on Benchmarking Multiconductor OPF for Distribution Systems, draft V0.2, 2026.
2. F. Geth, A. C. Chapman, R. Heidari, J. Clark, "Considerations and design goals for unbalanced optimal power flow benchmarks," Electric Power Systems Research 235 (2024) 110646.
3. F. Geth, F. Pacaud, R. Heidari, "Solving Three-Phase Distribution OPF with Nonlinear Programming," PSCC 2026, Limassol.
4. J. R. Carson, "Wave propagation in overhead wires with ground return," Bell System Technical Journal 5 (1926) 539–554.
5. W. H. Kersting, Distribution System Modeling and Analysis, CRC Press, 2002.
6. S. Claeys, F. Geth, G. Deconinck, "Optimal power flow in four-wire distribution networks: Formulation and benchmarking," Electric Power Systems Research 213 (2022) 108522.
7. F. Geth, R. Heidari, A. Koirala, "Computational analysis of impedance transformations for four-wire power networks with sparse neutral grounding," Proc. ACM e-Energy '22, 2022, 105–113.
8. R. Heidari, F. Geth, S. Claeys, Four-wire low voltage power network dataset, CSIRO Data Collection, 2024, doi:10.25919/jaae-vc35; original data: ENWL Low Voltage Network Solutions project (LCNF closedown report, 2014); cable impedances: A. J. Urquhart, M. Thomson, Cable Impedance Data, figshare, 2019.
9. R. C. Dugan, T. E. McDermott, "An open source platform for collaborating on smart grid research," Proc. IEEE PES General Meeting, 2011; EPRI OpenDSS documentation, incl. Modeling Regulators as Autotransformers.
10. F. Dörfler, F. Bullo, "Kron reduction of graphs with applications to electrical networks," IEEE Trans. Circuits and Systems I 60 (2013) 150–163.
11. F. Zhang (ed.), The Schur Complement and Its Applications, Springer, 2005 (incl. D. Carlson, T. L. Markham, "Schur complements of diagonally dominant matrices," Czech. Math. J. 29 (1979) for the M-matrix closure).
12. M. Bazrafshan, N. Gatsis, "Comprehensive modeling of three-phase distribution systems via the bus admittance matrix," IEEE Trans. Power Systems 33 (2018) 2015–2029.
13. S. Babaeinejadsarookolaee et al., "The power grid library for benchmarking AC optimal power flow algorithms," arXiv:1908.02788, 2019.
14. F. Geth, M. Vanin, D. Van Hertem, "Data quality challenges in existing distribution network datasets," CIRED 2023, Rome.
15. D. M. Fobes, S. Claeys, F. Geth, C. Coffrin, "PowerModelsDistribution.jl: An open-source framework for exploring distribution power flow formulations," Electric Power Systems Research 189 (2020) 106664; arXiv:2004.10081.
16. R. C. Dugan, "A Perspective on Transformer Modeling for Distribution System Analysis," Proc. IEEE PES General Meeting, 2003, pp. 114–119 (the case for solving in actual values rather than per-unit; cites H. W. Dommel, EMTP Theory Book, 2nd ed., App. IV, on per-unit obsolescence for computer solution of unbalanced networks).
17. W. H. Kersting, "The Whys of Distribution System Analysis," Proc. IEEE Rural Electric Power Conference (REPC), 2010 (why the transmission assumptions of transposed lines and balanced loading — and hence the positive-sequence/symmetrical-component model — do not transfer to distribution; worked IEEE 13-node examples of non-transposed-line and neutral/ground-current effects).
18. A. Wächter, L. T. Biegler, "On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming," Mathematical Programming 106 (2006) 25–57 (Ipopt; the solver's initialization, barrier updates and stopping tests are scale-sensitive, and it applies gradient-norm scaling because good scaling cannot be inferred in general).
19. J. D. Hogg, J. A. Scott, On the effects of scaling on the performance of Ipopt, STFC Rutherford Appleton Laboratory technical report RAL-TR-2013-P-001, 2013; arXiv:1301.7283 (the benefit of scaling a nonlinear program is problem-dependent, not universal).
20. S. A. Sadat, K. Kim, "Numerical Performance of Different Formulations for Alternating Current Optimal Power Flow," Proc. IEEE PES ISGT, 2021; arXiv:2107.07700 (IPM numerical performance on AC-OPF is strongly formulation-dependent).
21. M. D. Wilkinson et al., "The FAIR Guiding Principles for scientific data management and stewardship," Scientific Data 3 (2016) 160018 (Interoperable and Reusable data require shared vocabularies and recorded provenance, not raw dumps).
22. H. Wickham, "Tidy Data," Journal of Statistical Software 59 (10) (2014) 1–23 (data is usually organised for ease of entry rather than analysis; standardising the mapping of semantics to representation is what makes reliable, composable tooling possible).
23. IEC 61968-11:2013, Application integration at electric utilities — System interfaces for distribution management — Part 11: Common Information Model (CIM) extensions for distribution; the network "wires model" represents connectivity through explicit Terminal and ConnectivityNode objects (the structure OpenDSS leaves implicit). See also the OpenDSS CIM100 export of [ref. 9].
24. F. Wiese et al., "Open Power System Data — Frictionless data for electricity system modelling," Applied Energy 236 (2019) 401–409 (a validated, schema-checked, reproducible path from raw data to results for energy-system modelling).
25. L. Moreau, P. Missier (eds.), PROV-DM: The PROV Data Model, W3C Recommendation, 2013 (provenance as the mechanism that makes a non-identity transformation trustworthy; validity is itself defined via a normalisation process).
26. D. K. Molzahn, B. C. Lesieutre, C. L. DeMarco, "Approximate Representation of ZIP Loads in a Semidefinite Relaxation of the OPF Problem," IEEE Trans. Power Syst. 29 (4) (2014) 1864–1865 (a constant-impedance load is a shunt admittance Sⱼ/|Vⱼ|²; the load/shunt identity is a modelling choice, not a physical one).
27. H. J. Kim et al., "A Comprehensive Review of Practical Issues for Interoperability Using the Common Information Model in Smart Grids," Energies 13 (6) (2020) 1435 (CIM as an asset-first, object-identity model for semantic interoperability and data exchange).
28. B. Bahrani et al., "Grid-Forming IBR-Based Resource Research Landscape: Understanding the Key Assets for Renewable-Rich Power Systems," IEEE Power & Energy Magazine 22 (2) (2024) 18–29 (IBR-based resources as a distinct asset class from synchronous generators — capability-limited, inertia-free, control-defined).