Incident replay
Report sequence → shared physics → compared with the reportEach replay sets the grid to the operating point on the day, steps through the loss sequence in the operator's report and moves the Stommel surface with it. The frequency trace is the model's own reconstruction — the same inertia, response and protection rules for every incident — read with the PMU inspector's instrument. Report figures are inputs or comparators, never tuning factors.
Inverter share: (wind 883 MW + Heywood import 525 MW) / SA demand 1,826 MW, from the report's pre-event balance. Project EnergyConnect did not exist in 2016, so SA's only AC path to the NEM was Heywood.
| Check | Report | Model |
|---|---|---|
| Island RoCoF | ≈ 6.25 Hz/sreport | 5.03 Hz/s · 0.80× report |
| Frequency collapse | Yes — black systemreport | Yes — 0.54 s after separation |
| Converter ride-through action | Yes — 456 MW wind reductionreport | Flagged — 3 zone(s), SLG fault |
Limits of this replay. The six faults are collapsed into one sequence; per-farm counter settings and the exact Heywood swing are not modelled. UFLS is set to zero because the report finds it could not act at that RoCoF. Traces and COMTRADE files are model reconstructions labelled as such — they are not the operator's recordings. Report figures were transcribed from the sources below; check them against the originals before external use.
Sources: AEMO, Black System South Australia 28 September 2016 — Integrated Final Report (March 2017)
A response you can define and reproduce
Balanced power modulation at two inertia-bearing nodes → their relative-frequency difference. Six discrete electrical pair experiments; no invented spatial interpolation.
Mechanism → evidence → next study
Four disturbances. Different questions.
A protection sequence, plant resonance, multiple inverter responses and series-compensated wind interaction do not establish one common cause.
Prescribed reconstruction
South Australia 2016
Repeated-fault ride-through and protection
- 1Storm faults
- 2Repeated voltage disturbances
- 3Wind control/protection response
- 4Interconnector separation
Local protection logic → interconnector and island. Mechanism extent is assigned, not a measured electrical radius.
- The study question
- Will the installed ride-through settings tolerate the relevant repeated-fault sequence?
- Appropriate next studies
- Repeated-fault protection/settings audit
- Plant control and network dynamic studies
- Minimum evidence
- Installed controller counters, reset logic, protection settings and the actual fault sequence.
- What this cannot establish
- An inertia total or generic converter cannot predict the installed fleet’s trip sequence.
AEMO final investigation; existing frequency reconstruction remains model-conditional. Executive summary; wind-farm response and generation reduction sections. Qualitative mechanism corroborated; embedded numerical inputs await page-level audit.
AEMO Black System Final Report (2017)An open solver is a check, not a certificate
Numerical verification. 4 frozen reduced configurations, independently reconstructed in SciPy. Maximum natural-frequency discrepancy: 8.72e-15; minimum mode-shape MAC: 1.00000000. This checks the implementation, not physical accuracy.
ANDES 2.0.0 RMS run. Full IEEE39 deck: 10 machines, 160 retained linear states, bus-14 balanced fault cleared after 100 ms. Time-step comparison: 0.000131 Hz maximum rotor-frequency difference. Its controllers and dispatch differ from the reduced model.
0/20 matched stress gates completed. No RMS/EMT parity, field-trip prediction or 70% acceptance probability is established. Incident transcriptions, prior-art review, funding, permissions and final author approval remain outstanding.
Unresolved reference findings: ANDES reports 6 positive-real eigenvalues, parameter corrections and ill-conditioning warnings. Eight seconds of successful integration is not stable long-term recovery. Lossless verification passed; nominal-resistance IEEE39 response is withheld for indefinite symmetrized stiffness.
Analytical companion: explicit +P/−P machine-pair ports and relative-frequency output, G in Hz/GW. The Gaussian Ψ stays a constructed screen; Ψ = 1 is not a proven relay boundary. Electrical pair lengths use one equivalent-400 kV-circuit convention.
V3 · Rolf Bastiaanssen, Bax & Company. The operating-region explorer separates physical inertia, equivalent virtual support and GFL strength; conditional screens are not certified dispatch. SSCI 2009 is source-led, not a new simulated replay. No submission or public DOI deposit has been made.
Laplacian eigenmode inspector
Kron-reduced swing modes on a network built from published corridor capabilities — no per-grid tuning. Click a corridor to cycle it in service → reinforced ×2 → out of service. The least-damped inter-area mode drives the oscillation ridge on the surface; the multi-infeed generalised SCR (see Advanced stability physics) drives the PLL band.
Reinforcing a corridor stiffens KL and raises f; damping depends on where synchronous machines, PSS and GFM sit. Instruments: power-oscillation damping on GFM / HVDC, WAMPAC separation schemes.
| Mode | Class | f (Hz) | ζ | Extent | Swing pair / node |
|---|---|---|---|---|---|
| ci-west | Control interaction | 20.00 | -10.0% | 186 km | Far West / Permian · no operating point (voltage collapse) |
| em3 | Local / intra-area | 1.62 | 3.4% | 124 km | Coast / STP ↔ Houston |
| em5 | Local / intra-area | 1.77 | 3.9% | 461 km | Far West / Permian ↔ Central / Austin |
| em6 | Local / intra-area | 1.90 | 4.1% | 351 km | Rio Grande Valley ↔ South / San Antonio |
| em4 | Local / intra-area | 1.69 | 4.2% | 172 km | Central / Austin ↔ North / DFW |
| em2 | Inter-area | 1.28 | 4.8% | 356 km | South / San Antonio ↔ North / DFW |
| em7 | Local / intra-area | 2.46 | 5.2% | 1054 km | Panhandle ↔ Rio Grande Valley |
| em1 | Inter-area | 1.20 | 6.0% | 381 km | Houston ↔ North / DFW |
| Observation | Observed | Model | Error |
|---|---|---|---|
ERCOT dominant inter-area mode Ringdown after unit trip, 10 Sep 2013 (UT Austin–Baylor PMUs) · SEL / Texas Synchrophasor Network 2014 Model: Houston ↔ North / DFW | 0.69–0.7 Hz ζ 11.6% | 0.73 Hz ζ 5.6% | +4% |
Type-4 wind / weak grid SSO Texas 2011 (location not public — mapped to Panhandle) · Cheng et al. 2023 / ERCOT 2024 Model: onset at SCR 1.28 · node SCR 8.79 at 15% IBR | 4 Hz | 8.62 Hz ζ 6.7% | +115% |
Each row re-runs the model at the IBR share of the observation, without interventions or corridor changes. Frequencies are predicted, not fitted. Damping uses generic coefficients (amortisseur 2 pu, load 1.5 pu, PSS ≤ 5 %), so ζ is indicative only; real damping depends on PSS / POD tuning held in operator models. Control-interaction rows compare the frequency at instability onset; fault-level rows compare the three-phase short-circuit power at the node.
| CREZ West–North 345 kV | 6,000 MW | estimated |
| CREZ West–Central 345 kV | 4,000 MW | estimated |
| Panhandle GTC → North | 3,500 MW | estimated |
| Panhandle–West 345 kV | 1,500 MW | estimated |
| North–Central 345 kV | 8,000 MW | estimated |
| North–Houston 345 kV | 6,000 MW | estimated |
| Central–South 345 kV | 6,000 MW | estimated |
| South–Coast 345 kV | 3,000 MW | estimated |
| STP–Houston 345 kV | 5,000 MW | estimated |
| South Texas–Valley 345 kV | 2,000 MW | estimated |
| Coastal–Valley 345 kV | 1,200 MW | estimated |
- Corridor stiffness K = κ·Pcap, κ = 1.94 rad⁻¹: capability reached at 30°, operated at 50 %.
- Node positions are real substation / zone coordinates; zonal load, synchronous-fleet and installed-IBR splits are estimates from public capacity statistics.
- Nodal SCR from the network Thevenin impedance (machines x″d 0.35 pu, GFM 0.25 pu); GFL limit SCR 1.28 from a 7-state PLL / current / voltage-loop model.
- D. Costello (SEL), Synchrophasor Applications, ERCOT STF, Feb 2014 — ringdown fit 0.696 Hz, ζ 0.116
- M. Grady, Compendium of Texas Synchrophasor Network Reports 2009–2010 (0.7 Hz mode always present)
- ERCOT, 2020 Panhandle Regional Stability Study (≈5.2 GW IBR behind the Panhandle GTC; WSCR ≥ 1.5 criterion)
- Y. Cheng (ERCOT), Managing System Oscillations in the ERCOT System — reported IBR SSO events table, 2024
Advanced stability physics
Four extensions behind the surface: interacting inverter plants, grid-forming control as a dynamic model, voltage stability under corridor outages, and uncertainty. Each uses one generic tuning for every grid.
| Infeed | IBR GW | SCR | MIESCR | Critical-mode participation |
|---|---|---|---|---|
| Panhandle | 5.72 | 1.47 | 0.27 | |
| Rio Grande Valley | 4.40 | 1.44 | 0.32 | |
| Far West / Permian | 26.39 | 0.74 | 0.51 | |
| Coast / STP | 3.30 | 4.48 | 0.86 | |
| South / San Antonio | 6.60 | 3.00 | 0.98 | |
| Central / Austin | 4.40 | 6.18 | 1.14 | |
| North / DFW | 8.80 | 4.66 | 1.79 | |
| Houston | 3.30 | 8.83 | 2.06 |
The infeed buses share network impedance, so a voltage change at one moves its neighbours: MIIFij = Zij/Zjj from the Z-bus of the fault-level network. With identical converter controls the multi-infeed system decouples into single-infeed systems whose SCRs are the eigenvalues of P−½YredP−½ (Dong et al., IEEE TPWRS 2019); the smallest, gSCR, is what the surface's PLL band now uses. Assumes identical GFL tuning and a quasi-static network.
Policy & dispatch lab
Regulatory decision matrix. The tab for the τ regime under the cursor is highlighted; changes reshape the surface in real time.
Virtual synchronous machine control; adds inertia and short-circuit strength.
H on the GFM rating. System contribution = H·P_GFM / S_base.
PMU / COMTRADE ingestion
Load a phasor event to compute its local Stommel profile (rolling-window RoCoF, Morlet wavelet energy by τ).
Beyond the linear, balanced model
Four tests of where the small-signal, positive-sequence, lossless picture breaks down: distance measured electrically, lossy lines that make the dynamics non-normal, converter current limits during faults, and unbalanced faults. Same network, same conventions for every grid.
| Corridor | Map km | Electrical km | Stretch | Bottleneck index |
|---|---|---|---|---|
| STP–Houston 345 kV | 125 | 41 | ×1.87 | |
| Central–South 345 kV | 119 | 36 | ×1.72 | |
| Coastal–Valley 345 kV | 357 | 103 | ×1.63 | |
| South Texas–Valley 345 kV | 359 | 90 | ×1.42 | |
| South–Coast 345 kV | 244 | 50 | ×1.16 | |
| Panhandle–West 345 kV | 376 | 67 | ×1.00 | |
| Panhandle GTC → North | 552 | 56 | ×0.57 | |
| North–Houston 345 kV | 363 | 36 | ×0.56 | |
| North–Central 345 kV | 293 | 23 | ×0.44 | |
| CREZ West–Central 345 kV | 477 | 33 | ×0.39 |
Effective distance dij = L⁺ii + L⁺jj − 2L⁺ij on the corridor susceptance Laplacian (Moore–Penrose pseudoinverse) is the Thevenin reactance between two buses through the whole mesh, shown as equivalent km of one 400 kV circuit (x = 0.30 Ω/km, 0.00187 pu/km on 1 GVA). Stretch = (electrical / map length) ÷ the network median: values above 2 are electrical bottlenecks that geography hides. Switch the network map above to Electrical to see the flattened layout, and the surface's mode markers to electrical extent with the toggle next to the map. Corridor reactance follows the same capability convention as the eigenmode model, so the ranking inherits its data basis.
Regulatory sandbox tools
Conditional operating-region and regulatory screens on the shared physics: derogation, locational value, permissible penetration and grid-code assessment. They use the scenario, inverter share, corridors and Policy Lab portfolio set above. Economic inputs are editable assumptions.
No pilot up to 3× the plant size restores the margins: the extra trip on a fault outweighs the pilot's support.
| Case | Local SCR | MIESCR | gSCR | Nodal RoCoF Hz/s | Load shed GW |
|---|---|---|---|---|---|
| Before connection | 0.74 | 0.51 | 0.61 | 0.25 | 3.15 |
| Derogated + GFM pilot | 0.74 | 0.52 | 0.61 | 0.33 | 5.07 |
| Derogated, no pilot | 0.73 | 0.50 | 0.60 | 0.33 | 5.07 |
Margin tests: gSCR ≥ 0.61 (already below the GFL limit before connection — must not get worse) · nodal RoCoF ≤ 0.25 Hz/s (already above the limit before connection — must not get worse).
A relaxed fault-ride-through standard means the derogated plant may trip on a nearby fault, so its output is added to the design loss at that zone. The pilot adds grid-forming strength and inertia at the same node. Nodal RoCoF is measured over 500 ms at the substations; risk counts only the load shed the derogation adds, over the derogation period, at the stated fault rate and a 0.5 h restoration time. Fault rate, VoLL and output value are inputs, not operator data.
Industry research workbench
Draft screening · not certificationNo invented OEM presets. Imported manufacturer names and parameters remain user-supplied until independently verified.