Learning goals¶
Use a classical CCT check (equal-area / energy idea) when assumptions hold, before trusting only bisection or a surrogate
State when those assumptions fail (damping, multi-swing, converters)
Keep converter energy-function TSA as an elective, not Lab 5 default
Reading¶
Equal-area and energy chapters of Kundur & Malik (2022) (check the edition before class)
Why direct methods belong in a SciML course¶
SciML surrogates speed trajectories and CCT search. Direct methods give an independent physics-based estimate of clearing margin under simplified models. Comparing search-based CCT to a classical estimate (when valid) catches criterion bugs and overconfident surrogates.
Equal-area idea (classical SMIB sketch)¶
For a highly idealized SMIB (constant mechanical power, no damping, classical “before / during / after” network strengths), the equal-area criterion balances accelerating and decelerating areas in the – plane. The critical clearing angle (and thus CCT, given fault-on dynamics) is the clearing angle at which the decelerating area just matches the accelerating area.
Teaching use:
State the assumptions explicitly.
Compute or look up the classical critical clearing angle / time for a chosen SMIB case.
Run Lab 5-style bisection with the same stability rule as elsewhere.
If assumptions hold and the rule is first-swing oriented, expect rough agreement; investigate large disagreements.
Do not treat equal-area as a general certificate for damped, multi-machine, or converter-rich cases.
Energy-function / Lyapunov ideas (preview)¶
Lyapunov-style transient energy functions compare “energy” after clearing to a critical energy associated with a stability boundary. They motivate direct TSA and CCT without a long time-domain sweep — under a stated model and energy function.
For this course:
Classical energy ideas deepen understanding of why clearing early helps.
GFM/GFL converter energy-function CCT is a research-strength topic and belongs as a later Advanced / elective case study, not as the assessed Lab 5 plant.
Relation to Labs and surrogates¶
| Tool | Role |
|---|---|
| Reference TDS + bisection | Operational CCT under a stated rule (Lab 5 core) |
| Equal-area / classical energy | Independent check when assumptions allow |
| Trajectory surrogate + same rule | Fast repeat of the search (Lab 2 → Lab 5) |
Same rule across all three. Trajectory RMSE alone does not validate CCT.
Exercise 1 (When equal-area is a fair check)
You have a classical SMIB Lab 5 bisection CCT under a first-swing rule. Name two modelling assumptions that must hold before you treat an equal-area CCT as a meaningful cross-check — and one situation where you should refuse the comparison.
Solution to Exercise 1
Fair when (for example) mechanical power is treated as constant and damping is negligible, and the network is reduced to classical before/during/after strengths matching the equal-area sketch. Refuse the comparison for strongly damped swings, multi-swing criteria, or converter-rich plants where classical equal-area assumptions do not hold — then use energy ideas only as elective background, not as a Lab 5 certificate.
Lab¶
Lab 5 — Stability and CCT: after SMIB bisection works, optionally compare to equal-area under documented assumptions
Surrogates: Surrogate models for stability tasks
Further reading¶
Classification context Kundur et al., 2004Hatziargyriou et al., 2021
Energy-function TSA for converter-dominated grids: see the Advanced part
Common misconceptions¶
“Equal-area replaces the need to state a simulation criterion.”
“Energy methods always apply to GFM/GFL without new models.”
Using direct-method CCT from one model to certify a surrogate trained on another plant.
- Kundur, P., & Malik, O. P. (2022). Power System Stability and Control (Second). McGraw-Hill Education. https://openlibrary.org/isbn/9781260473544
- Kundur, P., Paserba, J., Ajjarapu, V., Andersson, G., Bose, A., Canizares, C., Hatziargyriou, N., Hill, D. J., Stankovic, A., Taylor, C., Van Cutsem, T., & Vittal, V. (2004). Definition and Classification of Power System Stability IEEE/CIGRE Joint Task Force on Stability Terms and Definitions. IEEE Transactions on Power Systems, 19(3), 1387–1401. 10.1109/TPWRS.2004.825981
- Hatziargyriou, N., Milanovic, J., Rahmann, C., Ajjarapu, V., Canizares, C., Erlich, I., Hill, D., Hiskens, I., Kamwa, I., Pal, B., Pourbeik, P., Sanchez-Gasca, J., Stankovic, A., Van Cutsem, T., Vittal, V., & Vournas, C. (2021). Definition and Classification of Power System Stability – Revisited & Extended. IEEE Transactions on Power Systems, 36(4), 3271–3281. 10.1109/TPWRS.2020.3041774