Learning goals¶
Formulate forward dynamics, stability assessment, and inverse estimation as distinct tasks
Distinguish states from parameters
Contrast forward simulation with inverse identification
Reading¶
Power-system context: Kundur & Malik (2022); SciML landscape: Karniadakis et al. (2021)
Book map for the three applications
Three tasks (same SMIB, different questions)¶
| Task | Given | Infer | Evaluate |
|---|---|---|---|
| Forward dynamics | Model, initial state, inputs, parameters | Trajectories | Trajectory / rollout error |
| Stability assessment | Operating point, contingency, clearing rule | Stable/unstable or CCT | False-safe rate, CCT error |
| Inverse estimation | Measurements (+ known inputs) | Parameters (and often ) | Recovery, identifiability, held-out events |
Do not mix metrics: a model with low trajectory NRMSE can still be false-safe near a stability boundary, or recover the wrong parameters.
State vs parameter¶
State estimation asks: what is the system doing over time?
Examples: rotor angle , speed . States change with time.
Parameter estimation asks: what are the fixed unknown constants in the model?
Teaching examples: inertia , damping . (Converter virtual inertia / droop appear later as electives — keep estimands explicit.)
Analogy:
State = movie frames
Parameter = camera / machine settings
A network can draw a beautiful trajectory while guessing the wrong settings. Nice plots are not enough; later labs need recovery checks and held-out disturbances.
Forward vs inverse¶
FORWARD: known θ + inputs / disturbance → trajectories x(t)
INVERSE: measured trajectories (+ known inputs) → unknown θ| Style | Typical goal |
|---|---|
| Forward PINN / surrogate | Fast trajectories when is known or assumed |
| Inverse PINN | Calibrate named from PMU-like data |
| Classical simulator (e.g. ANDES later) | High-fidelity forward reference |
Changing in a simulator and re-running is forward. Given frequency after a load step and asking for is inverse.
Worked example¶
Specify one SMIB fault-on/clearing case in writing:
What is known? What is unknown?
Is the goal a trajectory, a stability label/CCT, or a parameter vector?
Which metric would decide success?
Lab¶
Foundations continue into Lab 1 — reference simulation
Further reading¶
SciML method families for how the three tasks map onto method choices
Identifiability for why inverse estimation needs more than a good fit
Common misconceptions¶
“Good waveform fit proves parameters are correct.” — No.
“PINN replaces the need to define the engineering task.” — No; the task defines the loss and metrics.
Treating converter GFM knobs and classical as interchangeable without saying so.
- Kundur, P., & Malik, O. P. (2022). Power System Stability and Control (Second). McGraw-Hill Education. https://openlibrary.org/isbn/9781260473544
- Karniadakis, G. E., Kevrekidis, I. G., Lu, L., Perdikaris, P., Wang, S., & Yang, L. (2021). Physics-informed machine learning. Nature Reviews Physics, 3(6), 422–440. 10.1038/s42254-021-00314-5