Measurements and excitation - Scientific Machine Learning (SciML) for Power Systems (PS)

Learning goals¶

Specify observation channels, noise models, and window lengths
Design excitation so target parameters are informative
Tie measurement contracts to Lab 3 protocols

Reading¶

Lab 3; foundations identifiability chapter; excitation design Ljung, 1999

Measurement contract¶

Before fitting, write down:

Field	Example (SMIB teaching)
Channels	$\delta(t)$ and/or $\omega(t)$ (or PMU-like proxies)
Sampling	$\Delta t$ , window $[t_0,t_1]$
Noise	e.g. i.i.d. Gaussian on $\omega$ with stated $\sigma$
Known inputs	$P_m$ , event times
Unknowns	$(H,D)$ inside bounds

Excitation¶

A single mild load step may leave $D$ nearly flat on the loss surface. Prefer:

Clear fault-on/clearing swings (Lab 1 events), or
Multiple magnitudes / clearing times, with at least one held-out event for validation

Worked example¶

Compare a 2-D $(H,D)$ loss surface for a short clearing time vs a longer (still stable) clearing time. Which experiment tightens the valley along $D$ ?

Lab¶

Lab 3

Common misconceptions¶

Using the same event for training and “validation” without saying so
Estimating two weakly excited parameters and claiming both are physical
Changing noise between LS and PINN comparisons

References¶

Ljung, L. (1999). System Identification: Theory for the User (Second). Prentice Hall PTR. https://openlibrary.org/isbn/0136566952