Machine learning for power-systems people

You already know models, measurements, and simulation. This page names the learning words these notes use, in power-system language. Training and neural networks: Bishop & Bishop (2024). Data and dynamical systems: Brunton & Kutz (2022). Physics-informed training: Karniadakis et al. (2021). Both readings of each word are in the glossary.

A model is a function with knobs¶

A neural network is a flexible function. Its knobs are called weights. Weights are free numbers inside the function. They are separate from inertia $H$ and damping $D$. When a chapter says the estimands are $(H, D)$, those two stay named parameters with units and bounds. The network is only there to represent a trajectory or a missing term.

Data¶

One example is one simulation run or one measured window. Inputs might be time, a clearing time, or a parameter value. Outputs might be rotor angle and speed over that window, or a stable/unstable label. A table of many runs is the dataset. The Lab 1 manifest is that table, written down.

Loss, in the language of least squares¶

A loss is a single number that is small when the model agrees with the evidence you named. Least squares between a simulated angle and a measured angle is a loss. Training moves the knobs to reduce that number.

Gradient descent takes a step downhill on the loss. Automatic differentiation computes that downhill direction for you. One pass through the training examples is an epoch. You will see these words in Automatic differentiation and Classical estimation. Classical least squares remains the baseline beside every neural estimator in this book.

Generalization¶

A fit can match the runs used to train it and fail on a new disturbance. Overfitting means the model memorized the training runs. These notes split data by scenario (a different clearing time or a different fault), and they ask you to report the scenarios that were held out. A low loss on the training window is a training result. A held-out disturbance is the check.

What “physics-informed” adds¶

A physics-informed neural network keeps the data loss and adds a residual of the differential equation. The swing equation you already trust becomes part of the number being minimized. The residual is small when the network’s angle and speed satisfy that equation at a set of time points. Details: Forward PINNs.

Where to go¶

1. Data and surrogates

2. Classical estimation (the baseline you already know how to judge)

3. Forward PINNs

If you have never run a notebook, start with Programming from zero and Your first lab. If the machine model itself should be refreshed, skim SMIB dynamics for the units this book uses.