We introduce a framework for physics-informed neural networks in power system applications. Exploiting the underlying physical laws governing power systems, and inspired by recent developments in the field of machine learning, we propose a neural network training procedure that can make use of the wide range of mathematical models describing power system behavior, both in steady-state and in dynamics. Physics-informed neural networks require substantially less training data and result in much simpler neural network structures, while achieving high accuracy. This work unlocks a range of opportunities in power systems, being able to determine dynamic states, such as rotor angles and frequency, and uncertain parameters such as inertia and damping at a fraction of the computational time required by conventional methods. We focus on introducing the framework and showcases its potential using a single-machine infinite bus system as a guiding example. Physics-informed neural networks are shown to accurately determine rotor angle and frequency up to 87 times faster than conventional methods.
The folder continuous_time_inference’ corresponds to the results presented in Section III.B. First, we load the input data file (swingEquation_inference.mat’). Then, we randomly define the training set based on the number of Nu. After the training process, the variables U_pred and Exact contain the predicted and actual values of the angle trajectories, respectively. The code also provides the L2 error between exact and predicted solutions for the angle (error_u).
The folder `continuous_time_identification’ corresponds to the results presented in Section III.C. By running the file swingEquation_identification.py we can predict system inertia and damping based on the input data (swingEquation_identification.mat). The exact values of the inertia and damping levels are 0.25 and 0.15. After the training process, the code prints the estimation error for the inertia (error_lambda_1) and damping (error_lambda_2), as well as the L2 error between exact and predicted solutions for the angle (error_u).
Code variables: lb : defines the lower bound for the inputs (P,t) ub: defines the upper bound for the inputs (P,t) Nu : number of initial and boundary data Nf : number of collocation points usol (δ): is an array containing the angle trajectories for different pair of (P,t) (output to the NN) x (P1): is an array containing different power levels in the range [0.08, 0.18] (input to the NN) t : is an array containing time instants in the range [0, 20] (input to the NN)
When publishing results based on this data/code, please cite: G. Misyris, A. Venzke, S. Chatzivasileiadis, " Physics-Informed Neural Networks for Power Systems", 2019. Available online: https://arxiv.org/abs/1911.03737
@misc{misyris2019physicsinformed, title={Physics-Informed Neural Networks for Power Systems}, author={George S. Misyris and Andreas Venzke and Spyros Chatzivasileiadis}, year={2019}, eprint={1911.03737}, archivePrefix={arXiv}, primaryClass={eess.SY} }