An Interpretable Approach to Load Profile Forecasting in Power Grids using Galerkin-Approximated Koopman Pseudospectra

• URL: http://arxiv.org/abs/2304.07832v2
• Date: Fri, 29 Nov 2024 13:13:09 GMT
• Title: An Interpretable Approach to Load Profile Forecasting in Power Grids using Galerkin-Approximated Koopman Pseudospectra
• Authors: Ali Tavasoli, Behnaz Moradijamei, Heman Shakeri,
• Abstract summary: This paper presents an interpretable machine learning approach that characterizes dynamics within an operator-theoretic framework for electricity forecasting in power grids. We represent the dynamics of load data using the Koopman operator, which provides a linear, infinite-dimensional representation of the nonlinear dynamics. Our approach captures temporal coherent patterns due to seasonal changes and finer time scales, such as time of day and day of the week.
• Score: 0.3160121582090025
• License:
• Abstract: This paper presents an interpretable machine learning approach that characterizes load dynamics within an operator-theoretic framework for electricity load forecasting in power grids. We represent the dynamics of load data using the Koopman operator, which provides a linear, infinite-dimensional representation of the nonlinear dynamics, and approximate a finite version that remains robust against spectral pollutions due to truncation. By computing $\epsilon$-approximate Koopman eigenfunctions using dynamics-adapted kernels in delay coordinates, we decompose the load dynamics into coherent spatiotemporal patterns that evolve quasi-independently. Our approach captures temporal coherent patterns due to seasonal changes and finer time scales, such as time of day and day of the week. This method allows for a more nuanced understanding of the complex interactions within power grids and their response to various exogenous factors. We assess our method using a large-scale dataset from a renewable power system in the continental European electricity system. The results indicate that our Koopman-based method surpasses a separately optimized deep learning (LSTM) architecture in both accuracy and computational efficiency, while providing deeper insights into the underlying dynamics of the power grid\footnote{The code is available at \href{https://github.com/Shakeri-Lab/Power-Grids}{github.com/Shakeri-Lab/Power-Grids}.

Related papers

• Learnable Infinite Taylor Gaussian for Dynamic View Rendering [55.382017409903305]
  This paper introduces a novel approach based on a learnable Taylor Formula to model the temporal evolution of Gaussians. The proposed method achieves state-of-the-art performance in this domain.
  arXiv  Detail & Related papers  (2024-12-05T16:03:37Z)
• KFD-NeRF: Rethinking Dynamic NeRF with Kalman Filter [49.85369344101118]
  We introduce KFD-NeRF, a novel dynamic neural radiance field integrated with an efficient and high-quality motion reconstruction framework based on Kalman filtering. Our key idea is to model the dynamic radiance field as a dynamic system whose temporally varying states are estimated based on two sources of knowledge: observations and predictions. Our KFD-NeRF demonstrates similar or even superior performance within comparable computational time and state-of-the-art view synthesis performance with thorough training.
  arXiv  Detail & Related papers  (2024-07-18T05:48:24Z)
• Temporally-Consistent Koopman Autoencoders for Forecasting Dynamical Systems [38.36312939874359]
  We introduce the Temporally-Consistent Koopman Autoencoder (tcKAE) tcKAE generates accurate long-term predictions even with limited and noisy training data. We demonstrate tcKAE's superior performance over state-of-the-art KAE models across a variety of test cases.
  arXiv  Detail & Related papers  (2024-03-19T00:48:25Z)
• Statistical and machine learning approaches for prediction of long-time excitation energy transfer dynamics [0.0]
  The objective here is to demonstrate whether models such as SARIMA, CatBoost, Prophet, convolutional and recurrent neural networks are able to bypass this requirement. Our results suggest that the SARIMA model can serve as a computationally inexpensive yet accurate way to predict long-time dynamics.
  arXiv  Detail & Related papers  (2022-10-25T16:50:26Z)
• Physics-Inspired Temporal Learning of Quadrotor Dynamics for Accurate Model Predictive Trajectory Tracking [76.27433308688592]
  Accurately modeling quadrotor's system dynamics is critical for guaranteeing agile, safe, and stable navigation. We present a novel Physics-Inspired Temporal Convolutional Network (PI-TCN) approach to learning quadrotor's system dynamics purely from robot experience. Our approach combines the expressive power of sparse temporal convolutions and dense feed-forward connections to make accurate system predictions.
  arXiv  Detail & Related papers  (2022-06-07T13:51:35Z)
• Accelerated Continuous-Time Approximate Dynamic Programming via Data-Assisted Hybrid Control [0.0]
  We introduce an algorithm that incorporates dynamic momentum in actor-critic structures to control continuous-time dynamic plants with an affine structure in the input. By incorporating dynamic momentum in our algorithm, we are able to accelerate the convergence properties of the closed-loop system.
  arXiv  Detail & Related papers  (2022-04-27T05:36:51Z)
• Stochastically forced ensemble dynamic mode decomposition for forecasting and analysis of near-periodic systems [65.44033635330604]
  We introduce a novel load forecasting method in which observed dynamics are modeled as a forced linear system. We show that its use of intrinsic linear dynamics offers a number of desirable properties in terms of interpretability and parsimony. Results are presented for a test case using load data from an electrical grid.
  arXiv  Detail & Related papers  (2020-10-08T20:25:52Z)
• Liquid Time-constant Networks [117.57116214802504]
  We introduce a new class of time-continuous recurrent neural network models. Instead of declaring a learning system's dynamics by implicit nonlinearities, we construct networks of linear first-order dynamical systems. These neural networks exhibit stable and bounded behavior, yield superior expressivity within the family of neural ordinary differential equations.
  arXiv  Detail & Related papers  (2020-06-08T09:53:35Z)
• Forecasting Sequential Data using Consistent Koopman Autoencoders [52.209416711500005]
  A new class of physics-based methods related to Koopman theory has been introduced, offering an alternative for processing nonlinear dynamical systems. We propose a novel Consistent Koopman Autoencoder model which, unlike the majority of existing work, leverages the forward and backward dynamics. Key to our approach is a new analysis which explores the interplay between consistent dynamics and their associated Koopman operators.
  arXiv  Detail & Related papers  (2020-03-04T18:24:30Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.