Characterizing the load profile in power grids by Koopman mode decomposition of interconnected dynamics

• URL: http://arxiv.org/abs/2304.07832v1
• Date: Sun, 16 Apr 2023 16:56:52 GMT
• Title: Characterizing the load profile in power grids by Koopman mode decomposition of interconnected dynamics
• Authors: Ali Tavasoli, Behnaz Moradijamei, Heman Shakeri
• Abstract summary: This paper presents an interpretable machine learning approach that identifies load dynamics using data-driven methods. We represent the load data using the Koopman operator, which is inherent to underlying dynamics. We evaluate our approach using a large-scale dataset from a renewable electric power system within the continental European electricity system.
• Score: 0.6629765271909505
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Electricity load forecasting is crucial for effectively managing and optimizing power grids. Over the past few decades, various statistical and deep learning approaches have been used to develop load forecasting models. This paper presents an interpretable machine learning approach that identifies load dynamics using data-driven methods within an operator-theoretic framework. We represent the load data using the Koopman operator, which is inherent to the underlying dynamics. By computing the corresponding eigenfunctions, we decompose the load dynamics into coherent spatiotemporal patterns that are the most robust features of the dynamics. Each pattern evolves independently according to its single frequency, making its predictability based on linear dynamics. We emphasize that the load dynamics are constructed based on coherent spatiotemporal patterns that are intrinsic to the dynamics and are capable of encoding rich dynamical features at multiple time scales. These features are related to complex interactions over interconnected power grids and different exogenous effects. To implement the Koopman operator approach more efficiently, we cluster the load data using a modern kernel-based clustering approach and identify power stations with similar load patterns, particularly those with synchronized dynamics. We evaluate our approach using a large-scale dataset from a renewable electric power system within the continental European electricity system and show that the Koopman-based approach outperforms a deep learning (LSTM) architecture in terms of accuracy and computational efficiency. The code for this paper has been deposited in a GitHub repository, which can be accessed at the following address github.com/Shakeri-Lab/Power-Grids.

Related papers

• Data-Driven Characterization of Latent Dynamics on Quantum Testbeds [0.23408308015481663]
  We augment the dynamical equation of quantum systems described by the Lindblad master equation with a parameterized source term. We consider a structure preserving augmentation that learns and distinguishes unitary from dissipative latent dynamics parameterized by a basis of linear operators. We demonstrate that our interpretable, structure preserving, and nonlinear models are able to improve the prediction accuracy of the Lindblad master equation.
  arXiv  Detail & Related papers  (2024-01-18T09:28:44Z)
• TimeGraphs: Graph-based Temporal Reasoning [64.18083371645956]
  TimeGraphs is a novel approach that characterizes dynamic interactions as a hierarchical temporal graph. Our approach models the interactions using a compact graph-based representation, enabling adaptive reasoning across diverse time scales. We evaluate TimeGraphs on multiple datasets with complex, dynamic agent interactions, including a football simulator, the Resistance game, and the MOMA human activity dataset.
  arXiv  Detail & Related papers  (2024-01-06T06:26:49Z)
• Leveraging Neural Koopman Operators to Learn Continuous Representations of Dynamical Systems from Scarce Data [0.0]
  We propose a new deep Koopman framework that represents dynamics in an intrinsically continuous way. This framework leads to better performance on limited training data.
  arXiv  Detail & Related papers  (2023-03-13T10:16:19Z)
• 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)
• Autoregressive Dynamics Models for Offline Policy Evaluation and Optimization [60.73540999409032]
  We show that expressive autoregressive dynamics models generate different dimensions of the next state and reward sequentially conditioned on previous dimensions. We also show that autoregressive dynamics models are useful for offline policy optimization by serving as a way to enrich the replay buffer.
  arXiv  Detail & Related papers  (2021-04-28T16:48:44Z)
• 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.