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This paper presents a methodology to achieve lower-dimensional Koopman quasi-linear representations of nonlinear system dynamics using Koopman generalized eigenfunctions. The proposed approach considers the analytically derived Koopman…

To address the challenge of the renewable energy uncertainty, the ISO New England (ISO-NE) has proposed to apply do-not-exceed (DNE) limits, which represent the maximum nodal injection of renewable energy the grid can accommodate.…

In a dynamic distribution market environment, residential prosumers with solar power generation and battery energy storage devices can flexibly interact with the power grid via power exchange. Providing a schedule of this bidirectional…

Optimisation and simulation models for the design and operation of grid-connected distributed energy systems (DES) often exclude the inherent nonlinearities related to power flow and generation and storage units, to maintain an…

Echo State Networks (ESNs) are recurrent neural networks usually employed for modeling nonlinear dynamic systems with relatively ease of training. By incorporating physical laws into the training of ESNs, Physics-Informed ESNs (PI-ESNs)…

The Gaussian Process (GP) based Chance-Constrained Optimal Power Flow (CC-OPF) is an open-source Python code developed for solving economic dispatch (ED) problem in modern power grids. In recent years, integrating a significant amount of…

This paper introduces a framework for solving time-autonomous nonlinear infinite horizon optimal control problems, under the assumption that all minimizers satisfy Pontryagin's necessary optimality conditions. In detail, we use methods from…

Distributed algorithms can be efficiently used for solving economic dispatch problem (EDP) in power systems. To implement a distributed algorithm, a communication network is required, making the algorithm vulnerable to noise which may cause…

We consider cooperative communications with energy harvesting (EH) relays, and develop a distributed power control mechanism for the relaying terminals. Unlike prior art which mainly deal with single-relay systems with saturated traffic…

Loss minimization in distribution networks (DN) is of great significance since the trend to the distributed generation (DG) requires the most efficient operating scenario possible for economic viability variations. Moreover, voltage…

The proliferation of intermittent distributed renewable energy sources (RES) in modern power systems has fundamentally compromised the reliability and accuracy of deterministic net load forecasting. Generative models, particularly diffusion…

Koopman operator theory shows how nonlinear dynamical systems can be represented as an infinite-dimensional, linear operator acting on a Hilbert space of observables of the system. However, determining the relevant modes and eigenvalues of…

We investigate network performance of ultra-dense heterogeneous networks (HetNets) and study the maximum energy-efficient base station (BS) deployment incorporating probabilistic non-line-of-sight (NLoS) and line-of-sight (LoS)…

The analysis of Integrated Energy Systems (IES) is crucial for enhancing the comprehensive and complementary utilization of clean energy across China, significantly impacting the effective planning, operational coordination, and security…

General Electric (GE) Gas Power, a leading manufacturer of gas and steam turbines, manufactures and installs these turbines in power generation plants worldwide. They source components for these turbines from suppliers globally and…

This paper addresses the problem of nonlinear state estimation for dynamical systems whose governing equations are approximated through Koopman operator liftings. While Koopman-based predictors have demonstrated broad approximation…

In this paper, we develop a discrete unified gas kinetic scheme (DUGKS) for general nonlinear convection-diffusion equation (NCDE), and show that the NCDE can be recovered correctly from the present model through the Chapman-Enskog…

We present an approach to construct approximate Koopman-type decompositions for dynamical systems depending on static or time-varying parameters. Our method simultaneously constructs an invariant subspace and a parametric family of…

We consider a distributed optimal control problem governed by an elliptic PDE, and propose an embedded discontinuous Galerkin (EDG) method to approximate the solution. We derive optimal a priori error estimates for the state, dual state,…

This paper presents a data-driven method for constructing a Koopman linear model based on the Direct Encoding (DE) formula. The prevailing methods, Dynamic Mode Decomposition (DMD) and its extensions are based on least squares estimates…