3,337 research outputs found
Applied Koopman Operator Theory for Power Systems Technology
Koopman operator is a composition operator defined for a dynamical system
described by nonlinear differential or difference equation. Although the
original system is nonlinear and evolves on a finite-dimensional state space,
the Koopman operator itself is linear but infinite-dimensional (evolves on a
function space). This linear operator captures the full information of the
dynamics described by the original nonlinear system. In particular, spectral
properties of the Koopman operator play a crucial role in analyzing the
original system. In the first part of this paper, we review the so-called
Koopman operator theory for nonlinear dynamical systems, with emphasis on modal
decomposition and computation that are direct to wide applications. Then, in
the second part, we present a series of applications of the Koopman operator
theory to power systems technology. The applications are established as
data-centric methods, namely, how to use massive quantities of data obtained
numerically and experimentally, through spectral analysis of the Koopman
operator: coherency identification of swings in coupled synchronous generators,
precursor diagnostic of instabilities in the coupled swing dynamics, and
stability assessment of power systems without any use of mathematical models.
Future problems of this research direction are identified in the last
concluding part of this paper.Comment: 31 pages, 11 figure
Estimation of Power System Inertia Using Nonlinear Koopman Modes
We report a new approach to estimating power system inertia directly from
time-series data on power system dynamics. The approach is based on the
so-called Koopman Mode Decomposition (KMD) of such dynamic data, which is a
nonlinear generalization of linear modal decomposition through spectral
analysis of the Koopman operator for nonlinear dynamical systems. The KMD-based
approach is thus applicable to dynamic data that evolve in nonlinear regime of
power system characteristics. Its effectiveness is numerically evaluated with
transient stability simulations of the IEEE New England test system.Comment: 10 pages, 4 figures, conferenc
Decomposition of Nonlinear Dynamical Systems Using Koopman Gramians
In this paper we propose a new Koopman operator approach to the decomposition
of nonlinear dynamical systems using Koopman Gramians. We introduce the notion
of an input-Koopman operator, and show how input-Koopman operators can be used
to cast a nonlinear system into the classical state-space form, and identify
conditions under which input and state observable functions are well separated.
We then extend an existing method of dynamic mode decomposition for learning
Koopman operators from data known as deep dynamic mode decomposition to systems
with controls or disturbances. We illustrate the accuracy of the method in
learning an input-state separable Koopman operator for an example system, even
when the underlying system exhibits mixed state-input terms. We next introduce
a nonlinear decomposition algorithm, based on Koopman Gramians, that maximizes
internal subsystem observability and disturbance rejection from unwanted noise
from other subsystems. We derive a relaxation based on Koopman Gramians and
multi-way partitioning for the resulting NP-hard decomposition problem. We
lastly illustrate the proposed algorithm with the swing dynamics for an IEEE
39-bus system.Comment: 8 pages, submitted to IEEE 2018 AC
Data-driven Identification and Prediction of Power System Dynamics Using Linear Operators
In this paper, we propose linear operator theoretic framework involving
Koopman operator for the data-driven identification of power system dynamics.
We explicitly account for noise in the time series measurement data and propose
robust approach for data-driven approximation of Koopman operator for the
identification of nonlinear power system dynamics. The identified model is used
for the prediction of state trajectories in the power system. The application
of the framework is illustrated using an IEEE nine bus test system.Comment: Accepted for publication in IEEE Power and Energy System General
Meeting 201
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