Takashi Hikihara

Yoshihiko Susuki, Igor Mezic, Fredrik Raak et al.

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.

Takashi Hikihara

This paper investigates the nonlinear dynamics and phase transitions in power packet network connected with routers, conceptualized as macroscopic information-ratchets. In the emerging paradigm of cyber-physical energy systems, the interplay between stochastic energy fluctuations and the thermodynamic cost of control information defines fundamental operational limits. We first formulate the dynamics of a single router using a Langevin framework, incorporating an exponential cost function for information acquisition. Our analysis reveals a discontinuous (first-order) phase transition, where the system adopts a strategic abandon of regulation as noise intensity exceeds a critical threshold $D_c$. This transition represents a fundamental information-barrier inherent to autonomous energy management. Here, we extend this model to network configurations, where multiple routers are linked through diffusive coupling, sharing energy between them. We demonstrate that the network topology and coupling strength significantly extend the bifurcation points, with collective resilient behaviors against local fluctuations. These results provide a rigorous mathematical basis for the design of future complex communication-energy network, suggesting that the stability of proposed systems is governed by the synergistic balance between physical energy flow and the thermodynamics of information exchange. It will serve to design future complex communication-energy networks, including internal energy management for autonomous robots.

Rutvika Manohar, Takashi Hikihara

This paper discusses a dispersed generation system of multiple DC/DC converters with DC power sources connected in a ring formulation. Here is presented the analysis of the system based on the stored energy and passivity characteristics of the system. Passivity Based Control (PBC), with its energy-modifying and damping-injection technique, is applied to a ring coupled converter system to stabilize itself at a desired DC voltage in the presence of external disturbances. The numerical results reveal the effective application of the control as a robust and flexible technique.

Shinya Nawata, Atsuto Maki, Takashi Hikihara

Power packet is a unit of electric power transferred by a power pulse with an information tag. In Shannon's information theory, messages are represented by symbol sequences in a digitized manner. Referring to this formulation, we define symbols in power packetization as a minimum unit of power transferred by a tagged pulse. Here, power is digitized and quantized. In this paper, we consider packetized power in networks for a finite duration, giving symbols and their energies to the networks. A network structure is defined using a graph whose nodes represent routers, sources, and destinations. First, we introduce symbol propagation matrix (SPM) in which symbols are transferred at links during unit times. Packetized power is described as a network flow in a spatio-temporal structure. Then, we study the problem of selecting an SPM in terms of transferability, that is, the possibility to represent given energies at sources and destinations during the finite duration. To select an SPM, we consider a network flow problem of packetized power. The problem is formulated as an M-convex submodular flow problem which is known as generalization of the minimum cost flow problem and solvable. Finally, through examples, we verify that this formulation provides reasonable packetized power.