We perform modal analysis of short-term swing dynamics in multi-machine power systems. The is based on the so-called Koopman operator, a linear, infinite-dimensional operator that defined for any nonlinear dynamical system and captures full information system. Modes derived through spectral called modes, provide extension linear oscillatory modes. Computation modes extracts single-frequency, spatial embedded non-stationary data short-term, dynamics, it provides novel technique identification...

The loss of stability-an instability-can become a critical cause emergent cascading outages leading to wide-spread blackouts. Penetration renewable energy sources makes the problem instability more urgent because highly fluctuating nature such sources. Here we show data-based approach stability assessment power systems without models. This is enabled by Koopman mode analysis for nonlinear dynamical systems, which detects an based on properties point spectrum operator. We apply technique data...

Koopman operator is a composition defined for dynamical system described by nonlinear differential or difference equation. Although the original and evolves on finite-dimensional state space, itself linear but infinite-dimensional (evolves function space). This captures full information of dynamics system. In particular, spectral properties play crucial role in analyzing first part this paper, we review so-called theory systems, with emphasis modal decomposition computation that are direct...

We interpret and explain a phenomenon in short-term swing dynamics of multi-machine power grids that we term the Coherent Swing Instability (CSI). This is an undesirable emergent synchronous machines grid, which most sub-grid coherently lose synchronism with rest grid after being subjected to finite disturbance. develop minimal mathematical model CSI for are strongly coupled loop transmission network weakly connected infinite bus. provides dynamical origin CSI: it related escape from...

We suggest a precursor to phenomena of loss transient stability in multi-machine power systems. This is based on discovery [Y. Susuki, I. Mezi ć , and T. Hikihara, J. Nonlinear Sci., vol. 21, no. 3, pp. 403–439, June 2011], an emergent transmission path energy from many oscillatory modes one mode that represents instability phenomenon interest. The pathway high frequency the lowest called coherent swing (CSI). are extracted sensor data or provided by simulation outputs system oscillations...

Koopman Mode Decomposition (KMD) is an emerging methodology to investigate a nonlinear spatiotemporal evolution via the point spectrum of so-called operator defined for arbitrary dynamical systems. Prony analysis widely used in applications and reconstruct sparse sum exponentials from finite sampled data. In this paper, we show that vector version provides approximation KMD. This leads alternative algorithm computing modes eigenvalues directly data especially suitable with small-spatial...

This work addresses the problem of transient stabilization a power grid, following destabilizing disturbance. The model considered is cascade interconnection seven New England test models with disturbance (e.g., powerline failure) occurring in first grid and propagating forward, emulating wide-area blackout. We consider data-driven control framework based on Koopman operator theory, where linear predictor, evolving higher dimensional (embedded) state-space, built from observed data...

This paper applies a new technique for modal decomposition based solely on measurements to test systems and demonstrates the technique's capability partitioning power network, which determines points of separation in an islanding strategy. The mathematical is called Koopman mode analysis (KMA) stems from spectral so-called operator. Here, KMA numerically approximated by applying Arnoldi-like algorithm recently first applied system dynamics. In this we propose practical data-driven...

In this paper, we describe an approach to the analysis and design of power grid dynamic performance based on hybrid systems theory. Power is a large-scale cyber-physical system for transmission electrical energy. The joint dynamics physical processes cyber elements in grids are typical mixture continuous discrete behaviors, that is, dynamics. We address problems stability basic concerns current future with Measures interpreted as safety specifications models translated into restrictions...

This paper develops a novel data-driven technique to compute the participation factors for nonlinear systems based on Koopman mode decomposition. Provided that certain conditions are satisfied, it is shown proposed generalizes original definition of linear mode-in-state factors. Two numerical examples provided demonstrate performance our approach: one relying canonical dynamical system, and other two-area four-machine power system. The decomposition capable coping with large class...

We propose an analytical construction of observable functions in the extended dynamic mode decomposition (EDMD) algorithm. EDMD is a numerical method for approximating spectral properties Koopman operator. The choice fundamental application to nonlinear problems arising systems and control. Existing methods either start from set dictionary look subset that best fits underlying dynamics or they rely on machine learning algorithms "learn" functions. Conversely, this paper, we dynamical system...

Dynamic Mode Decomposition (DMD) has attracted a fair amount of attention in recent years. Applications DMD have ranged from fluid mechanics, thermal dynamics building, power systems, and so on. Connections to the so-called Koopman operator been highlighted, variants called (KMD). In many applications, these techniques are used as an attempt derive reduced-order system or identify coherent dynamic structures characterized by modes oscillating with single frequencies. Therefore, they become...

We propose an analytical construction of observable functions in the extended dynamic mode decomposition (EDMD) algorithm. EDMD is a numerical method for approximating spectral properties Koopman operator. The choice fundamental application to nonlinear problems arising systems and control. Existing methods either start from set dictionary look subset that best fits underlying dynamics or they rely on machine learning algorithms "learn" functions. Conversely, this paper, we dynamical system...

We develop an algorithm for synthesizing a spatial pattern of charging/discharging operations in-vehicle batteries provision ancillary service (AS) in power distribution grids. The is based on the ordinary differential equation (ODE) model voltage that has been recently introduced. In this paper, first, we derive analytical solutions ODE single straight-line feeder through partial linearization, thereby providing physical insight to impact electric vehicle (EV) voltage. Second, solutions,...

This paper studies global instability in swing equations of multimachine power systems. Global is related to the undesirable phenomenon system, implying that most all generators a system coherently lose synchronism with remaining system. By analyzing loop transmission network, we analytically show can occur as result interplay between network topology and local dynamics suggests possibility control for by varying

We report a new approach to estimating power system inertia directly from time-series data on dynamics. The is based the so-called Koopman Mode Decomposition (KMD) of such dynamic data, which nonlinear generalization linear modal decomposition through spectral analysis operator for dynamical systems. KMD-based thus applicable that evolve in regime characteristics. Its effectiveness numerically evaluated with transient stability simulations IEEE New England test system.

This paper proposes a new method for partitioning power grids based on the nonlinear Koopman Mode Analysis (KMA). Grid is fundamental problem in controlled islanding strategy. The KMA technique of modal decomposition properties point spectrum so-called operator. key idea proposed to determine set islanded sub-grids using data voltage angle dynamics every bus. numerically investigated with IEEE 118-bus test system. It shown that provides partitions multiple frequency scale as well captures...