Low computational complexity model reduction of power systems with preservation of physical characteristics

A data-driven algorithm recently proposed to solve the problem of model reduction by moment matching is extended to multi-input, multi-output systems. The algorithm is exploited for the model reduction of large-scale interconnected power systems and it offers, simultaneously, a low computational complexity approximation of the moments and the possibility to easily enforce constraints on the reduced order model. This advantage is used to preserve selected slow and poorly damped modes. The preservation of these modes has been shown to be important from a physical point of view and in obtaining an overall good approximation. The problem of the choice of the socalled tangential directions is also analyzed. The algorithm and the resulting reduced order model are validated with the study of the dynamic response of the NETS-NYPS benchmark system (68-Bus, 16-Machine, 5-Area) to multiple fault scenarios

A note on the electrical equivalent of the moment theory

In this short note the relation between the moments of a linear system and the phasors of an electric circuit is discussed. We show that the phasors are a special case of moments and we prove that the components of the solution of a Sylvester equation are the phasors of the currents of the system. We point out several directions in which the phasor theory can be extended using recent generalizations of the moment theory, which can benefit the analysis of circuits and power electronics

Model reduction by matching the steady-state response of explicit signal generators

© 2015 IEEE.Model reduction by moment matching for interpolation signals which do not have an implicit model, i.e., they do not satisfy a differential equation, is considered. Particular attention is devoted to discontinuous, possibly periodic, signals. The notion of moment is reformulated using an integral matrix equation. It is shown that, under specific conditions, the new definition and the one based on the Sylvester equation are equivalent. New parameterized families of models achieving moment matching are given. The results are illustrated by means of a numerical example

Model reduction by moment matching for linear singular systems

© 2015 IEEE.The paper presents a moment matching approach to the model reduction problem for singular systems. Combining the interpolation-based and the steady-state-based description of moment, a partitioned formulation of the Krylov projector is obtained. Several implications of this result are investigated and different families of reduced order models are proposed. The possibility to maintain structural properties of system is studied. Two examples illustrate the results of the paper

Steady-state matching and model reduction for systems of differential-algebraic equations

The problem of model reduction for nonlinear differential-algebraic systems is addressed using the notions of moment and of steady-state response. These notions are formally introduced for this class of systems and families of nonlinear differential-algebraic reduced order models achieving moment matching with additional properties are presented. Stronger results for the special class of linear singular systems are provided. Two simple examples illustrate the proposed technique

Model reduction for hybrid systems with state-dependent jumps

In this paper we present a model reduction technique based on moment matching for a class of hybrid systems with state-dependent jumps. The problem of characterizing the steady-state for this class of systems is studied and a result which allows to described the steadystate response of hybrid systems through the use of a hybrid mapping is given. Then a family of hybrid reduced order models which achieve moment matching and are easily parameterizable is provided. The special case of periodic input signals is analyzed and conditions for applying the technique are given for this class. A numerical simulation illustrates the results

Moments at "discontinuous signals" with applications: model reduction for hybrid systems and phasor transform for switching circuits

We provide an overview of the theory and applications of the notion of moment at “discontinuous interpolation signals”, i.e. the moments of a system for input signals that do not satisfy a differential equation. After introducing the theoretical framework, which makes use of an integral matrix equation in place of a Sylvester equation, we discuss some applications: the model reduction problem for linear systems at discontinuous signals, the model reduction problem for hybrid systems and the discontinuous phasor transform for the analysis of circuits powered by discontinuous sources

A hybrid observer for practical observability of linear stochastic systems

This paper focuses on the problem of observability and observer design for linear stochastic systems. To introduce our idea, we first construct an idealistic observer. This idealistic observer is not causal as it requires perfect knowledge of the Brownian motion. However, after introducing an a posteriori method to reconstruct the variations of the Brownian motion in discrete time, we propose a realistic hybrid observer which approximates the idealistic observer. The performance of this hybrid observer can be made arbitrarily close to that of the idealistic observer. Numerical simulations illustrate the results of the paper