Abstract
Abstract. The simulation of large scale nonlinear dynamical interconnected systems, as they arise in all modern engineering disciplines, is a usual task. Due to the high complexity of the considered systems, the principle of thinking in hierarchical structures is essential and common among engineers. Therefore, this contribution proposes an approach for the numerical simulation of large systems, which keeps the hierarchical system structure alive during the entire simulation process while simultaneously exploiting it for order reduction purposes. This is accomplished by embedding the trajectory piecewise linear order reduction scheme in a modified variant of the component connection modeling for building interconnected system structures. The application of this concept is demonstrated by means of a widely used benchmark example and a modified variant of it.
Highlights
The design and operation of todays electrical systems, ranging from microelectronic circuits to power generation and distribution systems, is enabled by powerful simulation tools at hand. Models for such large scale systems are commonly built up hierarchically from smaller and less complex interconnected sub-systems. While this hierarchical point of view is the state-of-the-art, which is utilized within the modeling process itself, the actual simulation is performed by numerically integrating the resulting large scale system of nonlinear ordinary differential equations
The same is true for model order reduction methods for linear systems
2014; Rewienski and White, 2003a). All these methods start at a given description in form of an ordinary differential equation of the entire system to be reduced, dismissing possible hierarchical structures which could be exploited beneficially, e.g. by parallelizing the evaluation of the ordinary differential equation during a numerical integration for transient simulation
Summary
The design and operation of todays electrical systems, ranging from microelectronic circuits to power generation and distribution systems, is enabled by powerful simulation tools at hand. The same is true for model order reduction methods for linear systems, (cf Antoulas et al, 2001; Antoulas, 2005; Baur et al, 2014), as well as for nonlinear systems, (cf Baur et al, 2014; Rewienski and White, 2003a) All these methods start at a given description in form of an ordinary differential equation of the entire system to be reduced, dismissing possible hierarchical structures which could be exploited beneficially, e.g. by parallelizing the evaluation of the ordinary differential equation during a numerical integration for transient simulation. A slightly altered version of this example is utilized to show a significant sensitivity of a systems reducibility to the choice of output variables, which should be preserved during the order reduction process
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