Different time scales in dynamic systems with multiple outcomes

Systems with Multiple Time Scales

where A ( < ) is analytic in the small parameter e . Our basic result is a uniform asymptotic approximation to exp A ( e ) r that we obtain under a certain multiple semistability condition. This asymptotic approximation gives a complete multiple time scale decomposition of the above system and specifies a set of reduced order models valid at each time scale. Our contribution is threefold. 1...

Hyperbolic Systems with Different Time Scales

A Novel Approach to Trace Time-Domain Trajectories of Power Systems in Multiple Time Scales Based Flatness

This paper works on the concept of flatness and its practical application for the design of an optimal transient controller in a synchronous machine. The feedback linearization scheme of interest requires the generation of a flat output from which the feedback control law can easily be designed. Thus the computation of the flat output for reduced order model of the synchronous machine with simp...

Time domain simulation of power systems with different time scales

The time evolution of power systems is modeled by a system of differential and algebraic equations. The variables involved in the system may exhibit different time scales. In standard numerical time integration methods the most active variables impose the time step for the whole system. We present a strategy, which allows the use of different, local time steps over the variables. The partitioni...

Dynamic correlations at different time-scales with Empirical Mode Decomposition

The Empirical Mode Decomposition (EMD) provides a tool to characterize time series in terms of its implicit components oscillating at different time-scales. We apply this decomposition to intraday time series of the following three financial indices: the S&P 500 (USA), the IPC (Mexico) and the VIX (volatility index USA), obtaining time-varying multidimensional cross-correlations at different ti...