Read e-book online Time-Scale Modeling of Dynamic Networks with Applications to PDF

By Joe H. Chow (eds.)

ISBN-10: 3540121064

ISBN-13: 9783540121060

ISBN-10: 3540395431

ISBN-13: 9783540395430

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Additional resources for Time-Scale Modeling of Dynamic Networks with Applications to Power Systems

Example text

Our time-scale analysis represents a systematic approach to the development and use of such tools. 1. 20) 0 : Zls/R2 - (I/R 2 + l/R3)Z2s. 21) We use t d instead of the slow time t because the RC-parameters of the equivalent circuits remain e x p l i c i t . 23) and hence the slow subsystem is Cl dYs/dtd = -ys/(Rl + R2 + R3). 4a. This equivalent is obtainable from the original c i r c u i t by opening the small capacitors C2 and C3, which is a meaningful approximation for small capacitors in the slow time-scale.

The technique presented in this chapter is the main analytical tool to analyze time-scale in these dynamic networks as well as to obtain reduced equivalents. 1 Introduction Aggregation is commonly used to obtain reduced models for large scale interconnected systems. For example, in power systems, aggregatemachines are used to represent the dynamics of groups of machines [51, 41]. In economic systems, aggregate consumption and investment are used to describe the dynamic behavior of an industry [50].

10) CldXl/d% + C2dx2/dT + C3dx3/dT = O. 11) CIXI(T) + C2x2(T) + C3x3(%) = ClXl(O) + C2x2(0) + C3x3(0) = qo" This property is called the conservation property. 11) which is orthogonal i n i t i a l point x(O). 11) is constant when ¢ = O, but becomes slowly varying when ¢ > O, infinite. 2a and w i l l be derived in the next section. 3. 4), the state x ( t ) moves rapidly in a boundary layer near the plane F, and i f the motion the is stable, approaches the line S. Then, from a neighborhood of intersection of plane F with line S, x ( t ) slowly slides along l i n e S.

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Time-Scale Modeling of Dynamic Networks with Applications to Power Systems by Joe H. Chow (eds.)


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