Generalized Averaged Model
This chapter approaches methodologies of deriving averaged models able to also represent behavior of converters containing AC stages. This time, modeling is not restricted to DC variables and the resultant models – called generalized averaged models (GAM)
- PDF / 1,777,964 Bytes
- 51 Pages / 439.37 x 666.142 pts Page_size
- 92 Downloads / 253 Views
Generalized Averaged Model
This chapter approaches methodologies of deriving averaged models able to also represent behavior of converters containing AC stages. This time, modeling is not restricted to DC variables and the resultant models – called generalized averaged models (GAM) – can handle averages of higher-order harmonics. The chapter first provides basic ideas of generalized average modeling and the relation of GAM to the previously introduced classical averaged model, followed by examples of obtaining GAM for some simple cases. The GAM application range is identified and its building and implementation simplicity is shown. To this purpose two clear algorithmic approaches will be defined, namely the analytical approach and the graphical one, respectively. The relation between GAM and the real waveforms is shown, as well as the expression of active and reactive AC variable components using GAM. Relations with the classical averaged model (detailed in Chap. 4) and with the first-order-harmonic steady-state model will also be emphasized. Some case studies will serve at illustrating the various approaches. This chapter ends with some problems with solutions and some to be solved.
5.1
Introduction
Each of the various models presented until now applies to somehow dedicated area and therefore has different properties. They have, however, a common aspect: the precision of plant replication grows with model complexity. So, as the modeling effort is sometimes unworthy, especially if the required performances are not high, one should always envisage a trade-off between the two above listed requirements. One should also note that the reciprocal statement is not true: accuracy of the model is not necessarily due to complexity. The model presented by Sanders et al. (1990) – which was resumed later by Noworolsky and Sanders (1991) and by Sanders (1993) – shows this. This model, based on early nineteenth century works of Van der Pol, provides a good trade-off between accuracy and implementation simplicity; this statement is only valuable for converters having both DC stages and AC stages S. Bacha et al., Power Electronic Converters Modeling and Control: with Case Studies, 97 Advanced Textbooks in Control and Signal Processing, DOI 10.1007/978-1-4471-5478-5_5, © Springer-Verlag London 2014
98
5 Generalized Averaged Model
where the first-order harmonic prevails. In this context, the chosen application in the cited article is an ideal resonance power supply whose behavior has been illustrated by what the authors have called a generalized averaged model, or GAM. In the same article, the authors have modeled in the same way a DC-DC buck-boost power stage, obtaining satisfactory results only for values of duty ratio of around 50 %. A similar modeling approach was developed by Caliskan et al. (1999) for the DC-DC boost power stage, with similar results. In the latter literature this kind of modeling has been called generalized state-space average (GSSA) modeling (Rimmalapudi et al. 2007), and it is useful in any power ele
Data Loading...
