Reduced-Order Averaged Model
This chapter deals with modeling methodologies used for obtaining simplified – in the sense of reduced order – power electronic converter models, which are able to represent their low-frequency average behavior and are more easily employed in simulation o
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Reduced-Order Averaged Model
This chapter deals with modeling methodologies used for obtaining simplified – in the sense of reduced order – power electronic converter models, which are able to represent their low-frequency average behavior and are more easily employed in simulation or control law design. Reduced-order averaged modeling relies on splitting the converter dynamics in the frequency domain and preserving the main, low-frequency dynamic. This chapter attempts to bring these modeling approaches together under a single general methodology. First, the principles are introduced and the general methodology is derived. Some examples and case studies illustrate the application of this methodology for both AC and DC power stages. Finally, some problems are proposed to the reader.
6.1
Introduction
The reduced-order averaged model (denoted here by ROAM) presented by Chetty (1982) gave the solution to the problem that arose from modeling DC-DC power stages operating in discontinuous-conduction mode (where the classical averaging method failed). The principle of ROAM is to eliminate the incriminated variable and replace it by a function of other state variables; hence, a reduced-order model is obtained. This modeling framework has been further extended (see, for example, ´ uk 1991; Sun et al. 2001). The effect of algebraically linking two Maksimovic´ and C variables has been encountered for DC-DC converters controlled in (peak) currentprogrammed mode (Middlebrook 1985, 1989). Applications for the ROAM are larger and include: • the application domain of the classical averaged model (see Chap. 4); • power electronic converters having both DC and AC stages (Sun and Grotstollen 1992);
S. Bacha et al., Power Electronic Converters Modeling and Control: with Case Studies, 149 Advanced Textbooks in Control and Signal Processing, DOI 10.1007/978-1-4471-5478-5_6, © Springer-Verlag London 2014
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6 Reduced-Order Averaged Model
• converters whose switching is state-controlled and is also controlled by an independent input (e.g., thyristor-based converters); • converters having both DC and AC stages that operate in discontinuousconduction mode, which is a particular case of the previous class. Therefore, in general, this averaged modeling applies in cases where the power stage presents – either intrinsically or as the effect of a control loop – a dominant low-frequency dynamic and a high-frequency behavior that can be neglected. Reduced-order averaged modeling thus relies on splitting converter dynamics in the frequency domain and preserving the main, low-frequency dynamic. The ROAM is simple in both its construction and use. On the other hand, this model loses in precision what it gains in simplicity. If in certain cases this loss is acceptable, it could happen that in other cases dynamics that may be important by their effects (e.g., closed-loop instability) to be neglected.
6.2
Principle
The principle of ROAM relies upon separating the switched model into two dynamics: • one that must be kept, representing the ma
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