November 2021
Intermediate
416 pages
12h 42m
English
book
Harmonic Modeling of Voltage Source Converters using Basic Numerical Methods
by Ryan Kuo-Lung Lian, Ramadhani Kurniawan Subroto, Victor Andrean, Bing Hao Lin
Content preview from Harmonic Modeling of Voltage Source Converters using Basic Numerical Methods
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8Generalized Steady‐State Solution Procedure for Closed‐Loop Converter Systems
“One who tied the bell knot shall be the one who unknots it.”
– Hong Hui (1071–1128)
8.1 Introduction
Mathematically, a closed‐loop power converter can be described by transcendental equations, which do not have closed‐form solutions. This is evident from observing Fig. 8.1. As the figure indicates, the state variables, 
, are a function of the switching times, 
, and the input,1 
. In the feedforward direction the relationship is given by:
(8.1)
However, 
itself is also a function of both states and input, due to the feedback path:
(8.2)
Combining 8.1 and 8.2, one will obtain
(8.3)
Equation 8.3 in general can only be solved by iterative methods. Thus, the objectives of this chapter are:
- To present a unified ...
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