Harmonic Modeling of Voltage Source Converters using Basic Numerical Methods

10Loop‐Breaking 2 Method for Solving a VSC

“Divide the fire and you will soon put it out.”

– Greek Proverb

In this section, we will devote ourselves to using the loop‐breaking 2 (LB 2) method to solve a two‐level VSC. As mentioned in Chapter, the LB 2 method breaks within the individual blocks. It has been shown that such a method can be used to derive the generalized shooting method. In Section 10.1, an example of a dc‐dc buck converter is used to demonstrate how augmented matrix methods can be easily incorporated into the LB 2 method, which avoids evaluating convolution integrals. In Section 10.2, it is demonstrated how a VSC, whose controllers are described in the frame, can also be modeled by the LB 2 method. Finally, we will show how a line‐commutated power converter can be modeled by means of the LB 2 method. It is noted that for this type of converter, since the size of the state matrices may be different for different switching intervals, transition matrices are needed for harmonic evaluation.

10.1 Modeling for a Closed‐Loop DC‐DC Converter

Fig. 10.1 shows the schematic diagram of a closed‐loop buck converter.1 The parameter values are listed in Table 10.1. To simplify the analysis, and are assumed to switch in a complementary manner. The output voltage of the controller ...