Harmonic Modeling of Voltage Source Converters using Basic Numerical Methods

9Loop‐Breaking 1 Method

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

– Greek Proverb

The purpose of this chapter is to show in a stepwise manner how a three‐phase two‐level VSC can be modeled by the loop‐breaking 1 (LB 1) method. Readers can then follow these steps to model other types of closed‐loop VSCs. The LB 1 method requires the closed‐loop system at the connection point between blocks to be broken. According to the feasibility analysis done in Chapter 8, Fig. 9.1 is the legitimate way for LB 1 method. As can be seen from the figure, the power converter circuit is “separated” from the controller(s). Therefore, the open‐loop equation will only contain the model of the VSC power circuit, which is LTI for each switching time interval. Note that the PWM generator is not part of the open‐loop system equation because its modeling is simply obtained by solving algebraic equations (as in the case of regular sampled PWM or SVM) or transcendental equations (as in the case of the naturally sampled PWM), and it does not involve any state‐space differential equations. Furthermore, since the controller(s) are described in terms of transfer functions, they can be modeled in the frequency domain so that only algebraic calculations are involved.

The modeling procedure of the LB 1 method is described as follows:

1. Initialize modulating signal harmonics as shown in Fig. 9.1.
2. Supply ...