Harmonic Modeling of Voltage Source Converters using Basic Numerical Methods

12Small‐Signal Harmonic Model of a VSC

“Be approximately right rather than exactly wrong.”

– John W. Tukey

This chapter presents a time-domain SSM of a power electronic converter. It provides an analytical small signal VSC model for harmonic analysis. Also, such an SSM is required for constructing the Jacobian matrix for the LB 3 method if the interaction between power network and power converter is chosen to be Newton's method. The outline of this chapter is as follows: Section 12.1 explains the difference between the FCM presented in Chapter and the harmonic SSM to be presented in this chapter. Then, Section 12.2 illustrates how a Gauss–Seidel‐based LB 3 method is different from a Newton‐based LB 3 method from an equivalent circuit point of view. The rest of the chapter closely follows that of Chapter . First, a model for a dc‐dc converter is developed (in Section 12.3) to reveal some of the interesting patterns and characteristics of the proposed SSM. Then, in Section 12.4, a model for the VSC is developed, and its results are verified against the large‐signal model.

12.1 Problem Statement

In Chapter, an FCM of a VSC is derived based on the assumption that the switching times are known in advance. However, in reality, the information about the switching times is not easily accessible. In addition, due to control action, any perturbation in the input sources will cause changes in the switching times, leading to a different FCM. The goal of this chapter is to find a small‐signal ...