Harmonic Modeling of Voltage Source Converters using Basic Numerical Methods

3Basic Numerical Iterative Methods

“Simplicity is the ultimate sophistication.”

– Leonardo da Vinci

A numerical method is a mathematical tool designed to solve numerical problems. The implementation of a numerical method in a programming language is called a numerical algorithm. This chapter provides a basic review of some of the commonly used iterative numerical algorithms for solving nonlinear problems. Generally speaking, an iterative algorithm involves three steps, as shown in Fig. 3.1, and each step plays an important role. The first step is called initialization. This requires the unknown variables to be identified, and how to properly assign the estimated values for these unknown variables. In general, the closer the estimated values to the final solution, the faster the convergence and less likely to diverge. These estimated values in general can be obtained by applying the physical laws, existing knowledge about the system, and employing some simpler methods to get the first guess. The second step is the core of the algorithm, which is how the algorithm updates or improves the estimated values. For instance, Newton‐type methods rely on gradients to improve the next estimated values. On the other hand, a meta‐heuristic algorithm, called particle swarm optimization (PSO) updates its estimated values by using a linear combination of the global best estimated values and the current best estimated values. It is also this step that determines whether the algorithm is stable. ...