Review and comparison of frequency-domain curve-fitting techniques: Vector fitting, frequency-partitioning fitting, matrix pencil method and loewner matrix

摘要

It is a well-known practice to approximate the frequency-domain response of an electrical component or a subsystem with rational functions for electromagnetic transient (EMT) simulations of power systems. There are a variety of curve-fitting methods developed over time that offer different levels of accuracy, speed, and complexity. In some cases, the order of rational function may get very large to meet specified error criteria. Model order reduction (MOR) methods can be used to decrease the order of the function without a considerable deterioration of the approximation error. This paper presents a thorough review and comparison of the most popular curve-fitting methods, namely, the vector fitting (VF) method along with its later developments, the frequency-partitioning fitting (FpF) methods, matrix pencil method (MPM) and loewner matrix (LM) fitting technique. First, the fundamental theories of each one are briefly reviewed. Then, their accuracy and fitting order are compared together through three case studies. Lastly, the application of two different MOR methods to the resulted rational function is investigated.