Robust Tuning of Multiresonant Current Controllers for Grid-Tied Converters and Erroneous Use of the Naslin Polynomial Method

The majority of the paper is devoted to debunking flawed methods proposed in the literature within the context of multiresonant control systems for grid-connected converters and then a novel approach is proposed. Several flawed approaches to grid tied power electronic converters (rectifiers and shunt active power filters) are discussed to initiate a critical discussion regarding some tuning methods reported in the topical literature. In this paper we analytically show that some of them are even erroneous from the control theory point of view or are based on mathematically erroneous derivations. That is especially prevalent for papers in which the Naslin polynomial method is employed to tune proportional-multiresonant controllers. Some authors recognize that the resulting control systems are not robust, i.e. not practical, and use obtained gains only as a starting point for further tuning using the trial and error method or evolutionary global optimization. Robustness of such systems is often not guaranteed and if it occurs at all, it is by chance or thanks to a combination of luck and expert knowledge of the engineer (not by deliberate design). Therefore, the absence of such a guarantee motivates the search for better ways to tune such controllers. As a result, a practical robust controller tuning method for multiresonant grid current controllers is proposed and verified experimentally. We are convinced that one of the solutions can be based on the disk margin stability analysis and a global search algorithm. The required robustness is expressed as stability margins. The design procedure is very user-friendly and the disk size is the key design parameter to be selected by an engineer. The practicality of the tuning method is demonstrated empirically in a 10 kVA physical grid-tied converter.