Control Design and Stability Analysis of Power Converters: The MIMO Generalized Bode Criterion

Three-phase dynamic systems and multiphase generators are frequently modeled and controlled in the synchronous reference frame. To properly model the cross-coupling terms in this reference frame, complex vector theory and transfer function matrices are commonly applied, obtaining multiple-input multiple-output (MIMO) dynamic models. The stability of MIMO systems can be assessed through the Nyquist generalized stability criterion. However, the use of the Nyquist diagram complicates the controller design. The Bode diagram is a more intuitive tool for the controller design; however, the Bode stability criterion is not applicable to MIMO systems. In this article, the MIMO generalized Bode criterion is proposed. Since this stability criterion is based on the Nyquist generalized stability criterion, it can be applied to any system. Furthermore, it is simple to use, as it only requires information contained in the open-loop transfer matrix and the Bode diagram. The proposed stability criterion thus offers an interesting tool for the controller design procedure in MIMO systems, as it is shown in this article for two common applications: the current control loop of a power converter, a 2\times2 system, and the current control loop of two independent power converters in parallel, a 4\times4 system.