On the Stability of Advanced Power Electronic Converters: The Generalized Bode Criterion

A key factor in the design of power electronic converters is the development of control systems and, in particular, the determination of their stability. Due to ease of application, the Bode criteria are currently the most commonly used stability criteria, with regard to both its classic version and to the subsequent revisions proposed in the literature. However, as these criteria have a limited range of applicability, on occasions, it is necessary to resort to other universally applicable criteria, such as the Nyquist criterion. Unlike Bode, the Nyquist criterion can always be applied, although its use considerably complicates the tuning of the controller. This paper proposes a new stability criterion, called generalized Bode criterion, which is, on the one hand, based on the Nyquist criterion, and therefore, always applicable, and, on the other hand, calculated from both the Bode diagram and the 0 Hz phase of the open-loop transfer function, thus, making the criterion easy to be applied. This way, the proposed criterion combines the advantages of Nyquist and Bode criteria and provides an interesting and useful tool to be applied to the controller design process. The criterion is validated by means of simulation and experimental tests made on a voltage control loop for a stand-alone photovoltaic (PV), system, including a battery, a boost converter, an inverter, and an ac load. The tests are also used to show the limitations of the classic Bode criterion and its revisions to correctly determine the stability of complex systems.