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

Abstract

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, both with regard to 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 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.

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

“…From these equations, following the same reasoning procedure as before, the cases with a greater number of integrators are a repetition of the ones already analyzed, changing the number of complete revolutions. It should be noticed that the table provided in [24] for SISO systems, matches Table I if b = 0, meaning that the transfer function under analysis has no complex valued coefficients.…”

“…If G(s) is a transfer function with real valued coefficients, it satisfies that G(jω) = G(−jω), meaning that the Bode diagrams are symmetric with respect to zero. Consequently, C + and C − can be counted for positive frequencies and multiplied by 2 [24].…”

“…However, these criteria are only valid under certain application conditions and can fail in correctly determining the stability of some systems. Recently, a new criterion, called Generalized Bode Criterion, has been proposed that overcomes these limitations and can be applied to any SISO system [24].…”

Active Damping based on the Capacitor Voltage Positive-Feedback for Grid-Connected Power Converters with LCL filter

“…3 (a) shows the Bode diagram for the inner capacitor voltage positive-feedback, from V conv,α (s) to V PF,α (s) for three short circuit ratios (SCRs) equal to 1, 40 and 100. Normally, the stability of a negative feedback loop can be determined by counting ±n180 • crossings (n odd integer) with positive magnitude in the Bode diagram [14]. The loop under study has a positive feedback, for this reason, in this Bode diagram, −G conv (s)G vv (s)LPAF v (s) has been represented.…”

The Generalized Bode Criterion: application to the dc voltage control of a three-phase photovoltaic grid-tied inverter

“…Due to the expansion of renewable energy systems, power electronic converters are becoming more important. The decreasing cost of these systems is creating new challenges in the converter design process related not only to their components but also to their control loops [2]. Particularly, the stability analysis of the control loops and the tuning of the controller are becoming important issues.…”