Nyquist Stability Criterion and its Application to Power Electronics Systems

Abstract

The Nyquist stability criterion is a graphical technique for determining the stability of a dynamical system. It relates the stability of a closed‐loop system to the open‐loop frequency response and open‐loop pole location. The Nyquist technique is limited to linear, time‐invariant (LTI) systems and has been widely used for designing and analyzing systems with feedback. A practical advantage of the technique is that it can be applied directly to measured frequency response data, due to which the technique is widely used in power electronics systems, where the complexity of a mathematical model would make its widespread use unfeasible. In its first part, this article guides through the fundamentals of the Nyquist stability criterion applied to feedback systems with SISO and MIMO representations. The generalized Nyquist criterion for MIMO systems is then discussed to illustrate its application to the stability assessment of three‐phase power electronics systems. In the second part, four representative cases are introduced to illustrate the applicability of Nyquist criterion–based stability analysis for power electronics systems: a dc‐dc converter, an HVDC system, a three‐phase converter, and a wind farm–HVDC grid integrated system. In the last section of this article, some advanced topics related to large‐scale power electronics systems are introduced. Inherent aspects that are essential for the proper use of these stability techniques are elaborated and discussed in detail, for instance, impedance transformation and modified sequence impedance or the system‐level analysis.

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Classification of Converter-Driven Stability and Suitable Modeling and Analysis Methods

“…This example is here given in qd-coordinates. MIMO system stability studies can be performed using the generalized Nyquist criterion presented in [107]. [107] introduces a reformulation of this criterion for MIMO systems with negative feedback loop: If L(s) is the open loop transfer function of the MIMO system, the loci of the eigenvalues λ i of L(s) can be determined with…”

The porosity of high‐voltage transmission lines as an indicator of steady‐state stability of electric power transmission

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