Unterminated Admittance Passivity for Robust Stability of Multi-Port Grid-Connecting Power Electronic Converters

Power electronic converters play a major role in replacing fossil fuel-based energy infrastructure with more sustainable alternatives. Still, their high proliferation poses ever increasing challenges in terms of stability. This dissertation addresses these challenges by exploring two distinct, but, still, closely correlated topics. The first one involves advanced control and modeling for preventing high-frequency instabilities between a converter is and a grid. Due to its inherent capability to reduce delays within a converter’s digital control system, multi-sampled PWM can successfully prevent high frequency instabilities in grid-tied applications. Furthermore, it allows high bandwidths to be achieved while preserving high stability margins. However, there are several issues that must be handled. To this end, the first part of this dissertation addresses the following: small-signal modeling of multi-sampled (phase-shifted) PWM; modulating signal discontinuity-related non-linearities and their mitigation in unbalanced multi-cell converters; switching noise sensitivity and its suppression in systems with oversampled feedback. Multi-sampled PWM in combination with median-based feedback filtering is experimentally demonstrated as capable of achieving not only high noise immunity and enhanced modulator linearity, but also high bandwidths and stability margins. The proposed PWM models are demonstrated as pivotal for predicting dependency of the converter's high frequencies stability properties on the steady-state operating point. Namely, as a prerequisite for predicting and preventing possible instabilities in various grid-tied scenarios, an adequate small-signal model of the converter is required. Modeling is especially challenging at very high frequencies, near and above the Nyquist frequency, where the impact of the sampling and modulation sidebands must be examined. To tackle these challenges, the first part of this dissertation concludes by developing multiple-frequency models that are experimentally demonstrated to accurately predict a converter’s small-signal dynamics, even at frequencies far above the Nyquist frequency. The second part of this dissertation explores the potential of all-port unterminated representation for the small-signal stability assessment and termination independent robust stability-oriented controller design of interlinking converters in various, including meshed, grids. The all-port unterminated (device-level) impedance-based method and the corresponding admittance passivity criterion for multi-port dc-dc, ac-dc, and ac-ac converters are established. The device-level impedance-based method assesses stability by applying the generalized Nyquist criterion to the product of the grid's all-port unterminated impedance matrix and the converter's all-port unterminated admittance matrix. Stemming from this and assuming a passive grid's all-port unterminated impedance matrix, the device-level admittance passivity criterion imposes passivity of the converter’s all-port unterminated admittance matrix as a sufficient condition for system stability. This admittance matrix characterizes the converter's small-signal dynamics under ideal termination and can be used as a building block for analyzing interconnection dynamics. Thus, contrary to the existing port-level admittance passivity criterion, which is applied at a certain port, the proposed device-level admittance passivity criterion allows to analyze the impact of an interlinking converter in the general case of an arbitrary (even meshed) passive termination. As such, it is used as a basis for establishing a general passivity-oriented controller design framework that is applicable to interlinking converters with an arbitrary number of dc and ac ports. The proposed approach is exemplified and experimentally demonstrated as effective for preventing a converter's destabilizing impact in various grid-connecting scenarios.