Modelling and stability analysis of inverter-based resources

Abstract

Over the past few decades, climate change concerns have accelerated the transition from fossil fuel-based generation to power-electronic interfaced renewable energy, i.e., inverter-based resource (IBR). This shift is essential for decarbonising the energy sector, but also introduces new challenges, particularly in modelling, stability analysis, and controller design of inverter-dominated systems.Grid-following (GFL) and grid-forming (GFM) represent two types of power electronic inverters. This thesis first explores the modelling requirements for both AC and DC sides of inverters. The single-bus system is commonly used on AC side to study the interaction between inverter control and grid; however, such models may feature algebraic loops and solvability issues. A new approach, closed-form L-filter model, is proposed to analytically reformulate these models for reliable and fast simulations without any accuracy loss. The equivalent model for GFM is further developed to capture DC-side dynamics and represent the limitations of primary energy sources, which requires only a few readily available parameters. These models provide a comprehensive study of inverter modelling to establish a theoretical foundation for further stability analysis.This thesis also focuses on the small-signal analysis of GFL and GFM under different operating conditions. The concept of stability boundary is introduced to visualise the stability behaviour, providing a generic framework for analysis. A boundary tracking algorithm is developed to determine the stability region for an arbitrary number of dimensions in a computationally efficient manner. The dynamic performance of GFL and GFM is comparatively assessed at different grid strengths, in conjunction with varying parameters of interest. The observations indicate that the merged boundary plots enable a combined analysis and allow assessment of the stability behaviour of different inverter variants.The GFM/GFL comparison reveals a grey area where both are stable but exhibit different dynamic behaviours. This thesis further explores this to identify a boundary where their small-signal dynamics become equal, thus introducing the equivalence boundary concept. This is the first time to quantitatively determine when the two controllers behave the same. The observed equivalence characteristic is implemented in an equivalence-based GFL/GFM switching scheme, enabling seamless switching and adaptive control. The adaptive criteria enable real-time transition between GFM and GFL to respond to changing conditions, in stark contrast to the fixed empirical thresholds commonly used in the literature. The proposed algorithms and control strategies are tested on the IEEE 14-bus system to confirm the theoretical analysis and their performance in practice.

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Identifiers

ORCID for Xi Luo: orcid.org/0000-0001-6654-5087

ORCID for Stratis Batzelis: orcid.org/0000-0002-2967-3677

ORCID for Abhinav Kumar Singh: orcid.org/0000-0003-3376-6435

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