Thesis

Modelling and stability analysis of power systems considering multiple converter interactions

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Awarding institution
  • University of Strathclyde
Date of award
  • 2026
Thesis identifier
  • T17685
Person Identifier (Local)
  • 202176428
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Qualification Name
Department, School or Faculty
Abstract
  • The rapid integration of converter-based renewable generation is fundamentally changing the dynamic behaviour of modern power systems. The progressive displacement of synchronous machines reduces natural inertia and short-circuit capacity, thereby increasing the system’s sensitivity to oscillatory, frequency, and voltage instabilities. These challenges are particularly severe in weak networks characterised by long transmission distances, high impedance levels, and a high penetration of power electronic converters. Under such conditions, dynamic interactions between converter control systems and the surrounding network may introduce resonances, restrict controllability, and reduce stability margins. This thesis addresses these challenges through a systematic impedance-based stability analysis of multi-converter power systems. The work first develops detailed small-signal models of converters and networks. Converter control dynamics, including phase-locked loop and current control effects, are represented together with the frequency-dependent behaviour of cables and transmission components. Both single-input single-output and multi-input multioutput impedance representations are formulated. The multi-input multi-output framework enables the analysis of cross-coupling effects that cannot be captured by conventional scalar impedance methods. Stability assessment is conducted using the Generalized Nyquist Criterion, ensuring consistency with established impedance-based theory. A principal contribution of this thesis is the formulation and application of two impedance-based stability measures: the Impedance Ratio (IR) and the Eigenvalue-Impedance Ratio (EIR). Although impedance ratios and eigenvalue analysis are established concepts, their structured combination within a multi-converter, frequency-dependent framework has not previously been formalised in this manner. The novelty lies in integrating impedance interactions with eigenvalue sensitivity information to provide a quantitative link between impedance characteristics and system pole movement. This integration enables the identification of dominant interaction paths and the quantification of stability margins under realistic operating conditions. Unlike conventional grid-strength indices such as Short Circuit Ratio (SCR), General Short Circuit Ratio (GSCR), Grid Strength Impedance Matrix (GSIM), and Multi-Infeed Interaction Factor (MIIF), the proposed application of IR and EIR explicitly incorporates converter control dynamics and frequency-dependent network behaviour. The contribution therefore lies in their methodological integration, analytical interpretation, and validation within multi-converter systems. The methods are validated through frequency domain analysis and time-domain simulations for two-converter and multi-converter case studies. The results demonstrate how converter spacing, control mode selection, and impedance composition influence resonance formation and stability margins. The relationship between IR, EIR, and pole trajectories is explicitly demonstrated, providing physical insight into interaction mechanisms. The impact of grid-following and grid-forming converter placement is systematically examined, showing how their proportion and location affect system strength and interaction patterns. To improve computational efficiency, a structured model-reduction approach is also developed. An error index is defined to quantify deviations between full-order and reduced-order models. The results show that weak grids require higher-order representations to preserve critical dynamics, whereas stronger grids permit simplification without significant loss of accuracy. The limitations of this work are acknowledged. The analysis is based on linearised small-signal models around specific operating points and does not address large-disturbance transient stability or electromagnetic transients. In addition, the validation is conducted through simulation studies rather than experimental implementation. Despite these limitations, the thesis provides a coherent and methodologically justified extension of impedance-based stability analysis and offers practical guidance for the design and operation of converter-dominated power systems.
Advisor / supervisor
  • Chen, Yen
  • Egea-Álvarez, Agustí
  • Xu, Lie
  • Chen, Dong
Resource Type
DOI

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