Modelling and Identification of Interaction Effects for Stability Analysis in LVDC Power Networks

Power electronic converters play a vital role in the transition towards low voltage (LV)DC distributed power systems (DPSs) with the proliferation of renewables and end-use electrification. These systems are prone to oscillations from small disturbances due to interactions occurring between sources and loads — power electronic converters, with their tight regulation, introduce a negative impedance characteristic that may destabilize poorly damped oscillatory modes of the network. Recent evidence of the existence of modal interactions that may occur between loads gives rise to additional complexity in dynamic behaviour. As DPSs are subject to many inherent uncertainties and a wide range of operating conditions, different interaction phenomena may influence the small-signal dynamics in a nonlinear manner. Hence, with highly uncertain systems, extrapolating behaviour based on ideal and nominal models can lead to serious qualitative errors.
The thesis focuses on the modelling and small-signal analysis of LVDC DPSs with uncertainties arising from parameter variability. A new automated tool, SymMIAL, is developed to help synthesise high-fidelity state-space system models based on a modular approach. Symbolic linearisation is performed to ensure models represent small-signal dynamics over all possible operating points. Probabilistic variance-based sensitivity analysis (VBSA) is proposed to quantify the influence of parameters and their interactions over the full-range of uncertainties.
Using this novel methodology and newly developed modelling tools, the impact of uncertain parameters on the small-signal dynamics of LVDC DPSs can now be comprehensively investigated. A test DC power system was constructed featuring two parallel filter-converter subsystems fed from a common point through a resistive line. For the first time, an apparent dichotomy in the effect of source-side line resistance is revealed through small-signal sensitivity analysis — line resistance is shown to contribute to both positive and negative damping to filter modes, depending on precise operating conditions.
To resolve this contention, linear mode coupling theory is applied to system state-space models. Contribution of line resistance to damping of modes is quantified and ap-portioned to different interaction phenomena. Positive damping occurs through source-load interaction; negative damping occurs through modal interaction. Analytical results based on theoretical models are validated against measured data from experimental hard-ware LVDC DPSs and simulations.