Bifurcation-Induced Behaviour in Inverter-Connected Power Systems: Characterisation and Advancement Techniques
Creators: name: Bryant, Jack
Publisher: name: RMIT University
Year: 2024
Subjects: classificationCode: 400805
subject: Electrical energy transmission, networks and systems
classificationCode: 400803
subject: Electrical energy generation (incl. renewables, excl. photovoltaics)

description: A paradigm shift in power systems driven primarily by global warming concerns is rapidly integrating renewable energy sources such as wind and solar at the transmission and distribution levels. Power electronic inverters that connect renewable energy sources to the power system are now ubiquitous and will increasingly underpin power generation in the future. However, grid-connected inverter behaviour fundamentally differs from traditional power generators, challenging conventional approaches to power system modelling, control, and maintaining stability.

This thesis focuses on two main situations concerning power systems with large amounts of inverter-connected resources: "weak grid" conditions and power system frequency response. High-impedance power system points characterise weak grids, which can occur with significant inverter-connected resource integration. Hence, large voltage fluctuations can occur given slight changes in power system conditions, and instability can manifest in the inverter's controls. Moreover, since inverter-connected resources do not inherently participate in power system frequency control, effectively utilising conventional generation assets' frequency response will be imperative to control power system frequency during the energy supply transition.

The thesis's first part characterises grid-connected inverters' weak grid behaviour. Nonlinear and small-signal analytical formulations accurately capture the salient dynamics of grid-forming and grid-feeding inverter topologies using a common synchronous reference frame. Eigenvalue and participation factor analyses demonstrate that a grid-feeding inverter is more sensitive to grid inductance variations than a grid-forming inverter. While the grid-forming inverter maintains stability under weak grid conditions, the grid-feeding inverter succumbs to a Hopf bifurcation, motivating the need for better characterisation and advancement techniques. A unified approach is proposed to discern between (bifurcation-induced) inverter-driven and network-driven instability in paralleled grid-feeding inverter systems with weak grid connections. The approach embeds the power system's critical voltage stability limit into the small-signal model's equilibrium point calculations, retaining a conventional state-space framework and overcoming the challenges of inherent nonlinearities associated with multiple synchronous reference frames. The thesis then extends the insights from the unified approach to characterise bifurcation-induced grid-feeding inverter behaviour under weak grid conditions. Floquet theory, in conjunction with a time-domain shooting method, characterises the stability of periodic behaviour emanating from the inverter controls. Other periodic phenomena theoretically exist alongside limit cycles, including Neimark-Sacker and period-doubling bifurcations. The current regulator parameters significantly influence the periodic behaviour in conjunction with the phase-locked loop. The approach provides a new behavioural taxonomy not provided by traditional small-signal stability analyses.

The thesis's second part proposes advancement techniques for inverter-connected power systems. A deterministic analytical method is developed for optimally selecting the current regulator gains of LCL-filtered grid-feeding inverters. The design significantly improves the performance of a grid-feeding inverter employing a traditional proportional-integral control structure, allowing the inverter to operate up to the grid connection's critical voltage stability limit. Consequently, reformulating the control scheme is not required to guarantee the inverter's stability under weak grid conditions. Time-domain simulations using a detailed inverter model confirm the performance improvement. The thesis then proposes an advanced design principle to effectively utilise synchronous generator governor response in power systems operating with high shares of inverter-connected resources. IEEE 14-bus and East Australian power system case studies explore the impact of synchronous generator governor response on power system frequency control with increasing inverter penetration. While higher amounts of inverter-connected resources impact the power system's frequency nadir, governor deadbands are shown to play a demonstrable role in ensuring stability by enabling faster response times. The power system topology and operating point also significantly influence whether a governor deadband setting is sufficient to maintain or improve the electricity supply's continuity. Thus, an optimal (or "one-size-fits-all") governor deadband is shown not to exist. Tuned governor deadbands facilitate effective governor response, leading to power system frequency control characterised by minor (and tolerable) frequency nadirs, small steady-state frequency errors, and steady frequency behaviour.