- Doctoral Thesis
Rights / licenseIn Copyright - Non-Commercial Use Permitted
This thesis fundamentally concerns with stability analysis of power systems from a system norm viewpoint. A major part of this thesis is devoted to frequency stability problems in low-inertia power grids. Subsequently, the viability of system norms as an effective control-theoretic tool for performance analysis of primal-dual saddle-point algorithms and variations thereof is elaborated upon. While the share of renewable-based distributed generation has been on the rise, there has also been a decline in the conventional synchronous-based generation. The renewable-based power generation interfaced with the grid via power electronic converters, however, does not provide rotational inertia, an inherent feature of synchronous machines. This absence of inertia has been highlighted as the prime source for the increasing frequency violations which have severely impacted grid stability. As a countermeasure, virtual or synthetic inertia, fast frequency response, emulated by advanced control techniques have been proposed. We discuss in depth, the appositeness, implementation, and optimal tuning of such devices. To factor in for the economics of the provision of such virtual inertia devices, we also construct a market mechanism inspired by the ancillary service markets, pivoted around social welfare optimization and the VCG payment rule. The resulting mechanism ensures truthful bidding to be the dominant bidding strategy and guarantees non-negative payoffs for agents providing virtual inertia while maximizing social welfare. Conventionally, time-domain and spectral metrics have been engaged to gauge the resilience of power systems. In this work, we focus on performance metrics based on the notion of system norms, accounting for network coherency as well as efficient use of control energy. We illustrate how such an approach constitutes a compelling tool and results in tractable reformulations of power system stability problems. We motivate the analysis by considering small-scale, linear multi-machine/ multi-inverter power system models and develop computational approaches for solving the non-convex optimal inertia placement problem. Next, we develop explicit models of two particular implementations of virtual inertia and fast frequency response, the grid-following and grid-forming schemes. These implementations, while conclusively capturing the key dynamic characteristics of virtual inertia emulation also remain amenable for integration with large- scale, non-linear, high-fidelity power system models. The parameters of these devices are tuned and the specific location in the power system optimized, in order to improve resilience. A comprehensive case study based on the model of the South-East Australian system is used to illustrate the effectiveness of such devices. The system norm approach developed in this thesis can also be used to study optimal frequency regulation problems in power systems. These problems can be solved via saddle-point methods, which have recently attracted renewed interest as a systematic technique to design distributed algorithms for solving convex optimization problems. However, when implemented online as dynamic feedback controllers, these algorithms are often subject to disturbances and noise. As the conventional standalone convergence rate evaluation fails to provide the complete picture of performance, quantifying the input-output performance becomes more meaningful, thereby, also underscoring the wide-applicability of system norms. Lastly, we extend our analysis to a more generic resource allocation problem and compare the input-output performance of various centralized and distributed saddle-point implementations. Show more
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ContributorsExaminer: Dörfler, Florian
Examiner: Jovanović, Mihailo R.
Examiner: Simpson-Porco, John W.
SubjectLow-inertia power systems; System norms; Power system stability; Optimization methods; Virtual inertia; Saddle-point algorithms
Organisational unit09478 - Dörfler, Florian / Dörfler, Florian
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