The emergence of distributed energy resources has led to new challenges in the operation and planning of power networks. Of particular significance is the introduction of a new layer of complexity that manifests in the form of new uncertainties that could severely limit the resiliency and reliability of modern power networks. Some of the new uncertainties that emerge as a direct consequence of the integration of distributed energy resources include generation uncertainties typical of solar and wind power, uncertain consumer demand patterns due to the increasing adoption of un-conventional loads such as Plug-in Hybrid Electric Vehicles, topological uncertainties that include outages of one or many components of a power system. To facilitate the widespread adoption of distributed energy resources, it is thus essential to develop robust methodologies that would adequately capture and quantify the uncertainties associated with using them. Such decision-making problems that involve uncertainties embedded in the input data naturally lend themselves to be addressed by statistical decision-theoretic methods.
A natural advantage of using statistical decision theory in addressing power system uncertainties is using sample information to make inferences about the unknown quantities. Thus, using computational methods like Bayesian statistics and Markov Chain Monte Carlo is natural within the context of decision-making under uncertainty in energy systems. This research proposes the use of computational methods such as scenario generation techniques, probabilistic mixture models, Bayesian analysis, and Markov Chain Monte Carlo to model the complex stochastic processes such as solar generation, power system load, and various topological uncertainties like accelerated aging and the premature failing of components such as On-load Tap Changers and switched capacitor banks.
Furthermore, this research work is also concerned with investigating the impact of modern reactive power compensation in the form of a solid-state-based capacitor-less power quality compensator to further the integration of distributed resources, particularly distributed roof-top solar generation in low voltage distribution networks. To that end, a stochastic cost-benefit equation is developed, considering the uncertainties associated with distributed energy resources. The cost-benefit study investigates the economic viability of deploying such power electronics-based reactive power compensation devices in low-voltage distribution networks
