Markov chain methods for rare event sampling and applications to energy systems

This thesis attempts to address the problems of sampling rare events in power system operations, global optimisation studies and in higher dimensions. Our primary algorithmic tool is the skipping sampler, an existing Metropolisclass algorithm designed to efficiently draw samples from a distribution π, whose support C, consists of connected components. First, we apply the skipping sampler to a cyber-physical-statistical power system simulation model to sample power injections from renewable energy sources, conditioned on the activation of frequency-related emergency responses. Such emergency responses, designed to protect sensitive equipment from deviations in system frequency, occur infrequently, and can be considered a rare event. We also explore how the application of large battery energy storage systems can mitigate this risk. Methodologically, we apply the skipping sampler to the field of global optimisation, where we present the basin hopping with skipping algorithm, which replaces the perturbation step of the well-known basin hopping routine with the proposal function of the skipping sampler. Results indicate that, for energy landscapes with well-separated basins, the basin hopping with skipping algorithm is both more effective and efficient at locating the global minima than the basin hopping routine. Finally, to address the problem of drawing samples of rare events in higher dimensions, we propose the Sequential Monte Carlo with skipping (SMC-S) algorithm, which use the skipping sampler as the transition kernel of a sequential Monte Carlo framework. To address the challenge of sampling particle paths which intersect with regions of interest in high dimensions, the skipping sampler kernel samples the direction particle paths from a data-driven, empirical distribution, based on the relative positions of particles. Experiments suggest that the SMC-S, using this approach, outperforms both MCMC and other SMC routines in drawing samples of rare events in high dimensions

Uncovering Load-Altering Attacks Against N-1 Secure Power Grids:A Rare-Event Sampling Approach

Load-altering attacks targetting a large number of IoT-based high-wattage devices (e.g., smart electric vehicle charging stations) can lead to serious disruptions of power grid operations. In this work, we aim to uncover spatiotemporal characteristics of LAAs that can lead to serious impact. The problem is challenging since existing protection measures such as $N-1$ security ensures that the power grid is naturally resilient to load changes. Thus, strategically injected load perturbations that lead to network failure can be regarded as \emph{rare events}. To this end, we adopt a rare-event sampling approach to uncover LAAs distributed temporally and spatially across the power network. The key advantage of this sampling method is the ability of sampling efficiently from multi-modal conditional distributions with disconnected support. Furthermore, we systematically compare the impacts of static (one-time manipulation of demand) and dynamic (attack over multiple time periods) LAAs. We perform extensive simulations using benchmark IEEE test simulations. The results show (i) the superiority and the need for rare-event sampling in the context of uncovering LAAs as compared to other sampling methodologies, (ii) statistical analysis of attack characteristics and impacts of static and dynamic LAAs, and (iii) cascade sizes (due to LAA) for different network sizes and load conditions

Uncovering Load-Altering Attacks Against N-1 Secure Power Grids: A Rare-Event Sampling Approach

Load-altering attacks targetting a large number of IoT-based high-wattage devices (e.g., smart electric vehicle charging stations) can lead to serious disruptions of power grid operations. In this work, we aim to uncover spatiotemporal characteristics of LAAs that can lead to serious impact. The problem is challenging since existing protection measures such as $N-1$ security ensures that the power grid is naturally resilient to load changes. Thus, strategically injected load perturbations that lead to network failure can be regarded as \emph{rare events}. To this end, we adopt a rare-event sampling approach to uncover LAAs distributed temporally and spatially across the power network. The key advantage of this sampling method is the ability of sampling efficiently from multi-modal conditional distributions with disconnected support. Furthermore, we systematically compare the impacts of static (one-time manipulation of demand) and dynamic (attack over multiple time periods) LAAs. We perform extensive simulations using benchmark IEEE test simulations. The results show (i) the superiority and the need for rare-event sampling in the context of uncovering LAAs as compared to other sampling methodologies, (ii) statistical analysis of attack characteristics and impacts of static and dynamic LAAs, and (iii) cascade sizes (due to LAA) for different network sizes and load conditions

Hopping between distant basins

We present and numerically analyse the Basin Hopping with Skipping (BH-S) algorithm for stochastic optimisation. This algorithm replaces the perturbation step of basin hopping (BH) with a so-called skipping mechanism from rare-event sampling. Empirical results on benchmark optimisation surfaces demonstrate that BH-S can improve performance relative to BH by encouraging non-local exploration, that is, by hopping between distant basins

Analysis of cascading failures due to dynamic Load-Altering Attacks

Large-scale load-altering attacks (LAAs) are known to severely disrupt power grid operations by manipulating several internet-of-things (IoT)-enabled load devices. In this work, we analyze power grid cascading failures induced by such attacks. The inherent security features in power grids such as the N−1 design philosophy dictate LAAs that can trigger cascading failures are \emph{rare} events. We overcome the challenge of efficiently sampling critical LAAs scenarios for a wide range of attack parameters by using the so-called ``skipping sampler'' algorithm. We conduct extensive simulations using a three-area IEEE-39 bus system and provide several novel insights into the composition of cascades due to LAAs. Our results highlight the particular risks to modern power systems posed by strategically designed coordinated LAAs that exploit their structural and real-time operating characteristics

The formation of nitrogen oxides in a pulverised coal boiler

The oxides of nitrogen (NOx) are airborne pollutants that result from the combustion of pulverised coal. The aim of this project is to identify operational methods that reduce the NOx emissions from a coal fired boiler whilst maintaining satisfactory performance. This project describes important combustion properties and the processes occurring during the combustion of pulverised coal. Detail is provided on the pulverisation plant, draught plant and steam system of a large utility boiler. The dominant NOx formation mechanisms in coal fired boilers are discussed and NOx reduction strategies applicable to these boilers are described. Engineering models are developed to describe initial flame temperature, furnace residence times, furnace heat pickup and thermal NOx formation. A series of tests were designed and undertaken to measure and assess the effect on NOx formation and boiler performance to variations in:- - The distribution of secondary air to each windbox, and - The level of excess oxygen measure at the boiler exit. During each test the following was undertaken:- - Detailed temperature survey of the furnace region - Coal sampling for laboratory analysis - Fly Ash sampling to determine loss of ignition - Logs of relevant data to determine plant performance. Difficulties and shortcomings regarding the predictive models are discussed and the performance of the boiler under each test is compared

Exploring nonlinear diffusion equations for modelling dye-sensitized solar cells

2020 by the authors. Dye-sensitized solar cells offer an alternative source for renewable energy by means of converting sunlight into electricity. While there are many studies concerning the development of DSSCs, comprehensive mathematical modelling of the devices is still lacking. Recent mathematical models are based on diffusion equations of electron density in the conduction band of the nano-porous semiconductor in dye-sensitized solar cells. Under linear diffusion and recombination, this paper provides analytical solutions to the diffusion equation. Further, Lie symmetry analysis is adopted in order to explore analytical solutions to physically relevant special cases of the nonlinear diffusion equations. While analytical solutions may not be possible, we provide numerical solutions, which are in good agreement with the results given in the literature

Althorne district plan

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