With the emergence of energy communities, where a number of prosumers (consumers with their own energy generation) invest in shared renewable generation capacity and battery storage, the issue of fair allocation of benefits and costs has become increasingly important. The Shapley value, a solution concept in cooperative game theory initially proposed by Nobel prize-winning economist Lloyd Shapley, has attracted increasing interest for redistribution in energy settings. However, due to its high time complexity, it is intractable beyond communities of a few dozen prosumers. This study proposes a new deterministic method for approximating the Shapley value in realistic community energy settings and compares its performance with existing methods. To provide a benchmark for the comparisons of these methods, we also design a novel method to compute the exact Shapley value for communities of up to several hundred agents by clustering consumers into a smaller number of demand profiles. Experimental analyses with large-scale case studies of a community of up to 200 household consumers in the UK show that the newly proposed method can achieve very close redistribution to the exact Shapley values but at a much lower (and practically feasible) computation cost. Furthermore, it performed similarly to the probabilistic, state-of-the-art approximation method while having smaller time complexity as well as other desirable characteristics for cost redistribution in energy communities. ... Read more

In a world replete with observations (physical as well as virtual), many data sets are represented by time series. In its simplest form, a time series is a set of data collected sequentially, usually at fixed intervals of time. In a number of applications, the mean and the variance of the time series is time-invariant and there is no seasonality in the data (such time series is called stationary). However, in many more applications, e.g., time series that are related to smart energy systems, the data have non-stationary characteristics. This thesis focuses primarily on matrices as an alternative representation of the latter type of time series, in order to take advantage of matrix decomposition methods. The rationale is straightforward: numerically stable matrix decomposition techniques enable us to extract underlying patterns in the data and use them to construct approximations of the corresponding time series. In particular, we will focus on singular value decomposition (SVD) as a powerful and numerically stable matrix factorization technique. Therefore, as the first step in this thesis, the SVD and its geometrical interpretation are extensively studied, in order to acquire a firm understanding of how it performs. That in turn enables us to look at different problems in time series analysis from a fresh perspective. For most of the applications of SVD in various fields, it is important to understand the properties of the SVD of a matrix whose entries show some degree of random fluctuations. Therefore, to determine how the noise level affects the singular value spectrum, it is essential to study the singular value decomposition of random matrices. As we will explain in the introductory chapter, one of the early applications of the SVD in time series analysis is in periodicity detection of the time series data. Therefore, we explore how the geometry of a matrix (the position of the data points with respect to the origin) and the aspect ratio of the matrix (the ratio between the number of columns and the number of rows) can affect its SVD results. Matrix factorisation techniques such as principal component analysis (PCA) and singular value decomposition (SVD) are both conceptually simple and effective. However, it iswell-known that they are sensitive to the presence of noise and outliers in input data. One way to mitigate this sensitivity is to introduce regularisation. To this aim, we hark back to the interpretation of SVD and PCA in terms of low-rank approximations, which involve the minimisation of specific functionals. We then derive algorithms for the minimisation of the regularised version of such functionals... ... Read more

We consider energy systems in the built environment. With the transition to a more sustainable, distributed, and 'smart' energy system, such local grids are undergoing significant changes. Among other developments, the new role of end-users as 'prosumers' - users that can either produce or consume power depending on the situation - is turning energy systems in the built environment into autonomous microgrids with complex internal interactions.

One of the primary challenges for these local grids is maintaining grid stability, which requires constant balancing of supply and demand. Because local grids were not designed for distributed energy generation and large loads such as electric vehicle charging, their limited capacity is now leading to congestion. Since the responsibility for resolving congestion falls increasingly on the individual prosumers and their flexibility, the concept of fairness must take a central role in congestion management.

In this dissertation we present our research on supply-demand matching mechanisms for fair congestion management. The local networks populated by users can be represented by radial multi-agent commodity flow systems. For the resource allocation problems in this setting we draw on the fields of mechanism design and fair division to design provably fair congestion management mechanisms. We evaluate the merit of different notions of fairness and present algorithmic mechanisms that align agent incentives with fair allocations.

We find that notions of fairness regarding congested commodity flow networks can either focus on local or global fairness. Agents can have differing opinions on the two, depending on how wide they draw the circle of peers that they compare themselves to. We find that the mix of producers and consumers requires slight adaptation of notions of fairness, with agents envying one group while welcoming the other. Furthermore, we find that it is possible to combine notions of fairness with welfare optimization by letting individual agents decide which of the two is more important, and protecting their fair shares.

We are able to use the radial structure prevalent in energy systems in the built environment to design algorithmic mechanisms of consistently low computational complexity. The congestion solutions of these mechanisms satisfy different local and global fairness criteria, for which we provide rigorous proofs. We prove that our mechanisms are individually rational and, for variations of egalitarian fairness, also incentive compatible. Finally, we introduce a congestion aftermarket where agents compensate their peers for flexibility. ... Read more

The volatile production of renewable energy sources is often considered a key issue in future sustainable energy systems. Drawing on microgrid research, we argue that the potential synergy between microgrid energy management and provision of flexibility services to the wider grid could be further explored. In addition, the trade-off between cost minimisation and energy autarky of a community microgrid has not yet been fully investigated. This study therefore investigates the role of community microgrids in managing the volatility of renewable energy production in the wider grid, while also considering local optimisation trade-offs. The goal of this study is threefold: (1) identifying possibilities for market interactions, (2) developing simulation models and optimization/decision software, and (3) conducting exploratory experiments.

To illustrate our ideas, the community microgrid of Schoonschip was used as a case study. This Schoonschip microgrid contains 30 floating houseboats, that are equipped with the following energy resources: PV panels, batteries, modulating heat pumps, thermal collectors, buffer tanks, underfloor heating systems and electrical boilers. The resources are centrally controlled by an energy management system and the Schoonschip microgrid is connected via an interconnection of 160kVA. Simulation models were created for simulating the energy resources and heat demand of the houses. Optimization/decision software was developed and used for microgrid energy management and control of flexibility services.

This thesis provides insights into (1) potential market interactions between a community microgrid and the Dutch electricity wholesale market, (2) the trade-off between maximisation of the forecasted solar self-consumption and minimisation of electricity costs, and (3) the potential value and the problems associated with the provision of grid stability services. This study has resulted in a simulation model and decision software, which can also be used and further extended for additional experimental studies into microgrids and flexibility services.
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