From Electrical Power Flows to Unsplittabe Flows: A QPTAS for OPF with Discrete Demands in Line Distribution Networks

The {\it AC Optimal Power Flow} (OPF) problem is a fundamental problem in power systems engineering which has been known for decades. It is a notoriously hard problem due mainly to two reasons: (1) non-convexity of the power flow constraints and (2) the (possible) existence of discrete power injection constraints. Recently, sufficient conditions were provided for certain convex relaxations of OPF to be exact in the continuous case, thus allowing one to partially address the issue of non-convexity. In this paper we make a first step towards addressing the combinatorial issue. Namely, by establishing a connection to the well-known {\it unsplittable flow problem} (UFP), we are able to generalize known techniques for the latter problem to provide approximation algorithms for OPF with discrete demands. As an application, we give a quasi-polynomial time approximation scheme for OPF in line networks under some mild assumptions and a single generation source. We believe that this connection can be further leveraged to obtain approximation algorithms for more general settings, such as multiple generation sources and tree networks

A Classification Scheme for Local Energy Trading

The current trend towards more renewable and sustainable energy generation leads to an increased interest in new energy management systems and the concept of a smart grid. One important aspect of this is local energy trading, which is an extension of existing electricity markets by including prosumers, who are consumers also producing electricity. Prosumers having a surplus of energy may directly trade this surplus with other prosumers, which are currently in demand. In this paper, we present an overview of the literature in the area of local energy trading. In order to provide structure to the broad range of publications, we identify key characteristics, define the various settings, and cluster the considered literature along these characteristics. We identify three main research lines, each with a distinct setting and research question. We analyze and compare the settings, the used techniques, and the results and findings within each cluster and derive connections between the clusters. In addition, we identify important aspects, which up to now have to a large extent been neglected in the considered literature and highlight interesting research directions, and open problems for future work.Comment: 38 pages, 1 figure, This work has been submitted and accepted at OR Spectru

Peer-to-Peer Energy Trading in Smart Residential Environment with User Behavioral Modeling

Electric power systems are transforming from a centralized unidirectional market to a decentralized open market. With this shift, the end-users have the possibility to actively participate in local energy exchanges, with or without the involvement of the main grid. Rapidly reducing prices for Renewable Energy Technologies (RETs), supported by their ease of installation and operation, with the facilitation of Electric Vehicles (EV) and Smart Grid (SG) technologies to make bidirectional flow of energy possible, has contributed to this changing landscape in the distribution side of the traditional power grid. Trading energy among users in a decentralized fashion has been referred to as Peer- to-Peer (P2P) Energy Trading, which has attracted significant attention from the research and industry communities in recent times. However, previous research has mostly focused on engineering aspects of P2P energy trading systems, often neglecting the central role of users in such systems. P2P trading mechanisms require active participation from users to decide factors such as selling prices, storing versus trading energy, and selection of energy sources among others. The complexity of these tasks, paired with the limited cognitive and time capabilities of human users, can result sub-optimal decisions or even abandonment of such systems if performance is not satisfactory. Therefore, it is of paramount importance for P2P energy trading systems to incorporate user behavioral modeling that captures users’ individual trading behaviors, preferences, and perceived utility in a realistic and accurate manner. Often, such user behavioral models are not known a priori in real-world settings, and therefore need to be learned online as the P2P system is operating. In this thesis, we design novel algorithms for P2P energy trading. By exploiting a variety of statistical, algorithmic, machine learning, and behavioral economics tools, we propose solutions that are able to jointly optimize the system performance while taking into account and learning realistic model of user behavior. The results in this dissertation has been published in IEEE Transactions on Green Communications and Networking 2021, Proceedings of IEEE Global Communication Conference 2022, Proceedings of IEEE Conference on Pervasive Computing and Communications 2023 and ACM Transactions on Evolutionary Learning and Optimization 2023

Local energy trading for microgrids:Modeling human behavior, uncertainty and grid constraints

Electricity is one of the major drivers of today’s society and its rapid development, however, it also significantly contributes to the ongoing global warming. To reduce its impact, the energy transition aims to change the electricity production by switching from fossil fuels to more renewable and sustainable energy sources. In adition, the energy transition also addresses required changes in the heating and mobility sector.These changes have a significant impact on the electricity system, and an intelligent (active) management of the electricity production and consumption is required. Throughout the last years, many approaches have been proposed to manage production and consumption. At the core of this thesis, we focus on three different aspects of such approaches.1: We consider and analyze the impact of human behavior on the outcome of a local electricity market. Due to the direct participation of households, the question arises how human preferences and behavior affect the outcome of the market. Therefore, we translate a behavioral model from social science into a multi-objective optimization problem, which uses the personal preferences and motives of households and creates tailor-made bidcurves. We analyze the results on an household and the market level to derive implications for future maket design.2: The shift in electricity production leads to increased uncertainties in the future energy system. To deal with such uncertainties, we focus on a joint energy management of a neighborhood. We apply ideas and techniques from robust optimization to deal with the uncertainty, and mainly focus on an approach combining static robust optimization with a rolling horizon framework. Hereby, we generalize the rolling horizon by allowing more flexible starting time slots and compare and analyze two such generalized rolling horizon versions.3: The increased peaks due to the additional production and generation pose a serious burden to the current electricity grid. To ensure a safe operation, we focus on grid constraints in the context of a real-time control approach, which implements day-ahead and intraday market solutions. We use the planned solutions to guide the real-time decisions, and identify an interesting connection between day-ahead operations and their real-time realization