Distributed Optimization with Application to Power Systems and Control

In many engineering domains, systems are composed of partially independent subsystems—power systems are composed of distribution and transmission systems, teams of robots are composed of individual robots, and chemical process systems are composed of vessels, heat exchangers and reactors. Often, these subsystems should reach a common goal such as satisfying a power demand with minimum cost, flying in a formation, or reaching an optimal set-point. At the same time, limited information exchange is desirable—for confidentiality reasons but also due to communication constraints. Moreover, a fast and reliable decision process is key as applications might be safety-critical. Mathematical optimization techniques are among the most successful tools for controlling systems optimally with feasibility guarantees. Yet, they are often centralized—all data has to be collected in one central and computationally powerful entity. Methods from distributed optimization control the subsystems in a distributed or decentralized fashion, reducing or avoiding central coordination. These methods have a long and successful history. Classical distributed optimization algorithms, however, are typically designed for convex problems. Hence, they are only partially applicable in the above domains since many of them lead to optimization problems with non-convex constraints. This thesis develops one of the first frameworks for distributed and decentralized optimization with non-convex constraints. Based on the Augmented Lagrangian Alternating Direction Inexact Newton (ALADIN) algorithm, a bi-level distributed ALADIN framework is presented, solving the coordination step of ALADIN in a decentralized fashion. This framework can handle various decentralized inner algorithms, two of which we develop here: a decentralized variant of the Alternating Direction Method of Multipliers (ADMM) and a novel decentralized Conjugate Gradient algorithm. Decentralized conjugate gradient is to the best of our knowledge the first decentralized algorithm with a guarantee of convergence to the exact solution in a finite number of iterates. Sufficient conditions for fast local convergence of bi-level ALADIN are derived. Bi-level ALADIN strongly reduces the communication and coordination effort of ALADIN and preserves its fast convergence guarantees. We illustrate these properties on challenging problems from power systems and control, and compare performance to the widely used ADMM. The developed methods are implemented in the open-source MATLAB toolbox ALADIN-—one of the first toolboxes for decentralized non-convex optimization. ALADIN- comes with a rich set of application examples from different domains showing its broad applicability. As an additional contribution, this thesis provides new insights why state-of-the-art distributed algorithms might encounter issues for constrained problems

Distributed Optimization with Application to Power Systems and Control

Mathematical optimization techniques are among the most successful tools for controlling technical systems optimally with feasibility guarantees. Yet, they are often centralized—all data has to be collected in one central and computationally powerful entity. Methods from distributed optimization overcome this limitation. Classical approaches, however, are often not applicable due to non-convexities. This work develops one of the first frameworks for distributed non-convex optimization

Distributed Optimization with Application to Power Systems and Control

Mathematical optimization techniques are among the most successful tools for controlling technical systems optimally with feasibility guarantees. Yet, they are often centralized—all data has to be collected in one central and computationally powerful entity. Methods from distributed optimization overcome this limitation. Classical approaches, however, are often not applicable due to non-convexities. This work develops one of the first frameworks for distributed non-convex optimization

International Conference on Continuous Optimization (ICCOPT) 2019 Conference Book

The Sixth International Conference on Continuous Optimization took place on the campus of the Technical University of Berlin, August 3-8, 2019. The ICCOPT is a flagship conference of the Mathematical Optimization Society (MOS), organized every three years. ICCOPT 2019 was hosted by the Weierstrass Institute for Applied Analysis and Stochastics (WIAS) Berlin. It included a Summer School and a Conference with a series of plenary and semi-plenary talks, organized and contributed sessions, and poster sessions. This book comprises the full conference program. It contains, in particular, the scientific program in survey style as well as with all details, and information on the social program, the venue, special meetings, and more

Network-Secure Consumer Bidding in Energy and Reserve Markets

Electricity systems are undergoing a fundamental transformation from centralised generation to a distributed paradigm in which electricity is produced at a smaller scale by numerous distributed energy resources (DER). The replacement of centralised facilities by DER brings economic and environmental benefits. However, it also makes it challenging for the market operator to secure the system with sufficient frequency response in the absence of centralised facilities -- dominant providers of such services -- in the electricity markets. Fortunately, the aggregate response of DER can fulfil systems' need for frequency reserve services. However, DER are operated within distribution networks whose technical limits are not accounted for within the wholesale market. This raises the question of how DER can participate in the energy and reserve markets while respecting the distribution network's constraints. To ensure network constraints, consumer and grid constraints / preferences should be modelled simultaneously within a large-scale optimisation problem. Yet, the need for scale, involvement of multiple stakeholders (grid operator and consumers) who possibly have conflicting interests, privacy concerns, and the uncertainty around consumer data and market prices make this extra challenging. This thesis contributes to addressing these challenges by developing network-secure consumer bids that account for the distributed nature of the problem, consumer data and market price uncertainties. Note that when bidding in the market, consumers, and thus, the network operating point is not clear, as it depends on the dispatch in the energy market and whether a contingency occurs. Therefore, we ensure grid feasibility for operating envelopes that include any possible operating points of consumers. We first use the alternating direction method of multipliers (ADMM) to enable network-secure consumer biding. Using ADMM, consumers optimise for their energy and reserve bids and communicate with the grid their required operating envelopes. The network then solves OPFs to see whether any constraint is violated and updates the ADMM parameters. Such communications continue until converging on a consensus solution. We learnt that our ADMM-based solution approach is able to maintain grid's constraints as long as consumers commit to their envelopes -- a requirement that might not hold due to uncertainty. Thus, we further improve our bidding approach by modelling uncertainties around solar PV and demand, using a piecewise affinely adjustable robust constrained optimisation (PWA-ARCO). We observed that not only is PWA-ARCO able to compensate for live uncertainty variabilities, but also it can improve the reliability of consumer bids, especially in reserve markets. We also extend our initial envelopes by enabling consumers to provide reactive power support for the grid. We next enable consumers to bid (possibly) their entire flexibility by developing price-sensitive offers. Such offers include a bid curve chunked into several capacity bands, each being submitted at a different price. We identified that when the prices cannot be forecast accurately, the price-sensitive bidding approach can improve consumer benefit. To ensure network feasibility, instead of an iterative ADMM approach, we propose a more scalable one-shot policy in which the network curtails the part of the consumer bid that violates the network. Compared to ADMM, the one-shot policy significantly reduced the computation complexity at the cost of a slightly less optimum outcome. Overall, this thesis investigates different techniques to provide network-secure energy and reserve market services out of residential DER. It expands the knowledge in the area of consumer bidding solutions, adjustable robust optimisation, and distributed optimisation. It also discovers a range of interesting future research topics, including distribution network modelling and uncertainty characterisation