Consensus-based approach to peer-to-peer electricity markets with product differentiation

With the sustained deployment of distributed generation capacities and the more proactive role of consumers, power systems and their operation are drifting away from a conventional top-down hierarchical structure. Electricity market structures, however, have not yet embraced that evolution. Respecting the high-dimensional, distributed and dynamic nature of modern power systems would translate to designing peer-to-peer markets or, at least, to using such an underlying decentralized structure to enable a bottom-up approach to future electricity markets. A peer-to-peer market structure based on a Multi-Bilateral Economic Dispatch (MBED) formulation is introduced, allowing for multi-bilateral trading with product differentiation, for instance based on consumer preferences. A Relaxed Consensus+Innovation (RCI) approach is described to solve the MBED in fully decentralized manner. A set of realistic case studies and their analysis allow us showing that such peer-to-peer market structures can effectively yield market outcomes that are different from centralized market structures and optimal in terms of respecting consumers preferences while maximizing social welfare. Additionally, the RCI solving approach allows for a fully decentralized market clearing which converges with a negligible optimality gap, with a limited amount of information being shared.Comment: Accepted for publication in IEEE Transactions on Power System

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

Decentralized Proximal Method of Multipliers for Convex Optimization with Coupled Constraints

In this paper, a decentralized proximal method of multipliers (DPMM) is proposed to solve constrained convex optimization problems over multi-agent networks, where the local objective of each agent is a general closed convex function, and the constraints are coupled equalities and inequalities. This algorithm strategically integrates the dual decomposition method and the proximal point algorithm. One advantage of DPMM is that subproblems can be solved inexactly and in parallel by agents at each iteration, which relaxes the restriction of requiring exact solutions to subproblems in many distributed constrained optimization algorithms. We show that the first-order optimality residual of the proposed algorithm decays to $0$ at a rate of $o(1/k)$ under general convexity. Furthermore, if a structural assumption for the considered optimization problem is satisfied, the sequence generated by DPMM converges linearly to an optimal solution. In numerical simulations, we compare DPMM with several existing algorithms using two examples to demonstrate its effectiveness