Optimality condition decomposition approach to distributed model predictive control

International audienceThis paper presents a new methodology for distributed model predictive control of large-scale systems. The methodology involves two distinct stages, i.e., the decomposition of large-scale systems into subsystems and the design of subsystem controllers. Two procedures are used: in the first stage, the structure of the Karush-Kuhn-Tucker matrix resulting from the necessary optimality conditions is exploited to yield a decomposition of the large-scale system into several subsystems. In the second stage, a particular technique, the so-called optimality condition decomposition makes it possible to synthesize distributed coordinated subcontrollers thus achieving an optimal distributed control of the large-scale system. The convergence of the proposed approach is stated

Final Causality in the Thought of Thomas Aquinas

Throughout his corpus, Thomas Aquinas develops an account of final causality that is both philosophically nuanced and interesting. The aim of my dissertation is to provide a systematic reconstruction of this account of final causality, one that clarifies its motivation and appeal. The body of my dissertation consists of four chapters. In Chapter 1, I examine the metaphysical underpinnings of Aquinas’s account of final causality by focusing on how Aquinas understands the causality of the final cause. I argue that Aquinas holds that an end is a cause because it is the determinate effect toward which an agent’s action is directed. I proceed by first presenting the general framework of causality within which Aquinas understands final causality. I then consider how Aquinas justifies the reality of each of the four kinds of cause, placing special emphasis on the final cause. In Chapter 2, I consider final causality from the perspective of goodness and explore the reasons why Aquinas thinks that the end of an action is always good. For even if one was convinced that the end of an action is indeed a cause, one might still resist attributing any normative or evaluative properties to the end, much less a positively-valenced normative property like goodness. In this chapter, I show how, given Aquinas’s metaphysics of powers and his characterization of goodness as that which all desire, it follows that every action is for the sake of some good. In Chapter 3, I consider Aquinas’s account of the relation between final causality and cognition. In many passages throughout his corpus—most famously in the fifth of his Five Ways—Aquinas advances the claim that cognition plays an essential role in final causality. In this chapter, I explore Aquinas’s account of the relation between final causality and cognition by reconstructing his Fifth Way and investigating the metaphysical foundations on which it rests. While the first three chapters of my dissertation focus on Aquinas’s account of final causality from the perspective of the ends of individual agents, in Chapter 4 I broaden my focus to consider the way in which the account of final causality developed in these earlier chapters shapes Aquinas’s philosophical cosmology. I argue that, on Aquinas’s view, when an individual agent acts for an end, it is plays a role in a larger system, e.g. a polis, an ecosystem, or the universe itself

Consensus ALADIN: A Framework for Distributed Optimization and Its Application in Federated Learning

This paper investigates algorithms for solving distributed consensus optimization problems that are non-convex. Since Typical ALADIN (Typical Augmented Lagrangian based Alternating Direction Inexact Newton Method, T-ALADIN for short) [1] is a well-performed algorithm treating distributed optimization problems that are non-convex, directly adopting T-ALADIN to those of consensus is a natural approach. However, T-ALADIN typically results in high communication and computation overhead, which makes such an approach far from efficient. In this paper, we propose a new variant of the ALADIN family, coined consensus ALADIN (C-ALADIN for short). C-ALADIN inherits all the good properties of T-ALADIN, such as the local linear or super-linear convergence rate and the local convergence guarantees for non-convex optimization problems; besides, C-ALADIN offers unique improvements in terms of communication efficiency and computational efficiency. Moreover, C-ALADIN involves a reduced version, in comparison with Consensus ADMM (Alternating Direction Method of Multipliers) [3], showing significant convergence performance, even without the help of second-order information. We also propose a practical version of C-ALADIN, named FedALADIN, that seamlessly serves the emerging federated learning applications, which expands the reach of our proposed C-ALADIN. We provide numerical experiments to demonstrate the effectiveness of C-ALADIN. The results show that C-ALADIN has significant improvements in convergence performance

Optimization approaches for exploiting the load flexibility of electric heating devices in smart grids

Energy systems all over the world are undergoing a fundamental transition to tackle climate change and other environmental challenges. The share of electricity generated by renewable energy sources has been steadily increasing. In order to cope with the intermittent nature of renewable energy sources, like photovoltaic systems and wind turbines, the electrical demand has to be adjusted to their power generation. To this end, flexible electrical loads are necessary. Moreover, optimization approaches and advanced information and communication technology can help to transform the traditional electricity grid into a smart grid. To shift the electricity consumption in time, electric heating devices, such as heat pumps or electric water heaters, provide significant flexibility. In order to exploit this flexibility, optimization approaches for controlling flexible devices are essential. Most studies in the literature use centralized optimization or uncoordinated decentralized optimization. Centralized optimization has crucial drawbacks regarding computational complexity, privacy, and robustness, but uncoordinated decentralized optimization leads to suboptimal results. In this thesis, coordinated decentralized and hybrid optimization approaches with low computational requirements are developed for exploiting the flexibility of electric heating devices. An essential feature of all developed methods is that they preserve the privacy of the residents. This cumulative thesis comprises four papers that introduce different types of optimization approaches. In Paper A, rule-based heuristic control algorithms for modulating electric heating devices are developed that minimize the heating costs of a residential area. Moreover, control algorithms for minimizing surplus energy that otherwise could be curtailed are introduced. They increase the self-consumption rate of locally generated electricity from photovoltaics. The heuristic control algorithms use a privacy-preserving control and communication architecture that combines centralized and decentralized control approaches. Compared to a conventional control strategy, the results of simulations show cost reductions of between 4.1% and 13.3% and reductions of between 38.3% and 52.6% regarding the surplus energy. Paper B introduces two novel coordinating decentralized optimization approaches for scheduling-based optimization. A comparison with different decentralized optimization approaches from the literature shows that the developed methods, on average, lead to 10% less surplus energy. Further, an optimization procedure is defined that generates a diverse solution pool for the problem of maximizing the self-consumption rate of locally generated renewable energy. This solution pool is needed for the coordination mechanisms of several decentralized optimization approaches. Combining the decentralized optimization approaches with the defined procedure to generate diverse solution pools, on average, leads to 100 kWh (16.5%) less surplus energy per day for a simulated residential area with 90 buildings. In Paper C, another decentralized optimization approach that aims to minimize surplus energy and reduce the peak load in a local grid is developed. Moreover, two methods that distribute a central wind power profile to the different buildings of a residential area are introduced. Compared to the approaches from the literature, the novel decentralized optimization approach leads to improvements of between 0.8% and 13.3% regarding the surplus energy and the peak load. Paper D introduces uncertainty handling control algorithms for modulating electricheating devices. The algorithms can help centralized and decentralized scheduling-based optimization approaches to react to erroneous predictions of demand and generation. The analysis shows that the developed methods avoid violations of the residents\u27 comfort limits and increase the self-consumption rate of electricity generated by photovoltaic systems. All introduced optimization approaches yield a good trade-off between runtime and the quality of the results. Further, they respect the privacy of residents, lead to better utilization of renewable energy, and stabilize the grid. Hence, the developed optimization approaches can help future energy systems to cope with the high share of intermittent renewable energy sources

Competitive and Cooperative Approaches to the Balancing Market in Distribution Grids

The electrical grid has been changing in the last decade due to the presence, at the distribution level, of renewables, distributed generation, storage systems, microgrids, and electric vehicles. The introduction of new legislation and actors in the smart grid\u2019s system opens new challenges for the activities of companies, and the development of new energy management systems, models, and methods. In order to face this revolution, new market structures are being defined as well as new technologies and optimization and control algorithms for the management of distributed resources and the coordination of local users to contribute to active power reserve and ancillary services. One of the main problems for an electricity market operator that also owns the distribution grid is to avoid congestions and maximize the quality of the service provided. The thesis concerns the development and application of new methods for the optimization of network systems (with multi-decision makers) with particular attention to the case of power distribution networks This Ph.D. thesis aims to address the current lack of properly defined market structures for the determination of balancing services in distribution networks. As a first study, to be able to handle the power flow equation in a computationally better way, a new convex relaxation has been proposed. Thereafter, two opposite types of market structure have been developed: competitive and cooperative. The first structure presents a two-tier mechanism where the market operator is in a predominant position compared to other market players. Vice versa in the cooperative mechanism (solved through distributed optimization techniques ) all actors are on the same level and work together for social welfare. The main methodological novelties of the proposed work are to solve complex problems with formally correct and computationally efficient techniques

Energy Management Systems of Microgrids

The distributed operation of parts of the system, denoted as microgrids or, more generally, as local energy communities, could be an effective answer to the issues posed by the increasing complexity of the modern power distribution systems facing the increasing penetration of renewable energy sources and the electrification of urban transportation. The results of the research activities described in the thesis can be divided into three main parts. The first one is the modeling and analysis of low voltage power distribution networks feeding residential, commercial and small-scale industrial consumers including distributed generation units and storage systems. It focuses on an optimization model that has been applied to the energy management system of an experimental microgrid. A mixed integer linear programming model is developed and presented, which takes into account the unbalanced operation of the LV network. The second part focuses on the day-ahead operational planning of a local energy community, which is assumed able to implement transactive energy control actions with allocation of the network power loss. The problem has been addressed by means of two different optimization procedures, namely a centralized mathematical programming model and a specific distributed optimization procedure based on the adoption of the alternating direction method of multipliers (ADMM). The third part is the day-ahead optimization of the operation of a local energy system consisting of photovoltaic units, energy storage systems and loads aimed at minimizing the electricity procurement cost, considering the uncertainties in the load and generation forecasts. Two mixed integer linear programming models are adopted, each for a different representation of the battery: a simple energy balance constraint and the Kinetic Battery Model. The chapter describes the generation of the scenarios, the construction of the scenario tree and the intraday decision-making procedure based on the solution of the multistage stochastic programming