Decentralized and Fault-Tolerant Control of Power Systems with High Levels of Renewables

Inter-area oscillations have been identified as a major problem faced by most power systems and stability of these oscillations are of vital concern due to the potential for equipment damage and resulting restrictions on available transmission capacity. In recent years, wide-area measurement systems (WAMSs) have been deployed that allow inter-area modes to be observed and identified.Power grids consist of interconnections of many subsystems which may interact with their neighbors and include several sensors and actuator arrays. Modern grids are spatially distributed and centralized strategies are computationally expensive and might be impractical in terms of hardware limitations such as communication speed. Hence, decentralized control strategies are more desirable.Recently, the use of HVDC links, FACTS devices and renewable sources for damping of inter-area oscillations have been discussed in the literature. However, very few such systems have been deployed in practice partly due to the high level of robustness and reliability requirements for any closed loop power system controls. For instance, weather dependent sources such as distributed winds have the ability to provide services only within a narrow range and might not always be available due to weather, maintenance or communication failures.Given this background, the motivation of this work is to ensure power grid resiliency and improve overall grid reliability. The first consideration is the design of optimal decentralized controllers where decisions are based on a subset of total information. The second consideration is to design controllers that incorporate actuator limitations to guarantee the stability and performance of the system. The third consideration is to build robust controllers to ensure resiliency to different actuator failures and availabilities. The fourth consideration is to design distributed, fault-tolerant and cooperative controllers to address above issues at the same time. Finally, stability problem of these controllers with intermittent information transmission is investigated.To validate the feasibility and demonstrate the design principles, a set of comprehensive case studies are conducted based on different power system models including 39-bus New England system and modified Western Electricity Coordinating Council (WECC) system with different operating points, renewable penetration and failures

System Level Synthesis

This article surveys the System Level Synthesis framework, which presents a novel perspective on constrained robust and optimal controller synthesis for linear systems. We show how SLS shifts the controller synthesis task from the design of a controller to the design of the entire closed loop system, and highlight the benefits of this approach in terms of scalability and transparency. We emphasize two particular applications of SLS, namely large-scale distributed optimal control and robust control. In the case of distributed control, we show how SLS allows for localized controllers to be computed, extending robust and optimal control methods to large-scale systems under practical and realistic assumptions. In the case of robust control, we show how SLS allows for novel design methodologies that, for the first time, quantify the degradation in performance of a robust controller due to model uncertainty -- such transparency is key in allowing robust control methods to interact, in a principled way, with modern techniques from machine learning and statistical inference. Throughout, we emphasize practical and efficient computational solutions, and demonstrate our methods on easy to understand case studies.Comment: To appear in Annual Reviews in Contro

H_2-Optimal Decentralized Control over Posets: A State-Space Solution for State-Feedback

We develop a complete state-space solution to H_2-optimal decentralized control of poset-causal systems with state-feedback. Our solution is based on the exploitation of a key separability property of the problem, that enables an efficient computation of the optimal controller by solving a small number of uncoupled standard Riccati equations. Our approach gives important insight into the structure of optimal controllers, such as controller degree bounds that depend on the structure of the poset. A novel element in our state-space characterization of the controller is a remarkable pair of transfer functions, that belong to the incidence algebra of the poset, are inverses of each other, and are intimately related to prediction of the state along the different paths on the poset. The results are illustrated by a numerical example.Comment: 39 pages, 2 figures, submitted to IEEE Transactions on Automatic Contro

Stochastic and Optimal Distributed Control for Energy Optimization and Spatially Invariant Systems

Improving energy efficiency and grid responsiveness of buildings requires sensing, computing and communication to enable stochastic decision-making and distributed operations. Optimal control synthesis plays a significant role in dealing with the complexity and uncertainty associated with the energy systems. The dissertation studies general area of complex networked systems that consist of interconnected components and usually operate in uncertain environments. Specifically, the contents of this dissertation include tools using stochastic and optimal distributed control to overcome these challenges and improve the sustainability of electric energy systems. The first tool is developed as a unifying stochastic control approach for improving energy efficiency while meeting probabilistic constraints. This algorithm is applied to demonstrate energy efficiency improvement in buildings and improving operational efficiency of virtualized web servers, respectively. Although all the optimization in this technique is in the form of convex optimization, it heavily relies on semidefinite programming (SP). A generic SP solver can handle only up to hundreds of variables. This being said, for a large scale system, the existing off-the-shelf algorithms may not be an appropriate tool for optimal control. Therefore, in the sequel I will exploit optimization in a distributed way. The second tool is itself a concrete study which is optimal distributed control for spatially invariant systems. Spatially invariance means the dynamics of the system do not vary as we translate along some spatial axis. The optimal H2 [H-2] decentralized control problem is solved by computing an orthogonal projection on a class of Youla parameters with a decentralized structure. Optimal H∞ [H-infinity] performance is posed as a distance minimization in a general L∞ [L-infinity] space from a vector function to a subspace with a mixed L∞ and H∞ space structure. In this framework, the dual and pre-dual formulations lead to finite dimensional convex optimizations which approximate the optimal solution within desired accuracy. Furthermore, a mixed L2 [L-2] /H∞ synthesis problem for spatially invariant systems as trade-offs between transient performance and robustness. Finally, we pursue to deal with a more general networked system, i.e. the Non-Markovian decentralized stochastic control problem, using stochastic maximum principle via Malliavin Calculus

A Convex Parameterization of Controllers Constrained to use only Relative Measurements

We consider the optimal controller design problem for distributed systems in which subsystems are equipped with sensors that measure only differences of quantities such as relative (rather than absolute) positions and velocities. While such problems can be set up as a standard problem of robust output feedback control, we illustrate with a counterexample that this may be undesirable and then propose an alternate equivalent formulation. In particular, we provide an example of sparsity constraints that are not quadratically-invariant with respect to a standard formulation of a given plant, but that can be written as quadratically-invariant constraints with respect to a transformed version of this problem. In effect, our transformation provides a path to convert the controller design problem to an equivalent convex program. This problem transformation relies on a novel parameterization of controllers with general relative measurement structures that we derive here. We further illustrate the usefulness of this novel parameterization through an example of optimal consensus design with prescribed communication delays within the controller.Comment: 8 pages, 3 figure