Robust optimization based energy dispatch in smart grids considering demand uncertainty

In this study we discuss the application of robust optimization to the problem of economic energy dispatch in smart grids. Robust optimization based MPC strategies for tackling uncertain load demands are developed. Unexpected additive disturbances are modelled by defining an affine dependence between the control inputs and the uncertain load demands. The developed strategies were applied to a hybrid power system connected to an electrical power grid. Furthermore, to demonstrate the superiority of the standard Economic MPC over the MPC tracking, a comparison (e.g average daily cost) between the standard MPC tracking, the standard Economic MPC, and the integration of both in one-layer and two-layer approaches was carried out. The goal of this research is to design a controller based on Economic MPC strategies, that tackles uncertainties, in order to minimise economic costs and guarantee service reliability of the system.Postprint (author's final draft

Stochastic MPC for Controlling the Average Constraint Violation for Periodic Linear System with Additive Disturbance

This paper deals with stochastic model predictive control of constrained discrete-time periodic linear systems. Control inputs are subject to periodically time-varying polytopic constraints with possibly time-dependent state and input dimensions. A stochastic constraint is instead enforced on the system state process imposing a bound on the average over time of state constraint violations. Disturbances are additive, bounded and described by a periodically time-dependent probabilistic distribution. The aim of this paper is to develop a receding horizon control scheme which enforces recursive feasibility for the closed-loop state process. The effectiveness of the proposed algorithm is finally shown through a simulation study on a building climate control case

Model-based predictive control methods for distributed energy resources in smart grids.

This thesis develops optimization-based techniques for the control of distributed energy resources to provide multiple services to the power network. It is divided into three parts. The first part of this thesis focuses on the development of a framework for the efficient control of a single resource that is subject to the effect of periodic stochastic uncertainties. More specifically, resources that can be described by the general class of periodic constrained linear systems are considered and a method, based on Stochastic MPC, to control the over-time-average constraint violations is developed. Finally, the effectiveness of the control framework is tested, by means of a simulation analysis, for the case of the climate control of a building. The second part of the thesis introduces the required background for the electric power grid, energy markets, and distributed energy resources providing grid support services. First, the control problem of scheduling the operation of a set of energy resources offering multiple services to the grid is formally stated as a multi-stage uncertain optimization problem. In particular, the problem is designed so as to maximize the provision of a shared tracking service while enforcing the satisfaction of the operational constraints on both the individual resources, as well as on the hosting distribution network. Two computationally tractable approximated solution methods are then presented, which are based on robust-optimization techniques and on a linearization of the power flow equations around a general linearization point. A simulation-based analysis demonstrates the capability of the proposed framework to adapt to different levels of uncertainty acting on the overall system. Finally, a quantitative and qualitative comparison between the two approximation schemes is presented and general guidelines are given. The last part of the thesis demonstrates the practical relevance of the control framework developed in Part II. In particular, the aggregation of an electrical battery system and of an office building is considered, and two case studies are investigated. The first deals with the provision of secondary frequency control in the Swiss market, whereas the second deals with the problem of dispatching the operation of an active distribution feeder characterized by the presence of stochastic prosumers. In both cases, we show how to adapt the general framework of Part II so as to accommodate the given application. Then, we design a hierarchical multi-timescale controller in order to reliably deliver the service by coordinating the controllable resources during real-time operation. The results of both experimental campaigns demonstrate the effectiveness and robustness of the control methodology against the wide range of uncertainty involved. In fact, in both cases, high-quality tracking performance could be achieved without jeopardizing the occupants' comfort in the building nor violating the operational constraints of the battery. Finally, the results also show the benefit of combining resources with complementary technical capabilities as the building and the battery

On model predictive control for economic and robust operation of generalised flow-based networks

This thesis is devoted to design Model Predictive Control (MPC) strategies aiming to enhance the management of constrained generalised flow-based networks, with special attention to the economic optimisation and robust performance of such systems. Several control schemes are developed in this thesis to exploit the available economic information of the system operation and the disturbance information obtained from measurements and forecasting models. Dynamic network flows theory is used to develop control-oriented models that serve to design MPC controllers specialised for flow networks with additive disturbances and periodically time-varying dynamics and costs. The control strategies developed in this thesis can be classified in two categories: centralised MPC strategies and non-centralised MPC strategies. Such strategies are assessed through simulations of a real case study: the Barcelona drinking water network (DWN). Regarding the centralised strategies, different economic MPC formulations are first studied to guarantee recursive feasibility and stability under nominal periodic flow demands and possibly time-varying economic parameters and multi-objective cost functions. Additionally, reliability-based MPC, chance-constrained MPC and tree-based MPC strategies are proposed to address the reliability of both the flow storage and the flow transportation tasks in the network. Such strategies allow to satisfy a customer service level under future flow demand uncertainty and to efficiently distribute overall control effort under the presence of actuators degradation. Moreover, soft-control techniques such as artificial neural networks and fuzzy logic are used to incorporate self-tuning capabilities to an economic certainty-equivalent MPC controller. Since there are objections to the use of centralised controllers in large-scale networks, two non-centralised strategies are also proposed. First, a multi-layer distributed economic MPC strategy of low computational complexity is designed with a control topology structured in two layers. In a lower layer, a set of local MPC agents are in charge of controlling partitions of the overall network by exchanging limited information on shared resources and solving their local problems in a hierarchical-like fashion. Moreover, to counteract the loss of global economic information due to the decomposition of the overall control task, a coordination layer is designed to influence non-iteratively the decision of local controllers towards the improvement of the overall economic performance. Finally, a cooperative distributed economic MPC formulation based on a periodic terminal cost/region is proposed. Such strategy guarantees convergence to a Nash equilibrium without the need of a coordinator and relies on an iterative and global communication of local controllers, which optimise in parallel their control actions but using a centralised model of the network.Esta tesis se enfoca en el diseño de estrategias de control predictivo basado en modelos (MPC, por sus siglas en inglés) con la meta de mejorar la gestión de sistemas que pueden ser descritos por redes generalizadas de flujo y que están sujetos a restricciones, enfatizando especialmente en la optimización económica y el desempeño robusto de tales sistemas. De esta manera, varios esquemas de control se desarrollan en esta tesis para explotar tanto la información económica disponible de la operación del sistema como la información de perturbaciones obtenida de datos medibles y de modelos de predicción. La teoría de redes dinámicas de flujo es utilizada en esta tesis para desarrollar modelos orientados a control que sirven para diseñar controladores MPC especializados para la gestión de redes de flujo que presentan tanto perturbaciones aditivas como dinámicas y costos periódicamente variables en el tiempo. Las estrategias de control propuestas en esta tesis se pueden clasificar en dos categorías: estrategias de control MPC centralizado y estrategias de control MPC no-centralizado. Dichas estrategias son evaluadas mediante simulaciones de un caso de estudio real: la red de transporte de agua potable de Barcelona en España. En cuanto a las estrategias de control MPC centralizado, diferentes formulaciones de controladores MPC económicos son primero estudiadas para garantizar factibilidad recursiva y estabilidad del sistema cuya operación responde a demandas nominales de flujo periódico, a parámetros económicos posiblemente variantes en el tiempo y a funciones de costo multi-objetivo. Adicionalmente, estrategias de control MPC basado en fiabilidad, MPC con restricciones probabilísticas y MPC basado en árboles de escenarios son propuestas para garantizar la fiabilidad tanto de tareas de almacenamiento como de transporte de flujo en la red. Tales estrategias permiten satisfacer un nivel de servicio al cliente bajo incertidumbre en la demanda futura, así como distribuir eficientemente el esfuerzo global de control bajo la presencia de degradación en los actuadores del sistema. Por otra parte, técnicas de computación suave como redes neuronales artificiales y lógica difusa se utilizan para incorporar capacidades de auto-sintonía en un controlador MPC económico de certeza-equivalente. Dado que hay objeciones al uso de control centralizado en redes de gran escala, dos estrategias de control no-centralizado son propuestas en esta tesis. Primero, un controlador MPC económico distribuido de baja complejidad computacional es diseñado con una topología estructurada en dos capas. En una capa inferior, un conjunto de controladores MPC locales se encargan de controlar particiones de la red mediante el intercambio de información limitada de los recursos físicos compartidos y resolviendo sus problemas locales de optimización de forma similar a una secuencia jerárquica de solución. Para contrarrestar la pérdida de información económica global que ocurra tras la descomposición de la tarea de control global, una capa de coordinación es diseñada para influenciar no-iterativamente la decisión de los controles locales con el fin de lograr una mejora global del desempeño económico. La segunda estrategia no-centralizada propuesta en esta tesis es una formulación de control MPC económico distribuido cooperativo basado en una restricción terminal periódica. Tal estrategia garantiza convergencia a un equilibrio de Nash sin la necesidad de una capa de coordinación pero requiere una comunicación iterativa de información global entre todos los controladores locales, los cuales optimizan en paralelo sus acciones de control utilizando un modelo centralizado de la red

Formal methods for resilient control

Many systems operate in uncertain, possibly adversarial environments, and their successful operation is contingent upon satisfying specific requirements, optimal performance, and ability to recover from unexpected situations. Examples are prevalent in many engineering disciplines such as transportation, robotics, energy, and biological systems. This thesis studies designing correct, resilient, and optimal controllers for discrete-time complex systems from elaborate, possibly vague, specifications. The first part of the contributions of this thesis is a framework for optimal control of non-deterministic hybrid systems from specifications described by signal temporal logic (STL), which can express a broad spectrum of interesting properties. The method is optimization-based and has several advantages over the existing techniques. When satisfying the specification is impossible, the degree of violation - characterized by STL quantitative semantics - is minimized. The computational limitations are discussed. The focus of second part is on specific types of systems and specifications for which controllers are synthesized efficiently. A class of monotone systems is introduced for which formal synthesis is scalable and almost complete. It is shown that hybrid macroscopic traffic models fall into this class. Novel techniques in modular verification and synthesis are employed for distributed optimal control, and their usefulness is shown for large-scale traffic management. Apart from monotone systems, a method is introduced for robust constrained control of networked linear systems with communication constraints. Case studies on longitudinal control of vehicular platoons are presented. The third part is about learning-based control with formal guarantees. Two approaches are studied. First, a formal perspective on adaptive control is provided in which the model is represented by a parametric transition system, and the specification is captured by an automaton. A correct-by-construction framework is developed such that the controller infers the actual parameters and plans accordingly for all possible future transitions and inferences. The second approach is based on hybrid model identification using input-output data. By assuming some limited knowledge of the range of system behaviors, theoretical performance guarantees are provided on implementing the controller designed for the identified model on the original unknown system

A Framework for Explicit Model Predictive Control using Adjustable Robust Optimization and Economic Optimization of an Industrial-Scale Sulfuric Acid Plant

Optimization plays an important role in the operation of chemical engineering systems. Due to their typical size, different optimization tools and techniques are required to improve the efficiency in process operations. In this thesis, a mathematical tool is developed to address the issue of optimal control for linear systems under uncertainty. Also, a comprehensive plant model describing the behaviour of an industrial-scale Sulphuric Acid plant is developed to assist in identification of the optimal operating conditions under uncertainty Model predictive control (MPC) is considered an attractive strategy for the optimal control of complex chemical engineering systems. Conventional MPC involves solving an optimization problem online to determine the control actions that minimize a performance criterion function. The high computational expense associated with conventional MPC may make its application challenging for large-scale systems. Explicit MPC has been developed to solve the optimization problem offline. In this work, adjustable robust optimization (ARO) is used to obtain the explicit solution to the MPC optimization problem offline for discrete-time linear time invariant systems with constraints on inputs and states. In the robust model formulation an uncertain additive time-varying error is introduced to account for model uncertainty resulting from plant-model mismatch caused by un-measurable disturbances or process nonlinearities. The explicit solution is an optimal time-varying sequence of feedback control laws for the control inputs parameterized by the system’s states. The control laws are evaluated in a time-varying manner when the process is online using state measurements. This study shows that the resulting control laws ensure the implemented control actions maintain the system states within their feasible region for any realizations of the uncertain parameter within the uncertainty set. Three case studies are presented to demonstrate the proposed approach and to highlight the benefits and limitations of this method. The optimal operating condition to which an optimal controller will drive a large industrial-scale plant is identified using a different set of tools. In this thesis, an industrial-scale sulfuric acid plant is considered. The production of sulfuric acid is an important process due to its many applications and its use as a mitigation strategy for Sulphur dioxide (SO2). The reactor of the sulfuric acid plant has been the focus of many studies, and thus there has been very limited works in the literature that have analyzed the complete sulfuric acid plant. In this work, the flowsheet for an industrial-scale sulfuric acid plant with scrubbing tower is presented. The model is developed in Aspen Plus V8.8 and it is validated using historical data from an actual industrial plant. A sensitivity analysis was carried out, followed by optimization using two alternative objective functions: maximization of plant profitability or productivity. The optimization was extended to consider uncertainty in key operating and economic parameters. The results show that changes could be made in the current optimal operating condition of the plant to improve the annual profit of the process