Decentralised reliable guaranteed cost control of uncertain systems: an LMI design

© 2007 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes,creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.The problem of designing a decentralised control scheme for a class of linear large scale interconnected systems with norm-bounded time-varying parameter uncertainties under a class of control failures is addressed. These failures are described by a model that considers possible outages or partial failures in every single actuator of each decentralised controller. The control design is performed through two steps. First, a decentralised reliable guaranteed cost control set is derived and, second, a feasible linear matrix inequalities procedure is presented for the effective construction of the control set. A numerical example illustrates the efficiency of the proposed control schemePeer ReviewedPostprint (published version

Distributed Smart Grid Asset Control Strategies for Providing Ancillary Services

With large-scale plans to integrate renewable generation driven mainly by state-level renewable portfolio requirements, more resources will be needed to compensate for the uncertainty and variability associated with intermittent generation resources. Distributed assets can be used to mitigate the concerns associated with renewable energy resources and to keep costs down. Under such conditions, performing primary frequency control using only supply-side resources becomes not only prohibitively expensive but also technically difficult. It is therefore important to explore how a sufficient proportion of the loads could assume a routine role in primary frequency control to maintain the stability of the system at an acceptable cost. The main objective of this project is to develop a novel hierarchical distributed framework for frequency based load control. The framework involves two decision layers. The top decision layer determines the optimal gain for aggregated loads for each load bus. The gains are computed using decentralized robust control methods, and will be broadcast to the corresponding participating loads every control period. The second layer consists of a large number of heterogeneous devices, which switch probabilistically during contingencies so that aggregated power change matches the desired amount according to the most recently received gains. The simulation results show great potential to enable systematic design of demand-side primary frequency control with stability guarantees on the overall power system. The proposed design systematically accounts for the interactions between the total load response and bulk power system frequency dynamics. It also guarantees frequency stability under a wide range of time varying operating conditions. The local device-level load response rules fully respect the device constraints (such as temperature setpoint, compressor time delays of HVACs, or arrival and departure of the deferrable loads), which are crucial for implementing real load control programs. The promise of autonomous, Grid Friendly™ response by smart appliances in the form of under-frequency load shedding was demonstrated in the GridWise Olympic Peninsula Demonstration in 2006. Each controller monitored the power grid voltage signal and requested that electrical load be shed by its appliance whenever electric power-grid frequency fell below 59.95 Hz. The controllers and their appliances responded reliably to each shallow under-frequency event, which was an average of one event per day and shed their loads for the durations of these events. Another objective of this project was to perform extensive simulation studies to investigate the impact of a population of Grid Friendly™ Appliances (GFAs) on the bulk power system frequency stability. The GFAs considered in this report are represented as demonstration units with water heaters individually modeled

Decentralized sliding mode control and estimation for large-scale systems

This thesis concerns the development of an approach of decentralised robust control and estimation for large scale systems (LSSs) using robust sliding mode control (SMC) and sliding mode observers (SMO) theory based on a linear matrix inequality (LMI) approach. A complete theory of decentralized first order sliding mode theory is developed. The main developments proposed in this thesis are: The novel development of an LMI approach to decentralized state feedback SMC. The proposed strategy has good ability in combination with other robust methods to fulfill specific performance and robustness requirements. The development of output based SMC for large scale systems (LSSs). Three types of novel decentralized output feedback SMC methods have been developed using LMI design tools. In contrast to more conventional approaches to SMC design the use of some complicated transformations have been obviated. A decentralized approach to SMO theory has been developed focused on the Walcott-Żak SMO combined with LMI tools. A derivation for bounds applicable to the estimation error for decentralized systems has been given that involves unknown subsystem interactions and modeling uncertainty. Strategies for both actuator and sensor fault estimation using decentralized SMO are discussed.The thesis also provides a case study of the SMC and SMO concepts applied to a non-linear annealing furnace system modelderived from a distributed parameter (partial differential equation) thermal system. The study commences with a lumped system decentralised representation of the furnace derived from the partial differential equations. The SMO and SMC methods derived in the thesis are applied to this lumped parameter furnace model. Results are given demonstrating the validity of the methods proposed and showing a good potential for a valuable practical implementation of fault tolerant control based on furnace temperature sensor faults

Robust Decentralized Control of Power Systems: A Matrix Inequalities Approach

This dissertation presents an extension of robust decentralized control design techniques for power systems, with special emphasis on design problems that can be expressed as minimizing a linear objective function under linear matrix inequality (LMI) in tandem with nonlinear matrix inequality (NMI) constraints. These types of robust decentralized control design problems are generally nonconvex optimizations, and are proven to be computationally challenging. Therefore, this dissertation proposes alternative computational schemes using: i) bordered-block diagonal (BBD) decomposition algorithm for designing LMI based robust decentralized static output feedback controllers, ii) sequential LMI programming method for designing robust decentralized dynamic output feedback controllers, and, iii) generalized parameter continuation method involving matrix inequalities for designing reduced-order decentralized dynamic output feedback controllers. First, this dissertation considers the problem of designing robust decentralized static output feedback controllers for power systems that guarantee connective stability despite the presence of uncertainties among the interconnected subsystems. The design problem is then solved using BBD decomposition algorithm that clusters the state, input and output structural information for the direct computation of the appropriate gain matrices. Moreover, the approach is flexible enough to allow the inclusion of additional design constraints such as the size of the gain matrices and the degree of robust stability while at the same time maximizing the tolerable upper bounds on the class of perturbations. Second, this research considers the problem of designing a robust decentralized fixed-order dynamic output feedback controller for power systems that is formulated as a nonconvex optimization problem involving LMIs coupled through bilinear matrix equation. In the design, the robust connective stability of the overall system is guaranteed while the upper bounds of the uncertainties arising from the interconnection of the subsystems as well as nonlinearities within each subsystem are maximized. The (sub)-optimal robust decentralized dynamic output feedback control design problem is then solved using sequential LMI programming method. Moreover, the local convergence property of this algorithm has shown the effectiveness of the proposed approach for designing (sub)-optimal robust decentralized dynamic output feedback controllers for power systems. Third, this dissertation considers the problem of designing a robust decentralized structure-constrained dynamic output feedback controller design for power systems using LMI-based optimization approach. The problem of designing a decentralized structure-constrained H2/Hinf controller is first reformulated as an extension of a static output feedback controller design problem for the extended system. The resulting nonconvex optimization problem which involves bilinear matrix inequalities (BMIs) is then solved using the sequentially LMI programming method. Finally, the research considers the problem of designing reduced-order decentralized Hinf controllers for power systems. Initially a fictitious centralized Hinf robust controller, which is typically high-order controller, is designed to guarantee the robust stability of the overall system against unstructured and norm bounded uncertainties. Then the problem of designing a reduced-order decentralized controller is reformulated as an embedded parameter continuation problem that homotopically deforms from the centralized controller to the decentralized controller as the continuation parameter monotonically varies. The design problem, which guarantees the same robustness condition of the centralized controller, is solved using a two-stage iterative matrix inequality optimization algorithm. Moreover, the approach is flexible enough to allow designing different combinations of reduced-order controllers between the different input/output channels. The effectiveness of these proposed approaches are demonstrated by designing realistic power system stabilizers (PSSs) for power system, notably so-called reduced-order robust PSSs that are linear and use minimum local-feedback information. Moreover, the nonlinear simulation results have confirmed the robustness of the system for all envisaged operating conditions and disturbances. The proposed approaches offer a practical tool for engineers, besides designing reduced-order PSSs, to re-tune PSS parameters for improving the dynamic performance of the overall system

Modélisation et commande non linéaire des hydroliennes couplées à un réseau électrique

This thesis develops nonlinear and robust control strategies in order to ensure a successful connection of marine turbine systems into grid. In addition, it is a question to examine in simulation and practice the dynamic behavior of controlled marine turbine systems under severe perturbations. Firstly, we have modeled all production chain elements of marine turbine system. Secondly, we have proposed three nonlinear control strategies ; one for marine turbine system single machine connected to infinite bus and the both others for two multimachine electrical networks. The developed strategies control stability is proven mathematically by using Lyapunov method and one specific property of variable structure. These strategies control particularity is the two outputs regulation (terminal voltage and frequency) trough a single input (synchronous machine excitation). Finally, simulation results under mechanical and electrical perturbations are presented in order to highlight the robustness qualities of the proposed controllers compared to nonlinear controller CNL and classical AVR-PSS. In view of industrial applications, the proposed control for marine turbine single machine system is implemented on experimental bench. The obtained practical results under hard perturbations are very satisfactory. These results are used to realize a comparative study between the proposed control, the CNL and the AVR-PSS.L’objectif de cette thèse est de développer des stratégies de commande non linéaire et robuste afin d’assurer une connexion avec succès des systèmes hydroliens dans un réseau électrique de forte puissance. Il s’agira en plus, d’étudier en simulation et en pratique le comportement dynamique de ses systèmes hydroliens commandés suite à des perturbations sévères. Dans un premier temps, nous nous sommes intéressés à la modélisation de tous les éléments de la chaine de production d’énergie hydrolienne, en partant de la marée jusqu’à la génératrice synchrone. Dans un second temps, nous avons proposé trois lois de commande non linéaire ; une pour un système hydrolien mono machine et les deux autres pour deux types de réseau électrique multi-machine. La stabilité de ces lois de commandes est prouvée en utilisant la méthode de Lyapunov et les propriétés spécifiques à la structure variable. La particularité de ces lois de commandes est qu’elles régulent simultanément la tension terminale et la fréquence en agissant uniquement sur l’excitation de la génératrice synchrone. Finalement, nous avons étudié en simulation le comportement dynamique des systèmes hydroliens commandés et les résultats obtenus sous perturbations électrique et mécanique ont montré l’efficacité de la commande proposée par rapport aux commandes CNL et AVR-PSS. Dans un souci de valider pratiquement ces résultats de simulation, la commande non linéaire proposée pour le système hydrolien mono machine est implantée sur un banc d’essai. Les résultats satisfaisants obtenus sous perturbations soutenues sont ensuite comparés à ceux obtenus pratiquement avec les commandes, CNL et AVR-PSS