Robust Stabilization of Nonlinear Systems by Quantized and Ternary Control

Results on the problem of stabilizing a nonlinear continuous-time system by a finite number of control or measurement values are presented. The basic tool is a discontinuous version of the so-called semi-global backstepping lemma. We derive robust practical stabilizability results by quantized and ternary controllers and apply them to some significant control problems.Comment: 14 pages, 4 figure

Optimal generation in structure-preserving power networks with second-order turbine-governor dynamics

Recently we have been exploring the role of passivity and the internal model principle in power network control in the presence of uncertainties due to unmeasured demand and supply. In this work we continue this line of research and extend our results to include more complex dynamics at the generation side. Namely, we study frequency stabilization by primary control and frequency regulation by optimal generation control, where we additionally incorporate second-order turbine-governor dynamics. The power network is represented by the structure-preserving Bergen-Hill model [1]. Distributed controllers that require local frequency measurements are proposed and are shown to minimize the generation costs. Asymptotic convergence is proven when the generators satisfy a local matrix condition. The effectiveness of proposed controllers is demonstrated in a case study

Nonlinear Analysis of an Improved Swing Equation

In this paper, we investigate the properties of an improved swing equation model for synchronous generators. This model is derived by omitting the main simplifying assumption of the conventional swing equation, and requires a novel analysis for the stability and frequency regulation. We consider two scenarios. First we study the case that a synchronous generator is connected to a constant load. Second, we inspect the case of the single machine connected to an infinite bus. Simulations verify the results

A modular design of incremental Lyapunov functions for microgrid control with power sharing

In this paper we contribute a theoretical framework that sheds a new light on the problem of microgrid analysis and control. The starting point is an energy function comprising the kinetic energy associated with the elements that emulate the rotating machinery and terms taking into account the reactive power stored in the lines and dissipated on shunt elements. We then shape this energy function with the addition of an adjustable voltage-dependent term, and construct incremental storage functions satisfying suitable dissipation inequalities. Our choice of the voltage-dependent term depends on the voltage dynamics/controller under investigation. Several microgrids dynamics that have similarities or coincide with dynamics already considered in the literature are captured in our incremental energy analysis framework. The twist with respect to existing results is that our incremental storage functions allow for an analysis of the coupled microgrid obviating the need for simplifying linearization techniques and for the restrictive decoupling assumption in which the frequency dynamics is fully separated from the voltage one

A Robust Consensus Algorithm for Current Sharing and Voltage Regulation in DC Microgrids

In this paper a novel distributed control algorithm for current sharing and voltage regulation in Direct Current (DC) microgrids is proposed. The DC microgrid is composed of several Distributed Generation units (DGUs), including Buck converters and current loads. The considered model permits an arbitrary network topology and is affected by unknown load demand and modelling uncertainties. The proposed control strategy exploits a communication network to achieve proportional current sharing using a consensus-like algorithm. Voltage regulation is achieved by constraining the system to a suitable manifold. Two robust control strategies of Sliding Mode (SM) type are developed to reach the desired manifold in a finite time. The proposed control scheme is formally analyzed, proving the achievement of proportional current sharing, while guaranteeing that the weighted average voltage of the microgrid is identical to the weighted average of the voltage references.Comment: 12 page

A Lyapunov Approach to Control of Microgrids with a Network-Preserved Differential-Algebraic Model

We provide sufficient conditions for asymptotic stability and optimal resource allocation for a networkpreserved microgrid model with active and reactive power loads. The model considers explicitly the presence of constantpower loads as well as the coupling between the phase angle and voltage dynamics. The analysis of the resulting nonlinear differential algebraic equation (DAE) system is conducted by leveraging incremental Lyapunov functions, definiteness of the load flow Jacobian and the implicit function theorem

An energy-based analysis of reduced-order models of (networked) synchronous machines

Stability of power networks is an increasingly important topic because of the high penetration of renewable distributed generation units. This requires the development of advanced techniques for the analysis and controller design of power networks. Although there are widely accepted reduced-order models to describe the power network dynamics, they are commonly presented without details about the reduction procedure. The present article aims to provide a modular model derivation of multi-machine power networks. Starting from first-principle fundamental physics, we present detailed dynamical models of synchronous machines and clearly state the underlying assumptions which lead to some of the standard reduced-order multi-machine models. In addition, the energy functions for these models are derived, which allows to represent the multi-machine systems as port-Hamiltonian systems. Moreover, the systems are proven to be shifted passive, which permits for a power-preserving interconnection with other passive components. [GRAPHICS]

Stability of quantized time-delay nonlinear systems: A Lyapunov-Krasowskii-functional approach

Lyapunov-Krasowskii functionals are used to design quantized control laws for nonlinear continuous-time systems in the presence of constant delays in the input. The quantized control law is implemented via hysteresis to prevent chattering. Under appropriate conditions, our analysis applies to stabilizable nonlinear systems for any value of the quantization density. The resulting quantized feedback is parametrized with respect to the quantization density. Moreover, the maximal allowable delay tolerated by the system is characterized as a function of the quantization density.Comment: 31 pages, 3 figures, to appear in Mathematics of Control, Signals, and System