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Abstract-This paper investigates an event condition for event-driven controllers based on Lyapunov functions. Considering that constant values of a Lyapunov function define contour curves that form closed regions around the equilibrium point, in this paper we present a sampling mechanism that enforces job executions (sampling, control algorithm computation and actuation) each time the system trajectory reaches a given contour curve. By construction, the sequence of generated samples is stable in the discrete Lyapunov sense. However, in order to ensure that the system trajectory will tend to zero as time tends to infinity, it must be ensured that the sequence of samples is infinite. We provide conditions to ensure this property. The approach is illustrated by simulated examples.

Abstract-Flexibility and reliability of AC microgrids are enhanced by reducing the dependence on communications in multi-layer hierarchical control. In this sense, this paper presents a secondary control with no communications for islanded microgrids. It is based on a control scheme that switches between two configurations according to a time-dependent protocol. With this proposal, an excellent performance in terms of transient response and frequency restoration in steady-state is achieved. The paper also presents design considerations for the control parameters. In addition, the theoretical predictions are validated by experimental results from a laboratory microgrid.Index Terms-Distributed generation, hierarchical control, islanded microgrids, secondary control, switched control, time-dependent protocol. I. INTRODUCTIONICROGRIDS have recently emerged as a potential solution for electrical supply due to their advantages as environmental impacts reduction, reliability, and flexible operability [1], [2]. Basically, a microgrid is a cluster of distributed generators (DGs), loads, and energy storage systems which can operate in two possible modes: gridconnected or islanded [3].In islanded mode, microgrids are disconnected from the main grid intentionally or by an electrical fault and the DGs provide active and reactive power to the local loads [4]. To control frequency, voltage amplitude or power sharing, a multi-layer hierarchical scheme can be implemented, normallyManuscript received Month xx, 2xxx; revised Month xx, xxxx; accepted Month x, xxxx. This work has been supported by ELAC2014/ESE0034 from the European Union and its linked Spanish national project PCIN-2015-001. We also appreciate the support from the Ministry of Economy and Competitiveness of Spain and the European Regional Development Fund (FEDER) under projects ENE2015-64087-C2-1-R and TEC2013-46938-R.Juan M. Rey is with Escuela de Ingenierías Eléctrica, Electrónica y de Telecomunicaciones (E3T), Universidad Industrial de Santander (UIS), 680002 Bucaramanga, Colombia and with the Electronic Engineering Department, Technical University of Catalonia, Av. Victor Balaguer s/n, 08800 Vilanova i Ia Geltrú, Spain (e-mail: juanmrey@uis.edu.co).Pau Marti and Manel Velasco are with the Automatic Control Department, Technical University of Catalonia, Pau Gargallo 5, 08028 Barcelona, Spain.Jaume Miret and Miguel Castilla are with the Electronic Engineering Department, Technical University of Catalonia, Av. Victor Balaguer s/n, 08800 Vilanova i la Geltrú, Spain. divided in three control layers: primary, secondary and tertiary layer [5].Primary layer rapidly controls power sharing and stabilizes frequency and output voltage amplitude in each DG. However, steady-state errors or deviations are introduced, which are corrected by the secondary layer. Tertiary layer manages and coordinates the operation of the power flows at optimal points considering economic concerns (i.e., energy prices and electricity markets) and grid requirements (i.e., reactive power flows contr...

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