Finite-time Frequency Synchronization in Microgrids Ali Bidram and Ali Davoudi Electrical Engineering Department University of Texas at Arlington Arlington, TX ali.bidram@mavs.uta.edu, davoudi@uta.edu Frank L. Lewis University of Texas at Arlington Research Institute University of Texas at Arlington Fort Worth, TX lewis@uta.edu Abstract— This paper proposes a finite time frequency controller that synchronizes the microgrid frequency to the nominal frequency and shares the active power among distributed generators (DG) based on their active power ratings. The finite-time control accelerates the synchronization speed and provides the synchronization for microgrid frequency and DG active powers in a finite period of time. In addition, the proposed control is distributed; i.e., each DG only requires its own information and the information of its neighbors on the communication network graph. The efficacy of the proposed finite-time frequency control subsequent to islanding process and load changes is verified for an islanded microgrid test system. I. INTRODUCTION Microgrids are equipped with a control hierarchy to provide the frequency and voltage stability and restoration, and active and reactive power flow control. A microgrid can enter the islanded mode due to the pre-planned contingencies or unplanned disturbances. Primary control, as the lowest control hierarchy, maintains the frequency stability of the microgrid subsequent to the islanding process. However, the primary control alone may lead to slight deviation of frequency from its nominal value. To restore the microgrid frequency, the secondary control is commonly adopted [1]-[9]. The secondary control can be implemented either through a centralized or distributed structure. The centralized control structure requires a central controller with star communication network. The requirements for a central controller and star communication network reduce the system reliability and pose the control system to the single point of failure [10]-[13]. Alternatively, the distributed control framework has been exploited in recent works to improve the reliability of secondary controller and feature the peer-to-peer concept (Peer-to-peer concept means that the reliable operation of the microgrid is not affected by the malfunction of a single central or master controller.) [14]-[16]. Microgrid, as a collocation of several distributed generators (DG), is considered as a multi-agent system with each DG as an agent. The distributed control protocol on each DG would require only its own information and the information of its neighbors on the communication network [17]-[19]. Safety-critical loads in a microgrid require operation at the nominal frequency, e.g., 50 or 60 Hz. Therefore, it is of paramount value to accelerate the synchronization process and improve the convergence of the frequency control. The conventional distributed frequency control protocols (e.g., [17], [19]) lead to synchronization over an infinite time period with an exponential convergence rate. The convergence speed is dictated by the properties of the communication graph facilitating information exchange among agents. For a general multi-agent system, corrective schemes have been proposed in the literature to speed up the convergence speed of the conventional consensus protocols. For example, [20] has improved the synchronization speed by adjusting the weights of the communication links among the agents. Most of the existing work modifies the communication network and increases the algebraic connectivity of the graph to increase the convergence speed [20]-[21]. Despite accelerating the synchronization process, such corrective schemes fail to synchronize the multi-agent system over a finite time horizon. This requirement has been achieved here through the finite-time control protocols [22]- [30]. The finite-time control protocols are inspired by the natural synchronization phenomena with only two states [25]. For example, in the synchronization of hundreds of fireflies, two states exist for each firefly which corresponds to the on and off state of its photic organ [25]. Inspired by these phenomena, the finite-time control protocols have been recently presented in the literature that exploit binary signals based on the relative information measurements among the neighboring agents. These control protocols are robust against the perturbations and measurement errors, and are faster than the conventional distributed control protocols (e.g., [17]-[19]) [20]-[22]. In this paper, the convergence speed of the conventional distributed frequency control in [17] is improved by exploiting the finite-time control scheme. Finite-time This paper is supported by NSF grants ECCS-1137354, ECCS-1128050, NSFCs 61374087, China NNSF grant 61120106011, and China Education Ministry Project 111 (No.B08015). 2648 U.S. Government work not protected by U.S. copyright