1949-3053 (c) 2019 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TSG.2019.2945250, IEEE Transactions on Smart Grid IEEE TRANSACTIONS ON SMART GRID, VOL. X, NO. X, MONTH YYYY A Zeno-Free Event-Triggered Secondary Control for AC Microgrids Babak Abdolmaleki, Qobad Shafiee, Senior Member, IEEE, Ali Reza Seifi, Mohammad Mehdi Arefi, Senior Member, IEEE, and Frede Blaabjerg, Fellow, IEEE Abstract—This paper proposes a secondary voltage, frequency, and active power sharing control for autonomous inverter-based microgrids with event-triggered communications. A proportional- integral consensus-based control scheme is introduced which benefits from need-based (event-triggered) data exchange among distributed generators. The employed event-triggering condition i) ensures the system stability, ii) ensures that the system is Zeno- free and there exists a controllable minimal inter-event time, iii) removes the redundant communications during both transient and steady-state stages, iv) accounts for directed communication network architectures, and v) is fully distributed from both design and implementation standpoints. Effectiveness of the proposed con- troller for various case studies is verified via MATLAB/Simulink- based simulations. Comparison between different cases and con- ventional strategies are also included. Index Terms—Consensus algorithm, event-triggered control, frequency control, microgrid, power sharing, secondary control, voltage control, Zeno behavior. NOMENCLATURE δ i i th distributed generator’s (DG’s) phase angle. P i ,Q i i th DG’s measured active & reactive powers. ˆ P i , ˆ Q i i th DG’s actual active & reactive powers. P ∗ i ,Q ∗ i i th DG’s rated active & reactive powers. f i ,V i i th DG’s output frequency & voltage. f ∗ ,V ∗ Rated frequency & voltage. f ref ,V ref Reference frequency & voltage. f c Power measurement filter’s cutoff frequency. m i ,n i Droop coefficients. Ω i , Γ i Frequency & voltage correction terms. G ij ,B ij Conductance & susceptance among DGs i & j . G ii ,B ii i th DG’s shunt conductance & susceptance. Δf, ΔV Maximum frequency & voltage deviations. K f i ,K V i Nonnegative proportional gains. I f i ,I V i Nonnegative integral gains. b f i ,b V i ,b Ω i Logical indicators. a ij Communication weighting from j th DG to i th DG. Manuscript received September 10, 2018; revised March 25, 2019, July 28, 2019; accepted September 22, 2019. Date of publication XXXX XX, XXXX; date of current version XXXX XX, XXXX. Paper no. TSG-01323-2018. B. Abdolmaleki and Q. Shafiee are with the Smart/Micro Grids Research Center (SMGRC), University of Kurdistan, Sanandaj, Iran (e-mail: abdol- maleki.p.e@gmail.com, q.shafiee@uok.ac.ir). A. R. Seifi and M. M. Arefi are with the School of Electrical and Com- puter Engineering, Shiraz University, Shiraz, Iran (e-mail: seifi@shirazu.ac.ir, arefi@shirazu.ac.ir). F. Blaabjerg is with the Department of Energy Technology, Aalborg Univer- sity, Denmark (e-mail: fbl@et.aau.dk). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier XX.XXXX/TSG.20XX.XXXXXXX d i ,d o i i th DG’s in-degree & out-degree in the CN. A, D, L CN’s matrices. Refer to Section II-A. t i ki k th i triggering instant associated with i th DG. t i , t i 0 i th DG’s local clock and activation instant. ˜ Ω i , ˜ V i The latest sampled signals of Ω i , V i at t i ki . τ Minimal inter-event (inter-communication) time. σ Positive parameter governing the state-dependent part of the triggering conditions in (8). γ Ω ,γ V Positive parameters governing the constant parts of the triggering conditions in (8). 1 n , 0 n Vectors of ones and zeros in R n . I n Identity matrix in R n×n . I. I NTRODUCTION S ECONDARY CONTROL of islanded microgrids (MGs) compensates for voltage and frequency deviations caused by droop control as well as provides proper power sharing between distributed generators (DGs) [1]. This control level is realized by using a communication network (CN). Therefore, distributed control architectures using sparse CNs, are preferred to the centralzied ones with complex CNs [2]. Most of the previous works in the context of secondary control are conducted based on the continuous CNs (e.g. see [3]–[14]), while the realistic data exchange infrastructures are sample-based and have limited bandwidths [15], [16]. Thus, from a system scaling standpoint, efficient usage of commu- nication medium is mandatory. In networked control systems, a solution to avoid probable network congestions and reduce the communication burden is to use event-triggered (ET) control strategies eliminating redundant communications [17], [18]. Generally, ET control is a strategy under which the desired state is sampled and broadcasted, and the control rule is updated (i.e., an event is triggered), only if some condition(s) is(are) satisfied. Any ET condition must satisfy two system requirements: Sta- bility and Zeno-freeness. Zeno behavior is a phenomenon under which excessive redundant events are triggered over a finite time interval. Because of limited communication and computational capabilities, no control system can be implemented on a digital platform, if the behavior exists [17], [18]. Triggered control of MGs has been introduced in the literature [19]–[28]. Reference [19], proposes a self-triggered coordinated power control scheme for ac MGs where the next event time is determined at any current event time. Thus, the controller cannot respond quickly to the disturbances. A distributed ET load sharing control is proposed in [20]. In this work, an average- consensus algorithm is used to control the inter-DG active power Downloaded from https://iranpaper.ir https://www.tarjomano.com/order