424 IEEE/CAA JOURNAL OF AUTOMATICA SINICA, VOL. 6, NO. 2, MARCH 2019 Adaptive Decentralized Output-Constrained Control of Single-Bus DC Microgrids Jiangkai Peng, Student Member, IEEE, Bo Fan, Student Member, IEEE, Jiajun Duan, Member, IEEE, Qinmin Yang, Member, IEEE, and Wenxin Liu, Senior Member, IEEE Abstract—A single-bus DC microgrid can represent a wide range of applications. Control objectives of such systems include high-performance bus voltage regulation and proper load sharing among multiple distributed generators (DGs) under various operating conditions. This paper presents a novel decentralized control algorithm that can guarantee both the transient voltage control performance and realize the predefined load sharing percentages. First, the output-constrained control problem is transformed into an equivalent unconstrained one. Second, a two-step backstepping control algorithm is designed based on the transformed model for bus-voltage regulation. Since the overall control effort can be split proportionally and calculated with locally-measurable signals, decentralized load sharing can be realized. The control design requires neither accurate parameters of the output filters nor load measurement. The stability of the transformed systems under the proposed control algorithm can indirectly guarantee the transient bus voltage performance of the original system. Additionally, the high-performance control design is robust, flexible, and reliable. Switch-level simulations under both normal and fault operating conditions demonstrate the effectiveness of the proposed algorithm. Index Terms—DC microgrids, decentralized control, paralleled converters, output constraint. I. I NTRODUCTION I N recent years, microgrids are gaining popularity due to the penetration of renewable energy sources, the distributed allocation of generation, and the increasing participation of consumers [1]. A microgrid usually consists of multiple dis- tributed generators (DGs) such as fuel cells, photovoltaics; distributed energy storages such as batteries, ultra-capacitors; Manuscript received October 10, 2018; revised November 29, 2018; ac- cepted December 5, 2018. This work was supported in part by the U.S. Office of Naval Research (N00014-16-1-3121, N00014-18-1-2185) and in part by the National Natural Science Foundation of China (61673347, U1609214, 61751205). Recommended by Associate Editor Ge Guo. (Corresponding author: Wenxin Liu.) Citation: J. K. Peng, B. Fan, J. J. Duan, Q. M. Yang, and W. X. Liu, “Adaptive decentralized output-constrained control of single-bus DC microgrids,” IEEE/CAA J. Autom. Sinica, vol. 6, no. 2, pp. 424-432, Mar. 2019. Jiangkai Peng and Wenxin Liu are with the Smart Microgrid and Renewable Technology (SMRT) Research Laboratory, Department of Electrical and Computer Engineering, Lehigh University, Bethlehem, PA 18015 USA (e- mail: jip216@lehigh.edu; wliu@lehigh.edu). Jiajun Duan is with the GEIRI North America, San Jose, CA 95134 USA (e-mail: Jiajun.duan@geirina.net). Bo Fan and Qinmin Yang are with the State Key Laboratory of In- dustrial Control Technology, College of Control Science and Engineering, Zhejiang University, Hangzhou 310027, China (e-mail: kanade@zju.edu.cn; qmyang@zju.edu.cn). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/JAS.2019.1911387 and loads [2]-[4]. Since the majority of DGs, energy storage devices, and modern electronic loads operate in direct current (DC) [5], the formation of DC microgrids is recognized as a simple and natural solution by avoiding additional AC/DC conversion stages. Moreover, a DC microgrid has several advantages over its AC counterpart, e.g., the circumvention of problems with harmonics, unbalances, synchronization, and reactive power flows [6]. One typical DC microgrid topology is derived from connect- ing multiple converter-interfaced DGs in parallel to a common DC bus, which supplies electric power to the loads [7]. The parallel operation of DGs offers several advantages including expandability, reliability, efficiency, and ease of maintenance [8]. This single-bus topology represents a wide range of applications such as electrical power systems of avionics, automotive, telecom, marine, and rural areas [9]-[11]. It is a DC microgrid in its simplest form that can be regarded as the building blocks of multiple-bus systems [6]. If such a DC microgrid can be well regulated, the control of large- scale microgrids can be achieved by integrating appropriate secondary and tertiary controllers. To achieve a safe and efficient operation of DC microgrids with paralleled converters, two control objectives should be realized: voltage regulation and load sharing [1]. Voltage regulation ensures the common DC bus voltage tracking a predefined trajectory under various loading conditions. Load sharing properly shares the load according to the capacities and operating costs of DGs [12]. Many control methods [13]-[23] have been proposed for such DC microgrids. Existing solutions can be mainly classified into two categories according to the use of communication links [24] as introduced below. The first type of control solutions requires various schemes of communications to coordinate operations of subsystems. Accordingly, the solutions can be classified into centralized control [14], master-slave control (MSC) [15], [16], average load sharing (ALS) [25] and circular chain control (3C) [17]. These control schemes usually can achieve both control objectives satisfactorily. However, the requirement for commu- nications may lead to other problems, such as increased cost, decreased reliability, and lack of scalability and flexibility [26]. In comparison, the second type of control solutions is communication-free and mainly based on droop control [18]-[20]. Such solutions linearly adjust the bus voltage references based on predefined droop equations. However, traditional droop control method has some drawbacks. The voltage regulation and load sharing cannot be realized simulta- neously. To overcome its limitations, some improvements have