## 1 Introduction  
The growth of distributed generation (DG) systems has provided many solutions to local energy demand and supply problems. The concept of the microgrid was introduced in the early 2000s [1; 2]. One important characteristic of the microgrid is that it can be isolated from or connected to the main power grid. During grid-connected mode operation, the microgrid voltage is maintained by the main grid, and in this mode, the main grid manages load changes in the microgrid with little impact on the system frequency, since the main grid has large inertia relative to the microgrid. In contrast, during islanded mode operation, the microgrid has small or zero mass moment of inertia (e.g., a microgrid with only inverter-interfaced units) [3; 4; 5; 6; 7]. Due to their weak inertia, islanded microgrids are vulnerable to load changes. Therefore, controllable distributed generators in an islanded microgrid must respond quickly to frequency deviation. Energy storage systems (ESSs) have been widely used as primary control units for mitigating the effects of load changes, due to their fast-acting capability [8; 9; 10; 11]. Primary control involves grid support and load sharing, which are usually achieved by droop control, and hence can be implemented locally in a decentralized way. The conventional _P-f_ droop control, virtual impedance loop-based control, adaptive droop control, and robust droop control are included in the droop control category as a primary control [12]. At the secondary control level, the state of charge (SOC) of ESSs and the frequency must be managed to operate an islanded microgrid securely. From the perspective of secondary control architecture, two approaches can be distinguished: centralized and decentralized [13]. Fully centralized control relies on a dedicated central controller with data-gathering capacity and extensive communication between the central controller and controlled units [13]. Hence, a fully centralized control method largely depends on a communication infrastructure that transfers all critical data for microgrid operation, and may limit system reliability in the case of communication failure. In particular, communication failures are more serious in islanded microgrids, since they are isolated from the main grid and must supply loads with limited resources. In contrast, in a fully decentralized control method, each unit only receives local data to operate the system and does not require full awareness of system-wide variables [14; 15; 16]. Most previous studies implemented a decentralized secondary control system using the multi-agent system (MAS) framework [17; 18; 19; 20; 21; 22]. In reference [17], a secondary control method based on the MAS concept for microgrids is proposed as an alternative for the coordinated operation of microgrids. In reference [18], power flow calculations are performed to validate that the dispatched values from the market comply with the operational constraints. In [19], additional agents assigned to different tasks are shared by the DG units in proportion to their available unused capacity. A special case of MAS, i.e., a gossip-based technique, is proposed in [20]; here, different units exchange information regarding their operation, such as mismatches between programmed and actual power outputs, and marginal costs. In [21], additional agents that enable multi-stage operation scheduling of microgrids are included in a proposed architecture based on a MAS. A similar architecture, which considers demand-side bids and a sequential negotiation process, is proposed in [22]. Although MAS-based control strategies are largely based on agents' autonomy and performed locally, they are still based on a communication procedure. Technically, therefore, they are not fully decentralized and are still exposed to the risks of communication failure. In reference [23], a wireless load-sharing controller for islanding parallel inverters in an AC-distributed system is proposed.