## 1 Introduction
The resistive output impedance of the parallel-connected inverters in an islanded microgrid is considered in the proposed controller. However, this does not take secondary control into account. In reference [24], a decentralized voltage control algorithm that minimizes power losses in a microgrid is proposed. Although the power losses are reduced using the proposed method, it does not consider SOC control of electric vehicles or the frequency of the microgrid. In reference [25], a control method for DG units to implement active power sharing and frequency recovery in an islanded microgrid is proposed. By using self-frequency recovery control, the frequency can be restored to the nominal value in a decentralized way. However, to offset the power-sharing mismatches among DGs after frequency recovery, communication is applied momentarily. In reference [26], the distributed controllers for secondary frequency and voltage control in islanded microgrids is proposed. The proposed controller used local information and communication to perform secondary control. The authors mentioned that the communication between DGs has been a core ingredient in achieving the goal of the secondary control, which makes this paper more noticeable since the main contribution of this paper is to get rid of the communication on a secondary control level. In reference [27], the distributed cooperative control in an islanded microgrid secondary control is proposed. The authors used event-triggered strategy to reset the actual values in the feedback control schemes. The proposed method makes a profound contribution in terms of reducing communication dependency among DGs, but it still uses the communication in the secondary control level. In reference [28], the authors proposed the restoration control method of droop-controlled inverter-based microgrids. In reference [29], the authors used a distributed event-triggered secondary control method to deal with the economic dispatch and frequency restoration control for microgrids consisting of droop-controlled DGs. The authors of [30] and [31] also proposed distributed control methods to restore the voltage and frequency deviation. Some distributed control methods are proposed to coordinate the secondary and tertiary control together [32; 33; 34]. However, all of them could not be performed in a communication-free manner. In this paper, a fully decentralized control method for inverter-interfaced DGs, and an ESS without communication, are proposed. As reviewed in the previous works, the communication has been the most important but also the cost-inefficient ingredient in secondary control [26; 27; 28; 29]. To the best of our knowledge, no literature has proposed a fully communication-free way in the secondary control of frequency and SOC restoration so far. In this context, this paper makes the major contribution of proposing a fully communication-free way of frequency and SOC restoration in the secondary control of islanded microgrids. Moreover, by introducing the communication-free secondary control for islanded microgrids for the first time, this paper can encourage many other future research projects on the secondary control of islanded microgrids without communication. The proposed method assumed that all DGs and ESSs in an islanded microgrid have predetermined hourly output power set points, which are determined at the tertiary control level in accordance with the load pattern and economic benefits, so that the proposed method can be adapted more securely. Only the controllable DGs (i.e., diesel generator, fuel cell, biomass, etc.) are considered to adopt the proposed control method in this paper. The uncontrollable DGs such as renewable energy sources cannot or or partially (by using de-loaded control) able to adopt the proposed method. The proposed control method focuses on secondary control of DGs and the ESS. To ensure a rapid response to load changes, ESSs are used as droop-controlled grid-forming sources.