**1. Introduction**

Currently, with abundant natural resources in remote areas, numerous renewable energy sources (RESs) including photovoltaic (PV) and wind power are integrated into small isolated grids [1,2]. RESs have advantages in terms of cost effectiveness and environmental impact, but they can degrade the system stability through, for example, frequency fluctuations. Furthermore, since isolated grids generally have small inertia compared to large transmission networks, the intermittent outputs of RESs induce large frequency fluctuations [3]. These problems evoke the transition from conventional isolated grids, which have been operating with diesel-powered generators alone, to isolated microgrids which include battery energy storage systems (BESSs) in addition to the thermal generators [4]. In contrast to grids supported solely by slow diesel generators, the frequency can be regulated much more tightly with BESSs because they have short response times [4–6]. However, for utilizing BESSs as frequency-supporting resources in an isolated microgrid, the state of charge (SOC) of the BESSs must be managed efficiently because the capacity of batteries is limited [7].

To overcome the slow response of diesel generators and limited capacity of BESSs, complementary control schemes with diesel generators and BESSs for signals of different time scales were proposed [7–10]. With complementary control, diesel generators compensate for long-time-scale energy imbalances, while BESSs compensate for short-time-scale energy imbalance. As BESSs only

compensate for frequent active power imbalances in the complementary control scheme, batteries with a relatively small capacity are required for frequency regulation in an isolated microgrid. Additionally, the system operator can efficiently take advantage of the attributes of diesel-powered thermal generators efficiently because diesel generators are used to compensate for long time-scale fluctuations [11]. As shown in Figure 1, complementary control strategies can be classified into three categories: (1) coordinated droop control (CD) [8], (2) control based on frequency distribution techniques (FD) [9,10], and (3) coordinated SOC and frequency control (CSF) [7].

**Figure 1.** Complementary control methods with diesel generator and battery energy storage system (BESS) for system imbalance: (**a**) coordinated droop control (CD); (**b**) control based on frequency distribution techniques (FD); (**c**) coordinated state of charge (SOC) and frequency control (CSF).

In the CD method, diesel generators and BESSs regulate frequency with droop control. Additionally, for eliminating steady-state error resulting from droop characteristics, supplementary control is implemented in diesel generators [8], which implies that BESSs are only responsible for short-time-scale active power imbalances and diesel generators are responsible for imbalances of both time scales. In the FD method, filters, such as the wavelet transform [9] and discrete Fourier transform [10], are used for clearly dividing power imbalances of long and short time scales. After dividing power imbalances of different time scales, long and short time-scale imbalances are controlled by diesel generators and BESSs, respectively [9,10]. However, although imbalances of long and short time scales can be regulated complementarily by using the CD and FD methods, the SOC of BESSs is difficult to be managed because the energy stored in BESSs is not considered in these methods.

In the CSF method, which was proposed in [7], the grid frequency is rapidly regulated by a BESS, while a diesel generator controls the SOC of the BESS for capacity managemen<sup>t</sup> which can lower the required capacity of batteries. With information only about the SOC of the BESS, the system can not only regulate short and long time-scale imbalances complementarily, but also manage the SOC of the BESS. However, the authors of [7] only focused on isolated microgrids featuring only one BESS and one diesel generator. For expanding the scale and enhancing the reliability, a system with several BESSs and diesel generators should be considered. However, it is difficult to apply the CSF method for multiple BESSs and diesel generators because the parallel operation of such devices and the SOC managemen<sup>t</sup> of individual BESSs were not considered in the previous research.

In the present paper, we propose a new CSF control strategy for multiple BESSs and diesel generators in an isolated microgrid. In the proposed method, diesel generators manage an equivalent SOC, which represents the SOCs of all BESSs, with a hierarchical control scheme. BESSs control the

frequency of the system with a hierarchical control structure, and a self SOC control mechanism of each BESS is proposed. Finally, a case study with the data of a real isolated microgrid in South Korea demonstrates the e ffectiveness of the proposed control method compared to conventional complementary control. The case study verifies that the proposed control method can regulate the frequency and individual SOCs of BESSs and enable the parallel operation of diesel generators and BESSs.
