**5. Case Study**

The isolated microgrid shown in Figure 2 was modeled and simulated by Simulink/MATLAB for the case study. All converters for RESs and BESSs in the system consisted of two-level half-bridge (HB) converters with switch models. Sine-pulse width modulation (SPWM) with switching frequency of 2 kHz was adopted to generate gate signals of switch model converters. The PV generator model consisted of photovoltaic source and converter [22]. The PV converter was controlled by the MPPT algorithm and inner dc voltage and current control loop. For MPPT, the perturbation and observation (P&O) algorithm in [23] was utilized and reference value of dc voltage was determined. To control the dc voltage of photovoltaic source as the reference value, the nested dc voltage and current control loops in [17] were used. On the other hand, the wind generator consisted of a permanent magnetic synchronous generator (PMSG), wind turbine, machine side converter, and grid side converter [22]. We utilized a permanent magne<sup>t</sup> synchronous generator model provided by Simulink/MATLAB. Wind turbine and controllers of the machine and grid side converters were modelled by the same procedure of [17]. The detailed parameters of the diesel generators and BESSs are listed in Tables 2 and 3. For voltage control, conventional reactive power (*Q*)—magnitude of the ac voltage (*Vac*) droop method was adopted in diesel generators and BESSs [24]. *Q–Vac* droop constants for three diesel generators were 0.05/20 (*Vp.u.*/kVar) respectively and *Q–Vac* droop constant for BESS 1 was 0.05/250 (*Vp.u.*/kVar) and for BESS 2 was 0.05/125 (*Vp.u.*/kVar). As the reactive power and magnitude of ac voltage were not the major concern of this paper, we just adopted the conventional method in [24].

The capacity of BESSs was scaled down from its real values, 500 and 300 kWh, by a factor of 1/100 in the simulation to illustrate the variation of SOCs clearly. The supplementary controllers of diesel generators have a sample time of 0.5 s to ensure slower response compared to the droop controller. Other components including transformers, lines, and loads were modeled with the parameters shown in Figure 2. Considering the fact that the efficiency of batteries is dependent on SOC level [25,26], we assumed that BESS 1 and 2 have the highest efficiency at 60% and 40% of SOCs, respectively.


**Table 2.** Control parameters in the conventional and proposed method.

**Table 3.** Parameters of diesel generators and BESSs for the internal controllers.


### *5.1. Case 1: Step Load Change with the Conventional and Proposed Control Method*

In Case 1, to verify the effectiveness of the proposed strategy, the proposed method was compared to the CD method for the step load change. As CD method can be adopted in the system with multiple diesel generators and BESSs, has been widely adopted in many researches [27,28], and was the original control method in Geocha Island, we selected CD method for comparison. Before 10 s, all loads except the load at bus 7 were connected. After 10 s, the load at bus 7 was connected to the system. The active power consumption for loads was constant, as shown in Figure 2. The active power generated by the PV and wind generators was constant at 80 and 75 kW respectively. SOC reference values for BESS 1 and 2 were 60% and 40%, respectively.

Figure 10 shows the responses of frequency and *SOCeq* in the conventional and proposed methods. As shown in Figure 10a, the frequency eventually maintains its rated value irrespective of the control method. However, while the conventional control method takes approximately 20 s to restore frequency, the proposed control takes less than 2 s, as shown in Figure 10a. BESSs are exploited for frequency restoration in the proposed scheme, while diesel generators are used for the conventional method. For this reason, the performance of frequency regulation is much better in the proposed method than the conventional method. Furthermore, as shown in Figure 10b, *SOCeq* can be constant in both methods because long-time-scale energy imbalances are compensated for by diesel generators. However, as SOC managemen<sup>t</sup> is not considered in the conventional method, *SOCeq* deviates from the reference value. On the other hand, *SOCeq* is regulated at the reference value by using the proposed strategy. This implies that BESSs with a relatively small capacity are required with the proposed method.

**Figure 10.** Frequency and *SOCeq* in the conventional and proposed methods: (**a**) frequency; (**b**) *SOCeq*.

Figure 11 shows the active power of diesel generators and BESSs in the conventional and proposed methods. In both methods, diesel generators share the load equally at the desired power-sharing ratio, as shown in Figure 11a, and BESSs make zero output equally as desired, as shown in Figure 11b. In the proposed method, parallel operation and power sharing of diesel generators and BESSs are possible, as desired.

**Figure 11.** Active power in the conventional and proposed methods: (**a**) diesel generators; (**b**) BESSs.

### *5.2. Case 2: Step Load Change with and without Self SOC Controller (SSC)*

In Case 2, the loads, PV generation, and wind generation are the same as in Case 1. To verify the necessity of SSC, the responses of BESSs with and without SSC were compared. SOC reference values for BESS 1 and 2 were 60% and 40%, respectively. Figure 12 shows the frequency and *SOCeq* with and without SSC. In both cases, the responses of the frequency and *SOCeq* are almost identical, which implies that, except for the individual SOCs of BESSs, the SSC hardly affects the performance of the system.

**Figure 12.** Frequency and *SOCeq* of BESSs in Case 2: (**a**) frequency; (**b**) *SOCeq*.

Figure 13 shows the individual SOCs of BESSs in the proposed control with and without SSC. Although *SOCeq* is regulated at the reference value irrespective of whether SSC is applied, the SOC of each BESS in the proposed control with and without SSC has different responses. In the case without SSC, the SOC of each BESS deviates from its corresponding reference value. This phenomenon is similar to the occurrence of a circulating current, in which summation is equal to the desired value but individual components have different sign [29]. In the proposed control with SSC, the SOC of each BESS can be restored to its reference value. Thus, SSC is necessary to maintain the individual SOCs of BESSs. Furthermore, as SOCs of BESS 1 and 2 are maintained as 60% and 40% respectively, we can utilize BESSs at their highest efficient points with SSC.

**Figure 13.** SOC of each BESS in Case 2: (**a**) BESS 1; (**b**) BESS 2.

*5.3. Case 3: Fluctuation of Renewable Energy Sources (RESs) with the Conventional and Proposed Control Method*

In Case 3, to verify the robustness of the system with the proposed control, fluctuations of the outputs of RESs were simulated when applying the proposed and conventional CD methods. The loads were constant, as shown in Figure 2. SOC reference values for BESS 1 and 2 were 60% and 40%, respectively. PV generation and wind generation were varied, as shown in Figure 14.

**Figure 14.** Variation of the active power of photovoltaic (PV) and wind generation in Case 3: (**a**) PV; (**b**) wind.

Figure 15 shows the frequency and *SOCeq*. As shown in Figure 15a, the frequency is fluctuated by the intermittent outputs of RESs with the conventional method. However, with the proposed method, the frequency is near the nominal value and can be controlled quickly. In addition, as shown in Figure 15b, while *SOCeq* deviates from the reference value with the conventional method, the proposed method maintains *SOCeq* near the reference value with a small fluctuation, which was due to the slow response of diesel generators. These results imply that the proposed method can make the system robust and improve its reliability, even with a high penetration of RESs.

**Figure 15.** Frequency and *SOCeq* in Case 3: (**a**) frequency; (**b**) *SOCeq*.

Figure 16 shows the individual SOCs of BESSs. As shown in Figure 16, while the SOC of each BESS deviates from the reference value in the conventional method, the SOC of each BESS is near the reference value in the proposed method, similar to *SOCeq* in Figure 15b. Thus, the proposed method can manage not only *SOCeq* but also the SOC of each BESS. Even if a large power fluctuation occurred in the system, the individual SOCs of BESSs can be maintained and bounded tightly. This implies that batteries with a relatively small capacity are required, even with a high penetration of RESs, when the proposed method is adopted.

**Figure 16.** SOC of each BESS in Case 3: (**a**) BESS 1; (**b**) BESS 2.

### *5.4. Case 4: Consideration of Communication Delays*

In Case 4, we verify the performance of the proposed method when communication delays are considered. When diesel generators control *SOCeq* and SSCs of BESSs are operated, the information of *SOCeq* is required. Because capacities of BESSs are constant, only simple communication lines for transmitting information of SOCs are required. In the case of Geocha Island microgrid, diesel generators and BESSs are located in the same station as shown in Figure 3. For this reason, communication delay can be ignored in Geocha Island microgrid. However, to adopt the proposed control method in other islanded microgrids where BESSs and diesel generators are far away from each other, we have to verify the performance of the proposed method when communication delays exist. The communication delays range from several milliseconds to about 100 ms in the wide area measurement/monitoring system for the large scale power system [30], hence, communication delays in islanded microgrids may be smaller than 100 ms. To verify the possibility for application of the proposed method, we tested the system when communication delays were 0, 50, and 100 ms. All other conditions are the same as Case 1. Figure 17 shows frequency and *SOCeq* of the proposed method with 0, 50, and 100 ms delay when load change occurred at 10 s.

**Figure 17.** Frequency and *SOCeq* in Case 4: (**a**) frequency; (**b**) *SOCeq*.

As shown in Figure 17, if communication delays are prolonged, saturation time of frequency and *SOCeq* takes a little longer. However, regardless of communication delays, frequency and *SOCeq* are eventually saturated. To ensure that individual SOCs of BESSs can be controlled even with communication delays, Figure 18 shows individual SOCs of BESSs.

As shown in Figure 18, if communication delays are prolonged, SOCs of BESSs are a little more slowly saturated. But, SOCs of BESSs can be regulated as the reference values regardless of communication delays. Therefore, the proposed method can be implemented in other islanded microgrids where communication delays should be considered.

**Figure 18.** SOC of each BESS in Case 4: (**a**) BESS 1; (**b**) BESS 2.

*5.5. Case 5: Regulating Active Power of BESSs by the Linear Time-Varying Control of SOCs*

In Case 5, to verify that the active power outputs of BESSs can be controlled as the desired values, we provided continuous responses of BESSs and diesel generators for linear time-varying control of SOCs of which reference values were determined by the active power references. All loads and wind and PV generation are the same as Case 1. Before 30 s, active power references, *P\*BESS*(1) and *P\*BESS*(2) were 20 and −10 kW (negative sign means that BESS was charged), respectively. After 30 s, *P\*BESS*(1) and *P\*BESS*(2) were 30 and 10 kW. According to determining active power references, SOC reference values were decided as shown in (11). Figure 19 shows SOCs and SOC reference values of BESSs.

**Figure 19.** SOCs and SOC reference values of BESSs in Case 5: (**a**) BESS1; (**b**) BESS2.

As shown in Figure 19, by the active power reference values, the linear time-varying SOC reference values are determined. The slopes of SOC reference values are varied when the active power references are changed. Regardless of the slopes of SOC reference values, the SOCs of BESSs can be controlled as the reference values. To verify that frequency and active power outputs of BESS are controlled, Figure 20 shows the frequency and active power outputs of BESSs.

**Figure 20.** Frequency and active power outputs of BESSs in Case 5: (**a**) frequency; (**b**) active power outputs of BESSs.

Frequency can be regulated as the nominal value, as shown in Figure 20a. Although the active power references of BESSs are changed, frequency maintains the nominal value with just small fluctuation. As described in Figure 20b, active power outputs of BESSs are near the reference values. Case 5 implies that by adopting the proposed control method, frequency and active power outputs of BESSs can be controlled simultaneously as the desired values.
