2.1 Demand Response Control

The DR can be defined as the change in demand by contracted customers in response to price signals, incentives, or direction from grid operators. The DR which responses to the frequency deviation is divided into three categories which are centralized, decentralized, and hybrid control ⁽⁹⁾. The DR centralized control scheme is mostly applied in the microgrid system. In the centralized control scheme, the control center calculates the system frequency deviation to determine the amount of load regulation. The amount of load regulation will be sent to a large number of responsive loads.

2.2 Battery Energy Storage System

Due to the high variability of DERs in the islanded microgrid, fast response rates of a power supply backup is needed. In this case, the BESS is possible to inject active power in a short time to maintain system stability ⁽¹⁰⁾. The participation of BESS can be presented in the classic swing equation as follow,

where, $H$ is the combination of inertia constant of synchronous generators and $S_{base}$ is the generation’s rated power. $k_{D}$ is the inverse of the load damping coefficient and $k_{prim}$ is the inverse of the equivalent generator droop coefficient. $\Delta P$ is the total active power imbalance between generation and load. $P_{BESS}$ represents the total active power injection by BESS.

The common control that used for BESS is droop based control. According to the droop characteristic, BESS control will follow a power-frequency (P-f) characteristic as shown in Fig. 1. The parameter $k_{droop}$ represents the inverse of the BESS droop coefficient or the slope in the P-f characteristic. During the over-frequency problem, the BESS is absorbing the excess power in the microgrid. On the contrary, the BESS is injecting power into the microgrid when the under-frequency occurs. The amount of charge/discharge power can be calculated corresponding to the $k_{droop}$ parameter as follow, in which $f_{th}BESS$ is the threshold value for BESS to operate.

3.1 Proposed Control

In the proposed scheme, the combination of DR and BESS is proposed as the two-stage frequency regulation control considering the maximum allowable value of frequency nadir. The first stage frequency regulation will be carried by using the DR control and the second stage will be carried by BESS. The frequency deviation value will be used to determine the stage operation for the frequency controller to keep the frequency within limits. The frequency deviation threshold has been categorized into the two-level for DR and BESS control with different values.

DR control is put in the first stage to regulate the small deviation of frequency to a determined limit by manipulating the responsive load without causing the BESS to work.. The load manipulation by DR control is performed according to an Adaptive Hill-Climbing (AHC) algorithm ⁽³⁾. The frequency measured will be used as an input variable to the controller and the load manipulation will be directly proportional to the frequency deviation to minimize the frequency nadir value.

The DR frequency threshold value ($f_{th DR}$) in this control is set as 0.05 Hz. The percentage of the responsive load will turn On when the microgrid frequency is higher than the acceptable value (∆f > 0.05 Hz). On the other hand, the percentage of the responsive load will turn Off when the frequency is lower than the acceptable value (∆f < -0.05 Hz). The calculation of the responsive load percentage (%load) by AHC algorithm in the time step can be computed as follow,

where, $%load(k-1)$ is the percentage of the manipulation load at time step $k-1$, and $\Delta f\times M$ is the perturbation para- meter. The constant factor $M$ is the weight factor used to scale down the frequency deviation. The value of $M$ sets as 0.03 in this control. A high value of $M$ factor results in quick restoration of frequency. However, at the same time, it may cause discomfort on the consumer side due to a large amount of load manipulation.

To prevent a large amount of load manipulation and large frequency deviation, the BESS control is placed as a second stage control. When the frequency deviation exceeds the BESS threshold (|∆f| >$f_{th BESS}$), the DR control will be stopped and the BESS based on fixed droop control will operate to minimize the frequency deviation. The block diagram of the BESS frequency controller is shown in Fig. 2.

3.2 Optimal BESS Threshold Value Based on Particle Swarm Optimization

To ensure that the BESS threshold value is properly selected, an optimization method is needed. In this paper, particle swarm optimization (PSO) is used to determine the optimal BESS threshold value ($f_{th BESS}$). PSO is implemented by having a group of particles around in the search space, where these particles are population of candidate solution. The particles will move by updating the velocity and position of each particle toward the best solution based on specified objective function ⁽¹¹⁾. The velocity and position of each particles can be update by using equations below,

$v_{j}$ and $x_{j}$ are the velocity and the position of the j-th particle, respectively. $c_{1}$ and $c_{2}$ are individual global learning rate, and $w$ is weight constant. $r_{1}$ and $r_{2}$ are random numbers, $p_{bestj}$ is the position of j-th particle, and $g_{best}$ is the optimal BESS threshold solution.

The optimal BESS threshold value is determined based on the maximum allowable frequency nadir in the system. This will make the frequency nadir to be kept at a similar level when a disturbance occurs. This objective is formulated by minimizing fitness function describe as below,

where, $f_{nadir,\:\max}$ is the maximum allowable frequency nadir in the system and $f_{nadir}$ is the frequency nadir when the disturbance occurs in the system. The proposed control scheme with the PSO algorithm is shown in Fig. 3. In the PSO algorithm, the maximum number of iteration used is 15 with 10 particles. The weight constant $w$ sets as 0.729 and the learning rate $c_{1}$ and $c_{2}$ are both set as 2.

4.1 Scenario 1: Loss of DG Unit 2

The comparison performance for No-DR and proposed DR-BESS for this scenario are shown in Table 3 and Fig. 5. The results show that the No-DR (BESS only) control and the proposed DR-BESS control with optimal BESS threshold value could maintain the frequency nadir within 49.53 Hz and 49.5 Hz when the 750 kW DG unit 2 is loss, respectively. Moreover, the proposed DR-BESS control could provide a better steady state value of frequency after disturbance. The amount of load reduction is 0.103 MW with 45.7% of the responsive load is manipulated. The load reduction of two stage DR control provide in ⁽⁷⁾ with a fixed threshold value (0.1 Hz) is 0.222 MW (98.6%) with frequency nadir 49.45 Hz which is lower than 49.5 Hz. It shows that by using the proposed method with the optimal threshold value, lower load manipulation is obtained while it still able to maintain the frequency nadir.

Table 3 also shows the energy usage by the BESS. Compared to the No-DR control, the proposed DR-BESS uses about 36.7% less energy to maintain the frequency within the limit as required. This shows that using the proposed method, a greater BESS threshold value could be selected and could reduce the energy usage of the BESS while maintain the frequency nadir value. The reduction of BESS energy usage could increase the BESS lifetime and reduce the cost for frequency regulation control. Also, these results can help in determining the proper BESS capacity in power system planning.

4.2 Scenario 2: PV Power Ramp Down

The comparison performance for No-DR and proposed DR-BESS for this scenario are shown in Table 4 and Fig. 6. The results show that the No-DR (BESS only) control and the proposed DR-BESS control could maintain the frequency nadir within 49.5 Hz when the PV power output loss 70% of its rated capacity in 1 second. The amount of load reduced is 0.156 MW with 69.3% of the responsive load is manipulated. Compared to the control in ⁽⁷⁾, a better response of load reduction and frequency nadir are obtained while using the proposed control.

Table 4 also shows the energy usage by the BESS in both control. Compared to the No-DR control, the proposed DR-BESS uses about 35.1% less energy to maintain the frequency within the limit as required. The reduction of BESS energy usage could increase the BESS lifetime and reduce the cost for frequency regulation control. This shows that using the optimal proposed method, a new BESS threshold value could be selected and could reduce the energy usage of the BESS while maintain the frequency nadir value.

4.3 Proposed Method in Different PV Penetration

The proposed method is also applied in different PV pene- tration to show the effectiveness of this proposed method. The results is summarized in the Table 5. Table 5 shows that by using the PSO, a different optimal threshold value of BESS can be obtained subjected to the level of PV penetration. Lower optimal threshold value is obtained in the higher PV penetration. The same disturbance of loss of DG unit 2 and the PV ramp down is applied to verified the effectiveness of the proposed method. The results show that the proposed method is effective to maintain the frequency nadir within 49.5 Hz for different penetration level of PV in the microgrid. The frequency response for each cases subject to the different PV penetration level is shown in Fig. 7and Fig. 8.