The increasing of Distributed Energy Resources (DERs) interconnection such as PV into the microgrid has increase the case of frequency instability. The combination of Demand Response (DR) and Battery Energy Storage System (BESS) can be used as the two-stage frequency regulation to keep the frequency stability in the system. In this paper, a method to select the optimal BESS threshold value in the DR and BESS two-stage frequency regulation is proposed. The IEEE standard 13-bus distribution network was modified as an islanded microgrid and used to perform the simulation. The simulation results shows that the combined DR and BESS with an optimal BESS threshold value can keep the frequency within the maximum allowable frequency nadir value and reduce the energy usage of BESS.

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## 1. Introduction

Recently, a research number of microgrid and Distributed Energy Resources (DERs) such
as photovoltaic (PV) or wind turbine has been extremely increased. An integration
between microgrid and DERs can be a solution for the modern distri- bution system
^{(1)}. The microgrid can offer many positive aspects including economic operation, stability,
reliability, and grid resiliency ^{(2)}. Moreover, DERs are viewed as environmentally friendly energy sources, which take
care of the concerns related to carbon emission problems. Despite having many advantages,
the high penetration of DERs may cause a frequency instability because of an intermittency
problem, especially in an islanded microgrid mode ^{(3)}. Therefore, a primary frequency control scheme needs to be considered.

The primary frequency control in a power system includes balancing between the generation and demand to stabilize the system frequency in a short term. Normally, a turbine-governor control has used to stabilize the system frequency immediately referred to as a droop control. Even though the governor droop control is used, frequency instability may remain to occur when the penetration of DERs is increased in the microgrid. Therefore, an alternative method needs to develop to allow a greater penetration level of DERs and to improve microgrid stability.

Battery Energy Storage System (BESS) can be used to handling the frequency instability of the islanded microgrid with a high number of DERs. The BESS with fast response plays the role of the spinning reserve of a conventional power system for balancing between the generation and demand in a short time. To compensate for the highly variable of DERs, the greater capacity, complex control, and more expensive BESS will be required. These challenges cause the need for other available options, such as Demand Response (DR) control.

The DR has been introduced to adjust the demand-side power consumption whenever necessary. The DR offers a variety of operational benefits for electricity consumers and grid operators. DR programs is also effective to obtain a balance between generation and demand in the islanded microgrid. Moreover, utility-offered DR programs have been shown to be effective for active customer participation in frequency control.

Several kinds of research according to DR or BESS as a frequency regulation had been
done by many researchers. A decentralized dynamic DR control has proposed which shows
a reliable contribution to primary frequency control ^{(4)}. Demand response and virtual inertia control have been proposed in ^{(5)} for frequency regulation service in a power system. A new PI controller based on
dynamic demand control to maintain system frequency is proposed for smart grid applications
^{(6)}. A smart DR control for regulating responsive load by using two-mode control in a
centralized DR has been studied in ^{(3)}. A similar adaptive approach was proposed in ^{(7)}, which consider a two- level of DR control in different frequency threshold. Moreover,
other research ^{(8)} have proposed primary frequency regulation through droop-based generation, demand
response, and energy storage at the same time.

This work proposes a combination of DR control and BESS as an effective control strategy on the two-stage primary frequency regulation to maintain the frequency within the maximum allowable frequency nadir value. The first stage control will be carried out by manipulating load using the DR control algorithm. In this paper, the optimal threshold value for BESS to operate is obtained based on particle swarm optimization (PSO) method. The validity of the proposed control scheme is observed through simulation on an islanded microgrid system.

Remainders of this paper are organized as follows. Section 2 explains the primary frequency control, and section 3 describes the proposed scheme. Section 4 introduces the test system scenarios and discusses the results while section 5 concludes the paper.

## 2. Primary Frequency Control

In this section, frequency control is discussed. The main cause of frequency instability in the power system is the imbalance between supply and demand power. Moreover, in the microgrid system which has a low inertia response, a slight power imbalance will lead to a high-frequency deviation. The frequency deviation ( ) can be calculated as follow,

where, the is the measured frequency and the is the nominal frequency. The primary frequency control must be active when the frequency deviation exceeds a pre-defined threshold value. The primary controls such as the turbine governor, DR, or energy storage need to restore the power balance according to the frequency deviation in a short time period.

### 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,

##### (2)

$\dfrac{df}{dt}=\dfrac{f_{ref}}{2HS_{base}}\left[-\left(k_{D}+k_{prim}\right)f+\Delta P-P_{BESS}\right]$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)

$P_{BESS}=\begin{cases} P_{rated}&(\Delta f < -f_{th})\\ k_{droop}(\Delta f)&(-f_{th BESS}\le\Delta f\le -f_{th})\\ 0&(-f_{th BESS}<\Delta f <f_{th BESS})\\ k_{droop}(\Delta f)&(f_{th BESS}\le\Delta f\le f_{th})\\ -P_{rated}&(\Delta f >f_{th}) \end{cases}$

## 3. Proposed Scheme

### 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,

##### (5)

\begin{align*} v_{j,\:i+1}=w\bullet v_{j,\:1}+c_{1}\bullet r_{1}(pbest_{j}-x_{j,\:i})\\ +c_{2}\bullet r_{2}(gbest-x_{j,\:i}) \end{align*}$v_{j}$ 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. Results and Discussion

The proposed control scheme is tested in the microgrid system adapted from the IEEE standard 13-bus distribution network as shown in Fig. 4and the system parameter described in Table 1. The system is modified as an isolated microgrid system by replacing the utility source with DG synchronous machine to be able to observe the frequency behavior. Five units of DG with total rated capacity of 5.5 MVA equipped with a governor and excitation system is connected to the system. Moreover, 1.5 MW PV system and 0.5 MW / 1 MWh BESS are connected as a variable DERs in the microgrid. Some modifications including the limitation of DG control and load model have been done in purpose.

DIgSILENT PowerFactory is used to perform the simulation of the optimization and the performance of the proposed scheme. The microgrid total load is 3.50 MW and the load characteri- stics are shown in Table 2. The loads are divided into two categories, responsive and non-responsive. Each load L1, L2, L3, L4, and L5 has a 15% responsive load to participate in DR control. Meanwhile, the fixed load will remain constant. The DR control can manipulate only these responsive loads to maintain the frequency value. The maximum frequency nadir sets as 49.5 Hz or within $\pm$1% of the nominal frequency value thus, the proposed control should be able to keep the frequency nadir greater or equal to 49.5 Hz.

Different scenarios are simulated in the system carried out for the proposed control and conventional BESS control. The first scenario is loss of DG unit 2 with power output 750 kW and the second scenario is the ramp down event of PV power output within 70% of PV rated capacity. The loss of DG unit 2 is used as system disturbance to determine the optimal BESS threshold value. Based on the PSO algorithm, the optimal BESS threshold for this condition is obtained as 0.121 Hz. The results of the simulation are described as below.

Table 1. Specification of Microgrid Test System

System Parameter |
Specification |

Total diesel capacity |
5.5 MVA |

PV system rated |
1.5 MWp |

BESS rated capacity |
0.5 MW / 1 MWh |

Nominal frequency |
50 Hz |

Nominal voltage |
20 kV |

Table 2. Load Characteristic for Demand Response

### 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.

Table 3. Comparison for the loss of DG unit 2

Control |
$|f_{th BESS}|$ (Hz) |
$f_{nadir}$ (Hz) |
Reduction load (MW) |
BESS (kWh) |

No DR |
0.050 |
49.53 |
0 |
24.290 |

DR-BESS |
0.121 |
49.50 |
0.103 |
15.371 |

Control |
0.100 |
49.47 |
0.222 |
- |

### 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.

Table 4. Comparison for the PV ramp down

Control |
$|f_{th BESS}|$ (Hz) |
$f_{nadir}$ (Hz) |
Reduction load (MW) |
BESS (kWh) |

No DR |
0.050 |
49.55 |
0 |
26.553 |

DR-BESS |
0.121 |
49.53 |
0.156 |
17.228 |

Control |
0.100 |
49.48 |
0.247 |
- |

### 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.

Table 5. BESS optimal threshold value in different PV penetration

## 5. Conclusion

In this paper, the two-stage frequency regulation for microgrid with DR control and BESS while considering the BESS optimal threshold value to operate has proposed. The PSO method is used to determine the optimal BESS threshold value. The DR control operates as the first stage control to regulate a small frequency deviation when the frequency deviation greater than 0.05 Hz by manipulating responsive loads. On the other, BESS will operate as the second stage control to prevent a large load manipulation, when the frequency deviation greater than the BESS optimal threshold value. The simulation has conducted on the islanded microgrid system. Based on the simulation results, using the proposed DR control and BESS with optimal BESS threshold value, the value of frequency nadir can be maintain within the 49.5 Hz. The performance of the proposed method has also verified in the case of different PV power output penetration. The optimal BESS threshold that obtained is decreased when the PV output penetration increased. Moreover, this proposed method could also maintain the frequency nadir within the allowable value when a disturbance occurs for different PV output penetration.

### Acknowledgements

This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (No. 2018R1A2A1A05078680).

### References

## 저자소개

He received a B.S degree from the School of Electrical Engineering and Informatics, Bandung Institute of Technology, Indonesia, in 2019.

At present, he is enrolled in the master’s program.

His research interests include distributed gener- ation, microgrid, and energy storage system

He received a B.S degree from the College of Information and Technology, Gachon University, Korea, in 2019.

At present, he is enrolled in the master program.

His research interests include distributed generation, power system analysis, microgrid and energy storage system.

He received a B.S degree from the College of Engineering, Inje University, Korea, in 2019.

At present, he is enrolled in the master program.

His research interests include power system analysis, distributed energy resource and energy storage system.

He received the B.S., M.S., and Ph.D. degrees in electrical engineering from Sungkyunkwan University, Suwon, Korea, in 1982, 1984, and 1990, respectively.

In 1990, he joined Jeju National University, Jeju, Korea, as a Full- Time Lecturer.

He was a Visiting Academic with the University of Bath, Bath, U.K., in 1996, 1998, and 1999.

He has been a Professor with the College of Information and Communication Engineering, Sungkyunkwan University, since 1992, where he is currently the Director of the Center for Power Information Technology.

His current research interests include power system protection, artificial intelligence appli- cations for protection and control, modeling/ protection of underground cable, and electro- magnetic transients program software.