# Fuzzy Logic Control of a Battery Energy Storage System for Stability Improvement in an Islanded Microgrid

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## Abstract

**:**

## 1. Introduction

## 2. The Perspective of Microgrid

#### Operation Modes

## 3. The Control Method of BESS

#### 3.1. Establishment of Fuzzy Logic Control

#### 3.2. Establishment of Robust Control

## 4. Simulation Results

## 5. Conclusions

## Author Contributions

## Acknowledgments

## Conflicts of Interest

## Appendix A

**Parameters of the studied system:**The machine data, line data, transformer data, PV and controller data, and BESS and controller data are given in Table A1, Table A2, Table A3, Table A4, Table A5 and Table A6, respectively. The external grid data, exciter data, and governor data are given below. All components are built-in models in DIgSILENT PowerFactory.

**External grid data:**Short Circuit Power ${S}_{k}^{\u2033}=130\phantom{\rule{3.33333pt}{0ex}}MVA$, $R/X$ ratio = 0.0392.

**Exciter data of hydro generator and diesel generator:**$avr$_$ESAC4A\phantom{\rule{3.33333pt}{0ex}}type,\phantom{\rule{3.33333pt}{0ex}}{T}_{r}=0.01,\phantom{\rule{3.33333pt}{0ex}}{T}_{b}=0.05,\phantom{\rule{3.33333pt}{0ex}}{T}_{c}=0.1,\phantom{\rule{3.33333pt}{0ex}}{T}_{a}=\phantom{\rule{3.33333pt}{0ex}}0.01,\phantom{\rule{3.33333pt}{0ex}}{K}_{a}=\phantom{\rule{3.33333pt}{0ex}}50,\phantom{\rule{3.33333pt}{0ex}}{K}_{c}=0.1,\phantom{\rule{3.33333pt}{0ex}}{V}_{rmin}=-20,\phantom{\rule{3.33333pt}{0ex}}{V}_{rmax}=20,\phantom{\rule{3.33333pt}{0ex}}{V}_{imin}=-2,\phantom{\rule{3.33333pt}{0ex}}{V}_{imax}=2$.

**Governor data of hydro generator:**$gov$_$TGOV1\phantom{\rule{3.33333pt}{0ex}}type,\phantom{\rule{3.33333pt}{0ex}}{T}_{1}=0.1,\phantom{\rule{3.33333pt}{0ex}}{T}_{2}=0.03,\phantom{\rule{3.33333pt}{0ex}}{T}_{3}=0.2,\phantom{\rule{3.33333pt}{0ex}}{A}_{t}=1,\phantom{\rule{3.33333pt}{0ex}}{D}_{t}=0.02,\phantom{\rule{3.33333pt}{0ex}}R=\phantom{\rule{3.33333pt}{0ex}}0.2,\phantom{\rule{3.33333pt}{0ex}}{V}_{min}=0,\phantom{\rule{3.33333pt}{0ex}}{V}_{max}=1$.

**Governor data of diesel generator:**$DEGOV1\phantom{\rule{3.33333pt}{0ex}}type,\phantom{\rule{3.33333pt}{0ex}}{T}_{1}=0.2,\phantom{\rule{3.33333pt}{0ex}}{T}_{2}=0.1,\phantom{\rule{3.33333pt}{0ex}}{T}_{3}=0.5,\phantom{\rule{3.33333pt}{0ex}}{T}_{4}=1,\phantom{\rule{3.33333pt}{0ex}}{T}_{5}=0.1,\phantom{\rule{3.33333pt}{0ex}}{T}_{6}=0.2,\phantom{\rule{3.33333pt}{0ex}}TD=0.01,\phantom{\rule{3.33333pt}{0ex}}K=15,\phantom{\rule{3.33333pt}{0ex}}Droop=0.05\phantom{\rule{3.33333pt}{0ex}}p.u.,\phantom{\rule{3.33333pt}{0ex}}{T}_{min}=0\phantom{\rule{3.33333pt}{0ex}}p.u.,\phantom{\rule{3.33333pt}{0ex}}{T}_{max}=1.1\phantom{\rule{3.33333pt}{0ex}}p.u.$

Generator | ${\mathit{x}}_{\mathit{l}}$ | ${\mathit{x}}_{2}$ | ${\mathit{x}}_{0}$ | ${\mathit{x}}_{\mathit{d}}$ | ${\mathit{x}}_{\mathit{d}}^{\prime}$ | ${\mathit{x}}_{\mathit{d}}^{\u2033}$ | ${\mathit{x}}_{\mathit{q}}$ | ${\mathit{x}}_{\mathit{q}}^{\prime}$ | ${\mathit{x}}_{\mathit{q}}^{\u2033}$ |
---|---|---|---|---|---|---|---|---|---|

(p.u.) | (p.u.) | (p.u.) | (p.u.) | (p.u.) | (p.u.) | (p.u.) | (p.u.) | (p.u.) | |

Hydro Generator | 0.1 | 0.2 | 0.1 | 2.0 | 0.3 | 0.2 | 2.0 | 0.55 | 0.2 |

Diesel Generator | 0.1 | 0.2 | 0.1 | 2.0 | 0.3 | 0.16 | 2.0 | 0.3 | 0.2 |

Generator | ${\mathit{T}}_{\mathit{d}0}^{{}^{\prime}}$ | ${\mathit{T}}_{\mathit{d}0}^{\u2033}$ | ${\mathit{T}}_{\mathit{q}0}^{{}^{\prime}}$ | ${\mathit{T}}_{\mathit{q}0}^{\u2033}$ | H | MVA | kV |
---|---|---|---|---|---|---|---|

(p.u.) | (p.u.) | (p.u.) | (p.u.) | (s) | |||

Hydro Generator | 6.67 | 0.08 | 0.4 | 0.05 | 6 | 1.5 | 3.3 |

Diesel Generator | 6.67 | 0.09 | 6.67 | 0.08 | 4 | 7.5 | 0.38 |

Bus No. | $\mathit{R}1$ | $\mathit{X}1$ | $\mathit{R}0$ | $\mathit{X}0$ | Length | Nominal Voltage | |
---|---|---|---|---|---|---|---|

From | To | (ohm/km) | (ohm/km) | (ohm/km) | (ohm/km) | (km) | (kV) |

6 | 3 | 0.0018 | 0.0360 | 0.0036 | 0.0594 | 1.2 | 22 |

6 | 7 | 0.0066 | 0.1320 | 0.0132 | 0.2178 | 6.6 | 22 |

6 | 9 | 0.0010 | 0.0200 | 0.0020 | 0.0330 | 1.0 | 22 |

6 | 10 | 0.0010 | 0.0200 | 0.0020 | 0.0330 | 1.0 | 22 |

7 | 8 | 0.0010 | 0.0200 | 0.0020 | 0.0330 | 1.0 | 22 |

11 | 6 | 0.0550 | 1.1000 | 0.1100 | 1.8150 | 105 | 22 |

Bus No. | $\mathit{R}1$ | $\mathit{X}1$ | ${\mathit{u}}_{\mathit{k}}$ | ${\mathit{u}}_{\mathit{k}0}$ | Vector | Tap | HV | LV | |
---|---|---|---|---|---|---|---|---|---|

From | To | (p.u.) | (p.u.) | (p.u.) | (p.u.) | Group | (kV) | (kV) | |

6 | 1 | 0.5 | 0.5 | 6.30 | 3.0 | YNd11 | 1.0 | 22 | 0.415 |

6 | 5 | 0.5 | 0.5 | 3.00 | 3.0 | YNd11 | 1.0 | 22 | 0.415 |

8 | 4 | 0.5 | 0.5 | 6.09 | 3.0 | YNd11 | 1.0 | 22 | 0.415 |

3 | 2 | 0.5 | 0.5 | 6.48 | 3.0 | YNd11 | 1.0 | 22 | 0.415 |

PQ Control Description | Parameters | Units | Values |

Minimum cut frequency | $fmin$ | (Hz) | 47 |

Frequency to start limitation | $fr$ | (Hz) | 51 |

Frequency to be at 0 | $fmax$ | (Hz) | 52.5 |

PV Array Description | Parameters | Units | Values |

Open-circuit voltage of module | $Ul0$ | (V) | 43.8 |

MPP voltage of module | $Umpp0$ | (V) | 35 |

MPP current of module | $Impp0$ | (A) | 4.58 |

Short-circuit current of module | $Ik0$ | (A) | 5 |

Serial module number | − | − | 20 |

Parallel module number | − | − | 140 |

Time constant of module | $Tr$ | (s) | 0 |

PQ Control Description | Parameters | Units | Values |

Proporional gain for id_PI-controller | $Kp$ | (p.u.) | 1 |

Proporional gain for iq_PI-controller | $Kq$ | (p.u.) | 1 |

Integrator time constant id_PI-controller | u_$min$ | (p.u.) | 0.2 |

Integrator time constant iq_PI-controller | u_$max$ | (p.u.) | 0.002 |

Minimum discharging current | $id$_$min$ | (p.u.) | −5 |

Maximum discharging current | $id$_$max$ | (p.u.) | 1 |

Minimum reactive current | $iq$_$min$ | (p.u.) | −5 |

Maximum reactive current | $iq$_$max$ | (p.u.) | 1 |

Simple Battery Description | Parameters | Units | Values |

State of charge at initialisation | $SOC0$ | (int) | 0.8 |

Capacity per cell | $CellCapacity$ | (Ah) | 80 |

Voltage of empty cell | $Impp0$ | (V) | 12 |

Voltage of full cell | $Ik0$ | (V) | 13.85 |

Amount of parallel cells | $CellsParallel$ | (int) | 60 |

Amount of parallel row | $CellsInRow$ | (int) | 65 |

Internal resistance per cell | $RiCell$ | (ohm) | 0.001 |

Frequency Control Description | Parameters | Units | Values |

Deadband for frequency control | $SOC0$ | (db) | 0.004 |

Full active power within 1Hz/ 2Hz | $droop$ | (p.u./p.u.) | 0.0002 |

## Appendix B

**The state-space matrices (A, B, C, and D) for the Q and P controller loops:**

**The weighting transfer functions for the Q and P controller loops:**

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**MDPI and ACS Style**

Tephiruk, N.; Kanokbannakorn, W.; Kerdphol, T.; Mitani, Y.; Hongesombut, K.
Fuzzy Logic Control of a Battery Energy Storage System for Stability Improvement in an Islanded Microgrid. *Sustainability* **2018**, *10*, 1645.
https://doi.org/10.3390/su10051645

**AMA Style**

Tephiruk N, Kanokbannakorn W, Kerdphol T, Mitani Y, Hongesombut K.
Fuzzy Logic Control of a Battery Energy Storage System for Stability Improvement in an Islanded Microgrid. *Sustainability*. 2018; 10(5):1645.
https://doi.org/10.3390/su10051645

**Chicago/Turabian Style**

Tephiruk, Naowarat, Weerawoot Kanokbannakorn, Thongchart Kerdphol, Yasunori Mitani, and Komsan Hongesombut.
2018. "Fuzzy Logic Control of a Battery Energy Storage System for Stability Improvement in an Islanded Microgrid" *Sustainability* 10, no. 5: 1645.
https://doi.org/10.3390/su10051645