# Optimal Capacity and Cost Analysis of Battery Energy Storage System in Standalone Microgrid Considering Battery Lifetime

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## Abstract

**:**

## 1. Introduction

## 2. DGs and BESS Models

#### 2.1. PV Model

#### 2.2. Wind Turbine Model

#### 2.3. BESS Model

#### 2.4. BESS Capacity Model

#### 2.5. BESS Lifetime Estimation

## 3. Optimization Model

#### 3.1. Objective Function

#### 3.2. PSO Algorithm

## 4. Results

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Conflicts of Interest

## Abbreviations

BESS | Battery Energy Storage System |

${c}_{1},{c}_{2}$ | Acceleration factors |

${C}_{initial}$ | Initial cost |

${C}_{om}$ | Fixed operation and maintenance cost |

${C}_{re}$ | Replacement cost |

$CTF$ | Cycles to failure |

${C}_{total}$ | Total cost |

d | Discount rate |

DGs | Distributed generation system |

$DOD$ | Depth of discharge |

${E}_{B}$ | Battery energy |

${E}_{B,rated}$ | Battery capacity |

${E}_{B,Orated}$ | Battery’s oversize energy |

${E}_{throughput}$ | Battery throughput corresponding to a specified DOD |

${E}_{throughput,avg}$ | Average battery throughput |

${g}_{best}$ | The best global solution |

${G}_{c}$ | The solar irradiance on the operating time |

${G}_{STC}$ | The solar irradiance on the standard test condition (STC) (1000w/${\mathrm{m}}^{2}$) |

i | Particle index |

$it{e}_{max}$ | Maximum iteration |

${k}_{c}$ | Temperature coefficient |

k | Discrete time index |

${k}_{B,om}$ | The operation and maintenance cost set to 5% of the initial cost ($/kWh/year) |

${k}_{BE,initial}$ | The BESS initial cost per energy ($/kWh) |

${k}_{BP,initial}$ | The BESS initial cost per power ($/kW) |

${L}_{B}$ | BESS lifetime |

${L}_{life}$ | Life loss |

LPSP | Loss of power supply probability |

n | Number of particles in the swarm |

$NPVC$ | Net present value of cost |

$NPV$ | Net present value |

$N{R}_{B}$ | Number of BESS replacement throughput the project |

${p}_{best}$ | Personal pest solution |

${P}_{B}$ | Output power limit of BESS |

${P}_{B,ch},{P}_{B,d}$ | Charging and discharging power of BESS |

${P}_{B,required}$ | BESS’s required power |

${P}_{B,rated}$ | BESS’s rated power |

${P}_{B,ch}^{max},{P}_{B,d}^{max}$ | Upper limits of charging and discharging power of BESS |

${P}_{PV}$ | Output power of PV system |

${P}_{rated-wt}$ | Rated output power of WT |

${P}_{STC}$ | Rated output power at standard test condition |

PV | Photovoltaic |

${P}_{WT}$ | Output power of WT |

${q}_{B}$ | Adjusting factor |

${r}_{1},{r}_{2}$ | Random number [0, 1] |

$SOC$ | State of charge |

${T}_{C}$ | The PV temperature on the operating time |

$USW$ | Uniform series presents the worth factor |

v | Wind speed (m/s) |

${v}_{i}$ | Velocity of the particle i |

${v}_{ci},{v}_{r},{v}_{co}$ | Cut-in speed, rated speed and cut-off speed of WT |

w | Inertia factor |

${W}_{SOC}$ | Weight factor |

x | Position of particle i |

$\beta $ | Battery’s self discharge rate |

${\eta}_{B,ch},{\eta}_{B,d}$ | Charging and discharging efficiency of BESS |

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**Figure 4.**Flowchart for determination of the optimal BESS capacity. The ${q}_{B}$ value is changed from 1 to 5 in 0.001 increments.

**Figure 6.**Industrial load, PV source and WT powers taken from [31].

**Figure 7.**BESS−power for the case shown in Figure 6.

Parameter | Variable | Unit | Value |
---|---|---|---|

Project life | ${L}_{p}$ | years | 20 |

BESS Calendar life | ${L}_{B}$ | years | 10 |

BESS SOC limits | $SO{C}_{min}$-$SO{C}_{max}$ | % | 20–80 |

Charge/discharge efficiency | ${\eta}_{B,ch}$$/{\eta}_{B,d}$ | % | 90/90 |

Initial cost per energy [32,33,34] | ${k}_{BE,initial}$ | $/kWh | 183.86 |

Initial cost per power | ${k}_{BP,initial}$ | $/kW | 183.86 |

Operation & maintenance cost | ${k}_{B,om}$ | $/kWh/year | 9.19 |

Discount rate [35] | d | % | 5 |

${\mathit{q}}_{\mathit{B}}$ | ${\mathit{L}}_{\mathit{B}}$ | ${\mathit{NR}}_{\mathit{B}}$ | ${\mathit{C}}_{\mathit{initial}}$ ($) | ${\mathit{NPVC}}_{\mathit{om}}$ ($) | ${\mathit{NPVC}}_{\mathit{re}}$ ($) | ${\mathit{NPVC}}_{\mathit{total}}$ ($) |
---|---|---|---|---|---|---|

1.0 | 1.20 | 16 | 18,419 | 23.48 | 185,992 | 204,436 |

1.5 | 1.72 | 11 | 25,958 | 35.23 | 178,562 | 204,557 |

1.761 | 2.00 | 9 | 29,896 | 41.36 | 170,468 | 200,653 |

2.0 | 2.25 | 8 | 33,497 | 46.97 | 168.626 | 202,172 |

2.2 | 2.46 | 8 | 36,513 | 51.67 | 176,524 | 213,088 |

3.0 | 3.31 | 6 | 48,573 | 70.46 | 171,838 | 220,482 |

4.0 | 4.38 | 4 | 63,649 | 93.94 | 153,539 | 217,284 |

5.0 | 5.44 | 3 | 78,724 | 117.43 | 142,152 | 220,994 |

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**MDPI and ACS Style**

Wongdet, P.; Boonraksa, T.; Boonraksa, P.; Pinthurat, W.; Marungsri, B.; Hredzak, B.
Optimal Capacity and Cost Analysis of Battery Energy Storage System in Standalone Microgrid Considering Battery Lifetime. *Batteries* **2023**, *9*, 76.
https://doi.org/10.3390/batteries9020076

**AMA Style**

Wongdet P, Boonraksa T, Boonraksa P, Pinthurat W, Marungsri B, Hredzak B.
Optimal Capacity and Cost Analysis of Battery Energy Storage System in Standalone Microgrid Considering Battery Lifetime. *Batteries*. 2023; 9(2):76.
https://doi.org/10.3390/batteries9020076

**Chicago/Turabian Style**

Wongdet, Pinit, Terapong Boonraksa, Promphak Boonraksa, Watcharakorn Pinthurat, Boonruang Marungsri, and Branislav Hredzak.
2023. "Optimal Capacity and Cost Analysis of Battery Energy Storage System in Standalone Microgrid Considering Battery Lifetime" *Batteries* 9, no. 2: 76.
https://doi.org/10.3390/batteries9020076