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Battery Characterization and Dimensioning Approaches for Micro-Grid Systems^{ †}

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## Abstract

**:**

## 1. Introduction

^{2}[1]) in order to decrease its external dependence on fossil fuel products (e.g., coal, fuel, oil, natural gas), which is around 95%. For these advantages, MG systems have been broadly studied and deployed in order to decrease the power consumption from the electric grid while minimizing the greenhouse emissions. Though, because of the intermittent nature of RES, it is mandatory to store the excess of produced energy from RES (e.g., solar energy) in order to supply electricity to the building’s appliances when there is no production. On the other hand, several energy storage systems exist, such as batteries, flywheel energy storage systems, superconductors, and Pumped Hydroelectric Energy Storage (PHES) [2]. Among these storage devices, batteries are the most used component in MG systems due to their benefits (e.g., modularity, fast response and good energy efficiency). Besides, for remote and rural regions, which are not linked to the electric grid, figuring out the suitable size of energy production systems and storage devices is necessary for continuous electricity supply.

## 2. Proposed Methodology

## 3. Simulation and Experimental Results of the MG System

_{batt}is the battery voltage (V), E

_{0}is the battery constant voltage (V), K is the polarization constant (V/(Ah)) or polarization resistance (Ω), Q is the battery capacity (Ah), i

_{t}is the actual battery capacity (Ah), R is the internal resistance (Ω), i is the battery current (A), i* is the filtered current (A), and exp(t) is an expression that represents the exponential zone voltage (V). The latter term represents the hysteresis phenomenon between the charge and the discharge that takes place in the exponential zone as follows [15]:

^{(−1)}.

## 4. Sizing of the Stand-Alone System

_{elec}is the maximal daily electricity consumption (kWh/day), ${I}_{{r}_{0}}$ is the irradiance at standard conditions STC (equal to 1000 W/m

^{2}), E

_{i}is the lowermost average monthly solar irradiation all over the year (kWh/m

^{2}/day); for our site, it is equal to 4790 kWh/m

^{2}/day that corresponds to the December’s irradiation, PR (Performance Ratio) that depends on many parameters, such as battery’s efficiency, converter’s efficiency, voltage drop in the cables, other losses in the installation, the integration mode, is a correction coefficient for stand-alone systems, which is between 0.55 and 0.75 [31]. The value used in our case is equal 0.70.

_{t}= $\frac{{P}_{c}}{{P}_{module}}$, with a total peak power of 265 W and a total area of 1.63 m

^{2}. Concerning the regulator, the same one as in the previous experiment have been used because the PV module has not changed. Furthermore, the battery’s capacity (C

_{Ah}), which is in Ah, is expressed by the following equation [5]:

_{elec}is the maximal daily electricity consumption (Wh/day), N

_{Aut}is the number of days of autonomy (day), DoD is the Depth of Discharge (%), η

_{B}is the battery’s efficiency (%), and V

_{bat}is the battery’s voltage (V). The estimation of the battery’s capacity requires the knowledge of the number of days of autonomy, which differs from site to another according to weather conditions. The objective is to supply the electricity to the building from batteries when there is no production. In our case, the number of days of autonomy fluctuates between one and three days. In our computations, the value used is one day. A battery of 12 V with a DoD equal to 60% and a battery’s efficiency of 85% has been chosen. 70.26 Ah was found to be the required capacity to install. As a result, we have chosen to work with one battery of 12 V and 75 Ah manufactured by “Electra”. Besides, the electric grid is connected to the system through a rectifier that provides 12 V as output voltage with the current needed by the ventilation system.

## 5. Conclusions and Perspectives

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 5.**(

**a**) The battery’s current in the charging mode; (

**b**) The simulation and experimental battery’s voltage in the charging mode.

**Figure 6.**(

**a**) The battery’s current in the discharging mode; (

**b**) The simulation and experimental battery’s voltage in the discharging mode.

**Figure 8.**(

**a**) The battery’s SoC; (

**b**) The state of the relay (0: electric grid, 1: PV-Battery system); (

**c**) The simulation and experimental battery’s voltage.

**Figure 10.**(

**a**) The battery’s SoC and the state of the actuator from simulation and experiment; (

**b**) The battery’s SoC and the PV power; (

**c**) The simulation and experimental battery’s voltage.

Parameters | E_{0} (V) | R (Ω) | K (Ω or V/Ah) | A (V) | B (Ah^{−1}) |
---|---|---|---|---|---|

Values | 13.32 | 0.54306 | 0.0531 | 1.557 × 10^{−5} | 1.7233 |

Parameters | E_{0} (V) | R (Ω) | K (Ω or V/Ah) | A (V) | B (Ah^{−1}) |
---|---|---|---|---|---|

Values | 13.64 | 0.514 | 0.0465 | 6.94 × 10^{−5} | 1.31 |

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**MDPI and ACS Style**

Boulmrharj, S.; NaitMalek, Y.; Elmouatamid, A.; Bakhouya, M.; Ouladsine, R.; Zine-Dine, K.; Khaidar, M.; Siniti, M. Battery Characterization and Dimensioning Approaches for Micro-Grid Systems. *Energies* **2019**, *12*, 1305.
https://doi.org/10.3390/en12071305

**AMA Style**

Boulmrharj S, NaitMalek Y, Elmouatamid A, Bakhouya M, Ouladsine R, Zine-Dine K, Khaidar M, Siniti M. Battery Characterization and Dimensioning Approaches for Micro-Grid Systems. *Energies*. 2019; 12(7):1305.
https://doi.org/10.3390/en12071305

**Chicago/Turabian Style**

Boulmrharj, Sofia, Youssef NaitMalek, Abdellatif Elmouatamid, Mohamed Bakhouya, Radouane Ouladsine, Khalid Zine-Dine, Mohammed Khaidar, and Mostapha Siniti. 2019. "Battery Characterization and Dimensioning Approaches for Micro-Grid Systems" *Energies* 12, no. 7: 1305.
https://doi.org/10.3390/en12071305