# Day-Ahead Optimization of Prosumer Considering Battery Depreciation and Weather Prediction for Renewable Energy Sources

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*Applied Sciences*: Invited Papers in Electrical, Electronics and Communications Engineering Section)

## Abstract

**:**

## 1. Introduction

## 2. Overall Description of the Model

#### 2.1. System Architecture

#### 2.2. The Role of Prosumer

## 3. Methodology

#### 3.1. Mathematical Modeling of RESs

#### 3.1.1. PV Unit

#### 3.1.2. WT Unit

#### 3.1.3. Energy Storage Systems

#### 3.1.4. Depreciation of ESSs

#### 3.2. Predicting Weather Parameters Using Time Series FF-ANN

#### 3.3. Optimization Modeling

## 4. Simulation Results and Discussion

#### 4.1. Prediction Results

#### 4.2. Case Studies

- Case 1: Day-ahead scheduling of the prosumer considering predicted weather data.
- Case 2: Day-ahead scheduling of the prosumer considering ESSs depreciation cost and predicted weather data.
- Case 3: Day-ahead scheduling of the prosumer considering real weather data.

#### 4.3. Results of Case Studies

#### 4.3.1. Case 1

#### 4.3.2. Case 2

#### 4.3.3. Case 3

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## Nomenclature

Parameters | |

$SO{C}_{0}$ | Initial ESS SOC (kWh) |

$SO{C}_{24}$ | Final ESS SOC (kWh) |

$SO{C}_{\mathrm{max}}$ | Upper band of ESS SOC (kWh) |

$SO{C}_{\mathrm{min}}$ | Lower band of ESS SOC (kWh) |

${P}_{chargarge}^{min}$ | Lower band of ESS charge (kWh) |

${P}_{chargarge}^{max}$ | Upper band of ESS charge (kWh) |

${P}_{dischargarge}^{min}$ | Lower band of ESS discharge (kWh) |

${P}_{dischargarge}^{max}$ | Upper band of ESS discharge (kWh) |

${\eta}_{chargarge}$ | Charge coefficient of ESS (%) |

${\eta}_{dischargarge}$ | Charge coefficient of ESS (%) |

${N}_{pv}$ | Number installed PV modules |

${A}_{pv}$ | Area of the module (m^{2}) |

${R}_{SB}$ | Replacement cost of SB ($) |

${L}_{SB}$ | Lifetime of the SB (year) |

${E}_{SB}$ | Square root of both ways of efficiency of the SB (%) |

${R}_{PHEV}$ | Replacement cost of PHEV ($) |

${L}_{PHEV}$ | Lifetime of the PHEV (year) |

${E}_{PHEV}$ | Square root of both ways of efficiency of the PHEV (%) |

${B}_{SB}$ | SB depreciation cost coefficient per kWh |

${B}_{PHEV}$ | PHEV depreciation cost coefficient per kWh |

${\eta}_{pvrated}$ | Rated efficiency of PV measured at referenced temperature (25 °C) |

$NOCT$ | Normal cell operation temperature (°C) |

${T}_{ref}$ | Reference temperature (25 °C) |

$\alpha $ | Temperature coefficient for cell efficiency (0.004/°C) |

${V}_{c}$ | Cut-out speed (m/s) |

${V}_{ci}$ | Cut-in speed (m/s) |

${V}_{r}$ | Wind speed at rated power (m/s) |

${P}_{\mathrm{max}}^{s}$ | Upper bound of import power from grid (kWh) |

${P}_{\mathrm{min}}^{s}$ | Power export limit to grid (kWh) |

Variables | |

${\eta}_{t}^{PV}$ | Efficiency of PV module (%) |

${G}_{t}$ | Hourly solar irradiance (kW×m^{−2}) |

${T}_{t}$ | Hourly ambient temperature (°C) |

${V}_{t}^{wind}$ | Hourly wind speed (V) |

${K}_{t}$ | Hourly electricity price ($) |

${P}_{t}^{chargarge}$ | Charge power of ESS (kWh) |

${P}_{t}^{dichargarge}$ | Discharge power of ESS (kWh) |

${P}_{t}^{s}$ | Power flow from or to grid (kWh) |

${P}_{t}^{PV}$ | Output power of PV (kWh) |

${P}_{t}^{WT}$ | Output power of WT (kWh) |

${P}_{t}^{contract}$ | Contracted power (kWh) |

${P}_{t}^{load}$ | Prosumer load profile (kWh) |

$SO{C}_{d}^{\mathrm{min},SB}$ | Minimum SB SOC at the end of the day (kWh) |

$SO{C}_{d}^{\mathrm{min},PHEV}$ | Minimum SOC of PHEV at the end of the day (kWh) |

$SO{C}_{t}$ | SOC in each hour (kWh) |

${D}_{d}^{ESS}$ | Total EES depreciation cost ($) |

${D}_{d}^{{}_{SB}}$ | SB depreciation cost ($) |

${D}_{d}^{{}_{PHEV}}$ | PHEV depreciation cost ($) |

$x$ | Original data value |

$y$ | Normalized data value |

${x}_{\mathrm{min}},{x}_{\mathrm{max}}$ | Minimum and maximum value of x |

${y}_{\mathrm{min}},{y}_{\mathrm{max}}$ | [0,1] |

${U}_{t}^{charge}$ | ESS charge binary variable |

${U}_{t}^{discharge}$ | ESS discharge binary variable |

Indices | |

t | Index of time |

d | Index of day |

Abbreviations | |

RES | Renewable Energy Source |

SB | Stationary Battery |

EV | Electric Vehicle |

FEV | Fully Electric Vehicle |

FCEV | Fuel Cell Electric Vehicle |

PHEV | Plug-in Hybrid Electrical Vehicle |

ESS | Energy Storage System |

PV | Photovoltaic |

WT | Wind Turbine |

PCU | Power Conversion Unit |

EMS | Energy Management System |

ANN | Artificial Neural Network |

FF | Feedforward |

MLP | Multilayer Perceptron |

DOD | Depth of Charge |

SOC | State of Charge |

MILP | Mixed-Integer Linear Programming |

BP | Back Propagation |

TOU | Time of Use |

DR | Demand Response |

DSO | Distribution System Operator |

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**Figure 3.**A typical multilayer perceptron artificial neural network (MLP-ANN) model for time series prediction.

**Figure 10.**Contracted power that the prosumer is committed to providing to the consumer during the day.

**Figure 11.**Charging and discharging of a (

**a**) stationary battery (SB) and (

**b**) plug-in hybrid electric vehicle (PHEV).

**Figure 14.**Exchanged power between prosumer and utility grid based on predicted and real weather data.

Weather Parameter | Training | Testing | Validation | All |
---|---|---|---|---|

Solar irradiance | 0.957 | 0.948 | 0.954 | 0.956 |

Temperature | 0.989 | 0.988 | 0.987 | 0.988 |

Wind speed | 0.227 | 0.229 | 0.232 | 0.230 |

**Table 2.**Technical parameters photovoltaic (PV) and wind turbine (WT) units [44].

PV Parameter | Value | WT Parameter | Value |
---|---|---|---|

Module Nominal Power | 225 W | ${P}_{nom}$ | 5 kW |

$\alpha $ | −0.38% | ${V}_{ci}$ | 2 m/s |

$NOCT$ | 45 C | ${V}_{r}$ | 12 m/s |

${T}_{ref}$ | 25 C | ${V}_{c}$ | 25 m/s |

${\eta}_{pvrated}$ | 15% | ||

${A}_{pv}$ | 1.244 | ||

${N}_{pv}$ | 30 |

Parameter | SB | PHEV | Unit |
---|---|---|---|

$Vnom$ | 12 | 12 | V |

$SO{C}_{0}$ | 5 | 4 | kW |

$SO{C}_{max}$ | 10 | 8 | kW |

${P}_{chargarge}^{min}$ | 0 | 0 | kW |

${P}_{chargarge}^{max}$ | 9 | 7 | kW |

${P}_{dischargarge}^{min}$ | 0 | 0 | kW |

${P}_{dischargarge}^{max}$ | 8 | 6 | kW |

${\eta}_{chargarge}$ | 0.93 | 0.9 | % |

${\eta}_{dischargarge}$ | 0.95 | 0.9 | % |

${B}_{SB},{B}_{PHEV}$ | 0.6 | 0.2 | $ |

Time of Day (h) | Price ($/kWh) |
---|---|

23:00 to 07:00 | 0.0075 |

07:00 to 13:00 | 0.03 |

13:00 to 17:00 | 0.12 |

17:00 to 19:00 | 0.03 |

19:00 to 23:00 | 0.12 |

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## Share and Cite

**MDPI and ACS Style**

Faraji, J.; Abazari, A.; Babaei, M.; Muyeen, S.M.; Benbouzid, M.
Day-Ahead Optimization of Prosumer Considering Battery Depreciation and Weather Prediction for Renewable Energy Sources. *Appl. Sci.* **2020**, *10*, 2774.
https://doi.org/10.3390/app10082774

**AMA Style**

Faraji J, Abazari A, Babaei M, Muyeen SM, Benbouzid M.
Day-Ahead Optimization of Prosumer Considering Battery Depreciation and Weather Prediction for Renewable Energy Sources. *Applied Sciences*. 2020; 10(8):2774.
https://doi.org/10.3390/app10082774

**Chicago/Turabian Style**

Faraji, Jamal, Ahmadreza Abazari, Masoud Babaei, S. M. Muyeen, and Mohamed Benbouzid.
2020. "Day-Ahead Optimization of Prosumer Considering Battery Depreciation and Weather Prediction for Renewable Energy Sources" *Applied Sciences* 10, no. 8: 2774.
https://doi.org/10.3390/app10082774