# Day-Ahead Optimal Battery Operation in Islanded Hybrid Energy Systems and Its Impact on Greenhouse Gas Emissions

^{*}

## Abstract

**:**

## 1. Introduction

_{2}) emissions from 90% to 72%, whereas renewable power curtailment reduces from 33% to 9%. In the case of Texas, CO

_{2}emissions could be reduced from 58% to 54% and renewable power curtailment could be reduced from 3% to 0.3% [4]. Combination of carbon capture and storage devices with conventional generation units is also an option to reduce GHG emissions. However, the combination of renewable generation with ESS can be energetically more effective [5].

^{®}[7], iHOGA

^{®}[8], and Hybrid2

^{®}[9], among others. Dispatch strategies implemented in most of these tools are based on load following and cycle charging concepts. Load following consists of generating power from conventional units only to satisfy net load (NL), and this approach is frequently suggested in a HES with high share of renewable power, which is much higher than load demand over the year. Conversely, a cycle charging strategy forces conventional generator to operate at its rating power when needed to charge BESS with the remaining energy, so this strategy is frequently implemented when renewable generation is limited [10]. It is important to mention that these strategies do not require any forecast of renewable generation or load demand. However, they are very effective in the management of HES of small scale used on rural electrification projects.

#### 1.1. Literature Review

_{2}emissions, and the cycling process of thermal units is not accurately described.

#### 1.2. Main Contributions

_{X}), CO

_{2}, and particulate matter (PM) is investigated.

## 2. Hybrid Energy System Model

#### 2.1. Wind Generator Model

#### 2.2. BESS and Power Converter Models

#### 2.3. Diesel Generator Model

## 3. Optimization of Day-Ahead Operation

#### 3.1. Problem Formulation

#### 3.2. Optimization by TVMS-BPSO

## 4. Testing the Problem Formulation

^{®}, using a personal computer with i7-3630QM CPU at 2.4 GHz, 8 GB of memory and a 64-bit operating system.

#### 4.1. Case I: Low Wind Speed with Fully Charged Battery

_{x}(left) and CO

_{2}(right) emissions, and Figure 11 presents PM emissions. It is possible to observe how all of them slightly increase at the end of the day, due to the fact that BESS management strongly focuses on NL-peak mitigation.

_{x}, CO

_{2}, and PM is clearly observed.

_{x}, CO

_{2}, and PM are approximately 51.02%, 20.80%, 12.59%, and 32.92%, respectively.

#### 4.2. Case II: High Wind Speed with Empty Battery

_{X}(left) and CO

_{2}(right), and in Figure 20 for PM.

#### 4.3. Case III: Very High Wind Speed with Empty Battery

_{x}, CO

_{2}, and PM to the atmosphere.

## 5. Performance of TVMS-BPSO

## 6. Conclusions and Remarks

## Author Contributions

## Funding

## Conflicts of Interest

## Abbreviations

$i$ | Index for each individual ($i=1:\dots ,I$). |

$k$ | Index for each iteration ($k=1,\dots ,K$). |

$t$ | Index for each time step ($t=1,\dots ,T=24$). |

${S}_{W\left(t\right)}$ | Wind speed at time $t$ (m/s). |

${S}_{W}^{o},{S}_{W}^{r}$ and ${S}_{W}^{f}$ | Cut-in, rated, and cut-off wind speed, respectively (m/s). |

${S}_{W}^{a}$ | Average wind speed (m/s). |

${S}_{W}^{b}$ | Diurnal pattern strength. |

${S}_{W}^{c}$ | Hour of peak wind speed (h). |

${P}_{W\left(t\right)}$ | Wind power at time $t$ (kW). |

${P}_{W}^{max}$ | Rated wind turbine power (kW). |

${P}_{W}^{a},{P}_{W}^{b}$ and ${P}_{W}^{c}$ | Parameters of wind turbine power curve. |

${T}_{E}$ | Electrolyte temperature (K). |

${U}_{B\left(t\right)}$ | Battery voltage at time $t$ (V). |

${\eta}_{B\left(t\right)}$ | Battery efficiency at time $t$ (V). |

$SO{C}_{B\left(t\right)}$ | Battery state of charge at time $t$. |

${P}_{B\left(t\right)}$ | Battery power at time $t$ (kW). |

${P}_{C\left(t\right)}$ | Converter power at time $t$ (kW). |

${P}_{C\left(i,t,k\right)}$ | Converter power of individual $i$ at time $t$ and iteration $k$ (kW). |

${P}_{L\left(t\right)}$ | Load demand at time $t$ (kW). |

${P}_{N\left(t\right)}$ | Net load at time $t$ (kW). |

${P}_{D\left(t\right)}$ | Diesel power at time $t$ (kW). |

${P}_{D}^{a}$ | Parameter of diesel power calculation (kW). |

${P}_{EXC\left(t\right)}$ | Power surplus at time $t$ (kW). |

${P}_{ENS\left(t\right)}$ | Power not supplied at time $t$ (kW). |

${U}_{B}^{min}$, ${U}_{B}^{max}$ | Minimum and maximum battery voltage (V), respectively. |

$SO{C}_{B}^{min}$, $SO{C}_{B}^{max}$ | Minimum and maximum state of charge, respectively. |

${P}_{B}^{max}$ and ${P}_{C}^{max}$ | Maximum battery and converter power (kW), respectively. |

${E}_{B}^{max}$ | Maximum battery capacity (kWh). |

${P}_{D}^{min}$, ${P}_{D}^{max}$ | Minimum and maximum diesel power (kW). |

${U}_{B\left(t\right)}^{ch}$ | Battery voltage during charge at time $t$ (V). |

${U}_{ch}^{a}-{U}_{ch}^{h}$, ${U}_{ch}^{j}-{U}_{ch}^{n}$, ${U}_{ch}^{p}$, ${U}_{ch}^{q}$ | Parameters of battery voltage during charging. |

${\eta}_{B\left(t\right)}^{ch}$ | Battery efficiency during charge at time $t$ (V). |

${\eta}_{V\left(t\right)}^{ch}$ | Voltage efficiency during charge at time $t$. |

${\eta}_{E\left(t\right)}^{ch}$ | Energy efficiency during charge at time $t$. |

${U}_{B\left(t\right)}^{dis}$ | Battery voltage during discharge at time $t$ (V). |

${U}_{dis}^{a}-{U}_{dis}^{h}$, ${U}_{dis}^{j}-{U}_{dis}^{m}$ | Parameters of battery voltage during discharging. |

${\eta}_{B\left(t\right)}^{dis}$ | Battery efficiency during discharge at time $t$ (V). |

${\eta}_{V\left(t\right)}^{dis}$ | Voltage efficiency during discharge at time $t$. |

${\eta}_{E\left(t\right)}^{dis}$ | Energy efficiency during discharge at time $t$. |

${P}_{C}^{a},{P}_{C}^{b}$ | Parameters of power converter. |

${\overrightarrow{g}}_{\left(i,k\right)}$ | Agent or individual $i$ at iteration $k$. |

${G}_{\left(k\right)}$ | Population or swarm at iteration $k$. |

${O}_{\left(i,k\right)}$ | Objective function of individual $i$ at iteration $k$. |

$\varnothing ,\chi ,{C}_{PSO}^{a},{C}_{PSO}^{b}$ | Coefficient of particle swarm optimization. |

${R}_{PSO}^{a}-{R}_{PSO}^{d}$ | Random variables. |

${v}_{\left(i,t,k\right)}$ | Velocity of agent $i$ at time $t$ and iteration $k$. |

${g}_{\left(i,t,k\right)}$ | Position of agent $i$ at time $t$ and iteration $k$. |

${g}_{\left(t\right)}^{PBEST}$ | Position of best agent in the group ($i=1,\dots ,I$) at time $t$. |

${g}_{\left(t\right)}^{GBEST}$ | Position of best agent until the actual iteration ($k$) at time $t$. |

${\sigma}_{\left(k\right)}$ | Time-varying variable for iteration $k$. |

${\sigma}_{min}$, ${\sigma}_{max}$ | Minimum and maximum value of ${\sigma}_{\left(k\right)}$. |

${S}_{PSO\left(i,t,k\right)}^{a}$, ${S}_{PSO\left(i,t,k\right)}^{b}$ | Sigmoid function values for agent $i$ at time $t$ for iteration $k$. |

${J}_{PSO\left(i,t,k\right)}^{a}$, ${J}_{PSO\left(i,t,k\right)}^{b}$ | Binary variables for agent $i$ at time $t$ for iteration $k$. |

${O}_{\left(i,k\right)}^{a}$, ${O}_{\left(i,k\right)}^{b}$ | Objective function values for agent $i$ and iteration $k$. |

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${\mathit{S}}_{\mathit{W}}^{\mathit{b}}$ | THC (kg) | CO (kg) | NO_{X} (kg) | CO_{2} (kg) | PM (kg) |
---|---|---|---|---|---|

0 | 1.37 | 7.18 | 31.18 | 1444.12 | 0.49 |

0.1 | 1.38 | 7.08 | 31.13 | 1442.31 | 0.48 |

0.2 | 1.38 | 6.94 | 30.98 | 1438.01 | 0.48 |

0.3 | 1.39 | 6.75 | 30.76 | 1431.30 | 0.47 |

0.4 | 1.40 | 6.53 | 30.47 | 1422.96 | 0.46 |

${\mathit{S}}_{\mathit{W}}^{\mathit{b}}$ | THC (g) | CO (g) | NO_{X} (kg) | CO_{2} (kg) | PM (g) |
---|---|---|---|---|---|

0 | 1.57 | 3.51 | 24.70 | 1261.25 | 0.32 |

0.1 | 1.57 | 3.50 | 24.65 | 1260.11 | 0.32 |

0.2 | 1.58 | 3.36 | 24.57 | 1257.46 | 0.32 |

0.3 | 1.58 | 3.30 | 24.36 | 1251.68 | 0.31 |

0.4 | 1.58 | 3.22 | 24.09 | 1244.37 | 0.31 |

${\mathit{S}}_{\mathit{W}}^{\mathit{b}}$ | THC (%) | CO (%) | NO_{X} (%) | CO_{2} (%) | PM (%) |
---|---|---|---|---|---|

0 | −14.43 | 51.19 | 20.79 | 12.66 | 33.54 |

0.1 | −14.10 | 50.61 | 20.79 | 12.63 | 32.98 |

0.2 | −13.97 | 51.54 | 20.68 | 12.56 | 33.37 |

0.3 | −13.48 | 51.09 | 20.80 | 12.55 | 32.72 |

0.4 | −12.92 | 50.66 | 20.95 | 12.55 | 32.00 |

$\mathit{t}$/${\mathit{S}}_{\mathit{W}}^{\mathit{b}}$ | Without BESS | With BESS | ||||||||
---|---|---|---|---|---|---|---|---|---|---|

0 | 0.1 | 0.2 | 0.3 | 0.4 | 0 | 0.1 | 0.2 | 0.3 | 0.4 | |

1 | 66.8 | 67.3 | 67.5 | 67.6 | 67.6 | 66.8 | 67.3 | 67.5 | 67.6 | 67.6 |

2 | 60.8 | 61.3 | 61.5 | 61.5 | 61.5 | 60.8 | 61.3 | 61.5 | 61.5 | 61.5 |

3 | 57.4 | 57.9 | 58.2 | 58.2 | 58.2 | 57.4 | 57.9 | 58.2 | 58.2 | 58.2 |

4 | 55.7 | 56.2 | 56.5 | 56.5 | 56.5 | 55.7 | 56.2 | 56.5 | 56.5 | 56.5 |

5 | 56.2 | 56.6 | 56.9 | 56.9 | 56.9 | 56.2 | 56.6 | 56.9 | 56.9 | 56.9 |

6 | 57.6 | 58.0 | 58.3 | 58.4 | 58.4 | 57.6 | 58.0 | 58.3 | 58.4 | 58.4 |

7 | 63.9 | 64.2 | 64.4 | 64.6 | 64.6 | 63.9 | 64.2 | 64.4 | 64.6 | 64.6 |

8 | 71.0 | 71.2 | 71.3 | 71.4 | 71.5 | 71.0 | 71.2 | 71.3 | 71.4 | 71.5 |

9 | 80.6 | 80.6 | 80.6 | 80.6 | 80.6 | 80.6 | 80.6 | 80.6 | 80.6 | 80.6 |

10 | 89.2 | 89.0 | 88.8 | 88.6 | 88.3 | 89.2 | 89.0 | 88.8 | 88.6 | 88.3 |

11 | 95.7 | 95.3 | 94.9 | 94.3 | 93.7 | 58.4 | 58.0 | 57.6 | 57.0 | 56.4 |

12 | 96.7 | 96.2 | 95.5 | 94.6 | 93.6 | 61.6 | 61.0 | 60.3 | 59.5 | 58.4 |

13 | 97.8 | 97.1 | 96.2 | 95.0 | 93.6 | 64.7 | 64.0 | 63.0 | 61.9 | 60.5 |

14 | 99.2 | 98.4 | 97.4 | 96.0 | 94.4 | 68.1 | 67.3 | 66.2 | 64.9 | 63.2 |

15 | 96.1 | 95.3 | 94.1 | 92.7 | 91.0 | 66.9 | 66.0 | 64.9 | 63.4 | 61.7 |

16 | 91.9 | 91.1 | 90.0 | 88.7 | 87.0 | 64.4 | 63.6 | 62.6 | 61.2 | 87.0 |

17 | 89.4 | 88.7 | 87.8 | 86.6 | 85.2 | 89.4 | 88.7 | 87.8 | 86.6 | 85.2 |

18 | 89.6 | 89.1 | 88.4 | 87.5 | 86.5 | 63.8 | 63.2 | 88.4 | 87.5 | 86.5 |

19 | 89.4 | 89.0 | 88.6 | 88.1 | 87.4 | 67.4 | 67.0 | 88.6 | 88.1 | 60.0 |

20 | 89.4 | 89.2 | 89.0 | 88.8 | 88.5 | 79.5 | 79.3 | 63.2 | 62.9 | 62.7 |

21 | 98.6 | 98.6 | 98.6 | 98.6 | 98.6 | 94.3 | 94.3 | 76.6 | 76.6 | 76.6 |

22 | 98.2 | 98.4 | 98.5 | 98.6 | 98.7 | 95.9 | 96.0 | 88.6 | 88.8 | 88.9 |

23 | 88.8 | 89.1 | 89.3 | 89.5 | 89.5 | 87.2 | 87.6 | 85.0 | 85.2 | 85.2 |

24 | 77.3 | 77.7 | 77.9 | 78.0 | 78.0 | 76.1 | 76.6 | 75.6 | 75.7 | 75.7 |

${\mathit{S}}_{\mathit{W}}^{\mathit{b}}$ | THC (kg) | CO (kg) | NO_{X} (kg) | CO_{2} (kg) | PM (kg) |
---|---|---|---|---|---|

0 | 1.17 | 0.62 | 8.48 | 629.60 | 0.14 |

0.1 | 1.17 | 0.62 | 8.48 | 629.60 | 0.14 |

0.2 | 1.17 | 0.62 | 8.48 | 629.60 | 0.14 |

0.3 | 1.53 | 0.82 | 11.13 | 826.35 | 0.19 |

0.4 | 1.68 | 0.90 | 12.19 | 905.05 | 0.21 |

${\mathit{S}}_{\mathit{W}}^{\mathit{b}}$ | THC (kg) | CO (kg) | NO_{X} (kg) | CO_{2} (kg) | PM (kg) |
---|---|---|---|---|---|

0 | 1.02 | 0.55 | 7.42 | 550.90 | 0.13 |

0.1 | 1.02 | 0.55 | 7.42 | 550.90 | 0.13 |

0.2 | 1.10 | 0.59 | 7.95 | 590.25 | 0.14 |

0.3 | 1.53 | 0.82 | 11.13 | 826.35 | 0.19 |

0.4 | 1.68 | 0.90 | 12.19 | 905.05 | 0.21 |

${\mathit{S}}_{\mathit{W}}^{\mathit{b}}$ | THC (%) | CO (%) | NO_{X} (%) | CO_{2} (%) | PM (%) |
---|---|---|---|---|---|

0 | 12.5 | 12.5 | 12.5 | 12.5 | 12.5 |

0.1 | 12.5 | 12.5 | 12.5 | 12.5 | 12.5 |

0.2 | 6.25 | 6.25 | 6.25 | 6.25 | 6.25 |

0.3 | 0 | 0 | 0 | 0 | 0 |

0.4 | 0 | 0 | 0 | 0 | 0 |

$\mathit{t}$/${\mathit{S}}_{\mathit{W}}^{\mathit{b}}$ | Without BESS | With BESS | ||||||||
---|---|---|---|---|---|---|---|---|---|---|

0 | 0.1 | 0.2 | 0.3 | 0.4 | 0 | 0.1 | 0.2 | 0.3 | 0.4 | |

1 | 0 | 0 | 0 | 50 | 50 | 0 | 0 | 0 | 50 | 50 |

2 | 0 | 0 | 0 | 50 | 50 | 0 | 0 | 0 | 50 | 50 |

3 | 0 | 0 | 0 | 50 | 50 | 0 | 0 | 0 | 50 | 50 |

4 | 0 | 0 | 0 | 50 | 50 | 0 | 0 | 0 | 50 | 50 |

5 | 0 | 0 | 0 | 50 | 50 | 0 | 0 | 0 | 50 | 50 |

6 | 0 | 0 | 0 | 0 | 50 | 0 | 0 | 0 | 0 | 50 |

7 | 0 | 0 | 0 | 0 | 50 | 0 | 0 | 0 | 0 | 50 |

8 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |

9 | 50 | 50 | 50 | 50 | 50 | 50 | 50 | 50 | 50 | 50 |

10 | 50 | 50 | 50 | 50 | 50 | 50 | 50 | 50 | 50 | 50 |

11 | 50 | 50 | 50 | 50 | 50 | 50 | 50 | 50 | 50 | 50 |

12 | 50 | 50 | 50 | 50 | 50 | 0 | 0 | 50 | 50 | 50 |

13 | 50 | 50 | 50 | 50 | 50 | 0 | 0 | 0 | 50 | 50 |

14 | 50 | 50 | 50 | 50 | 50 | 50 | 50 | 50 | 50 | 50 |

15 | 50 | 50 | 50 | 50 | 50 | 50 | 50 | 50 | 50 | 50 |

16 | 50 | 50 | 50 | 50 | 50 | 50 | 50 | 50 | 50 | 50 |

17 | 50 | 50 | 50 | 50 | 50 | 50 | 50 | 50 | 50 | 50 |

18 | 50 | 50 | 50 | 50 | 50 | 50 | 50 | 50 | 50 | 50 |

19 | 50 | 50 | 50 | 50 | 50 | 50 | 50 | 50 | 50 | 50 |

20 | 50 | 50 | 50 | 50 | 50 | 50 | 50 | 50 | 50 | 50 |

21 | 50 | 50 | 50 | 50 | 50 | 50 | 50 | 50 | 50 | 50 |

22 | 50 | 50 | 50 | 50 | 50 | 50 | 50 | 50 | 50 | 50 |

23 | 50 | 50 | 50 | 50 | 50 | 50 | 50 | 50 | 50 | 50 |

24 | 50 | 50 | 50 | 50 | 50 | 50 | 50 | 50 | 50 | 50 |

${\mathit{S}}_{\mathit{W}}^{\mathit{b}}$ | THC (kg) | CO (kg) | NO_{X} (kg) | CO_{2} (kg) | PM (kg) |
---|---|---|---|---|---|

0 | 1.17 | 0.62 | 8.48 | 629.60 | 0.14 |

0.1 | 0.94 | 4.59 | 18.35 | 899.93 | 0.32 |

0.2 | 0.90 | 5.28 | 20.30 | 953.02 | 0.35 |

0.3 | 0.90 | 5.28 | 20.30 | 953.02 | 0.35 |

0.4 | 0.90 | 5.28 | 20.30 | 953.02 | 0.35 |

${\mathit{S}}_{\mathit{W}}^{\mathit{b}}$ | THC (kg) | CO (kg) | NO_{X} (kg) | CO_{2} (kg) | PM (kg) |
---|---|---|---|---|---|

0 | 1.02 | 0.55 | 7.42 | 550.90 | 0.13 |

0.1 | 1.02 | 2.89 | 16.05 | 833.17 | 0.24 |

0.2 | 0.98 | 3.59 | 18.01 | 886.27 | 0.27 |

0.3 | 0.98 | 3.59 | 18.01 | 886.27 | 0.27 |

0.4 | 0.98 | 3.59 | 18.01 | 886.27 | 0.27 |

${\mathit{S}}_{\mathit{W}}^{\mathit{b}}$ | THC (%) | CO (%) | NO_{X} (%) | CO_{2} (%) | PM (%) |
---|---|---|---|---|---|

0 | 12.50 | 12.50 | 12.50 | 12.50 | 12.50 |

0.1 | −9.30 | 36.98 | 12.51 | 7.42 | 23.93 |

0.2 | −9.73 | 32.12 | 11.31 | 7.00 | 21.86 |

0.3 | −9.73 | 32.12 | 11.31 | 7.00 | 21.86 |

0.4 | −9.73 | 32.12 | 11.31 | 7.00 | 21.86 |

$\mathit{t}$/${\mathit{S}}_{\mathit{W}}^{\mathit{b}}$ | Without BESS | With BESS | ||||||||
---|---|---|---|---|---|---|---|---|---|---|

0 | 0.1 | 0.2 | 0.3 | 0.4 | 0 | 0.1 | 0.2 | 0.3 | 0.4 | |

1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |

2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |

3 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |

4 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |

5 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |

6 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |

7 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |

8 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |

9 | 50 | 50 | 50 | 50 | 50 | 50 | 50 | 50 | 50 | 50 |

10 | 50 | 50 | 90 | 90 | 90 | 50 | 50 | 90 | 90 | 90 |

11 | 50 | 96.4 | 96.4 | 96.4 | 96.4 | 50 | 96.4 | 96.4 | 96.4 | 96.4 |

12 | 50 | 97.5 | 97.5 | 97.5 | 97.5 | 0 | 70.2 | 70.2 | 70.2 | 70.2 |

13 | 50 | 98.5 | 98.5 | 98.5 | 98.5 | 0 | 72.9 | 72.9 | 72.9 | 72.9 |

14 | 50 | 100 | 100 | 100 | 100 | 50 | 79.7 | 79.7 | 79.7 | 79.7 |

15 | 50 | 96.9 | 96.9 | 96.9 | 96.9 | 50 | 87.9 | 87.9 | 87.9 | 87.9 |

16 | 50 | 92.7 | 92.7 | 92.7 | 92.7 | 50 | 88.7 | 88.7 | 88.7 | 88.7 |

17 | 50 | 90.2 | 90.2 | 90.2 | 90.2 | 50 | 88 | 90.2 | 90.2 | 90.2 |

18 | 50 | 90.4 | 90.4 | 90.4 | 90.4 | 50 | 88.9 | 88.2 | 88.2 | 88.2 |

19 | 50 | 90.2 | 90.2 | 90.2 | 90.2 | 50 | 89.1 | 88.7 | 88.7 | 88.7 |

20 | 50 | 50 | 90.2 | 90.2 | 90.2 | 50 | 50 | 89.1 | 89.1 | 89.1 |

21 | 50 | 50 | 50 | 50 | 50 | 50 | 50 | 50 | 50 | 50 |

22 | 50 | 50 | 50 | 50 | 50 | 50 | 50 | 50 | 50 | 50 |

23 | 50 | 50 | 50 | 50 | 50 | 50 | 50 | 50 | 50 | 50 |

24 | 50 | 50 | 50 | 50 | 50 | 50 | 50 | 50 | 50 | 50 |

${\mathit{S}}_{\mathit{W}}^{\mathit{b}}$ | GA | BPSO | Difference (%) |
---|---|---|---|

0 | −24,680.21 | −24,679.41 | 0.00326 |

0.1 | −24,528.93 | −24,520.42 | 0.03469 |

0.2 | −24,348.18 | −24,331.04 | 0.07039 |

0.3 | −24,134.06 | −24,116.79 | 0.07154 |

0.4 | −23,877.54 | −23,877.54 | 0 |

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Lujano-Rojas, J.M.; Yusta, J.M.; Artal-Sevil, J.S.; Domínguez-Navarro, J.A.
Day-Ahead Optimal Battery Operation in Islanded Hybrid Energy Systems and Its Impact on Greenhouse Gas Emissions. *Appl. Sci.* **2019**, *9*, 5221.
https://doi.org/10.3390/app9235221

**AMA Style**

Lujano-Rojas JM, Yusta JM, Artal-Sevil JS, Domínguez-Navarro JA.
Day-Ahead Optimal Battery Operation in Islanded Hybrid Energy Systems and Its Impact on Greenhouse Gas Emissions. *Applied Sciences*. 2019; 9(23):5221.
https://doi.org/10.3390/app9235221

**Chicago/Turabian Style**

Lujano-Rojas, Juan M., José M. Yusta, Jesús Sergio Artal-Sevil, and José Antonio Domínguez-Navarro.
2019. "Day-Ahead Optimal Battery Operation in Islanded Hybrid Energy Systems and Its Impact on Greenhouse Gas Emissions" *Applied Sciences* 9, no. 23: 5221.
https://doi.org/10.3390/app9235221