# Multi-Objective Optimization of Hybrid Renewable Energy System Using an Enhanced Multi-Objective Evolutionary Algorithm

^{*}

## Abstract

**:**

## 1. Introduction

_{2}and SO

_{2}emissions are minimized and the output power is maximized.

## 2. Mathematical Model of the HRES

#### 2.1. Optimization Model

- Payment of purchasing and installing the PV panels, wind turbines, batteries, diesel generators, inverters and rectifiers, denoted as ${C}_{initial}$. Among them, the cost of the wind turbines includes that of the wind generator and the tower, and the expense in tower is positively related to its height.
- Cost of repair and maintenance of the devices, denoted as ${C}_{repair}$.
- Expenditure on the fuel consumed through the lifespan, denoted as ${C}_{fuel}$, which is defined by unit price (${C}_{unifuel}$) multiplying the quantity of fuel consumption (${F}_{cons}$).
- Cost of replacing the old batteries with the new ones, denoted as ${C}_{replace}$. It is calculated by ${C}_{replace}={C}_{unitBat}\times {N}_{bat}\times {N}_{replace},$ where ${C}_{unitBat}$ and ${N}_{replace}$ are the unit price of a battery and the number of replacement, respectively.
- Cost/profit of exchanging power with the public power grid (positive for buying power and negative for selling power), denoted as ${C}_{grid}$.

#### 2.2. Systematic Planning of Operation Mechanism

- Mode I: in this mode, the system is not connected to the power grid, thus the A module in Figure 2 is not considered. The energy produced by the PV panels and the wind turbines is directly provided for the direct-current (DC) load and flows to the alternating-current (AC) load through the inverter. If the provided energy exceeds the total demand (DC load plus AC load), the surplus energy will be saved in the battery storage after meeting the load. On the contrary, if it cannot satisfy the load demand, the batteries will discharge based on the $SOC$. If there still exists unmet load, the diesel generators start as the emergency power-supply. Note that the power from the diesel generators is alternating current and the part used to supply DC load is converted by the AC-to-DC rectifier.
- Mode II: in this mode, when the produced renewable energy is more than the demanded quantity and the batteries have been charged to the maximum, the surplus energy will be sold to the power grid for the profit. On the contrary, if the produced energy cannot meet the load demand, the method of obtaining the supplement is determined by the electricity price (${C}_{ep}$). Providing low ${C}_{ep}$, all of the deficit power will be bought from the public power grid and supplied to the load. On this condition, the B module does not operate. However, if the ${C}_{ep}$ is high, first the battery storage and the diesel generators are used as supplement power. Once these devices still cannot cover the gap, the required power will be bought from the power grid. To describe it more clearly, the choosing strategy when the renewable energy is insufficient is shown in Algorithm 1.

Algorithm 1: Decision strategy for the source of supplementing deficit energy in mode II. |

## 3. Multi-Objective Optimization Using MOEA/D-LPBI

#### 3.1. The Localized PBI Method

#### 3.2. MOEA/D-LPBI

Algorithm 2: MOEA/D-LPBI. |

## 4. Experimental Results

- Algorithm runs: the maximum generation is set to 50.
- Individuals: the population size is N = 100. Each candidate solution consists of six variables in the form: [${N}_{pv}|{N}_{wg}|{N}_{bat}|{N}_{dg}\left|{H}_{wg}\right|\alpha $], which, respectively, represent the number of four main components, the height of the wind tower and the inclination angle of the tilted PV panel. Assuming that each PV string connects four units in series, the number of ${N}_{pv}$ is a multiple of four.
- MOEA/D parameters: the neighbourhood size ${T}_{b}$ is set to be 10 and the probability of selecting in the neighbourhood is set as $\delta =0.8$. In the reference algorithm, the replacement size $nr$ is 2.
- Penalty values: the considered penalty values are $\theta =\left(\right)open="\{"\; close="\}">0,0.05,0.1,0.5,1,5,20,100$.

- in mode I, if the decision maker prefers to meet the energy demand 100% and limit the emission within 250 kg, then one can set ${P}_{u}$ = 0% and ${F}_{e}<250$. Then, the three filtered are shown in Table 5. Amongst these solutions, the one that produces the minimum cost is selected, i.e., the third one (in
**bold**). - in mode II, if the decision maker prefers to minimize the fuel emission and the utility of non-renewable energy, the solution having minimum ${F}_{e}$ and ${P}_{nre}$ is selected, i.e., the first one (in
**bold**). Additionally, it can be observed that the diesel generators are not used in this case.

## 5. Conclusions

## Supplementary Materials

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## Appendix A

**Figure A1.**The approximation of Pareto front (PF) under different penalty values for Walking Fish Group (WFG)45-2 (color online). (

**a**) $\theta =0$; (

**b**) $\theta =0.05$; (

**c**) $\theta =0.1$; (

**d**) $\theta =0.5$; (

**e**) $\theta =1$; (

**f**) $\theta =5$; (

**g**) $\theta =20$; and (

**h**) $\theta =100$.

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**Figure 1.**Illustration of the hybrid renewable energy system (HRES) with power grid. PV: photovoltaic.

**Figure 3.**Flowchart of system simulation. (

**a**) the isolated-island mode; and (

**b**) the grid-connected mode. SOC: state of charge.

**Figure 4.**Demonstration of the localized localized penalty-based boundary intersection (LPBI) method.

**Figure 5.**Hourly mean values of meteorological conditions. (

**a**) solar irradiation; (

**b**) wind velocity; (

**c**) temperature; and (

**d**) load.

**Figure 7.**Power generation in mode I. (

**a**) PV; (

**b**) wind generator; (

**c**) battery; (

**d**) diesel generator.

**Table 1.**The initial cost (per unit) and the annual repair expenses of the system components in HRES.

Cost | PV Panel | Wind Turbine | Wind Tower | Battery | Diesel Generator | Inverter | Rectifier |
---|---|---|---|---|---|---|---|

${C}_{initial}$ ($) | 300 | 3000 | 250/m | 126 | 1514 | 240 | 225 |

${C}_{repair}$ ($) | 30 | 50 | 2.5/m | 1.26 | 0.17/h | 12 | 8 |

Parameter | Value | Parameter | Value | Parameter | Value |
---|---|---|---|---|---|

${F}_{loss}$ | 0.73 | ${A}_{wg}\left({\mathrm{m}}^{2}\right)$ | 12.59 | $SO{C}_{max}$ | 1 |

${V}_{c}$ (m/s) | 4 | ${P}_{wgr}$ (kW) | 1 | ${P}_{dgr}$ (kW) | 2 |

${V}_{r}$ (m/s) | 14 | ${H}_{r}\left(\mathrm{m}\right)$ | 10 | ${\gamma}_{1}$ (L/kWh) | 0.08 |

${V}_{f}$ (m/s) | 20 | ${C}_{bat}$ (Ah) | 100 | ${\gamma}_{2}$ (L/kWh) | 0.25 |

${C}_{p}$ | 0.4 | ${V}_{bat}$ (V) | 12 | ${E}_{f}$ (kg/L) | 2.5 |

$\rho $ (kg/${\mathrm{m}}^{3}$) | 1.29 | $SO{C}_{min}$ | 0.2 | ${C}_{unifuel}$ ($/L) | 1.2 |

**Table 3.**The mean hypervolume (HV) results of MOEA/D-LPBI and the original version with different $\theta $ for HRES. The symbol “+”, “−” or “=” means that the counterpart is statistically better than, worse than or comparable to MOEA/D-LPBI. The best HV value for each problem is marked in

**boldface**.

HRES | Algorithm | $\mathit{\theta}=0$ | $\mathit{\theta}=0.05$ | $\mathit{\theta}=0.1$ | $\mathit{\theta}=0.5$ | $\mathit{\theta}=1$ | $\mathit{\theta}=5$ | $\mathit{\theta}=20$ | $\mathit{\theta}=100$ |
---|---|---|---|---|---|---|---|---|---|

mode I | PBI | 0.921 ${}^{-}$ | 0.903 ${}^{+}$ | 0.907 ${}^{-}$ | 0.710 ${}^{-}$ | 0.569 ${}^{-}$ | 0.694 ${}^{-}$ | 0.723 ${}^{-}$ | 0.704 ${}^{-}$ |

LPBI | 0.947 | 0.865 | 0.923 | 0.948 | 0.957 | 0.891 | 0.965 | 0.963 | |

mode II | PBI | 0.622 ${}^{=}$ | 0.621 ${}^{-}$ | 0.646 ${}^{-}$ | 0.616 ${}^{-}$ | 0.620 ${}^{-}$ | 0.559 ${}^{-}$ | 0.632 ${}^{-}$ | 0.585 ${}^{-}$ |

LPBI | 0.625 | 0.647 | 0.658 | 0.695 | 0.700 | 0.662 | 0.710 | 0.702 |

**Table 4.**The mean HV results and the standard deviations (in the parentheses) of MOEA/D-LPBI, PICEA-g and MOEA/D-TE for HRES. Just as above, their comparable results are marked by “+”, “−” or “=”.

HV | MOEA/D-LPBI | PICEA-g | MOEA/D-TE |
---|---|---|---|

mode I | 0.965 (0.089) | 0.892 (0.112) ${}^{-}$ | 0.935 (0.127) ${}^{-}$ |

mode II | 0.710 (0.068) | 0.655 (0.077) ${}^{-}$ | 0.681 (0.043) ${}^{-}$ |

Mode I | |||||||||

Solution | ${\mathit{N}}_{\mathit{pv}}$ | ${\mathit{N}}_{\mathit{wg}}$ | ${\mathit{N}}_{\mathit{bat}}$ | ${\mathit{N}}_{\mathit{dg}}$ | ${\mathit{H}}_{\mathit{wg}}$ | $\mathit{\alpha}$ | ${\mathit{F}}_{\mathit{e}}$ (kg) | ${\mathit{P}}_{\mathit{u}}(\%)$ | ${\mathit{C}}_{\mathit{s}}$ ($) |

1 | 28 | 17 | 30 | 5 | 21.605 | 58.545 | 109.404 | 0 | 13,324.550 |

2 | 28 | 18 | 30 | 8 | 14.546 | 59.662 | 151.846 | 0 | 12,345.850 |

3 | 28 | 12 | 28 | 7 | 19.081 | 48.441 | 219.842 | 0 | 10,186.780 |

Mode II | |||||||||

Solution | ${\mathit{N}}_{\mathit{pv}}$ | ${\mathit{N}}_{\mathit{wg}}$ | ${\mathit{N}}_{\mathit{bat}}$ | ${\mathit{N}}_{\mathit{dg}}$ | ${\mathit{H}}_{\mathit{wg}}$ | $\mathit{\alpha}$ | ${\mathit{F}}_{\mathit{e}}$ (kg) | ${\mathit{P}}_{\mathit{nre}}(\%)$ | ${\mathit{C}}_{\mathit{s}}$ ($) |

1 | 28 | 12 | 4 | 0 | 30 | 46.733 | 0 | 34.085 | 5733.406 |

2 | 28 | 11 | 4 | 0 | 30 | 49.870 | 0 | 34.243 | 5416.173 |

3 | 28 | 7 | 3 | 0 | 26.597 | 46.099 | 0 | 36.245 | 3903.858 |

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**MDPI and ACS Style**

Ming, M.; Wang, R.; Zha, Y.; Zhang, T.
Multi-Objective Optimization of Hybrid Renewable Energy System Using an Enhanced Multi-Objective Evolutionary Algorithm. *Energies* **2017**, *10*, 674.
https://doi.org/10.3390/en10050674

**AMA Style**

Ming M, Wang R, Zha Y, Zhang T.
Multi-Objective Optimization of Hybrid Renewable Energy System Using an Enhanced Multi-Objective Evolutionary Algorithm. *Energies*. 2017; 10(5):674.
https://doi.org/10.3390/en10050674

**Chicago/Turabian Style**

Ming, Mengjun, Rui Wang, Yabing Zha, and Tao Zhang.
2017. "Multi-Objective Optimization of Hybrid Renewable Energy System Using an Enhanced Multi-Objective Evolutionary Algorithm" *Energies* 10, no. 5: 674.
https://doi.org/10.3390/en10050674