# Multi-Objective Optimal Design of Stand-Alone Hybrid Energy System Using Entropy Weight Method Based on HOMER

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## Abstract

**:**

## 1. Introduction

_{2}emissions and cost of energy, then, GA was applied as secondary algorithm to search the optimum control strategy for each feasible combination of components with least cost. Apparently, the meta-heuristic approaches have excellent performance on identifying the global optimum solution. However, it should be noted that, complicated codification and long computational time due to massive iterative calculations are the two main shortcomings of metaheuristic approaches. In addition, a set of trade-off solutions known as the Pareto optimal set is mostly obtained by using the Pareto based meta-heuristic method. Although the Pareto optimal set is able to provide an effective support on decision-making, the final decision still relies heavily on the subjective judgments of designer.

## 2. Description of HES

#### 2.1. Mathematical Model of Major Components

#### 2.1.1. Model of Photovoltaic (PV) Panel

#### 2.1.2. Model of Wind Turbine (WT)

#### 2.1.3. Model of Battery Bank

#### 2.1.4. Model of Diesel Generator

#### 2.2. Control Strategy

## 3. Problem Formulation

#### 3.1. Evaluation Indices

#### 3.1.1. Reliability Index

#### 3.1.2. Economic Index

#### 3.1.3. Practical Index

^{2}, the occupied area of a PV array is 141 m

^{2}(each PV array contains 66 PV panels with a rated capacity of 27.885 kWp), the occupied area of a battery bank is 14.77 m

^{2}(there are 274 batteries in one battery bank). OA of HES can be described as follows:

#### 3.1.4. Environmental Sustainability Index

#### 3.2. Objective Function

## 4. Methodology

#### 4.1. Entropy Weight Method

- Step 1: Initialization of the decision matrix. Assuming that there are $m$ alternatives need to be evaluated in terms of $n$ indices, the initial decision matrix can be established as follows:$$A={\left({a}_{ij}\right)}_{m\times n}=\left[\begin{array}{ccc}{a}_{11}& \cdots & {a}_{1n}\\ \vdots & \ddots & \vdots \\ {a}_{m1}& \cdots & {a}_{mn}\end{array}\right]$$
- Step 2: Normalization of the decision matrix. In order to solve the uniformity of indices’ units, the normalization of all indices is performed. For benefit type, the higher value the better performance, the normalization can be conducted by the listed expression [41]:$${r}_{ij}=\frac{{a}_{ij}-{\mathrm{min}}_{j}\left({a}_{ij}\right)}{{\mathrm{max}}_{j}\left({a}_{ij}\right)-{\mathrm{min}}_{j}\left({a}_{ij}\right)}$$For cost type, the lower value the better property, the normalization can be conducted by the listed expression:$${r}_{ij}=\text{}\frac{{\mathrm{max}}_{j}\left({a}_{ij}\right)\text{}-\text{}{a}_{ij}}{{\mathrm{max}}_{j}\left({a}_{ij}\right)\text{}-\text{}{\mathrm{min}}_{j}\left({a}_{ij}\right)}$$Then, the normalized decision matrix $R={\left({r}_{ij}\right)}_{m\times n}$ can be obtained.
- Step 3: Calculation of weighting factors. The information entropy of each index is calculated by:$${E}_{j}=-{\left(\mathrm{ln}m\right)}^{-1}{\displaystyle \sum _{i=1}^{m}{p}_{ij}\mathrm{ln}}{p}_{ij}$$$${p}_{ij}=\frac{{r}_{ij}}{{\displaystyle \sum _{i=1}^{m}{r}_{ij}}}$$Based on the value of the information entropy, the weighting factors of each index can be calculated by:$${\omega}_{j}=\frac{1-{E}_{j}}{n-{\displaystyle \sum _{j=1}^{n}{E}_{j}}}$$

#### 4.2. Description of the Proposed Method

- Step 1: System simulation with HOMER. Several types of data including load profile, component specifications, meteorological data, system control, search space, and constraints are fed into HOMER. After that, every feasible combination in search space will be simulated in each time step of the year, and the desired output such as LPSP, LCOE, OA and RF will be calculated for further use.
- Step 2: Evaluation system establishment. Multi-objective function is carried out by adopting the weight sum method. Then, weighting factors of each index is calculated according to the output data obtained from previous step.
- Step 3: Decision making process. The rating values of each feasible configuration is calculated by multiplying the index value and corresponding weighting factors. Finally, the configuration with maximum rating value will be recommended as the optimal one.

## 5. Results and Discussions

#### 5.1. Case Study

^{2}/day and 7.29 m/s, respectively.

^{2}and 4250 m

^{2}, respectively. Therefore, the rated power of PV panel is set between 0 kWp to 948.09 kWp (correspond to 4794 m

^{2}) with a step size of 55.77 kWp, the rated number of wind turbine is predefined from 0 to 22 (correspond to 4202 m

^{2}) with a step size of 1, and the $AH$ is set between 1 h to 5 h with a step size of 1 h, which means there are 2070 configurations in the search space and to be simulated by HOMER.

#### 5.2. Economic Analysis

#### 5.3. Environmental Analysis

#### 5.4. Optimal Design of HES

- Scenario 1: The most economical scenario. Only LCOE is taken into consideration, and the rest of the indices in Equation (18) are neglected. Configuration with least LCOE would be recognized as the most economical scenario.
- Scenario 2: The most practical scenario. According to simulation results from HOMER, there are only 1941 feasible configurations compliant with the regulations presented by the State Grid Corporation of China (LOLE ≤ 8). Among them, the configuration with least OA would be recognized as the most practical scenario.
- Scenario 3: The environmental best scenario. This scenario is similar to the most economical one, except the index is composed of RF only, and the configuration with maximum RF would be recognized as the environmental best scenario.

^{2}(about 2% of the island area), still has a high practicability. Therefore, we can draw a conclusion that the best configuration can be recognized as the best trade-off solution among system reliability, economy, practicability and environmental sustainability.

#### 5.5. Analysis of the Best Configuration

#### 5.6. Sensitivity Analysis

## 6. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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

Capital cost ($/kW) | 2250 |

Operation and maintenance cost ($/year) | 0 |

Replacement cost ($/kW) | 2250 |

Derating factor (%) | 93.5 |

Efficiency at standard test condition (%) | 19.5 |

Nominal operating cell temperature (°C) | 46 |

Temperature coefficient of power (%/°C) | −0.38 |

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

Capital cost ($) | 96,500 |

Operation and maintenance cost ($/year) | 8100 |

Replacement cost ($) | 81,000 |

Cut-in wind speed (m/s) | 3 |

Cut-out wind speed (m/s) | 25 |

Rated wind speed (m/s) | 13 |

Hub height (m) | 16 |

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

Capital cost ($/battery) | 314 |

Operation and maintenance cost ($/battery/year) | 31 |

Replacement cost ($) | 314 |

Nominal capacity (kWh) | 1.92 |

Roundtrip efficiency (%) | 86 |

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

Capital cost ($) | 56,000 |

Operation and maintenance cost ($/h) | 0.277 |

Replacement cost ($) | 40,000 |

Minimum load ratio (%) | 30 |

Life time (h) | 90,000 |

Indices | LPSP | LCOE | OA | RF |
---|---|---|---|---|

Information entropy | 0.99392 | 0.991628 | 0.986248 | 0.9959 |

Weighting factors (%) | 12.7 | 18.8 | 42.6 | 25.9 |

Scenarios | Most Economical | Most Practical | Environmental Best | Best Configuration |
---|---|---|---|---|

PV panel (kW) | 613.47 | 111.54 | 948.09 | 613.47 |

Wind turbine | 15 | 1 | 22 | 9 |

Battery bank (kWh) | 898 | 449 | 2245 | 1796 |

LOLE (h/year) | 0 | 8 | 0 | 0 |

LCOE ($/kWh) | 0.2488 | 0.405 | 0.2836 | 0.2592 |

OA (m^{2}) | 4505 | 506 | 6728 | 3361 |

RF (%) | 86 | 13 | 97 | 81 |

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**MDPI and ACS Style**

Lu, J.; Wang, W.; Zhang, Y.; Cheng, S.
Multi-Objective Optimal Design of Stand-Alone Hybrid Energy System Using Entropy Weight Method Based on HOMER. *Energies* **2017**, *10*, 1664.
https://doi.org/10.3390/en10101664

**AMA Style**

Lu J, Wang W, Zhang Y, Cheng S.
Multi-Objective Optimal Design of Stand-Alone Hybrid Energy System Using Entropy Weight Method Based on HOMER. *Energies*. 2017; 10(10):1664.
https://doi.org/10.3390/en10101664

**Chicago/Turabian Style**

Lu, Jiaxin, Weijun Wang, Yingchao Zhang, and Song Cheng.
2017. "Multi-Objective Optimal Design of Stand-Alone Hybrid Energy System Using Entropy Weight Method Based on HOMER" *Energies* 10, no. 10: 1664.
https://doi.org/10.3390/en10101664