# Techno-Economic Optimization of an Off-Grid Solar/Wind/Battery Hybrid System with a Novel Multi-Objective Differential Evolution Algorithm

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Component Models and Energy Management Strategy

#### 2.1. Wind turbine

#### 2.2. PV Panel

^{2}) represent the power output and solar radiation under standard test conditions, ${G}_{t}$ (kW/m

^{2}) represents the actual solar incident radiation on the PV array in time t, and ${f}_{\mathrm{PV}}$(%) is the PV derating factor.

#### 2.3. Battery System

#### 2.4. Load Profile

#### 2.5. Economic Model

_{k}(year) mean the system life time of the system and the k-th component respectively, ${N}_{k}^{{}_{\mathrm{rem}}}$ (year) means the surplus life of the k-th component when the system ends, ${R}_{k}^{\mathrm{rp}}$ (year) means the last replaced time of the k-th component, INT(.) is a function that returns the smallest integer that is greater than or equal to the input number, and the relationship of the real discount rate ${i}_{\mathrm{r}}$ (%), nominal discount rate r (%) and expected inflation rate u (%) is shown as Equation (16):

#### 2.6. Rule-Based Energy Management Strategy

_{p}) is defined to represent whether the electric power generated is sufficient, and a binary variable (S

_{c}) is defined to represent whether the converter capacity is sufficient. Their definitions are shown as Equations (19) and (20).

_{p}and S

_{c}, the rule-based EMS is designed with four case scenarios as follows: Case 1,the electric power generated and the converter capacity are both sufficient (${S}_{\mathrm{p}}>0\text{}\mathrm{and}\text{}{S}_{\mathrm{c}}0$); Case 2, the electric power generated is sufficient while the converter capacity is insufficient (${S}_{\mathrm{p}}>0\text{}\mathrm{and}\text{}{S}_{\mathrm{c}}0$); Case 3, the electric power generated is insufficient while the converter capacity is sufficient (${S}_{\mathrm{p}}<0\text{}\mathrm{and}\text{}{S}_{\mathrm{c}}0$); and, Case 4, the electric power generated and the converter capacity are both insufficient (${S}_{\mathrm{p}}<0\text{}\mathrm{and}\text{}{S}_{\mathrm{c}}0$).

#### 2.7. Objective Function and Constraints

## 3. Optimization Algorithm

#### 3.1. MOEA/DADE

#### 3.1.1. Differential Evolution Mechanism

#### 3.1.2. Parameter Adaptive Mechanism

_{Cr}and S

_{F.}

_{Cr}and ${\mathrm{mean}}_{\mathrm{L}}({S}_{\mathrm{F}})$ is calculated by Equation (34).

#### 3.2. Algorithm Contrast

^{*}represents sampling points from the true Pareto frontier (PF), P represents the PF obtained by the optimization algorithm, $\mathrm{d}({x}^{*},x)$ represents the Euler distance between any two elements in P

^{*}and P, and $\left|{P}^{*}\right|$ denotes the number of elements of P

^{*}.

## 4. Case Study

#### 4.1. Data

^{2}/day) and 6.63 (m/s) respectively. The load profile is obtained by Equation (8) where ${\delta}_{\mathrm{d}}$ and ${\delta}_{\mathrm{t}}$ are assumed 10% and 20% respectively. The data profile of load, solar radiation and wind speed of each hour are shown as Figure 3.

#### 4.2. Techno-Economic Analysis

#### 4.3. Sensitivity Analysis

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## Nomenclature

DOD | BS’s allowable depth of discharge |

${f}_{\mathrm{PV}}$ | PV derating factor (%) |

${G}_{t}$ | solar incident radiation on the PV (kW/m^{2}) |

${G}_{\mathrm{STC}}$ | solar radiation under standard test conditions (${G}_{\mathrm{STC}}$ = 1 kW/m^{2}) |

$h$ | turbine hub altitude (m) |

${h}_{\mathrm{ref}}$ | anemometer altitude (m) |

$IC$ | initial capital cost ($/kW) |

${i}_{\mathrm{r}}$ | real discount rate (%) |

${k}_{\mathrm{cv}}$ | perturbation factor of load |

$O\&M$ | maintenance and operation cost ($/kW) |

${P}_{\mathrm{L}}$ | electrical load (kW) |

${P}_{\mathrm{PV}}$ | output power of PV (kW) |

${P}_{\mathrm{r}}$ | rated output power of WT (kW) |

${P}_{\mathrm{WT}}$ | output power of WT (kW) |

$r$ | nominal discount rate (%) |

$Rp$ | replacement cost ($/kW) |

$RV$ | salvage value($/kW) |

${S}_{\mathrm{c}}$ | a binary variable denoting whether the converter capacity is sufficient |

${S}_{\mathrm{p}}$ | a binary variable denoting whether the electric power generated is sufficient |

$SO{C}_{\mathrm{B}}$ | SOC BS’s state of charge |

u | expected inflation rate (%) |

$v$ | wind speed at the turbine hub altitude (m/s) |

${v}_{\mathrm{cut}-\mathrm{in}}$ | cut-in speed (m/s) |

${v}_{\mathrm{cut}-\mathrm{out}}$ | cut-out speed (m/s) |

${v}_{\mathrm{r}}$ | nominal speed (m/s) |

${v}_{\mathrm{ref}}$ | wind speed measured by anemometer (m/s) |

${\alpha}_{\mathrm{d}}$ | daily variation percent of load |

${\alpha}_{\mathrm{t}}$ | hourly variation percent of load |

${\eta}_{\mathrm{c}}$ | charge efficiency of BS |

${\eta}_{\mathrm{d}}$ | discharge efficiency of BS |

${\eta}_{\mathrm{inv}}$ | converter efficiency |

## Abbreviation

BS | battery system |

CRF | capital recovery factor |

DG | diesel system |

EMS | energy management strategy |

HRES | hybrid renewable energy systems |

LCC | life cycle cost |

LCOE | levelized cost of electricity |

LPSP | loss of power supply probability |

WT | wind turbine |

PF | Pareto frontier |

PS | Pareto set |

## References

- Huang, Y.; Li, S.; Ding, P.; Zhang, Y.; Yang, K.; Zhang, W. Optimal Operation for Economic and Exergetic Objectives of a Multiple Energy Carrier System Considering Demand Response Program. Energies
**2019**, 12, 3995. [Google Scholar] [CrossRef] [Green Version] - Yang, Y.; Guo, S.; Liu, D.; Li, R.; Chu, Y. Operation optimization strategy for wind-concentrated solar power hybrid power generation system. Energy Convers. Manag.
**2018**, 160, 243–250. [Google Scholar] [CrossRef] - Kyritsis, A.; Voglitsis, D.; Papanikolaou, N.; Tselepis, S.; Christodoulou, C.; Gonos, I.; Kalogirou, S.A. Evolution of PV systems in Greece and review of applicable solutions for higher penetration levels. Renew. Energy
**2017**, 109, 487–499. [Google Scholar] [CrossRef] - Anoune, K.; Bouya, M.; Astito, A.; Abdellah, A.B. Sizing methods and optimization techniques for PV-wind based hybrid renewable energy system: A review. Renew. Sustain. Energy Rev.
**2018**, 93, 652–673. [Google Scholar] [CrossRef] - Zahraee, S.M.; Khalaji Assadi, M.; Saidur, R. Application of Artificial Intelligence Methods for Hybrid Energy System Optimization. Renew. Sustain. Energy Rev.
**2016**, 66, 617–630. [Google Scholar] [CrossRef] - Nogueira, C.E.C.; Vidotto, M.L.; Niedzialkoski, R.K.; de Souza, S.N.M.; Chaves, L.I.; Edwiges, T.; dos Santos, D.B.; Werncke, I. Sizing and simulation of a photovoltaic-wind energy system using batteries, applied for a small rural property located in the south of Brazil. Renew. Sustain. Energy Rev.
**2014**, 29, 151–157. [Google Scholar] [CrossRef] - Malheiro, A.; Castro, P.M.; Lima, R.M.; Estanqueiro, A. Integrated sizing and scheduling of wind/PV/diesel/battery isolated systems. Renew. Energy
**2015**, 83, 646–657. [Google Scholar] [CrossRef] [Green Version] - Li, J.L.; Guo, B.Q.; Niu, M.; Xiu, X.Q.; Tian, L.T. Optimal Configuration Strategy of Energy Storage Capacity in Wind/PV/Storage Hybrid System. Trans. China Electrotech. Soc.
**2018**, 33, 1189–1196. [Google Scholar] - Smaoui, M.; Abdelkafi, A.; Krichen, L. Optimal sizing of stand-alone photovoltaic/wind/hydrogen hybrid system supplying a desalination unit. Sol. Energy
**2015**, 120, 263–276. [Google Scholar] [CrossRef] - Bhuiyan, F.A.; Yazdani, A.; Primak, S.L. Optimal sizing approach for islanded microgrids. IET Renew. Power Gener.
**2015**, 9, 166–175. [Google Scholar] [CrossRef] - Al-falahi, M.D.A.; Jayasinghe, S.D.G.; Enshaei, H. A review on recent size optimization methodologies for standalone solar and wind hybrid renewable energy system. Energy Convers. Manag.
**2017**, 143, 252–274. [Google Scholar] [CrossRef] - HOMER Pro Version 3.7 User Manual. Available online: https://www.homerenergy.com (accessed on 15 December 2019).
- Lambert, T.; Gilman, P.; Lilienthal, P. Micropower System Modeling with HOMER. 2006. Available online: http://homerenergy.com/documents/MicropowerSystemModelingWithHOMER.pdf (accessed on 15 December 2019).
- Shahzad, M.K.; Zahid, A.; ur Rashid, T.; Rehan, M.A.; Ali, M.; Ahmad, M. Techno-economic feasibility analysis of a solar-biomass off grid system for the electrification of remote rural areas in Pakistan using HOMER software. Renew. Energy
**2017**, 106, 264–273. [Google Scholar] [CrossRef] - Halabi, L.M.; Mekhilef, S.; Olatomiwa, L.; Hazelton, J. Performance analysis of hybrid PV/diesel/battery system using HOMER: A case study Sabah, Malaysia. Energy Convers. Manag.
**2017**, 144, 322–339. [Google Scholar] [CrossRef] - Hossain, M.; Mekhilef, S.; Olatomiwa, L. Performance evaluation of a stand-alone PV-wind-diesel-battery hybrid system feasible for a large resort center in South China Sea, Malaysia. Sustain. Cities Soc.
**2017**, 28, 358–366. [Google Scholar] [CrossRef] - Li, C.; Zhou, D.; Wang, H.; Lu, Y.; Li, D. Techno-economic performance study of stand-alone wind/diesel/battery hybrid system with different battery technologies in the cold region of China. Energy
**2020**, 192, 116702. [Google Scholar] [CrossRef] - Park, E.; Kwon, S.J. Towards a Sustainable Island: Independent optimal renewable power generation systems at Gadeokdo Island in South Korea. Sustain. Cities Soc.
**2016**, 23, 114–118. [Google Scholar] [CrossRef] - Rajbongshi, R.; Borgohain, D.; Mahapatra, S. Optimization of PV-biomass-diesel and grid base hybrid energy systems for rural electrification by using HOMER. Energy
**2017**, 126, 461–474. [Google Scholar] [CrossRef] - Singh, A.; Baredar, P.; Gupta, B. Techno-economic feasibility analysis of hydrogen fuel cell and solar photovoltaic hybrid renewable energy system for academic research building. Energy Convers. Manag.
**2017**, 145, 398–414. [Google Scholar] [CrossRef] - Zahboune, H.; Zouggar, S.; Krajacic, G.; Varbanov, P.S.; Elhafyani, M.; Ziani, E. Optimal hybrid renewable energy design in autonomous system using Modified Electric System Cascade Analysis and Homer software. Energy Convers. Manag.
**2016**, 126, 909–922. [Google Scholar] [CrossRef] - Sinha, S.; Chandel, S.S. Review of recent trends in optimization techniques for solar photovoltaic–wind based hybrid energy systems. Renew. Sustain. Energy Rev.
**2015**, 50, 755–769. [Google Scholar] [CrossRef] - Singh, S.; Kaushik, S.C. Optimal sizing of grid integrated hybrid PV-biomass energy system using artificial bee colony algorithm. IET Renew. Power Gener.
**2016**, 10, 642–650. [Google Scholar] [CrossRef] - Shivaie, M.; Mokhayeri, M.; Kiani-Moghaddam, M.; Ashouri-Zadeh, A. A reliability-constrained cost-effective model for optimal sizing of an autonomous hybrid solar/wind/diesel/battery energy system by a modified discrete bat search algorithm. Sol. Energy
**2019**, 189, 344–356. [Google Scholar] [CrossRef] - Bukar, A.L.; Tan, C.W.; Lau, K.Y. Optimal sizing of an autonomous photovoltaic/wind/battery/diesel generator microgrid using grasshopper optimization algorithm. Sol. Energy
**2019**, 188, 685–696. [Google Scholar] [CrossRef] - Ramli, M.A.M.; Bouchekara, H.R.E.H.; Alghamdi, A.S. Optimal sizing of PV/wind/diesel hybrid microgrid system using multi-objective self-adaptive differential evolution algorithm. Renew. Energy
**2018**, 121, 400–411. [Google Scholar] [CrossRef] - Kamjoo, A.; Maheri, A.; Dizqah, A.M.; Putrus, G.A. Multi-objective design under uncertainties of hybrid renewable energy system using NSGA-II and chance constrained programming. Int. J. Electr. Power Energy Syst.
**2016**, 74, 187–194. [Google Scholar] [CrossRef] - Nasiraghdam, H.; Jadid, S. Optimal hybrid PV/WT/FC sizing and distribution system reconfiguration using multi-objective artificial bee colony (MOABC) algorithm. Sol. Energy
**2012**, 86, 3057–3071. [Google Scholar] [CrossRef] - Mazzeo, D.; Baglivo, C.; Matera, N.; Congedo, P.M.; Oliveti, G. A novel energy-economic-environmental multi-criteria decision-making in the optimization of a hybrid renewable system. Sustain. Cities Soc.
**2020**, 52, 101780. [Google Scholar] [CrossRef] - Qingfu, Z.; Hui, L. MOEA/D: A Multiobjective Evolutionary Algorithm Based on Decomposition. IEEE Trans. Evol. Comput.
**2007**, 11, 712–731. [Google Scholar] [CrossRef] - Xinye, C.; Yexing, L.; Zhun, F.; Qingfu, Z. An External Archive Guided Multiobjective Evolutionary Algorithm Based on Decomposition for Combinatorial Optimization. IEEE Trans. Evol. Comput.
**2015**, 19, 508–523. [Google Scholar] [CrossRef] - Amrollahi, M.H.; Bathaee, S.M.T. Techno-economic optimization of hybrid photovoltaic/wind generation together with energy storage system in a stand-alone micro-grid subjected to demand response. Appl. Energy
**2017**, 202, 66–77. [Google Scholar] [CrossRef] - Zhang, J.; Sanderson, A.C. JADE: Adaptive differential evolution with optional external archive. IEEE Trans. Evol. Comput.
**2009**, 13, 945–958. [Google Scholar] [CrossRef] - Tian, Y.; Cheng, R.; Zhang, X.; Jin, Y. PlatEMO: A MATLAB Platform for Evolutionary Multi-Objective Optimization [Educational Forum]. IEEE Comput. Intell. Mag.
**2017**, 12, 73–87. [Google Scholar] [CrossRef] [Green Version] - Zitzler, E.; Deb, K.; Thiele, L. Comparison of multiobjective evolutionary algorithms: Empirical results. Evol. Comput.
**2000**, 8, 173–195. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Coello, C.A.; Cortés, N.C. Solving multiobjective optimization problems using an artificial immune system. Genet. Program. Evolvable Mach.
**2005**, 6, 163–190. [Google Scholar] [CrossRef] - 2019 ATB. Available online: https://atb.nrel.gov/electricity/2019/ (accessed on 12 March 2020).

**Figure 1.**Structure diagram of photovoltaic/wind turbine/battery system hybrid renewable energy system (PV/WT/BS HRES).

**Figure 6.**The slope of minimum levelized cost of electricity (LCOE) varying with loss of power supply probability (LPSP).

Algorithm | Parameters |
---|---|

NSGA-II | P_{c} = 0.9, P_{m} = 1/D, η_{c} = 20, η_{m} = 20 |

MOEA/D | T = 10, P_{c} = 0.9, P_{m} = 1/D, η_{c} = 20, η_{m} = 20 |

MOEA/DADE | T = 10, ${\mu}_{\mathrm{Cr}}=0.8$, ${\mu}_{\mathrm{F}}=0.5$, δ = 0.9 |

Function | NSGA-II Mean (std) | MOEA/D Mean (std) | MOEA/DADE Mean (std) |
---|---|---|---|

ZDT1 | 1.7218 × 10^{−1} (1.10 × 10^{−1}) − | 1.6737 × 10^{−1} (5.91 × 10^{−2}) − | 4.7928 × 10^{−2} (1.62 × 10^{−2}) |

ZDT 2 | 5.5298 × 10^{−1} (1.01 × 10^{−1}) − | 3.2507 × 10^{−1} (1.88 × 10^{−1}) − | 1.2261 × 10^{−1} (1.63 × 10^{−1}) |

ZDT 3 | 1.3700 × 10^{−1} (8.06 × 10^{−2}) − | 2.1748 × 10^{−1} (1.12 × 10^{−1}) − | 6.6407 × 10^{−2} (3.45 × 10^{−2}) |

ZDT 4 | 1.4230 × 10^{1} (4.08 × 10^{0}) + | 1.4189 × 10^{1} (4.79 × 10^{0}) + | 3.8489 × 10^{1} (9.88 × 10^{0}) |

ZDT 6 | 3.8877 × 10^{0} (3.78 × 10^{−1}) − | 2.3380 × 10^{0} (4.81 × 10^{−1}) − | 1.8724 × 10^{0} (3.83 × 10^{−1}) |

+/-/= | 1/4/0 | 1/4/0 |

Factor | Value | Factor | Value | ||
---|---|---|---|---|---|

Project | Lifetime (year) | 25 | Battery | Lifetime (year) | 10 |

Discount rate (%) | 6 | Initial capital ($/kW∙h) | 160 | ||

Inflation rate (%) | 2 | Replacement ($/kW∙h) | 128 | ||

PV | Lifetime (year) | 25 | O&M ($/year/kW∙h) | 1 | |

Initial capital ($/kW) | 1857 | Round trip efficiency (%) | 80 | ||

Replacement ($/kW) | 1486 | Converter | Lifetime (year) | 15 | |

O&M ($/year/kW) | 18 | Initial capital ($/kW) | 890 | ||

Wind Turbine | Lifetime (year) | 20 | Replacement ($/kW) | 800 | |

Initial capital ($/kW) | 1610 | O&M ($/year/kW) | 10 | ||

Replacement ($/kW) | 1288 | Efficiency (%) | 95 | ||

O&M ($/year/kW) | 32 |

Algorithm | NSGA-II | MOEA/D | MOEA/DADE |
---|---|---|---|

IGD | 4.7809 × 10^{−4} | 1.3926 × 10^{−3} | 7.5655 × 10^{−5} |

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**MDPI and ACS Style**

Yang, Y.; Li, R.
Techno-Economic Optimization of an Off-Grid Solar/Wind/Battery Hybrid System with a Novel Multi-Objective Differential Evolution Algorithm. *Energies* **2020**, *13*, 1585.
https://doi.org/10.3390/en13071585

**AMA Style**

Yang Y, Li R.
Techno-Economic Optimization of an Off-Grid Solar/Wind/Battery Hybrid System with a Novel Multi-Objective Differential Evolution Algorithm. *Energies*. 2020; 13(7):1585.
https://doi.org/10.3390/en13071585

**Chicago/Turabian Style**

Yang, Yong, and Rong Li.
2020. "Techno-Economic Optimization of an Off-Grid Solar/Wind/Battery Hybrid System with a Novel Multi-Objective Differential Evolution Algorithm" *Energies* 13, no. 7: 1585.
https://doi.org/10.3390/en13071585