# Multi-Objective Sizing Optimization of a Grid-Connected Solar–Wind Hybrid System Using Climate Classification: A Case Study of Four Locations in Southern Taiwan

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## Abstract

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_{2}) emissions lower than 50% for the total project lifecycle time of 20 years. The case study reveals that for all four locations and two building types an HES system comprising a 15 kW photovoltaic system and a small capacity battery bank provides the optimal balance between economic and environmental objectives.

## 1. Introduction

_{2}emission in particular). Many studies have proposed sizing optimization methods and strategies for hybrid energy systems [11,12]. Optimal sizing of a hybrid renewable energy system (HRES), considering the economic objectives like NPC, initial capital and system payback period, are discussed in detail in [13,14]. Weather and energy price data are important for hybrid energy system (HES) cost optimization. Using this concept, a quantitative control approach to reduce the HES energy cost is proposed by [15]. The clear advantages of multi-objective optimization using meta-heuristics approaches as opposed to the iterative method and linear programming is discussed in [16]. Many multi-objective approaches for HES optimization have also been proposed over the years, considering several criteria, including technical, economic, environmental and socio-political objectives [17,18,19,20].

- This study proposes a general framework for multi-objective optimization of the NPC, total power bought from the grid and total CO
_{2}emission objectives for a project lifecycle of 20 years. The power trading method includes different FiT rates for solar and wind power, as stated by the local government. Climate classification scales are used to obtain the hourly load profiles. Maximum solar power and installation area constraints are used. - A fitness evaluation method with a balanced selection strategy is introduced for Pareto optimal sets to maximize the savings from the HES system while keeping the CO
_{2}emissions at least 50% lower than the “No-HES” systems. - The results of the case study show that by using the proposed balanced strategy to select a balanced HES configuration, residential building users can save up to 49% in urban building areas and up to 32% in rural buildings.
- The case study shows that wind power is crucial for reducing the total CO
_{2}emissions and reducing the dependability on the utility grid while being constrained by a limited installation area. However, the higher NPC rates makes it non-feasible for independent electricity users to use wind power without government incentives. - The case study also shows that an HES system consisting of a 15 kW PV system and small capacity battery bank provides the optimal balance between the economic and environmental objectives.

## 2. Hybrid Energy System

#### 2.1. Photovoltaic System

#### 2.2. Wind Energy Conversion System

#### 2.3. Battery Bank

#### 2.4. Hybrid Energy System

_{pv}, and wind turbine system’s power output, P

_{wt}, were calculated. Residual power, P

_{res}, was calculated by subtracting P

_{pv}and P

_{wt}from the hourly load on the system, P

_{L}. If the P

_{res}is greater than zero, the required power is bought from the utility grid, else the battery SoC is checked for maximum SoC. If the SoC is at the maximum level, the residual energy is sold to the grid, else the battery is charged and the SoC is recalculated. If the SoC is greater than or equal to the maximum SoC, the extra power is sold to the utility grid. The simulation then continues the process for maximum time limit, T (175, 200 h, 20 years).

## 3. Methodology

#### 3.1. Problem Formulation

_{cap}), replacement cost of batteries in the battery bank (C

_{rep}), operating and maintenance cost of the system (C

_{op}) and the total salvage cost of the system (C

_{s}) at the end-of-lifecycle time, T. The method for calculating the NPC is given in Equation (6).

_{cap}; also, the ${C}_{g}$ is sensitive to the market prices of fuels used by the electricity provider to generate electricity. After studying the price trends of electricity in Taiwan, an annual increase of 1.86% was applied to the electricity prices. The salvage cost, C

_{s}, of the total system was considered 20% of C

_{cap}for a system lifetime of 20 years.

_{2}emissions by the HES. Since the HES configuration used in this study does not include biomass or diesel generators, the contribution to CO

_{2}emissions was calculated by considering the total amount of electricity bought from the grid. According to Taipower’s annual sustainability report [62] for the year 2019, the current CO

_{2}emissions per kWh, CO

_{2}e, is 0.421 kg/kWh. Total CO

_{2}emissions, F

_{e}, during the project’s life-time for the grid-connected HES system can be calculated using P

_{g}, as in Equation (7).

_{area}and maximum PV system power PV

_{max}. For this study, the maximum installation area available for urban residential buildings equals 99.17 m

^{2}(30 ping) and for rural residential buildings equals 397 m

^{2}(120 ping). The maximum installation area used in this study corresponds to the average rooftop area available on these types of buildings in Taiwan. Ping is a Chinese unit of measurement for area, 1 ping = 3.3057 m

^{2}.

_{bat}), number of wind turbines (N

_{wt}), wind turbine hub height (h

_{hub}), wind turbine model (Wt

_{id}), number of PV modules in series (N

_{s}) and number of PV modules in parallel (N

_{p}); where, the values for each variable are integers, except for h

_{hub}.

#### 3.2. Optimization Algorithm

^{307}) according to the rate of satisfied constraints. The Pareto front of the final result was sorted using the method described in [68]. The complete process flowchart of the MOEA/D-DE algorithm used in this study is shown Figure 5a and the flow chart of the HES optimization is shown is Figure 5b. The optimization was carried out using the Pygmo/Python library, which is the python binding of the C++ library Pagmo [69]. The parameters used for the MOEA/D-DE algorithm for a population size of 55 are as follows: (a) generations = 60, (b) neighborhood size = 20, (c) crossover probability = 0.9, (d) differential evolution parameter = 0.5, (e) distribution index = 20 (polynomial mutation), (f) neighborhood consideration probability = 0.8 and (g) diversity preservation by inserting and replacing the old with a new population every generation = 2.

## 4. Data and Discussion

#### 4.1. Köppen–Geiger Climate Classification System

#### 4.2. Locations and Hourly Load Profile

#### 4.3. Weather Data

^{2}. Location 1 and 2 receive the highest hourly GHI throughout the year with the average maximum monthly GHI being over 600 W/m

^{2}. However, during the months of June, July and August, we can observe several variations in GHI at all locations due to the rainy season. Location 4 has the highest wind speed throughout the year, as shown in Figure 11. Locations 1, 2 and 3 show similar wind speed trends with the average wind speed value being slightly over 3 m/s. The air temperature variation between day and night is also the highest at Locations 1, 2 and 3, as shown in Figure 12. We can also confirm from Figure 12 that summer and winter temperature variations correspond to that of the hourly load profile, shown in Figure 9. It should be noted that Location 3 is a location in re-entrant terrain and, due to a higher humidity and temperature, it leads to higher electricity usages during summer.

## 5. HES Components

#### 5.1. PV Components

_{sys}). The efficiency curve for the inverters can be found in the CEC database. The cost data listed in Table 3 and Table 4 are the average of multiple online references.

#### 5.2. WECS Components

#### 5.3. Battery

## 6. Results

#### 6.1. Optimization Results

_{e}, which is consistent with the fact that a lower amount of power bought from the grid decreases the carbon emission contribution of the building. The value of PB was below zero for the NPC values below 270,000. However, in this range of the same NPC value, multiple possibilities for PB and Fe can be observed. However, in order to reach the F

_{e}target of below 40,000, a significant increase in NPC is required. Due to the larger area constraint in “Farm” buildings (Figure 14b), the multiple possibilities of PB and Fe for same value of NPC is reduced and we can observe a less complicated tradeoff curve. The higher NPC for lower F

_{e}arises due to the higher initial capital cost required by the wind turbines. Since the wind energy is not abundant in Location 1, as shown in Figure 11, the optimization converges towards a higher number of wind turbines.

_{e}and NPC with PB, for the NPC values below 300,000. At Location 2, the optimization results show a higher number of multi-configuration possibilities for these two pairs of objectives.

_{e}in a very narrow range of NPC with multiple possibilities. We can observe several configurations of variables that lead to different PB and F

_{e}values for an NPC in the range of 10,000 to 280,000. For “Farm” buildings, due to a higher availability of installation area, the trade-off curves are less complicated, as shown in Figure 16b.

_{e}sets for each location, which confirms the complexity of the HES optimization problem at these four locations. The number of batteries, N

_{bat}, in the battery bank has a high influence on the NPC; therefore, we can see multiple options. Similarly, as the value of N

_{bat}increases, the total carbon emission of the building also decreases. The higher number of batteries leads to a higher PB, since the excess power generated by the HES system is used to charge the batteries instead of being sold to the utility grid. Therefore, the higher feed-in rates are not well utilized to maximize the savings from the HES system. Therefore, the trade-off curve suggests having a lower number of batteries is preferable for profit-maximization. For Locations 1, 2 and 3, the wind speed values are not high; therefore, in the optimized results we only see two options: either 0 turbines or 2 turbines. However, for Location 4, we can find diverse combinations for WCES. Since the initial capital cost for the PV modules are much lower than the wind turbines, all the optimization results tend to converge towards a total number of 44 PV modules. The distribution of N

_{s}and N

_{p}varies at different location but does not show any significant interaction with the other variables and objectives. For both types of buildings, the wind turbine hub height does not show any significant effect for Location 1 and 2. However, for Location 3 and 4, multiple options for hub height can be observed in the converged population. We classified the results of the Pareto set into four strategies: minimum NPC (other than no HES), minimum PB, minimum F

_{e}and balanced. The method of finding the balanced configuration is discussed in the subsection below.

#### 6.2. Optimal Configuration Selection

_{e}values greater or equal to 50% of the F

_{e}of the “No HES” configuration. Therefore, the higher the fitness value of the Pareto value indicates higher savings with respect to the “No HES” configuration, while satisfying the government target of a 50% reduction in GHS/CO2 reduction. A balanced strategy can be deployed for choosing the best configuration, which has the highest fitness value. We also consider the minimum value configuration for each objective for comparison. In Table 7 and Table 8 we list the “No HES”, minimum NPC, minimum PB, minimum F

_{e}and balanced (highest fitness) for each location and two types of buildings.

_{e}strategy that by incorporating the maximum battery bank capacity, a WCES system and PV system, the HES systems at all locations can reduce total carbon emissions substantially at the cost of a very high NPC.

_{2}emissions, while preserving the economic interest of independent electricity users. Using a balanced strategy, for “Residential” buildings (Table 9), the average NPC for all four locations is approximately US$25,000, with Location 4 requiring the least NPC. The HES installation for “Residential” buildings at Location 1 can generate the maximum savings over the lifecycle period of 20 years and has a shorter payback period of 10.7 years. Location 2 also generates high savings and has the shortest payback period of 10.3 years. It is due to the highest availability of solar energy throughout the year at Locations 1 and 2, as discussed in Section 4. However, at Location 3, the highest reduction in CO

_{2}emissions can be observed but at a price of a higher NPC, less savings and a longer payback period. A longer payback period for Location 3 can be justified due to less availability of solar energy and higher electricity demands. As shown in Table 9, the average NPC for “Farm” buildings at the four locations is approximately US$26,250. The savings are also much lower than that of “Residential” buildings, with Location 3 being the only exception. On average, payback period for “Farm” buildings are longer than residential buildings. When using models with higher number of parameters and more precise equations, the simulation results tends to be more realistic but at the cost of computation time. The grid-connected HES model used in this study takes an average of 4.7 s/evaluation (using multi-threading and multi-processing techniques). The optimization problem considers 25 × 3 × 150 × 3 × 44 × 6 combinations (8,910,000) for “Residential” and 17,820,000 combinations for “Farm” building types. Using the enumerative technique, it would take 1.33 years and 2.66 years for two types of buildings. However, using the MOEA/D_DE technique it only requires 55 × 60 combinations (3300) for each building type, approximately equal to 4.3 h.

## 7. Conclusions

- This study provides a general multi-objective optimization framework for an HES sizing, considering the climate classification of location, feed-in tariff, installation area restrictions and maximum HES capacity restrictions using economic and environmental objectives. A case study of four locations in the southern Taiwan region is presented, for two types of residential buildings, which analyzes the HES system feasibility and optimal sizing using multi-objective Pareto set analysis.
- A balanced strategy for choosing the optimal configuration of an HES system is introduced that maximizes the savings for independent users while meeting the government set goals of reducing carbon emissions.

- Feed-in tariff can significantly affect the economic objectives. However, the higher NPC of wind turbines makes it economically unfeasible for residential users to utilize the maximum potential of wind energy, even in presence of significantly higher FiT rates for wind-generated electricity.
- Higher NPC systems, which includes wind turbines, does not significantly reduce the reliability on the utility grid, neither affect the total cost of power bought from the grid during the project lifetime, as PV-only systems with a lower NPC can provide a significant reduction in PB.
- An HES configuration with two small wind turbines and a high battery bank capacity can significantly reduce the total carbon emission contribution of a residential building and reduce the cost of power bought from the grid.
- A balanced strategy for choosing an HES configuration that can generate maximum profit for independent electricity users while preserving the environment can be utilized to encourage the usage of an HES among residential buildings.

- For the two building types at all four locations studied in this research, an HES with a 15 kW PV system and a small capacity battery bank can generate maximum savings for the user and also reduces the carbon emission contribution by more than 50%.
- Solar energy availability of a location does not significantly affect the NPC. However, it does significantly affect the amount of power bought and sold to the grid. The total payback period of the system is also increased at Locations 3 and 4, where less GHI throughout the year is observed. However, at Locations 1 and 2, where solar energy availability is higher, a payback period shorter than 11 years is observed for “Residential” and 15.7 and 13.6 years is observed for “Farm” buildings, respectively.

_{2}emissions, a battery bank is crucial to the HES. As shown in this study, a battery bank of capacity ranging from 700 Ah to 1100 Ah is suitable for “Residential” and 900 Ah to 1900 Ah is suitable for “Farm” buildings. The future directions for this work include creating an hourly electric load database for the different cities and locations of Taiwan using TMY3 data and average monthly electricity consumption for the location based on different building types. A graphical user interface also will be developed for the sizing optimization framework presented in this study. Improvements in simulation and evaluation time is another possibility. We will also explore other meta-heuristic algorithms, in order to improve the convergence time.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Abbreviations

C_{bat} | Nominal capacity of individual battery |

C_{cap} | Total capital cost of the HES system |

CEC | California Energy Commission |

C_{g} | Cost of electricity bought from the utility grid |

CO_{2}e | CO_{2} emission |

C_{op} | Operating and maintenance cost of the HES system |

C_{rep} | Replacement cost for batteries |

C_{s} | Salvage cost of the HES system at the end-of-lifecycle time |

DHI | Direct horizontal irradiance |

DISC | Direct insolation solar code |

DNI | Direct normal irradiance |

F | Objective function |

F_{e} | Total CO_{2} emission |

FiT | Feed-in-tariff |

FiT_{pv} | Feed-in tariff for PV energy |

FiT_{we} | Feed-in tariff for wind energy |

gen | Generation |

GHG | Greenhouse gas |

GHI | Global horizontal irradiance |

HES | Hybrid energy system |

h_{hub} | Wind turbine hub height |

h_{measured} | Wind speed data measurement height |

HRES | Hybrid renewable energy system |

I_{area} | Installation area constrain for HES system |

I_{L} | Light generated current (PV module) |

I_{mp} | Maximum power current (PV module) |

I_{sc} | Short circuit current (PV module) |

lat | Latitude |

lon | Longitude |

MOEA/D | Multi-objective evolutionary algorithm based on decomposition |

MOEA/D-DE | Differential evolution variant of multi-objective evolutionary algorithm based on decomposition |

N_{bat} | Number of batteries in battery bank |

N_{cell} | Number of cells (PV module) |

No-HES | Without hybrid energy system |

N_{p} | Number of PV modules in parallel |

NPC | Net present cost |

N_{s} | Number of PV modules in series |

NSGA-II | Non-dominated sorting genetic algorithm |

N_{wt} | Number of wind turbines |

PB | Total cost of power bought from grid |

P_{g}, P_{bought} | Power bought from utility grid |

P_{L} | Power required by electrical load |

P_{pv} | Power produced by PV system |

P_{rated} | Rated Power |

P_{res} | Residual power |

P_{smooth} | Smoothed power curve at standard wind speed in manufacturer power curve |

P_{sold} | Power sold to utility grid |

P_{spv} | PV power sold to utility grid |

P_{STC} | Power at standard test condition (PV module) |

P_{swe} | Wind energy power sold to utility grid |

P_{sys} | Total PV system power |

P_{t} | Power at time step t |

PV | Photovoltaic |

PV_{max} | Maximum PV power constrain |

P_{wt} | Power produced by wind turbines |

R_{sh} | Shunt resistance (PV module) |

SoC | State of charge of battery |

t | Time step |

T | Maximum time step, end-of-life cycle time |

T_{NOCT} | Nominal operating condition temperature (PV module) |

V_{bat} | Nominal voltage of individual battery |

v_{hub} | Wind speed at wind turbine hub height |

v_{i} | Wind speed at interval I in the manufacturer’s power curve |

V_{mp} | Maximum power voltage (PV module) |

V_{rated} | Rated output voltage |

v_{std} | Standard wind speed in the manufacturer’s power curve |

WECS | Wind energy conversion system |

WT | Wind turbine |

Wt_{id} | Wind turbine identification number |

z_{0} | Surface roughness length |

Δt | Interval between two time steps |

Δvi | Wind speed step in manufacturer power curve |

η_{bat} | Round-trip efficiency of an individual battery |

η_{sd} | Self-discharge rate of an individual battery |

## References

- World Meteorological Organization. WMO Statement on the Status of the Global Climate in 2019; World Meteorological Organization: Geneva, Switzerland, 2019; ISBN 9789263111081. [Google Scholar]
- Rogelj, J.; Shindell, D.; Jiang, K.; Fifita, S.; Forster, P.; Ginzburg, V.; Handa, C.; Kheshgi, H.; Kobayashi, S.; Kriegler, E.; et al. Mitigation Pathways Compatible with 1.5 °C in the Context of Sustainable Development; Intergovernmental Panel on Climate Change: Genève, Switzerland, 2018; p. 82. [Google Scholar]
- Global Climate Action Summit. Report of the Secretary-General on the 2019 Climate Action Summit and the Way Forward in 2020; Global Climate Action Summit: San Francisco, CA, USA, 2019. [Google Scholar]
- IRENA. Future of Solar Photovoltaic: Deployment, Investment, Technology, Grid Integration and Socio-Economic Aspects; IRENA: Abu Dhabi, UAE, 2019; ISBN 9789292601560. [Google Scholar]
- IRENA Future of Wind Deployment. Investment, Technology, Grid Integration and Socio-Economic Aspects; IRENA: Abu Dhabi, UAE, 2019; ISBN 9789292601553. [Google Scholar]
- Wu, T. Green Energy Promotion Policies and Industry Development in Taiwan; Industrial Technology Research Institute: Zhudong, Taiwan, 2015. [Google Scholar]
- Bureau of Energy Ministry of Economic Affairs. Policy for Promoting Renewable Energy in Taiwan; Bureau of Energy Ministry of Economic Affairs: Taipei, Taiwan, 2013. [Google Scholar]
- Bureau of Energy Ministry of Economic Affairs. 2020 Feed-In Tariffs of Renewable Energy; Bureau of Energy Ministry of Economic Affairs: Taipei, Taiwan, 2020; pp. 1–2. [Google Scholar]
- Environmental Protection Administration. Taiwan’s Strategies and Achievements in Greenhouse Gas Emission Reduction. Environ. Policy Mon.
**2015**, 18, 1–12. [Google Scholar] - International Carbon Action Partnership, Berlin. Taiwan passes GHG Reduction Law and Considers Emissions Trading, 22 June 2015. Available online: https://icapcarbonaction.com/en/news-archive/285-taiwan-passes-ghg-reduction-law-and-considers-emissions-trading (accessed on 3 January 2020).
- Conti, P.; Lutzemberger, G.; Schito, E.; Poli, D.; Testi, D. Multi-objective optimization of off-grid hybrid renewable energy systems in buildings with prior design-variable screening. Energies
**2019**, 12, 3026. [Google Scholar] [CrossRef][Green Version] - Singh, R.; Bansal, R.C.; Singh, A.R.; Naidoo, R. Multi-objective optimization of hybrid renewable energy system using reformed electric system cascade analysis for islanding and grid connected modes of operation. IEEE Access
**2018**. [Google Scholar] [CrossRef] - González, A.; Riba, J.R.; Rius, A.; Puig, R. Optimal sizing of a hybrid grid-connected photovoltaic and wind power system. Appl. Energy
**2015**, 154, 752–762. [Google Scholar] - González, A.; Riba, J.R.; Rius, A. Optimal sizing of a hybrid grid-connected photovoltaic-wind-biomass power system. Sustainability
**2015**, 7, 12787–12806. [Google Scholar] - Taebnia, M.; Heikkilä, M.; Mäkinen, J.; Kiukkonen-Kivioja, J.; Pakanen, J.; Kurnitski, J. A qualitative control approach to reduce energy costs of hybrid energy systems: Utilizing energy price and weather data. Energies
**2020**, 13, 1401. [Google Scholar] [CrossRef][Green Version] - Alaaeddin, M.H.; Zakaria, A.; Jani, J.M.; Seyajah, N. Optimization techniques and multi-objective analysis in hybrid solar- wind power systems for grid-connected supply. IOP Conf. Ser. Mater. Sci. Eng.
**2019**, 538, 6–12. [Google Scholar] [CrossRef] - Eriksson, E.L.V.; Gray, E.M. Optimization of renewable hybrid energy systems—A multi-objective approach. Renew. Energy
**2018**, 133, 971–999. [Google Scholar] [CrossRef] - Mohammed, O.H.; Amirat, Y.; Benbouzid, M. Economical evaluation and optimal energy management of a stand-alone hybrid energy system handling in genetic algorithm strategies. Electronics
**2018**, 7, 233. [Google Scholar] [CrossRef][Green Version] - Murty, V.V.S.N.; Kumar, A. Multi-objective energy management in microgrids with hybrid energy sources and battery energy storage systems. Prot. Control. Mod. Power Syst.
**2020**, 5, 1–20. [Google Scholar] [CrossRef][Green Version] - Mazzeo, D.; Oliveti, G.; Baglivo, C.; Congedo, P.M. Energy reliability-constrained method for the multi-objective optimization of a photovoltaic-wind hybrid system with battery storage. Energy
**2018**, 156, 688–708. [Google Scholar] [CrossRef] - Deb, K.; Pratap, A.; Agarwal, S.; Meyarivan, T. A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans. Evol. Comput.
**2002**, 6, 182–197. [Google Scholar] [CrossRef][Green Version] - Zhang, Q.; Li, H. MOEA/D: A multiobjective evolutionary algorithm based on decomposition. IEEE Trans. Evol. Comput.
**2007**, 11, 712–731. [Google Scholar] [CrossRef] - Mohamad, F.; Teh, J.; Abunima, H. Multi-objective optimization of solar/wind penetration in power generation systems. IEEE Access
**2019**, 7, 169094–169106. [Google Scholar] [CrossRef] - Ren, H.; Lu, Y.; Wu, Q.; Yang, X.; Zhou, A. Multi-objective optimization of a hybrid distributed energy system using NSGA-II algorithm. Front. Energy
**2018**, 12, 518–528. [Google Scholar] [CrossRef] - Li, F.F.; Qiu, J.; Wei, J.H. Multiobjective optimization for hydro-photovoltaic hybrid power system considering both energy generation and energy consumption. Energy Sci. Eng.
**2018**, 6, 362–370. [Google Scholar] [CrossRef] - Yong, Y.; Rong, L. Techno-economic optimization of an off-grid solar/wind/battery hybrid system with a novel multi-objective differential evolution algorithm. Energies
**2020**, 13, 1585. [Google Scholar] [CrossRef][Green Version] - Xiao, J.; Li, J.J.; Hong, X.X.; Huang, M.M.; Hu, X.M.; Tang, Y.; Huang, C.Q. An improved MOEA/D based on reference distance for software project portfolio optimization. Complexity
**2018**, 2018, 1–16. [Google Scholar] [CrossRef] - Ju, Y.; Zhang, S.; Ding, N.; Zeng, X.; Zhang, X. Complex network clustering by a multi-objective evolutionary algorithm based on decomposition and membrane structure. Sci. Rep.
**2016**, 6, 33870. [Google Scholar] [CrossRef][Green Version] - Ellefsen, K.O.; Lepikson, H.A.; Albiez, J.C. Multiobjective coverage path planning: Enabling automated inspection of complex, real-world structures. Appl. Soft Comput. J.
**2017**, 61, 264–282. [Google Scholar] [CrossRef][Green Version] - Hsiao, J.C.; Shivam, K.; Chou, C.L.; Kam, T.Y. A shape design optimization of a robot arm using a surrogate-based evolutionary approach. Appl. Sci.
**2020**, 10, 2223. [Google Scholar] [CrossRef][Green Version] - 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. [Google Scholar] [CrossRef][Green Version] - Control, J.; Muthukumar, R.; Balamurugan, P. A novel power optimized hybrid renewable energy system using neural computing and bee algorithm. Automatika
**2019**, 60, 332–339. [Google Scholar] - Aziz, A.S.; Tajuddin, M.F.N.; Adzman, M.R.; Ramli, M.A.M.; Mekhilef, S. Energy management and optimization of a PV/diesel/battery hybrid energy system using a combined dispatch strategy. Sustainability
**2019**, 11, 683. [Google Scholar] [CrossRef][Green Version] - Mohamed, A.A.A.; Ali, S.; Alkhalaf, S.; Senjyu, T.; Hemeida, A.M. Optimal allocation of hybrid renewable energy system by multi-objectivewater cycle algorithm. Sustainability
**2019**, 11, 6550. [Google Scholar] [CrossRef][Green Version] - Shi, B.; Wu, W.; Yan, L. Size optimization of stand-alone PV/wind/diesel hybrid power generation systems. J. Taiwan Inst. Chem. Eng.
**2017**, 73, 93–101. [Google Scholar] [CrossRef] - Maheri, A. Multi-objective design optimisation of standalone hybrid wind-PV-diesel systems under uncertainties. Renew. Energy
**2014**, 66, 650–661. [Google Scholar] [CrossRef][Green Version] - Donado, K.; Navarro, L.; Quintero, M.C.G.; Pardo, M. HYRES: A multi-objective optimization tool for proper configuration of renewable hybrid energy systems. Energies
**2019**, 13, 26. [Google Scholar] [CrossRef][Green Version] - Fu, T.; Wang, C. A novel ensemble wind speed forecasting model in the longdong area of loess plateau in china. Math. Probl. Eng.
**2018**, 2018, 672–685. [Google Scholar] [CrossRef] - Ascencio-Vásquez, J.; Brecl, K.; Topič, M. Methodology of Köppen-Geiger-Photovoltaic climate classification and implications to worldwide mapping of PV system performance. Sol. Energy
**2019**, 191, 672–685. [Google Scholar] [CrossRef] - De Carli, M.; Bernardi, A.; Cultrera, M.; Santa, G.D.; Di Bella, A.; Emmi, G.; Galgaro, A.; Graci, S.; Mendrinos, D.; Mezzasalma, G.; et al. A database for climatic conditions around europe for promoting GSHP solutions. Geosciences
**2018**, 8, 1–19. [Google Scholar] [CrossRef][Green Version] - 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] - Braun, R.; Haag, M.; Stave, J.; Abdelnour, N.; Eicker, U. System design and feasibility of trigeneration systems with hybrid photovoltaic-thermal (PVT) collectors for zero energy office buildings in different climates. Sol. Energy
**2020**, 196, 39–48. [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] - Holmgren, W.; Hansen, C.; Mikofski, M. pvlib python: A python package for modeling solar energy systems. J. Open Source Softw.
**2018**, 3, 884. [Google Scholar] [CrossRef][Green Version] - De Soto, W.; Klein, S.A.; Beckman, W.A. Improvement and validation of a model for photovoltaic array performance. Sol. Energy
**2006**, 80, 78–88. [Google Scholar] [CrossRef] - Kratochvil, J.A.; Boyson, W.E.; King, D.L. Photovoltaic Array Performance Model. Ph.D. Thesis, Sandia National Laboratories, Albuquerque, NM, USA, December 2004. [Google Scholar]
- Reda, I.; Andreas, A. Solar position algorithm for solar radiation applications. Sol. Energy
**2004**, 76, 577–589. [Google Scholar] [CrossRef] - Ineichen, P.; Perez, R. A new airmass independent formulation for the Linke turbidity coefficient. Sol. Energy
**2002**, 73, 151–157. [Google Scholar] [CrossRef][Green Version] - Perez, R.; Ineichen, P.; Moore, K.; Kmiecik, M.; Chain, C.; George, R.; Vignola, F. A new operational model for satellite-derived irradiances: Description and validation. Sol. Energy
**2002**, 73, 307–317. [Google Scholar] [CrossRef][Green Version] - Hay, J.E.; Davies, J.A. Calculation of the solar radiation incident on an inclined surface. Proc. First Can. Sol. Radiat. Data Work.
**1980**, 23, 301–307. [Google Scholar] - System Advisor Model. Available online: https://github.com/NREL/SAM/tree/develop/deploy/libraries (accessed on 10 February 2020).
- King, D.; Gonzalez, S.; Galbraith, G.; Boyson, W. Performance model for grid-connected photovoltaic inverters. Sandia Natl. Lab.
**2007**, 38. [Google Scholar] [CrossRef][Green Version] - Maxwell, E.L. A Quasi-Physical Model for Converting Hourly Global Horizontal to Direct Normal Insolation; Solar Energy Research Inst.: Golden, CO, USA, 1987; pp. 35–46. [Google Scholar]
- Maxwell, E. DISC Model. Available online: https://www.nrel.gov/grid/solar-resource/disc.html (accessed on 12 February 2020).
- Jordan, D.C.; Kurtz, S.R. Photovoltaic degradation rates—An analytical review. Prog. Photovolt. Research Appl.
**2012**. [Google Scholar] [CrossRef][Green Version] - Knorr, K. Modellierung Von Raum-Zeitlichen Eigenschaften Der Windenergieeinspeisung Für Wetterdatenbasierte Windleistungssimulationen; Kassel University Press GmbH: Kassel, Germany, 2016. [Google Scholar]
- Staffell, I.; Pfenninger, S. Using bias-corrected reanalysis to simulate current and future wind power output. Energy
**2016**, 114, 1224–1239. [Google Scholar] [CrossRef][Green Version] - Gasch, R.; Twele, J. Wind Power Plants; Springer: Berlin, Germany, 2012; ISBN 978-3-642-22937-4. [Google Scholar]
- Sabine, H.; Schachler, B.; Krien, U. Windpowerlib—A python library to model wind power plants (Version V0.2.0). Zenodo
**2019**. [Google Scholar] [CrossRef] - Staffell, I.; Green, R. How does wind farm performance decline with age? Renew. Energy
**2014**, 66, 775–786. [Google Scholar] [CrossRef][Green Version] - Taiwan Power Company. Rate Schedules. Available online: https://www.taipower.com.tw/upload/317/2018032816540459885.pdf (accessed on 24 January 2020).
- Taiwan Power Company. 2019 Sustainability Report. Available online: https://csr.taipower.com.tw/upload/132/2019110109130980581.pdf (accessed on 24 February 2020).
- Liu, B.; Fernández, F.V.; Zhang, Q.; Pak, M.; Sipahi, S.; Gielen, G. An enhanced MOEA/D-DE and its application to multiobjective analog cell sizing. In Proceedings of the 2010 IEEE Congress on Evolutionary Computation, Barcelona, Spain, 18–23 July 2010. [Google Scholar]
- Li, H.; Zhang, Q. Multiobjective optimization problems with complicated pareto sets, MOEA/ D and NSGA-II. IEEE Trans. Evol. Comput.
**2009**, 13, 284–302. [Google Scholar] [CrossRef] - Peng, W.; Zhang, Q.; Li, H. Comparison between MOEA/D and NSGA-II on the multi-objective travelling salesman problem. Stud. Comput. Intell.
**2009**, 171, 309–324. [Google Scholar] - Ma, X.; Zhang, Q.; Tian, G.; Yang, J.; Zhu, Z. On tchebycheff decomposition approaches for multiobjective evolutionary optimization. IEEE Trans. Evol. Comput.
**2018**, 22, 226–244. [Google Scholar] [CrossRef] - Kuri Morales, A.F.; Quezada, C.C. A universal eclectic genetic algorithm for constrained optimization. In Proceedings of the 6th European Congress on Intelligent Techniques & Soft Computing EUFIT’98, Aachen, Germany, 7–10 September 1998. [Google Scholar]
- Deb, K.; Agrawal, S.; Pratap, A.; Meyarivan, T. A fast elitist non-dominated sorting genetic algorithm for multi-objective optimization: NSGA-II. CEUR Workshop Proc.
**2000**, 1133, 849–858. [Google Scholar] - Biscani, F.; Izzo, D.; Jakob, W.; GiacomoAcciarini, M.; Märtens, M.C.; Mereta, A.; Kaldemeyer, C.; Lyskov, S.; Corlay, S. esa/pagmo2: Pagmo 2.15.0. Zenodo
**2020**. [Google Scholar] [CrossRef] - Wilcock, A.A. Köppen after fifty years. Ann. Assoc. Am. Geogr.
**1968**, 58, 12–28. [Google Scholar] [CrossRef] - Beck, H.E.; Zimmermann, N.E.; McVicar, T.R.; Vergopolan, N.; Berg, A.; Wood, E.F. Present and future köppen-geiger climate classification maps at 1-km resolution. Sci. Data
**2018**, 5, 1–12. [Google Scholar] [CrossRef] [PubMed][Green Version] - Central Weather Bureau, Taiwan. Available online: https://www.cwb.gov.tw/eng/ (accessed on 22 April 2020).
- Office of Energy Efficiency & Renewable Energy (EERE)Commercial and Residential Hourly Load Profiles for all TMY3 Locations in the United States. Available online: https://openei.org/doe-opendata/dataset/commercial-and-residential-hourly-load-profiles-for-all-tmy3-locations-in-the-united-states (accessed on 14 March 2020).
- Copernicus Climate Change Service (C3S) (2017): ERA5: Fifth Generation of ECMWF Atmospheric Reanalyses of the Global Climate. Copernicus Climate Change Service Climate Data Store (CDS). Available online: https://cds.climate.copernicus.eu/cdsapp#!/home (accessed on 20 March 2020).
- Petrelli, P. coecms/era5: Python base codes to interface the CDS api and automate ERA5 download: First release v0.1. Zenodo
**2019**. [Google Scholar] [CrossRef] - Garche, J.; Dyer, C.K.; Moseley, P.T.; Ogumi, Z.; Rand, D.A.J.; Scrosati, B. Encyclopedia of Electrochemical Power Sources, 2nd ed.; Elsevier Science: Amsterdam, The Netherlands, 2009; ISBN 9780444520937. [Google Scholar]

**Figure 5.**(

**a**) Process flow chart of the multi-objective evolutionary algorithm based on decomposition (MOEA/D-DE). (

**b**) HES optimization flow chart.

**Figure 6.**Köppen–Geiger climate map of Taiwan [71].

**Figure 7.**Köppen–Geiger climate map of the USA [71].

**Figure 8.**Locations used for the optimization study, chosen based on the Köppen–Geiger climate scale.

**Figure 16.**Pareto optimal sets for Location 3 (Cwa), for building type (

**a**) Residential and (

**b**) Farm.

**Figure 18.**Pairwise plots of the optimized solution for “Residential” buildings for (

**a**) Location 1 (Aw), (

**b**) Location 2 (Am), (

**c**) Location 3 (Cwa) and (

**d**) Location 4 (Af).

**Figure 19.**Pairwise plots of the optimized solution for “Farm” buildings for (

**a**) Location 1 (Aw), (

**b**) Location 2 (Am), (

**c**) Location 3 (Cwa) and (

**d**) Location 4 (Af).

Serial Number | Parameter Name | Value |
---|---|---|

1. | Surface azimuth angle | 178° |

2. | Surface tilt angle | 18° |

3. | Performance degradation | 0.64%/year |

Location | Climate | TMY3 Dataset ID |
---|---|---|

1. | Aw | USA_FL_Key.West.Intl.AP.722010 |

2. | Am | USA_FL_Miami-Kendall-Tamiami.Executive.AP.722029 |

3. | Cwa | USA_SC_Anderson.County.AP.723125 |

4. | Af | USA_FL_West.Palm.Beach.Intl.AP.722030 |

Parameters | Value |
---|---|

P_{STC} | 329.9 W |

N_{cell} | 72 |

V_{mp} | 37.66 V |

I_{mp} | 8.76 A |

I_{sc} | 9.27 A |

I_{L} | 9.272 A |

T_{NOCT} | 45.2 °C |

R_{sh} | 1294.5 Ω |

Length | 1.966 m |

Width | 0.992 m |

Cost | 0.3 US$/W_{p} |

Yearly operation cost | 0.018 US$/W_{p} |

Parameters | P_{sys} < 5.3 kW | P_{sys} < 6.6 kW | P_{sys} < 7.6 kW | P_{sys} < 10 kW | P_{sys} < 12.5 kW | P_{sys} < 15 kW |
---|---|---|---|---|---|---|

Model | Motech Industries PVMate 5300U | Delta ElectronicsSOLIVIA 6.6 G4 | Delta ElectronicsSOLIVIA 7.6 G4 | SolarEdge Tech. Ltd. SE10000H | Fronius Primo 12.5 | Fronius Primo 15.0 |

P_{rated} (W) | 5300 | 6600 | 7600 | 10,000 | 12,500 | 15,000 |

V_{rated} (V) | 240 | 240 | 240 | 240 | 240 | 240 |

Cost (US$) | 900 | 1500 | 1930 | 2300 | 3950 | 4500 |

Parameters | DS-700 | DS-1500W | DS-3000 |
---|---|---|---|

Configuration ID | 0 | 1 | 2 |

Rated Power (W) | 700 | 1500 | 3000 |

Rated wind speed (m/s) | 12 | 12 | 12 |

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

Cut-out wind speed (m/s) | 15 | 15 | 15 |

Survival wind speed (m/s) | 60 | 60 | 60 |

Rotor diameter (m) | 1.93 | 2.8 | 4.0 |

Rotor height (m) | 1.6 | 2.99 | 4.16 |

Controller rated power (W) | 2000 | 2000 | 4000 |

Controller efficiency (%) | 97 | 97 | 97 |

Controller output Voltage (V) | 180~270 | 180~270 | 180~270 |

Cost (US$) | 12,530 | 24,725 | 26,370 |

Cost of hub (US$/m) | 100 | 120 | 120 |

Yearly Operation cost (US$) | 550 | 750 | 850 |

Parameters | Values |
---|---|

Type | Lead–Acid |

Rated Voltage (V) | 12 |

Rated Capacity (Ah) | 100 |

Charge efficiency (%) | 80 |

Discharge efficiency (%) | 100 |

Self-discharge rate (%/720 h) | 5 |

Standard warranty period (years) | 4 |

Replacement period (years) | 4 |

Cost (US$) | 150 |

Replacement cost (US$) | 100 |

Location | Climate | Strategy | N_{bat} | N_{wt} | h_{hub} | Wt_{id} | Ns | Np | NPC (×10 ^{3}) | PB (×10 ^{3}) | Fe (×10 ^{3}) | Fitness |
---|---|---|---|---|---|---|---|---|---|---|---|---|

1 | Aw | No HES | - | - | - | - | - | - | 0.0 | 36.7 | 153.7 | −∞ |

NPC | 0 | 0 | - | - | 17 | 1 | 6.7 | 22.6 | 110.5 | −∞ | ||

PB | 0 | 2 | 34 | 0 | 44 | 1 | 1389.8 | −16.5 | 85.4 | −36.4 | ||

F_{e} | 24 | 2 | 33 | 0 | 44 | 1 | 1392.5 | 537.9 | 35.4 | −36.96 | ||

Balanced | 8 | 0 | - | - | 44 | 1 | 24.6 | −4.9 | 71.2 | 0.46 | ||

2 | Am | No HES | - | - | - | - | - | - | 0.0 | 32.9 | 137.9 | −∞ |

NPC | 0 | 0 | - | - | 17 | 1 | 6.7 | 18.6 | 95.8 | −∞ | ||

PB | 0 | 2 | 32 | 0 | 44 | 1 | 1284.6 | −19.7 | 76.9 | −37.4 | ||

F_{e} | 24 | 2 | 33 | 0 | 44 | 1 | 1342.8 | −2.03 | 24.4 | −39.7 | ||

Balanced | 9 | 0 | - | - | 44 | 1 | 25.3 | −8.4 | 56.3 | 0.49 | ||

3 | Cwa | No HES | - | - | - | - | - | - | 0.0 | 30.4 | 127.3 | −∞ |

NPC | 0 | 0 | - | - | 3 | 5 | 5.7 | 19.5 | 93.4 | −∞ | ||

PB | 2 | 2 | 33 | 0 | 14 | 3 | 1364.8 | −12.2 | 65.4 | −43.49 | ||

F_{e} | 24 | 2 | 34 | 0 | 44 | 1 | 1450.2 | −0.7 | 24.6 | −46.68 | ||

Balanced | 11 | 0 | - | - | 11 | 4 | 26.3 | −1.0 | 50.7 | 0.17 | ||

4 | Af | No HES | - | - | - | - | - | - | 0.0 | 33.9 | 141.9 | −∞ |

NPC | 0 | 0 | - | - | 23 | 1 | 8.9 | 15.5 | 95.6 | −∞ | ||

PB | 0 | 2 | 34 | 2 | 36 | 1 | 1449.7 | −50.6 | 45.9 | −40.27 | ||

F_{e} | 24 | 2 | 26 | 2 | 36 | 1 | 9268.4 | −36.6 | 13.1 | −25.26 | ||

Balanced | 7 | 0 | - | - | 43 | 1 | 23.6 | −1.7 | 67.5 | 0.35 |

Location | Climate | Strategy | N_{bat} | N_{wt} | h_{hub} | Wt_{id} | Ns | Np | NPC (×10 ^{3}) | PB (×10 ^{3}) | Fe (×10 ^{3}) | Fitness |
---|---|---|---|---|---|---|---|---|---|---|---|---|

1 | Aw | No HES | - | - | - | - | - | - | 0.0 | 47.7 | 199.8 | −∞ |

NPC | 0 | 0 | - | - | 9 | 2 | 6.9 | 33.6 | 150.7 | −∞ | ||

PB | 0 | 2 | 34 | 2 | 44 | 1 | 1492.1 | −5.9 | 114.1 | −30.16 | ||

F_{e} | 50 | 2 | 34 | 2 | 44 | 1 | 1515.5 | 12.4 | 62.2 | −31.03 | ||

Balanced | 19 | 0 | - | - | 44 | 1 | 26.8 | 10.6 | 99.0 | 0.21 | ||

2 | Am | No HES | - | - | - | - | - | - | 0.0 | 42.8 | 179.3 | −∞ |

NPC | 0 | 0 | - | - | 4 | 4 | 5.3 | 30.7 | 134.8 | −∞ | ||

PB | 0 | 2 | 33 | 2 | 44 | 1 | 1399.3 | −8.2 | 105.0 | −31.49 | ||

F_{e} | 50 | 2 | 34 | 2 | 44 | 1 | 1485.8 | 10.5 | 50.6 | −33.95 | ||

Balanced | 9 | 0 | - | - | 44 | 1 | 25.3 | 3.8 | 85.8 | 0.32 | ||

3 | Cwa | No HES | - | - | - | - | - | - | 0.0 | 39.5 | 165.5 | −∞ |

NPC | 0 | 0 | - | - | 4 | 4 | 5.3 | 28.4 | 126.6 | −∞ | ||

PB | 0 | 2 | 33 | 0 | 44 | 1 | 1344.4 | −6.7 | 96.3 | −32.86 | ||

F_{e} | 50 | 2 | 34 | 0 | 44 | 1 | 1449.8 | 10.2 | 46.8 | −35.96 | ||

Balanced | 9 | 0 | - | - | 44 | 1 | 25.3 | 4.7 | 81.3 | 0.24 | ||

4 | Af | No HES | - | - | - | - | - | - | 0.0 | 44.1 | 184.5 | −∞ |

NPC | 0 | 0 | - | - | 23 | 1 | 8.9 | 27.1 | 131.3 | −∞ | ||

PB | 0 | 2 | 22 | 2 | 20 | 2 | 703.7 | −36.1 | 68.1 | −14.14 | ||

F_{e} | 50 | 2 | 33 | 2 | 20 | 2 | 1183.6 | −18.5 | 23.5 | −25.41 | ||

Balanced | 12 | 0 | - | - | 44 | 1 | 27.6 | 12.5 | 89.4 | 0.091 |

**Table 9.**Economic and environmental analysis of a balanced selection strategy for a lifetime cycle of 20 years.

Location | Climate | Building | NPC (×10 ^{3} US$) | Savings (×10 ^{3} US$) | Payback (years) | CO_{2} Reduction(%) |
---|---|---|---|---|---|---|

1 | Aw | Residential | 24.6 | 17.0 | 10.7 | 53.7 |

Farm | 26.8 | 10.3 | 15.7 | 50.5 | ||

2 | Am | Residential | 25.3 | 16.0 | 10.3 | 59.8 |

Farm | 25.3 | 13.7 | 13.6 | 52.2 | ||

3 | Cwa | Residential | 26.3 | 5.0 | 16.7 | 60.2 |

Farm | 25.3 | 9.5 | 15.2 | 50.9 | ||

4 | Af | Residential | 23.6 | 12.0 | 12.29 | 52.1 |

Farm | 27.6 | 4.0 | 18.2 | 51.5 |

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**MDPI and ACS Style**

Shivam, K.; Tzou, J.-C.; Wu, S.-C.
Multi-Objective Sizing Optimization of a Grid-Connected Solar–Wind Hybrid System Using Climate Classification: A Case Study of Four Locations in Southern Taiwan. *Energies* **2020**, *13*, 2505.
https://doi.org/10.3390/en13102505

**AMA Style**

Shivam K, Tzou J-C, Wu S-C.
Multi-Objective Sizing Optimization of a Grid-Connected Solar–Wind Hybrid System Using Climate Classification: A Case Study of Four Locations in Southern Taiwan. *Energies*. 2020; 13(10):2505.
https://doi.org/10.3390/en13102505

**Chicago/Turabian Style**

Shivam, Kumar, Jong-Chyuan Tzou, and Shang-Chen Wu.
2020. "Multi-Objective Sizing Optimization of a Grid-Connected Solar–Wind Hybrid System Using Climate Classification: A Case Study of Four Locations in Southern Taiwan" *Energies* 13, no. 10: 2505.
https://doi.org/10.3390/en13102505