# Investigating the Impact of Economic Uncertainty on Optimal Sizing of Grid-Independent Hybrid Renewable Energy Systems

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## Abstract

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## 1. Introduction

_{2}) is provided by renewable means.

_{2}-based FC, renewable H

_{2}-based boiler, natural gas (NG)-fueled boiler, and biomass generator (BMG) are scrutinized to ascertain optimal sizing and their techno-economic performance for co-supplying a touristy village, Mesr in Isfahan province of Iran, with electricity and heat. To increase sustainability and efficiency of the proposed models, the excess electricity is sent to electrolyzer for generating H

_{2}. Then, during the times when solar and wind electricity cannot meet electric and thermal demands, this stored renewable H

_{2}is utilized to react with oxygen (O

_{2}) for electricity generation. This transition occurs in a electrochemical process within FC-engaging electrodes and electrolytes, releasing water as a by-product [21]. This effective usage of the surplus electricity implies the necessity of adding FC to the system, otherwise a great deal of electricity would be dumped without ever being exploited [22]. Additionally, in each of other two proposed systems, it is supposed that boiler consumes renewable H

_{2}or NG for meeting thermal energy demands. Furthermore, to comprehensively examine the available resources in the area, a HRE system, which includes a BMG, is investigated. Finally, among these three systems, the most suitable one, with respect to technical, economic, environmental, and reliability aspects, is selected to be further analyzed under economic uncertainty.

## 2. Literature Review

_{2}per year in comparison with an autonomous DG plant [49]. Brenna et al. [50] utilized HOMER to assess the different integrations of PV, WT, hydro, DG, battery, and H

_{2}for electrifying a rural area in Ethiopia. Isa et al. [51] proposed an on-grid PV/FC/ battery system for co-supplying electricity and heat to a hospital in Malaysia with a TNPC of $106,551, an LCOE of 0.091 $/kWh, and an emission reduction of 25,873 kg/yr. Singh and Baredar [52] studied the electricity generation potential via an off-grid system consisting of PV, FC, BMG, and battery. Singh et al. [53] employed HOMER to verify the results of optimal sizing of an HRE system which was obtained by swarm-based artificial bee colony and particle swarm optimization. The comparison proved that these three methods had close results as to the sizing of the components. Das et al. [54] explored the techno-economic feasibility of an HRE system using HOMER. The software was employed to compare PV/FC/battery and PV/battery systems with a benchmark of the current DG plant [55]. Khemariya et al. [56] used HOMER to evaluate a PV/FC/battery/electrolyzer system to electrify a village in India. Similarly, HOMER optimized a PV/BMG/DG/battery system considering different peak loads, energy demands, and grid availability [57]. Shahzad et al. [58] designed an integrated PV/BMG/battery system for the irrigation and residential applications in Pakistan. Furthermore, HOMER assessed the techno-economic feasibility of a grid-tied PV/WT/BMG system for electrifying a village in Pakistan [59]. Duman and Guler [60] explored the utilization of an autonomous PV/WT/FC plant to supply electricity for vacation homes in Turkey. HOMER revealed that the displacement of FC with batteries would turn the system more cost-effective. Moreover, stand-alone HRE systems were scrutinized using HOMER for a nursing home in Turkey [61]. Apart from those above-mentioned studies, these papers [62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88] also applied HOMER for different purposes, which are helpful in learning about the software and its practicality.

## 3. Geographical Specifications

## 4. Materials and Methods

#### 4.1. Economic Analysis

#### 4.2. PV Modeling

^{2}, ${G}_{T,NOCT}$ = 800 W/m

^{2}.

#### 4.3. WT Modeling

#### 4.4. Electrolyzer Modeling

_{2}is the most favorable, futuristic energy carrier as it releases virtually zero emissions when being applied. There are no pure H

_{2}molecules available in the surrounding environment. However, it can be obtained via several chemical processes. To this end, water electrolysis is the promising method in which an electrolyzer utilizes electricity to make the decompaction of water into H

_{2}and O

_{2}molecules happen [99]. The essential factor connected with modeling and sizing of an electrolyzer is the H

_{2}production rate which can be projected via Equation (14) [79].

_{2}and the mass flowrate of H

_{2}, respectively.

#### 4.5. FC Modeling

_{2}generated via the aid of the excess electricity [16,88]. In this study, it is postulated that the type of FC is proton exchange membranes, owing to its benefits such as low-cost maintenance, high energy conversion efficiency, and low operating temperature [101]. To evaluate the output voltage of a FC, Equation (16) can be used [102].

_{2}which is considered usually between 120 and 142 MJ/kg [104].

#### 4.6. BMG Modeling

#### 4.7. Converter Modeling

#### 4.8. Thermal Load Controller (TLC) Modeling

#### 4.9. H_{2} Tank Modeling

_{2}in excess of the amount required by FC or boiler, a storage should be incorporated in the proposed system. The most vital feature of this component is its ability to endure holding the high-pressure H

_{2}[92]. Equation (21) can calculate the pressure of H

_{2}stored in the tank [107].

_{2}, the gas constant, with a H

_{2}value at 4124.18 Nm/kg·K, and temperature, respectively. ${V}_{H2}$ is also the specific volume. Similar to TLC, HOMER software just allows the users to set the volume of H

_{2}tank and its price.

#### 4.10. Boiler Modeling

## 5. Technical Characteristics, Cost of Equipment and Assumptions

^{3}[92]. Finally, it is presumed that the project lifespan would be 25 years.

- (I)
- PV/WT/electrolyzer/H
_{2}-based FC/H_{2}-based boiler - (II)
- PV/WT/electrolyzer/H
_{2}-based FC/NG-based boiler - (III)
- PV/WT/BMG/electrolyzer/H
_{2}-based boiler

## 6. Analysis

#### 6.1. The Benchmark Case ($i$ = 17.5% and $f$= 18%)

_{2}yielded by electrolyzer. In the second model boiler, it would use NG as fuel and just FC would consume renewable H

_{2}. In the third model, BMG would be utilized instead of FC and just boiler would run on renewable H

_{2}. LCOE and $TNPC$ of the first model in its benchmark case would equate to 0.33 $/kWh and $647,708, respectively, which are higher than those of the two other configurations. However, at the end of the project lifetime, the salvage value of components utilized in the first model would be greater than that of the other models. Table 2 provides the results of optimal sizing and economic assessment of the models.

_{2}which is its main disadvantage, as it is not being eco-friendly. Based on the findings represented in Table 3, the first model would perfectly meet all electric and thermal energy demands, and would also be the most environmentally-friendly one. Thus, in the following sub-section, this model is analyzed considering economic uncertainty.

#### 6.2. Analysis of the First Model under Economic Uncertainty

_{2}-based FC/H

_{2}-based boiler system, the least and the highest prospective amounts of these rates were incorporated into the projections. To this end, the nominal discount rate and inflation were considered to vary in the range of 15–20% and 10–26%, respectively, based on the 20-year average from mid-2000 to mid-2020.

## 7. Discussion and Suggestions for Implementation

_{2}-based FC/H

_{2}-based boiler, would not be cost-competitive to conventional methods of electricity generation under the majority of likely values of the discount rate and inflation. Here, the role of the government and its underwriting policies are extremely decisive in the implementation of the proposed system in the nominated remote area. To achieve energy security, to decarbonize and decentralize energy sector, to meet the Paris Agreement emission targets, and to sustain the environment, governments should underpin such schemes by the following.

- (I)
- Furnishing the investors or private companies with zero percent or low-rate loans.
- (II)
- Introducing carbon tax to encourage the generation and use of renewable electricity.
- (III)
- Setting strict rules and regulations against carbon-intensive means of generating electricity.
- (IV)
- Developing the concept of green tourism to attract as many national and international visitors as possible. The corresponding revenues can cover a substantial proportion of the project’s costs.
- (V)
- Subsidizing the price of renewable electricity for residents (can be achieved from the resource of funding allocated to operating and maintaining the transmission and distribution network as it would no longer be needed).
- (VI)
- Lifting tariffs on importing equipment such as PV, WT, electrolyzer, FC, etc.

## 8. Conclusions

- The first model, the PV/WT/electrolyzer/H
_{2}-based FC/H_{2}-based boiler, had the highest TNPC ($647,708), the lowest unmet electric load, and the highest reliability without any detrimental impact on the environment. - The second model, the PV/WT/electrolyzer/H
_{2}-based FC/NG-based boiler, possessed the second least TNPC ($548,906), and it could meet almost all electric demand. Whereas, utilizing it would end up releasing some 11.5 tons of CO_{2}per year. This carbon footprint constitutes a challenging negative point for the second model which may strongly inhibit all the attempts to accomplish the Paris Agreement targets. - The techno-economic analysis of the third model, the PV/WT/BMG/electrolyzer/H
_{2}-based boiler, showed that it would not be reliable, as 20.5% of total electric load could not be met via this system. However, its TNPC, $488,878, was the least amongst the three analyzed configurations.

- The amount of LCOE would vary from 0.102 $/kWh to 0.662 $/kWh, meaning LCOE could be between one-third of the benchmark value and two-fold that (LCOE for the benchmark case = 0.33 $/kWh). Additionally, TNPC would fluctuate between $478,704 and $814,905 from 26% less than the benchmark value up to 26% more than that (TNPC for the benchmark case = $647,708).
- The optimal size of PV and the number of WT units would change from 25.9 to 52.5 kW and from 11 to 18, respectively. Comparing with the benchmark case (PV size = 33.8 kW and number of WT units = 14), the PV size could vary from an amount of 23% less than the benchmark case up to 55% more than that, and corresponding figures for WT would be 21% and 29%, respectively.
- The amount of renewable H
_{2}consumed by boiler and FC would be in the ranges of 1815–1962 kg and 559–665 kg, respectively. When comparing with the benchmark (H_{2}consumption in boiler = 1922 kg and that in FC = 618), the former would fluctuate from an amount of 6% less than the benchmark value up to an amount of 2% more than that, and related numbers for FC would be 10% and 8%, respectively.

## 9. Future Research Direction

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Nomenclature

AC | Alternating Current |

${A}_{Ele}$ and ${B}_{Ele}$ | Curve consumption coefficients (kW/kg/h) of electrolyzer |

BMG | Biomass generator |

${C}_{bio}$ | Biomass’s calorific value |

${C}_{H2}$ | Compressibility rate of hydrogen |

${C}_{op}$ | Operating cost ($) |

${C}_{rep}$ | Replacement cost ($) |

$CRF$ | Capacity rate factor |

${C}_{total,an}$ | Total annualized cost ($) |

${C}_{total,ini}$ | Total initial capital cost ($) |

$CUF$ | Capacity utilization factor |

DC | Direct Current |

DG | Diesel generator |

$E$ | Open circuit voltage (v) |

${E}_{bio}$ | Annual output electricity of a biomass gasifier (kW) |

${E}_{Ele}$ | Required electricity by the electrolyzer (kW) |

${E}_{grid,Ex}$ | Electricity sold to the grid (kWh/yr) |

${E}_{Prim,AC}$ | AC primary load served (kWh/yr) |

${E}_{Prim,DC}$ | DC primary load served (kWh/yr) |

$f$ | Annual inflation rate (%) |

$F$ | Faraday constant |

FC | Fuel cell |

${f}_{PV}$ | Degradation factor (%) of PV |

${\overline{G}}_{T}$ | Solar radiation (W/m^{2}) |

${G}_{T,NOCT}$ | Amount of solar radiation at which NOCT is defined which equals 800 W/m^{2} |

${\overline{G}}_{T,STC}$ | Standard radiation (W/m^{2}) |

${h}_{0}$ | Surface roughness length (m) |

${H}_{2}$ | Hydrogen |

${h}_{anem}$ | Anemometer height (m) |

${h}_{hub}$ | Hub height (m) |

$HPR$ | Hydrogen production rate |

HRE | Hybrid renewable energy |

$i$ | Real annual discount rate (%) |

${i}^{\prime}$ | Nominal discount rate (%) |

${I}_{Ele}$ | Electrolyzer current (A) |

${I}_{FC}$ | Fuel cell current (A) |

kg | Kilogram |

kW | Kilowatt |

kWh | Kilowatt hour |

LCOE | Levelized cost of electricity ($/kWh) |

LHV | Lower heating value (MJ/kg) |

NG | Natural gas |

${\rho}_{0}$ | Air density at standard pressure and temperature (kg/m^{3}) |

$n$ | Project lifetime (yr) |

${n}_{c}$ | Number of cells in series in the electrolyzer |

${n}_{com}$ | Lifetime of a component (yr) |

${n}_{c,FC}$ | Total number of cells in the fuel cell |

${O}_{bio}$ | Hours of operating biomass gasifier (h) |

${O}_{2}$ | Oxygen |

${P}_{bio}$ | Rating of a biomass gasifier system |

${P}_{bio}^{max}$ | Maximum rating of biomass gasifier |

${P}_{inv,in}$ | Input power of inverter |

${P}_{inv,out}$ | Output power of inverter |

${P}_{H2,tank}$ | Pressure of hydrogen in the tank |

${P}_{PV}$ | Power output of PV system (kW) |

PV | Photovoltaic |

${P}_{WT}$ | Power output of wind turbine (kW) |

${P}_{WT,STC}$ | Wind turbine output under STC (kW) |

$Q$ | Mass flowrate of hydrogen (kg/h) |

${Q}_{N}$ | Nominal mass flowrate of hydrogen (kg/h) |

${S}_{val}$ | Salvage value of a component ($) |

$T$ | Temperature |

${T}_{\alpha}$ | Ambient temperature (°C) |

${T}_{\alpha ,NOCT}$ | Ambient temperature at which NOCT is defined which equals 20 °C |

${T}_{bio}$ | Total amount of biomass |

${T}_{c}$ | PV cell temperature (°C) |

${T}_{c,NOCT}$ | Nominal operating cell temperature (°C) |

${T}_{c,STC}$ | Standard PV cell temperature (°C) |

TLC | Thermal load controller |

TNPC | Total net present cost ($) |

${U}_{anem}$ | Wind speed at the anemometer height (m/s) |

${U}_{hub}$ | Wind speed at the hub height (m/s) |

${U}_{L}$ | The coefficient of heat transfer (kW/m^{2}) |

$\overline{{V}_{c}}$ | Average voltage of a cell in the fuel cell (v) |

${V}_{act}$ | Activation fuel cell overvoltage (v) |

${V}_{conc}$ | Concentration fuel cell overvoltage (v) |

${V}_{FC}$ | Fuel cell output voltage (v) |

${V}_{H2}$ | Volume of hydrogen in tank |

${V}_{ohm}$ | Ohmic fuel cell overvoltage (v) |

W | Watt |

WT | Wind turbine |

${Y}_{PV}$ | Rated capacity of PV system (kW) |

yr | Year |

α | Solar absorption of PV array (%) |

${\alpha}_{P}$ | Temperature coefficient (%/°C) |

°C | Degree Celsius |

τ | Transmittance of the cover over PV system |

$\rho $ | Real air density (kg/m^{3}) |

${\eta}_{c}$ | Electrical conversion efficiency of PV system |

${\eta}_{bio}$ | Biomass to electricity conversion efficiency |

${\eta}_{FC}$ | Fuel cell efficiency |

${\eta}_{inv}$ | Inverter efficiency |

${\theta}_{H2}$ | Hydrogen gas constant (4124.18 Nm/kg.K) |

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**Figure 1.**The fluctuations in (

**a**) the nominal discount rate and (

**b**) inflation from mid-2000 to mid-2020.

**Figure 8.**Changes of TNPC considering the fluctuations of the nominal discount rate and inflation (numbers inside the surface plot refer to LCOE).

**Figure 9.**Changes of annual electric production considering the fluctuations of the nominal discount rate and inflation (Numbers inside the surface plot refer to LCOE).

**Figure 10.**Changes of annual thermal energy generation considering the fluctuations of the nominal discount rate and inflation (numbers inside the surface plot refer to the amount of H

_{2}consumed by boiler).

**Figure 11.**Changes of electricity generation via FC considering the fluctuations of the nominal discount rate and inflation (numbers inside the surface plot refer to the amount of H

_{2}consumed by FC).

**Figure 12.**Changes of electricity generation via PV considering the fluctuations of the nominal discount rate and inflation (numbers inside the surface plot refer to the optimal size of PV).

**Figure 13.**Changes of electricity generation via WT units considering the fluctuations of the nominal discount rate and inflation (numbers inside the surface plot refer to the optimal number of the wind turbines).

Component | Model (Abbreviation) | Technical Specifications | Capital Cost | Replacement Cost | Operation and Maintenance Cost | Ref. for Costs |
---|---|---|---|---|---|---|

PV | Fronius Symo 4.5-3-S (Fron4.5) | Rated capacity: 4.4 kW Lifetime: 25 yr Electrical bus: AC Derating factor: 96% Temperature coefficient: −0.41%/°C Operating temperature: 45 °C Efficiency at standard test conditions: 17.3% Ground reflectance: 20% Tracking system: no tacking Panel type: flat plate | 2000 ($/kW) | 2000 ($/kW) | 10 ($/kW.yr) | [97] |

WT | Bergey Excel 6 (XL6) | Rated capacity: 6 kW Lifetime: 20 yr Electrical bus: AC Hub height: 30 m Rotor diameter: 6.2 m Cut-in wind speed: 2.5 m/s Cut-out wind speed: none | 2000 ($/kW) | 1600 ($/kW) | 50 ($/#.yr) | [62] |

BMG | Generic Biogas Genset (Bio) | Size: 20 kW Lifetime: 20,000 h Electrical bus: AC Fuel type: animal manure LHV = 19 MJ/kg Gasification ratio: 0.047 kg/kg Density of biogas: 1.15 kg/m ^{3}Carbon content: 44% Daily available biomass: 2000 kg Biogas fuel price: 0 $/kg | 2300 ($/kW) | 1500 ($/kW) | 0.01 ($/op.h) | [53] |

FC | Generic Fuel Cell (FC) | Size: 20 kW Lifetime: 50,000 h Electrical bus: DC Heat recover ratio: 60% Minimum runtime: 20 min Fuel type: stored hydrogen LHV = 120 MJ/kg Carbon content: 0 Stored hydrogen price: 0 $/kg | 2000 ($/kW) | 1860 ($/kW) | 0.01 ($/op.h) | [92] |

TLC | Generic thermal load controller (TLC) | Size: 100 kW Lifetime: 20 yr Electrical bus: DC and AC | 54 ($/kW) | 54 ($/kW) | 0 ($/kW) | [97] |

Boiler | Generic boiler | Efficiency: 85% Fuel type 1: stored hydrogen LHV= 120 MJ/kg Carbon content: 0 Stored hydrogen price: 0 $/kg Fuel type 2: natural gas LHV = 45 MJ/kg Density: 0.79 kg/m ^{3}Carbon content: 67% Natural gas price: 0.3 $/m ^{3} | - | - | - | - |

Converter | Leonics S-219Cp 5 kW (Leon5) | Lifetime: 10 yr Rectifier efficiency: 94% Rectifier relative capacity: 80% Inverter efficiency: 96% | 550 ($/kW) | 550 ($/kW) | 10 ($/kW/yr) | [108] |

Electrolyzer | Generic Electrolyzer | Size: specified in model Lifetime: 15 yr Electrical bus: DC Efficiency: 85% | 2000 ($/kW) | 2000 ($/kW) | 50 ($/kW/yr) | [93] |

H_{2} Tank | Generic hydrogen tank (H2Tank) | Initial tank level: 0 | 600 ($/kg) | 600 ($/kg) | 10 ($/yr) | [109] |

Model | PV (kW) | WT (#) | FC (kW) | BMG (kW) | Electrolyzer (kW) | TLC (kW) | H_{2} Tank(kg) | Converter (kW) | TNPC ($) | LCOE ($) | Salvage Value ($) |
---|---|---|---|---|---|---|---|---|---|---|---|

No. 1 | 33.8 | 14 | 20 * | - | 40 * | 100 * | 10 * | 48.7 | 647,708 | 0.33 | −177,219 |

No. 2 | 28.4 | 9 | 20 * | - | 20 * | 100 * | 10 * | 28.8 | 548,906 | 0.248 | −139,048 |

No. 3 | 43 | 8 | - | 20 * | 30 * | 100 * | 10 * | 37.1 | 488,878 | 0.313 | −131,344 |

_{2}, while in the other models is 30 and 40 kW.

Model No. 1 | Model No. 2 | Model No. 3 | |
---|---|---|---|

Total electricity production (kWh/yr) | 241,422 | 180,162 | 181,722 |

The share of PV (%) | 25.6 | 29 | 40.9 |

The share of WT (%) | 65.9 | 56.7 | 50 |

The share of FC (%) | 8.5 | 14.3 | - |

The share of BMG (%) | - | - | 9.1 |

Excess electricity (kWh/yr) | 30,773 | 27,869 | 15,719 |

Unmet electric load (%) | 0.051 | 0.065 | 20.5 |

Renewable fraction | 43.9 | 41.7 | 53.3 |

Total thermal energy production (kWh/yr) | 85,234 | 80,134 | 71,153 |

The share of boiler (%) | 63.9 | 65.2 | 77.9 |

The share of excess electricity (%) | 36.1 | 34.8 | 22.1 |

Excess thermal energy (kWh/yr) | 25,655 | 20,556 | 11,574 |

H_{2} consumption by FC (kg/yr) | 618 | 771 | - |

Capacity factor of FC (%) | 11.7 | 14.7 | - |

Biomass consumption by BMG (tonnes/yr) | - | - | 730 |

Capacity factor of BMG (%) | - | - | 9.5 |

Total renewable production divided by load (%) | 109 | 105 | 114 |

Capacity factor of PV (%) | 20.9 | 21 | 19.7 |

Capacity factor of WT (%) | 21.6 | 21.6 | 21.6 |

H_{2} consumption by boiler (kg/yr) | 1922 | - | 1956 |

NG consumption by boiler (m^{3}/yr) | - | 6905 | - |

Total H_{2} generation by electrolyzer (kg/yr) | 2759 | 1575 | 2167 |

Capacity factor of electrolyzer (%) | 36.5 | 41.7 | 38.3 |

CO_{2} emission (kg/yr) | 0 | 11,535 | 1175 |

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**MDPI and ACS Style**

Rezaei, M.; Dampage, U.; Das, B.K.; Nasif, O.; Borowski, P.F.; Mohamed, M.A.
Investigating the Impact of Economic Uncertainty on Optimal Sizing of Grid-Independent Hybrid Renewable Energy Systems. *Processes* **2021**, *9*, 1468.
https://doi.org/10.3390/pr9081468

**AMA Style**

Rezaei M, Dampage U, Das BK, Nasif O, Borowski PF, Mohamed MA.
Investigating the Impact of Economic Uncertainty on Optimal Sizing of Grid-Independent Hybrid Renewable Energy Systems. *Processes*. 2021; 9(8):1468.
https://doi.org/10.3390/pr9081468

**Chicago/Turabian Style**

Rezaei, Mostafa, Udaya Dampage, Barun K. Das, Omaima Nasif, Piotr F. Borowski, and Mohamed A. Mohamed.
2021. "Investigating the Impact of Economic Uncertainty on Optimal Sizing of Grid-Independent Hybrid Renewable Energy Systems" *Processes* 9, no. 8: 1468.
https://doi.org/10.3390/pr9081468