# Optimal Distribution of Renewable Energy Systems Considering Aging and Long-Term Weather Effect in Net-Zero Energy Building Design

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## Abstract

**:**

## 1. Introduction

## 2. Problem Identification

## 3. System Generation Reliability Model

## 4. Evaluation Indicator

## 5. Building Features

^{2}) with the air-conditioned area of approximately 990 m

^{2}. Two types of generation systems, i.e., photovoltaic (PV) of 1015 m

^{2}and a biodiesel generator (BDG) with a rated power of 100 kW, are employed to provide energy for the grid-connected building. In this study, the wind turbine (WT) system was also assumed to be one of the potential generation systems, in addition to PV and BDG. The cooling load of the building was undertaken by three electric chillers, one absorption chiller driven by BDG, and the peak cooling load was about 163 kW. A schematic diagram of the energy systems in the studied building is shown in Figure 6.

_{ec}is the power consumed by electric chillers, P

_{pump}is the power consumed by cooling water pumps and chiller water pumps, P

_{ct}is the power consumed by cooling tower fans, ${P}_{fan}$ is the power consumed by AHU (air handling unit) fans, and P

_{other}is the power consumed by other appliances, such as lighting and socket outlet. The power supply system consists of on-site RES (i.e., PV, WT, and BDG) and the grid, as shown in (22). The hourly electricity consumption in the building should be equal to the amount of supplied power by the sources given in (22). It is noted that heating load does not exist for the building in Hong Kong since Hong Kong belongs to the hot summer and warm winter zone.

## 6. Results and Discussion

#### 6.1. Performance Evaluation: Annual Energy Balance

^{2}in Case 1, whilst the PV size increased to be 400 m

^{2}in Case 2, and it increased to be 3,600 m

^{2}in Case 3. The main reason was that a slight reduction of availability was found in each generation unit (it was more than 0.95) in Case 2, whilst a large variation range of availability (between 0.4 and 0.95) was seen in Case 3, as shown in Table 3. In addition, the total cost (${T}_{Cn}$) and grid interaction index ($GI{I}_{n}$) in Case 3 were identified to be two times and three times, respectively, that of Case 1.

#### 6.2. Performance Evaluation: 100-Years Energy Balance

^{2}under annual year balance concerned (Table 5) to 600 m

^{2}under 100-years energy balance. The total cost did not show much reduction in Case 1 and Case 2, however, in Case 3, compared to the annual year balance, the cost was reduced to half. In addition, a remarkable reduction from 92% to 3% was seen in the mismatch ratio in Case 3, indicating a much smaller size was required for the 100-years energy balance. A similar tendency was found for the performance of the grid interaction index. A further comparison of annual energy generation and annual mismatch ratio in the three cases under 100-years energy balance is presented, when the aging effect was taken into consideration, in Figure 11 (regarding $T{C}_{n}$) and Figure 12 (regarding $GI{I}_{n}$).

#### 6.3. Relationship between Probabilities and Mismatch Ratio

^{2}of the three fitting formula were all above 0.98, indicating a good relationship between the mismatch ratio and the probabilities.

- Case 1: y
_{1}= 36.914x^{5}− 0.8983x^{4}− 16.554x^{3}+ 0.3929x^{2}+ 2.9041x + 0.4636; −0.5 < x < 0.5 (R² = 0.988); - Case 2: y
_{2}= 37.906x^{5}− 1.9154x^{4}− 16.716x^{3}+ 0.6118x^{2}+ 2.9024x + 0.4563; −0.5 < x < 0.5 (R² = 0.988); - Case 3: y
_{3}= -0.5495x^{5}+ 1.5527x^{4}− 1.2653x^{3}− 0.4425x^{2}+ 1.2506x + 0.4552; −0.5 < x < 1.0 (R² = 0.997).

## 7. Conclusions

- (1)
- In terms of the annual energy balance, the optimal size of RES in Case 3 (i.e., mismatch ratio of above 90%) was much larger than that in Case 1 and Case 2 (i.e., mismatch ratio of below 50%). Meanwhile, the aging effect of the generation system was identified to be a vital factor in system selection and the expected target for NZEB.
- (2)
- In terms of the 100-years energy balance, a much smaller RES size was required, especially in Case 3, where a remarkable reduction of mismatch ratio was found from 92% to 3%. Meanwhile, the number of years for net-zero energy balance was also identified to be an essential factor in system selection and expected target for NZEB.
- (3)
- The fitting formula with a good coefficient of determination was obtained to describe the relationship between the mismatch ratio and the probabilities for each case. In all cases, the probability to be NZEB was 0% under a mismatch ratio of below −0.4 and was around 45% under a mismatch ratio of 0.0. In addition, a mismatch ratio of over 1.0 was required to ensure a 100% NZEB in Case 3 when considering the aging effect, and it was over 0.6 that required for a 100% NZEB in Case 1 and Case 2.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Nomenclature

${\mathit{A}}_{\mathit{d}\mathit{e}\mathit{s}}$ | total area of PV [m^{2}] |

${\mathit{A}}_{\mathit{W}\mathit{T}}$ | blade area of wind turbine [m^{2}] |

$\mathit{A}\mathit{C}$ | imposed cost |

BDG | biodiesel generator |

CCHP | combined heating, cooling, and power |

$\mathit{C}\mathit{O}{\mathit{P}}_{\mathit{e}\mathit{c}}$ | coefficient of performance of electric chiller |

${\mathit{c}}_{\mathit{p},\mathit{w}}$ | coefficient of the wind turbine performance |

Pother | load |

${\mathit{F}}_{\mathit{b}\mathit{i}\mathit{o}}$ | fuel consumption of the biodiesel generator |

$\mathit{G}\mathit{I}\mathit{I}$ | grid interaction index |

$\mathit{G}\mathit{I}{\mathit{I}}_{\mathit{n}}$ | normalized grid interaction index |

HVAC | heating, ventilation, and air conditioning |

${\mathit{I}}_{\mathit{i}\mathit{r}\mathit{r}\mathit{a}}$ | hourly irradiance [kWh/m^{2}] |

$\mathit{I}\mathit{C}$ | initial cost |

${\mathit{m}}_{\mathit{w}}$ | water flow rate (m^{3}/s) |

${\mathit{n}}^{\prime}$ | number of years satisfying NZEB requirement |

$\mathit{n}$ | number of simulations [year] |

$\mathit{O}\mathit{C}$ | operation cost |

PV | photovoltaic |

${\mathit{P}}_{\mathit{B}\mathit{D}\mathit{G}}$ | power generation of generator [kW] |

${\mathit{P}}_{\mathit{B}\mathit{D}\mathit{G},\mathit{r}\mathit{a}\mathit{t}\mathit{e}\mathit{d}}$ | power generation of generator [kW] |

${\mathit{P}}_{\mathit{g}\mathit{r}\mathit{i}\mathit{d}}$ | imported/exported electricity from/to the grid [kW] |

${\mathit{P}}_{\mathit{i}\mathit{m}}/{\mathit{P}}_{\mathit{e}\mathit{x}}$ | imported electricity to the building/exported electricity to the grid [kW] |

${\mathit{P}}_{\mathit{o}\mathit{t}\mathit{h}\mathit{e}\mathit{r}}$ | power consumption from other appliances [kW] |

${\mathit{P}}_{\mathit{P}\mathit{V}}$ | power generation of photovoltaic [kW] |

${\mathit{P}}_{\mathit{W}\mathit{T}}$ | power generation of wind turbine [kW] |

${\mathit{P}}_{\mathit{e}\mathit{c}}$ | power consumption of electric chillers [kW] |

${\mathit{P}}_{\mathit{p}\mathit{u}\mathit{m}\mathit{p}}$ | power consumption of cooling water pumps and chiller water pumps [kW] |

${\mathit{P}}_{\mathit{c}\mathit{t}}$ | power consumption of cooling tower fans [kW] |

${\mathit{P}}_{\mathit{f}\mathit{a}\mathit{n}}$ | power consumption of AHU fans [kW] |

${\mathit{P}}_{\mathit{e}\mathit{q}\mathit{u}\mathit{i}\mathit{p}\mathit{m}\mathit{e}\mathit{n}\mathit{t}}$ | power consumption from equipment [kW] |

${\mathit{P}}_{\mathit{s}\mathit{u}\mathit{p}\mathit{p}\mathit{l}\mathit{y}}$ | electrical supply [kW] |

${\mathit{P}}_{\mathit{d}\mathit{e}\mathit{m}}$ | electrical demand [kW] |

${\mathit{P}}_{\mathit{g}\mathit{e}\mathit{n}}$ | power generation from renewable energy system [kW] |

${\mathit{Q}}_{\mathit{c}}$ | building cooling demand [kW] |

${\mathit{Q}}_{\mathit{a}\mathit{c}}$ | cooling provided by the absorption chiller [kW] |

${\mathit{Q}}_{\mathit{a}\mathit{c},\mathit{d}\mathit{e}\mathit{s}\mathit{i}\mathit{g}\mathit{n}}$ | cooling capacity of the absorption chiller [kW] |

${\mathit{Q}}_{\mathit{e}\mathit{c}}$ | cooling provided by electric chillers [kW] |

${\mathit{Q}}_{\mathit{c}\mathit{t}}$ | cooling capacity of the cooling tower [kW] |

RES | renewable energy system |

$\mathit{T}\mathit{C}$ | annual total cost including initial cost, operation cost, and imposed cost [USD/year] |

$\mathit{T}{\mathit{C}}_{\mathit{n}}$ | normalized annual total cost including initial cost, operation cost, and imposed cost |

${\mathit{v}}_{\mathit{w}\mathit{i}\mathit{n}\mathit{d}}$ | wind speed [m/s] |

ZCB | zero-carbon building |

ZEB/NZEB | net-zero energy building |

${\mathit{\eta}}_{\mathit{c}\mathit{w}\mathit{p}}$ | pump efficiency |

${\mathit{\eta}}_{\mathit{f}\mathit{a}\mathit{n}}$ | fan efficiency |

${\mathit{\eta}}_{\mathit{B}\mathit{D}\mathit{G}}$ | BDG efficiency |

${\mathit{\eta}}_{\mathit{h}\mathit{r}\mathit{s}}$ | heat recovery system efficiency |

${\mathit{\eta}}_{\mathit{m}}$ | PV module efficiency |

${\mathit{\eta}}_{\mathit{P}\mathit{C}}$ | power conditioning efficiency |

${\mathit{\eta}}_{\mathit{W}\mathit{T}}$ | combined efficiency of the generator and wind turbine |

${\mathit{\rho}}_{\mathit{a}}$ | air density [kg/m^{3}] |

$\mathit{\upsilon}\mathit{a}$ | air flow rate [m^{3}/s] |

$\mathsf{\epsilon}$ | mismatch ratio |

${\mathit{\lambda}}_{\mathit{r}}$ | failure rate [1/h] |

${\mathit{\mu}}_{\mathit{r}}$ | repair rate [1/h] |

${\mathit{\lambda}}_{\mathit{F}}$ | degradation rate of the component [1/h] |

$\mathit{T}\mathit{W}$ | lifetime of the component [years] |

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**Figure 1.**Main approaches to achieve net-zero energy buildings (NZEBs). RES: renewable energy system.

**Figure 4.**Markov chain model: (

**a**) two states without the aging effect; (

**b**) three states considering the aging effect.

**Figure 7.**Annual performance of NZEB under optimal options with the aging effect (considering $T{C}_{n}$): (

**a**) Annual energy generation; (

**b**) Annual mismatch ratio.

**Figure 8.**Annual performance of NZEB under optimal options with the aging effect (considering GIIn): (

**a**) Annual energy generation; (

**b**) Annual mismatch ratio.

**Figure 9.**Average performance of NZEB under optimal options with the aging effect (considering $T{C}_{n}$): (

**a**) Annual energy generation; (

**b**) Probability of being NZEB.

**Figure 10.**Average performance of NZEB under optimal options with the aging effect (considering $GI{I}_{n}$): (

**a**) Annual energy generation; (

**b**) Probability of being NZEB.

**Figure 11.**Annual performance of NZEB under optimal options with the aging effect (considering $T{C}_{n}$): (

**a**) Annual energy generation; (

**b**) Annual mismatch ratio.

**Figure 12.**Annual performance of NZEB under optimal options with the aging effect (considering $GI{I}_{n}$): (

**a**) Annual energy generation; (

**b**) Annual mismatch ratio.

**Figure 13.**Average performance of NZEB under optimal options with the aging effect (considering $T{C}_{n}$): (

**a**) Average annual energy generation; (

**b**) Probability of being NZEB.

**Figure 14.**Average performance of NZEB under optimal options with the aging effect (considering GIIn): (

**a**) Average annual energy generation; (

**b**) Probability of being NZEB.

**Figure 15.**Mismatch ratio and the corresponding probability of NZEB in (

**a**) Case 1; (

**b**) Case 2; (

**c**) Case 3.

**Table 1.**Summary of the design optimization of generation systems for NZEB. (WT-Wind turbine, BDG-Biodiesel generator, TES-Thermal energy system, EES-Electrical energy storage, SDHW- solar domestic hot water, COP-Coefficient of performance).

Ref. | Energy Production System | Uncertainty/Reliability Analysis | Factors Considered for Reliability Analysis |
---|---|---|---|

[7] | PV/WT/BDG | N | None |

[8] | PV/WT, PV/BDG, WT/BDG, PV/WT/BDG | Y | Solar radiation, wind velocity, cooling load, other electricity load. |

[9] | PV/WT/Battery | Y | Physical parameters (e.g., U value of window, shading coefficient), design parameters (e.g., occupant number, light ratio), scenario parameters (e.g., ambient temperature, ambient relative humidity). |

[10] | PV/WT/BDG | Y | Solar radiation, wind speed, demand load, wind turbine power coefficient model, PV array efficiency. |

[11] | PV/WT/BDG | Y | Solar radiation, wind velocity, cooling load, other electricity load. |

[12] | PV/WT/TES/EES | Y | Ambient temperature, relative humidity, solar radiation, and wind speed. |

[13] | PV/WT | Y | Physical parameters (e.g., U value of window, shading coefficient), design parameters (e.g., occupant number, light ratio), scenario parameters (e.g., ambient temperature, ambient relative humidity). |

[14] | PV/WT/BDG | Y | Solar radiation, wind velocity, cooling load, other electricity load. |

[15] | PV/WT/Battery | Y | Solar radiation, wind speed, and demand load. |

[16] | PV/WT/Battery | Y | 18 scenario parameters (e.g., occupant density, infiltration rate, solar radiation), 5 design parameters (e.g., window/wall thermal resistance, chiller capacity, and COP), degradation parameters of HVAC system, PV array, WT, energy storage system. |

[17] | PV/WT/Battery | Y | Solar radiation, wind speed, and load. |

[18] | PV/WT/Hydro | Y | Diesel cost, PV capital, and replacement cost. |

[19] | PV/WT/BDG/Battery | Y | Different parameters of the house, e.g., the area of the house. |

[20] | PV/WT/Battery | N | None. |

[21] | PV/WT/BDG/Battery | Y | Cost of PV panel, wind turbine, as well as fossil fuel. |

[22] | PV/SDHW | N | None. |

**Table 2.**Reliability data of PV, WT, and BDG [27].

Generation | ${\mathit{\lambda}}_{\mathit{r}}[1/\mathbf{yr}]$ | ${\mathit{\mu}}_{\mathit{r}}[1/\mathbf{yr}]$ | ${\mathit{T}}_{\mathit{W}}\left(\mathbf{Year}\right)$ |
---|---|---|---|

PV | 3 | 90 | 25 |

WT | 4.6 | 80 | 25 |

BDG | 9.2 | 50 | 25 |

Generation | Availability | ||
---|---|---|---|

Case 1 | Case 2 | Case 3 | |

PV | 1.00 | 0.97 | 0.42–0.94 |

WT | 1.00 | 0.96 | 0.41–0.93 |

BDG | 1.00 | 0.95 | 0.41–0.92 |

Items | Parameters | Conditions |
---|---|---|

Design variables | WT [kW] | 0:20:160 |

BDG [kW] | 20:20:100 | |

PV [m^{2}] | 0:200:4000 | |

Energy system | Heat recovery system efficiency [%] | 80 |

Biodiesel generator efficiency [%] | 30 | |

Chiller coefficient of absorption [%] | 70 | |

Lifetime for biodiesel generator [year] | 25 | |

Lifetime for photovoltaic [year] | 25 | |

Lifetime for wind turbine [year] | 25 | |

Rated power of electric chillers [kW] | 70 × 3 | |

Rated power of absorption chillers [kW] | 70 × 1 | |

Price | Unit price of biodiesel generator [USD/kW] | 205.53 |

Unit price for photovoltaic [USD/m^{2}] | 378.17 | |

Unit price for wind turbine [USD/kW] | 714.29 | |

Oil price [USD/l] | 1.3 | |

Delivered/Exported price [USD/kWh] | 0.13/0.065 | |

Uncertain parameters | Solar radiation (${I}_{irra}$) | Uniform (${\delta}_{I}=\pm 0.2$) |

Wind velocity (${v}_{wind}$) | Uniform (${\delta}_{wind}=\pm 0.1$) | |

Cooling load (${Q}_{c}$) | Uniform (${\delta}_{Q}=\pm 0.3$) | |

Other load (${P}_{other}$) | Uniform (${\delta}_{Oth}=\pm 0.15$) |

Case | Indicator (Objective) | WT (kW) | BDG (kW) | PV (m ^{2}) | F [–] | ɛ [%] |
---|---|---|---|---|---|---|

1: Deterministic | ${T}_{Cn}$ | 160 | 20 | 200 | 0.71 | 46.4 |

$GI{I}_{n}$ | 40 | 60 | 800 | 0.76 | 32.5 | |

2: Markov—No aging effect | ${T}_{Cn}$ | 160 | 20 | 400 | 0.74 | 49.1 |

$GI{I}_{n}$ | 40 | 80 | 400 | 0.77 | 22.8 | |

3: Markov—aging effect | ${T}_{Cn}$ | 160 | 20 | 3600 | 1.52 | 91.2 |

$GI{I}_{n}$ | 160 | 80 | 2200 | 2.37 | 96.2 |

Case | Indicator (Objective) | WT (kW) | BDG (kW) | PV (m ^{2}) | F [–] | ɛ [%] |
---|---|---|---|---|---|---|

1: Deterministic | ${T}_{Cn}$ | 160 | 20 | 0 | 0.69 | 36.0 |

$GI{I}_{n}$ | 40 | 60 | 200 | 0.57 | 0.52 | |

2: Markov—No aging effect | ${T}_{Cn}$ | 160 | 20 | 0 | 0.69 | 29.9 |

$GI{I}_{n}$ | 40 | 60 | 400 | 0.60 | 5.05 | |

3: Markov—aging effect | ${T}_{Cn}$ | 160 | 20 | 600 | 0.78 | 3.05 |

$GI{I}_{n}$ | 60 | 60 | 1200 | 1.03 | 1.34 |

ɛ. | C1 | C2 | C3 |
---|---|---|---|

<−0.4 | 0.0% | 0.0% | 0.0% |

−0.4 | 2.7% | 2.3% | 1.1% |

−0.2 | 1.9% | 1.8% | 20.0% |

0.0 | 45.6% | 46.4% | 45.5% |

0.2 | 93.7% | 93.8% | 68.0% |

0.4 | 98.6% | 98.4% | 83.8% |

0.6 | 100.0% | 100.0% | 93.1% |

0.8 | 100.0% | 100.0% | 98.1% |

≥1 | 100.0% | 100.0% | 100.0% |

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Lu, Y.; Alghassab, M.; Alvarez-Alvarado, M.S.; Gunduz, H.; Khan, Z.A.; Imran, M.
Optimal Distribution of Renewable Energy Systems Considering Aging and Long-Term Weather Effect in Net-Zero Energy Building Design. *Sustainability* **2020**, *12*, 5570.
https://doi.org/10.3390/su12145570

**AMA Style**

Lu Y, Alghassab M, Alvarez-Alvarado MS, Gunduz H, Khan ZA, Imran M.
Optimal Distribution of Renewable Energy Systems Considering Aging and Long-Term Weather Effect in Net-Zero Energy Building Design. *Sustainability*. 2020; 12(14):5570.
https://doi.org/10.3390/su12145570

**Chicago/Turabian Style**

Lu, Yuehong, Mohammed Alghassab, Manuel S. Alvarez-Alvarado, Hasan Gunduz, Zafar A. Khan, and Muhammad Imran.
2020. "Optimal Distribution of Renewable Energy Systems Considering Aging and Long-Term Weather Effect in Net-Zero Energy Building Design" *Sustainability* 12, no. 14: 5570.
https://doi.org/10.3390/su12145570