net zero energy buildings

Accepted Manuscript Performance Analysis of Optimal Designed Hybrid Energy Systems for Gridconnected Nearly/Net Zero Energy Buildings

Zhijia Huang, Yuehong Lu, Mengmeng Wei, Jingjing Liu PII:

S0360-5442(17)31951-5

DOI:

10.1016/j.energy.2017.11.093

Reference:

EGY 11881

To appear in:

Energy

Received Date:

19 May 2017

Revised Date:

12 November 2017

Accepted Date:

16 November 2017

Please cite this article as: Zhijia Huang, Yuehong Lu, Mengmeng Wei, Jingjing Liu, Performance Analysis of Optimal Designed Hybrid Energy Systems for Grid-connected Nearly/Net Zero Energy Buildings, Energy (2017), doi: 10.1016/j.energy.2017.11.093

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ACCEPTED MANUSCRIPT

Highlights o Four optimal hybrid energy systems are compared for designing nZEBs; o Monte Carlo simulation is applied for uncertainty analysis; o Impact of weighting factor combinations on nZEBs performance is investigated. o Correlative dependency between design mismatch ratio and probability is identified. o PV& BDG system has a robust performance among the four HESs.

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Performance Analysis of Optimal Designed Hybrid Energy Systems for Grid-

2

connected Nearly/Net Zero Energy Buildings

3

Zhijia Huang, Yuehong Lu*, Mengmeng Wei, Jingjing Liu

4 5

Department of Civil Engineering and Architecture, Anhui University of Technology, Ma’anshan, 243002, China

6

Abstract:

7

Hybrid energy systems have provided a promising way to realize nearly/net zero energy

8

buildings (nZEB) including isolated buildings in remote areas and grid-connected buildings. This

9

study aims to investigate and compare several typical hybrid energy systems (HESs) for

10

designing grid-connected nearly/net zero energy buildings (nZEB). Specially, an exhaustive

11

searching method and Monte Carlo simulation are utilized to optimize hybrid energy systems for

12

Hong Kong Zero Carbon Building considering uncertainty impacts. The performance of

13

nearly/net zero energy buildings is evaluated in terms of a combined performance comprised of

14

the cost, CO2 emissions and grid interaction index. Subsequently, the effects of design mismatch

15

ratio, weighting factor combination and the probability to be nZEB on the performance are

16

analyzed and compared under the four hybrid energy systems. The study results show that the

17

probability for a building to achieve annual energy balance is highly depending on the design

18

mismatch ratio, and the correlative dependencies between the two parameters are fitted in

19

formulas for the studied hybrid energy systems. In addition, an nZEB designed with PV& BDG

20

system is found to have a robust performance compared with that designed with other three

21

hybrid energy systems under the same design condition.

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Keywords: Net zero energy building, Hybrid energy systems, Monte Carlo simulation, design mismatch ratio

24

____________________________________________________________

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* Corresponding author. E-mail address: [email protected]

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1. Introduction

28

The world energy requirements and CO2 emissions would increase by 65% and 70% respectively

29

between 1995 and 2020, as reported by International Energy Agency (IEA) [1]. Buildings

30

consume about 40% of the total world energy production, which is strongly depending on the

31

low cost fossil fuels resources. Renewable energy resources, as environmental friendly and

32

alternative energy clean sources, are expected to contribute the world energy requirements from

33

14% at present up to 80% in 2100 [2]. Due to the intermittent nature of the renewable energy

34

sources, hybrid energy systems (HES) usually consist of two or more renewable energy sources

35

together to provide a reliable power to the load. And the hybrid energy system is widely accepted

36

as a promising approach for future buildings to achieve primary energy savings, pollution

37

emissions reductions and sustainable low-carbon society [3-4].

38

Recently, hybrid energy systems have been widespread utilized to provide power for rural and

39

remote areas as well as micro-grid system applications [5-6]. Different types of HESs, e.g.

40

photovoltaic & wind turbine (PV&WT) [7-9], photovoltaic & wind turbine & diesel generator

41

(PV&WT&BDG) [10-12], photovoltaic & wind turbine & battery or fuel cell (PV&WT&BAT or

42

PV&WT&FC) [13-18] etc, have been investigated in previous studies. In Ref. [7], a 30 kW

43

PV&WT hybrid energy system dynamic model was presented to investigate the control strategy

44

for a sustainable micro-grid application and it was finally demonstrated to be a feasible option

45

for grid application. As indicated by Gomes et al. [8], the variability in non-dispatchable

46

PV&WT power generation poses great challenges to the integration of renewable energy sources

47

into the electricity power grid. Therefore, they formulated the PV&WT coordinated trading as a

48

stochastic linear programming problem, and then obtained the optimal bidding strategy that

49

maximizes the total profit. In order to achieve a fast and stable respond for the power grid control,

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a diesel engine and an intelligent controller were proposed for the PV &WT by Hong et al. [10],

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and it is demonstrated to be more efficiency and better transient as well as more stability even

52

under different load conditions and disturbance. In another study, Dufo-López et al. [11]

53

developed a new stochastic-heuristic methodology for optimal the electrical supply of off-grid

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photovoltaic & wind & diesel with battery storage, which takes into account uncertain

55

parameters impact. Energy storage systems (e.g. battery or fuel cell) are usually employed to

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complement the renewable energy systems in stand-alone applications and shift the peak load to

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relieve the power imbalance in grid-connected buildings. Ma et al. [13] employed the HOMER

58

software to conduct a feasibility study and techno-economic evaluation on a hybrid solar-wind

59

system with battery energy storage for a standalone island, the optimal autonomous system

60

configuration is finally obtained in terms of system net present cost and cost of energy.

61

Moghaddam et al [14] presented an expert multi-objective Adaptive Modified Particle Swarm

62

Optimization algorithm (AMPSO) for optimal operation of a back-up Micro-Turbine/Fuel

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Cell/Battery hybrid power to minimize the total operating cost and the net emission

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simultaneously. By considering the daily energy consumption variations for winter and summer

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weekdays and weekends, Tazvinga et al [15] conducted a study on the photovoltaic & diesel &

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battery model for remote consumers and compared it with the case where the diesel generator

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satisfies the load on its own. Yang et al [16] presented a power management system of a

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household photovoltaic & battery hybrid power system within demand side management under

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time of use electricity tariff, and the proposed strategies can largely reduce energy cost and

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energy consumption from the grid. With the fast development of smart grids and “nearly/net zero

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energy buildings (nZEBs)” for future buildings, four typical HESs, i.e. PV&WT, PV&BDG,

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WT&BDG and PV&WT&BDG, are desirable design options for designing grid-connected

73

nZEBs. Therefore, it is necessary and meaningful to evaluate and compare the performance of

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the four types of HESs, which can assist designers with system selection and design optimization

75

for grid-connected nZEBs.

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In the study of designing hybrid energy systems for buildings, control strategies applied for

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energy systems must be considered simultaneously. Two basic operation strategies are

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commonly applied for combined cooling, heating and power system (CCHP/CHP/CCP):

79

following the electric load (FEL) and following the thermal load (FTL) [19-20]. Other strategies

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for operating CCHP system such as operational strategy based on the ratio of the cooling

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generated to actual building cooling load [21] and a novel operation strategy aiming at

82

minimizing an integrated index [22]. There are also considerable studies conducted on model

83

predictive control (MPC)-based optimal scheduling of energy storage systems [23-24] and

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distribute energy generation systems [3, 15, 25]. Zhao et al. [3] adopted the MPC method based

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on nonlinear programming algorithm programming to optimize the operation of integrated

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energy systems in low energy buildings under day-ahead electricity price. The proposed optimal

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scheduling strategy can help the building to achieve significant reductions in operation cost,

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primary energy consumption and CO2 emissions. In order to compare the corresponding fuel

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costs and evaluate the operational efficiency of the hybrid system for a 24-h period, Tazvinga et

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al [15] investigated the photovoltaic & diesel & battery model for remote consumers by

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considering the daily energy consumption variations for winter and summer weekdays and

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weekends. The results show that it can achieve 73% and 77% fuel savings in winter and 80.5%

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and 82% fuel savings in summer for days considered when compared to the case where the diesel

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generator satisfies the load on its own.

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Selection of evaluation criteria is also an important work necessary for evaluating the designed

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HES for an nZEB. The evaluation criteria considered in previous studies are classified into four

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aspects: technological factors (e.g. Feasibility, risk and reliability), economic factors (e.g.

98

pollutant emission, land requirements), socio-political factors (e.g. political acceptance, social

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acceptance) and environmental factors (e.g. implementation cost, economic value) [26-27].

100

Balaras et al. [28] studied 193 European apartment buildings on the environmental impact of

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energy consumption due to the building heating. They demonstrated that about 30% of the

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buildings had higher airborne emissions. Li et al. [29] conducted a techno-economic feasibility

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study on an autonomous hybrid PV&WT&battery power system for a household in Urumqi of

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China. The Hybrid Optimization Model for Electric Renewables (HOMER) simulation software

105

was employed in this study to estimate the total net present cost (NPC) and the levelized cost of

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energy (COE) of the system. Dufo-López et al. [11] proposed a new stochastic-heuristic

107

methodology for the optimization of stand-alone (off-grid) hybrid photovoltaic & wind & diesel

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with battery storage systems, and the aim is to minimize the net present cost of the system.

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Considering the random and intermittent nature of solar and wind source, the reliability of

110

energy systems becomes an important issue. Loss of power supply probability (LPSP) is a

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widely used indicator to assess the system reliability [30-31]. In the grid-connected nZEB, two-

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way information flow between the buildings and smart grid brings some new challenges for grid

113

system and therefore the interaction should be considered and evaluated [32-35]. Cao et al [32]

114

defined six matching indices based on the extension of two commonly used basic indices (i.e.

115

on-site energy fraction and on-site energy matching), and these extended indices are

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demonstrated to be powerful tools for assessing the matching situation of complicated building

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energy systems. Deng et al [33] conducted a review on the evaluation method for net zero energy

118

buildings, the load matching and grid interaction are recommended to evaluate the NZEB

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performance on different time-scales. However, the features of different types of HESs are still

120

lacking investigation in term of the interaction between the buildings and smart grid.

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Previous studies on the size optimization of hybrid energy system are usually carried out using a

122

deterministic approach and some take into account uncertainties in renewable sources. However,

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selection of HES for nZEB is an uphill task as it is not only dependent of the load requirements

124

but also greatly affected by the randomly varied input parameters of the sources. Kamjoo et al.

125

[36] optimized a PV & wind & battery system using Genetic Algorithm (GA) considering

126

uncertainties by the method of chance-constrained programming (CCP) and comparing the

127

results with Monte Carlo Simulation (MCS). In Ref. [37], Maheri investigated the reliability of

128

different PV & wind & diesel & battery systems under the deterministic design method. In his

129

later Ref. [38], two algorithms (with MCS) were employed to the optimization based on the

130

margin of safety. Other studies on uncertainty analysis of renewable energy system design can be

131

found in Ref. [39-42].

132

Our previous study [43] has developed a robust optimal design method for sizing renewable

133

energy systems in nZEB. Based on the developed robust optimal design method, this study aims

134

to investigate and compare the robust performance of a nearly/net zero energy building designed

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with four typical HESs. This will help the system designer to select suitable design options while

136

implementing hybrid energy systems for grid-connected buildings. The remainder of this paper is

137

organized by five subsections as follows. Section 2 presents an outline of performance analysis

138

of nZEB designed with different HESs when uncertainty is concerned. Section 3 describes the

139

information of the studied building and energy systems. Section 4 discusses the obtained results

140

in terms of four aspects. Finally, the conclusion of this study is given in Section 5.

141

2. Outline of performance analysis

142

2.1 Problem description

143

It is acknowledged that hybrid energy system (HES) is one of the most important elements for

144

buildings to be nZEB, and different types of HESs may be preferred for different conditions. As

145

the target of annual energy balance for nZEB is highly depending on the selection of HES, it is

146

meaningful to investigate how the design mismatch ratio affects the probability of achieving

147

nZEB. In addition, uncertain parameters (e.g. solar radiation, wind velocity, ambient temperature

148

etc.) may have significant impact on nZEB performance since they affect both building energy

149

consumption and energy generation.

150

The capability of the building to realize annual energy balance as well as undertake the

151

performance fluctuation is greatly affected by the types of HES. As shown in Fig.1, when

152

uncertainty is concerned for the design optimization, building energy consumption and energy

153

generation will fluctuate under the design option of HES. An increase in HES design size

154

indicates that a larger design mismatch ratio will be obtained, and the probability to be nZEB

155

will also be increased. For example, three types of HES, e.g. S1, S2 and S3, are considered for

156

nZEB respectively. It is obvious that a larger design mismatch ratio brings in a higher probability

157

to be nZEB using any of the three systems. Under the same design mismatch ratio, the

158

probability of being nZEB designed with S2, however, may be higher than that designed with S1

159

and S3. In addition, nZEB designed with S2 may have a much more stable performance than that

160

designed with S1 or S3.

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This study analyzes four typical HESs, i.e. PV&WT, PV&BDG,WT&BDG and PV&WT&BDG,

162

which is based on an robust design method concerning uncertainties for sizing HES in nZEB. It

163

aims to identify how the design mismatch ratio affects the probability to be nZEB under the four

164

typical HESs, and compare the performance stability of the four optimal designed systems facing

165

uncertainty impacts. It will assist nZEB designers in selecting an appropriate design option based

166

on a systemic analysis. Probability VS mismatch ratio under different HESs

Uncertainties Solar radiation Wind velocity

xi

1.0

Probability

S1 S2

S3 Design mismatch ratio

Ambient humidity

167

S3

S1

Ambient Temperature

...

Performance

S2

+a -a

Fluctuation of nZEB performance

t

S1/S2/S3: different hybrid energy systems (HESs)

-△x x △x -△x x △x -△x x △x x：design parameter，△x：variation range of x

168

Fig.1. Impact of uncertainties and the types of HES on the probability to be nZEB and

169

performance

170

2.2 Performance analysis based on design optimization

171

This study focuses on investigating how design mismatch ratio affect the probability of being

172

nZEB under four types of HESs and comparing the stability of the nZEB performance facing

173

uncertain impacts, as shown in Fig. 2. It can be explained as follows:

174



In the first step, a zero energy building model is built in TRNSYS to simulate the cooling

175

load file. Then, uncertain parameters U, e.g. solar radiation, wind velocity and cooling load,

176

are identified and assumed to be independent. It should be noted that both solar radiation and

177

other load have direct effect on the cooling load in the real case but the effect of those

178

parameters on cooling load is different in different types of buildings. As our study aims to

179

identify the overall effect of uncertain parameters on the design of four types of nZEB, we

180

assume the four key parameters to be independent. These uncertain parameters are usually

181

assumed to follow a certain distribution, e.g. the uniform distribution, normal distribution, t-

182

distribution and F-distribution. Then, Monte Carlo method can be used to generate the

183

sample parameters in MATLAB, which are stored in the set U'.

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t,i

t,i

t,i

t,i

184

U = [I ;vwind;Q ;Wother]

185

U ∊[U ‒ δ × U,U + δ × U]

186

(1)

'



In the second step, the HES models (e.g. PV, WT, BDG, etc.) and building energy system

187

models (e.g. pump, cooling tower fan, AHU fan, etc.) are developed in MATLAB. Select the

188

type of HES available and set the searching ranges of HES size for the design optimization,

189

and then each design option can be represented by the design mismatch ratio (ε). It is

190

defined as the ratio of the difference between electricity generation and building electricity

191

demand to the building electricity demand in one year, as shown in Eq-2. It is obviously that

192

a higher value indicates a larger HES size.

193

ε=

t t ∑8760(Wgeneration ‒ Wdemand) t=1 t ∑8760Wdemand

(2)

t=1

194

Then, exhaustive searching method is employed to find the optimal design option among the

195

searching ranges. As deterministic design method simply applies the typical year parameters

196

for system design, which is not suitable for energy system design in the types of sensitive

197

buildings such as nZEB. In order to satisfy the required probability to achieve annual energy

198

balance considering uncertainty, an indicator (γ) is defined, as shown in Eq-3, for designers

199

to classify the type of nZEB. Where, a high value of γrepresents that the design option has

200

a high probability for buildings to achieve nZEB

201

γ=

'

202



n (the number of year satifying nZEB requirement) × 100% n(total number ofsimulation year)

(3)

In the third step, nZEB performance (e.g. annual total cost, CO2 emissions, grid interaction

203

index, etc.) is evaluated on annual assessment and can be computed under each design

204

option. On the basis of the required nZEB, design mismatch ratio and the associated optimal

205

design option can be ranked according to their performance. The relationship between the

206

design mismatch ratio and the probability to be nZEB can also be identified and compared.

207

In addition, the stability of system performance could be investigated by cumulative

208

distribution function.

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Uncertain parameters Solar radiation

Wind velocity

Cooling load

Building other load

(ZEB model in TRNSYS)

(On-site measured data in BMS)

Monte Carlo Simulation Select the type of HES

Design optimization (Exhaustive Searching Method) (MATLAB)

Sample file (Eq-1) Search size ranges (Num)

HES model (e.g PV, WT, BDG, etc.) (Eq-21~Eq-24)

Building energy system model (e.g HVAC) (Eq-4~Eq-20)

Design mismatch ratio

Probability

Performance

(Eq-2)

(Eq-3)

(Eq-25~Eq-29)

Completed

N

Y

Results Optimal design option Performance evaluation (i.e. Total cost, CO2 emission, Grid stress)

Cumulative distribution function Relationship between the design mismatch ratio and the probability to be nZEB

209

Fig.2. Design optimization of HES for ZEB under uncertainties

210 211

3. Case study

212

3.1 Building description

213

The Construction Industry Council (CIC) Zero-Carbon Building (ZCB) in Hong Kong is a net

214

zero-carbon building designed in hot and humid climate zone, as shown in Fig. 3. The three-

215

storey building includes a basement and it covers a total site area of 14,700 m2. In this building,

216

20% of energy saving is obtained through passive design technology (i.e. wind catcher, high

217

performance glazing and ultra-low thermal transfer etc) and 25% of energy saving is obtained

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218

through green active energy systems (i.e. active skylight and high temperature cooling system

219

etc.). The total air conditioned area in the building is 995 m2 and the designed building peak

220

cooling load is about 160 kW. 1015 m2 PV combined with 100 kW bio-diesel generator are

221

installed to provide electricity for the building demand. The estimated output from PV and bio-

222

diesel generator are 87 MWh/a and 143 MWh/a respectively, and the predicted energy use

223

intensity of the building is 86kW/m2. The basic information of the energy systems studied is

224

listed in Table 1.

225 226

Fig.3. Aerial view of Zero Carbon Building in Hong Kong (adapted from Ref. [44]).

227

Table 1 Specifications of energy systems in this study Parameters

Specification

Orientation Total net floor area (A, m2) Window-to-wall ratio Shading Wall U value (W/(m2*K))/absorption Roof U value (W/(m2*K))/absorption Designed peak cooling load (Qc, kW) Rated capacity of electrical chiller (Pec,rated, kW) Rated capacity of absorption chiller (Pec,ab , kW) Heat recovery system efficiency (𝜂𝐵𝐷𝐺)

South-east 1520 <10–40% 45◦ (angle) <1.0/<0.4 <1.0/<0.3 160 70×3, COPN=4.2 70×1, COPN=0.7 0.8 0.3 205.53

Bio-diesel generator efficiency (𝜂ℎ𝑟𝑠) Unit price of bio-diesel generator (TCBDG, USD/kW)

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Unit price for photovoltaic (TCpv, USD/m2)

378.17 714.29 1.3 0.13 0.065 40,000h 20 years 20 years 0.608 0.552

Unit price for wind turbine (TCwT,USD/kW) Oil price (TCoil, USD/l) Delivered electricity price (USD/kWh) Exported electricity price (USD/kWh) Lifetime for bio-diesel generator Lifetime for photovoltaic Lifetime for wind turbine Emission factors of electricity from the grid Emission factors of bio-diesel combustion 228

A schematic of the studied building and its energy system are shown in Fig 4. In this building,

229

the electricity consumption comes from HVAC system (i.e. electric chillers, pumps and AHU

230

fans) and other appliances (lighting, office equipment, etc.). PV, WT and BDG are the three

231

systems comprising the HES, which can provide electricity for the building. The BDG can

232

generate both electricity and heating, and the heating is used to drive the absorption chiller. In

233

this study, The BDG is controlled according to the building cooling load. The electric chiller is

234

the backup cooling supplier when the cooling provided by the adsorption chiller is not sufficient.

235

The grid is the backup power supplier and receiver for the building. Therefore, building thermal

236

and electricity is subjected to energy balance described as follows. t

237

t

t

(4)

Qc = Qec + Qac t

238

t

t

t

t

t

Pdemand = Pec + Ppump + Pct + Pfan + Pother t

239

t

t

t

t

Psupply = PPV + PWT + PBDG + Pgrid

(5) (6)

240

The building cooling load (Qc) is undertook by absorption chiller (Qac) and electric chillers (Qec),

241

as shown in Eq-4. The building electrical demand (Pdemand) is comprised of electric chillers (Pec),

242

pumps (Ppump), cooling tower fans (Pct), AHU (air handling unit) fans (Pfan) and other appliances

243

(Pother) including power consumed by lighting, socket outlet, fuse spur, etc., as shown in Eq-5.

244

The power suppliers are the PV (PPV), wind turbine (PWT), bio-diesel generator (PBDG) and the

245

grid, as shown in Eq-6.

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On-site generation systems PV WT BDG Electricity Heating energy

Solar gains Energy use

Heat transmissions

Electric chiller

Appliances

Delivered energy

Grids

Adsorption chiller

Pumps

Heat recovery system

AHU fans & cooling tower fans

Exported energy

246 247

Fig.4. Energy flows among building energy systems

248

3.2 Energy system models and formulation of objective function

249

Energy system models in this study are developed in MATLAB, which are simply described as

250

follows. It is noted that the developed energy system models are validated by the on-site data

251

recorded by building management system (BMS) in ZCB. Detail description and validation of

252

models can refer to Ref. [44].

253

The electricity consumption of the electric chiller (Pec) is calculated as shown in Eq-7. The

254

COPec is obtained based on the partial cooing load ratio (PLR) and can be calculated by an

255

empirical model (Eq-8). Where, a=-1.6757, b=0.3083, c=3.5093, d=0.853 are obtained by fitting

256

the models. The normal capacity of chiller (COPN) is 4.2, and the outlet water temperature of the

257

evaporator (Teva,out) is set to be 7℃, while the inlet water temperature of condenser (Tcon,in) is

258

assumed to have a difference of 5 K with the wet-bulb temperature of the cooling tower inlet air.

259

𝑄𝑒𝑐

𝑃𝑒𝑐 = 𝐶𝑂𝑃

𝑒𝑐

(7)

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260

𝐶𝑂𝑃𝑒𝑐 = 𝐶𝑂𝑃𝑁 × 𝑇

𝑇𝑒𝑣𝑎,𝑜𝑢𝑡

3

𝑐𝑜𝑛,𝑖𝑛 ‒ 𝑇𝑒𝑣𝑎,𝑜𝑢𝑡

2

(8)

× (𝑎 × 𝑃𝐿𝑅 + 𝑏 × 𝑃𝐿𝑅 + 𝑐 × 𝑃𝐿𝑅 + 𝑑)

261

The cooling water pumps are assumed to be constant speed pumps working at rated power. And

262

the chiller water pumps are variable speed pumps with the electricity consumption (Pcwp)

263

depending on the pressure drop (△pcwp), the water flow rate (mw) and pump efficiency (ηcwp) as

264

shown by Eq-9, The pressure drop of the chilled water loop in the building is assumed to be

265

linear to the water flow rate (mw), representing the operation of pumps at medium level energy

266

efficiency in general practice, as shown in Eq-10. Eq-12 is obtained by merging Eq-10 and Eq-

267

11.. The rated power of chilled water pumps is 9 kW at the design flow rate, and the power

268

consumption is about 2 kW at the minimum water flow rate (20% of design flow rate). These

269

parameters are identified by using the on-site data in the building. Where, mw,design is the design

270

water flow rate, △pcwp,min is the minimum pressure drop of the chilled water loop.

271

𝑃𝑐𝑤𝑝 =

∆𝑝𝑐𝑤𝑝 × 𝑚𝑤

(9)

η𝑐𝑤𝑝 '

272

∆𝑝𝑐𝑤𝑝 = ∆𝑝𝑐𝑤𝑝,𝑚𝑖𝑛 + 𝛼 ×

273

𝑃𝑐𝑤𝑝 = 𝛼𝑐𝑤𝑝 ×

274

𝑃𝑐𝑤𝑝 = 10 × 𝑚

𝑚𝑤 𝑚𝑤,𝑑𝑒𝑠𝑖𝑔𝑛

𝑚𝑤 𝑤,𝑑𝑒𝑠𝑖𝑔𝑛

𝑚𝑤

+ 𝛽𝑐𝑤𝑝 × (𝑚

‒ 1 × (𝑚

(10)

𝑚𝑤,𝑑𝑒𝑠𝑖𝑔𝑛

𝑚𝑤

2

)

𝑤,𝑑𝑒𝑠𝑖𝑔𝑛

𝑚𝑤

2

)

𝑤,𝑑𝑒𝑠𝑖𝑔𝑛

(11) (12)

275

The fan power consumption of the cooling tower, (Pct) is calculated as Eq-13. Where, ma is the

276

air flow rate of cooling tower fan, A and k are determined according to the tower size. As the air

277

flow rate (ma) is proximately proportional to the fan speed (n) and the cooling tower cooling

278

capacity (Qct) also varies proximately in direct proportion to the fan speed, as shown in Eq-14.

279

The power consumption of cooling tower fan can also be reformulated as Eq-15. Where, ndesign,

280

ma,design and Qct,design are the design fan speed, design air flow rate and design cooling capacity of

281

cooling tower respectively. k is selected as 1.5 which is determined on the basis of practical in-

282

situ operation data.

283

𝑃𝑐𝑡 = 𝐴 × 𝑚𝑎

𝑘

(13)

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𝑚𝑎

284

𝑛𝑎

𝑄𝑎

(14)

𝑚𝑎,𝑑𝑒𝑠𝑖𝑔𝑛 = 𝑛𝑎,𝑑𝑒𝑠𝑖𝑔𝑛 = 𝑄𝑎,𝑑𝑒𝑠𝑖𝑔𝑛

𝑃𝑐𝑡

285

𝑃𝑐𝑡,𝑑𝑒𝑠𝑖𝑔𝑛

286

= (𝑄

𝑃𝑐𝑡 = 𝑊𝑐𝑡,𝑑𝑒𝑠𝑖𝑔𝑛 × (𝑄

𝑘

𝑄𝑐𝑡

(15)

)

𝑐𝑡,𝑑𝑒𝑠𝑖𝑔𝑛

1.5

𝑄𝑐𝑡

(16)

)

𝑐𝑡,𝑑𝑒𝑠𝑖𝑔𝑛

287

The power consumption (Pfan) of AHU fan is calculated according to the pressure head of the fan

288

(△pfan), the air flow rate (υa) and the fan efficiency (ηfan), as shown in Eq-17. In general, the fan

289

pressure head (△pfan) consists of the pressure drop after the pressure sensor point (VAV box etc.)

290

(△psen) and pressure drop in other parts of the air system (△pothers) (e.g. supply duct, cooling coil

291

and return main duct), as shown in Eq-18. Thus, the fan power consumption can be given by Eq-

292

19. By assuming △psen=0.4×△pfan, an empirical fan power model is finally obtained as Eq-

293

20.Where, υa,design is the design air flow rate that can be identified by using the on-site data in

294

ZCB.

295

𝑃𝑓𝑎𝑛 =

296

297

∆𝑝𝑓𝑎𝑛 × 𝑣𝑎

(17)

η𝑓𝑎𝑛

(18)

∆𝑝𝑓𝑎𝑛 = ∆𝑝𝑠𝑒𝑛 + ∆𝑝𝑜𝑡ℎ𝑒𝑟𝑠

𝑃𝑓𝑎𝑛 =

∆𝑝𝑠𝑒𝑛 × 𝑣𝑎,𝑑𝑒𝑠𝑖𝑔𝑛 η𝑓𝑎𝑛

×𝑣

𝑣𝑎

𝑎,𝑑𝑒𝑠𝑖𝑔𝑛

3

+

𝑣𝑎

298

𝑣𝑎,𝑑𝑒𝑠𝑖𝑔𝑛

χ × 𝑣𝑎,𝑑𝑒𝑠𝑖𝑔𝑛 η𝑓𝑎𝑛

𝑣𝑎

× (𝑣

3

)

𝑎,𝑑𝑒𝑠𝑖𝑔𝑛

+ 12 × (𝑣

𝑣𝑎

3

)

𝑎,𝑑𝑒𝑠𝑖𝑔𝑛

(19)𝑃𝑓𝑎𝑛 = 8 × (20)

299

The PV power generation is calculated as shown in Eq-21. Where, the PV area is Ades (m2), PV

300

module efficiency is ηm, the packing factor is Pf, the power conditioning efficiency is ηPC and the

301

hourly irradiance is I (kWh/m2).

302

𝑃𝑃𝑉 = 𝐴𝑑𝑒𝑠 × 𝜂𝑚 × 𝑃𝑓 × 𝜂𝑃𝐶 × 𝐼

(21)

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303

The power consumption of the WT is calculated as shown in Eq-22. Where, the air density is ρa

304

(kg/m3), the area of blade is AWT (m2), the coefficient of the wind turbine performance is cp,w, the

305

combined efficiency of the generator and wind turbine is ηWT and the wind velocity is vwind (m/s).

306

3

𝑃𝑊𝑇 = 0.5 × 𝜌𝑎 × 𝐴𝑊𝑇 × 𝑣𝑤𝑖𝑛𝑑 × 𝑐𝑝,𝑤 × 𝜂𝑊𝑇

(22)

307

The power consumption of Bio-diesel generator (BDG) is calculated as shown in Eq-23. The fuel

308

consumption of BDG can be estimated by Eq-24. Where, WBDG and Wrated,BDG are the actual

309

power output and the rated power of the BDG respectively. The coefficient AG = 0.246 (l/kWh)

310

and BG = 0.08145 (l/kWh). Heat recovery system efficiency (𝜂ℎ𝑟𝑠) is assumed to be 0.8 and the

311

BDG efficiency (𝜂𝐵𝐷𝐺)is assumed to be 0.3, as shown in table 1.

312 313

𝑃𝐵𝐷𝐺 = (1 ‒ 𝜂

𝑄𝑟 𝐵𝐷𝐺) × 𝜂ℎ𝑟𝑠

× 𝜂𝐵𝐷𝐺

𝐹𝑏𝑖𝑜 = 𝐴𝐺 × 𝑊𝐵𝐷𝐺 + 𝐵𝐺 × 𝑊𝑟𝑎𝑡𝑒𝑑,𝐵𝐷𝐺

(23) (24)

314

In this study, to evaluate the performance of nZEB designed with in different types of HESs, the

315

annual total cost (f1), CO2 emissions (f2) and grid interaction index (f1) are the three indicators to

316

be concerned. The cost (Eq-25) is the sum of HES investment cost divided by its lifetime cost

317

TCresi and annual operational cost TCoperation (i.e. oil cost and electricity bill cost). The total

318

carbon dioxide emissions (CDE) are presented by Eq-26. Where, CDEele and CDEbio are the

319

emissions from delivered electricity and bio-diesel generator on-site combustion respectively.

320

f1(X) = TCresi + TC0peration

(25)

321

f2(X) = CDEele + CDEBDG

(26)

322

The building-grid interaction is defined based on the ratio between net exported energy and the

323

average energy demand in the building during a given period, as shown in Eq-27. Grid

324

interaction index (GII) is defined as the standard deviation of the building-grid interaction over

325

the period as shown in Eq-28. It is used to estimate the average stress of a building on the power

326

grid and a low standard deviation is usually preferred.

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'

327

fgrid,i,T =

Wex,i ‒ Wim,i ∫t2Ei dt/T

(27)

t1

'

328

f3(X) = STD(fgrid,i,T)

(28)

329

As the designers may prefer different indicators, the three indicators can simplified into one

330

indicator by using weighted-sum of the three indicators, as shown in Eq-29. The sum of

331

weighting factors w1, w2 and w3 is 1. Where, X is a vector of design variables at the design stage

332

(i.e, PV area, rated power of wind turbine, rated power of BDG), the set U' is a form of

333

uncertainty set representing uncertain parameters in the operation stage, as shown in Eq-1. Here,

334

f1,i, f2,i and f3,i

335

grid interaction index respectively in the year of i. AX≤a is used to define the searching range

336

of design variables. For instance, the maximum design value of WT rated power, BDG rated

337

power and PV area is 100, 100 and 2000 respectively. Here, A is actually a coefficient of 1 in our

338

study. Function g1 is used to classify those design variables that the power generation minus

339

building energy consumption is equal to or more than zero, which means that the aim of net zero

340

energy building is achieved under the selected size. Function g2 is used to give a constraint that

341

building energy balance must be meet under all design variables.

342 343

are the normalized total cost, normalized carbon dioxide emissions and normalized

n Min 𝑓 = ∑i = 1(w1 × f1,i(X,U') + w2 × f2,i(X,U') + w3 × f3,i(X,U'))/n,

s.t.

(29)

AX ≤ a

344

g1(X,U') ≥ 0

345

g2(X,U') = 0

346

3.3 Description of parameters and systems studied

347

In this study, four types of HESs are considered for the design of nZEB, and they are assumed to

348

follow the rule-based control. The size ranges for both WT and BDG are set between 0 and 100

349

kW with an interval of 5 kW, and the size ranges for PV is between 0 and 2000 m2 with an

350

interval of 100 m2. The concerned uncertain parameters are solar radiation, wind velocity,

351

cooling load and other load, which are all assumed to follow uniform distributions. Different

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352

users may give priority to different performance indicators, four weighting factor combinations

353

are investigated in this study, as shown in Table 2. The typical meteorological year (i.e. 1987) in

354

Hong Kong is selected as the basic year for simulation, and the daily average temperature,

355

relative humidity, solar radiation and wind velocity are shown in Fig. 5.

356

Table 2 Parameters set for design optimization of HES under uncertainty Types

System studied

Design variables (X)

Uncertain parameters

Feature

Specification

PV&WT&BDG

Rule-based control

PV&WT

/

PV&BDG

Rule-based control

WT&BDG

Rule-based control

WT (kW)

0:5:100

BDG(kW)

0:5:100

PV(m2)

0:100:2000

Solar radiation (Iirra)

Uniform (δI=±0.2)

Wind velocity (vwind)

Uniform (δvwind=±0.1)

Cooling load (Qc)

Uniform (δQ=±0.3)

Other load (Wother)

Uniform (δOther=±0.15) (1/3,1/3,1/3)

Weighting factors

(w1,w2,w3)

(1,0,0) (0,1,0) (0,0,1)

357

50 45 40 35 30 25 20 15 10 5 0

Temperature Relative humidity

℃

1

25 49 73 97 121 145 169 193 217 241 265 289 313 337 361

Day Solar irradiation Wind velocity

Solar irradiation (W/m2)

1200 1000

16 14 12

800

10

600

8 6

400

4 200 0

2 1 25 49 73 97 121 145 169 193 217 241 265 289 313 337 361

Wind velocity (m/s)

358

0

Day

359 360

100 90 80 70 60 50 40 30 20 10 0

Relative humidity (%)

Temparature( )

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Fig.5. Ambient conditions of a representative year in Hong Kong

361

4. Results and discussions

362

In this study, Hong Kong Zero Carbon Building (ZCB) model is developed in TRNSYS and

363

energy system models are developed based MATLAB. It aims to investigate the following four

364

aspects: (1) Influence of the type of nZEB on optimal design mismatch ratio; (2) Influence of

365

weighting factors on optimal design mismatch ratio; (3) The relationship between design

366

mismatch ratio and the probability of achieving nZEB; (4) Evaluation of performance stability.

367

The hourly renewable energy resources and building loads in six days (three days in summer and

368

three days in winter) are shown in Fig. 6.

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Summer

120 80 40 1

Wind velocity (m/s)

369 16

Summer Winter

12 8 4

1

371

20 15 10 5 1

8 15 22 29 36 43 50 57 64 71 Time (h)

0

370

Summer Winter

0

0

8

15 22 29 36 43 50 57 64 71 Time (h)

Solar radiation (W/m2)

Cooling load (W/m2)

160

Other load (W/m2)

25

8

15 22 29 36 43 50 57 64 71 Time (h)

800

Summer Winter

600 400 200 0 1

8 15 22 29 36 43 50 57 64 71 Time (h)

Fig.6. Renewable energy resources and building load in three summer/winter days.

372

4.1 Influence of the type of nZEB on optimal design mismatch ratio

373

To design an nZEB, it is important to identify the type of nZEB to be achieved. In this study,

374

four types of nZEB, i.e. 0% nZEB, 50% nZEB, 80% nZEB and 100% nZEB, are investigated.

375

Table 3 shows the results of optimal HES size, the associated optimal design mismatch ratio and

376

performance evaluation for the four types of nZEB, which is obtained based on robust design

377

method and the weighting factors to be equally treated (w1= w2= w3=1/3). .

378

It can be found that when designing the type of 100% nZEB, the optimal design mismatch ratio

379

is 0.28, 0.32, 0.28 and 0.31 for PV&WT&BDG, PV&WT, PV&BDG and WT&BDG respectively.

380

And power from/to grid under the four HESs is compared in six days as shown in Fig. 7a (in

381

summer) and Fig. 7b (in winter). On the third day in summer, all the four systems provide a large

382

amount of power to grid due to the presence of high wind speed and strong solar radiation. In

383

winter, the PV&WT has the greatest potential to generate power due to the non-operating BDG

384

in other three systems.

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385

In terms of designing the type of 50% nZEB, the optimal design mismatch ratio is 0.12, 0.08,

386

0.05 and 0.05 for PV&WT&BDG, PV&WT, PV&BDG and WT&BDG respectively. It indicates

387

that when design mismatch ratio is selected to be around 0.0, the probability for the building to

388

achieve nZEB is about 50%. In terms of designing HES for conventional buildings (No

389

constraint on the mismatch between energy generation and energy consumption), the optimal

390

design mismatch ratio is identified between -0.20 and -0.40.

391

Table 3 Optimal design size of HES for nZEB according to the probability required System

PV&WT& BDG

PV&WT

PV&BDG

WT&BDG

392

p (Constraint: γ>=p)

Design mismatch ratio (ε)

0% 50% 80% 100% 0% 50% 80% 100% 0% 50% 80% 100% 0% 50% 80% 100%

-0.21 0.12 0.15 0.28 -0.24 0.08 0.16 0.32 -0.38 0.02 0.12 0.28 -0.28 0.05 0.15 0.31

Optimal design option WT BDG PV (kW) (kW) (m2) 60 15 600 100 5 1100 100 10 1000 100 10 1300 80 0 700 100 0 1200 100 0 1400 100 0 1800 0 30 700 0 35 1400 0 35 1600 0 40 1800 100 10 0 100 35 0 95 45 0 100 55 0

Performance f

γ

0.685 0.642 0.643 0.651 0.687 0.645 0.648 0.668 0.776 0.882 0.922 0.999 0.729 0.733 0.757 0.797

0% 75% 83% 100% 0% 67% 84% 100% 0% 53% 87% 100% 0% 59% 84% 100%

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40

Power from/to grid (W/m2)

20 0 -20

1

5

9

13 17 21 25 29 33 37 41 45 49 53 57 61 65 69

-40

Time (h)

-60 -80 -100 -120

393

WT&BDG

-140

PV&BDG

-160

PV&WT

-180

PV&WT&BDG

(a) In summer

Power from/to grid (W/m2)

40 20 0 1

5

9

13 17 21 25 29 33 37 41 45 49 53 57 61 65 69

-20

Time (h)

-40 WT&BDG

-60

PV&BDG PV&WT

394

-80

PV&WT&BDG

(b) In winter

395 396

Fig.7. Power from/to the grid in three days under four types of HESs (γ=100%).

397

4.2 Influence of weighting factors on optimal design mismatch ratio

398

In Section 4.1, the annual performance of nZEB is evaluated based on the weighting factors

399

assumed to be equal. In order to explore the influence of weighting factors on the optimal design

400

option, four combinations (A, B, C and D) representing typical cases are selected and studied for

401

the type of 100% nZEB as shown in Table 4.

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402

In terms of weighting factor combination A and B, there is a similar results on design mismatch

403

ratio and the corresponding optimal system sizes, which may indicate that the cost has a great

404

impact on nZEB performance even the three indicators are equally treated. In the weighting

405

factor combination C (0, 1, 0), i.e. the CO2 emissions are concerned only, a higher design

406

mismatch ratio is obtained compared with that in other three weighting factor combinations. It

407

indicates that a larger HES design size is preferred for reducing CO2 emissions. However, in the

408

weighting factor combination D (0, 0, 1), i.e. the grid interaction index is concerned only, the

409

design mismatch ratio is found to be around 20% in the four systems. It indicates that a favorable

410

grid interaction index prefers neither too large nor too small HES size.

411

The features of power communication between the building and grid under PV&WT&BDG

412

system are displayed in six days for the four scenarios, as shown in Fig. 8a (In summer) and Fig.

413

8b (In winter) respectively. A higher design mismatch ratio, i.e. combination C (0, 1, 0) is

414

concerned, brings in a higher power to the grid in both summer and winter days. In contrast, the

415

power from/to grid is the lowest for combination D (0, 0, 1) and a lowest design mismatch ratio

416

is required. Table 4 Optimal size of HES based on four weighting factor combinations

417 System

PV&WT& BDG

PV&WT

PV&BDG

WT&BDG

Weighting factor combination (w1,w2,w3)

Design mismatch ratio (ε)

A: (1/3,1/3,1/3) B: (1,0,0) C: (0,1,0) D: (0,0,1) A: (1/3,1/3,1/3) B: (1,0,0) C: (0,1,0) D: (0,0,1) A: (1/3,1/3,1/3) B: (1,0,0) C: (0,1,0) D: (0,0,1) A: (1/3,1/3,1/3)

0.28 0.28 1.80 0.18 0.32 0.32 0.40 0.28 0.28 0.31 0.96 0.18 0.31

Optimal design option WT BDG PV (kW) (kW) (m2) 100 10 1300 100 5 1500 100 100 2000 35 60 600 100 0 1800 100 0 1800 100 0 2000 80 0 2000 0 40 1800 0 35 2000 0 100 2000 0 80 800 100 55 0

Performance f

γ

0.651 1.038 -1.046 0.686 0.668 1.051 -0.386 1.236 0.999 1.952 -0.473 0.957 0.797

100% 100% 100% 100% 100% 100% 100% 100% 100% 100% 100% 100% 100%

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B: (1,0,0) C: (0,1,0) D: (0,0,1)

0.31 0.66 0.23

100 100 65

55 100 75

0 0 0

1.430 -0.267 0.882

100% 100% 100%

40

Power from/to grid (W/m2)

0 1

5

13 17 21 25 29 33 37 41 45 49 53 57 61 65 69 Time (h)

-80 -120 -160 -200

(1,0,0) (0,1,0)

-240

(0,0,1) (1/3,1/3,1/3)

-280

418

9

-40

(a) In summer

Power from/to grid (W/m2)

40 20 0 1

5

9

13 17 21 25 29 33 37 41 45 49 53 57 61 65 69

-20

Time (h)

-40 (1,0,0)

-60

(0,1,0) (0,0,1)

419 420

-80

(1/3,1/3,1/3)

(b) In winter

Fig.8. Power from/to the grid in three days under four combinations (PV&WT&BDG).

421

4.3 The relationship between design mismatch ratio and the probability of achieving nZEB

422

It is meaningful to identify the probability for a building to achieve nZEB under different design

423

mismatch ratios, which can provide a benchmark for selecting appropriate HES size in different

424

types of nZEB. The influence of design mismatch ratio on the probability is investigated for the

ACCEPTED MANUSCRIPT

425

four types of HESs, as shown in Fig. 9. It is interesting to find that the probability is highly

426

depending on the design mismatch ratio for all types of HESs. In addition, the probability is

427

increased from 10% to about 80% when the design mismatch ratio is increased from -10% to

428

10%. The obtained fitting formulas are shown as follows:

429

PV&WT&BDG: y = -352.3x6 + 208.5x5 + 43.98x4 - 40.26x3 - 1.087x2 + 3.626x + 0.484; R² =

430

0.981

431

PV&WT: y = 7.611x6 + 6.173x5 - 10.03x4 - 9.552x3 + 1.241x2 + 2.538x + 0.462; R² = 0.987

432

PV& BDG: y = 367.7x6 + 398.7x5-47.15x4 – 64.36x3 +1.885x2 + 4.402x + 0.470; R² = 0.993

433

WT&BDG: y = -256.1x6 + 255.3x5 + 27.88x4 - 44.61x3 - 0.381x2 + 3.686x + 0.475; R² = 0.983

434

Where, these formulas are obtained on the basis of the design mismatch ratio varied between -30%

435

and 30%. When the design mismatch ratio is less than -30%, the probability is 0.0. In contrast,

436

the probability is 1.0 when the design mismatch ratio is more than 30%. Therefore, the fitting

437

formula can be used to identify the expected probability to achieve zero energy target based on

438

the design mismatch ratio during the initial design stage. 1.2

Probability(γ)

1.0 0.8 0.6 0.4 0.2 0.0 -0.2 -30%

439

-20%

-10%

0%

10%

Design mismatch ratio (PV&WT&BDG)

20%

30%

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1.2 1.0 Probability(γ)

0.8 0.6 0.4 0.2 0.0 -0.2 -30%

-20%

-10%

0%

10%

20%

30%

-20% -10% 0% 10% 20% Design mismatch ratio (PV&BDG)

30%

-20%

30%

Design mismatch ratio (PV&WT)

440 1.2 1.0 Probability(γ)

0.8 0.6 0.4 0.2 0.0 -0.2 -30%

441 1.2 1.0 Probability(γ)

0.8 0.6 0.4 0.2 0.0 -0.2 -30%

-10%

0%

10%

20%

Design mismatch ratio (WT&BDG)

442 443

Fig.9. Influence of the design mismatch ratio on the probability

444

Table 5 Comparison of probability under different types of HESs Design

PV&WT&BDG

PV&WT

PV&BDG

WT&BDG

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mismatch ratio -30% -25% -20% 15% -10% -5% 0% 5% 10% 15% 20% 25% 30%

0.00% 2.08% 1.85% 5.39% 15.28% 30.52% 48.40% 65.79% 80.16% 90.16% 95.82% 98.29% 100.00%

0.00% 1.10% 6.29% 13.60% 22.91% 33.93% 46.20% 59.07% 71.77% 83.39% 92.92% 99.35% 100.00%

0.00% 0.92% 0.04% 1.94% 10.47% 26.22% 47.00% 68.66% 86.43% 96.61% 98.66% 97.76% 100.00%

0.00% 2.38% 2.60% 5.59% 14.72% 29.54% 47.50% 65.30% 80.03% 89.94% 95.00% 97.14% 100.00%

445

On the basis of the four fitting formulas, the probability to be nZEB can be predicted for

446

applying each type of HESs, as shown in Table 5 and Fig. 10. It is found that the boundary of

447

design mismatch ratio is around 0%. In more specific, when the design mismatch ratio is selected

448

to be less than 0%, the probability under PV&WT is generally higher than that under the other

449

three systems, while the probability under PV&BDG is the lowest. The record, however, shows a

450

reverse trend when the design mismatch ratio is selected to be above 0%. In addition, it is found

451

that the probability under PV&WT&BDG and WT&BDG have a similar trend under different

452

design mismatch ratios. 1.2 Probability(γ)

1.0 0.8 0.6 0.4

PV&WT&BDG PV&WT PV&BDG WT&BDG

0.2 0.0 -0.2

-30%-25%-20%-15%-10%-5% 0% 5% 10%15%20%25%30% 453 454

Design mismatch ratio

Fig.10. Comparison of probability under different HESs

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455

4.4 Evaluation of performance stability under uncertainty

456

Fig. 11, 12, 13 and 14 show the performance distributions and the associated cumulative

457

distribution function for 100% nZEB designed with four types of HESs respectively, which is

458

obtained by 100 years Monte Carlo simulation and the weighting factor combination A (1/3, 1/3,

459

1/3). It is found that the performance of nZEB designed with PV&WT&BDG and PV&WT has a

460

similar performance distribution, varied from 0.58 to 0.72 and 0.58 to 0.74 respectively, while

461

the cumulative probability of 90% is at the performance of 0.693 and 0.723 for PV&WT&BDG

462

and PV&WT respectively. In terms of nZEB designed with PV& BDG, the performance is

463

distributed at the range between 0.98 and 1.07 while the cumulative probability of 90% is at the

464

performance around 1.0. The main reason of the narrowed performance fluctuation range was

465

that the uncertainty from wind speed can be neglected in PV& BDG system and the uncertainty

466

from building cooling load can be relieved by BDG operation. In terms of nZEB designed with

467

WT & BDG, the performance is distributed in the range between 0.76 and 0.83 while the

468

cumulative probability of 90% is at the performance around 0.812.

Frenquency

0.7

12

0.6 0.5

9

0.4

6

0.3 0.2

3

469 470

0.9 0.8

15

0 0.58

1

0.1 0.6

0.62

0.64 0.66 f (PV&WT&BDG)

0.68

0.7

Cumulative Distribution Function (CDF)

18

(0.6929,0.9) Frenquency Cumulative Distribution Function (CDF)

0 0.72

Fig.11. Performance distribution of 100% nZEB designed with PV&WT&BDG

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18

0.9 0.8

15

Frenquency

0.7 12

0.6 0.5

9 0.4 6

0.3 0.2

3 0.1 0 0.58

0.6

0.62

0.64

0.68

0.7

0.72

0.74

0

f (PV&WT)

471

Fig.12. Performance distribution of 100% nZEB designed with PV&WT 1

24

(1.0088, 0.9)

0.9

21

Frenquency 0.8 Cumulative Distribution Function (CDF) 0.7

Frenquency

18 15

0.6

12

0.5 0.4

9

0.3 6

0.2

3 0 0.97

473 474

0.1 0.98

0.99

1

1.01

1.02

1.03

1.04

1.05

1.06

Cumulative Distribution Function (CDF)

472

0.66

Cumulative Distribution Function (CDF)

1 Frenquency (0.7231,0.9) Cumulative Distribution Function (CDF)

0 1.07

f (PV&BDG)

Fig.13. Performance distribution of 100% nZEB designed with PV& BDG

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18

(0.8115,0.9)

0.9 0.8

15

Frenquency

0.7 12

0.6 0.5

9 0.4 6

0.3 0.2

3 0.1 0 0.76

0.77

0.78

0.79

0.8

0.81

0.82

Cumulative Distribution Function (CDF)

1 Frenquency Cumulative Distribution Function (CDF)

0 0.83

f (WT&BDG)

475

Fig.14. Performance distribution of 100% nZEB designed with WT&BDG

476 477

5. Conclusion

478

This study aims to investigate and compare the performance of a nearly/net zero energy building

479

designed with four typical HESs which are optimal sized considering uncertainty. The uncertain

480

parameters considered are solar radiation, wind velocity, building cooling load and other load.

481

Monte Carlo simulation and exhaustive searching method are employed to find the optimal HES

482

size concerning the uncertainty impacts. Influence of the selected weighting factors, design

483

mismatch ratio, the probability of achieving nZEB on the performance are investigated and

484

compared in the four types of HESs. Based on the results, the following conclusions can be

485

obtained:

486

(1) Both the required probability and selected weighting factors affect the optimal design

487

mismatch ratio greatly, which should be considered carefully at the beginning of design stage.

488

(2) Four fitting formulas are obtained to identify the relationship between the probability of a

489

building to achieve nZEB and the design mismatch ratio for the four typical HESs respectively,

490

which can provide a benchmark for selecting appropriate HES size in different types of nZEB.

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491

(3) An nZEB, designed with PV& BDG, is demonstrated to have a robust performance under the

492

same variable condition compared with that designed with PV&WT&BDG, PV&WT or

493

WT&BDG.

494

This study presents a systematic analysis on the performance evaluation of a nearly/net zero

495

energy building designed with four typical HESs, which is conducted based on robust design

496

optimization method. It aims to assist system designers to select an appropriate design option

497

while implementing hybrid energy system for grid-connected nZEB.

498 499

Acknowledgement

500

The authors acknowledge Hong Kong Zero Carbon Building for providing the building

501

information and on-site monitored data. And also the support by Natural Science Foundation of

502

China (Project No. 51608001 and Project No. 51478001) for the financial support to carry out

503

the research work reported in this paper.

504

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