Comparative study of posteriori decision-making methods when designing building integrated energy systems with multi-objectives

Energy & Buildings 194 (2019) 123–139

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Energy & Buildings journal homepage: www.elsevier.com/locate/enbuild

Comparative study of posteriori decision-making methods when designing building integrated energy systems with multi-objectives Rui Jing a, Meng Wang b, Zhihui Zhang a, Jian Liu c, Hao Liang d, Chao Meng a, Nilay Shah e, Ning Li a, Yingru Zhao a,∗ a

College of Energy, Xiamen University, Xiamen, China School of Mechanical and Energy Engineering, Tongji University, Shanghai, China Fabu Tech Corporation Limited, Hangzhou, China d Center of Science and Technology Industrial Development, Ministry of Housing and Urban-Rural Development, Beijing, China e Department of Chemical Engineering, Imperial College London, London, UK b c

a r t i c l e

i n f o

Article history: Received 12 February 2019 Revised 1 April 2019 Accepted 14 April 2019 Available online 16 April 2019 Keywords: Building energy system Integrated energy system Multi-objective optimization Pareto frontier Decision making

a b s t r a c t By multi-objective optimization of designing integrated energy systems for buildings, the Pareto frontier can be obtained consisting of a series of optimal compromise solutions. Since all solutions on Pareto frontiers are non-dominated, it is challenging to identify one “best of the best” solution, which requires posteriori multi-criteria decision-making. However, most existing research only presented the obtained Pareto frontiers, while neglected the decision-making. Therefore, this paper compares four posteriori decisionmaking approaches in recent publications by solving one identical problem to emphasize the importance of decision-making. An illustrative Pareto frontier is generated by two multi-objective optimization approaches, i.e., eps (ɛ)-constraint and Non-dominated Sorting Genetic Algorithm (NSGA-II). Four categories of multi-criteria decision-making methods, i.e., Shannon entropy, Eulerian distance, fuzzy membership function and evidential reasoning, are further implemented. The decision-making results are different when various approaches are applied. The underlying reasons are analyzed including two key factors, i.e. selection of objectives and shape of Pareto frontier, which provides suggestions of using decision-making approaches in future multi-objective optimization research on building energy systems. © 2019 Elsevier B.V. All rights reserved.

1. Introduction Building integrated energy systems (BIES) draw increasing attention worldwide due to renewable energy access, low emission commitment, and distributed generation development. Technically, BIES is efficient by recovering the heat along with the power generation [1]. Meanwhile, the local energy resources such as wind, solar or underground heat can be integrated with BIES systems, which not only brings environmental benefits, but also reduces the energy cost for consumers [2]. Since BIES involves more technologies than conventional energy systems, the optimal design and dispatch of such system has become a popular research topic. 1.1. Research background At present, an increasing number of research are focusing on the multi-objective optimization problem (MOP) for designing

∗

Corresponding author. E-mail address: [email protected] (Y. Zhao).

https://doi.org/10.1016/j.enbuild.2019.04.023 0378-7788/© 2019 Elsevier B.V. All rights reserved.

building integrated energy systems (BIES) [3]. A literature review of recent (last 3 years) multi-objective optimization research on BIES has been listed in Table 1. Relevant research is categorized by authorship, proposed systems, optimal planning or dispatch, objectives considered, model type and algorithms, decision-making approaches, and the platform or engine to solve the problem. Based on the literature review in Table 1, a paradigm of conducting multi-objective optimization is summarized in Fig. 1. The problem is firstly formulated as a mathematical model, and solved by both classical and emerging multi-objective optimization approaches [4]. Then, all obtained optimal solutions can be plotted as the Pareto frontier. Once the Pareto frontier is obtained, the problem is not completely solved as the decision-makers or designers still need to determine one overall best solution on the Pareto frontier, in other words, which solution they should choose to build in practice. Therefore, posteriori decision-making cannot be neglected to select one “best of best” solution among all nondominated solutions on Pareto frontier. A brief count of occurrence frequencies of various MOP solving algorithms and decision-making approaches appeared in 2016– 2018 s publications are presented in Fig. 2. Both classic and

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Nomenclature ATC ACE ASHP CCHP CRF ER HEX LINMAP

BIES

annual total cost annual carbon emission air source heat pump combined cooling heating and power capital recovery factor evidential reasoning heat exchanger linear programming technique for multidimensional analysis of preference linear/non-linear programming mixed integer non-linear programming mixed integer programming multi-objective optimization problem multi-criteria decision-making operating expenditures solid oxide fuel cell solar radiation index stochastic programming technique for order preference by similarity to an ideal solution building integrated energy system

Symbols AM B C CAP d e E EDi+ EDiF f fij norm fj ideal fj n-ideal h H K m PL Q S T UA u v

air mass entropy value cost ($) installed capacity (kW) deviation index basic attribute electrical power (kW) distance to ideal point distance to non-ideal point aggregated objective function part load efficiency function location of each optimal point location of ideal point location of non-ideal point hour evaluation grade normalization factor probability mass part load ratio thermal energy (kW) basic assessment temperature (°C) unit area (m2/kW) utility wind speed

LP/NLP MINLP MIP MOP MCDM OPEX SOFC SRI SP TOPSIS

Greek symbols ω weight η nominal efficiency α charge/discharge status μ import/export status θ on/off status φ fuzzy fitness ϕ start limit variable ∂ emission factor δ energy conversion factor λ scaling factor ξ entropy weight β degree of belief



spread index fluctuation index

Subscripts/superscript ac absorption chiller b boiler cap capital cost cool cooling energy c-in cut in speed c-out cut out speed ec electrical chiller ex electricity export fc solid oxide fuel cell h hour heat heating energy hp heat pump im electricity import LHV low heating value limit installed capacity limit maint maintenance cost norm rated speed NG natural gas n project life obj objective pv photovoltaic re heat recovered r interest rate s season st-in heat storage charge st-out heat storage discharge t each technology tc thermal collector wt wind turbine metaheuristic approaches are popular to solve the problem as shown in Fig. 2(a). Meanwhile, it is surprising to observe from Fig. 2(b) that many multi-objective optimization studies for building integrated energy systems did not conduct the decisionmaking, which means even though the Pareto frontier have been obtained, the “best of the best” solution is still unknown. Based on such observation, the decision-making seems lack of enough attention. So far, growing but not enough attention has been paid to the multi-objective decision-making issue in energy system research community. Cho et al. [55] provided a comprehensive summary of MOP solving algorithms, where the interactive and trade-off analytical strategies were analyzed to determine the solution space efficiently. Cui et al. [4] summarized the MOP solving methods in energy saving relevant fields and provided suggestions in terms of obtaining the Pareto frontier efficiently. These two studies formed a good basis for MOP, however, the posterior decision-making issue is not specified. Wang et al. [56] analyzed the decision-making issue in distributed energy system applications with uncertain circumstance. The weighting of criteria turns out to have significant impacts on the sustainability rankings of alternative solutions. Yang et al. [57] applied different decision-making approaches to deal with the phase change material selection. A fuzzy-analytic hierarchy process and TOPSIS combined approach is proposed to make decisions. The decision-making issue is analyzed in-depth by these two articles, while less attention has been paid to achieve criteria values via optimizations. Li et al. [42] proposed a two-stage approach combining multi-objective optimization with decisionmaking for CCHP dispatch problem, which fits the paradigm (Fig. 1) as summarized in present study. A similar framework of combining multi-objective optimization with decision-making and

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Table 1 Literature review on multi-objective optimization of building integrated energy systems. Modeling and algorithm

Author

Energy system

Scope

Objectives

Zeng et al. [5]

CCHP∗ +HP∗ +Boiler

D

PV∗ +Battery+ICE∗

D

Primary energy saving Total cost saving Emissions CAPEX LCOE Emissions Fuel cost Capital cost Fuel cost

• MILP • GA

Sachs et al. [6]

1) 2) 3) 1) 2) 3) 1) 2) 1) 2) 3) 4) 1) 2) 1) 2) 3) 1) 2) 3) 1) 2) 1) 2) 1) 2) 3) 1) 2) 1) 2) 3) 1) 2) 3) 1) 2) 1) 2)

Voltage stability Power loss Voltage deviation Operation cost System reserve Power loss Cost Voltage deviation Energy loss Power loss Capacity release Daily energy cost CO2 emissions Annual cost CO2 emissions Utilization of renewable Annual total cost System area Daily energy cost CO2 emissions Utilization of renewable Energy cost CO2 emissions Energy rate Total operation cost CO2 emissions Total cost CO2 emissions Total cost CO2 emissions

• MGSO-ACL

Behzadi et al. [7]

PV+WT∗ +Battery+ICE

S

Zheng et al. [8]

DR∗ +Grid+WT+CCHP+ SH∗ +EC∗ +Boiler

S

Soares et al. [9]

EV∗ +PV+WT+Grid+180-bus

S

Yammani et al. [10]

PV+FC∗ +mGT∗ +WT+IEEE 33-bus

S

Kanwar et al. [11]

IEEE 33-bus+69-bus

D

Zhang et al. [12]

DR+CHP+Boiler+Battery+TS∗

S

Mahbub et al. [13] Soheyli et al. [14]

Grid+WT+Biomass+Boiler+CCGT PV+FC+Battery+TS+WT+Boiler

D D

Somma et al. [15]

ICE-CCHP+Grid+SH+HP+TS

S

Elsied et al. [16]

Grid+FC+WT+PV

S

Ju et al. [17]

CCHP+PV+WT+Boiler

S

Falke et al. [18]

CHP+Boiler+PV+HP

D

Morvaj et al. [19]

Grid+PV+CHP+HP+TS+Boiler

D

Ascione et al. [20]

Envelop+Boiler+EC+HP

D

Yuan et al. [21]

ICE-CCHP+Grid+Boiler+EC

S

Ascione et al. [22]

PV+HP+Envelop+EC+Boiler

D

Chen et al. [23]

PV+WT+FC+Battery+H2 tank+Electrolyzer

D

Yousefi et al. [24]

PV+CHP+Battery

Baghaee et al. [25]

PV+WT+FC+H2 tank+Electrolyzer D

Azaza et al. [26]

PV+WT+ICE+Battery

D

Majewski et al. [27]

CCHP+Grid+Boiler+EC

D

Wouters et al. [28]

CHP+PV+TS+Grid

D

Pratama et al. [29]

PV+WT+Biomass+GeoThermal+Hydro+IGCC

D

D

1) Polluting emissions 2) Global cost 1) Energy-saving ratio 2) Energy cost 1) Investment cost 2) Primary energy consumption 3) Global lifecycle cost 1) Capital cost 2) 3) 1) 2) 1) 2) 3) 1) 2) 3) 1) 2) 3) 1) 2) 1)

Electrical efficiency Supply reliability Total cost Energy recovery Cost of system Loss of load Loss of energy Reliability Electricity cost Renewable factor Global warming investment Total annual cost Annual energy cost Unavailability Generation cost

2) CO2 emissions

Decision-making

Engines

Subjective

MATLAB

None

HOMER

• MILP

TOPSIS

NM∗

• LP

Evidential reasoning

NM

• MILP • PSO

None

MATLAB

• SBA • NSGA-II

None

MATLAB

• MIP • PSO

None

MATLAB

• Weight sum • MILP

None

GAMS

• eps-constraint • Energyplan

None

NM

• MOEA • NLP

LINMAP

NM

Exhaustive method

CPLEX

Fitness function

MATLAB

• MILP • Goal programming

Entropy weighting

GAMS+ CPLEX

• NLP • NSGA-II

None

NM

• MILP • eps-constraint

None

MATLAB

Subjective

MATLAB

• MILP • NSGA-II

None

TRNSYS+MATLAB

• GA

None

MATLAB

• NLP-SQP

None

NM

• NSGA-II

TOPSIS

HOMER+MATLAB

• NLP • MOPSO

Fuzzy membership function MATLAB

• NLP • MOPSO

None

NM

• MILP • Min-max robust

None

NM

• MILP • Weighted sum • MILP

Subjective

GAMS

Subjective

NM

• Weighted sum • MINLP • Weighted sum

• CC-MOPSO • MILP • Weighted sum • MILP • PSO

• NSGA-II • GA

• eps-constraint

• Weighted sum

(continued on next page)

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Table 1 (continued) Author

Energy system

Scope

Objectives

Modeling and algorithm

Decision-making

Engines

Perera et al. [30]

PV+Battery+WT+Grid+ICE

D

• EA • eps-constraint

TOPSIS

NM

Sarshar et al. [31]

FC+PV+WT+Battery+mGT

S

• MILP • NSGA-II

TOPSIS

NM

Zheng et al. [32]

D Grid+PV+CHP+Boiler+Battery+HP+EC+TS

1) 2) 3) 1) 2) 1)

• MINLP

Entropy weighting

GAMS

Cascio et al. [33]

Grid+CHP+Boiler+Expander

• Weighted sum • NLP

Subjective

• GA • Weighted sum • MILP

Unisim+ MATLAB

None

NM

Wang et al. [34]

Majidi et al. [35]

DR∗ +Grid+HP+PV+CCHP+Battery

PV+Battery+FC+Grid

S

S

S

Sameti et al. [36]

HP+CCGT+Boiler+EC+Lake cooling D

Mahbub et al. [37]

D PV+TS+Boiler+HP+EV+Grid+Biomass CHP+SH

Lu et al. [38]

PV+Grid+WT+ICE+mGT+EV

S

Lin et al. [39]

Boiler+CHP+Grid+IEEE bus

S

Bre et al. [40]

Envelop+Boiler+EC+HP

D

Zhang et al. [41]

IEEE 33-bus+61-bus

D

Li et al. [42]

Grid+CHP+Heat-only

Wu et al. [43]

PV+envelop+Boiler+EC+household D appliances

S

Jing et al. [44]

D FC+PV+Grid+Battery+TH+SH+EC+AC

Morshed et al. [45]

PV+WT+EV+Grid+IEEE bus

D

Roberts et al. [46]

PV+WT+Diesel+Battery

D

Abdelkader et al. [47]

PV+WT+Battery

D

Xu et al. [48]

WT+Battery

D

Wang et al. [49]

Battery+IEEE 33-bus

D

Chen et al. [50]

PV+SH

D

Saber et al. [51]

WT+Battery+IEEE 24-bus

D

Wang et al. [52]

PV+EV+household appliances

D

Kianmehr et al. [53] IEEE 33-bus

Gabrielli et al. [54]

D

D Grid+PV+SH+HP+mGT+FC+Boiler+Battery

Levelized cost Grid integration level Capital cost Total cost Pollutant emissions NPV

2) CO2 emissions 1) CO2 emissions 2) Total cost 1) Operation cost 2) CO2 emissions

1) 2) 1) 2) 1)

Total cost CO2 emissions Total cost CO2 emissions Annual cost

2) 1) 2) 1) 2) 1) 2) 1) 2) 1) 2) 1)

CO2 emissions Electricity cost Pollution Operation cost Total emission Thermal comfort Energy consumption Annual total cost Risk of the network Fuel cost Gas emission Life-cycle cost

2) Life-cycle energy consumption 1) Annual total cost 2) 1) 2) 1) 2) 1)

Annual carbon emission Total cost of fuel Emission of power units NPV LPSP∗ Total cost of electricity

2) LPSP 1) Annual profit 2) Wind curtailment rate 1) Total active power loss 2) System voltage deviation 1) Prime energy saving 2) Life cycle savings 1) Wind curtailment cost 2) Transmission congestion cost 3) Normalized profit 1) Consumer satisfaction 2) Energy cost 3) Peak-to-average ratio 1) DG owner’s profit 2) Distribution company’s cost 1) Annual cost 2) CO2 emissions

∗

• Min-max • MOCE • NSGA-II • MILP

Fuzzy membership function GAMS

• Weight sum • MIP

None

CPLEX

• GA

None

EnergyPLAN

• MILP • PSO

None

NM

• MILP • NSAG-II

None

NM

• NSGA-II

LINMAP

Python

• NSGA-II

None

•

θ -DEA

FCM-GRP

NM ∗

NM

• NSGA-II

Grey-box theory

MATLAB

• MINLP

LINMAP TOPSIS

GAMS

• eps-constraint • MOGA

None

MATLAB

• NSGA-II

None

MATLAB

• NSGA-II

None

NM

• NSGA-II

VIKOR

NM

• NSGAII

None

NM

• NSGA-II

None

• MILP • NSGA-II

None

MATLAB TRNSYS MATLAB

• Pareto tribe evolution Equilibrium-based

MATLAB

• MINLP • eps-constraint

Fuzzy

GAMS

• MILP

None

CPLEX

• eps-constraint

D – design (including configuration and scheduling), DR – demand response, EC – electrical chiller, EV – electric vehicle, FC – fuel cell, HP – heat pump, ICE – internal combustion engine, LPSP –loss of power supply probability, (m)GT – (micro) gas turbine, NM – not mentioned in the paper, PV – photovoltaic, S – scheduling, SH – solar heater, TS – thermal storage, WT – wind turbine.

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Fig. 1. Problem solving paradigm of multi-objective optimization problem.

Fig. 2. Occurrence frequency of MOP solving strategies and decision-making approaches.

assessment is proposed by Perera et al. [30] when designing the energy hub.

analysis methods to select one best solution for multi-objective optimization of BIES, which is of interest to the wider energy research community.

1.2. Motivation 1.3. Contribution Seen from the literature review, a few challenges still exist in the multi-objective optimization research of building integrated energy systems, (1) Previous studies mainly focus on how to achieve the Pareto frontier, i.e., developing multi-objective optimization algorithms. But little attention is paid on selecting one final solution from a set of Pareto solutions, while many research contributions even neglected this procedure, which must ultimately be performed by the key decision maker, who must take account of the views of a range of stakeholders. (2) The decision-making issues are particularly relevant to building integrated energy systems (BIES), because of many different involved stakeholders and perspectives. However, there is a lack of systematic analysis on posteriori decisionmaking problems currently in the field of BIES optimal design. The effects of different methods and key factors affecting decision-making process need to be investigated, and approaches to down selecting to a final choice should be described. Even though the selection of an overall best solution could be subjective in some cases, this study aims to maximize the rationality of decision-making by utilizing the posteriori multi-criteria

Compared to previous work, the major contributions of present study are listed as follows: - Summarize a paradigm for solving the multi-objective optimal planning problem of building integrated energy systems (BIES) with posteriori multi-criteria decision-making. - Utilize both classic (CLPEX) and metaheuristic (NSGA-II) approaches to solve one identical BIES problem, generate an illustrative Pareto frontier, and further make comparisons from optimality and computational cost perspectives. - Analyze how different approaches will affect the decisionmaking process and final results; and further propose two evaluation indexes to compare four categories of most frequently utilized decision-making approaches in recent publications, i.e., Shannon entropy, Euclidean distance, fuzzy membership function, and evidential reasoning. The rest of the paper is organized as follows: Section 2 introduces two types of MOP solving methods as well as each type of decision-making approaches. Then a case study is presented in Section 3, and the results are discussed in Section 4. At last, Section 5 draws some conclusions. The illustrative building integrated energy system model is provided in the Appendix A.

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2. Methodology Multi-objective optimization and Multi-criteria decision-making methods adopted in present study are introduced in this section. 2.1. Multi-objective optimization As summarized in the paradigm of Fig. 1, to compare different decision-making methods, the Pareto frontier needs to be obtained in the first place. This section applies two multi-objective optimization strategies, i.e., eps-constraint and NSGA-II, to generate the Pareto frontier for verification purpose. The detailed modeling objectives and constraints for the illustrative BIES are presented in Appendix A. 2.1.1. Eps-constraint method The idea of eps-constraint method is to keep only one objective, and then subdivide other objectives into several segments and further convert them into inequality constraints [58]. Thus the remaining objective is optimized within the inequality constraints of the discretized objectives. The advantages of this method are: (1) the optimality of each run of single objective optimization is guaranteed when other objectives are converted to inequality constraints (2) the step length of each segment can be altered based on the different applications considering the rationality and the model solving time [4]. Therefore, by the eps-constraint method, the Pareto optimal solution set can be obtained. 2.1.2. Elitist non-dominated sorting genetic algorithm For comparison and verification of optimal results, the Elitist Non-dominated Sorting Genetic Algorithm (NSGA-II) is adopted to achieve the Pareto frontier. The algorithm is proposed by Deb [59]. It is one of the most popular metaheuristic algorithms for solving the BIES MOP as summarized in Fig. 2. The elite-preserving strategy and an explicit diversity-preserving mechanism are applied to improve the solving efficiency. More details are presented in Refs. [21,59]. 2.2. Multi-criteria decision-making After obtaining the Pareto frontier, it is not possible to find a solution with all objectives optimized simultaneously [55]. In order to identify one most desired solution on the Pareto frontier, MCDM is an essential procedure for solving MOP, which is easily neglected by previous research. In this study, four kinds of MCDM approaches are introduced and compared, which come from recent publications referring to multi-objective optimization of building integrated energy systems. 2.2.1. Shannon entropy The concept of Shannon entropy was firstly introduced by Shannon for informatics to quantify the uncertainty of the information source [60]. In multi-criteria decision-making (MCDM) applications, Ej is the entropy value of j objective, and i denotes each solution as shown in Fig. 3. A larger value of Shannon entropy indicates larger uncertainty, which means the weight of such information during the decision-making should be smaller. The weight of each objective can be determined, and the overall entropy value of one solution can be calculated accordingly. 2.2.2. Euclidean distance based methods Euclidean distance based methods are applied for MCDM by measuring the distance between each alternative point and the “Ideal”/“Nadir” points [14]. Since the dimensions and scales of objectives might be different, unifications are required in the first

Fig. 3. Illustrations of LINMAP TOPSIS and Shannon entropy approaches.

place as illustrated in Eq. (1) and (2).

finorm = j

fi j − min( fi j ) for minimization objectives max( fi j ) − min( fi j )

(1)

finorm = j

max( fi j ) − fi j for miximization objectives max( fi j ) − min( fi j )

(2)

where i is the series number of points on the Pareto frontier, and j denotes the index of the objective considered. Then, two Euclidean distance based methods: the LINMAP and the TOPSIS are applied in this study. In the LINMAP decision approach, an “Ideal” point within the solution space is defined as shown in Fig. 3. Then the LINMAP approach defines the Euclidean distance between the Ideal point and each point on the Pareto frontier as EDi+ . Thus, the point with minimum EDi+ is considered as the most desired point. More details are presented in Ref. [61]. The TOPSIS approach further introduces the “Nadir” point and defines the Euclidian distance between the Nadir point and the points on the Pareto frontier as EDi- . Interested readers can also refer to Ref. [24] for more knowledge of TOPSIS method. In addition, a deviation index (d) is also introduced as follows. A smaller value of d indicates closeness to the Ideal point, which is considered preferable.



d=



n

2

( f j − f jideal )  n n ideal )2 + nadir )2 ( f − f j=1 j=1 ( f j − f j j j j=1

(3)

2.2.3. Fuzzy membership function method To avoid the inaccuracy of personal judgment, the fuzzy membership function is introduced. Many modified types of membership function exist such as linear, truncated sinusoidal and trapezoidal. In this study, the trapezoidal membership function is selected as a representative. The φ fj denotes the fuzzy membership function of objective j as shown in Fig. 4. The lower the value of objective j is, the larger value of membership function is obtained since minimizations are desired in this study for all objectives. Ref. [62] provides more descriptions on this method. Then the overall fuzzy fitness of one non-dominated point can be determined by different aggregating operators such as “max-min”, “max-product”, “max-geometric mean” and “normalized”, as expressed in Refs. [21,25]. respectively. Hence, the solution with maximum φ total value is the most desired solution.

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Table 2 Technical parameters of each equipment. System

Parameters

Value

Unit

SOFC

Design efficiency (ηfc ) Daily start limit (ϕ ) Maximum capacity (CAPfclimit ) Cut-in speed Cut-out speed Rotor and generator efficiency (ηwt ) Efficiency (ηb ) Maximum capacity (CAPblimit ) Efficiency (ηac ) limit ) Maximum capacity (CAPac COP (ηec ) limit ) Maximum capacity (CAPec COP (ηhp ) limit Maximum capacity (CAPhp ) Efficiency (ηhex ) Heat stored efficiency (ηst ) Heat charge efficiency (ηst-in ) Heat discharge efficiency (ηst-out ) Maximum capacity (CAPstlimit )

48 1 800 1.3 45 53 85 1600 1.0 1200 4 900 3.5 900 90% 95% 95% 95% 1500

%

Wind turbine Boiler Fig. 4. Illustration of trapezoidal fuzzy membership function.

2.2.4. Evidential reasoning The evidential reasoning based approach aims to address the multi-criteria decision-making (MCDM) issue with uncertainty [42], where objectives are defined as basic attributes, the evaluation grades are defined as: Poor, Not good, Ordinary, Good, Excellent, Uncertain. The whole process can be categorized as multi-attribute belief analysis, Dempster-Shafer (D-S) based belief combination and the expected utility based sorting. More details can be found in Ref. [63]. 3. Case study To compare various multi-criteria decision-making (MCDM) approaches, a case study is conducted by implementing the illustrative building integrated energy system (BIES) to a hotel in Beijing. 3.1. Input parameters Beijing is in the “Cold” climate zone of China, and the hotel is all-day operational. For simplicity, the entire year is sub-divided into three seasons (summer, winter and transition), and the typical daily energy demand obtained from previous energy audit is assumed as the representative for the corresponding season as shown in Fig. 5(a)–(c). In addition, Fig. 5(d) shows the time-of-use energy prices, and the Solar Radiation Index (SRI) as well as the average wind speed are presented in Fig. 5(e) and (f) respectively. The state-of-the-art technical, economic and environmental input parameters are listed below. Table 2 lists the technical parameters of the SOFC, wind turbine, solar PV, boiler, electrical chiller, absorption chiller, heat pump, heat exchanger and the heat storage tank [64–66].

Absorption chiller Electrical chiller Heat pump Heat exchanger Heat storage

kWe m/s m/s % % kWh kWc kWc kWh

kWh

Table 3 Capital and maintenance cost of each equipment. Device

Capital cost (Ccap ) $/kW

Maintenance cost (Cmaint ) $/kWh

SOFC Boiler Absorption chiller Electrical chiller Heat storage Heat pump Solar PV Wind turbine

3900 50 230 150 25 200 1600 1150

0.005 0.0 0 03 0.002 0.002 0.0 0 03 0.002 0.002 0.003

The economic parameters consist of two parts: (1) capital cost and (2) maintenance cost as shown in Table 3 [12,23]. It is noteworthy that the accurate prediction of the SOFC capital cost is difficult, and the value ranges from US $12,0 0 0/kW to US $20 0 0/kW. In this study, a capital cost of US $3900/ kW is assumed considering the potential government subsidies for clean energy technology, and the necessary stack substitution is also considered [67]. The case specifically environmental parameters and project general information are listed in Table 4 [68–70].

Fig. 5. Energy demand for three seasons (a-c), time-of-use energy prices (d), 24-hour solar radiation index (e) and hourly average wind speed (f) of the case study.

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Fig. 6. Optimal results and computational cost comparison between NSGA-II and eps-constraint methods.

Table 4 Emission factors and project general information.

4.1. Multi-objective optimization results

Parameters

Value

Unit

Project lifetime Interest rate Natural gas emission factor (∂ NG ) Grid electricity emission factor (∂ grid )

15 6 0.18 1.01

Years % kg/kWh (LHV) kg-CO2 /kWh

3.2. Modeling and settings The modeling platforms and algorithm settings are different for classic and metaheuristic strategies as depicted as follows. 3.2.1. Classical strategy The proposed building integrated energy system is modeled in GAMS 24.0 on a PC with an Intel (R) Core (TM) i5 CPU, 3.30 GHz CUP and 8.0 GB of RAM [71]. The length of the planning horizon is 10 years assuming the demand is stable during this period, and the temporal resolution is 1 h The model involves 4954 constraints and 4500 variables, where 720 of them are binary variables occuring in 1374 constraints. The optimality setting is 0.1% and other settings remain as default. 32.2. Metaheuristic strategy The illustrative BIES model is also developed in MATLAB 2016a [72] and solved by NSGA-II for validation and comparison. The number of independent variables is 439. Considering the computational capacity and diversity of Pareto solutions, the population size is set as 300 and the number of generations is set to 10 0 0. In addition, MATLAB is also utilized for multi-criteria decisionmaking after obtaining the Pareto frontier by both classical and metaheuristic strategies. 4. Results and discussion The multi-objective optimization and decision-making results are analyzed in this section.

Fig. 6(a) presents the results for 120 times of simulations for NSGA-II algorithm, where the number of generations is set to 10 0 0 and the population size is ranging from 50 to 500 as marked in orange referring to the secondary Y-axis. With the population size goes up, the consumed CPU time increase generally (blue dot). When the population size is larger than 400, the consumed CPU time becomes fluctuating significantly. In contrast, the consumed time by eps-constraint method is stable around 1800 s (grey asterisk), which is generally longer than the NSGA-II algorithm. Therefore, by proper parameter tuning, the metaheuristic algorithm can greatly save computational cost compared to the classic method, but some priori knowledge is required to adjust the settings. Fig. 6(b) compares the achieved annualized total cost (ATC) and annualized carbon emissions (ACE) optimal values. For NSGAII algorithm, both optimal ATC and ACE values vary for each run of simulation even if all the parameter settings are the same as shown by red and green dots, respectively. In contrast, the optimal values for eps-constraint method remain similar all the time as shown by the purple and black long-dash-dot lines, respectively. Meanwhile, when the number of population goes up, both ATC and ACE optimal values decrease slightly for NSGA-II algorithm. The optimality gap between NSGA-II and eps-constraint method reduces accordingly. In general, the NSGA-II algorithm is often considered to offer more flexibility for multi-objective optimization problem with relatively easy coding, particularly when the elite strategy and degree of congestion strategies are adopted [73]. The case study indicates that by proper parameter settings, the NSGA-II algorithm can achieve less CPU time, but the results fluctuate slightly and a tiny optimality gap exists between NSGA-II and eps-constraint method. Furthermore, the eps-constraint method is applied to generate the illustrative Pareto optimal surface as an example. Both cost and installation area objectives are converted into inequality constraints. Hence, the emission (ACE) objective has to be minimized within certain ranges of the ATC and area. A 3-D view of the identified Pareto frontiers is presented as a fitted surface as shown in

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131

Fig. 8. Illustration of spread index calculation.

bias level. Meanwhile, the fluctuation index aims to quantify the numerical significance of the decision-making process. (a) Spread index ( ) Fig. 7. 3-D view of Pareto frontiers.

Fig. 7, where only 54 optimal points are identified due to the computational capacity limit. Hence, the points may not be evenly distributed. Another possible reason for non-uniformness is the utilization of a significant amount of binary and integer variables in our proposed model, which may make the solution space discontinuous. After obtaining the Pareto surface, different decision-making approaches can be adopted to identify the overall best solutions on it. 4.2. Decision-making result The posterior decision-making is one of the multi-objective decision-making (MODM) methods. So far, there is still no consensus which MODM approach always performs best [74]. Different techniques may yield different results when applied to one identical problem, and the difficulty always occurs when trying to compare decision methods [75]. Zanakis et al. [76] compared different MODM approaches by doing a series of simulations via changing the number of objectives, the number of alternative solutions and the distribution of alternative solutions. Junior et al. [77] suggested using the “adequacy and agility to changes of criteria” method to compare different MODM approaches, where evaluating the impact of adding one additional criterion to the decision result. However, as suggested by Zamani-Sabzi et al. [78], selecting an appropriate MODM technique largely depends on the effort required to obtain that decision. Above mentioned measures may not be applicable directly to the issue tackled in this study as the posterior decision-making is based on a generated Pareto frontier during multi-objective optimization of integrated energy system. Changing the number of criteria (i.e., objectives) needs one to reformulate and rerun the model, which is time consuming and complex. In contrast, Parreiras et al. [62] introduced a spread index to determine how well the selected solutions are distributed on the Pareto frontier. Following a similar idea, Perera et al. [30] proposed a spread matrix which measures the distribution uniformness of alternative solutions. These measures do not need to run simulation tests by changing the number of objectives or distribution of alternative solutions, but focusing on existing alternative solutions, which is more suitable for integrated energy systems. Inheriting this concept, this study attempts to propose two evaluation measures for BIES practice, but they are not mathematically proven yet. 4.2.1. Decision-making performance metrics The proposed spread index in this study not only measures the distribution uniformity of selected solutions, but also quantify the

The spread index ( ) is introduced to measure how uniform the selected top 12 solutions (marked in red in Fig. 9) are distributed on the Pareto frontier, as defined in Eq. (4).

=

S − Snorm Snorm

(4)

where S’ represent the encircled surface by each decision-making approach as illustrated by the blue scenario in Fig. 8, and Snorm is the encircled surface for benchmarking scenario. For each decision-making method, the selected top 12 solutions are assigned by value of 1, the rest solutions are assigned by 0. Then, the assignments of all 54 solutions are mapped to a waterfall diagram as shown in Fig. 8, where horizontal axis is the serial number of each solution, and vertical axis represents the accumulated value of all 54 solutions’ assignments. It is seen that Scenario 3 (marked in red) is the benchmarking, where selected top 12 solutions are well-distributed on the Pareto frontier. Scenario 4 (marked in blue) indicates that the selected top 12 solutions tend to locate at the latter part of the Pareto frontier with larger serial numbers, and the corresponding encircled surface is displayed by the blue shadow. In this scenario, it is obvious that the value will be negative and the absolute value of is relatively large. In contrast, the selected top 12 solutions by Shannon entropy decision-making method in this case tend to locate at the first half of the Pareto frontier as displayed by Scenario 1 (marked in green), where the value will be positive and the absolute value of is relatively large. Meanwhile, Scenario 2 (marked in purple) illustrates the decision-making results by LINMAP method, where the distribution is more uniform than Scenario 1, so the is slightly positive. Therefore, by the proposed spread index, the degree of uniformity for different decision-making methods’ results can be quantified. The decision-making method with lower absolute value of

can achieve a more well-distributed decision-making result. The sign of positive or negative represents the whether the selected solutions tend to locate in the earlier part or latter part of a Pareto frontier. (b) Fluctuation index () The fluctuation index () is utilized to quantify the decision’s numerical variation for 54 solutions when different decisionmaking methods are applied. Larger value of  indicates the overall best solutions are clearer identified with better numerical significance by certain decision-making method. Since the numerical scale of decision-making results are different for various decision-making methods, the fluctuation index is defined as Eq. (5).



=

1 N

N i

(xi − μ )2

μ

(5)

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R. Jing, M. Wang and Z. Zhang et al. / Energy & Buildings 194 (2019) 123–139 Table 5 Performance comparison for posteriori decision-making approaches. Method Euclidean distance based

Shannon entropy Fuzzy membership function

LINAMP TOPSIS Deviation index Max-min Max-product Max-geometric mean Normalized

Evidential reasoning based

where N represents total number of optimal solutions on Pareto frontier. Which is 54 in this case; xi is the decision-making result for each solution; μ is the average value of all decision-making results for certain decision-making methods. By above two metrics, the performance of different decisionmaking approaches is quantified and compared in Table 5. Seen from the spread index ( ), the Euclidean distance based three methods can achieve better distributed decision-making results compared to the else three categories of methods. The LINMAP method has the lowest value of spread index, which means the selected top 12 overall best solutions are most uniform distributed. Meanwhile, only the Deviation index method achieves a negative value of , which indicates other method tend to select the first half of solutions as the overall best solutions. As shown by the fluctuation index () in Table 5, the TOPSIS decision-making results have minimum value variation, while the Deviation index and Fuzzy membership function with max-product operator have larger results’ fluctuation. The rest methods achieve intermediate value fluctuations when making decisions. In accordance with the performance metrics, a better visualization of the detailed decision-making processes are presented in Fig. 9. 4.2.2. Euclidean distance based decision-making The decision-making results for LINMAP and TOPSIS are presented in the Fig. 9(a) and (b), with the top 12 desired solutions marked in red out of 54 solutions. The decision-making results are evenly more distributed and numerical significant by LINMAP than TOPSIS in accordance with the performance metrics. Considering the entire solution set (54 solutions) is divided into 6 sub-sets, the selected overall best solutions tend to locate at the intermediate section of each sub-set, where the geometric distances between the intermediate section points and the ideal point are shorter for each sub-set. Fig. 9(b) presents the TOPSIS decision-making details, where the shape of the Pareto frontier has significant impact on the index value. In the present case, the degree of convexity for all six subsets’ Pareto frontiers are small, and the degree of convexity for the first four sub-sets is relatively larger than the latter two subsets. Thus, the solutions of the first four sub-sets are more likely to be selected as the overall best solutions. Furthermore, since the degree of convexity in the intermediate section of each sub-set’s Pareto frontier is relatively larger than the two endpoints’ sides, intermediate section solutions are more likely to be selected. Fig.9(c) displays the decision-making results for deviation index. The major difference between the deviation index and LINMAP/TOPSIS is that the deviation index method quantifies the geometric distance without normalization. By contrast, LINMAP/TOPSIS methods conduct normalization in the first place. Therefore, deviation index’s value variations are much more significant than LINMAP/TOPSIS’s, but the corresponding 54 solutions’ indexes are all more evenly distributed than other decision-making approaches’.

Spread index ( )

Fluctuation index ()

0.07 0.14 −0.08 0.31 0.28 0.26 0.26 0.23 0.22

0.24 0.07 0.61 0.26 0.17 0.69 0.41 0.17 0.15

4.2.3. Shannon entropy decision-making The 54 solutions’ overall Shannon entropy values are illustrated in Fig. 9(d). All the higher ranking solutions tend to involve the smaller installation area sub-sets. Furthermore, within the first two sub-sets, the desired solutions tend to be located at the higher cost and lower emission side. This may be explained by the Shannon entropy concepts, where the uncertainty of information is reflected as the curvature varying rate of the obtained Pareto optimal surface. If the curvature varying rate is not constant, the desired point identified would be partial to a certain side, and the 3-D visualization of the obtained Pareto surface in Fig. 7 validates this phenomenon. Meanwhile, the installation area for the first sub-set (less than 100 m2 ) is significantly smaller compared to other subsets, which may lead to the identified points falling in the first sub-set. 4.2.4. Fuzzy membership function decision-making The fuzzy membership function method is implemented for decision-making, where the trapezoidal membership function is constructed. Four types of aggregating operators, i.e., max-min, max-product, max-geometric mean, and normalized are applied and compared as illustrated in Fig. 9(e)–(f) respectively. It is seen that max-min – (e) and normalized – (h) aggregation operators make similar decision. By contrast, the values’ fluctuation of maxproduct – (f) and max-geometric mean – (g) aggregation operators is significant, but the identified top 12 solutions are similar as well. In addition, the identified overall best solutions tend to locate in the smaller installation area sub-set, but the concentration phenomenon is not as great as the Shannon entropy method. 4.2.5. Evidential reasoning based decision-making As described by the methodology in Section 2.2.4, the multiattribute analysis can be conducted when all optimal solutions are obtained. Then the basic assessments of selected solutions can be done, where the value of each evaluation grade of each solution is given based on the optimal values of objectives of corresponding solutions. The unassigned value of each attribute (objective) is set to 0.1 without loss of generality. Then, by the Dempster-Shafer (DS) belief combination, the distributed assessment of each solution can be obtained, which aggregates the ATC, the ACE and the area. To precisely rank all solutions, the utility of each solution is estimated based on the probability method, which assumes the utility values of corresponding evaluation grades are [59]:

u(H1 ) = u(poor ) = 0, u(H2 ) = u(not good ) = 0.35, u(H3 ) = u(ordinary ) = 0.55

(6a)

u(H4 ) = u(good ) = 0.85, u(H5 ) = u(excellent ) = 1

(6b)

Therefore, the expected utilities of each solution can be determined. The “best of the best” solution is identified accordingly. Comparing the ultimate solutions selected by different decisionmaking approaches, 1) Euclidean distance based approaches tend

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Fig. 9. Decision-making details of LINMAP – (a), TOPSIS – (b), Deviation Index – (c), Entropy Weighting – (d). Fuzzy membership function decision-making with four aggregation operators: max-min – (e), max-product – (f), max-geometric mean – (g) and normalized – (h).

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to select solutions with moderate size of each device and moderate amount of electricity purchasing/feed-back to the grid. Fuzzy membership function based approaches make similar selection as Euclidean distance based approaches. 2) While Entropy based approach and Evidential reasoning based approach tend to select ultimate solutions with less interaction to the grid and larger size of CHP and other devices. Hence, the independence of these solutions tends to be higher, nevertheless, these solutions have more availability for the grid peak-shaving if needed, due to the larger capacities of CHP. 4.3. Discussion The results indicates that each posteriori multi-criteria decision-making approach makes different decisions on one identical Pareto frontier. The decision indexes’ (distance, entropy value or fitness value) distributions and fluctuations among 54 optimal solutions are different as well. Several key factors that may affect the results are discussed as follows. 4.3.1. Selection of objectives In terms of the objective functions’ selection, the selected objectives should cover different perspectives as much as possible. In the meantime, the legibility and computational cost should also be considered. Firstly, the trade-off between two objectives and three objectives can be illustrated by two-dimensional Pareto curve and 3-dimensional Pareto surface. Once over three objectives are selected, it is difficult to display the obtained Pareto frontier by fourdimension, even though the algorithms are still feasible. Secondly, the computational cost will significantly increase for both classical and metaheuristic approaches. Therefore, in terms of the quantity of selected objectives, it is recommended to select two or three objectives from different aspects. This paper selects the annual total cost (ATC) and annual carbon emission (ACE) as objectives, which are most frequently used objectives. While attentions should be paid for the selection of the third objective, since many objectives are available such as installation area, system reliability and renewable ratio. The reason of selecting installation area as the third objective is to keep the selected three objectives having different range of value variation. In other words, the optimal value of ATC ranges from 8.5 × 105 to 9.2 × 105 , i.e., the variation range is (9.2 × 105 – 8.5 × 105 )/9.2 × 105 = 8% which is relatively small. The variation range of ACE is (2.8 × 103 – 1.9 × 103 )/2.8 × 103 = 39%, which is intermediate. While the installation area has a larger variation range, i.e., (697 – 75)/697 = 89%. The value variation ranges of cost and emissions are case-specific and not evenly distributed generally, while the value of installation area is controllable. In order to generate an extensive Pareto surface and avoid optimal solutions overcrowd at certain side, the constraint on installation area is set by 7 bands from 75 m2 to 697 m2 with each band step of 100 m2 . By intentionally keeping the diversity of objectives, the impacts of objective functions’ selection on decision-making can be analyzed. It turns out most of the decision-making approaches do consider the value variation issue by conducting normalization beforehand, e.g., the LINMAP/TOPSIS conducting normalization before distance calculation, the entropy weighting conducting normalization before weights assignment, and the fuzzy membership function approach conducting normalization by mapping all original values to a membership function. Overall, the system modeling scale or objectives only affect the computational cost and legibility, but they will not affect the process of decision-making. Meanwhile, all decision-making approaches address the value ranging issue by conducting normalization. Furthermore, in order to avoid the objective value ranging issue during the decision-making stage, it is recommended to

Fig. 10. Illustration of different convexity and curvature conditions for a Pareto frontier.

transform all objective functions to be dimensionless at the model establishment stage. 4.3.2. Shape of Pareto frontier The case study results also indicate that the shape of the obtained Pareto frontier will affect the decision-making process, where the shape can be described by two indexes, i.e., curvature and convexity. Fig. 10 presents four examples of two-dimensional Pareto frontiers with different curvature and convexity. In present study, the Pareto frontier of the first optimal solution sub-set (i.e., installation area < 100 m2 ) is similar to the blue frontier, and the rest five sub-sets’ Pareto frontier are similar to the purple one. For the purple type of frontier, the curvature of it is constant throughout the Pareto frontier, the solutions on the frontier are evenly distributed, and the degree of convexity is stable. In such case, decision-making approaches tend to choose the intermediate section solutions. As for the blue frontier, the curvature is not constant throughout the Pareto frontier and the solutions on the frontier are not evenly distributed. In that case, the selection would partial to a certain side and it has significant impact on the entropy weighting decision-making method as shown in Fig. 9(d). Notice that the curvature and convexity of a Pareto frontier and the solution distribution are case specific. However, if the ultimate situation (i.e., black frontier) occurs as shown in Fig. 10, the TOPSIS and the entropy weighting methods are no longer effective (i.e., each solution scores the same) as the specific distance calculated by TOPSIS is always equal to 0.5 for every solution, and the weights in entropy weighting method for two objectives are always be 0.5. In contrast, the LINMAP approach is still applicable in such ultimate situation, where the solutions in the intermediate section still have the relatively shorter Euclidean distance to the Ideal point compared to the two end-side solutions. Another ultimate situation (i.e., green frontier) is also presented in Fig. 10, where the obtained frontier is not completely convex. In the present study, such ultimate situation does not occur. But this situation is possible since the significant amount of binary and integer variables are utilized during the system modeling, which may lead to a discontinuous and incompletely convex solution space. In addition, it is noteworthy that the shape of the Pareto frontier is very case specific. Since the convexity and curvature will affect the decision-making process, future researchers may plot the case specific Pareto frontier first, and then choose the proper approaches for decision-making depending on the above analysis. 5. Conclusions Building integrated systems (BIES) are particularly relevant to the decision-making issue because of many different stakeholders and perspectives involved. This study summarizes the paradigm of

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solving the BIES’ multi-objective optimization problem and further identifies the gap that many research contributions neglected this procedure of selecting one “best of best” solution among all Pareto solutions, which must ultimately be performed by the key decision maker. To explore how different methods, which may reflect the different views of stakeholders, affect the overall solution, a parallel comparison is conducted by utilizing different decision-making methods, i.e., Shannon entropy based, Euclidean distance based, fuzzy membership function based, and evidential reasoning based. An illustrative Pareto frontier is generated by two types of algorithms, i.e., eps-constraint and NSGA-II for verification. Although no one decision-making method always performs best, preliminary efforts are spent to explore the detailed decision-making process which leads to several conclusions as follows. (1) The Euclidean distance based decision-making approaches, i.e., LINMAP, TOPSIS and deviation index, tend to have a more evenly distributed results compared to other approaches. Although the LINMAP is relatively simple, it is less susceptible by the selection of objectives or shape of Pareto frontiers. (2) The Shannon entropy based decision-making method is completely objective but relatively sensitive to the solutions’ distribution on the Pareto frontier. Meanwhile, if not all objectives need to be maximized (or minimized) simultaneously, the reciprocal of certain objective functions is recommended, so as to convert all objective functions to maximization (or minimization). (3) In present study, four aggregating operators of fuzzy membership function decision-making method draw similar conclusions. If one objective is significantly weaker than the others, the “max-geometric” operator is recommended, which can reflect the closeness of solutions to the ideal one. (4) The basic assignment of attributes for the Evidential Reasoning and Expected Utility combined approach is still with certain subjectivity. Future research may try to combine evidential reasoning with fuzzy membership function approaches since these two methods are both to assess the degree of objectives belonging to certain targets theoretically. Acknowledgment Dr. Yanjie Zhou from Pusan National University is acknowledged for valuable discussion on methodologies. This work received the support from No. 51876181 of National Natural Science Foundation

135

of China; the Science and Technology Planning Projects of Fujian Province, China with grant no. 2018H0036, and the China Scholarship Council no. 201806310046. Conflicts of interest statement The authors whose names are listed immediately below certify that they have NO affiliations with or involvement in any organization or entity with any financial interest (such as honoraria; educational grants; participation in speakers’ bureaus; membership, employment, consultancies, stock ownership, or other equity interest; and expert testimony or patent-licensing arrangements), or nonfinancial interest (such as personal or professional relationships, affiliations, knowledge or beliefs) in the subject matter or materials discussed in this manuscript. Appendix.A. Model description An illustrative renewable assisted Solid Oxide Fuel Cell (SOFC)based BIES optimization model is proposed as shown in Fig. A1. The SOFC is fueled by natural gas, and the generated power is integrated with solar PV power, wind turbine power, less the potential consumption of the electrical chiller (EC) and the air source heat pump (ASHP). Interaction with the grid is also enabled considering the intermittence of solar and wind power. Meanwhile, the heat along with the power generation of the SOFC is recovered to preheat the air, fuel and water first, then the residual heat is further utilized for heating supply by merging the heating flow with the boiler and the ASHP, less the potential consumption of absorption chiller, and a heating storage tank is considered. The objective functions as well as the model constraints are described below. A.1. Objectives Multiple objectives are considered not only to minimize the cost, the carbon emissions, but also take the system installation area into consideration. A.1.1. Annual total cost An economic objective is one of the most frequently utilized objectives in building integrated energy systems (BIES). In this study, the annual total cost (ATC) is considered as the economic objective, which consists of five parts, i.e., (1) the capital cost

Fig. A1. Renewable assisted SOFC-based BIES system layout.

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R. Jing, M. Wang and Z. Zhang et al. / Energy & Buildings 194 (2019) 123–139 Table A1 Installation unit area of certain devices. Device

Unit area (m2 /kW)

Wind turbine (WT) Photovoltaic (PV) SOFC Heat storage (HS) Absorption chiller (AC) Electrical chiller (EC) Boiler Air source heat pump (ASHP)

3 6.434 0.015 0.0 0 02 0.040 0.018 0.011 0.020

A.2.1. Energy balances Electrical, heating and cooling balances are established in accordance with the system layout as illustrated in Fig. A1. The electrical demand is fulfilled by the solar PV panel (Epv ), the wind turbine (Ewt ), the SOFC (Efc ), the imported electricity from the grid (Eim ), minus the possible consumption by the electrical chiller (Eec ) and the heat pump (Ehp ) or export to grid (Eex ) as shown in Eq. (A5). heat Meanwhile, the heating demand (Qdemand ) is supplied by the reheat ), the gas boiler (Q heat ), the air covered heat from the SOFC (Qre b heat ), considering the interaction with source heat pump (ASHP) (Qhp

heat /Q heat ), minus the possible heat conthe heat storage tank (Qst −in st−out

(CAPEX), (2) the fuel cost (FC), (3) the maintenance cost (MC), (4) the grid electricity purchasing cost (EPC), and (5) the electricity feed-in revenue (EFR), as shown in Eq. (A1).

cool ). the absorption chiller (Qac

AT C = CAP EX + F C + MC + EPC − EF R  = CAPt × C CAP × CRFt annualized capital cost t

+





Efc,s,h

ηfc

s,h

+



+

Qbheat ,s,h

Edemand,s,h = Ewt,s,h + Epv,s,h + Eim,s,h + Efc,s,h − Eex,s,h − Eec,s,h

heat Qhp /b/st,s,h

+

cool Qec /ac,s,h

heat heat heat heat heat heat Qdemand ,s,h = Qre,s,h + Qb,s,h − Qst−in,s,h + Qst−out,s,h + Qhp,s,h



heat − Qac ,s,h

× Ctmaint maintenance cost  + Cim × Eim,s,h grid electricity cost Eex,s,h export revenue

(A1)

s,h

r × (1 + r )

n

CRF =

(A2)

(1 + r )n − 1

where the annual capital cost is calculated by the sum of capital recovery factor (CRF) multiplied by the corresponding installed devices’ capital cost, and r is the interest rate, n is the project life (years). A.1.2. Annual carbon emission An environmental objective is another key factor for developing integrated energy systems. In our case, the annual carbon emissions (ACE) is considered as the environmental objective as defined in Eq. (A3).

ACE =

∂NG ×

 s,h

+ ∂grid ×



Efc,s,h



ηfc

+

Qbheat ,s,h

ηb



natural gas emission

Eim,s,h purchased electricity emission

(A3)

s,h

where ∂ NG and ∂ grid are the emission factors of natural gas and the grid, respectively. A.1.3. Installation area The installation area is considered as the technical objective assuming the available space of buildings is limited. The area function can be presented as:

A = U At × CAPt

∀s, h

(A6)

∀s, h

cool cool cool Qdemand ,s,h = Qac,s,h + Qec,s,h

s,h

− Cex ×

(A5)

× CNG fuel cost

s,h



∀s, h

− Ehp,s,h



ηb

Epv/fc/wt,s,h +

heat ) as presented in Eq. (A6). sumption by the absorption chiller (Qac In addition, Eq. (A7) illustrates the cooling balance, where the coolcool cool ) and ing demand (Qdemand ) is fulfilled by the electrical chiller (Qec

(A4)

where UA denotes the unit area of each device as presented in Table A1 [14], and CAP represents the installed capacity accordingly. A.2. Constraints The model of each device as well as the sizing and operation constraints of the whole system are presented in this section.

(A7)

where s denotes the season, h means the hour, which is the time step of the proposed model. To handle the intermittence of the solar and wind power, electricity purchasing and feed-in to the grid are enabled by Eq. A8 [79]. limit 0 ≤ Eex,s,h ≤ μex,s,h × Eex

∀s, h

(A8a)

limit 0 ≤ Eim,s,h ≤ μim,s,h × Eim

∀s, h

(A8b)

μex,s,h + μim,s,h ≤ 1

(A8c)

where μex, s, h and μim, s, h are binary variables to control the status of electricity purchasing and feed-in, and avoid both happening simultaneously. cool ), the absorpThe thermal output of the electrical chiller (Qec cool ), the ASHP (Q heat ), and the boiler (Q heat ) are detion chiller (Qac hp b

fined by Eq. A9, where θ is a binary variable to control the on/off status of each device at each time step accordingly. Meanwhile, η indicates the efficiency of certain device, thus the energy conversion of corresponding devices can be illustrated as Eq. A10, where NG denotes the energy content of natural gas. cool Qec ,s,h ≤ θec,s,h × CAPec

∀s, h

(A9a)

cool Qac ,s,h ≤ θac,s,h × CAPac

∀s, h

(A9b)

heat Qhp ,s,h ≤ θhp,s,h × CAPhp heat Qb,s,h ≤ θb,s,h × CAPb

∀s, h

(A9c)

∀s, h

(A9d)

cool Qec ,s,h = θec,s,h × ηec × Eec,s,h

∀s, h

(A10a)

cool heat Qac ,s,h = θac,s,h × ηac × Qac,s,h

∀s, h

(A10b)

heat Qhp ,s,h = θhp,s,h × ηhp × Ehp,s,h

∀s, h

(A10c)

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enough value to ensure the charge and discharge rate not over the limit, i.e., the stored heat by last time-step. limit Qstheat ,s,h ≤ CAPst

Qstheat ,s,h =

∀s, h

(A14a)

heat ηst × Qstheat ,s,h−1 + ηst−in × Qst−in,s,h −

Qstheat −out,s,h

and h ∈ (1, 23 )

∀s (A14b)

heat heat Qstheat ,s,h1 = ηst × Qst,s,h24 + ηst−in × Qst−in,s,h24 −

Fig. A2. Power curve of the wind turbine.

ηst−out

Qstheat −out,s,h24

ηst−out

∀s (A14c)

heat Qb,s,h = θb,s,h × ηb × N Gb,s,h

∀s, h

(A10d)

To avoid oversizing of the installed capacity of the devices, capacity limits (CAPlimit ) are given as shown in Eq. (A11), where t indicates all installed thermal energy devices.

C APt ≤ C APtlimit

∀s, h

(A11)

A.2.2. Photovoltaic model The building’ roof is potentially available for installation of solar PV panel, and the power output of a PV panel is defined by Eq. A12 [80].



ηpv,s,h = P1 ×

SRIs,h SRI0

AMs,h + P5 × AM0

P2

 + P3 ×



SRIs,h SRI0



1 + P4 ×

∀s, h

Epv,s,h = Apv × ηpv,s,h × SRIs,h



∀s, h

Ts,h T0

P2

(A12a) (A12b)

where the PV panel efficiency ηpv is related to solar radiation index (SRI) in the unit of (W/m2 ), the ambient temperature (T), and the air mass (AM), SRI0 = 10 0 0 W/m2 , T0 = 25 °C, AM0 = 1.5, P1 = 0.2820, P2 = 0.3967, P3 = −0.4473, P4 = −0.093, P5 = 0.1601.

0 ≤ Qstheat −in,s,h ≤ αchr,s,h × M 0 ≤ Qstheat −out,s,h ≤ αdis,s,h × M

Ewt,s,h =

ηwt × 0.5 × ρair × A × min (vnorm , vw,s,h )3 0

∀s, h

αchr,s,h + αdis,s,h ≤ 1 ∀s, h

A.2.4. Heat storage model Heat storage is considered in this study, where the heat stored heat ) is equal to the heat in the tank (Q heat at time h (Qst ) at ,s,h st,s,h−1 heat time h-1, minus the heat discharge (Qst ), plus the heat charge −in,s,h

heat (Qst ) [65]. As shown in Eq. (A14d)–A14f, since the heat −out,s,h charge and discharge cannot happen simultaneously, two binary variables α chr and α dis are introduced to ensure only one status can occur in each time-step. When α chr is 1, which means heating is charged to the storage tank, at the same time, the α dis has to be 0, and vice versa. If both α chr and α dis equal to 0, then the storage tank is neither charge nor discharge. In addition, M is a big

(A14e) (A14f)

A.2.5. Solid Oxide Fuel Cell model The Solid Oxide Fuel Cell (SOFC) part-load electrical efficiency (ηfc ) is given by an empirical fitted function as shown in Eq. A15, where (PLfc ) is the part-load ratio of the SOFC [81]. Meanwhile, to avoid drastic variation of the SOFC power output (Eq. A16) as well as very low load operation (lower than 30% of full capacity) of SOFC (Eq. A17), specific constraints are applied. In addition, only one startup and shutdown per day is allowed (Eq. A18) to avoid the frequent start of SOFC.

Efc,s,h ≤ CAPfc

∀s, h

(A15a)

Efc,s,h = ηfc,s,h × N Gfc,s,h

∀s, h

(A15b)

∀s, h

(A15c)

ηfc,s,h = 0.494 × (PLfc,s,h )3 − 1.196 × (PLfc,s,h )2 + 0.945 × PLfc,s,h + 0.236

(A15d)

vc−in ≤ vw,s,h ≤ vc−out ∀s, h vw,s,h ≥ vc−out ∪ vc−in ≥ vw,s,h

where ηwt indicates the wind turbine rotor and generator efficiency, ρ air is the air density, A denotes the blade area, and vnorm is the rated speed of the wind turbine. The power curve of the wind turbine is illustrated in Fig. A2.

(A14d)

The heat losses during the charge/discharge process as well as during storage are considered by introducing efficiencies of ηst , ηst-in and ηst-out accordingly. Meanwhile, Eq. A14 also avoids the stored heat over-day accumulation.

CAPfc × P Lfc,s,h = Efc,s,h A.2.3. Wind turbine model Considering the space limitation, a vertical-axis wind turbine is considered and shared the available roof space with the PV panel. The power output of the wind turbine (Ewt, s,h ) is defined by Eq. (A13), where the output is constrained by cut-in (vc-in ) and cut-out (vc-out ) wind speed [14].

∀s, h

(A13)

Efc,s,h+1 − Efc,s,h ≤ 50% × CAPfc

∀s and h ∈ (1, 23)

(A16a)

Efc,s,h1 − Efc,s,h24 ≤ 50% × CAPfc

∀s

(A16b)

∀s, h

(A17a)

Efc,s,h ≥ 30% × CAPfc × θfc,s,h Efc,s,h ≤ 100% × CAPfc 24 

∀s, h

ϕfc,s,h ∀s

(A17b)

(A18a)

h=1

ϕfc,s,h+1 ≥ θfc,s,h+1 − θfc,s,h ∀h, s

(A18b)

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R. Jing, M. Wang and Z. Zhang et al. / Energy & Buildings 194 (2019) 123–139

ϕfc,s,h+1 ≤ 1 − θfc,s,h ∀h, s

(A18c)

ϕfc,s,h+1 ≤ θfc,s,h+1 ∀h, s

(A18d)

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