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Impacts of Uncertainties in Life Cycle Cost Analysis of Buildings Energy Efficiency Measures: Application to a Case Study
Available online at www.sciencedirect.com
ScienceDirect Energy Procedia 111 (2017) 442 – 451
8th International Conference on Sustainability in Energy and Buildings, SEB-16, 11-13 September 2016, Turin, ITALY
Impacts of uncertainties in Life Cycle Cost analysis of buildings energy efficiency measures: application to a case study Elisa Di Giuseppea*, Andrea Massia, Marco D’Orazioa a
Department of Construction Civil Engineering and Architecture, UNIVPM, Via Brecce Bianche 12, Ancona 60131, Italy
Abstract Life Cycle Cost (LCC) analysis in the field of building renovation is considered an important decision support of the design process in order to compare the effectiveness of different energy efficiency measures (EEMs). Nevertheless, data uncertainty is a well-recognised issue associated with LCC deterministic calculation methods and probabilistic methodologies could instead provide a more effective decision support. This paper proposes a Monte Carlo based methodology for uncertainty quantification that combines parametric building simulation and LCC analysis, showing a great potential in the possibility of combining several EEMs and undertake the uncertainty calculation with low computational costs and high accuracy of the result. The work aimed to identifying and quantifying the main uncertain inputs of the LCC assessment and developing a tools suite to automate the process of evaluation of the energy impact due to the combination of several EEMs and quantification of the uncertainty distribution of the output. Results from the application to a case study are mainly intended to illustrate the methodology application and underline the impact that input uncertainties may have on the output variable. The difficulty to identify the robust EEMs is particularly due to the great influence of macroeconomic parameters uncertainty used in the calculation. © 2017 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of KES International. Keywords: LCC, Monte-Carlo, uncertainty, probabilistic, building renovation, cost-optimal.
1.Introduction An important part of the design process of a building renovation project is a cost-benefit analysis in order to compare the effectiveness of different energy efficiency measures (EEMs) to apply and finally chose the most
*
Corresponding author. Tel.: +39-071-2204380. E-mail address: [email protected]
1876-6102 © 2017 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of KES International. doi:10.1016/j.egypro.2017.03.206
Elisa Di Giuseppe et al. / Energy Procedia 111 (2017) 442 – 451
profitable design option. Total expected costs and benefits (expressed in terms of money) due to the application of an EEM during a building renovation project could be evaluated during an established time frame and be adjusted for the time value of money, through Life Cycle Cost (LCC) methodologies. The importance of using LCC analysis in the field of buildings and building renovation has been introduced at regulatory level in Europe by Directive 2010/31/EU on the energy performance of buildings [1]. The Directive established that Member States shall calculate “cost-optimal levels” of minimum energy performance requirements using a comparative methodology framework according to the consequent Commission Delegated Regulation and its Guidelines [2,3] based on EN 15459:2007 [4]. Unfortunately, accurate Cost Analysis rely on quality of data and data uncertainty is a well-recognised issue associated with LCC deterministic calculation methods [5–8]. In particular results are heavily dependent on future trends for economic data and the corresponding uncertainty (i.e. inflation rate and energy prices). In the methodology framework established by Directive 2010/31/EU, the practice of using constant market interest rate for calculating the discount rate ignores the possibility of variations over the life cycle of the building resulting from changes in national and international monetary and fiscal policies. Also the prediction of inflation rates over a longterm period increases the uncertainty. Another uncertain area in LCC forecasting is determining the service life of building components [9]. If LCC methodologies in the field of buildings are considered as important decision supports, it is then necessary to assess and communicate the problem of uncertainties properly. Otherwise decisions might be made, which are based on faulty assumptions [6]. Several studies address probabilistic analysis in Building Energy Simulation (BES) [6,10–12], in order to overcome the limits of deterministic models and to credit the solutions with “robustness” [13]. Nevertheless, specific literature on probabilistic methodologies in LCC of buildings is still very fragmented. While a deterministic LCC analysis approach requires input variables that are fixed and distinct in both time and cost, in a probabilistic approach variables are modelled using a probability distribution function (PDF) and the quantification of the uncertainty of the outputs is a result of possible variance of the input parameters. In this paper a methodology for uncertainty quantification that combines parametric building simulation and LCC analysis is developed. The methodology is useful to: provide decision support during the design phase, giving insight into design robustness and possible ranges of the economic indicator of different design options; investigate and compare different EEMs, in order to identify the best performing alternative minimizing the likelihood of exceeding cost thresholds; provide an idea of the significance of uncertainties and their impact on the result. This paper presents a preliminary part of the work, which aims to: • Identify and quantify the main uncertain inputs of the LCC assessment; • Develop a tools suite to automate the process of evaluating the energy impact due to the combination of several EEMs and quantifying the uncertainty distribution of the LCC output variable; • Underline the impact that LCC input uncertainties may have on the LCC output variable. The methodology developed is based on an uncertainty analysis via Monte Carlo (MC) approaches. These are effective methods used to build the model output distribution as a function of the input parameters’ distribution. In MC methods, every input parameter can be considered as a stochastic variable with a specified probability distribution. The distribution of outcomes is calculated by running the model a number of times with randomly selected parameter representations (or according to precise sampling schemes). The potential and effectiveness of MC methods are widely documented in the activities of Annex 55 [14] and could be briefly summarized as the possibility to use various parameter distributions (different types of PDFs or discrete variables) in the models and the ability to manage complex and non-linear models. If necessary, the computational efforts needed to increase the quality of the output can be reduced by using efficient sampling techniques and/or developing more efficient models (or metamodels). The methodology proposed is applied to a building renovation case-study but can be scalable depending on individual project requirements. Further development are identified in the conclusions.
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Nomenclature LCC Life Cycle Cost EEM Energy Efficiency Measure BES Building Energy Simulation MC Monte Carlo PDF Probability Distribution Function A area [m2] C cost [€] η efficiency [-] R rate [-] t time [h] Th thickness [m] U thermal transmittance (U-value) [Wm-2K-1] V volume [m3] Val value [€] Subscripts a annual coll solar collector disc discount (rate) env envelope f floor F final fl slab g gross gn generation (subsystem) I initial if internal net height n net w window wl wall 2.Methodology The work can be summarized by the following phases, further described in the paragraphs below: • Selection of a case study, definition of several EEMs and related costs; • Characterization of the PDF of the input variables of the LCC calculation methodology; • Energy simulations for the assessment of the impact on the energy performance of the selected EEMs (applied individually or combined with each other); • Uncertainty propagation through the application of MC methods. 2.1.Building case-study and Energy Efficiency Measures The object of the evaluation is a “virtual” building, whose geometrical and thermal features have been selected in order to make it representative of a typical Italian single-family house of the period 1976-1990 (Table 1), also according to [15]. The walls are made by brick based hollow blocks with 3 cm of insulation in the air gap and plaster in both sides (U=0.590 W/m2K). The roof consists of a hollow bricks slab structure plastered on the inside
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with a 4 cm insulation and clay roof tiles (U=0.546 W/m2K). The windows have wood frames and single glass (U=5 W/m2K). The heating system consists on a natural gas standard boiler with a thermal efficiency of 0.88 and radiators. Table 1. Main geometrical and thermal features of the building case study. Geometrical data 3
Wall (from int to ext)
Roof (from int to ext)
Vg
[m ] 686
Plaster
[m] 0.015 [W/mK] 0.900
Plaster
Af,n
[m2] 138.4
Hollow brick
[m] 0.08 [W/mK] 0.350
Hollow brick slab [m] 0.26 [W/mK] 0.667
Air
[m] 0.05 [W/mK] -
Insulation board [m] 0.04 [W/mK] 0.04
Aenv/Vg [m-1] 0.82 2
[m] 0.015 [W/mK] 0.900
Awl
[m ] 180.9
Insulation board [m] 0.03 [W/mK] 0.04
Concrete screed
[m] 0.10 [W/mK] 0.41
Aw
[m2] 17.4
Hollow brick
[m] 0.12 [W/mK] 0.350
Bitumen sheet
[m] 0.005 [W/mK] 0.23
hif
[m] 3.4
Plaster
[m] 0.015 [W/mK] 0.900
Roof tiles
[m] 0.018 [W/mK] 1.00
floors
[-] 2
2
Uwl
o
n . units [-] 1
Thwl
[W/m K] 0.59
[W/m2K] 0.546
Uwl
[m] 0.31
[m] 0.43
Thwl
At the aim of the energy renovation of the reference building, several EEMs have been selected (Table 2), with two further performance levels in addition to the actual baseline level (level 1): a level in accordance with the Italian Legislative Decree no. 311/2006 in force until October 2015 [16] (level 2) and a level according to Italian Ministerial Decree 26/06/2015 [17] currently in force (level 3). Concerning the envelope insulation, two insulating materials have been selected, in relation to the different installation costs and heat capacity (EPS and wood fiber). With regard to the windows, interventions consisted on their replacement with wooden frame double glass windows (level 1) and PVC frame triple glass windows (level 2). For the thermal plant requalification, the current boiler has been replaced with a sealed chamber one with efficiency 0.93 (level 2) and finally a condensing boiler with efficiency 1.00 (level 3). Finally the heating system has been integrated with a solar collector system (absent in the current situation, level 1) with a surface area of 8 m2 (level 1) and 10 m2 (level 2). The work basically followed the same methodology used in Italy in application to the Directive 2010/31/EU [18], but in a simplified form. In particular, just some of the possible EEMs applicable during a renovation intervention were selected (those considered more commonly used) and at the aim of being able to combine all them with each other (differently from e.g. [19]). The combination of different EEMs gave rise to 218 cases of building renovation. Table 2. Energy efficiency measures. Measure Internal insulation – Woodfiber External insulation – Woodfiber Internal insulation – EPS External insulation – EPS Windows Heating system Thermal solar system
Unit 2
Lv. 1
Lv. 2
Lv. 3
Uenv
[W/m K]
0.59
0.36
0.26
cost
[€/m2]
-
53.19
70.80
Uenv
[W/m2K]
0.59
0.56
0.26
cost
[€/m2]
-
75.60
91.34
Uenv
[W/m2K]
0.59
0.36
0.26
cost
[€/m2]
-
40.89
48.65
Uenv
[W/m2K]
0.59
0.36
0.26
2
cost
[€/m ]
-
62.02
70.86
Uw
[W/m2K]
5.00
2.10
1.20
cost
[€/m2]
-
363.00
435.00
ηgn
[-]
0.88
0.93
1
cost
[€]
-
2800
4000
Acoll
[m2]
0
8
10
cost
[€]
-
8000.00
10000.00
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The heating energy consumption was calculated according to the Italian technical specification UNI/TS 11300 [20], with the following assumptions: climatic data of Ancona (climatic zone D, one of the most representative in Italy); ventilation rate at 0.5 h-1, simplified approach for the calculation of internal heat gains, building internal heat capacity, temperature of unconditioned spaces, and thermal bridge effects (percentage increase of the transmission heat transfer), conversion coefficient to primary energy fixed at 1.05 for fossil fuels. 2.2.Global cost calculation method and definition of the PDFs of the stochastic inputs The evaluation of the cost-benefits of the EEMs has been carried out based on the global costs calculation, according to European standard EN 15459:2007 [4]. The global costs Cg(t) referred to the starting year t0 are calculated by summing, for each component j, the initial investment costs CI, the annual costs Ca discounted by the rate Rdisc(i) for every year I, and the residual value ValF, as shown in eq.1.
⎤ ⎡ t C g (t ) = C I + ∑ ⎢∑ (Ca ,i ( j ) ⋅ Rdisc (i )) − ValF ,t ( j )⎥ j ⎣ i =1 ⎦
(1)
The initial investment cost CI represents the construction/installation cost of the EEM considered. The annual costs Ca include recurrent costs such as components maintenance costs, operating costs (insurance, taxes …) and energy carriers’ costs. The replacement costs of components are to be considered in recurrent costs too, but with a frequency depending on the lifespan of the j component concerned (Fig.1). Finally, the residual value ValF is calculated based on a straight-line depreciation of the initial investment or replacement cost of the component until the end of the calculation, discounted at the beginning of the evaluation period. As the main objective of the evaluation is the comparison of different design options, the only investment cost items included in the LCC evaluation are those relating to EEMs. The following cost items are therefore omitted from the calculation (according to the methodology framework): the costs related to building elements which have no influence on the energy performance, and the costs which are the same for all the measures. The initial investment costs related to the envelope insulation were determined through the analysis of regional pricing lists for public works, taking into account the cost variability in different Italians regions. Concerning windows and heating components, prices reported in RdS-2013-144 ENEA report have been used [18]. In table 2 the costs related to each EEM are reported. Maintenance costs and components lifespan were assumed according to Annex A of EN 15459 (respectively: 2,0% for the envelopes and window elements, 4,0% for the heating system components and 0,5% for the solar panels; and: 30 years for windows, 15 years for heating system components and 20 years for the solar panels). The global cost is directly linked to the duration of the calculation period t, that has been considered of 30 years, as suggested by the Commission Delegated Regulation and its Guidelines [2,3] for residential buildings. In order to lead the global costs calculation in probabilistic terms and perform the Monte Carlo simulation, to the following LCC input variables a PDF has been assigned with the widest range that can be regarded as realistic, based on literature data or authors’ judgment: (1) Inflation rate, (2) Interest rate, (3) Energy prices evolution, (4) Component costs, (5) Maintenance costs. Inflation rate and interest rate affect the calculation of the discount rate in eq. 1. Their stochastic character depends on the extreme uncertainty of the financial market, whose evolution in the future is difficult to be exactly predicted. For this assessment, we considered a “baseline” scenario, based on the analysis of time series of the last years. In particular, for the inflation rate we obtained a normal distribution from the fitting of the inflation rate time series in Italy, in the period from the adoption of euro currency, when European Central Bank started its monetary policies that aims to maintain inflation rates below, but close to 2% over the medium term. For the interest rate we chose a triangular distribution with a median value of 4.09 %, coming from Bank of Italy survey on personal loans rates. The minimum value was based on the EURIRS 30 years average rate and the maximum rate is the usury limit assumed in Italy. For the energy prices trend and its uncertainty we referred to the Annual Energy Outlook 2015’s
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projections until 2040 of the EIA/DOE [21]. The uncertainty attributed to the component costs is the result of the authors’ judgment. The surveys carried out on the Italian national price lists led to a prices variation on a geographical basis of about 10%. This uncertainty interval has been considered representative of the price variations that could affect a design choice because of an unforeseen during the design/execution of the work. Therefore it was decided to attribute a uniform distribution (±10%) to the component and maintenance costs. Table 3 summarizes the uncertain inputs considered in the calculation of global costs and related PDFs.
Fig. 1. Cost categorization according to the methodology framework in [2]. Table 3. Uncertainty parameters. Parameter
Unit
Standard value
Distribution*
Inflation rate
[-]
1.9 %
Nor(0.019,0.010946)
Interest rate
[-]
4.09 %
Tri(0.0149,0.0908,0.0409)
Energy price
[-]
1.59%
Nor(0.0159, 0.014037)
Component costs
[€]
μcost
Uni(μcost -10%, μcost +10%)
Maintenance costs
[€]
μmaint
Uni(μmaint -10%, μmaint +10%)
* Uni(a,b): uniform distribution between a and b. Nor(μ,σ): normal distribution with mean value μ and standard deviation σ. Tri(a,b,c): triangular distribution with lower limit a, upper limit b and mode c, where a < b and a c b.
2.3.Energy calculation and uncertainty propagation on the global costs evaluation The simulation of building energy performance with the application of different EEMs was realized through jEPlus [22], an Energy Plus [23] simulation manager designed for setting up and managing parametric simulations. Results have been collected into CSV tables, directly read by and excel sheet. In the same spreadsheet, the evaluation of the global costs according to EN 15459 has been implemented for each EEM.
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Through a development with Visual Basic Application code, the uncertainty propagation of inputs PDFs into an uncertainty distribution of the output variable has been realized through basic random Monte Carlo methods (Fig.2). Five sets of simulations were run with an increasing number of iterations (10, 30, 50, 100, 250, 500, 1000) and the quality of the related outcome (the PDF of the output sample) has been compared with a reference simulation of 2500 runs (this represents the maximum number of possible iterations in Excel and VBA environment with the EEMs combination considered in this case study1). For each simulation, the mean value and standard deviation were calculated.
Fig. 2. Diagram of the tools suite for the MC based methodology for uncertainty quantification that combines parametric building simulation and Life Cycle Costs analysis.
3.Results To assess whether the number of simulation runs was sufficient to guarantee the quality of the outcome (a PDF of the output sample), the convergence of the mean and standard deviation of the output parameters has been investigated, compared to the reference simulation of 2500 iterations. From Table 4 it is possible to observe the results in terms of mean and standard deviation, and normalized mean and standard deviation (ratio with the reference simulation). Table 4. Global Cost convergence. Number of iterations (n)
Execution Time (s)
Mean (μ)
SD (σ)
Norm. Mean A (μ)
Norm. SD (σ)
10
5.2
402.86
53.81
0.016863118
0.165309658
30
14.
416.50
52.21
0.016423848
0.130489389
50
23.5
409.44
49.89
0.00080533
0.080337809
100
46.4
409.42
48.17
0.000863899
0.043135557
250
111.1
410.12
47.22
0.000863899
0.02256388
500
233.1
410.174
45.60
0.000985919
0.012646167
1000
472.0
409.46
46.15
0.00074676
0.000736249
As also shown in Fig. 3, a good approximation of the output sample is already obtained starting from 250 iterations. The best convergence, however, is achieved by increasing the number of iterations at 500 and 1000, with a greater reduction of the standard deviation normalized with respect to the reference simulation. This is reflected by a more accurate PDF and cumulative frequency of the output, as in Fig.4 for the “cost-optimal” solution.
Computer System: CPU: Intel Core i7-4790 @3.60GHz; RAM: 8.00 GB; HD: SSD 500GB.
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Fig. 3. (a) Mean μ and standard deviation σ with different number of runs. The lines represent the reference simulation (2500 runs); (b) Normalized μ and standard deviation σ with different number of runs (ratio with the reference simulation, 2500 runs).
Fig. 4. PDF and cumulative frequency of the “cost-optimal” solution.
Fig.5(a) shows the value of Cg(t) in function of the energy performance per unit area of the building, for each EEM considered. Black dots represent the "deterministic" results. The minimum area of the curve identifies the solution with lower Cg(t) (“economic optimum area” according to [3]). The EEMs to the left of this area are those which entail lower energy costs during building operating phase, but against higher investment costs. The right-most solutions are those which involve greater energy consumption and consequently costs during building operating phase. The grey dots represent the results of the iterations performed (1000 runs). The deterministic result "moves" along the vertical axis of the costs due to the variability in the input parameters of Cg(t) calculation (the building energy performance due to each EEM is “deterministic”). Fig.5(b) shows the same result expressed in a bubble chart, where the centre of the bubble represents the Cg(t) mean value, while the diameter its variance. The EEMs more “robust” in terms are those with lower energy consumption in the operating phase (bottom and left of the graphs). This highlights the great influence on the results given by the uncertainty on the macroeconomic parameters used in the calculation (inflation rate, interest rate, energy prices evolution). The result is further revealed in the Box-Whiskers plot graph in Fig.6, where the results for the different EEMs are ranked in relation to their energy consumption.
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Fig. 5.(a) Deterministic cost-optimal (black dots) and probabilistic iterations (grey dots); (b) Circles: Centre represents the Cg(t) mean value (μ), the diameter represent its variance (σ2).
Fig. 6. Box-Whiskers plot of the different EEMs ranked by energy demands.
4.Conclusions Data uncertainty is a well-recognised issue associated with LCC deterministic calculation methods. Probabilistic LCC methodologies could instead provide powerful decision support for undertaking building energy efficiency measures. Nevertheless, their development in the field of LCC is still at the beginning. This paper proposed a Monte Carlo based methodology for uncertainty quantification that combines parametric building simulation and Life Cycle Costs analysis. It showed a great potential in the possibility of combining several EEMs and undertake the uncertainty calculation with low computational costs and high accuracy of the result. Nevertheless results from the application to a case study underlined the difficulty to identify the robust EEMs, particularly due to the great influence of macroeconomic parameters used in the calculation (inflation rate, interest rate, energy prices evolution) on the output distribution. The methodology therefore requires future developments mainly aimed at: • Identifying optimization procedures for the combination of the different EEMs; • Assess the impact of all the input variables through a more thorough sensitivity analysis;
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• Undertaking a detailed study of the macroeconomic variables impact, considering several alternative scenarios rather than one baseline scenario with wide margins of uncertainty. These scenarios would represent alternative general macroeconomic conditions and perspectives. Macroeconomic variables are interdependent and scenarios express possible combinations of these variables that can be encountered under different economic conditions and medium and long-term growth patterns. As the event of an economy falling in one of these conditions is largely unpredictable, the choice among scenarios, therefore, should be driven by other orders of arguments: political relevance, ethical concerns, attitude towards risk, etc. References [1]Directive 2010/31/EU of the European Parliament and of the Council of 19 May 2010 on the energy performance of buildings (recast). Off J Eur Union 2010;53:13–35. [2]Commission Delegated Regulation (EU) No 244/2012 of 16 January 2012 supplementing Directive 2010/31/EU of the European Parliament and of the Council. Off J Eur Union 2012;55:18–36. [3]Guidelines accompanying Commission Delegated Regulation (EU) No 244/2012 of 16 January 2012 supplementing Directive 2010/31/EU of the European Parliament and of the Council. Off J Eur Union 2012;55:1–28. [4]EN 15459:2007 Energy performance of buildings - Economic evaluation procedure for energy systems in buildings. [5]Pittenger D, Gransberg D, Zaman M, Riemer C. Stochastic Life-Cycle Cost Analysis for Pavement Preservation Treatments. Transp Res Rec J Transp Res Board 2012;2292:45–51. [6]Burhenne S, Tsvetkova O, Jacob D, Henze GP, Wagner A. Uncertainty quantification for combined building performance and cost-benefit analyses. Build Environ 2013;62:143–54. [7]Wang N, Chang Y-C, El-Sheikh A. Monte Carlo simulation approach to life cycle cost management. Struct Infrastruct Eng 2012;8:739–46. [8]Das P, Van Gelder L, Janssen H, Roels S. Designing uncertain optimization schemes for the economic assessment of stock energy-efficiency measures. J Build Perform Simul 2015;1493:1–14. [9]Rahman S, Vanier DJ. Life cycle cost analysis as a decision support tool for managing municipal infrastructure. CIB 2004 Triennial Congress. Toronto, Ontario; 2004. p. 1–12. [10]Van Gelder L, Janssen H, Roels S. Probabilistic design and analysis of building performances: Methodology and application example. Energy Build 2014;79:202–11. [11]Macdonald I. Quantifying the Effects of Uncertainty in Building Simulation. PhD Dissemination, University of Strathclyde; 2002. [12]Hopfe CJ. Uncertainty and sensitivity analysis in building performance simulation for decision support and design optimization. PhD Dissemination, Eindhoven University; 2009. [13]Janssen H. Monte-Carlo based uncertainty analysis: Sampling efficiency and sampling convergence. Reliab Eng Syst Saf; 2013;109:123–32. [14]Janssen H, Roels S, Van Gelder L, Das P. IEA Annex 55 Reliability of Energy Efficient Building Retrofitting - Probability Assessment of Performance & Cost (RAP-RETRO) - Probabilistic Tools. Chalmers University of Technology; 2015. [15]Corrado V, Ballarini I, Corgnati SP. Building Typology Brochure – Italy. Fascicolo sulla Tipologia Edilizia Italiana, nuova edizione; 2014. [16]Decreto Legislativo 29 dicembre 2006, n. 311 Disposizioni correttive ed integrative al decreto legislativo 19 agosto 2005, n. 192, recante attuazione della direttiva 2002/91/CE, relativa al rendimento energetico nell’edilizia. [17]Decreto Ministeriale 26.06.2015: Applicazione delle metodologie di calcolo delle prestazioni energetiche e definizione delle prescrizioni e dei requisiti minimi degli edifici. [18]Moneta R, Bonacci E, et al. Applicazione della metodologia di calcolo dei livelli ottimali in funzione dei costi per i requisiti minimi di prestazione energetica (Direttiva 2010/31/UE art. 5); 2013. [19]Corrado V, Ballarini I, Paduos S. Assessment of cost-optimal energy performance requirements for the Italian residential building stock. Energy Procedia 2014;45:443–52. [20]UNI/TS 11300-1:2014 Prestazioni energetiche degli edifici - Parte 1: Determinazione del fabbisogno di energia termica dell’edificio per la climatizzazione estiva ed invernale. [21]http://www.eia.gov/forecasts/aeo/pdf/0383(2015).pdf [cited 2016 May 13]. [22]http://www.jeplus.org [cited 2016 May 13]. [23]https://energyplus.net [cited 2016 May 13].
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ScienceDirect Energy Procedia 111 (2017) 442 – 451
8th International Conference on Sustainability in Energy and Buildings, SEB-16, 11-13 September 2016, Turin, ITALY
Impacts of uncertainties in Life Cycle Cost analysis of buildings energy efficiency measures: application to a case study Elisa Di Giuseppea*, Andrea Massia, Marco D’Orazioa a
Department of Construction Civil Engineering and Architecture, UNIVPM, Via Brecce Bianche 12, Ancona 60131, Italy
Abstract Life Cycle Cost (LCC) analysis in the field of building renovation is considered an important decision support of the design process in order to compare the effectiveness of different energy efficiency measures (EEMs). Nevertheless, data uncertainty is a well-recognised issue associated with LCC deterministic calculation methods and probabilistic methodologies could instead provide a more effective decision support. This paper proposes a Monte Carlo based methodology for uncertainty quantification that combines parametric building simulation and LCC analysis, showing a great potential in the possibility of combining several EEMs and undertake the uncertainty calculation with low computational costs and high accuracy of the result. The work aimed to identifying and quantifying the main uncertain inputs of the LCC assessment and developing a tools suite to automate the process of evaluation of the energy impact due to the combination of several EEMs and quantification of the uncertainty distribution of the output. Results from the application to a case study are mainly intended to illustrate the methodology application and underline the impact that input uncertainties may have on the output variable. The difficulty to identify the robust EEMs is particularly due to the great influence of macroeconomic parameters uncertainty used in the calculation. © 2017 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of KES International. Keywords: LCC, Monte-Carlo, uncertainty, probabilistic, building renovation, cost-optimal.
1.Introduction An important part of the design process of a building renovation project is a cost-benefit analysis in order to compare the effectiveness of different energy efficiency measures (EEMs) to apply and finally chose the most
*
Corresponding author. Tel.: +39-071-2204380. E-mail address: [email protected]
1876-6102 © 2017 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of KES International. doi:10.1016/j.egypro.2017.03.206
Elisa Di Giuseppe et al. / Energy Procedia 111 (2017) 442 – 451
profitable design option. Total expected costs and benefits (expressed in terms of money) due to the application of an EEM during a building renovation project could be evaluated during an established time frame and be adjusted for the time value of money, through Life Cycle Cost (LCC) methodologies. The importance of using LCC analysis in the field of buildings and building renovation has been introduced at regulatory level in Europe by Directive 2010/31/EU on the energy performance of buildings [1]. The Directive established that Member States shall calculate “cost-optimal levels” of minimum energy performance requirements using a comparative methodology framework according to the consequent Commission Delegated Regulation and its Guidelines [2,3] based on EN 15459:2007 [4]. Unfortunately, accurate Cost Analysis rely on quality of data and data uncertainty is a well-recognised issue associated with LCC deterministic calculation methods [5–8]. In particular results are heavily dependent on future trends for economic data and the corresponding uncertainty (i.e. inflation rate and energy prices). In the methodology framework established by Directive 2010/31/EU, the practice of using constant market interest rate for calculating the discount rate ignores the possibility of variations over the life cycle of the building resulting from changes in national and international monetary and fiscal policies. Also the prediction of inflation rates over a longterm period increases the uncertainty. Another uncertain area in LCC forecasting is determining the service life of building components [9]. If LCC methodologies in the field of buildings are considered as important decision supports, it is then necessary to assess and communicate the problem of uncertainties properly. Otherwise decisions might be made, which are based on faulty assumptions [6]. Several studies address probabilistic analysis in Building Energy Simulation (BES) [6,10–12], in order to overcome the limits of deterministic models and to credit the solutions with “robustness” [13]. Nevertheless, specific literature on probabilistic methodologies in LCC of buildings is still very fragmented. While a deterministic LCC analysis approach requires input variables that are fixed and distinct in both time and cost, in a probabilistic approach variables are modelled using a probability distribution function (PDF) and the quantification of the uncertainty of the outputs is a result of possible variance of the input parameters. In this paper a methodology for uncertainty quantification that combines parametric building simulation and LCC analysis is developed. The methodology is useful to: provide decision support during the design phase, giving insight into design robustness and possible ranges of the economic indicator of different design options; investigate and compare different EEMs, in order to identify the best performing alternative minimizing the likelihood of exceeding cost thresholds; provide an idea of the significance of uncertainties and their impact on the result. This paper presents a preliminary part of the work, which aims to: • Identify and quantify the main uncertain inputs of the LCC assessment; • Develop a tools suite to automate the process of evaluating the energy impact due to the combination of several EEMs and quantifying the uncertainty distribution of the LCC output variable; • Underline the impact that LCC input uncertainties may have on the LCC output variable. The methodology developed is based on an uncertainty analysis via Monte Carlo (MC) approaches. These are effective methods used to build the model output distribution as a function of the input parameters’ distribution. In MC methods, every input parameter can be considered as a stochastic variable with a specified probability distribution. The distribution of outcomes is calculated by running the model a number of times with randomly selected parameter representations (or according to precise sampling schemes). The potential and effectiveness of MC methods are widely documented in the activities of Annex 55 [14] and could be briefly summarized as the possibility to use various parameter distributions (different types of PDFs or discrete variables) in the models and the ability to manage complex and non-linear models. If necessary, the computational efforts needed to increase the quality of the output can be reduced by using efficient sampling techniques and/or developing more efficient models (or metamodels). The methodology proposed is applied to a building renovation case-study but can be scalable depending on individual project requirements. Further development are identified in the conclusions.
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Nomenclature LCC Life Cycle Cost EEM Energy Efficiency Measure BES Building Energy Simulation MC Monte Carlo PDF Probability Distribution Function A area [m2] C cost [€] η efficiency [-] R rate [-] t time [h] Th thickness [m] U thermal transmittance (U-value) [Wm-2K-1] V volume [m3] Val value [€] Subscripts a annual coll solar collector disc discount (rate) env envelope f floor F final fl slab g gross gn generation (subsystem) I initial if internal net height n net w window wl wall 2.Methodology The work can be summarized by the following phases, further described in the paragraphs below: • Selection of a case study, definition of several EEMs and related costs; • Characterization of the PDF of the input variables of the LCC calculation methodology; • Energy simulations for the assessment of the impact on the energy performance of the selected EEMs (applied individually or combined with each other); • Uncertainty propagation through the application of MC methods. 2.1.Building case-study and Energy Efficiency Measures The object of the evaluation is a “virtual” building, whose geometrical and thermal features have been selected in order to make it representative of a typical Italian single-family house of the period 1976-1990 (Table 1), also according to [15]. The walls are made by brick based hollow blocks with 3 cm of insulation in the air gap and plaster in both sides (U=0.590 W/m2K). The roof consists of a hollow bricks slab structure plastered on the inside
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with a 4 cm insulation and clay roof tiles (U=0.546 W/m2K). The windows have wood frames and single glass (U=5 W/m2K). The heating system consists on a natural gas standard boiler with a thermal efficiency of 0.88 and radiators. Table 1. Main geometrical and thermal features of the building case study. Geometrical data 3
Wall (from int to ext)
Roof (from int to ext)
Vg
[m ] 686
Plaster
[m] 0.015 [W/mK] 0.900
Plaster
Af,n
[m2] 138.4
Hollow brick
[m] 0.08 [W/mK] 0.350
Hollow brick slab [m] 0.26 [W/mK] 0.667
Air
[m] 0.05 [W/mK] -
Insulation board [m] 0.04 [W/mK] 0.04
Aenv/Vg [m-1] 0.82 2
[m] 0.015 [W/mK] 0.900
Awl
[m ] 180.9
Insulation board [m] 0.03 [W/mK] 0.04
Concrete screed
[m] 0.10 [W/mK] 0.41
Aw
[m2] 17.4
Hollow brick
[m] 0.12 [W/mK] 0.350
Bitumen sheet
[m] 0.005 [W/mK] 0.23
hif
[m] 3.4
Plaster
[m] 0.015 [W/mK] 0.900
Roof tiles
[m] 0.018 [W/mK] 1.00
floors
[-] 2
2
Uwl
o
n . units [-] 1
Thwl
[W/m K] 0.59
[W/m2K] 0.546
Uwl
[m] 0.31
[m] 0.43
Thwl
At the aim of the energy renovation of the reference building, several EEMs have been selected (Table 2), with two further performance levels in addition to the actual baseline level (level 1): a level in accordance with the Italian Legislative Decree no. 311/2006 in force until October 2015 [16] (level 2) and a level according to Italian Ministerial Decree 26/06/2015 [17] currently in force (level 3). Concerning the envelope insulation, two insulating materials have been selected, in relation to the different installation costs and heat capacity (EPS and wood fiber). With regard to the windows, interventions consisted on their replacement with wooden frame double glass windows (level 1) and PVC frame triple glass windows (level 2). For the thermal plant requalification, the current boiler has been replaced with a sealed chamber one with efficiency 0.93 (level 2) and finally a condensing boiler with efficiency 1.00 (level 3). Finally the heating system has been integrated with a solar collector system (absent in the current situation, level 1) with a surface area of 8 m2 (level 1) and 10 m2 (level 2). The work basically followed the same methodology used in Italy in application to the Directive 2010/31/EU [18], but in a simplified form. In particular, just some of the possible EEMs applicable during a renovation intervention were selected (those considered more commonly used) and at the aim of being able to combine all them with each other (differently from e.g. [19]). The combination of different EEMs gave rise to 218 cases of building renovation. Table 2. Energy efficiency measures. Measure Internal insulation – Woodfiber External insulation – Woodfiber Internal insulation – EPS External insulation – EPS Windows Heating system Thermal solar system
Unit 2
Lv. 1
Lv. 2
Lv. 3
Uenv
[W/m K]
0.59
0.36
0.26
cost
[€/m2]
-
53.19
70.80
Uenv
[W/m2K]
0.59
0.56
0.26
cost
[€/m2]
-
75.60
91.34
Uenv
[W/m2K]
0.59
0.36
0.26
cost
[€/m2]
-
40.89
48.65
Uenv
[W/m2K]
0.59
0.36
0.26
2
cost
[€/m ]
-
62.02
70.86
Uw
[W/m2K]
5.00
2.10
1.20
cost
[€/m2]
-
363.00
435.00
ηgn
[-]
0.88
0.93
1
cost
[€]
-
2800
4000
Acoll
[m2]
0
8
10
cost
[€]
-
8000.00
10000.00
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The heating energy consumption was calculated according to the Italian technical specification UNI/TS 11300 [20], with the following assumptions: climatic data of Ancona (climatic zone D, one of the most representative in Italy); ventilation rate at 0.5 h-1, simplified approach for the calculation of internal heat gains, building internal heat capacity, temperature of unconditioned spaces, and thermal bridge effects (percentage increase of the transmission heat transfer), conversion coefficient to primary energy fixed at 1.05 for fossil fuels. 2.2.Global cost calculation method and definition of the PDFs of the stochastic inputs The evaluation of the cost-benefits of the EEMs has been carried out based on the global costs calculation, according to European standard EN 15459:2007 [4]. The global costs Cg(t) referred to the starting year t0 are calculated by summing, for each component j, the initial investment costs CI, the annual costs Ca discounted by the rate Rdisc(i) for every year I, and the residual value ValF, as shown in eq.1.
⎤ ⎡ t C g (t ) = C I + ∑ ⎢∑ (Ca ,i ( j ) ⋅ Rdisc (i )) − ValF ,t ( j )⎥ j ⎣ i =1 ⎦
(1)
The initial investment cost CI represents the construction/installation cost of the EEM considered. The annual costs Ca include recurrent costs such as components maintenance costs, operating costs (insurance, taxes …) and energy carriers’ costs. The replacement costs of components are to be considered in recurrent costs too, but with a frequency depending on the lifespan of the j component concerned (Fig.1). Finally, the residual value ValF is calculated based on a straight-line depreciation of the initial investment or replacement cost of the component until the end of the calculation, discounted at the beginning of the evaluation period. As the main objective of the evaluation is the comparison of different design options, the only investment cost items included in the LCC evaluation are those relating to EEMs. The following cost items are therefore omitted from the calculation (according to the methodology framework): the costs related to building elements which have no influence on the energy performance, and the costs which are the same for all the measures. The initial investment costs related to the envelope insulation were determined through the analysis of regional pricing lists for public works, taking into account the cost variability in different Italians regions. Concerning windows and heating components, prices reported in RdS-2013-144 ENEA report have been used [18]. In table 2 the costs related to each EEM are reported. Maintenance costs and components lifespan were assumed according to Annex A of EN 15459 (respectively: 2,0% for the envelopes and window elements, 4,0% for the heating system components and 0,5% for the solar panels; and: 30 years for windows, 15 years for heating system components and 20 years for the solar panels). The global cost is directly linked to the duration of the calculation period t, that has been considered of 30 years, as suggested by the Commission Delegated Regulation and its Guidelines [2,3] for residential buildings. In order to lead the global costs calculation in probabilistic terms and perform the Monte Carlo simulation, to the following LCC input variables a PDF has been assigned with the widest range that can be regarded as realistic, based on literature data or authors’ judgment: (1) Inflation rate, (2) Interest rate, (3) Energy prices evolution, (4) Component costs, (5) Maintenance costs. Inflation rate and interest rate affect the calculation of the discount rate in eq. 1. Their stochastic character depends on the extreme uncertainty of the financial market, whose evolution in the future is difficult to be exactly predicted. For this assessment, we considered a “baseline” scenario, based on the analysis of time series of the last years. In particular, for the inflation rate we obtained a normal distribution from the fitting of the inflation rate time series in Italy, in the period from the adoption of euro currency, when European Central Bank started its monetary policies that aims to maintain inflation rates below, but close to 2% over the medium term. For the interest rate we chose a triangular distribution with a median value of 4.09 %, coming from Bank of Italy survey on personal loans rates. The minimum value was based on the EURIRS 30 years average rate and the maximum rate is the usury limit assumed in Italy. For the energy prices trend and its uncertainty we referred to the Annual Energy Outlook 2015’s
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projections until 2040 of the EIA/DOE [21]. The uncertainty attributed to the component costs is the result of the authors’ judgment. The surveys carried out on the Italian national price lists led to a prices variation on a geographical basis of about 10%. This uncertainty interval has been considered representative of the price variations that could affect a design choice because of an unforeseen during the design/execution of the work. Therefore it was decided to attribute a uniform distribution (±10%) to the component and maintenance costs. Table 3 summarizes the uncertain inputs considered in the calculation of global costs and related PDFs.
Fig. 1. Cost categorization according to the methodology framework in [2]. Table 3. Uncertainty parameters. Parameter
Unit
Standard value
Distribution*
Inflation rate
[-]
1.9 %
Nor(0.019,0.010946)
Interest rate
[-]
4.09 %
Tri(0.0149,0.0908,0.0409)
Energy price
[-]
1.59%
Nor(0.0159, 0.014037)
Component costs
[€]
μcost
Uni(μcost -10%, μcost +10%)
Maintenance costs
[€]
μmaint
Uni(μmaint -10%, μmaint +10%)
* Uni(a,b): uniform distribution between a and b. Nor(μ,σ): normal distribution with mean value μ and standard deviation σ. Tri(a,b,c): triangular distribution with lower limit a, upper limit b and mode c, where a < b and a c b.
2.3.Energy calculation and uncertainty propagation on the global costs evaluation The simulation of building energy performance with the application of different EEMs was realized through jEPlus [22], an Energy Plus [23] simulation manager designed for setting up and managing parametric simulations. Results have been collected into CSV tables, directly read by and excel sheet. In the same spreadsheet, the evaluation of the global costs according to EN 15459 has been implemented for each EEM.
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Through a development with Visual Basic Application code, the uncertainty propagation of inputs PDFs into an uncertainty distribution of the output variable has been realized through basic random Monte Carlo methods (Fig.2). Five sets of simulations were run with an increasing number of iterations (10, 30, 50, 100, 250, 500, 1000) and the quality of the related outcome (the PDF of the output sample) has been compared with a reference simulation of 2500 runs (this represents the maximum number of possible iterations in Excel and VBA environment with the EEMs combination considered in this case study1). For each simulation, the mean value and standard deviation were calculated.
Fig. 2. Diagram of the tools suite for the MC based methodology for uncertainty quantification that combines parametric building simulation and Life Cycle Costs analysis.
3.Results To assess whether the number of simulation runs was sufficient to guarantee the quality of the outcome (a PDF of the output sample), the convergence of the mean and standard deviation of the output parameters has been investigated, compared to the reference simulation of 2500 iterations. From Table 4 it is possible to observe the results in terms of mean and standard deviation, and normalized mean and standard deviation (ratio with the reference simulation). Table 4. Global Cost convergence. Number of iterations (n)
Execution Time (s)
Mean (μ)
SD (σ)
Norm. Mean A (μ)
Norm. SD (σ)
10
5.2
402.86
53.81
0.016863118
0.165309658
30
14.
416.50
52.21
0.016423848
0.130489389
50
23.5
409.44
49.89
0.00080533
0.080337809
100
46.4
409.42
48.17
0.000863899
0.043135557
250
111.1
410.12
47.22
0.000863899
0.02256388
500
233.1
410.174
45.60
0.000985919
0.012646167
1000
472.0
409.46
46.15
0.00074676
0.000736249
As also shown in Fig. 3, a good approximation of the output sample is already obtained starting from 250 iterations. The best convergence, however, is achieved by increasing the number of iterations at 500 and 1000, with a greater reduction of the standard deviation normalized with respect to the reference simulation. This is reflected by a more accurate PDF and cumulative frequency of the output, as in Fig.4 for the “cost-optimal” solution.
Computer System: CPU: Intel Core i7-4790 @3.60GHz; RAM: 8.00 GB; HD: SSD 500GB.
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Fig. 3. (a) Mean μ and standard deviation σ with different number of runs. The lines represent the reference simulation (2500 runs); (b) Normalized μ and standard deviation σ with different number of runs (ratio with the reference simulation, 2500 runs).
Fig. 4. PDF and cumulative frequency of the “cost-optimal” solution.
Fig.5(a) shows the value of Cg(t) in function of the energy performance per unit area of the building, for each EEM considered. Black dots represent the "deterministic" results. The minimum area of the curve identifies the solution with lower Cg(t) (“economic optimum area” according to [3]). The EEMs to the left of this area are those which entail lower energy costs during building operating phase, but against higher investment costs. The right-most solutions are those which involve greater energy consumption and consequently costs during building operating phase. The grey dots represent the results of the iterations performed (1000 runs). The deterministic result "moves" along the vertical axis of the costs due to the variability in the input parameters of Cg(t) calculation (the building energy performance due to each EEM is “deterministic”). Fig.5(b) shows the same result expressed in a bubble chart, where the centre of the bubble represents the Cg(t) mean value, while the diameter its variance. The EEMs more “robust” in terms are those with lower energy consumption in the operating phase (bottom and left of the graphs). This highlights the great influence on the results given by the uncertainty on the macroeconomic parameters used in the calculation (inflation rate, interest rate, energy prices evolution). The result is further revealed in the Box-Whiskers plot graph in Fig.6, where the results for the different EEMs are ranked in relation to their energy consumption.
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Fig. 5.(a) Deterministic cost-optimal (black dots) and probabilistic iterations (grey dots); (b) Circles: Centre represents the Cg(t) mean value (μ), the diameter represent its variance (σ2).
Fig. 6. Box-Whiskers plot of the different EEMs ranked by energy demands.
4.Conclusions Data uncertainty is a well-recognised issue associated with LCC deterministic calculation methods. Probabilistic LCC methodologies could instead provide powerful decision support for undertaking building energy efficiency measures. Nevertheless, their development in the field of LCC is still at the beginning. This paper proposed a Monte Carlo based methodology for uncertainty quantification that combines parametric building simulation and Life Cycle Costs analysis. It showed a great potential in the possibility of combining several EEMs and undertake the uncertainty calculation with low computational costs and high accuracy of the result. Nevertheless results from the application to a case study underlined the difficulty to identify the robust EEMs, particularly due to the great influence of macroeconomic parameters used in the calculation (inflation rate, interest rate, energy prices evolution) on the output distribution. The methodology therefore requires future developments mainly aimed at: • Identifying optimization procedures for the combination of the different EEMs; • Assess the impact of all the input variables through a more thorough sensitivity analysis;
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• Undertaking a detailed study of the macroeconomic variables impact, considering several alternative scenarios rather than one baseline scenario with wide margins of uncertainty. These scenarios would represent alternative general macroeconomic conditions and perspectives. Macroeconomic variables are interdependent and scenarios express possible combinations of these variables that can be encountered under different economic conditions and medium and long-term growth patterns. As the event of an economy falling in one of these conditions is largely unpredictable, the choice among scenarios, therefore, should be driven by other orders of arguments: political relevance, ethical concerns, attitude towards risk, etc. References [1]Directive 2010/31/EU of the European Parliament and of the Council of 19 May 2010 on the energy performance of buildings (recast). Off J Eur Union 2010;53:13–35. [2]Commission Delegated Regulation (EU) No 244/2012 of 16 January 2012 supplementing Directive 2010/31/EU of the European Parliament and of the Council. Off J Eur Union 2012;55:18–36. [3]Guidelines accompanying Commission Delegated Regulation (EU) No 244/2012 of 16 January 2012 supplementing Directive 2010/31/EU of the European Parliament and of the Council. Off J Eur Union 2012;55:1–28. [4]EN 15459:2007 Energy performance of buildings - Economic evaluation procedure for energy systems in buildings. [5]Pittenger D, Gransberg D, Zaman M, Riemer C. Stochastic Life-Cycle Cost Analysis for Pavement Preservation Treatments. Transp Res Rec J Transp Res Board 2012;2292:45–51. [6]Burhenne S, Tsvetkova O, Jacob D, Henze GP, Wagner A. Uncertainty quantification for combined building performance and cost-benefit analyses. Build Environ 2013;62:143–54. [7]Wang N, Chang Y-C, El-Sheikh A. Monte Carlo simulation approach to life cycle cost management. Struct Infrastruct Eng 2012;8:739–46. [8]Das P, Van Gelder L, Janssen H, Roels S. Designing uncertain optimization schemes for the economic assessment of stock energy-efficiency measures. J Build Perform Simul 2015;1493:1–14. [9]Rahman S, Vanier DJ. Life cycle cost analysis as a decision support tool for managing municipal infrastructure. CIB 2004 Triennial Congress. Toronto, Ontario; 2004. p. 1–12. [10]Van Gelder L, Janssen H, Roels S. Probabilistic design and analysis of building performances: Methodology and application example. Energy Build 2014;79:202–11. [11]Macdonald I. Quantifying the Effects of Uncertainty in Building Simulation. PhD Dissemination, University of Strathclyde; 2002. [12]Hopfe CJ. Uncertainty and sensitivity analysis in building performance simulation for decision support and design optimization. PhD Dissemination, Eindhoven University; 2009. [13]Janssen H. Monte-Carlo based uncertainty analysis: Sampling efficiency and sampling convergence. Reliab Eng Syst Saf; 2013;109:123–32. [14]Janssen H, Roels S, Van Gelder L, Das P. IEA Annex 55 Reliability of Energy Efficient Building Retrofitting - Probability Assessment of Performance & Cost (RAP-RETRO) - Probabilistic Tools. Chalmers University of Technology; 2015. [15]Corrado V, Ballarini I, Corgnati SP. Building Typology Brochure – Italy. Fascicolo sulla Tipologia Edilizia Italiana, nuova edizione; 2014. [16]Decreto Legislativo 29 dicembre 2006, n. 311 Disposizioni correttive ed integrative al decreto legislativo 19 agosto 2005, n. 192, recante attuazione della direttiva 2002/91/CE, relativa al rendimento energetico nell’edilizia. [17]Decreto Ministeriale 26.06.2015: Applicazione delle metodologie di calcolo delle prestazioni energetiche e definizione delle prescrizioni e dei requisiti minimi degli edifici. [18]Moneta R, Bonacci E, et al. Applicazione della metodologia di calcolo dei livelli ottimali in funzione dei costi per i requisiti minimi di prestazione energetica (Direttiva 2010/31/UE art. 5); 2013. [19]Corrado V, Ballarini I, Paduos S. Assessment of cost-optimal energy performance requirements for the Italian residential building stock. Energy Procedia 2014;45:443–52. [20]UNI/TS 11300-1:2014 Prestazioni energetiche degli edifici - Parte 1: Determinazione del fabbisogno di energia termica dell’edificio per la climatizzazione estiva ed invernale. [21]http://www.eia.gov/forecasts/aeo/pdf/0383(2015).pdf [cited 2016 May 13]. [22]http://www.jeplus.org [cited 2016 May 13]. [23]https://energyplus.net [cited 2016 May 13].
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