# Impact of Reference Years on the Outcome of Multi-Objective Optimization for Building Energy Refurbishment

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Methods

#### 2.1. Development of Reference Years

_{1}) EN ISO 15927-4 [20], (RY

_{2}) Wilcox and Marion’s method [25], (RY

_{3}) the method by Pissimanis et al. [22], (RY

_{4}) the minimum Finkelstein–Schafer statistic, (RY

_{5}) Best rank I, and (RY

_{6}) Best rank II. Their representativeness with respect to the multi-year weather data series was discussed both in terms of weather variables and in terms of impact on the building energy needs for space heating and cooling.

_{5}and RY

_{6}had generally a better accuracy with respect to those with multi-year series. However, none outperformed the others for all climates: for those considered in this study, the largest representativeness was registered for RY

_{5}and RY

_{6}in Trento (respectively, with +0.52% and +0.79%) and for RY

_{2}and RY

_{6}in Monza (respectively, with −0.02% and +0.7%).

#### 2.1.1. RY_{1}: EN ISO 15927-4 Reference Year

_{S}can be calculated as:

_{S}value for a given month, the poorer is its representativeness, rankings are prepared for each climate parameter, with months ordered by increasing F

_{S}values. Then, a global ranking is made by summing the positions of the candidate months in those partial rankings.

#### 2.1.2. RY_{2}: Reference Year by Wilcox and Marion

#### 2.1.3. RY_{3} and RY_{4}: Reference Years According to Pissimanis et al., and to the Minimum F_{s} Value

_{S}values for dry bulb temperature and solar global horizontal irradiation is taken as reference.

#### 2.1.4. RY_{5} and RY_{6}: Best Rank I and II Reference Years

_{S}values is taken into account: only those months with non-significant F

_{S}statistics are included in the partial rankings and only those shared by all primary climatic parameters included in the global one. Finally, as in the Best rank I, the candidate at the top of the ranking is included in the reference year. In the case of no candidates satisfying the requirements, some recommendations, giving priority to maximize the representativeness for dry bulb temperature and solar global horizontal irradiation, are also given in [27].

#### 2.2. Samples of Existing Buildings

^{2}, chosen in agreement with the weighted average surface of the European residential buildings [49], an internal height of 3 m and a window to floor ratio equal to 0.144 (Figure 1). The compactness ratio S/V of the module has been varied by imposing adiabatic boundary conditions, aimed at characterizing adjacency to other apartments assumed at the same setpoint conditions. All modules have an adiabatic vertical wall while ceiling and floor can be either adiabatic or exposed to the external environment, depending on the specific case modeled. Intermediate flats in multi-story buildings (S/V = 0.3 m

^{−1}) are characterized by both ceiling and floor as adiabatic, penthouses (S/V = 0.63 m

^{−1}) only by the floor, and semi-detached houses (S/V = 0.97 m

^{−1}) have no adiabatic horizontal components. Taking advantage of the findings reported in [39,50], in this study, the windows have been positioned only on the façade in front of the adiabatic wall and oriented towards east (east-oriented buildings) or south (south-oriented buildings).

^{−3}), coupled with radiators and ON-OFF system control operating between 20 °C and 22 °C. For each configuration, the system serves the building as a single thermal zone [53,54]. The heating season, from 15 October to 15 April for both climates, has been defined according to the laws currently in force in Italy, i.e., DPR 412/1993 [44] and 74/2013 [45].

#### 2.3. Energy Efficiency Measures

- Installation of an insulating layer of extruded polystyrene (λ = 0.04 W·m
^{−1}·K^{−1}; ρ = 40 kg·m^{−3}; c = 1470 J·kg^{−1}·K^{−1}) on the external side of the opaque components, with thickness d_{ins}ranging from 0.01 to 0.20 m with a step of 0.01 m, changed independently for non-adiabatic walls, ceiling (only for penthouses and semi-detached houses) and floor (only for semi-detached houses). The unit investment cost of this EEM can be estimated as in the following equations for both vertical, IC_{vw}, and horizontal walls, IC_{hw}:$$I{C}_{vw}=160\xb7{d}_{ins}\text{}+38.53\text{}\mathrm{EUR}\xb7{\mathrm{m}}^{-2}$$$$I{C}_{hw}\text{}=188\xb7{d}_{ins}\text{}+8.19\text{}\mathrm{EUR}\xb7{\mathrm{m}}^{-2}$$ - Substitution of existing windows with new solutions characterized by aluminum frames with thermal break (U
_{fr}= 1.2 W·m^{−2}·K^{−1}) and high performance glazing: DH: double glazing with high SHGC (U_{gl}= 1.14 W·m^{−2}K^{−1}; SHGC = 0.61; IC_{DH}= 404.33 EUR·m^{−2}); DL: double glazing with low SHGC (U_{gl}= 1.10 W·m^{−2}·K^{−1}; SHGC = 0.35; IC_{DL}= 439.06 EUR·m^{−2}); TH: triple glazing with high SHGC (U_{gl}= 0.61 W·m^{−2}·K^{−1}; SHGC = 0.58; IC_{TH}= 477.65 EUR·m^{−2}); and TL: triple glazing with low SHGC (U_{gl}= 0.6 W·m^{−2}·K^{−1}; SHGC = 0.34; IC_{TL}= 454.49 EUR·m^{−2}). - Replacement of the existing standard boiler, STD, due to obsolescence with an equivalent model (IC
_{STD}= 1000 EUR) or substitution with either a modulating boiler MOD (η = 96%; IC_{MOD}= 1500 EUR) or condensing boiler COND (η = 101%; IC_{COND}= 2000 EUR). Both modulating and condensing boilers are equipped with a climatic control system in order to vary the supply temperature as a function of the external air temperature. - Installation of a mechanical ventilation system, MVS, with heat recovery (IC
_{MVS}= 6000 EUR). The system has a nominal ventilation rate of 150 m^{3}h^{−1}, a power capacity of 59.7 W and a nominal heat recovery efficiency of 93%. The actual efficiency of the heat recovery η_{HR}clearly depends on the difference between internal and external temperatures and has been modeled as a function of the external temperature ϑ_{e}[°C] starting from the technical datasheet:$${\eta}_{HR}\text{}=0.0003\xb7{\vartheta}_{e}^{4}\text{}-0.0116\xb7{\vartheta}_{e}^{3}\text{}+0.1413\xb7{\vartheta}_{e}^{2}\text{}+0.7505\xb7{\vartheta}_{e}\text{}+83.051\text{}[\%]$$

- The additional insulation layers reduce the thermal losses due to thermal bridges and, to take account of that, new linear thermal transmittances have been calculated.
- The windows replacements increase air tightness, which has been considered by halving the infiltration rates estimated for the existing buildings.
- Even though radiators have not been substituted, the adoption of a climatic control system allows for supply water temperatures lower than those under design conditions.

#### 2.4. Building Energy Simulation and Optimization Objectives

_{h}, according to EN ISO 15217:2007 [66] which is also the first objective considered in optimization.

- periodic replacement costs due to substitution of building elements; and
- the residual value of the equipment with longer lifespan according to according to EN 15459:2007 [69].

#### 2.5. Multi-Objective Optimization with Genetic Algorithm

_{h}and NPV have been performed through a multi objective optimization based on the Elitist Non-dominated Sorting Genetic Algorithm (NSGA-II) [71], frequently chosen in the literature because of its superior performance [72]. A Matlab

^{®}fitness function has been written to launch TRNSYS simulation, read its output, calculate EP

_{h}and NPV and return their values to the genetic algorithm.

_{h}and NPV, the genetic algorithm performs the Tournament Selection Without Replacement [76,77], with a fraction set to 0.5, to identify the best configurations, i.e., the “parents”, whose characteristics are combined to give rise to the next generation. “Children” are a random [73] arithmetic mean of two “parents”, always feasible with respect to the bounds [78]. In this work, the crossover fraction has been set to 0.8 and mutation, based on Mersenne-Twister pseudo random generator [73], to 0.2. The convergence criterion is based on a variation of the average crowding distance of 10

^{−3}between two consecutive generations and the maximum number of generations is 100.

## 3. Results

#### 3.1. Comparison of Reference Years

_{18}, and in daily average global solar irradiation on horizontal surface during the heating season, H

_{sol}.

_{18}is 2610 K·d and is obtained with RY

_{1}, i.e., the EN ISO 15927-4 reference year, while the minimum, around 11% lower, is 2330 K·d and is found with RY

_{2}, i.e., the reference year according to Wilcox and Marion’s method. However, minimum and maximum daily average horizontal global solar irradiations are found for different reference years, specifically for RY

_{3}and RY

_{4}, i.e., Pissimanins et al., and minimum Finkelstein–Schafer reference years, with a deviation of about 6%.

_{18}is, with RY

_{3}(Pissimanis et al.) and the minimum one with RY

_{5}(Best rank I), around 13% lower. As regards average daily solar irradiation, the extreme values are found for the same reference years: the coldest year, RY

_{3}, also has the lowest H

_{sol}, and the warmest one, RY

_{5}, the largest H

_{sol}. In this climate, the deviation is larger and equal to 10%.

#### 3.2. Energy and Economic Performances of the Existing Buildings

_{2}, coherently with the HDD

_{18}in Table 2, but the maximum ones are found most frequently with RY

_{3}, which has the minimum H

_{sol}, except for east-oriented penthouses and semi-detached houses, for which RY

_{1}, the reference year with maximum HDD

_{18}, maximizes the values of EP

_{h}and NPV. On the contrary, in Monza, the minimum values are registered with RY

_{5}and the maximum ones with RY

_{3}, for all configurations, coherently with HDD

_{18}and H

_{sol}values in Table 2.

#### 3.3. Pareto Fronts: Shapes and EEMs

#### 3.3.1. Shapes of the Pareto Fronts

_{h}-NPV charts, and to the choice of natural ventilation, on the bottom.

_{h}and NPV are achieved with RY

_{2}and the maximum are registered either with RY

_{3}(south-oriented buildings) or RY

_{1}(east-oriented buildings), coherently with what observed in Section 3.2. In Monza, the differences are less marked and, for solutions with natural ventilation, they are even negligible. The minimum EP

_{h}and NPV are found with RY

_{5}, coherently with the analysis of the existing buildings’ performance, and the maximum ones for RY

_{3}and RY

_{6}.

_{5}and RY

_{6}if mechanical ventilation is installed but, in the case of natural ventilation, this result is observed with RY

_{3}.

#### 3.3.2. EEMs in the Pareto Fronts

_{3}, and, for semi-detached houses, either DH or TH are the most frequent EEMs in the front, respectively with RY

_{5}and RY

_{1}. The deviations in the shares of DH and TH are around 40% for both building configurations. Analyzing the south-oriented cases in Trento (Figure 6), similar trends are seen for windows’ substitutions, even if with different shares. The maximum deviation in frequency is only slightly larger than 20%, with the exception of semi-detached houses, where it increases to 44% and, for optimization with RY

_{5}, TH does not belong to the front. As regards the boiler, the existing standard system is recommended to be kept only for some solutions in intermediate flats (both orientations) and penthouses (only south-oriented configurations) while more efficient alternatives are proposed for the other types of buildings. Deviations can be detected for east-oriented semi-detached houses, with modulating boilers present in the front only if RY

_{1}, RY

_{2}and RY

_{4}are adopted. Changes of share between 30% and 35% are detected for modulating and condensing boilers in east-oriented penthouses and semi-detached houses. On the contrary, for south-oriented configurations, share deviations are slightly larger than 20%, except for the penthouses for which they are around 35%. Considering ventilation, mechanical solutions are more frequently found in penthouses and semi-detached houses but the impact of the weather data is more limited. As a whole, as far as the solutions in the Pareto fronts are considered, east-oriented penthouses and south-oriented intermediate flats are the most robust configurations to the choice of reference years for the climate of Trento.

#### 3.4. Economic and Energy Optimal Solutions

#### 3.4.1. EEMs for Economic and Energy Optima

_{4}and 18 cm with RY

_{5}and RY

_{6}. All RYs lead to the same results for south-oriented buildings in terms of window, boiler and ventilation preferences. For those east-oriented, instead, the recommendations are different: for example, RY

_{3}leads to the selection of TH glazings for intermediate flats while DH are preferred in all other cases, RY

_{1}and RY

_{2}lead to the recommendation of a modulating boiler (instead of a condensing one), respectively for the penthouse and the semi-detached house. Considering energy optima, the variability of insulation thicknesses is very limited (i.e., 1 cm) for the east-oriented configurations and, in particular, null for the intermediate flat, while for the south-oriented configurations we can detect both large sensitivity (e.g., up to 5 cm difference for walls’ insulation of the intermediate flat, 4 cm of difference for floor’s insulation for semi-detached houses) and null sensitivity (i.e., for the penthouse). Penthouses have the same results, independently of RY, in terms of window, boiler and ventilation preferences. For intermediate flats, windows and boiler selections are affected by RYs while for south-oriented semi-detached houses, this is true only for the windows.

_{5}and RY

_{6}, proposed thicknesses are generally different from those obtained with the other reference years. Furthermore, the EEMs regarding windows, boiler and ventilation are affected only for the type of boiler in the east-oriented penthouse and south-oriented semi-detached houses, for which modulating boiler is preferred to the condensing one when, respectively, RY

_{5}and RY

_{6}are adopted. Considering the energy optima, besides the choice of the optimal insulation thickness, TH, condensing boiler and mechanical ventilation system are always recommended, except for the south-oriented intermediate flat, for which TL glazings are proposed, as in Trento. The reference year has no impact on the ventilation system and affects slightly window and boiler selection: for example, for east-oriented semi-detached houses, RY

_{3}leads to a selection of DH, for east-oriented intermediate flats the output with the same reference year includes no substitution of the boiler and, similarly, for south-oriented penthouses the output with RY

_{2}includes the adoption of a modulating boiler instead of a condensing one.

#### 3.4.2. Performances of Economic and Energy Optima

_{h}in Trento, as shown in Figure 3, all reference years lead to EP

_{h}lower than 1 kWh·m

^{−2}·a

^{−1}for all intermediate flats, between 12 and 16 kWh·m

^{−2}·a

^{−1}and 1 and 2 kWh·m

^{−2}·a

^{−1}, respectively for east- and south-oriented penthouses, and between 23 and 30 kWh·m

^{−2}·a

^{−1}and 8 and 14 kWh·m

^{−2}·a

^{−1}, respectively, for east and south oriented semi-detached houses. In Monza, as in Figure 4, the reference years lead to EP

_{h}lower than 1 kWh·m

^{−2}·a

^{−1}for all intermediate flats, between 10 and 15 kWh·m

^{−2}·a

^{−1}and 2 and 5 kWh·m

^{−2}·a

^{−1}for penthouses, respectively east- and south-oriented, and between 24 and 31 kWh·m

^{−2}·a

^{−1}and between 11 and 18 kWh·m

^{−2}·a

^{−1}for semi-detached houses, respectively east- and south-oriented.

_{h}is more than 75% between the energy performances simulated with RY

_{2}and RY

_{3}. Similarly, for the same configurations, economic performances can change of more than 13%.

## 4. Discussion and Conclusions

- Analyzing the developed reference years, different values of Heating Degree-Days and daily average global solar irradiation on horizontal surface during the heating season can be observed. For the first one, the largest deviations are 11% and 13%, while, for the latter, they are 6% and 10%, respectively, for Trento and Monza.
- The deviations in the weather data impact differently on the energy and economic performances of the existing buildings: indeed, while for east-oriented configurations, the difference ranges are between 4% and 8% and between 9% and 13%, respectively in Trento and in Monza, for the south-oriented ones, they are shifted towards larger values (i.e., from 7% to 14% and from 11% to 17%). This suggests various sensitivities to the climatic solicitation and a role of the building’s features on the propagation of the uncertainty from weather data. In particular, the largest differences are met for the performances of the existing intermediate flats.
- Analyzing the Pareto fronts obtained through genetic algorithm multi-objective optimization, it is possible to see that they are not simply shifted according to the performance deviations of the considered existing buildings but also intersected. This is related to types of ventilation system, either natural or mechanical one, which lead to different shapes of Pareto fronts according to the selected reference year. Looking at the alternative solutions belonging to the Pareto fronts, it can be observed that their number varies significantly, and, in some cases, variations are also equal to 100%.
- Studying the energy efficiency measures of the solutions belonging to the Pareto fronts, it is possible to conclude that, in most of configurations, the impact of the reference years on the recommended insulation thicknesses for the envelope opaque components is modest and generally lower than 2 or 3 cm, respectively, for Trento and Monza modal values. An exception is found for the insulation of vertical walls in south-oriented intermediate flats in Trento, ranging from 13 to 20 cm of polystyrene. The impact is more relevant considering the other efficiency measures. Indeed, the shares of occurrence of specific alternatives of windows, boilers and ventilation systems, change with the reference years and, for some configurations and weather data, they are not even included among the solutions belonging to the Pareto front. Considering these three energy efficiency measures, in Trento, east-oriented penthouses and south-oriented intermediate flats are the most robust configurations while, in Monza, this is true for intermediate flats, independently of the orientation.
- Focusing on the solutions in the Pareto fronts maximizing either economic or energy objectives, it can be seen that the impact of reference years on the selected energy efficiency measures are slightly different for the two localities, with Trento presenting a larger sensitivity despite of the lower variability of performances of the existing building configurations. Besides the insulation thickness in Trento, which is particularly affected in south-oriented intermediate flats as mentioned above, proposed windows and boiler can be influenced as well while this does not occur for the type of ventilation system. The absolute deviations in terms of primary energy for space heating and net present value for the optima are similar or lower than those for the existing buildings’ performances for both localities, even if their relative impact is larger. The largest deviations are within 4000 EUR for the net present values and 7 kWh·m
^{−2}·a^{−1}for the space heating energy uses.

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## Abbreviations

Symbols | |

A | Area (m^{2}) |

ACH | Air change (h^{−1}) |

BES | Building energy simulation |

c | Specific heat capacity (J·kg^{−1}·K^{−1}) |

COND | Condensing boiler |

d | Thickness (m) |

DH | Double glazing with high SHGC |

DL | Double glazing with low SHGC |

EEM | Energy efficiency measure |

EP_{h} | Primary energy demand for space heating (kWh·m^{−2}·a^{−1}) |

F/Φ | Cumulative distribution functions |

F_{S} | Finkelstein–Schafer statistics |

H | Daily horizontal global solar irradiation (MJ·m^{−2}·d^{−1}) |

HDD_{18} | Heating degree-days with base temperature equal to 18 °C (K·d) |

HVAC | Heating ventilation and air-conditioning |

i | Day |

IC | Investment cost (EUR·m^{−2} if referred to the envelope, EUR if referred to the system) |

J/K | Rank order functions |

LHV | Lower heating value (MJ·Sm^{−3}) |

m | Month |

MOD | Modulating boiler |

MVS | Mechanical ventilation system |

n | Number of days of a calendar month |

N | Total number of days of a calendar month in the multi-year series |

NPV | Net present value (EUR) |

p | Daily average of a weather parameter |

PV | Photovoltaic |

RMSD | Root-mean square difference |

RY | Reference year |

S | Single glazing |

SHGC | Solar heat gain coefficient |

STD | Standard natural gas boiler |

S/V | Building compactness ratio |

TH | Triple glazing with high SHGC |

TL | Triple glazing with low SHGC |

TMY | Typical meteorological year |

U | Thermal transmittance (W·m^{−2}·K^{−1}) |

y | Year |

Greek | |

η | Nominal efficiency |

ϑ_{e} | External temperature (°C) |

λ | Thermal conductivity (W m^{−1}·K^{−1}) |

ρ | Density (kg·m^{−3}) |

Ψ | Linear thermal transmittance (W·m^{−1}·K^{−1}) |

Subscripts | |

corner | Referred to corner thermal bridges |

HR | Referred to heat recovery |

hw | Referred to horizontal wall |

ins | Referred to insulation layer |

int-floor | Referred to thermal bridges due to intermediate floor and walls |

fr | Referred to the window frame |

gl | Referred to the glazing |

roof | Referred to roof thermal bridges |

sol | Solar |

vw | Referred to vertical wall |

wall | Referred to the opaque components |

win | Referred to the window |

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**Figure 1.**Existing reference buildings: intermediate flat (

**Right**); penthouse (

**Center**); and semi-detached house (

**Left**).

**Figure 2.**Monthly statistics of climatic variables (dry bulb temperature, water vapor partial pressure and global horizontal irradiation) for the six reference years and the multi-year series in Trento and Monza.

**Figure 3.**Pareto fronts for Trento. The horizontal red dotted lines and the vertical green dotted lines delimitate the range between best NPV and EP

_{h}identified with the optimization with the six reference years.

**Figure 4.**Pareto fronts for Monza. The horizontal red dotted lines and the vertical green dotted lines delimitate the range between best NPV and EP

_{h}identified with the optimization with the six reference years.

**Figure 5.**Shares of the different alternative energy efficiency measures belonging to the Pareto fronts for east-oriented buildings in Trento.

**Figure 6.**Shares of the different alternative energy efficiency measures belonging to the Pareto fronts for south-oriented buildings in Trento.

Clay Block Wall | |||

λ = 0.25 W·m^{−1}·K^{−1} | ρ = 893 kg·m^{−3} | c = 840 J·kg^{−1}·K^{−1} | U_{wall} = 1.03 W·m^{−2}·K^{−1} |

Windows (Single Glazing, S) | |||

U_{gl} = 5.69 W·m^{−2}·K^{−1} | U_{fr} = 3.20 W·m^{−2}·K^{−1} | A_{fr}/A_{win} = 20% | SHGC = 0.81 |

Thermal Bridges (Calculated According to EN ISO 10211:2007 [52]) | |||

Ψ_{corner} = 0.098 W·m^{−1}·K^{−1} | Ψ_{int-floor} = 0.182 W·m^{−1}·K^{−1} | Ψ_{roof} = 0.182 W·m^{−1}·K^{−1} | Ψ_{win} = 0.06 W·m^{−1}·K^{−1} |

**Table 2.**Heating Degree-Days and daily average global solar irradiation on horizontal surface calculated for the different reference years. The minimum value is highlighted in blue and the maximum one in red.

Reference Year | Trento | Monza | ||
---|---|---|---|---|

HDD_{18} [K·d (day)] | H_{sol} [MJ·m^{−2}·d^{−1}] | HDD_{18} [K·d] | H_{sol} [MJ·m^{−2}·d^{−1}] | |

RY_{1} | 2610 | 7.51 | 2232 | 5.62 |

RY_{2} | 2330 | 7.65 | 2270 | 5.68 |

RY_{3} | 2496 | 7.27 | 2459 | 5.34 |

RY_{4} | 2448 | 7.70 | 2329 | 5.83 |

RY_{5} | 2484 | 7.50 | 2139 | 5.93 |

RY_{6} | 2504 | 7.49 | 2269 | 5.57 |

**Table 3.**EP

_{h}[kWh·m

^{−2}·a (year)

^{−1}] and NPV [10

^{3}EUR] for east- and south-oriented existing buildings in Trento. The minimum value is highlighted in blue and the maximum one in red.

RY_{1} | RY_{2} | RY_{3} | RY_{4} | RY_{5} | RY_{6} | ||
---|---|---|---|---|---|---|---|

East-Oriented Buildings | |||||||

Intermediate Flat | EP_{h} | 154.2 | 143.2 | 154.6 | 149.6 | 153.3 | 153.3 |

NPV | 42.7 | 39.7 | 42.8 | 41.4 | 42.4 | 42.4 | |

Penthouse | EP_{h} | 231.9 | 217.6 | 230.8 | 225.3 | 229.3 | 230.1 |

NPV | 63.8 | 59.9 | 63.5 | 62 | 63.1 | 63.3 | |

Semi-detached house | EP_{h} | 294.7 | 281 | 292.7 | 288.7 | 292 | 293 |

NPV | 80.9 | 77.2 | 80.4 | 79.3 | 80.2 | 80.5 | |

South-Oriented Buildings | |||||||

Intermediate Flat | EP_{h} | 119.8 | 106.5 | 122.1 | 112.6 | 116.7 | 116.9 |

NPV | 33.3 | 29.7 | 33.9 | 31.4 | 32.5 | 32.5 | |

Penthouse | EP_{h} | 197.9 | 182 | 200.4 | 190.3 | 194.6 | 195.5 |

NPV | 54.6 | 50.2 | 55.2 | 52.5 | 53.7 | 53.9 | |

Semi-detached house | EP_{h} | 265 | 248.2 | 266.8 | 256.7 | 260.8 | 262 |

NPV | 72.8 | 68.3 | 73.3 | 70.6 | 71.7 | 72 |

**Table 4.**EP

_{h}[kWh·m

^{−2}·a

^{−1}] and NPV [10

^{3}EUR] for east- and south-oriented existing buildings in Monza. The minimum value is highlighted in blue and the maximum one in red.

RY_{1} | RY_{2} | RY_{3} | RY_{4} | RY_{5} | RY_{6} | ||
---|---|---|---|---|---|---|---|

East-Oriented Buildings | |||||||

Intermediate Flat | EP_{h} | 140.4 | 145.6 | 157.8 | 149.5 | 139.0 | 146.8 |

NPV | 38.9 | 40.3 | 43.6 | 41.4 | 38.5 | 40.6 | |

Penthouse | EP_{h} | 214.1 | 220.6 | 236.1 | 226.0 | 212.4 | 222.5 |

NPV | 59.0 | 60.8 | 65.0 | 62.2 | 58.5 | 61.3 | |

Semi-detached house | EP_{h} | 274.7 | 282.5 | 298.7 | 288.4 | 272.9 | 283.8 |

NPV | 75.5 | 77.6 | 82.0 | 79.2 | 75.0 | 77.9 | |

South-Oriented Buildings | |||||||

Intermediate Flat | EP_{h} | 118.2 | 122.5 | 137.0 | 126.0 | 115.9 | 123.8 |

NPV | 32.9 | 34.0 | 38.0 | 35.0 | 32.2 | 34.4 | |

Penthouse | EP_{h} | 192.8 | 198.5 | 217.4 | 204.4 | 189.7 | 200.5 |

NPV | 53.2 | 54.7 | 59.9 | 56.3 | 52.3 | 55.3 | |

Semi-detached house | EP_{h} | 255.2 | 262.8 | 283.2 | 269.3 | 251.9 | 263.9 |

NPV | 70.2 | 72.2 | 77.8 | 74.0 | 69.3 | 72.5 |

**Table 5.**Cost optima for Trento. As regards windows, S (in dark blue) indicates single glazing, DH (red) double glazing with high SHGC, DL (green) double glazing with low SHGC, TH (yellow) triple glazing with high SHGC, TL (light blue) double glazing with low SHGC; as regards boiler, STD (blue) indicates standard boiler, MOD (red) modulating boiler, COND (green) condensing boiler; ventilation is distinguished by natural (NAT in blue) or provided by mechanical ventilation system (MVS in red).

East Orientation | South Orientation | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

RY_{1} | RY_{2} | RY_{3} | RY_{4} | RY_{5} | RY_{6} | RY_{1} | RY_{2} | RY_{3} | RY_{4} | RY_{5} | RY_{6} | |

Intermediate Flat | ||||||||||||

Insulation thickness [cm] | ||||||||||||

Wall | 19 | 17 | 18 | 19 | 19 | 18 | 17 | 15 | 17 | 14 | 18 | 18 |

Roof | - | - | - | - | - | - | - | - | - | - | - | - |

Floor | - | - | - | - | - | - | - | - | - | - | - | - |

Windows | DH | DH | TH | DH | DH | DH | DH | DH | DH | DH | DH | DH |

Boiler | STD | STD | STD | STD | STD | STD | STD | STD | STD | STD | STD | STD |

Ventilation | NAT | NAT | NAT | NAT | NAT | NAT | NAT | NAT | NAT | NAT | NAT | NAT |

Penthouse | ||||||||||||

Insulation thickness [cm] | ||||||||||||

Wall | 18 | 18 | 17 | 17 | 17 | 17 | 17 | 16 | 18 | 17 | 17 | 17 |

Roof | 17 | 19 | 17 | 17 | 17 | 17 | 15 | 17 | 16 | 18 | 16 | 16 |

Floor | - | - | - | - | - | - | - | - | - | - | - | - |

Windows | DH | DH | DH | DH | DH | DH | DH | DH | DH | DH | DH | DH |

Boiler | COND | MOD | COND | COND | COND | COND | STD | STD | STD | STD | STD | STD |

Ventilation | NAT | NAT | NAT | NAT | NAT | NAT | NAT | NAT | NAT | NAT | NAT | NAT |

Semi-Detached House | ||||||||||||

Insulation thickness [cm] | ||||||||||||

Wall | 19 | 18 | 17 | 18 | 16 | 18 | 17 | 18 | 17 | 17 | 17 | 17 |

Roof | 19 | 17 | 18 | 18 | 17 | 18 | 18 | 16 | 18 | 17 | 17 | 17 |

Floor | 18 | 18 | 18 | 18 | 17 | 19 | 17 | 17 | 16 | 16 | 18 | 16 |

Windows | DH | DH | DH | DH | DH | DH | DH | DH | DH | DH | DH | DH |

Boiler | MOD | COND | COND | COND | COND | COND | MOD | MOD | MOD | MOD | MOD | MOD |

Ventilation | NAT | NAT | NAT | NAT | NAT | NAT | NAT | NAT | NAT | NAT | NAT | NAT |

**Table 6.**Energy optima for Trento. As regards windows, S (in dark blue) indicates single glazing, DH (red) double glazing with high SHGC, DL (green) double glazing with low SHGC, TH (yellow) triple glazing with high SHGC, TL (light blue) double glazing with low SHGC; as regards boiler, STD (blue) indicates standard boiler, MOD (red) modulating boiler, COND (green) condensing boiler; ventilation is distinguished by natural (NAT in blue) or provided by mechanical ventilation system (MVS in red).

East Orientation | South Orientation | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

RY_{1} | RY_{2} | RY_{3} | RY_{4} | RY_{5} | RY_{6} | RY_{1} | RY_{2} | RY_{3} | RY_{4} | RY_{5} | RY_{6} | |

Intermediate Flat | ||||||||||||

Insulation thickness [cm] | ||||||||||||

Wall | 20 | 20 | 20 | 20 | 20 | 20 | 13 | 16 | 18 | 13 | 14 | 13 |

Roof | - | - | - | - | - | - | - | - | - | - | - | - |

Floor | - | - | - | - | - | - | - | - | - | - | - | - |

Windows | TH | TH | TH | TH | TH | TH | TH | TL | TL | TL | TL | TL |

Boiler | COND | STD | STD | COND | COND | COND | COND | COND | COND | COND | COND | COND |

Ventilation | MVS | MVS | MVS | MVS | MVS | MVS | MVS | MVS | MVS | MVS | MVS | MVS |

Penthouse | ||||||||||||

Insulation thickness [cm] | ||||||||||||

Wall | 20 | 19 | 19 | 19 | 19 | 20 | 20 | 20 | 20 | 20 | 20 | 20 |

Roof | 19 | 19 | 19 | 20 | 20 | 20 | 20 | 20 | 20 | 20 | 20 | 20 |

Floor | - | - | - | - | - | - | - | - | - | - | - | - |

Windows | TH | TH | TH | TH | TH | TH | TH | TH | TH | TH | TH | TH |

Boiler | COND | COND | COND | COND | COND | COND | COND | COND | COND | COND | COND | COND |

Ventilation | MVS | MVS | MVS | MVS | MVS | MVS | MVS | MVS | MVS | MVS | MVS | MVS |

Semi-Detached House | ||||||||||||

Insulation thickness [cm] | ||||||||||||

Wall | 20 | 19 | 18 | 19 | 18 | 18 | 19 | 19 | 19 | 18 | 18 | 18 |

Roof | 20 | 19 | 19 | 19 | 19 | 19 | 19 | 19 | 19 | 17 | 19 | 19 |

Floor | 20 | 20 | 20 | 20 | 19 | 19 | 18 | 18 | 20 | 18 | 20 | 16 |

Windows | TH | TH | TH | TH | TH | TH | TH | TH | TH | TH | TH | DH |

Boiler | COND | COND | COND | COND | COND | COND | COND | COND | COND | COND | COND | COND |

Ventilation | MVS | MVS | MVS | MVS | MVS | MVS | MVS | MVS | MVS | MVS | MVS | MVS |

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**MDPI and ACS Style**

Pernigotto, G.; Prada, A.; Cappelletti, F.; Gasparella, A.
Impact of Reference Years on the Outcome of Multi-Objective Optimization for Building Energy Refurbishment. *Energies* **2017**, *10*, 1925.
https://doi.org/10.3390/en10111925

**AMA Style**

Pernigotto G, Prada A, Cappelletti F, Gasparella A.
Impact of Reference Years on the Outcome of Multi-Objective Optimization for Building Energy Refurbishment. *Energies*. 2017; 10(11):1925.
https://doi.org/10.3390/en10111925

**Chicago/Turabian Style**

Pernigotto, Giovanni, Alessandro Prada, Francesca Cappelletti, and Andrea Gasparella.
2017. "Impact of Reference Years on the Outcome of Multi-Objective Optimization for Building Energy Refurbishment" *Energies* 10, no. 11: 1925.
https://doi.org/10.3390/en10111925