# Accuracy of Simplified Modelling Assumptions on External and Internal Driving Forces in the Building Energy Performance Simulation

^{*}

## Abstract

**:**

## 1. Introduction

#### 1.1. Validation Techniques of the Building Energy Models

#### 1.2. Validation Studies of the EN ISO 52016-1 Hourly Model

#### 1.3. Aims of the Research Work

- detect the modelling assumptions of the simplified hourly method on different levels, such as the modelling of the thermo-physical phenomena, the neglecting of some physical phenomena, the determination or the temporal discretisation of specific calculation parameters, or the definition of calculation boundary conditions,
- minimise the uncertainty in the validation of a calculation method due to inconsistencies in the input data,

## 2. Materials and Methods

#### 2.1. Simplified Modelling of External Driving Forces

#### 2.1.1. Convective Heat Transfer

_{conv,ext}, expressed in W·m

^{−2}) is calculated as

_{c,ext}is the external convective heat transfer coefficient (in W·m

^{−2}·K

^{−1}), and T

_{air,ext}and T

_{surf}are the temperatures (in K) of the outdoor air and of the surface, respectively.

^{−1}). On the other hand, EnergyPlus offers a wide selection of calculation models for the h

_{c,ext}determination; for the sake of the present study, the Thermal Analysis Research Program (TARP) algorithm [24] was assumed as reference. According to the TARP formulation, the external convection is split into its natural and forced components, and h

_{c,ext}is calculated as the sum of the respective heat transfer coefficients. The forced component is calculated by means of the Sparrow et al. formulation [25], which takes into account the surface geometrical characteristics, roughness and wind exposure, and the wind speed. The natural component is instead calculated by means of three different formulations for vertical, upward, and downward facing surfaces [24].

#### 2.1.2. Longwave Radiation Heat Transfer

_{lwr}, expressed in W·m

^{−2}) is calculated by applying the Stefan-Boltzmann law in EnergyPlus, as

^{−8}W·m

^{−2}·K

^{−4}), while T

_{gnd}, T

_{sky}, T

_{air}and T

_{surf}are respectively the ground, the sky, the outdoor air and the surface temperatures (in K), and F

_{gnd}, F

_{sky}and F

_{air}are the view factors between the surface and the ground, the sky and the air, respectively. The linearised formulation is instead applied in the simplified hourly method of the EN ISO 52016-1 technical standard; the q

_{lwr}(in W·m

^{−2}) is calculated as

_{r,ext}is the external radiative heat transfer coefficient (in W·m

^{−2}·K

^{−1}), T

_{surf}and T

_{air}are the surface and the outdoor air temperatures (in K), respectively, and ΔT

_{sky}is the difference between the outdoor air temperature and the apparent sky temperature (in K).

_{m}is the average temperature of the surface and of its surroundings (in K). Moreover, the determination of the view factor between the surface and the sky, which is used in Equations (3) and (4), takes into account the presence of external obstacles—such shadings or other buildings—in EnergyPlus, while this aspect is not considered in the simplified method.

#### 2.1.3. Solar (Shortwave) Radiation

_{w}), as

_{gl,n}is the total solar energy transmittance at normal incidence. The solar properties of windows are considered time-independent in EN ISO 52016-1, and the F

_{w}factor is assumed constant over the calculation period. On the other hand, a solar angle-dependent F

_{w}is considered in the Italian National Annex (NA) to EN ISO 52016-1; it is calculated as a weighted average of a F

_{w}factor for diffuse radiation (assumed equal to 0.8 over the calculation period) and a F

_{w}factor for beam solar radiation. The latter is calculated on a timestep basis accordingly to the empirical model introduced by Karlsson and Roos [28].

#### 2.2. Simplified Modelling of Internal Driving Forces

#### 2.2.1. Convective Heat Transfer

_{conv,int}, expressed in W·m

^{−2}) is calculated both in the EN ISO 52016-1 simplified method and in the detailed method of EnergyPlus as

_{c,int}is the internal convective heat transfer coefficient (in W·m

^{−2}·K

^{−1}), and T

_{air,int}and T

_{surf}are the indoor air and the surface temperatures (in K), respectively.

_{c,int}on a timestep basis is instead performed by means of the TARP algorithm [24] in EnergyPlus, assumed as a reference for the sake of the present study.

#### 2.2.2. Longwave Radiation Heat Transfer

^{2}), h

_{r,int}is the radiative heat transfer coefficient (in W·m

^{−2}·K

^{−1}), θ

_{surf}is the indoor surface temperature (in K). As for the external radiative heat transfer coefficient, also the internal coefficient is assumed time-independent, and it is calculated by means of the EN ISO 6946 formulation (Equation (5)). Although this approach represents a simplification in the modelling on the considered physical phenomenon, this assumption was not tested in the present work. In fact, the temperature difference between the surfaces facing the thermal zone can be considered negligible, thus this approach may influence the energy behaviour of a building in a negligible way.

_{lwr,int}, expressed in W·m

^{−2}), as

_{tot}is the sum of the surface areas facing the thermal zone—including thermal mass surfaces—(in m

^{2}), f

_{int,c}is the convective fraction of internal gains, and Φ

_{int}is the total internal heat gains (in W). In EnergyPlus, instead, the radiant fraction of internal gains is distributed proportionally to the surface area and the surface emissivity (Φ

_{lwr,int}, expressed in W), as

^{2}) and the emissivity, respectively. The other parameters are described in Equation (9).

#### 2.2.3. Solar (Shortwave) Radiation

_{swr,sol}, expressed in W·m

^{−2}), as

_{tot}is the sum of the surface areas facing the thermal zone—including thermal mass surfaces—(in m

^{2}), f

_{sol,c}is the convective fraction of solar gains, and Φ

_{sol}is the total solar heat gains (beam plus diffuse solar radiation, in W). In EnergyPlus, instead, different approaches for the distribution of solar radiation are offered. For the sake of the present study, the “full exterior with reflections” distribution model of EnergyPlus was assumed as a reference. According to this approach, beam solar radiation entering the zone is assumed to fall on the floor, where it is absorbed according to the floor solar absorptance coefficient. The reflected solar radiation by the floor is added to the transmitted diffuse radiation (and eventual shortwave radiation from the lighting system), which is then distributed over the internal surfaces proportionally to the surface area and the surface solar absorptance (Φ

_{swr,sol}, expressed in W), as

^{2}), the absorption and the reflection coefficients, and Φ

_{sol,diff}is the diffuse solar radiation (transmitted solar radiation plus reflected beam solar radiation, in W). Finally, the solar reflectance is defined for transparent surfaces as

#### 2.3. Methodology

_{H/C}is the heating (H) or cooling (C) load (in W) at timestep t, for the test model and for the baseline, respectively, and n is the number of timesteps considered for the calculation (8760 for annual evaluations). The MBE is expressed as a percentage error, and measures how closely the predicted hourly heating or cooling loads corresponds to the baseline data. The variations in the energy needs are considered acceptable with MBE values in the range of ±10% (when using hourly data) [16]. The root-mean-square deviation (RMSD) was instead used to measure the variability in the prediction of the indoor operative temperatures (in K), and was calculated as

_{op}is the indoor operative temperature at timestep t, for the test model and for the baseline, respectively, and n is the number of timesteps considered for the calculation (8760 for annual evaluations). In this case, acceptable deviations in the prediction of the indoor operative temperatures are considered for RMSD values lower than 0.5 K [32].

## 3. Application

#### 3.1. Case Studies

^{2}area each, shaded by an overhang of 1 m depth; the North-oriented façade is instead characterised by two windows of 1.5 m

^{2}and 2.0 m

^{2}areas, respectively. As concerns the existing building variant (ExtB), the external walls are made of uninsulated hollow brick masonry with air gap (U

_{wall,res,ExtB}= 1.1 W·m

^{−2}·K

^{−1}), while the transparent components are characterised by a single glazing with wooden frame (U

_{win,res,ExtB}= 4.9 W·m

^{−2}·K

^{−1}, g

_{res,ExtB}= 0.85).

^{2}area, shaded by a side fin of 1 m depth. As concerns the existing building variant (ExtB), the external wall is made of a prefabricated concrete wall (U

_{wall,off,ExtB}= 0.8 W·m

^{−2}·K

^{−1}) with interposed low thickness thermal insulation material, while the window is a double-glazing unit with wooden frame (U

_{win,off,ExtB}= 2.8 W·m

^{−2}·K

^{−1}, g

_{off,ExtB}= 0.75).

#### 3.2. Modelling Options

- HC-Vw-av. The effect of a lack of detailed input data regarding the wind speed was assessed. In particular, the convective heat transfer coefficient was considered time-dependent and was calculated by means of the TARP algorithm [24]. Differently from the baseline model, the forced component is calculated by implementing annual average wind speed values; specifically, wind speeds of 0.9 and 3.8 m·s
^{−1}were used for Milan and Palermo, respectively. - HC-V. The effect of the formulation specified in Equation (2) for the h
_{c,ext}determination was evaluated. The convective heat transfer coefficient was considered variable on a timestep basis, and the site hourly wind speed was used. - HC-Cw-av. The annual average wind speed was implemented in Equation (2) to calculate an average heat transfer coefficient, assumed constant over the simulation period.
- HC-Cst. The effect of the h
_{c,ext}standard values was evaluated, assuming a constant convective heat transfer coefficient equal to 20 W·m^{−2}·K^{−1}over the simulation period, calculated by means of the reference wind speed value of 4 m·s^{−1}(Equation (2)).

- SKY. The influence of the direct sky temperature model for the apparent sky temperature calculation was assessed; specifically, the sky temperature was assumed 11 °C below the outdoor air temperature.
- HR. In EnergyPlus, the external net longwave radiation heat flux is calculated by applying the Stefan-Boltzmann law. Thus, the definition of the radiative heat transfer coefficients as input values was not possible. To assess the influence of the linearisation of the longwave heat transfer (Equation (4)), a simple modelling strategy was applied. Firstly, the outdoor surface emittances were set equal to 0 to annul the external longwave heat transfer automatically calculated by EnergyPlus. Then, an additional heat balance term, calculated as specified in Equation (4), was added to the external surface of the envelope components. The standard radiative heat transfer coefficient (h
_{r,ext}) equal to 4.14 W·m^{−2}·K^{−1}was used, and was calculated by assuming a surface emissivity equal to 0.9 and a reference mean temperature of 0 °C [23]. The EnergyPlus’s calculated view factor between the surface and the sky (F_{sky}) was assumed, as well as the Clark and Allen [27] calculated sky temperature. - HR-EU. The parameters described for the HR test model were used in this step, while the apparent sky temperature was calculated as direct difference from outdoor air (11 °C).

- GV-EU. The effect of considering the solar radiation entering the thermal zone as all shortwave radiation was assessed. To this purpose, the direct solar transmission coefficient of windows was set equal to the g-value (at normal incidence), while 0 was assumed for the absorption factor. The glazing solar properties were considered time- and solar angle-independent, by assuming a constant exposure factor (F
_{W}in Equation (6)) equal to 0.9 over the simulation period [2]. - GV-ITA. The parameters described for the GV-EU test model were used in this step, while the glazing solar properties were considered solar angle- and time-dependent, by assuming a variable exposure factor (F
_{W}in Equation (6)) calculated by means of the Italian National Annex approach [28].

- HC-Cst. A constant value of the convective heat transfer coefficient was considered over the simulation period, whose determination depends on the direction of the heat flow. As specified by the EN ISO 6946 technical standard [23], the h
_{c,int}values were assumed equal to 5.0, 2.5 and 0.7 W·m^{−2}·K^{−1}, for horizontal, upward and downward heat fluxes, respectively.

- IG. Firstly, only the convective fraction of internal gains (occupancy, appliances, and lighting) was set as input data in the EnergyPlus model (test model). Then, their radiative fraction was directly applied to the internal surfaces as additional heat balance term, calculated for each timestep as in Equation (9).

- BR. The assumption of EN ISO 52016-1 to not consider a fraction of solar radiation that is reflected back outside the zone from windows was evaluated. To this purpose, the “lost” solar radiation (Equation (13)) was added as an additional heat balance term to each surface, proportionally to the respective surface areas and solar absorption factors (Equation (12)).
- UD. The effect of the uniform distribution of solar radiation on the internal surfaces, specified by the EN ISO 52016-1 hourly method, was evaluated. A simple modelling procedure was applied; the internal surface solar absorption was set equal to 0 to annul the absorbed solar radiation automatically calculated by EnergyPlus. Then, the global (beam plus diffuse) solar radiation entering the zone at each timestep was distributed uniformly on the internal surfaces (Equation (11)). Solar heat gains were considered all radiant heat gains.
- UD-CSG. The influence of the fraction of solar radiation directly transferred to the internal air as convective heat gain was evaluated. The modelling approach of UD was applied. Differently from the UD test model, the solar radiation distributed over the internal surfaces was decreased by a 10%, considered as a convective heat gain.

## 4. Results

#### 4.1. Energy Needs Evaluation

#### 4.1.1. Simplified Modelling of the External Driving Forces

_{H/C,nd}), while the red and bold highlighted values represent the tested assumptions for which the mean bias error (MBE) exceeds the acceptable value (±10% [16]). Significant discrepancies between the baseline and the test models are highlighted when the EN ISO 52016-1 assumptions related to the definition of the external convective heat transfer coefficients are concerned. Generally, an increase of the annual energy needs for heating, and a decrease in the one for cooling occur for all the case study variants. Firstly, the effect related to the lack of specific input data regarding the local wind speed was assessed. The use of an average wind speed value for the determination of the h

_{c}s following the TARP algorithm (HC-Vw-av, variable heat transfer coefficient) leads to negligible variations in the cooling energy needs for all the considered building variants. In fact, the energy needs for cooling decreases with variations within −0.3 kWh·m

^{−2}, with respective Mean Bias Errors (MBEs) lower than −1%. Slightly increases occur instead in the energy needs for heating, especially for the residential apartment unit at the existing building (ExtB) insulation level in Milan (i.e., ΔEP

_{H,nd}equal to +1.3 kWh·m

^{−2}, and MBE equal to +2%). Negligible variations instead are reported for the cooling dominated climatic zone (Palermo), as well as for the well-insulated case studies (DM) in Milan.

_{H,nd}variations of +4.2 kWh·m

^{−2}(compared to 5.2 kWh·m

^{−2}of the baseline), and EP

_{C,nd}variations of −4.3 kWh·m

^{−2}(compared to 22.2 kWh·m

^{−2}of the baseline) are reported, with MBEs both exceeding the acceptable values (+83% and −19% for the heating and the cooling needs, respectively). Comparable situations occur in Milan for both the HC-Cw-av and HC-Cst tests (for heating, +11% and +24%, respectively; for cooling, −19% and −42%, respectively). Consistent discrepancies occur also for the ExtB office module in Milan when the HC-Cst assumption is implemented; in this case, the variations in the energy needs for heating and cooling are characterised by MBEs equal to +17% and −11%, respectively. Nevertheless, the implementation of the reference h

_{c}values specified by the EN ISO 13798 technical standard [29] leads to acceptable variations of the energy needs for all case studies characterised by the DM insulation level (e.g., for the DM apartment unit in Milan, +5% and −9% for the heating and the cooling energy needs, respectively), as well as for the existing office module in Palermo.

_{c,ext}hourly profiles (dashed lines in Figure 4) for the residential apartment unit (ExtB) in Milan are presented for a typical winter week (from 13 to 19 January). The hourly thermal loads are presented as well. The h

_{c,ext}values calculated by means of the formulation in Equation (2) on an hourly basis (HC-V) are consistently higher than the ones calculated by means of the TARP algorithm, using either a variable (baseline model) or an average constant wind speed (HC-Vw-av). Higher convection heat transfer rates occur for the HC-V assumption, leading to the reported discrepancies between the outcomes both on the annual energy needs and on the hourly thermal loads. The HC-Cw-av assumption leads to similar results to HC-V, since the constant h

_{c,ext}used in HC-Cw-av can be considered an average mean value of the hourly HC-V values. However, since HC-V is sensitive to the hourly fluctuation of the wind speed, slightly discrepancies can be highlighted between HC-Cw-av and HC-V. In particular, the HC-V test model tends to overestimate the h

_{c}values with respect to the baseline when high values of wind speed are reported, and thus to overestimate heating loads, while the HC-Cw-av constant value is similar to the baseline one.

^{−2}for the residential unit in Milan, for the existing building and the DM insulation levels, respectively, when the standard constant h

_{r,ext}and the EnergyPlus sky temperature are considered (HR). The introduction of the EN ISO 52016-1 assumption related to the sky temperature definition (HR-EU) shows comparable results with the HR modelling option. This is due to the fact that the actual average difference between the apparent sky and the outdoor air temperatures is similar to the reference value of 11 °C (i.e., equal to 11.5 °C for Milan, and 11.2 °C for Palermo) used in the simulations. Likewise, good agreements between the baseline and the test models can be found when the sky temperature is assumed to be 11°C below the external air temperature (SKY). In fact, the variation in the energy need for heating is around ±0.5 kWh·m

^{−2}for all the case studies, with mean errors within ±2%. For all the considered case study variants, the modelling assumptions related to the external longwave radiation guarantee a variation in the accuracy of the calculation model never exceeding the MBE assumed limits (±10%).

#### 4.1.2. Simplified Modelling of the Internal Driving Forces

_{H,nd}equal to 0 kWh·m

^{−2}for both the ExtB and the DM insulation levels), and for the ExtB residential apartment in Milan (i.e., ΔEP

_{H,nd}equal to +3.6 kWh·m

^{−2}, corresponding to MBEs of +5%).

^{−2}variation, with relative mean bias errors tending towards 0%. For the office module, in which the internal heat gains are consistently higher than in the residential building (overall 28 W·m

^{−2}compared to 7.6 W·m

^{−2}), the variations in the energy needs are slightly higher (e.g., +0.5 and −0.7 kWh·m

^{−2}for heating and cooling, respectively, for the well-insulated office module in Milan); the MBE values never exceed the acceptable values.

^{−2}compared to the baseline model, while a decrease of −3.0 kWh·m

^{−2}is reported for the ExtB residential apartment in Milan. Similar variations also occur for the case studies in Palermo, when the DM level of thermal insulation is considered (e.g., for the office module, −3% and +7% of the energy needs for heating and cooling, respectively). For four out of eight cases considered, the variations in the energy needs exceed the accepted ranges.

^{−2}for the office module, compared to 0.9 W·m

^{−2}for the apartment unit.

#### 4.2. Operative Temperatures Evaluation

## 5. Discussion

- The simplified determination of the external convective heat transfer coefficient generally leads to inaccuracies for uninsulated buildings. In well-insulated buildings, instead, good agreements can be obtained for annual energy performance evaluations, while significant errors are committed in the prediction of the indoor operative temperatures, especially in the warm season. Thus, the EN ISO 52016-1 simplifications on the external convection heat transfer may be applied in the design phases, or for compliance checks, for new buildings. However, for energy audits of existing buildings, or for thermal comfort evaluations, it may be preferable to use more accurate calculation models.
- The use of a constant indoor convective heat transfer coefficient may lead to inaccuracies in the estimation of the energy need for heating for uninsulated buildings, while its application in the prediction of the indoor operative temperatures can be considered.
- Inaccuracies in the temperature prediction occur when the simplification on the solar radiation entering into the zone is considered (i.e., back reflection and convective solar gains). However, generally they guarantee an acceptable accuracy in terms of energy needs estimation.

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 1.**Methodology framework applicable for the energy need (

**A**) and the indoor temperature (

**B**) evaluations.

**Figure 2.**3D visualization of the residential apartment unit (

**a**) and of the office module (

**b**) case studies.

**Figure 3.**Deviations of the energy needs for heating and cooling for the tested modelling assumptions and case study variants.

**Figure 4.**Existing residential unit in Milan: hourly heating loads and h

_{c,ext}values in a winter period for the analysed modelling assumptions.

**Figure 5.**Operative temperature RMSDs for a winter and a summer month for the tested modelling assumptions and case study variants.

**Figure 6.**Summary of the results for the annual energy performance and the hourly operative temperature evaluations.

Parameters | Residential Apartment-Unit | Office Module |
---|---|---|

Conditioned net floor area, A_{n} | 66.3 m^{2} | 17.8 m^{2} |

Conditioned net volume, V_{n} | 179.0 m^{3} | 48.1 m^{3} |

Transparent area (vs. external), A_{env,w} | 9.1 m^{2} | 4.8 m^{2} |

Opaque area (vs. external), A_{env,op} | 52.7 m^{2} | 5.5 m^{2} |

Compactness ratio, S/V | 0.35 m^{−1} | 0.21 m^{−1} |

Windows-to-wall ratio, WWR | 0.34 (South wall) | 0.47 (West wall) |

0.00 (West wall) | ||

0.27 (North wall) |

**Table 2.**Thermal transmittance values of the reference building in accordance with Interministerial Decree of 26 June 2015 [34].

Envelope Component | Milan (Climatic Zone E) ^{1} | Palermo (Climatic Zone B) ^{2} |
---|---|---|

External wall (U_{wall,DM}) | 0.26 W·m^{−2}·K^{−1} | 0.43 W·m^{−2}·K^{−1} |

Windows (U_{win,DM}) | 1.4 W·m^{−2}·K^{−1} (g = 0.50) | 3.0 W·m^{−2}·K^{−1} (g = 0.75) |

^{1}2274 °C·d HDD, 81 °C·d CDD.

^{2}1121 °C·d HDD, 166 °C·d CDD. Heating Degree Days (HDD) and Cooling Degree Days (CDD) calculated according to the UNI 10349-3 technical standard [38] using 20 °C and 26 °C, respectively, as base temperatures.

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**MDPI and ACS Style**

De Luca, G.; Bianco Mauthe Degerfeld, F.; Ballarini, I.; Corrado, V.
Accuracy of Simplified Modelling Assumptions on External and Internal Driving Forces in the Building Energy Performance Simulation. *Energies* **2021**, *14*, 6841.
https://doi.org/10.3390/en14206841

**AMA Style**

De Luca G, Bianco Mauthe Degerfeld F, Ballarini I, Corrado V.
Accuracy of Simplified Modelling Assumptions on External and Internal Driving Forces in the Building Energy Performance Simulation. *Energies*. 2021; 14(20):6841.
https://doi.org/10.3390/en14206841

**Chicago/Turabian Style**

De Luca, Giovanna, Franz Bianco Mauthe Degerfeld, Ilaria Ballarini, and Vincenzo Corrado.
2021. "Accuracy of Simplified Modelling Assumptions on External and Internal Driving Forces in the Building Energy Performance Simulation" *Energies* 14, no. 20: 6841.
https://doi.org/10.3390/en14206841