Identifying Key Parameters in Building Energy Models: Sensitivity Analysis Applied to Residential Typologies

1. Methodology

A SA is conducted to identify relevant parameters in residential BEMs in Uruguay. The study involves four different building archetypes: three of them are typical buildings defined by Curto-Risso et al. [29] and the fourth is a social interest archetype modelled by Pena et al. [30]. For the analysis, the GSA technique introduced by Morris [19] is implemented.

1.1. Morris Method for Sensitivity Analysis

In the Morris method, the user must define the number of parameters under study (k) and their range of possible values. This determines $\Omega$, a k-dimensional input space consisting of the model inputs $X=(X_1,X_2,...,X_k)$. $\Omega$ is discretized into a p-level grid where each $X_i$ for $i=1,2,...,k$ may assume values within the grid.

For a given value of X, the Elementary Effect (EE) of the ith input factor is defined as the magnitude of variation in the model output due to a variation in the ith parameter (as shown in Eq. 1). By randomly sampling different X from $\Omega$, the finite distribution of $E{E}_i$ (denoted $F_i$) is obtained.

$$E{E}_i={\displaystyle \frac{Y(X_1,...,X_{i-1},X_i+\Delta ,X_{i+1},...,X_k)-Y\left(X\right)}{\Delta }}$$

(1)

In Eq. 1, $X=(X_1,X_2,...,X_k)$ is any selected value in $\Omega$, $Y\left(X\right)$ is the model output and $\Delta$ is a predetermined multiple of $1/(p-1)$.

The method assumes $F_i$ to follow a Gaussian distribution and utilizes its mean ($\mu$) and standard deviation ($\sigma$) as indicators of the importance of the ith input. $\mu$ assesses the overall influence of the factor on the output, while $\sigma$ estimates higher-order effects such as non-linearity or interactions with other inputs. Therefore, the Morris method identifies the inputs that can be considered to have an effect:

• Negligible (low $\mu$ and low $\sigma$).
• Linear and additive (high $\mu$ and low $\sigma$).
• Non-linear or involved in interactions with other inputs (high $\sigma$).

Proposed by Campolongo et al. [31], a revised version of the measure $\mu$ is introduced, denoted ${\mu }^{*}$. This measure represents the mean of the distribution of the absolute values of the EEs. The utilization of ${\mu }^{*}$ adresses a potential issue that may arise when $F_i$ includes both positive and negative elements (when the model is non-monotonic). In such instances, when calculating $\mu$ some effects may cancel each other out, leading to a low value even for an important factor. When ${\mu }^{*}$ is employed in place of $\mu$, Garcia Sanchez et al. [3] propose that the value of $\sigma /{\mu }^{*}$ identifies the inputs that are:

• Almost linear ($\sigma /{\mu }^{*}<0.1$).
• Monotonic ($0.1<\sigma /{\mu }^{*}<0.5$).
• Almost monotonic ($0.5<\sigma /{\mu }^{*}<1$).
• Non-monotonic or with high interactions with other factors ($\sigma /{\mu }^{*}>1$)

To estimate the sensitivity measures $\mu$ (or $\mu *$) and $\sigma$, r EEs from each $F_i$ are sampled. The Morris method suggests a sampling strategy that entails generating r trajectories, each composed of $(k+1)$ points within the input space $\Omega$. At each point, one EE is computed for one input factor, resulting in a total of $r(k+1)$ sample points. This translates to simulating $r(k+1)$ building models.

Each trajectory is constructed by randomly selecting a base value from the p-level grid $\Omega$. Subsequently, all trajectory points are generated by incrementing (or decrementing) one of its k components at a time by $\Delta$. This design results in a trajectory comprising $(k+1)$ sampling points $X^{\left(1\right)},...,X^{(k+1)}$, where consecutive points differ in only one component by $\Delta$, and where each component has been increased (or decreased) once. This procedure is repeated r times, each time with randomly selected starting points.

Therefore, when employing the Morris method for SA, the user is required to specify not only the parameters to be analysed and their ranges of possible values but also the number of levels (p), the number of trajectories (r) and the value of $\Delta$. Morris [19] suggests that p should be an even number and $\Delta$ should be set as $\Delta =p/\left[2\right(p-1\left)\right]$. This choice ensures an equal probability of sampling from each $F_i$.

1.2. Previous Studies Using Morris Method in BEM

Neale et al. [4] implemented the Morris method to identify a subset of the most influential parameters affecting electricity consumption and heating load in five Irish building archetypes: a two-storey detached dwelling, a two-storey semi-detached dwelling, a single-storey detached dwelling, a mid-floor apartment and a top-floor apartment. They selected 24 parameters for the scope of the analysis, including building construction parameters (U values), building energy use, building equipment parameters, ventilation and occupancy. For the apartment archetypes some of these parameters were not examined (the floor and roof U-values for the mid-floor apartment, for example) resulting in 19 and 22 parameters to evaluate in the mid-floor and top-floor apartments, respectively. The study employed a triangular distribution to describe the parameter input space, except for the orientation, for which a uniform distribution was assigned. They used a value of $r=10$, resulting in 200-250 models for each archetype to simulate in EnergyPlus. There is no information provided regarding the values used for p and $\Delta$.

Garcia Sanchez et al. [3] conducted a SA using the Morris method in a seven-storey residential building with 32 dwellings. They employed ESP-r energy calculation software to model the building. In their analysis, the authors examined the impact on the heating load of 24 parameters. These parameters encompassed building design aspects (such as building and windows sizes, orientation and insulation thickness), operational factors (including temperature set-points, occupancy levels and ventilation rates), and meteorological variables (external temperature, solar radiation, ground reflectivity and wind speed). To ensure the analysis was representative of apartment buildings at a national level, the authors defined rather board intervals for possible parameter values. In their study, they set $p=10$, $\Delta =5/9$ and $r=10$.

Maučec et al. [32] utilized Morris method in six different timber building models developed in EnergyPlus. A total of 15 parameters where subjected to the analysis to assess their impact on heating and cooling thermal loads. These parameters included building geometry, insulation characteristics, glazing ratio and distribution, shading control and set-point temperatures. Three locations were considered, each with different climatic conditions: moderate, warm and cold. They evaluated the EE in $r=10$ trajectories, resulting in 160 simulations for each model. This led to a total of 2,880 simulations when considering the six building models and the three climate zones. There is no information provided regarding the values used for p and $\Delta$.

De Wit and Augenbroe [20] employed the Morris method in a naturally ventilated office located in the Netherlands. They subjected 89 parameters to the SA to evaluate their relative importance in assessing the uncertainty of a thermal comfort indicator defined as the number of hours per year that more than 10% of the occupants are dissatisfied with the climatic conditions in the building. The authors assumed normal distributions for all parameters. They conducted simulations using two thermal building model tools: ESP-r and BFEP. For the SA, they assessed five independent samples of the EE on the comfort performance indicator ($r=5$) resulting in a total of 450 simulation runs. There is no information provided regarding the values used for p and $\Delta$.

Petersen et al. [12] conducted a study to examine the impact of the choice of p and r on the results obtained from the Morris method. They compared these results with those obtained using the Sobol method. The case of study was a one-storey office building modelled in EnergyPlus. The authors found that, in order for the Morris method to identify the same cluster of parameters as the Sobol method, it required a higher value of r than what is typically applied. The authors commented on the limited attention given to the effect of the user-defined values for p and r when applying Morris method in BEM. As a result of their study, they recommend using $p⩾4$ and conducting simulations in steps of $r=100$ to qualitatively analyse convergence.

Menberg et al. [6] utilized the Morris method in a case study employing TRNSYS as the simulation tool. Their study focused on the Architecture Studio at the University of Cambridge, using the annual heating demand of the first floor as the quantity of interest in the SA. The authors selected 11 uncertain parameters within the TRNSYS model and defined board ranges for their possible values. The aim was to assess the performance of the SA method in situations with limited information about the actual parameter values. All parameters were assumed to follow uniform distributions. The researchers explored the method using different numbers of trajectories to identify the minimum value of r required for a robust ranking of parameters. They performed 10 independent evaluations of the Morris method, each with 10 trajectories, and observed significant variations in both ${\mu }^{*}$ and $\sigma$ across the 10 independent evaluations. Their conclusion was that the method performed reasonably well when $r⩾120$.

1.3. Implementation

In this study, the Morris method is employed to assess the influence of 14 uncertain parameters ($k=14$) on the annual heating and cooling requirements of four dwelling typologies. The buildings are modelled and simulated using EnergyPlus, while Python functions are utilized for designing the Morris samples, generating and executing the models, and processing the SA results. Taking into consideration the assessment by Petersen et al. [12] regarding the importance of analysing the impact of the selected values for p and r, four different levels are explored ($p=4$, 8, 12 and 16) in $r=400$ trajectories. This is a higher number of trajectories than what is typically chosen by Morris method users, and results in 6,000 simulations for each building typology and each value of p, leading to a grand total of 96,000 simulations.

Given that the aim of this analysis is to identify the input parameters crucial for describing the building stock as accurately as possible at a national level, broad ranges are defined for the parameters under study and uniform distributions are considered. The selected parameters and their variation ranges are presented in Table 1. The term conductance, denoted as $U_c$, represents the inverse of the sum of conduction resistances. The air permeability of windows is characterized by the air mass flow coefficient when the opening is closed per unit length at 1 Pa (denoted $C_q^{\prime }$). Windows blinds activation criteria establishes the level of solar irradiation on windows above which blinds are activated when the cooling system is in operation.

The ranges for conductances, thermal capacitances and air permeability are determined based on the minimum and maximum values defined for the Uruguayan housing stock in Curto-Risso et al. [29]. For orientation and solar absorptivities, the ranges encompass all possible values, while for blinds activation criteria, a broad range is defined. In the case of heating and cooling setpoints, narrower ranges are considered to prevent distorting the problem; for example, ensuring that the cooling setpoint is not lower than the heating setpoint.

Regarding the window-to-wall (WWR) and occupancy, the ranges are set as wide as possible while remaining reasonable for each typology. This results in different ranges for the four different case studies. The criteria for determining the WWR range involve maximizing (or minimizing) the size of existing windows wherever possible, with the exception of bathroom windows. For occupancy, a minimum floor area of 8 m²/person was established.

The value used for $\Delta$ is set as $p/\left[2\right(p-1\left)\right]$ as recommended by Morris [19]. The only exception is the value of $\Delta$ used to vary the orientation which is $1/(p-1)$. The reason behind this exception is that for the orientation $\Delta =p/\left[2\right(p-1\left)\right]$ results in values of angle variation of around 180º and in most of the case studies (due to the windows and exposed walls location) there is a rather cyclical relationship between energy consumption and orientation, with a period of 180º. Therefore, using $\Delta =p/\left[2\right(p-1\left)\right]$ for the orientation could lead to a low ${\mu }^{*}$ value even when orientation has a significant impact on energy consumption. This approach aligns with what is suggested by Morris [19] of assigning different values of $\Delta$ to some inputs when some prior knowledge of the function Y makes it desirable. Additionally, as orientation is a circular parameter (a step of $\Delta$ from the maximum value, returns the orientation to 0º), equal probability sampling is ensured regardless of the value used for $\Delta$.

1.4. Limitations of the Research

The selected SA approach provides a qualitative identification of input factors to which thermal loads are more sensitive, but does not quantify the effects of the different parameters on the outputs.

This study is limited to the four studied typologies and focuses on identifying the most relevant parameters affecting thermal loads among the 14 proposed parameters. Climatic factors such as exterior temperatures, irradiation, wind speed and direction, and precipitation were not considered. Additionally, the configuration of the surroundings, such as neighboring buildings or vegetation, was not included in the analysis. The design and dimensioning of heating and cooling systems and their efficiency were also not considered. The behavior of occupants is only accounted for through temperature setpoints and window blind activation criteria.

2. Case Studies

The study employs three of the building archetypes developed by Curto-Risso et al. [29] and a social interest building modelled by Pena et al. [30] and Favre et al. [33]. These are:

• A 27 m${\hspace{0.17em}}^2$ single-storey detached dwelling, hereafter referred to as the "house-studio".
• A 53 m${\hspace{0.17em}}^2$ two-storey attached dwelling, hereafter referred to as the "two-storey".
• A 117 m${\hspace{0.17em}}^2$ single-storey detached dwelling, hereafter referred to as the "ranch".
• A 66 m${\hspace{0.17em}}^2$ single-storey detached dwelling, hereafter referred to as the "bungalow".

The case studies are illustrated in Figure 1 to Figure 4. EnergyPlus models of these four typologies are employed for the SA and the weather file used for the simulations is the Typical Meteorological Year (TMY) of Montevideo in Uruguay, a city with a temperate climate. In the models, the thermal zones of the dwellings remain consistent with their original definitions in Curto-Risso et al. [29], Pena et al. [30] and Favre et al. [33]. The inside and outside convection coefficients are calculated using the defaults TARP and DOE-2 models. Solar distribution is modelled as full exterior and a simulation timestep of 10 minutes is utilized. The HVAC systems are modelled with the ideal load air system and are only considered in the occupied zones. Ventilation and infiltration loads are solved using the airflow network model.

The occupancy criteria are as follows: the main living room (denoted living room 1 when there is more than one living room) is occupied by 50% of the dwelling occupants from 14 to 18 hs and by 100% from 18 to 22 hs. The bedrooms are occupied from 22 to 8 hs, with 2 occupants using the largest bedroom (denoted bedroom 1), and the remaining occupants are distributed among the other bedrooms. For example, in a case with 3 people and 2 bedrooms, 2 people occupy the largest bedroom and one person occupies the other. In a case with 3 people and 3 bedrooms, 2 people occupy the largest bedroom, one person occupies the second largest, and the third bedroom remains unoccupied. No occupation is considered for living rooms other than living room 1 and bathrooms. The occupancy schedules are crucial because the HVAC system is only available when the zone is occupied, thus an empty bedroom does not consume energy from the HVAC system, at least directly.

Figure 3. Ranch.

Figure 3. Ranch.

Figure 4. Bungalow.

Figure 4. Bungalow.

The construction materials for floors, interior walls, ceilings and doors remain consistent with their original definitions in Curto-Risso et al. [29] and Pena et al. [30]. However, for the exterior walls, roofs and windows, new fictional materials are defined. These materials are adjusted in terms of conductivity, density and solar absorptivity to meet the required conductances, thermal capacitances and solar absorptivities. Additionally, for the windows, the air mass flow coefficient when the opening is closed is adjusted according to the value of the air permeability parameter.

All exterior windows are equipped with blinds. In occupied zones, the blinds are activated when cooling is on and solar irradiation exceeds the specified threshold defined by the blinds activation criteria parameter. In unoccupied zones, the blinds are activated when zone temperature exceeds 23ºC and solar irradiation exceeds the specified threshold parameter.

3. Results and Discussion

Considering the assessment by Petersen et al. [12] regarding the importance of analysing the impact of the selected values for p and r in the SA results, four levels are evaluated ($p=4$, 8, 12 and 16) in a total of $r=400$ trajectories. In this study, the classification of parameters by order of importance is based on the value of $\sqrt{{{\mu }^{*}}^2+{\sigma }^2}$, as elaborated later. Thus, to analyse the number of trajectories required, the resulting $\sqrt{{{\mu }^{*}}^2+{\sigma }^2}$ for each parameter is assessed in steps of $r=10$ to visually analyse its convergence. On the other hand, the impact of p is studied qualitatively by observing the resulting ranking of the parameters for the different values of p considered.

For the four studied typologies, up to $r=100$ there are important variations in the results (see Figure 5 and Figure 6 with the results for cooling and heating requirements, respectively). From $r=200$ results seem to have converged. Ranking changes that occur for larger values of r are between parameters with very similar final $\sqrt{{{\mu }^{*}}^2+{\sigma }^2}$ values, which should therefore be considered as equally relevant.

Regarding the impact of the defined number of levels (p), the findings reveal that changes in the obtained ranking occur up to $p=16$ (see Figure 7 and Figure 8). However, the most substantial variations are observed up to $p=12$. Changes between results for $p=12$ and $p=16$ primarily involve parameters with very similar $\sqrt{{{\mu }^{*}}^2+{\sigma }^2}$ values, indicating their roughly equal relevance.

For $r=400$ and $p=16$ the cooling, heating and total thermal loads in the four typologies fall within the ranges presented in Table 2. The considerable variability in the results for different combinations of the input parameters underscores the significant impact of the selected parameters on the thermal loads; at least for the wide ranges of variation considered.

The results from the Morris method are presented by plotting the ${\mu }^{*}$ and $\sigma$ of the EE for the parameters under study for cooling, heating and total thermal loads. Low values of both ${\mu }^{*}$ and $\sigma$ indicate a non-influential parameter and the greater the distance from (0,0) the more relevant the parameter (circles centered at (0,0) are plotted for reference). The $\sigma /{\mu }^{*}=0.1$, 0.5 and 1 are plotted to delimit the linear, monotonic, almost monotonic and non-monotonic or with high interactions with other factors zones.

The EE analysis for the house-studio (see Figure 9) shows that roof solar absorptivity, cooling setpoint, walls solar absorptivity, orientation and roof conductance are the parameters with the highest impact on cooling loads. The first three are all in the monotonic region ($0.1<\sigma /{\mu }^{*}<0.5$) whereas the orientation and the roof conductance are either non-monotonic or involved in interactions with other factors ($\sigma /{\mu }^{*}>1$). For heating loads, the heating setpoint, roof solar absorptivity, roof conductance, walls solar absorptivity and walls conductance are the most influential parameters; all in the monotonic or almost-monotonic regions ($0.1<\sigma /{\mu }^{*}<1$). Finally, when considering total thermal loads (cooling + heating), roof solar absorptivity, cooling setpoint, roof conductance, heating setpoint and orientation are the most relevant parameters. The first four in the monotonic or almost-monotonic regions ($0.1<\sigma /{\mu }^{*}<1$) while the orientation is either non-monotonic or involved in interactions with other factors ($\sigma /{\mu }^{*}>1$).

For the two-storey typology (see Figure 10), the orientation, cooling setpoint, occupancy, roof solar absorptivity and window-to-wall ratio have the highest impact on cooling loads; all in the monotonic region ($0.1<\sigma /{\mu }^{*}<0.5$) except for the orientation which is either non-monotonic or involved in interactions with other factors ($\sigma /{\mu }^{*}>1$). Heating setpoint, orientation, roof conductance, roof solar absorptivity and occupancy are the key parameters affecting heating loads; the orientation and occupancy are non-monotonic or involved in interactions with other factors ($\sigma /{\mu }^{*}>1$) whereas the other three are monotonic or almost monotonic ($0.1<\sigma /{\mu }^{*}<1$). For total thermal loads, the orientation, occupancy, cooling setpoint, roof solar absorptivity and heating setpoint are the most influential parameters; all in the monotonic or almost monotonic regions ($0.1<\sigma /{\mu }^{*}<1$), except for the orientation.

Results for the ranch typology (see Figure 11) show that roof solar absorptivity, cooling setpoint, occupancy and roof conductance are the key parameters for cooling loads; the first three are in the monotonic region whereas the roof conductance is non-monotonic or involved in interactions with other factors ($\sigma /{\mu }^{*}>1$). Heating setpoint, roof solar absorptivity, roof conductance and occupancy have the highest influence on heating loads, all in the monotonic or almost monotonic regions ($0.1<\sigma /{\mu }^{*}<1$). Considering total thermal loads, roof solar absorptivity, cooling setpoint, roof conductance, occupancy and heating setpoint are the most relevant parameters all in the monotonic or almost monotonic regions ($0.1<\sigma /{\mu }^{*}<1$).

Results for the bungalow EE analysis (see Figure 12) show that roof solar absorptivity, cooling setpoint, orientation, occupancy and roof conductance are the key parameters for cooling loads. The orientation and the roof conductance in the non monotonic or with relevant interactions region ($\sigma /{\mu }^{*}>1$) and the others in the monotonic or almost monotonic regions ($0.1<\sigma /{\mu }^{*}<1$). Heating setpoint, roof solar absorptivity, occupancy and roof conductance have the most influence on heating loads all in the monotonic or almost monotonic regions ($0.1<\sigma /{\mu }^{*}<1$), except for the occupancy which is either non monotonic or involved in interactions with other parameters ($\sigma /{\mu }^{*}>1$). For total thermal loads, the key parameters are roof solar absorptivity, occupancy, orientation, cooling setpoint and roof conductance all in the monotonic or almost monotonic regions ($0.1<\sigma /{\mu }^{*}<1$), except for the orientation which is either non monotonic or involved in interactions with other parameters ($\sigma /{\mu }^{*}>1$).

Analysing the EE results for all four case studies, both for cooling and heating loads, roof solar absorptivity, setpoint temperatures, orientation and roof conductance are among the parameters with greatest impact independently of the typology. On the other hand, windows conductance, walls thermal capacity and windows air permeability have the lowest impact on cooling, heating and total thermal loads for all four case studies.

The occupancy has high impact on cooling, heating and total thermal loads for all typologies with exception of the house-studio. This is reasonable given that in the house-studio, the occupancy takes values in a narrower range than in the other typologies (see Table 1) and also that there is only one area for thermal conditioning; while in the other three typologies conditioned area changes with changes in the amount of occupants (depending on the number of occupied bedrooms), in the house-studio it does not.

The orientation parameter appears to have a more significant impact on the two-storey and bungalow typologies. This can be attributed to the fact that these typologies only feature windows on the front and rear facades, whereas the other typologies have windows facing all four directions. Additionally, the two-storey model is attached on both sides, further emphasizing the relevance of orientation.

Walls and roof conductances are more relevant for heating than for cooling loads; whereas the opposite is true for WWR and blinds activation criteria. Conductances being more relevant for heating loads might be because temperature difference between inside and outside is grater in winter than in summer, making heat transferred through walls and roof higher for a given U-value. WWR has higher impact on cooling loads given that there are more energy gains through windows in summer than in winter, especially in east, south and west facing windows which have rather small (zero for south) solar gains during winter. It is also reasonable for blinds activaction criteria to be more relevant for cooling loads as the blinds are activated if cooling is on or if there is high temperature in an unoccupied zone.

As a syntethis, the Morris resulting top 5 most influential parameters for cooling and heating loads across the four typologies are presented in Table 3. Roof solar absorptivity, setpoint temperatures, orientation and roof conductance consistently rank among the most influential parameters in all the four studied typologies. Occupancy in also in the top 5 most relevant parameters for all typologies, except for the house-studio.

Neale et al. [4], for an Irish residential typology similar to the bungalow of this study, also found that heating setpoint, occupancy and roof transmittance are among the most relevant parameters affecting heating loads. However, and contrarily to the results obtained in this study, the authors found windows transmittance to be quite relevant and not the roof solar absorptivity. These differences might be due to the different climatic characteristics, as in Irish winter there is less solar irradiation and lower exterior temperatures than in Uruguayan winter.

Petersen et al. [12], for a Danish one-storey attached office, found that orientation is one of the most influential parameters both in heating and cooling loads. These findings align with the results obtained in this study, where orientation emerged as the most significant factor in the attached typology. Heating and cooling setpoints were also identified as relevant parameters, and roof insulation is among the key parameters for heating loads, also coherent with the results obtained in this study for roof conductance. The authors did not include solar absorptivities in their analysis.

Neale et al. [4] and Petersen et al. [12] found ventilation rates, equipment loads and solar heat gains coefficient of the windows to be relevant parameters, which were not subject of this study. Ventilation rates were not considered as input parameters because in Uruguayan dwellings, ventilation is typically managed by occupants through window operation rather than central systems. Therefore, characterizing ventilation rates for a specific typology is not reasonable, as they depend on occupant behaviour. On the other hand, equipment loads were not included in this study, as it was assumed that there is not much variation of this parameter among Uruguayan dwellings. This assumption differs from Neale et al. [4], who considered a wide range of equipment loads in a single-family dwelling. Lastly, this study did not examine the solar heat gain coefficient of windows, as the use of treated window panes to manage solar gains is not widespread in Uruguayan dwellings.

In the study by Garcia Sanchez et al. [3], which focused on a residential apartment building, the authors concluded that temperature setpoint and number of occupants are some of the key parameters affecting heating loads. This aligns with the findings of this study and of the reviewed studies in general. Additionally, Garcia Sanchez et al. [3] identified insulation thickness in walls as one of the most relevant inputs. This is a reasonable outcome for a seven-storey building, where the role of walls in terms of heat transfer becomes more critical compared to the roof.

Menberg et al. [6] similarly identified temperature setpoint as the key parameter affecting heating loads. However, they also found that infiltration rate is among the most relevant factors, which differs from the results obtained in this study, where air permeability of windows did not have a significant impact.

In the study by De Wit and Augenbroe [20], the focus was on environmental factors, which were not considered in this study. Therefore, their findings might not directly align with the results presented here.

4. Conclusions

The Morris method was applied in this study to conduct SA on four typologies representative of the Uruguayan housing stock, modeled using EnergyPlus. The main goal was to determine which parameters require detailed characterization for the development of accurate energy models. The study examined 14 parameters, with a majority related to building construction properties (walls and roof conductances, solar absorptivities and thermal capacitances, WWR, orientation and window permeability). Additionally, parameters related to building operation, such as setpoint temperatures, number of occupants and window blinds operation criteria, were considered. Uniform distributions with wide ranges were used for all these parameters.

The SA contemplated the use of four different levels ($p=4$, 8, 12 and 16) and a higher number of trajectories than typically used in Morris method SA ($r=400$). This was done to assess the influence of the user-defined values of p and r. The results indicate that for $p=16$, convergence was achieved after 200 trajectories and for $r=400$ practically the same rankings were obtained for $p=12$ and $p=16$, but not for the lower values of p.

It is important to note that for $r=10$, a number of trajectories frequently employed in SA using the Morris method, convergence of results was not achieved in this study. This observation raises a significant concern regarding the computational cost of the Morris method. While this method is often commended for its computational efficiency, the findings of this study suggest that achieving convergence and reliable results may require a substantially higher number of trajectories, such as $r=200$. Nevertheless, it is noteworthy that the number of simulations typically required for the Morris method with $r=200$ remains significantly lower than the number of simulations typically required by other methods. For instance, studies employing the Sobol method for SA in BEM have demanded between 10,000 and 250,000 simulations per model [4,6,12,34].

The results of the EE analysis reveal that certain parameters consistently rank among the most relevant in all four studied typologies, aligning with findings in previous research. Conversely, some parameters identified as significant in this study were not important or were not even examined in the reviewed studies, and vice versa.

This study identified setpoint temperatures, roof solar absorptivity, roof conductance and orientation among the most relevant parameters across all four case studies. Occupancy emerged as a critical parameter for all typologies except the house-studio, where the maximum number of occupants is low, and the conditioned area remains constant regardless of the number of occupants. Additionally, in the context of heating loads, walls solar absorptivity was found to be a significant input, along with walls conductance.

Differences in the results obtained with other studies might be explained, in some cases, by different climatic conditions and/or building characteristics. In other cases, there are important differences in the set of parameters selected for the analysis and their ranges of possible variations. These definitions depend on the objective of the analysis as well as on the expertise and knowledge of the local reality of the person doing it. This shows that the SA results are difficult to extrapolate to different countries thus proving the importance of performing local studies.

In summary, the main results of this study are as follows:

• Achieving convergence and reliable results using the Morris method for SA may require a higher number of trajectories and levels than typically employed, such as r = 200 and p=12. Yet, the number of simulations required is still lower than those required by other methods (e.g., Sobol method).
• Key parameters identified across all case studies include: setpoint temperatures, roof solar absorptivity, roof conductance and orientation.
• Occupancy was a critical parameter for all typologies except the house-studio.
• Solar absorptivity and conductance of walls were significant for heating loads.
• SA results are difficult to extrapolate to different countries due to different climatic conditions, different characteristics of buildings and thermal conditioning systems and cultural aspects related to housing use. This highlights the importance of local studies.