The uncertainty of manual shade control on west-facing facades and its influence on energy performance

Applied Thermal Engineering 165 (2020) 114611

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Research Paper

The uncertainty of manual shade control on west-facing facades and its influence on energy performance

T

Jian Yao Department of Architecture, Ningbo University, Ningbo, China

HIGHLIGHTS

uncertainty of manual shade control was quantified using correlation analysis. • The energy uncertainty of manual shades at spatial-temporal scales was simulated. • The high energy uncertainty is observed at small spatial-temporal scales. • AEnergy may be ignored at high spatial-temporal scales. • Energy uncertainty performance of simplified shade assumptions was compared with manual shades. • ARTICLE INFO

ABSTRACT

Keywords: Building energy Manual shades Uncertainty Occupant behavior Spatial-temporal scales

Due to the stochastic nature of occupant behavior on manual shades, energy prediction based on realistic shade behavior models differs largely from simplified shade assumptions adopted by building energy codes. Three important questions (when is it important to consider shade behavior models, when does shade behavior related energy uncertainty need to be accounted and when can simplified shade assumptions be used instead of behavior models?) remain unanswered. To address these issues, this paper investigates the impact of occupant uncertainty of solar shade control on building energy performance at temporal and spatial scales as well as predicted performance gaps between simplified shade assumptions and shade behavior models. A stochastic model of manual solar shades developed in a previous study based on field measurements was used in this paper. Co-simulation, statistical calculation and uncertainty analysis were conducted. The results show that energy uncertainty should be considered when evaluating the energy performance of a single room at hourly, daily, monthly and total annual scales. In other cases, shade behavior and related energy uncertainty may be ignored. Fully shade open or closed assumptions lead to a significant deviation of predicted energy performance and thus cannot be used for simulating energy performance of manual shades. Simplified shade assumptions (such as half-open in this research), which is capable of representing average shade behavior patterns, can be used to evaluate the annual energy performance of office buildings and to size cooling/heating equipment instead of a shade behavior model. While for commonly used pessimistic assumptions on manual shades (fully open in summer and fully closed in winter), they over-predict maximum cooling/heating rate by at least more than 5% compared to the shade behavior model.

1. Introduction 1.1. Building energy and shading devices The building sector is the largest energy consumer and the main contributor to global warming. To reduce building energy consumption, different energy-saving measures have been adopted such as wall and roof insulation [1], energy-efficient windows [2], shading devices [3]. During the design stage, building energy performance is usually

simulated or calculated to predict energy savings due to adopted energy-saving strategies. However, field measurement and monitoring data suggested that actual energy consumption is much lower than predicted values with a deviation of 86% [4]. Although studies have reported that building energy consumption is influenced by technology, culture, occupant behavior etc., evidence suggests that occupant behavior plays a significant role in influencing building energy performance [5] since the effectiveness of some of energy-saving measures is highly dependent on occupant behavior (e.g. manual solar shades). The

E-mail address: [email protected]. https://doi.org/10.1016/j.applthermaleng.2019.114611 Received 31 March 2019; Received in revised form 20 October 2019; Accepted 29 October 2019 Available online 31 October 2019 1359-4311/ © 2019 Elsevier Ltd. All rights reserved.

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Nomenclature

Greek letters

UI cv PTOU SC UC OP IP E

μ σ

uncertainty index of manual shades coefficient of variation percentage of time of occupant uncertainty the fraction of unshaded window area uncertainty coefficient for energy performance output parameter input parameter energy performance (Wh)

mean value standard deviation

Subscripts k i,j M m

deviations between predicted and actual energy consumption can partly be attributed to misunderstanding and underestimating the characteristics of occupant behavior [6]. Currently, shading devices have been widely used in buildings for improving building energy performance and thus different control approaches of shades have been well studied for the sake of controlling transmitted solar radiation and sunlight. However, solar shades or blinds were assumed to be deployed at fixed positions in some research studies when calculating or simulating annual heating and cooling demands [7]. A more dynamic model recommended by EN ISO 13790 (CEN 2008) [8] assumes that shading devices are activated whenever solar radiation falling on windows exceeds 300 W/m2. However, these simplified assumptions do not reflect the stochastic characteristics of occupant behavior on shading devices.

time of year (h) the i/j-th of simulation run maximum value minimum value

Besides, Haldi and Robinson [15] developed a comprehensive blind use model based on logistic regression curves. Although this model has the benefit of predicting partial shading events, it is based on a rather unusual external blind configuration, limiting the generalization of the model. According to the final report of IEA-EBC Annex 66 (Definition and Simulation of Occupant Behavior in Buildings) [5], only a few shade behavior models have been reported including logistic regression models, linear regression models and Markov chain models. Therefore, the main shortage of most research studies on solar shades models is that they assume only two shading states (fully open and fully closed) due to the limitation of logistic regression models, which is not in line with real situations (e.g. roller shades are usually deployed at partly shading positions). Although partial shading was considered by Haldi et al. [15], the research conclusion may not be applied directly to other buildings due to its unusual shading systems, which is different from manual solar shades widely used in China. Besides, Sutter et al. [18] found that occupants with motorized blinds move them three times as frequently as those with manually operated blinds and thus the model developed based on motorized blinds by Haldi et al. is not directly applicable to the current study which focuses on manual solar shades.

1.2. Behavior models of shading devices The decision-making process of occupant behavior is complex [9] and influenced by various complex factors (including physical, social, and psychological factors) [10]. Besides, occupant behavior has been recognized as the major cause of uncertainty in building energy performance [11]. Thus, occupant behavior has drawn increasing research efforts recent years [10] and a number of behavior/stochastic models have been developed to predict occupant presence and interactions with building systems including occupant presence [12], activity [13], and interaction with windows [14], blinds[15], building energy devices and systems [16]. For shading devices, occupant behavior has been investigated and many parameters such as workplane illuminance [17], external illuminance [18], luminance in the field of view [19], incoming solar radiation [20], indoor temperature [21] have been reported to be driving factors of shade adjustment. To have a better understanding of the relationship between shade adjustment and potential influencing factors, mathematical relationships and statistical occupant behavior models have been developed. For instance, Inoue et al. [22] established a quantitative relationship between shade use and the driving factor. They found that the best predictor of shade position is solar penetration depth rather than solar intensity. Mahdavi et al. [23] found that a linear relationship can be used to describe the correlation between the probability of closing shades and vertical solar radiation. However, regressed equations provided by these studies can only produce deterministic shade positions at a certain condition (cannot produce stochastic shade positions of manual shades). To introduce a certain level of randomness, Reinhart [24] developed a model (Lightswitch2002) for manual and automated control of electric lighting and blinds. The main limitation of this model is that it considered only two shade positions (fully opened or closed). Inkarojrit [19] reported similar behavior models to calculate the probability of a closing action of window blinds based on logistic regression. However, many of the driving factors in the behavior models in this research are difficult to define and measure with sensors (such as self-reported brightness sensitivity).

1.3. Simulation of shade behavior In order to simulate the energy uncertainty of manual shades, shade behavior needs to be considered in building simulation. However, most shade behavior models have not been integrated into or coupled with building energy simulation tools. Only a few studies attempted to simulate shade behavior and its influence on building energy performance. For example, Gunay et al. [25] proposed an adaptive occupantlearning system, in which window-blind control are adapted in real time to learn the modeled occupant preferences using a Kalman filter. To mitigate the energy performance uncertainty of occupant use of window blinds, O’Brien et al. [26] used robust design to minimize the occurrence of discomfort on a south-facing room. They adopted the logistic regression model for shade control developed by Haldi and Robinson [15]. The simulation study shows that it is possible to use passive or fixed building design features to reduce the frequency of visual comfort triggered shade control. In some cases, these robust design solutions help reduce both uncertainty and predicted energy use. They also pointed out that occupant behavior model for west-facing facade is lacking and distinctly different than for south-facing façade. Solar shading devices play a vital role in building energy performance, especially in subtropical climates of China where solar heat gain through windows accounts for the largest component of the building envelope cooling load [27]. Automated blind systems have been developed for maintaining low energy consumption and high thermal and visual comfort. However, Reinhart and Voss [17] report that occupants overrode 88% of the attempts of an automation system to control window blinds, indicting automated blind systems do not comply with occupant behavior of shade control. Thus, the real energy performance 2

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based on the office building in a previous research was used in this paper since it is a representative office building in China. For uncertainty analysis of solar shades, the number of repeated simulations required to get a converged result was first determined and then correlation analysis was performed to confirm the randomness between each single simulation. Finally, energy performance and uncertainty due to shade behavior uncertainty at different spatial-temporal scales were quantified and compared with simplified shade assumptions.

may be different from the prediction based on assumptions of automated blind and consequently, energy prediction based on stochastic shade models is required. 1.4. Research gaps According to the above discussion, relationships between manual shades and potential driving factors have been extensively studied but shade behavior model-based energy performance analysis is rare [10]. Although only a few research reported the influence of occupant behavior (manual shades) on energy performance [28–30], the blind models adopted in these research works were not applicable to other buildings, either due to unrealistic fully open and fully closed assumptions (since in reality most manual blinds/shade are deployed at partial shading states [31,32] with an average of 40%-50% blind/shade occlusion rate) or based on unusual shading systems with motorized control, which leads to a much higher blind movement rate compared to manual controls [26]. In addition, these shade behavior models are mainly developed on the south façade and not applicable to west-facing rooms, which is more susceptible to solar radiation [26]. Thus, a more general shade behavior model that not only deals with partial shading state but also represents manual shade control of west facade is needed for quantifying energy and uncertainty performance of manual shade control at different spatial-temporal scales. Furthermore, questions about whether simplified shade assumptions can be used instead of shade behavior model for energy prediction at different temporal-spatial scales and whether extreme conditions (fully open, fully closed) can be used for sizing equipment need to be answered. To address these issues, a more general stochastic model for westfacing facade developed in a previous study [32] based on field measurements was used in this paper. Energy savings compared to regular windows [32], thermal [33] and visual performance [34] have already been investigated. This work is a continuation of the previous research and the aims of this research are: (1) to quantify the uncertainty of occupant behavior on solar shades and its influence on building energy performance at spatial-temporal scales; (2) to provide insights into when it is important to consider shade behavior models; (3) to answer when it is relevant to study the energy uncertainty; and (4) to determine whether simplified shade assumptions (fully open, fully closed and average behavior patterns) can be used instead of shade behavior model for cooling/heating equipment sizing.

2.1. Building model A west-facing office room (4 × 4 × 3 m, see Fig. 1) of the typical building was considered in this paper. The size of the window on the west facade is 3.8 × 2.8 m. Two identical solar shades (manually controlled) side by side was installed inside the window (internal solar shades). This setting complies with the real condition and allows for more flexibility in shade control for thermal and visual comfort compared to previous studies [22,32,33]. During the previous research [32], occupant shade control was divided into 5 solar shading states (shade window area of 0%, 25%, 50%, 75% and 100%, respectively) and these 5 states were expressed as SC values for the following analysis (which represents fraction of unshaded window area). Thus these 5 shading states (0%, 25%, 50%, 75% and 100%) correspond to SC values of 1, 0.75, 0.5, 0.25 and 0 respectively. Since two shades were considered, the combination of the two shades results in a total of 9 possible SC values (0, 0.125, 0.25, 0.375, 0.5, 0.625, 0.75, 0.875 and 1). For example, if the SC values for the two shades are 0.75 and 0.5 respectively, then the overall SC of the combination is (0.75 + 0.5)/ 2 = 0.625. The simulation model setting (location, orientation and dimension) complies with the real condition (see the image at the top of Fig. 2(a)) in field measurement. The characteristics of the office room and the simulation settings (such as HVAC, interior heat generation, light density and fresh air etc.) comply with the “Design standard for energy efficiency of public buildings” in this region of China [35] and are shown in Table 1. It should be noted that weekends were not considered in the current research due to the complexity of modeling weekends and holidays in Building Controls Virtual Test Bed (BCVTB). 2.2. Stochastic model of manual solar shades 2.2.1. Model development Data-driven probabilistic methods for modeling occupant behavior were suggested by [10] and thus occupant behavior of manual shades was modeled as a probabilistic model in this paper. A brief description of the stochastic (probabilistic) behavior model for solar shades and cosimulation analysis is described in Fig. 2. Steps for developing shade

2. Methodology To carry out this research, a typical office building with manual solar shades and the stochastic model of manual solar shades developed

(a) Front view

(b) Section view

Fig. 1. Front and section views of the office room model. 3

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(a) Development of shade behavior model

(b) Framework for co-simulation showing data exchange between BCVTB and E+ Fig. 2. Flowchart of development of the shade behavior model and framework for co-simulation.

behavior model are as follows (see Fig. 2(a)): (1) time-lapse photography from the exterior of the building was used to record shade positions at each hour while concurrent measurement of environmental variables (including solar intensity and outdoor air temperature) was

conducted. The occupants’ stochastic behavior of solar control was divided into 5 discrete solar shading states (corresponding SC values are 0, 0.25, 0.5, 0.75 and 1 respectively); (2) cumulative odds logit regression was performed to determine the driving factor for shade 4

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Table 1 Characteristics of the office room and simulation settings. Parameter

Value

Location Orientation Dimension Building envelope

Ningbo city in China, latitude: 30oN, longitude: 120oE West Room: 4 × 4 × 3 m, Window: 3.8 × 2.8 m (window-to-wall ratio: 0.887) U-value for external wall:1 W/m2K, and adiabatic for internal walls, roof and floor; Window setting: clear double-pane window (U-value: 3.6 W/m2K and Tv: 0.78, g-value of the glazing: 0.698) + manually controlled internal shading (Tv: 0.2), frame ratio of the window: 0.12; Shade control: occupant shade control was divided into 5 solar shading states (shade window area of 0%, 25%, 50%, 75% and 100%, respectively) and thus the combination of two shades result in a total of 9 possible SC values (0, 0.125, 0.25, 0.375, 0.5, 0.625, 0.75, 0.875 and 1) 8:00–17:00 for all days during the year Temperature: 20–26 °C, run time: 8:00–17:00 Light density: 11 W/m2; equipment: 20 W/m2 40 m3/h.p

Work time HVAC Interior heat generation Fresh air

the required minimum number of simulations to achieve a converged solution, according to the graphical method recommended in [37], which is similar to the study by Feng et al. [38] for determination of the simulation repetition using statistical methods. The graphical method is a simple graphical approach that plots the cumulative mean of the simulation output data. After sufficient replications, the graph will become a flat line with no upward or downward trend. The number of replications required is defined by the point at which the line becomes flat.

movement and solar intensity was found to have a significant relationship with shade movement; (3) the first order and discrete-time Markov chain method was used to produce Markov chain transition matrix (the probability of solar shade changes from the current state to the next one); (4) a whole shade behavior model was developed by considering different Markov chains constructed based on solar intensity for different seasons (three seasons: summer, winter and transition). Since daylight, thermal and glare related manual shade actions are largely dependent on solar radiation and thus the developed shade behavior model (in this model solar radiation is the triggering factor) is capable of representing occupants’ shade actions due to these factors (daylight, thermal and glare). This model combined different occupant traits and used first order and time-constant Markov chain method to represent the stochastic behavior of solar shade control. Thus random control of solar shades is introduced and uncertainty of shade control can be simulated.

2.4. Uncertainty of shade control In this paper, uncertainty means the stochastic adjustment of shade devices due to occupant behavior, which results in the difference of SC value between occupants and thus the resulting building energy difference. To evaluate the uncertainty effect, coefficient of variation (cv), a standardized measure of the dispersion of a probability distribution, was used to derive uncertainty index in this paper:

2.2.2. Co-simulation The shade behavior model was modeled in BCVTB for co-simulation with EnergyPlus (E+) [36], as can be seen in Fig. 2(b). BCVTB is a software environment developed by Lawrence Berkeley National Laboratory and allows expert users to couple different simulation programs for co-simulation such as Energyplus, Matlab, Simulink and Radiance. The data exchanged per time step between E+ and BCVTB were solar intensity and shade position (see Fig. 2(b)). During each time step of co-simulation, E+ passed these data (solar intensity and shade position) to BCVTB, and then BCVTB generated a random number and determined if a shade movement occurred according to Markov transition probability matrix, which depends on solar intensity and shade position. The determined shade position by BCVTB was then fed back to E+ for simulating energy performance. Since two side by side solar shades were considered along with three Markov chains for three seasons, six Markov models (see Fig. 2(b)) were constructed (each shade has three models for three seasons). It should be noted that shade adjustment was assumed to occur during work time (8:00 to 17:00) and thus a time module was constructed in BCVTB to determine if it was during work time. Season module was used to determine which Markov transition probability matrix should be used. More detailed information on this stochastic model and the co-simulation can be found in the previous paper [32].

UIk =

k

µk

× 100% = cvk × 100%

(1)

where UI is the uncertainty index (it is a non-negative value), σk and μk are the standard deviation and mean of the SC values of the 25 repeated simulations (here 25 repeated simulations were determined according to Section 2.3, which is further described in Section 3.1.1) at k-th time step, respectively, and k is time of year (from 1 to 8760 h). Using this equation, hourly UI can be calculated and then annual average UI can also be obtained. Meanwhile, any two simulation runs have two different hourly SC sequences and thus uncertainty of occupant behavior can also be identified at the temporal scale by comparing these two sequences. Here another index, the percentage of time of occupant uncertainty (PTOU) which check whether there is a difference between hourly SC values of any two simulation runs, was introduced and it can be calculated as: 8760

PTOU = k=1

0, SCi,k = SCj,k ,i j 1, SCi,k SC j,k

(2)

where i,j = 1,2…, is the i/j-th simulation run (here it is 25). In addition, correlation coefficient was used to assesses how well the relationship between two variables (here hourly SC values between different simulations), which varies between +1 and −1. A value of +1 indicates a perfect positive correlation between the two variables, −1 represents a negative correlation and 0 corresponds to an absence of linear correlation. Since SC values in this paper are discrete and ordinal, Spearman rank correlation [39], a non-parametric test, was used. The Spearman rank correlation test does not carry any assumptions about the distribution of the data and thus is appropriate for correlation analysis for SC values. In addition, the cross-correlation analysis (which is a measure of similarity of different time series data) between different simulations was carried out since it is suitable for different sets of time-

2.3. Number of repeated simulations The above shade behavior models require random sampling from probability distribution functions (Markov transition chain) and thus repeated energy simulation runs generate different simulation outputs even using the same behavior model. As stated by other authors [28], additional simulation time needed for replicates can be considered as a weakness, especially with large models. Therefore this paper calculates 5

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series data (hourly SC values can be considered as time-series data). These two types of correlation analysis were done in R, a free software environment for statistical computing [40], with the libraries corrplot [41] and ggpubr [42].

2.5.2. Analysis at temporal scales For the temporal scale, energy uncertainty at 4 scales (hourly, daily and yearly) was calculated. Since the number of cooling and heating hours exceed 1800 and 700 respectively for each simulation run, the statistical tests showed that not all of these hourly energy data are normally distributed. Thus, energy uncertainty was directly compared using these 25 simulations (not MC method). In addition, cooling/ heating equipment sizing is commonly conducted by using pessimistic assumptions (shade always open in summer and always closed in winter). Whether these simplified assumptions lead to oversized equipment will be answered by comparing the maximum cooling/ heating rate between shade behavior model and these pessimistic assumptions.

2.5. Energy uncertainty at temporal and spatial scales Occupant shade control is random and thus leads to great uncertainty in building energy performance. To evaluate the uncertainty of building energy prediction, 25 co-simulation runs were conducted. Different temporal and spatial levels of energy prediction were selected to analyze the performance uncertainty due to uncertainty in shade control. The following energy uncertainty analysis considers the westfacing office room model described in Section 2.1 with fixed room geometry and thermal mass. The purpose of this analysis is to understand the level of energy uncertainty at temporal-spatial scales and to provide insights in to when it is important to consider shade behavior models and when it is relevant to study the energy uncertainty.

2.6. Energy uncertainty index When conducting energy uncertainty analysis, uncertainty coefficient is usually used to assess the impact degrees of input parameters on the output. It is a dimensionless value expressed in percentage. It implies the contribution of percentage change in input parameter to percentage change in output. The higher the absolute value of uncertainty coefficient is, the stronger the influence of input design parameter on energy use goes, and thus the more important the design parameter is. Uncertainty coefficient can be expressed as follows [45]:

2.5.1. Analysis at spatial scales For uncertainty at spatial scales, small (30 rooms), medium (50 rooms) and large (100 rooms) office buildings as well as a single room were considered. For room numbers of 30, 50 and 100, internal walls, roof and floor are considered as adiabatic and this assumption is reasonable since these rooms were kept at the same temperatures during cooling (26 °C) and heating (20 °C) periods. Thus there is no (or almost no) heat transfer between physically connected rooms in cooling and heating periods. Therefore, the summation of the energy demand of a single room can be used to calculate whole building energy performance (here it is the whole west-facing rooms since only shade behavior model for the west facade was considered). Although there might be different heating or cooling setpoints in reality, this effect is not considered in this paper for simplification. For calculating energy demands of various building sizes, the outputs of 25 co-simulations described in Sections 2.3 and 3.1.1 were statistically tested (which were given in Section 3.2) to determine the probability distribution of the energy data (annual heating, cooling and the total of heating and cooling). Based on the fitted distribution of energy data, the Monte Carlo (MC) analysis method (i.e. random sampling from the fitted energy distribution) was used to obtain the total energy demand for a given spatial scale. It should be noted that the MC analysis was used in the following two steps:

UC =

OP M OPm OP M IP M IPm IP M

× 100%

(3)

where OPM and OPm respectively are maximum and minimum values of output parameter. IPM and IPm respectively are maximum and minimum values of the input parameter. In this paper, the input parameter is the difference of shade control behavior between occupants. In fact, the same stochastic model was used for different occupants. Therefore, the denominator in uncertainty coefficient equation is not considered since a 0 denominator leads to an infinite UC (the same model means IPM - IPm = 0). Although it seems possible to use SC parameter (shade control influences SC value) as IP, it is not suitable to do so due to the following reasons: (1) SC value fluctuates significantly during the year (not a fixed value), (2) in some cases (IPM - IPm = 0) shades are deployed at the same positions (leads to an infinite UC). Thus, the uncertainty coefficient used in this paper can be rewritten as:

UC =

(1) Obtaining energy demand at a given spatial scale. For each sampling, an energy value was selected randomly from the fitted energy probability considering the uncertainty of fitted parameters (confidence intervals). For example, to get the energy demand at the spatial scale of 30 rooms, a total number of 30 random samplings were conducted and the summation of these 30 energy values represented the energy demand at this spatial scale. However, this sampling process (e.g. 30 samplings for 30 rooms) used to obtain the total energy demand only led to a deterministic total energy value (here total means the summation of every single energy value). Thus this sampling process should be repeated using the MC method again in order to obtain the possible range of the total energy value, which is given in step 2. (2) Repeating step one to obtain the possible range of total energy value. The accuracy of the sampling method is based on the number of MC analysis that has taken place. A study by McDonald [43] which compared three sampling techniques for Monte Carlo analysis suggests that the best combination for MC simulation in typical building applications is simple random sampling with 100 runs. In order to have higher accuracy, in this study simple random sampling using MATLAB [44] was chosen with 1000 repeated sampling for each spatial scale (10 times higher than the suggested simulation runs).

OPM OPm × 100% OPM

(4)

2.7. Comparison with simplified shade assumptions Building energy uncertainty is generally undesirable since it reduces performance robustness of building designs. To better illustrate when/ why it is important to consider probabilistic shading models and when it is relevant to study the uncertainty, an example comparison of energy performance of manual shades between the behavior model and simplified assumptions was provided. For simplified assumptions, three scenarios were considered: (1) always fully open, (2) always fully closed and (3) always half-open. The first two scenarios can be used as extreme conditions for cooling/heating equipment sizing, while the last one represents average shade behavior patterns since the following analysis shows that annual average SC is about 0.5. 3. Results and discussion 3.1. Uncertainty of shade control 3.1.1. Required simulation replicates It can be seen from Fig. 3 that the results (annual heating and cooling) converge at 20 replicates with a 95% confidence interval. This 6

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47.5%, indicating the covered window area by solar shades between occupants (or the same occupant at different time points) differs largely. Another index PTOU is 84.8%, indicating that 84.8% of times during the year shades are kept at different positions between two occupants. Therefore, it can be concluded that given the same environmental condition occupant uncertainty of shade control is significant and there is a need to analyze the impact of uncertainty of shade control behavior on energy performance and this behavior model can be used for energy uncertainty analysis. 3.1.3. Correlation coefficient Fig. 7 presents Spearman correlation coefficient of hourly SC values between the 25 simulations during the whole year. The areas of circles shown in this figure represent the absolute values of corresponding correlation coefficients. The larger the areas of circles are, the stronger the correlation between simulations. It can be seen that on the principal diagonal the areas of circles are the largest with Spearman correlation coefficient of 1, which is due to the fact that the calculation is based on the same SC value sequence (such as N1 vs. N1). However, the tinted circles are small which means that the correlation is poor. These correlation coefficients (off-diagonal elements) are close to 0 with only a

(a) Heating

(b) Cooling Fig. 3. Convergence of mean annual energy demand prediction: (a) heating and (b) cooling. The solid line indicates the mean value while the dashed lines indicate 95% confidence interval.

(a) Cooling

amount of replication is higher than the finding of Feng et al. [38] who reported that the minimum required simulation runs was 10 for a converged mean energy value. Performing more replications beyond this point will only give a marginal improvement in the estimate of the mean value. Thus, 25 simulation replicates (5 extra simulations beyond that point) were selected in this paper for the following energy uncertainty analysis. 3.1.2. UI index Fig. 4 presents the histogram of SC differences between two example simulation runs during cooling hours and heating hours, respectively. Due to the stochastic nature of occupant behavior, occupant uncertainty can be easily observed with most of the times SC difference being not 0 but mainly between about −0.8 to 0.8. In addition, the average SC value also differs largely among the 25 simulation runs. Fig. 5 illustrates a box plot of average SC values of two typical seasons for the 25 simulations. The summer SC value ranges from about 0.4 to 0.54 while the winter SC value ranges from about 0.44 to 0.58. The SC values of these two seasons are close and almost the same as annual average SC (0.42–0.53), indicating that average shade behavior pattern can be represented by using half-open shade which has a SC value of 0.5. Fig. 6 gives the distribution of hourly UI, it can be seen that uncertainty of occupant behavior is significant with hourly UI values ranging from mainly 30–70% and the annual average UI reaches

(b) Heating Fig. 4. Histogram of SC difference between two simulations during (a) cooling hours (1886 h) and (b) heating hours (746 h). 7

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(a) Cooling energy

Fig. 5. Box plot of average SC values of two typical seasons for 25 simulations (The ends of the whiskers indicate 5th and 95th percentiles. The bottom and the top of the boxes represent the 25th and 75th percentiles while the line within the box stands for the median, and “o” means average value).

(b) Heating energy

Fig. 6. Distribution of hourly UI.

(c) Total energy Fig. 8. A Q-Q plot comparing energy data on the vertical axis to a normal distribution on the horizontal axis.

few values reaching about 0.1/-0.1. In statistics, a correlation coefficient in the range of [-0.19, 0.19] indicates no or very weak relationship [46]. The cross-correlation coefficients between these 25 simulations are mainly between −0.19 and 0.19 (accounts for 99.3%) with only two values exceed this range. Therefore, there is no relationship between 25 simulations of occupant behavior in terms of hourly SC value sequence, indicating uncertainty was not suppressed by the behavior model.

Fig. 7. Spearman correlation coefficient of hourly SC values between the 25 simulations during the whole year (N1…N25 represent simulation1…simulation25).

8

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3.2. Distribution of the energy data To determine the distribution of annual cooling, heating and total energy data, a probability plot (Quantile-Quantile (Q-Q) plot) is used to graphically compare the distribution of these data to the normal distribution, which is represented by a straight line. If the data are normally distributed, then the points in the Q-Q plot will approximately lie on the straight line and fall in the gray region around the line (95% confidence interval). Fig. 8 shows a Q-Q plot comparing energy data on the vertical axis to a normal distribution on the horizontal axis. It can be seen that annual cooling, heating and total energy data all fall in the confidence region, suggesting that the data are normally distributed. Furthermore, a more rigorous statistical test of normality of these energy data was conducted by Shapiro–Wilk test, which is the best power for a given significance, followed closely by Anderson–Darling when comparing the Shapiro–Wilk, Kolmogorov–Smirnov, Lilliefors, and Anderson–Darling tests [47]. The null-hypothesis of this test is that the population is normally distributed. Thus, if the p-value is greater than the chosen alpha level (normally it is 0.05), then the null hypothesis that the data came from a normally distributed population cannot be rejected. Table 2 shows the Shapiro-Wilk test of energy data. It can be seen that these p-values are all higher than 0.05, indicating the null hypothesis cannot be rejected and the data are normally distributed. The above analysis shows that the energy data are from normal distribution, and thus the probability density function (PDF) of normal distribution can be determined using a two-parameter family of curves. The first parameter, μ, is the mean. The second, σ, is the standard deviation. And the normal PDF of the energy data (f (E )) can be expressed as:

f (E ) = f (E|µ , ) =

(E 1 exp 2 2

µ )2 2

Fig. 9. 1000 sampled curves of fitted probability density function (PDF) of total energy distribution (the thick, dark line represents the PDF using the point estimate of the parameter, μ and σ).

used to further derive sufficient variability of energy consumption induced by uncertainty of occupant behavior. The possible combinations of μ and σ which are randomly selected from the confidence intervals lead to a large variability of fitted probability density function (PDF) of total energy distribution. An example plot of 1000 sampled curves of PDF considering uncertainty in parameters estimation is shown in Fig. 9. The thick, dark line in the figure represents the PDF using the point estimate of the parameter, μ and σ. The relatively wide range around the thick, dark line indicates a larger uncertainty of generated energy performance compared to a single distribution curve (the thick, dark line). Thus it is clear that a significant uncertainty has been introduced after considering the confidence intervals for the two parameters. The above analysis showed that the cooling, heating and total energy data from the stochastic model of shade control behavior are normally distributed. However, it should be noted that uncertainty analysis of input parameters does not necessarily produce normal distributions of simulation outputs. Prada et al. [48] reported that the simulated heating and cooling needs are not always normally distributed (may resemble Weibull or lognormal distributions) when considering uncertain thermo-physical properties of structural layers. Thus, if the output data are not well fitted using normal distribution when analyzing the impact of occupant uncertainty, other distributions can be considered.

(5)

The normal fitting of the energy data gives the parameters of the distribution as well as their 95% confidence intervals, which are shown in the following Table 3. The point estimate of the parameters, μ and σ by itself is of limited usefulness because it does not reveal the uncertainty associated with the estimate. On the other hand, a confidence interval is how much uncertainty there is with any particular statistic. It provides an estimated interval, that is, a range of values around the point estimate within which the true value can be expected to fall. A wider range of confidence interval indicates a greater degree of uncertainty of parameters. Thus confidence intervals are widely used to measure uncertainty. Due to the uncertainty of occupant behavior, sampled possible energy consumption using the point estimation of the fitted distribution is unable to adequately reflect energy uncertainty and thus the 95% confidence intervals of these two parameters were Table 2 Shapiro–Wilk test of energy data.

p-value

3.3. Energy uncertainty analysis

Cooling energy

Heating energy

Total

0.2002

0.07764

0.1626

3.3.1. At temporal scales 3.3.1.1. Cooling. Uncertainty of energy performance at temporal scales was calculated for cooling rate. Fig. 10 shows an example of cooling rate difference between two simulations (these two simulations have

Table 3 The normal fitting of energy data.

μ Confidence interval for μ σ Confidence interval for σ

Cooling energy (Wh)

Heating energy (Wh)

Total (Wh)

2,245,200 [2,232,137, 2,258,221] 31,596 [24,671, 43,954]

430,170 [426,861, 433,489] 8029 [6269, 11,170]

2,675,400 [2,664,116, 2,686,592] 27,225 [21,258, 37,874]

9

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Fig. 10. An example of cooling rate difference between two simulations during cooling hours (for percentage difference, only cooling rate > 1100 W (exceed about half of cooling rates) is calculated and presented in this figure).

Fig. 11. An example of heating rate difference between two simulations during heating hours (for percentage difference, only heating rate > 500 W (exceed about half of heating rates) is calculated and presented in this figure).

the highest cooling rate difference) during cooling hours. For percentage difference, only cooling rate > 1100 W (exceed about half of cooling rates) is calculated and presented in this figure. This is because in some cases a small cooling difference during low cooling rate periods leads to a very large percentage difference (e.g. (10 W − 1 W)/ 10 W * 100% = 90%, according to UC index equation). On the contrary, a relatively small percentage difference during relatively high cooling rate periods (e.g. (2000 W − 1200 W)/2000 W * 100% = 40%) has a larger impact ((2000 W − 1200 W) > (10 W − 1 W)) on indoor thermal comfort and energy consumption although its percentage difference is lower (40% < 90%). Therefore, using the latter (40%) is more reasonable when considering UC index than the former to reflect the thermal impact due to occupant uncertainty. It should be noted that only UC at hourly scales was calculated based on a threshold value since there is currently no widely accepted method to judge which value is more suitable. Here 50% of maximum cooling or heating rate was selected as the threshold based on the fact that below this percentage the absolute difference of energy between every two simulations is small (less than 28% of the maximum difference) while the corresponding UC values can be higher than 500%. This threshold value was used to avoid an exaggeration of energy uncertainty percentage since energy uncertainty during high cooling or heating periods appears to have a higher impact on equipment sizing and operation optimization of HVAC systems, although other threshold values may be selected depending on application purpose. For daily, monthly and yearly UC values, no threshold value was introduced since no extreme low heating or cooling value was observed and thus there is no significant fluctuation of UC. After comparing the 25 co-simulations, the UC index for cooling is calculated and its value at hourly scales (hourly maximum difference at the same hour point) is as high as 50.1% (corresponding energy difference is 584.7 Wh), while it is 19.1% at daily scales (daily maximum difference, corresponding energy difference is 3191.6 Wh). The UC index reduces to 6.2% at monthly scales (monthly maximum difference, the corresponding energy difference is 18696.3 Wh). At yearly scales, the UC index is only 1.5% (the corresponding energy difference is 26371.9 Wh).

index at yearly scales is only 1.1% (the corresponding energy difference is 4125.4 Wh). A study by Jacob et al. [28] found that 90% of predicted heating demand results lie in the range of [100, 109] kWh/m2 for a typical office cell in the UK. The uncertainty of their research is much higher than the current study (only shade behavior model is considered). This may be explained by the fact that their research considered more stochastic models (including models of windows, lights, blinds and occupant presence), which in turn produced more uncertainty in occupant behavior and thus had a higher energy performance uncertainty. Other possible reasons may include the orientation difference of the shade behavior models (south vs. west), cooling/heating setpoints and climatic difference [28], which need further investigation. The above cooling and heating analysis gives a clear conclusion. For a long period of time (such as several months), the impact of occupant uncertainty on shade control is reduced significantly (UC index is less than 10%). In such a case, occupant related uncertainty may be ignored (according to required prediction accuracy) when evaluating total energy demand. However, for a short period of time (such as several hours or days), the uncertainty of energy prediction is very high and its influence cannot be ignored. As can be seen in Fig. 4, the SC difference between two random simulations is mainly between about −0.8 to 0.8 for most time of year. This difference directly impacts the transmitted solar radiation and thus hourly/daily cooling and heating energy consumption. Therefore, energy performance at small temporal scales is highly sensitive to occupant behavior while for a long period of time the uncertainty of energy performance may be ignored. 3.3.2. At spatial scales Fig. 12 gives total energy distribution at different spatial scales based on simple random sampling with 1000 runs. It can be seen that after 1000 MC sampling energy data points resemble normal distributions. The horizontal axis means the ratio of each run (annual total energy demand) to the average of 1000 simulation runs. Thus a ratio of 1 indicates the energy demand is equal to the average value and the difference between the maximum and minimum ratios represents the maximum difference (UC index) of energy demand. Therefore, this kind of horizontal axis helps readers easily get UC index. For example, it can be seen that the maximum difference (UC index) for a room is about 7% ((1.04–0.97) × 100%), while as the number of room increases the UC index decreases significantly. For 30 rooms, it can be seen from the figure that UC index is only about 1.6% (1.008–0.992 × 100%). And this value reduces to about 1.4% (1.008–0.994 × 100%) for both 50 and 100 rooms. Thus, annual energy uncertainty from stochastic shade control is not significant at spatial scales of more than 1 room. This means the uncertainty of energy or economic savings from manual

3.3.1.2. Heating. For the heating rate (an example is shown in Fig. 11, these two simulations have the highest heating rate difference), the threshold is selected at 500 W (exceed about half of heating rates). The UC index at hourly scales (hourly maximum difference at the same hour point) is 25.4% (the corresponding energy difference is 171.1 Wh). As temporal scales increase to daily and monthly levels, it reduces to 13.2% (corresponding energy difference is 1043.3 Wh) and 5.9% (the corresponding energy difference is 5962.6 Wh), respectively. The UC 10

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(a) 1 room

(c) 50 rooms

(b) 30 rooms

(d) 100 rooms

Fig. 12. Total energy distribution at different spatial scales based on random sampling with 1000 runs.

shades may be ignored at the building level, which also indicates that a relatively robust performance of manual shades can be achieved when predicting annual energy demand of a whole building. When considering both spatial and temporal scales simultaneously (such as daily or monthly uncertainty at different room levels), the conclusion may be different. Such kind of analysis is complex since the interaction between spatial and temporal parameters needs to be considered and further studies will be conducted in future to address this issue. In general, energy uncertainty at spatial scales is not significant from a long period of time (one year) perspective and the larger a building is, the less annual energy uncertainty it has. This can be explained as follows: as the number of offices increases, there is a tendency to have a sampling of the same normally or near normally distributed occupant behavior (average SC value since the shade behavior model was developed based on the aggregation of different occupant behaviors) and corresponding energy performance. Therefore, the difference (uncertainty) in energy consumption decreases with the increase in the number of offices.

uncertainty, a comparative simulation analysis was conducted. The following analysis assumes that a deviation (for the following question 1 and question 3) or uncertainty (for question 2) value of 5% is the threshold of whether shade behavior model should be considered in simulation. It should be noted that a higher or lower threshold value can also be selected depending on required prediction accuracy. 3.3.3.1. Question 1: When it is important to consider shade behavior models?. For the fully open assumption, it over-predicts annual cooling energy demand by 17.18% (min: 15.02% and max: 19.05%) compared to the shade behavior model and annual heating energy demand was underestimated by 20.33% (min: 16.71% and max: 24.85%). For the overall energy demand, an average overestimation is 12.81%. A higher difference is obtained at lower temporal scales. Similarly, the fully closed assumption also leads to a significant deviation of predicted energy performance. Thus, these two simplified assumptions cannot be used instead of shade behavior model for predicting the energy performance of manual shades. While for the half-open scenario, Fig. 13 gives deviation of annual energy demands between the shade behavior model and the half-open scenario. It can be seen that the deviation is relatively small with a total energy deviation of only 0.2%. For monthly cooling/heating demand,

3.3.3. Discussion In order to provide insights into when it is important to consider shade behavior models and when it is relevant to study the energy 11

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Fig. 13. Deviation of annual energy demands between the shade behavior model and half-open scenario.

(a) Heating

the average deviation is less than 0.6%/1.7%. Thus, monthly and annual energy can be predicted using the half-open scenario. For daily cooling/heating demand, Fig. 14 presents the relationship between deviation and daily energy demands. It can be seen that deviation decreases significantly from about 100% to less than 1% as daily energy demand increases, and for those days that daily energy higher than 50% of the maximum daily value, the deviation is mainly less than 1.5%. If an accurate prediction of low daily energy is required, then the half-open scenario cannot be considered. Otherwise, simplification using half-open mode is reasonable. Therefore, the situation for the daily scale is a little complex and whether daily energy can be predicted using half-open scenario depends on what amount of daily energy (low or high energy demand) is concerned. At the hourly scale, a higher deviation than daily scale is observed with 14.4% of hours being higher than the threshold (5%). Thus, simplified assumptions cannot be used instead of shade behavior model for predicting hourly energy demand. 3.3.3.2. Question 2: When it is relevant to study the energy uncertainty?. Section 3.3.1 has shown that hourly, daily and monthly cooling or heating energy demands of a single room have an uncertainty of higher than 5% and thus should be simulated using shade behavior model rather simplified assumptions. For annual total (heating and cooling) energy demands of a single room, shade behavior model should also be used since the deviation reaches about 7%. For other cases studied in this research, energy uncertainty is relatively small (< 5%). Thus energy savings and economic performance (such as payback periods) of manual shading systems can be evaluated using deterministic models (simplified assumptions) instead of the shade behavior model. However, it should be noted that deterministic shade models should be carefully selected in order to represent average shade behavior patterns (such as half-open in this research) rather than unrealistic assumptions such as fully open or closed for the whole year since these assumptions highly over/underestimate energy demand.

(b) Cooling Fig. 14. Deviation of daily energy demands between the shade behavior model and half-open scenario.

6.25% for heating) to cover the upper limit of cooling/heating load. This amount (> 5%) of over prediction indicates a higher initial cost for HVAC systems due to oversized equipment and thus the shade behavior model needs to be taken into account when sizing a cooling/heating system rather than pessimistic assumptions. While for the half-open scenario, the minimum deviation of cooling/heating rate is less than 0.5%. Thus, half-open shade scenario which represents average behavior patterns can be used instead of shade behavior model for simulating cooling/heating equipment sizing. 4. Limitations The shade behavior model used in this paper was developed based on a representative office building in hot summer and cold winter region of China. Findings of this research may help predict energy uncertainty in similar buildings in this climate region. However, other factors such as building types and climate regions may lead to a different stochastic model and thus different uncertainty effects and different conclusions about these three questions may be obtained. In addition, the relationships between solar shades and light switch/occupancy were not considered in this paper since light switch behavior and occupancy were not monitored during the development of this

3.3.3.3. Question 3: Whether simplified assumptions can be used for equipment sizing?. Simulation results show that shade always fully open (the pessimistic condition for cooling design) over-predicts maximum cooling load by an average percentage of 13.19% (min: 5.79% and max: 19.40%) compared to repeated simulation runs. For maximum heating load, shade always fully closed (the pessimistic condition for heating design) over-predicts by an average percentage of 8.33% (min: 6.25% and max: 10.44%). For equipment sizing, the minimum deviation between the shade model and simplified pessimistic assumptions should be considered (5.79% for cooling and 12

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solar shade behavior model, and thus a scheduled occupancy and a lighting intensity of 11 W/m2 were considered in simulation according to design standard in this climate region. This simplification may also lead to a biased energy prediction. Due to the limitations mentioned above, the findings of this paper may not be directly applicable to other buildings or climate regions. Nevertheless, the methodology used for developing shade behavior models and for energy uncertainty analysis is not building or climate-specific and thus is applicable to other buildings and climate regions.

Acknowledgement This work was supported by Natural Science Foundation of Zhejiang Province under Grant No. LY18E080012, National Natural Science Foundation of China under Grant No. 51878358 and National Key Technology R&D Program of the Ministry of Science and Technology under Grant 2013BAJ10B06. The author also would like to thank the K.C.Wong Magna Fund in Ningbo University. References

5. Conclusions

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This paper investigates the impact of occupant uncertainty of solar shade control on building energy performance at temporal and spatial scales as well as performance gaps between simplified shade assumptions and shade behavior model. A previously developed shade behavior model and was adopted in this paper and repeated co-simulation runs were conducted for uncertainty analysis and compared with simplified shade assumptions. Results show that the uncertainties of energy performance at the hourly scale are 50.1% and 25.4% for cooling and heating, respectively, indicating a significant impact of occupant behavior at small temporal scales. While for the annual scale, it reduces significantly. Similar trend (energy uncertainty reduces as spatial scale increases) was observed at spatial scales. In general, energy uncertainty should be considered when evaluating the energy performance of a single room at hourly, daily, monthly and total annual scales. In other cases, shade behavior and related energy uncertainty may be ignored. Regarding the question of when to use shade behavior model, the comparison shows that fully open and closed assumptions lead to a significant deviation of predicted energy performance, and thus it is not suitable to use these two assumptions for simulating energy performance of manual shades. While for the simplified model (half-open in this research) that represent average shade behavior patterns, it can be used to evaluate annual energy demand of office buildings (usually have more than 1 office room) instead of a shade behavior model. Commonly used pessimistic assumptions on manual shades (fully open in summer and fully closed in winter) over-predict maximum cooling/heating rate by more than 5% and thus they are not suitable for cooling/heating equipment sizing instead of a shade behavior model. If a simplified shade assumption (such as half-open in this research) is capable of representing average shade behavior patterns, this simplification is an alternative to complex shade behavior model for sizing cooling/heating equipment. The findings of this research provide insights into when it is important to consider shade behavior models and when simplified shade assumptions can be used, and contribute to improvements in unrealistic modeling assumptions of manual shades (such as fully open in winter and fully closed in summer) currently adopted by building energy standards/codes as well as a more accurate building energy prediction and cooling/heating equipment sizing. The combination of both spatial and temporal scales simultaneously (consider the interaction between spatial and temporal parameters) may have other impacts and further studies will be conducted in future to address this issue. Beside behavior uncertainty, inter-occupant diversity is another important factor influencing occupant behavior and resulting energy performance. Meanwhile, the relationship between occupancy/light switch and shade adjustment was neglected in this research. Therefore, more field measurements on a larger number of occupants in different building types and climate regions are required to further investigate occupant uncertainty/diversity and its influence on building energy performance. Declaration of Competing Interest The author declares no conflict of interest. 13

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