# Uncertainty_of_Energy_Consumption_Assessment_of_Domestic_Buildings民用建筑能耗评估的不确定性

Aalborg Universitet Uncertainty of Energy Consumption Assessment of Domestic Buildings Brohus, Henrik; Heiselberg, Per Kvols; Simonsen, A.; S?rensen, K.C. Published in: e-nova Internationaler Kongress 2009 Publication date: 2009 Document Version Publisher s PDF, also known as Version of record Link to publication from Aalborg University Citation for published version (APA): Brohus, H., Heiselberg, P., Simonsen, A., however, it is also found that significant differences may occur between calculated and measured energy consumption due to the spread and due to the fact that the result can only be determined with a certain probability. It is found that occupants’ behaviour is the major contributor to the variance of the energy consumption. INTRODUCTION In order to assess the influence of energy reduction initiatives, to determine the expected annual cost, to calculate life cycle cost, emission impact, etc. it is crucial to assess the energy consumption reasonably accurate. As buildings account for a substantial part of the overall energy consumption, as the energy prices increase due to lack of resources, and climate change consideration forces governments to control energy consumption more tightly it is increasingly important to be able to determine the actual energy consumption. However, several investigations reveal significant uncertainties in the estimation of energy consumption in buildings. Deviation between the calculated energy consumption and the actual energy consumption may exceed 100 % in extreme cases. This raises an important question as to the expected level of uncertainty in energy consumption assessment of buildings. The paper presents an empirical and theoretical investigation of the uncertainty of energy consumption assessment of domestic buildings. The energy consumption of a number of almost identical domestic buildings in Denmark is calculated and compared with the corresponding measured energy consumption. The uncertainty is determined by stochastic modelling using input distributions found by literature study, industry guidelines, measurements and a number of simple assumptions. The purpose of the work is to improve the understanding of uncertainty in building energy consumption calculations. As part of it the most important input parameters are identified and the total output variance is apportioned to the input parameters. Furthermore, the expected level of uncertainty is examined and expressed in terms of the coefficient of variation. The aim is to be able to improve the estimation of energy consumption and if possible reduce the uncertainty and for the remaining part, at the least, be able to quantify the uncertainty and, thus, to provide building owners and society at large with more detailed and accurate information. This could also be seen as a step towards a practical application where a reduced set of stochastic input parameters facilitates wider application of Monte Carlo simulation. In the following the building case is presented after which the measurements and the corresponding simulations (building model and Monte Carlo simulations) are presented. Finally, comparisons and conclusions are made. METHOD AND RESULTS Building description The building case applied for the measurements and simulations comprises eight almost similar red- bricked semi-detached houses located in the western part of Denmark, see Figures 1 - 4. The conditioned area is 149.2 m2 with 0.35 m cavity walls (0.11 m bricks - 0.125 m thermal insulation – 0.11 m bricks). Room height is 2.37 m. The U-values for ceiling, floor and walls are 0.19, 0.36 and 0.32 W/(m2K), respectively. The buildings are naturally ventilated and heated by means of district heating. Figure 1 Air photograph of the area around the eight Danish residential buildings applied in the present work. The buildings are part of the built-up area shown inside the circle. Figure 2 Photo of one of the eight residential buildings. Figure 3 Horizontal plan of one of the building types. Measurements in cm. Figure 4 Sectional view of building. Measurements A number of detailed measurements are made on the buildings both to obtain detailed knowledge on the building constructions, occupants’ behaviour and actual energy consumption, but also to be able to model the buildings properly. Figure 5 Equipment applied for the blower door pressure test to assess the infiltration and leakage of the buildings. The building leakage is determined by means of a standard blower door pressure test with pressure differences of 50 Pa, see Figure 5. The blower door test is combined with tracer gas measurements to supplement the knowledge of the overall leakage area with an investigation of the leakage distribution. The leakage information is used to determine the air infiltration and natural ventilation. Internal temperature is measured to assess the occupants’ preferences and determine the heating set- point. The temperature is measured at several locations as a function of time to obtain information on daily variation and general temperature swings. Time-dependent temperature measurement may also reveal information on window and door opening. Weather data are collected by local external temperature measurements and also by collecting data from the nearest local meteo station: wind speed, wind direction, external air temperature, relative humidity, atmospheric pressure, cloud cover and global solar radiation. A questionnaire is used to collect information on occupant number and age, occupied period, bathing habits, use of computers, TV, appliances, etc. This is combined with a registration of the use of district heating, water and electricity (readings of the meters in each house). Table 1 provides some statistics on selected main findings. Table 1 Results from measurements (8 buildings). μ is the mean value and, σ is the standard deviation. Conditioned space 149.2 m2. 2005 is reported to be a “typical year” according to the occupants. Measurement Unit μ σ Infiltration (leakage) l/(s·m2) @ 50Pa 3.00 0.23 Internal air temperature set-point °C 22.19 1.03 Internal heat load, appliances W/m2 (time average) 2.93 1.21 Internal heat load, occupants W/m2 (time average) 1.11 0.56 2005 total water consumption m3/year 125.3 41.2 2005 electricity consumption kWh/(m2·year) (kWh/year) 27.3 (4,079) 11.4 (1,697) 2005 district heating consumption kWh/( m2·year) (kWh/year) 73.0 (10,886) 16.6 (2,480) Simulations The building simulations including the determination of the energy consumption are made by means of the hygrothermal building simulation programme BSim (version 2007) which is developed by the Danish Building Research Institute (Wittchen et al., 2008). The layout of the building model is shown in Figure 6. Figure 6 Building model applied for the hygrothermal building simulations using the programme BSim (Wittchen et al., 2008). The present work on simulations comprises the determination of proper boundary conditions for the building simulation programme including input distributions for the stochastic parameters. To determine what parameters to treat stochastic and what to consider deterministic, an initial screening sensitivity analysis is performed. After the screening analysis a more elaborate quantitative sensitivity analysis is undertaken for the most important parameters to apportion the output variability on the input parameters. To include a proper description of the natural ventilation and infiltration Computational Fluid Dynamics (CFD) and multizone modelling are applied. The CFD simulations (by means of the programme Flovent 6.1 using the k-ε turbulence model) are used to determine the wind pressure distribution around the buildings for different wind directions to get the Cp-values, see Figure 7. Due to the building location beside some plantation and bushes the corresponding permeability is included in the investigation. The CFD calculations reveal substantial local variation of the wind pressure and, thus, significantly varying driving forces as to air infiltration and natural ventilation. Figure 7 CFD simulation of wind pressure distribution around buildings (Flovent). Multizone modelling (using the programme COMIS 3.1) applies the leakage information together with the pressure distribution, in shape of Cp-values, to determine the air change rate as a function of the wind speed, wind direction, external and internal densities. Two overall classes of sensitivity analysis exist, namely local and global analysis. The typical local analysis may usually comprise variation of one variable at a time e.g. by computing partial derivatives or changing a parameter within certain limits all other things being equal. A global sensitivity analysis is characterised by evaluating individual factors varying all other factors as well. Idealistically, the sensitivity analysis should quantify and apportion the total uncertainty related to the model applied for the energy calculation. However, due to the very high number of potential important parameters this procedure is usually not possible in practise. Thus, a screening method is applied in stead to identify the parameter subset the controls most of the output variability including a ranking of the parameters. This could be seen either as a standalone investigation or as part of a more elaborate work where the most important parameters are identified at the initial stage for further investigation. The screening method of Elementary Effects (Morris, 1991; Saltelli et al., 2000) is applied in this work. The method, which can be seen as an extension of a derivative-based screening method, can be characterised as a screening method with global characteristics. The method has been applied in several areas of building sciences e.g. natural night ventilation (Breesch and Janssens, 2004).and thermal building simulation (De Wit, 1997). The method determines the so-called elementary effect EE of a model y = y(x1,…,xk) with input factors xi. The Elementary Effect for the ith input factor in a point x is () ()() Δ ?Δ+ = +?kkiii k xxyxxxxxxy xxEE ,,,,,,,,, ,, 11121 1 KKK K (1) A number of elementary effects EEi of each factor are calculated within the factor’s range of variation. The method comprises a number of individually randomised one-factor-at-a-time simulations where all factors are varied within their input space in a way that spans the entire input space to form an approximate global sensitivity analysis (Morris, 1991; Saltelli et al., 2000). The model sensitivity to each factor is evaluated by the mean value and the standard deviation of the elementary effects ∑ = = r i i rEE 1 * μ (2) () ∑ = ?= r i i rEE 1 2 μσ (3) where μ* is the mean value of the absolute values of the elementary effects determining if the factor is important, and σ is the standard deviation of the elementary effects which is a measure of the sum of all interactions of xi with other factors and of all its nonlinear effects. r is the number of elementary effects investigated for each factor. One of the most important activities in simulation work is the determination of input distributions. When proper distributions are found they can be reused as long as the underlying data does not change. Some input parameters may be mutually correlated which, in theory, requires that measures of mutual correlation should be established and applied in the simulations. In practise correlation is most often disregarded due to the difficulties of both finding and applying the correlations. In the present screening analysis input distributions are established for 13 input parameters applied in the building simulation and energy calculations. The distributions are determined using a combination of measurements, questionnaires, literature, theoretical considerations, and also educated guesses depending on the accessibility of material in each case, see Table 4. Due to lack of information the input parameters are assumed to be independent, i.e. uncorrelated. This assumption is discussed later on. The results are presented in Figure 8 where each input factor is shown as a function of μ* and σ. The parameters are summarised in Table 4 and ranked according to importance. Figure 8 Screening sensitivity analysis performed using the method of elementary analysis based on 140 parameter combinations. The location of the four most important parameters are marked as circles the rest being shown as crosses, see Table 4. Based on the results from the screening analysis a reduced number of stochastic input parameters are chosen for further investigation, see Table 2. In the screening analysis infiltration and natural ventilation are treated rather simplified, thus, even though they are not ranked as the highest they are included in the quantitative analysis using a somewhat more detailed model in BSim, see formula (4), that considers the influence of wind and temperature ()vcttcnn v t eit p ?+??+= 0 (4) where n is the air change rate [h-1], n0 is the basic air change rate [h-1], ct is the temperature factor [1/(h·K)], ti is the internal temperature [°C], te is the external temperature [°C], tp is the temperature exponent [-], cv is the wind factor [s/(h·m)], and v is the wind speed [m/s] (Wittchen et al., 2008). As to weather data the Danish DRY (Design Reference Year) is applied. Multizone modelling using input from the local meteo station from 2005 and 2006, respectively, are compared with models using the Danish DRY. It is found that the DRY provides a reasonable good description of the infiltration and natural ventilation in this case. The quantitative sensitivity analysis is based on regression analysis. PEAR (Pearson product moment correlation coefficient) and SRC (Standardised Regression Coefficient) and their rank transformations SPEA (Spearman coefficient) and SRRC (Standardised Rank Regression Coefficient) are applied. Whereas PEAR is suited for linear models, SPEA is a good measure of correlation in case of non-linear models. Especially, the SPEA coefficient is assumed to work well in this case and taken as the most reliable quantitative measure of the sensitivity, i.e. how the output uncertainty is apportioned on the input parameters (Saltelli et al., 2000). Table 3 presents the results. Table 2 Input distributions for the detailed sensitivity and the uncertainty analysis Type N is a truncated normal distribution and E is a truncated exponential distribution. Interval defines distribution boundaries of the 99% confidence interval,μ is mean value and σ is standard deviation (Normal distribution) and d is a positive displacement of the distribution (Exponential) Input parameter Distribution Name Unit Type Interval; μ; σ or d Set-point space heating °C N 20 - 25; 22.27; 0.75 Infiltration / Nat. vent. Basic air change rate, n0 Temperature exponent, tp Wind factor, cv 1/h - s/(h·m) N N N 1.0 - 1.2; 1.1; 0.033 0.5 – 0.6; 0.55; 0.017 0.034 – 0.064; 0.058; 0.007 Occupied period h/day