Regression models for predicting UK office building ...

Energy and Buildings 59 (2013) 214–227

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Regression models for predicting UK office building energy consumption from heating and cooling demands Ivan Korolija a,∗ , Yi Zhang a , Ljiljana Marjanovic-Halburd b , Victor I. Hanby a a b

Institute of Energy and Sustainable Development, De Montfort University, Queens Building, The Gateway, Leicester, LE1 9BH, UK Bartlett School of Graduate Studies, University College London, Central House, 14 Upper Woburn Place, London, WC1H 0NN, UK

a r t i c l e

i n f o

Article history: Received 6 November 2012 Accepted 12 December 2012 Keywords: UK office buildings HVAC systems Regression models Parameters Energy performance

a b s t r a c t This paper described the development of regression models which are able to predict office building annual heating, cooling and auxiliary energy requirements for different HVAC systems as a function of office building heating and cooling demands. In order to represent the office building stock, a large number of building parameters were explored such as built forms, fabrics, glazing levels and orientation. Selected parameters were combined into a large set of office building models (3840 in total). As different HVAC systems have different energy requirements when responding to same building demands, each of the 3840 models were further coupled with five HVAC systems: VAV, CAV, fan-coil system with dedicated air (FC), and two chilled ceiling systems with dedicated air, radiator heating and either embedded pipes (EMB) or exposed aluminium panels (ALU). In total 23,040 possible scenarios were created and simulated using EnergyPlus software. The annual heating and cooling demands and their HVAC system’s heating, cooling and auxiliary energy requirements were normalised per floor area and fitted to two groups of statistical models. Outputs from the regression analysis were evaluated by inspecting models best fit parameter values and goodness of fit. Based on the described analysis, the specific regression models were recommended. © 2012 Elsevier B.V. All rights reserved.

1. Introduction The overall environmental impact of any building in terms of Carbon emission depends on the energy consumed by its HVAC system and the fuel type. Energy flow of principal HVAC system within buildings is presented in Fig. 1. HVAC system is usually divided into two parts, primary HVAC system and secondary HVAC system. Primary HVAC system is composed of equipment such as boilers and chillers, which generates heating/cooling energy (Qh , Qc ) from primary fuels and electricity. Heating/cooling energy is then distributed in a building by a secondary HVAC system in respond to the building’s heating/cooling demand. During this process, secondary HVAC system requires additional energy input, i.e. auxiliary energy (Qa ), to operate mechanical components of the system such as pumps, fans and control gears. Building heating/cooling demand is the amount of energy required to maintain desired indoor conditions. It is calculated by taking into account its heat gains and heat losses such as

∗ Corresponding author. Tel.: +44 0 116 207 8836; fax: +44 0 116 257 7977. E-mail addresses: [email protected], [email protected] (I. Korolija), [email protected] (Y. Zhang), [email protected] (L. Marjanovic-Halburd), [email protected] (V.I. Hanby). 0378-7788/$ – see front matter © 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.enbuild.2012.12.005

transmission heat gains/losses through building envelope elements, solar heat gains through fenestration areas, internal heat gains from occupant, artificial lighting and electrical equipment, infiltration air heat gains/losses, and fresh air ventilation heat gains/losses. Building heating/cooling demand depends on various building parameters such as building fabrics, glazing percentage and glazing properties, occupancy pattern, level of internal gains, etc. Although heating/cooling demand calculation is often used in practice for building’s energy performance evaluation, it unnecessarily reflects the actual energy consumption of the building in response to heating/cooling demand. This is because different HVAC systems have different energy requirements when responding to the same building heating/cooling demand. Such behaviour is predominantly affected by the way a particular HVAC system is designed and operated to match the characteristics of the building. In theory, an ideal HVAC system must meet the following criteria [1] in addition to the usual requirement for minimising circulation cost of the heating/cooling media:

1. The system has the ability to minimize outside air load while maintaining minimum fresh air supply to each zone as required by standards. 2. The system has the ability to eliminate simultaneous operation of cooling and heating sources, e.g. cooling at the main deck while

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Fig. 1. Energy flow of principal HVAC system within buildings.

reheating at the terminals; and to eliminate the occurrence of heating in the presence of cooling demand and vice versa. 3. The system can take advantage of free cooling when it is available. 4. The system can minimize occurrence of simultaneous heating and cooling demand between different zones, by the means of inter-zonal airflow or heat exchange. The ability of an HVAC system meeting the above criteria varies in a complex way. For example, systems which cover building demands by using only air as the heating/cooling medium (all-air systems such as VAV and CAV) can benefit from free cooling by allowing increased fresh air intake. However, all-air systems often suffer from simultaneous heating and cooling, and/or the inability for minimising fresh air load. Air–water and all-water systems (e.g. fan-coil based systems), on the other hand, are less prone to simultaneous heating and cooling, but having limited option for free cooling. It is not often possible to tell which HVAC system is a better option for a building without running detailed simulations. Detailed simulation of HVAC systems is usually complex and requires large numbers of input parameters to be specified in order to calculate the desired outputs. These input parameters include HVAC system components, connections, control system and set points, and operating schedules, amongst others. As a result, the complexity of the existing tools has been identified by Ellis and Mathews [2] as the biggest obstacle to wider adoption of detailed simulation in practice, despite the potential this method offers in achieving better building energy efficiency. Ellis and Mathews further suggested that thermal efficiency of buildings and the selection of HVAC systems are two areas that can benefit from simplified tools, which will simplify input complexity by identifying and focusing on critical parameters and defining them in architectural terms. In achieving these, the simpler tools might be more appropriate for the wide spread use by professionals in built environment especially at the conceptual design stage. Similar views are expressed by others, for example, Trcka and Hensen [3], who suggested that simple HVAC system performance representation can be used “when only load predictions are considered, and/or when energy saving options are investigated” in conceptual design stage. In addition to the benefit of simplifying modelling process, building models without detailed HVAC system models can simulate mush faster, too. Based on the simulation times of the models used in this research, Fig. 2 shows the ratio of simulation time of buildings with detailed HVAC system models in comparison with buildings without. In average detailed HVAC models take almost twice as long to simulate compared to the same building model. In the worst case, the simulation time can increase by three and a half folds. Simulation time is critical when multiple simulation runs are required in search of a better design solution. In this case, a simple model that can reliably predict HVAC system energy consumption from building demand can be used to accelerate optimisation of building parameters in early design stage.

Fig. 2. Simulation time ratio: detailed HVAC system model vs. building heating/cooling demand.

In short, simplified models for predicting secondary HVAC systems heating, cooling and auxiliary energy requirements as a function of building heating and cooling demand can be useful in several situations. For example, during early design stage when decisions, which have high impact on energy performance of a building, have to be made with limited information, simplified models can save time and provide a fast and effective way to explore different HVAC systems and their impact on building energy consumption and greenhouse gas emissions. In addition, simplified model can be also useful in refurbishment projects, especially for HVAC systems refits. The aim of this paper is to investigate the correlation between buildings’ heating and cooling demand and the energy requirement for different (secondary) HVAC systems, in order to create simplified models of HVAC systems. We will show that single or bi-variate regression models will be able to provide prediction of HVAC system energy requirement with sufficient accuracy for typical UK office buildings. 2. Regression models for HVAC systems Regression models have been widely used to describe performance characteristics of HVAC system components, such as fans and pumps, chillers, coils and so forth. Attempts to using regression models studying building and HVAC systems have also been reported. Sander et al. [4] developed simplified regression models which predict building annual heating and cooling energy requirements for a building equipped with a generic variable air volume (VAV) air-conditioning system based on location, building envelope characteristics and internal gains. The outputs form 5400 building simulations for 25 Canadian locations were used as regression analysis inputs. The accuracy of developed models was quite high with a difference between model predictions and simulation outputs within 10% in most cases, except for buildings with very low either heating or cooling requirements. In order to predict annual energy consumption of high rise fully air conditioned office buildings in Hong Kong [5,6], a generic office building was simulated in the DOE-2 energy simulation software by varying 62 input design parameters related to the building demand, HVAC system and HVAC refrigeration plant. Authors reported that from 62 input parameters, 28 correlate well with the predicted annual energy consumption. After performing a sensitivity analysis, 12 of 28 input parameters were considered to have the most significant impact on

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energy consumption and they were used in the regression analysis. A regression model based on the 12 parameters was able to predict building annual energy consumption with a high accuracy, having the coefficient of determination close to 0.99. Lam et al. [7] extended this study by including an additional four climate regions in China. The new model was also based on 12 parameters and was also capable to predict building annual energy consumption with a coefficient of determination between 0.89 and 0.97, depending on the climate. Bansal and Bhattacharya [8] also used the detailed simulation results for developing simplified equations which can predict a single zone building annual energy demand as well as maximum heating and cooling loads for the central India weather conditions. Equations were presented as a function of either the insulation thickness or the surface to volume ratio. Simplified equations presented in the paper provided a very good fit with a lowest coefficient of determination above 0.9. Ouarghi et al. [9] presented a simplified method, based on regression analysis, for office building annual cooling and total energy use in Kuwait and Tunis. Exemplar office buildings of various shapes were modelled using DOE-2 with typical office occupancy patterns and schedules with the same HVAC system in all cases: VAV with electric re-heat for both heating and cooling. The research found a strong correlation between annual total energy use and building relative compactness (“cubelikeness”), window to wall ratio and the glazing solar heat gain coefficient for cooling dominated climates. Jaffal et al. [10] developed simple polynomial functions which predict the annual energy demand as a function of building envelope parameters for both cold and moderate climate in France. Polynomial functions were based on the 11 most influential envelope parameters, which can be chosen in the design stage, and on environmental inputs. According to authors, the advantage of polynomial functions lies in simplicity, speed and precision in evaluating the energy saving potentials of various building elements, individual or in combination, for which dynamic simulation would be very time consuming. Abovementioned researches confirm that regression equation models are adequate alternative to complex building simulation tools for predicting HVAC system energy consumption and building demands, particularly during the early design stage when different designs need to be explored and evaluated. Regression equation models can provide precise and accurate results in an easier and faster way than building energy simulation tools, especially if they are developed from a comprehensive, broad and accurate input dataset. The aim of this paper is to develop regression models for various commonly used HVAC systems, for the purpose of quick prediction of HVAC system energy requirement from building heating and cooling energy demand. We focus on the office buildings in the UK in this study. The models to be developed will therefore be able to predict annual heating, cooling and auxiliary energy requirements of different secondary HVAC systems as a function of annual heating and cooling demands of office buildings. Using the annual heating and cooling demands of office buildings as the independent variables is an effective method to capture the dynamics of the type of building, yet significantly simplifies the resultant regression model. This method relies on a good sample of the type of building in question, so that diverse characteristics of the buildings’ thermal and occupancy properties can be covered in the model. Energy requirements of different HVAC systems will be modelled with the sample of buildings, using detailed simulation. Regression model will subsequently be created from the simulation results. In the following sections, we first discuss the creation of detailed models for buildings with different HVAC systems. Parametric simulations were then performed using EnergyPlus and the annual energy requirements were calculated. Regression models were selected and fitted to the simulation results, to predict HVAC

system energy consumption as a function of building heating and cooling demands. Accuracy of the regression models was established using statistical analysis. 3. Building and HVAC system models A sample of UK office building models and typical HVAC systems were created to provide a good coverage of the existing building stock. 3.1. Building models The selection of building model parameters is discussed in a separate paper [11]. The key information of the selected building models (simulation model archetypes) is provided here for the convenience of the readers. Based on the outputs from the ‘four towns’ survey [12] and proposed non-domestic built form classification [13], four office building archetype models were developed to represent the common office building built forms (Fig. 3). Types 1–4 represent open-plan side-lit buildings (OD), cellular side-lit buildings (CS), artificially lit open-plan buildings (OA), and composite side-lit cellular around artificially lit open plan buildings (CDO). The selected built forms correspond to over 65% of the total floor area of non-domestic buildings in the UK. Each storey in office building models is composed of office areas and common spaces, which are represented as separate thermal zones. Common spaces (zone 2 in diagrams in Fig. 3) represent areas such as reception areas, toilets, tea kitchens, circulation space, etc. Floor area of the each storey is roughly the same in all models and amounts around 510 m2 . Building types one and two are narrow plan buildings with a 32 m by 16 m footprint. Both buildings are side-lit and differ only in the office space arrangement. The office space in the building type one consists of one large open space (zone 1), while the office space in the building type two is divided by corridor into two zones of cellular offices (zone 1a and zone 1b). Building models three and four are square buildings with a 22.5 m by 22.5 m footprint. In the building model three, the floor plane is dominated by a single large open-plan office area (zone 1). The last model, building type four, has each storey divided into four zones. The main zone, zone 1a, has an open-plan office arrangement, while zones 1b and 1c represents cellular office layout. Zone 2, as in the previous building types, is reserved for common areas. All four building types are three storeys high with floor to ceiling height of 3.5 m. In order to represent a range of existing buildings as well as new buildings, each of these four building forms were coupled with five types of building fabrics. Building fabric type 1 (BF1) represents buildings with minimum or no insulation at all. Building fabric types 2, 3 and 4 (BF2, BF3 and BF4) represent buildings constructed according to Part L 1990 [14], Part L 1995 [15] and Part L 2002 [16] Building Regulations respectively, while the building type 5 (BF5) represent buildings build according to the current UK Best Practice. The U-values of major building elements, which are external wall, flat roof, ground floor and glazing, for each of these five building fabric types can be seen in Table 1.

Table 1 Building fabrics (BF) U-values. Building element

External wall Flat roof Ground floor Glazing

U-value [W/(m2 K)] BF1

BF2

BF3

BF4

BF5

1.62 2.48 1.03 5.87

0.54 0.43 0.82 3.15

0.40 0.31 0.34 2.73

0.32 0.17 0.25 1.92

0.24 0.14 0.14 1.78

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Fig. 3. Office building built forms.

Building fabric type BF1 corresponds to office buildings built after the World War II up until mid-1960’s. Building fabric type BF2 corresponds to office buildings built after mid-1960’s up until 1990’s whilst building fabric type BF3 corresponds to office buildings built during 1990’s. Building fabric type BF4 corresponds to buildings built 2002 onwards. Put together, these building fabric types represent around 75% of the office building stock in terms of its age. Besides the building form and fabrics, the size of the fenestration areas was also varied. Three levels of glazing ratios were included in the study: 25%, 50% and 75%. Furthermore, two measures of reducing solar heat gains were considered: placing horizontal overhangs (20 cm above a window with a depth of 0.7 m) and using reflective glazing. Both standard and reflective glazing properties, such as solar heat gain coefficient and light transmittance factor, are presented in Table 2. Daylight control was also implemented as a possible design option in order to reduce internal heat gains and artificial lighting electricity consumption. Finally, the orientation of buildings was also investigated by rotating the buildings at 45◦ intervals. In addition to building parameters, the environment and activity related parameters differed according to building type. These parameters are summarised in Table 3 and include: zone temperature heating and cooling setpoints; fresh air ventilation rate; occupant density and metabolic rate; internal heat gains from office equipment; and internal heat gains from artificial lighting. The values are chosen in accordance with various standards and good practice guides such as relevant ASHRAE standards and Handbooks [17–21], European standards [22–24] and CIBSE Guidebooks [25,26]. In addition, since the function of HVAC system is to provide and maintain satisfactory indoor environment conditions, it is important to mention that the only indoor air parameter which is precisely controlled is an air dry-bulb temperature and that a humidity control is excluded from the study. By combining the above building design parameters, 3840 different scenarios can be created, each of which represents one non-specific, yet typical, UK office building.

3.2. HVAC system models Five HVAC system models were investigated in this study. These are: variable air volume system (VAV), constant air volume system (CAV), fan-coil system with dedicated air (FC), chilled ceiling system with embedded pipes and radiator heating (EMB), and chilled ceiling system with aluminium panels and radiator heating (ALU). In all the above mentioned systems it was assumed that the primary HVAC system (not modelled) is capable of meeting energy demand of the secondary system at the desired temperature at all times. The hot water temperature delivered from the primary system was set to 82 ◦ C in all systems studied, and the chilled water supply temperature was set to 7 ◦ C except in the case of the chilled ceiling system where it was set to 14 ◦ C. The VAV System (Fig. 4) varies its supply air volume rate while keeping a supply air temperature constant to match the reduction of space load during part-load and so maintain a predetermined zone air dry-bulb temperature while conserving fan power at

Fig. 4. Variable air volume (VAV) system schematic.

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Table 2 Regular/reflective glazing properties. Glazing type

BF1

SHGC Light transmittance U-value [W/(m2 K)]

BF2

BF3

BF4

BF5

Reg.

Ref.

Reg.

Ref.

Reg.

Ref.

Reg.

Ref.

Reg.

Ref.

0.847 0.892 5.87

0.505 0.335 5.81

0.74 0.801 3.15

0.435 0.312 3.13

0.742 0.801 2.73

0.432 0.312 2.71

0.631 0.761 1.92

0.362 0.296 1.91

0.637 0.761 1.78

0.365 0.296 1.77

Table 3 Office building environment and activity related parameters.

Heating/cooling temperature setpoint [◦ C] Fresh air ventilation rates [l/person] Maximum occupant density [m2 /person] Metabolic rate [W/person] Equipment heat gain [W/m2 ] Lighting power density [W/m2 ]

Open plan office space

Cellular office space

Common areas

22/24 10 9 125 15 12

22/24 10 14 125 10 12

20/26 10 2.25 145 2 3.4

reduced volume flows. The main heating (HC) and cooling (CC) coils are controlled according to the supply air temperature (tsa ) which is set to 16 ◦ C. Preconditioned air is delivered to the zones through the air reheating boxes where it, if there is a need, is additionally heated. Each air reheat box is composed of a damper and hot water coil both operated by zone temperature sensor (tza ) with a reverse damper action. This means that in the heating mode it starts with minimum air flow and minimum hot water flow. With a load increment the hot water flow is increased until it reaches maximum flow, then the air damper starts to open to meet the load. In contrast to the VAV system the CAV system (Fig. 5) keeps the air volume flow rate constant while varying its supply air temperature (tsa ) from 16 ◦ C to 22 ◦ C according to the cooling demand of the warmest zone. This strategy minimizes zone reheat coil energy or overcooling. The amount of the outdoor air in both systems is controlled via an outdoor air mixing box equipped with an economizer which mixes return air and outdoor air in proportion to meet the mixed air temperature setpoint (tma ). The mixed air temperature is lower than supply air temperature by around one degree centigrade because the supply air stream, by passing over the fan motor, absorbs the fan dissipated heat. By using the economizer unit the amount of outdoor air is increased whenever it is possible to benefit from free cooling. The fan-coil system shown in Fig. 6 is composed of zones with four-pipe fan-coils and an air handing unit which distributes 100% fresh air, which is enough to meet fresh air requirements only. Fresh

air supply temperature is controlled to vary the supply air temperature between 16 ◦ C and 22 ◦ C in order to maximise the benefits of free cooling. However, free cooling is very limited due to a significantly lower supply air volume flow rate in comparison with the VAV and CAV systems. Each fan-coil unit is composed of a fan which recirculates room air, along with heating and cooling coils. The indoor temperature is controlled according to a local thermostat (tza ) which varies the water flow rate through the heating or cooling coil in response to the zone demand. In cases when there is no need for heating or cooling the fan-coil fan is switched off. The outdoor air is pre-treated using a heat recovery unit (HRU) with 65% effectiveness and this exchanges heat between the supply air stream and the exhaust air stream. The chilled ceiling system (Fig. 7) is composed of the following elements: a chilled ceiling element; an air handling unit equipped with a heat recovery unit which delivers only fresh air (the air side is controlled in the same way as in the fan-coil system); and radiators to meet heating demand. Due to the way this system delivers cooling and maintains comfort (partially by radiation and partially by convection), the zone cooling temperature setpoint was increased by 2 ◦ C; from 24 ◦ C to 26 ◦ C in offices and from 26 ◦ C to 28 ◦ C in common areas. Two types of chilled ceiling element were investigated in this research: a thermally lightweight element (aluminium panel), and a heavyweight application (chilled water pipes embedded directly into the concrete ceiling).

Fig. 5. Constant air volume (CAV) system schematic.

Fig. 6. Fan-coil with fresh air system schematic.

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weather file) were performed with EnergyPlus v7 (32-bit Linux version), while the HVAC system and equipment were automatically sized by using summer and winter design days. For a large parametric study like such, managing simulation runs and results would be difficult without a specialized tool. Fig. 8 shows the parameter tree encoded in jEPlus, a Java based EnergyPlus shell suitable to manage and run large and complex parametric simulations [27]. jEPlus allows users to define model parameters in a graphical user interface, and then automatically creates and run EnergyPlus simulations thus decreasing the number of input files which the user has to prepare. In this particular research, 49 input files plus 1 weather file, were required to run 23,040 EnergyPlus simulations. Zhang and Korolija [28] gave more in depth explanation of setting and running large parametric EnergyPlus study with a small number of input files by using jEPlus and EP-Macro. Fig. 7. Chilled ceiling with fresh air and radiator heating system schematic.

4. Parametric simulation 4.1. Simulation environment Coupling 3840 building models with five HVAC systems plus the ideal loads system (see Fig. 8) creates 23,040 possible scenarios, each of which represents one air-conditioned building. Annual simulations using London’s climatic information (London-Gatwick

4.2. Simulation results Selected outputs from 23,040 EnergyPlus simulations, such as HVAC systems annual cooling/heating energy requirements as well as HVAC system annual auxiliary requirements, normalised per floor area, were analysed against building cooling and/or heating demand. Fig. 9 presents HVAC systems cooling energy consumption as a function of building cooling demand whilst Fig. 10 presents HVAC systems heating energy consumption as a function of building heating demand.

Fig. 8. Parameter tree (the ‘internal source’ parameter refers to a type of hydronic equipment installed in a ceiling construction element).

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Fig. 9. HVAC system cooling energy requirement vs. building cooling demand.

The results presented in Fig. 9 and Fig. 10 show that both HVAC system cooling and heating requirements are in strong correlation with building cooling and heating demand, respectively. For HVAC system auxiliary energy consumption, however, the correlation with building heating and cooling demand is less apparent. Fig. 11 plots the auxiliary energy consumption of each case against the sum of heating and cooling demand. Table 4 presents the average number of hours per year when the heating/cooling setpoint was not met during the occupied hours by each of the five studied HVAC systems. The results confirm that the HVAC systems were sized properly and that they are capable of providing the desired zone conditions during occupied hours in each of 3840 simulated building models. In the next section, we will analyse the relationship between HVAC system energy requirement and building demand by using regression analysis. 5. Regression model There are number of different data driven modelling methods which are suitable for studies in which both input and output variables are known such as the variable-base degree-day method, data-driven bin method, Fourier series analysis, artificial neural

Fig. 11. HVAC system auxiliary energy requirement vs. building total demand.

networks [21]. In this study, however, preference was given to regression models for their simplicity. The aim of regression analysis is to determine simple and sufficiently accurate models for predicting energy requirement of HVAC systems from building’s heating and cooling demand. Several forms of regression models were considered. They were divided into two types; models based on a single independent variable (either heating or cooling demand), and models based on two independent variables (both heating and cooling demand). Detailed analysis has been carried out to determine the most suitable model forms, as reported by Korolija [29]. For bivariate regression (one dependent and one independent variables), the power law function in the form of Eq. (1) is selected. The second order polynomial function (Eq. (2)) is selected for multivariate regression. In addition to these two models, a linear function (Eq. (3)) which passes through origin (x = 0 and y = 0) is included in the analysis as a reference model since it represents the HVAC system conversion factor. The existence of a single coefficient, which could be used to determine HVAC system energy requirements as a function of building demands, would simplify the selection and comparison of HVAC systems. Such coefficients exist and they are widely used for defining energy performance of primary HVAC systems (boiler efficiency or chiller coefficient of performance), however, the results of statistical analysis suggested that, unfortunately, there is no single parameter which can be used to accurately predict the secondary HVAC system energy requirements as a function of building demands, especially when compared to the predictions of the power law function or even better predictions of the second order polynomial function.

Table 4 Average annual number of hours heating/cooling setpoint not met during occupied period. System

Fig. 10. HVAC system heating energy requirement vs. building heating demand.

Variable air volume (VAV) Constant air volume (CAV) Fan-coil (FC) Chilled ceiling with embedded pipes (EMB) Chilled ceiling with exposed aluminium panels (ALU)

Setpoint not met while occupied Heating [h/yr]

Cooling [h/yr]

26.94 23.62 32.23 31.96

7.68 10.59 2.09 19.17

31.94

21.87

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Table 5 Coefficients of bivariate models. System

Cooling y(x) = a·x

VAV CAV FC EMB ALU

Heating y(x) = a + b·xc a

b

c

a

a

b

c

7.044 × 10−1 5.184 × 10−1 1.357 1.534 1.341

1.277 4.191 × 10−1 3.796 × 10−1 −9.568 −4.864

2.221 1.682 1.627 6.062 4.155

6.557 × 10−1 6.574 × 10−1 9.464 × 10−1 6.621 × 10−1 7.108 × 10−1

8.832 × 10−1 7.556 × 10−1 6.062 × 10−1 5.829 × 10−1 5.751 × 10−1

−7.148 × 10−1 −2.803 −1.767 −1.591 × 10−1 3.616 × 10−1

8.400 × 10−1 5.699 × 10−1 1.341 × 10−1 3.101 × 10−1 2.662 × 10−1

1.015 1.079 1.361 1.149 1.178

(1) (2)

y(x) = a · x

(3)

The bivariate models predict HVAC systems cooling energy consumption as a function of building cooling demand, and HVAC systems heating energy consumption as a function of building heating demand. Bivariate model is not suitable for predicting the HVAC systems auxiliary energy consumption as shown in Fig. 11. On the other hand, multivariate models predict HVAC systems cooling, heating and auxiliary energy consumption as a function of both building cooling and heating demand, which are represented as x1 and x2 in Eq. (2), respectively. SPSS is used to fit model coefficients. The model best-fit coefficient values are evaluated by inspecting the 95% confidence interval. If the confidence interval is reasonably narrow, it can be concluded that the best fit parameter values are determined with a reasonable certainty. How close the predicted values are to the observed data is usually evaluated by checking either the residual sum of squares (RSS) or the coefficient of determination (R2 ). Residual sum of squares is the sum of the squares of differences between the observed value (yi ) and the associated value predicted by the model (ˆyi ), as presented in Eq. (4). The coefficient of determination is computed from the residual sum of squares and the total sum of squares (TSS), as it can be seen from Eq. (6), where the TSS represents the sum of squared differences between the observed data ¯ (Eq. (5)). The root points (yi ) and the mean of the whole dataset (y) mean square deviation (RMSD) is the square root of the variance in residual. It indicates the absolute error of the model prediction, to the observed data (Eq. (7)). Low RMSD and high R2 mean that the model predictions are similar to the observed data. Beside the RMSD and R2 , several parameters, which may give better view of goodness of fit, are also included in the analysis. Minimum residual (emin ) and maximum residual (emax ) might be useful to see the range of differences. In addition, the mean absolute difference (Eq. (8)) is computed to show the overall magnitude of the differences between predictions and simulations.

(yi − yˆ i )

2

(4)

i=1

TSS =

N 

(8)

i=1

6. Results and discussion HVAC systems energy consumptions calculated by EnergyPlus for five different system types (variable air volume system, constant air volume system, fan-coil system, chilled ceiling system with embedded pipes and chilled ceiling system with exposed aluminium panels) and 3840 different office buildings were fitted to two groups of regression models. The first group contained bivariate models (Eq. (1)) with one independent variable, either building’s cooling or heating demand. The second group are multivariate models based on two independent variables, building heating and cooling demand. The quality of regression models was measured against various statistical parameters such as root mean square deviation (RMSD, see Eq. (7)) and coefficient of determination (R2 , see Eq. (6)). 6.1. Bivariate models The coefficients a, b and c of the bivariate models for five HVAC systems are presented in Table 5. The regression models for each of the five analysed HVAC systems are presented in Fig. 12. Coefficients of determination of the fitted models are shown in the top left corners. The R2 value is above 95% in all cases, which means only less than 5% of variance in the EnergyPlus simulation result has not been accounted for by the corresponding regression model. Prediction errors of the bivariate models are summarized in Table 6. They are clearly more accurate than linear models, which represent the conventional conversion factor approach. Beside the VAV heating models and the FC cooling models, for which statistical parameters show that predictions of both models (linear and power law) are close to each other, in all other cases the power law models cooling and heating predictions are much closer to the simulation results. These models are simple to read and easy to use. For example, Fig. 12 can be used for selecting HVAC systems based on building’s heating and cooling demand. The accuracy of the regression models can be further improved by taking both heating and cooling demand as independent variables in Eq. (2). 6.2. Multivariate models

¯ 2 (yi − y)

(5)

i=1

R2 = 1 −

 1   yi − yˆ i  N N

|e| =

y(x1 , x2 ) = a + b · x1 + c · x2 + d · x12 + e · x1 · x2 + f · x22

N 

y(x) = a + b·xc

a

y(x) = a + b · xc

RSS =

y(x) = a·x

RSS TSS

(6)

  N 1 2 (yi − yˆ i ) RMSD =  N

i=1

(7)

The coefficients a, b, c, d, e and f of the fitted multivariate models are presented in Table 7. The graphical presentation of models is given in Fig. 13. The goodness of fit of the multivariate regression models is presented in Table 8. It can be seen from the table that all five HVAC system types cooling and heating models have very high coefficient of determination, (above 0.98). The models of auxiliary energy requirements for the HVAC systems are slightly less accurate, especially for the chilled ceiling systems where the coefficients of determination are close to 0.87.

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Fig. 12. Bivariate regression models for HVAC systems cooling and heating predictions.

6.3. Statistical models accuracy and error analysis High coefficients of determination characterises almost all nonlinear models. Model users may be more concerned about the level of error that the regression models may cause if used in place of dynamic simulation models. Analysis of relative differences between regression model predictions and results from dynamic simulation is carried out. The levels of relative difference between models are categorized into ±5%, ±10% and ±20% brackets. Regression model performance can then be evaluated as percentage of the dataset (office building scenarios) that falls into the ±5%, ±10% and ±20% categories. Table 9 shows the results of relative error analysis. For example, the power law model of the fan-coil (FC) system can predict cooling energy requirement within ±5% relative difference in more than 85% of cases. The second best prediction for cooling energy requirement is achieved for the VAV system, with close to 44% of

data within the ±5% category. For the rest of the analysed HVAC systems, around 40% of cases fall in this accuracy category. Predictions for the chilled ceiling systems (EMB and ALU) are among the least accurate in this category, as well as in the ±10% category. CAV and VAV systems had 73% and 77% of all data in this category. The power law function model predicted the FC system cooling energy requirement for all cases within ±10% relative error. All systems had the ±20% fit for more than 95.5% of simulated scenarios. The power law function heating model generated less accurate results when compared to the cooling model. Only the VAV system had more than 50% of all data in the ±5% fit category whilst all other systems had between 30% and 40% of predictions in this category. Between 55% and 80% of all data is in the ±10% fit category with the CAV system at the lower end and the VAV system at the higher end. The power law function model was capable to predict heating energy requirement with ±20% relative error in more than 95% of all data for all systems except for the CAV system which had almost

Table 6 Linear and power law models prediction errors. Cooling (kWh/m2 /yr)

System

Heating (kWh/m2 /yr)

y(x) = a·x

y(x) = a + b·xc

VAV

R RMSD emin emax |e|

0.6539 4.050 −13.65 7.04 3.51

0.9631 1.322 −3.44 5.68 1.04

0.9752 3.807 −7.94 21.73 2.72

0.9759 3.748 −7.58 20.87 2.51

CAV

R2 RMSD emin emax |e|

0.7081 2.856 −11.12 7.25 2.43

0.9518 1.160 −2.53 6.10 0.87

0.9587 4.622 −11.46 10.67 3.76

0.9748 3.608 −14.35 7.05 2.98

FC

R2 RMSD emin emax |e|

0.9937 1.439 −6.56 3.72 1.18

0.9976 0.892 −3.18 3.05 0.68

0.9067 6.556 −8.46 19.10 5.92

0.9902 2.121 −4.71 5.71 1.74

EMB

R2 RMSD emin emax |e|

0.9313 5.050 −22.96 17.50 3.67

0.9708 3.293 −9.92 14.85 2.45

0.9661 3.211 −5.03 12.90 2.64

0.9821 2.330 −5.83 7.57 1.77

ALU

R2 RMSD emin emax |e|

0.9240 4.563 −18.84 16.25 3.52

0.9670 3.007 −8.84 14.17 2.20

0.9635 3.305 −5.21 13.10 2.70

0.9813 2.369 −5.87 7.40 1.82

2

y(x) = a·x

y(x) = a + b·xc

I. Korolija et al. / Energy and Buildings 59 (2013) 214–227

Fig. 13. Second order polynomial regression models for HVAC systems cooling, heating and auxiliary predictions.

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Table 7 Coefficients of second-order polynomial models. y(x1 , x2 ) = a + b · x1 + c · x2 + d · x12 + e · x1 · x2 + f · x22

System

b

c

d

e

f

VAV

Cooling Heating Auxiliary

a 2.091 4.630 1.590

5.611 × 10−1 −4.578 × 10−1 2.462 × 10−1

7.075 × 10−2 7.162 × 10−1 5.493 × 10−2

−2.254 × 10−3 5.043 × 10−3 −1.019 × 10−3

3.042 × 10−3 8.231 × 10−3 5.893 × 10−3

−5.239 × 10−4 8.552 × 10−4 −6.711 × 10−6

CAV

Cooling Heating Auxiliary

2.481 4.463 3.557

3.893 × 10−1 −2.183 × 10−1 4.582 × 10−1

7.707 × 10−3 7.480 × 10−1 1.064 × 10−1

−1.474 × 10−3 2.590 × 10−3 −1.912 × 10−3

2.958 × 10−3 −5.659 × 10−3 1.144 × 10−2

−1.016 × 10−4 7.721 × 10−4 −1.797 × 10−4

FC

Cooling Heating Auxiliary

4.625 −6.861 3.118

1.350 3.238 × 10−2 1.640 × 10−1

−8.731 × 10−2 5.543 × 10−1 4.039 × 10−2

−1.131 × 10−3 3.639 × 10−4 −3.460 × 10−4

−6.381 × 10−4 −1.160 × 10−3 2.551 × 10−3

5.431 × 10−4 2.128 × 10−3 1.039 × 10−4

EMB

Cooling Heating Auxiliary

1.823 −2.558 4.136

1.511 −2.520 × 10−2 1.480 × 10−1

−8.483 × 10−2 5.370 × 10−1 1.063 × 10−2

−6.072 × 10−3 4.991 × 10−4 −8.392 × 10−4

8.194 × 10−3 1.431 × 10−3 3.299 × 10−4

4.431 × 10−4 8.907 × 10−4 3.730 × 10−5

ALU

Cooling Heating Auxiliary

7.493 −2.987 4.222

1.027 1.619 × 10−3 1.328 × 10−1

−1.776 × 10−1 5.263 × 10−1 1.167 × 10−2

−2.208 × 10−3 2.714 × 10−4 −6.838 × 10−4

9.476 × 10−3 1.275 × 10−3 4.024 × 10−4

9.111 × 10−4 9.695 × 10−4 2.080 × 10−5

15% of data outside this relative difference range. Such a large number of outliers make the power law function model less useful in predicting the CAV system heating energy requirements and it has to be used with caution. Percentages of HVAC systems cooling, heating and auxiliary energy requirements predictions calculated by the multivariate (second order polynomial function) model, which fell into ±5%, ±10% and ±20% relative differences categories, are also presented in Table 9. It is obvious that percentages in these categories are considerably higher for almost all systems in comparison with the power law function model, which proves that the multivariate model is more accurate. The multivariate model predicted both cooling and heating energy requirements with ±20% relative difference for more than 99.5% of data for all systems except in the case of the VAV heating energy requirements for which close to 97% of data are in this category and ALU cooling energy requirements Table 8 Multivariate models prediction errors. y(x1 , x2 ) = a + b · x1 + c · x2 + d · x12 + e · x1 · x2 + f · x22

System

Heating

Auxiliary

VAV

R2 RMSD emin emax |e|

Cooling 0.9939 0.536 −2.53 1.78 0.41

0.9832 3.130 −7.34 16.10 2.23

0.9653 0.903 −4.43 3.76 0.68

CAV

R2 RMSD emin emax |e|

0.9839 0.670 −2.63 3.22 0.50

0.9969 1.267 −5.67 4.11 1.00

0.9531 1.999 −8.54 8.50 1.53

FC

R2 RMSD emin emax |e|

0.9989 0.606 −3.17 2.05 0.42

0.9905 2.088 −4.87 6.00 1.71

0.9763 0.444 −2.60 1.67 0.34

EMB

R2 RMSD emin emax |e|

0.9844 2.408 −10.95 10.65 1.76

0.9838 2.216 −5.48 7.39 1.68

0.8671 0.525 −1.70 1.38 0.43

ALU

R2 RMSD emin emax |e|

0.9823 2.203 −9.03 8.82 1.69

0.9834 2.232 −5.49 7.26 1.70

0.8664 0.508 −1.55 1.42 0.42

for which close to 99% of data are in this category. Cooling energy requirement predictions within ±10% relative error were obtained for more than 90% data in all systems except the ALU system where close to 83% of data are in this category. ±5% cooling energy requirement fit is obtained in about 50% in chilled ceiling systems, 65% in the CAV system, 86% in the VAV system and close to 99% in the FC system. The multivariate model heating energy requirement predictions were less accurate when compared to the cooling energy requirement predictions for all models except for the CAV system. Heating energy requirements were predicted with ±5% relative difference for around 40% of data for chilled ceiling systems, 57% for VAV system data and 75% for CAV system data. These values are much higher for the ±10% fit category ranging from around 80%, 85% and 95% for chilled ceiling systems, VAV and CAV systems respectively. The FC system is the only systems for which the multivariate model does not provide major improvement when compared to the power law function model outputs. HVAC systems auxiliary energy requirements can also be predicted with a high accuracy by using the multivariate model. Three of five HVAC systems (VAV, FC and ALU) had all data in the ±20% relative difference category while both the CAV system and EMB system had more than 99.9% of data within this range. Close to 80% of chilled ceiling systems data are in the ±10% category which is the lowest percentage. All other systems had between 86% and 96% of data in this category. Between 48% and 60% of all data had the ±5% relative difference except in the case of the FC system which had more than 80% of data within this category. Coefficients of determination and the relative differences analysis showed that both the power law and the polynomial models are significantly more accurate than the linear model. They are therefore suitable for predicting secondary HVAC systems energy end-use for office buildings as a function of only building cooling and heating demands. The regression models can be adequate alternatives to complex energy simulation models, and can provide estimates for energy consumption instantly. Comparing the power law and the polynomial models (Table 9), the multivariate polynomial models are generally more accurate. However, the power law models are simpler to use and easier to visualize, since they depend only on the one independent variable. The choice of the model type is therefore dependent to applications. 6.4. Limitations and further model development The curvilinear regression models that have been developed from a comprehensive dataset are much more accurate than the

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Table 9 Percentages of models predicted values which have relative difference within ±5%, ±10% and ±20% ranges. System

y(x) = a + b·xc

y(x) = a·x

y(x1 , x2 ) = a + b · x1 + c · x2 + d · x12 + e · x1 · x2 + f · x22

|e| ≤ 5%

|e| ≤ 10%

|e| ≤ 20%

|e| ≤ 5%

|e| ≤ 10%

|e| ≤ 20%

|e| ≤ 5%

|e| ≤ 10%

|e| ≤ 20%

VAV

Cooling Heating Auxiliary

11.6 45

22.8 71.7

43.1 95.3

43.9 52.1

77.4 79.1

99.6 95.7

85.7 56.7 59.5

97.7 84.2 90.9

99.7 96.7 100

CAV

Cooling Heating Auxiliary

12 28.7

23.3 54.1

45.9 74.7

40.2 31.2

73 56.3

97.5 85.3

65.3 74.8 49.8

94.7 95 86.3

99.8 99.8 99.9

FC

Cooling Heating Auxiliary

55.6 7.5

83.8 19

99.2 36.5

86.8 33.5

100 64.2

100 97.9

98.7 33.6 80.7

99.8 65.2 95.6

100 99.5 100

EMB

Cooling Heating Auxiliary

26.4 25.4

52.4 48.1

84.6 77.1

39.2 40

67.4 74.4

96.2 100

53.9 40 48.9

90.7 83.4 78.5

99.9 100 99.9

ALU

Cooling Heating Auxiliary

21.1 24.6

42.8 47.3

80 76.4

40.6 38.5

69.6 71

95.6 100

48 37.8 49.4

82.7 79.2 79.5

98.7 100 100

linear models representing the conventional coefficient of performance (COP) approach. The important question is to what extent these models can be generalized. Although great care has been taken in the selection of parameter values for compiling the model set for the UK office building stock (findings discussed in a separate paper [11]), decisions made during this process may limit the application of these models. The first limitation is climatic condition. The London Gatwick weather file was used in EnergyPlus simulations to generate building demands and HVAC systems energy requirements. Since the coefficients of the regression models are sensitive to climatic conditions, we recommend that the models to be used only for the office buildings in the Greater London Area or in the South East England. The second set of limitations relates to the fixed office buildings and HVAC models parameters used in this research. In addition to the main parameters used in the archetypal model, many other building and HVAC related parameters were fixed. The choice of values of such parameters may have significant influence on building energy requirements. The dataset can be extended with buildings of different sizes and with more complex forms or shapes. Building construction elements were selected in accordance to the UK building practice. Typical construction materials are bricks and concrete, which means thermally light buildings were not included in the dataset. The multivariate models, which have both building cooling and heating demand as independent variables, are reasonably accurate for the office building scenarios included in this study. Fig. 14 shows the distribution of buildings heating and cooling demands covered by the data set used in the development of statistical models. The distribution showed a trade-off pattern between heating demand and cooling demand, which is commonly seen in real buildings. For example, well-insulated buildings (low heating demand) tend to show higher cooling demand, whereas poorly insulated buildings show lower cooling demand due to infiltration and natural cooling overnight. Buildings with both low heating and cooling demands are possible if HVAC operations can be improved, e.g. by employing freer cooling and a night ventilation strategy. On the other hand, buildings with both high heating and cooling demands (the empty area in the upper right quadrant of Fig. 14) are less likely to happen in mild climates. This area (heating demand over 70 kWh/m2 /yr whilst cooling demand over 40 kWh/m2 /yr) is nevertheless uncovered by the regression models. It should also be noted that extrapolation of bivariate models (the power law models) is not recommendable. The regression

Fig. 14. Building heating demand vs. building cooling demand.

models were generated from a limited data range, i.e. building heating and cooling demands between 20 kWh/m2 /yr and 120 kWh/m2 /yr, and 5 kWh/m2 /yr and 75 kWh/m2 /yr, respectively. The power law models cannot predict systems auxiliary energy requirements, either. 7. Conclusions This paper described the development of regression models which are able to predict, with a high level of accuracy, office building annual heating, cooling and auxiliary energy requirements for different HVAC systems as a function of office building heating and cooling demands. Building heating and cooling demands were chosen as input parameters as they are relatively easy to calculate at various stages of building design or refurbishment project. In order to represent the office building stock as accurately as possible, a large number of building parameters were explored in this study. Four building built forms were coupled with five building fabrics and three levels of glazing. Building orientation was also varied in 45◦ intervals. In addition, two measures of reducing solar gains, overhangs and reflective coating, were considered as well as

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implementation of daylight control. Selected built forms, insulation levels, glazing percentages, etc. were combined into a large set of office building models (3840 in total). As different HVAC systems have different energy requirements when responding to same building heating and cooling demands, each of the 3840 office building models were further coupled with five HVAC systems: variable air volume system (VAV), constant air volume system (CAV), fan-coil system with dedicated air (FC), chilled ceiling system with embedded pipes, dedicated air and radiator heating (EMB), and chilled ceiling system with exposed aluminium panels, dedicated air and radiator heating (ALU). In total 23,040 possible scenarios were created and the annual office building heating and cooling demands and their HVAC system’s heating, cooling and auxiliary energy requirements were calculated using EnergyPlus building simulation software. These results were normalised per meter square and fitted to two groups of statistical models. The first group included models based on the single independent variable, which was either building cooling demand or building heating demand. The second group was composed of models with two independent variables: heating and cooling demands. Outputs from the regression analysis were evaluated by inspecting models best fit parameter values and goodness of fit. Based on the described analysis, the specific regression models were recommended. The recommended bivariate regression model is based on the power law function and it can be used to predict HVAC systems heating/cooling energy requirements as a function of building heating/cooling demands. The limitation of this model is that it cannot calculate HVAC systems auxiliary requirements. This model showed extraordinary good prediction of both heating and cooling energy requirements for all analysed systems. The CAV system had the lowest coefficients of determination which were 0.952 and 0.975 for cooling and heating energy requirement models respectively. All other systems had higher coefficients of determination including the fan-coil system for which the power model provided the best fit with the R2 above 0.99 for both cooling and heating models. The multivariate model which provided the best fit was based on the second order degree polynomial function. This model provided even better overall fit than the power law function model. The lowest R2 was above 0.98 in the case of both the cooling energy requirements model and the heating energy requirements model for all analysed HVAC systems, which can be assumed almost perfect fit. Auxiliary energy requirements of VAV, CAV and fan-coil systems were also predicted very well with the R2 between 0.95 and 0.98. On the other side, chilled ceiling systems auxiliary energy requirements did not fit as good as other systems, having the R2 close to 0.87, which can also be accepted as relatively high coefficient of determination. Coefficient of determination is an excellent measure of models overall goodness of fit. We further evaluated the relative errors between the models’ predicted and observed values (from detailed simulations). The power law function model predicted cooling and heating energy requirements of all HVAC systems within ±20% relative difference range for more than 95% of data except for the CAV system heating energy requirements for which almost 15% of data were outside the ±20% relative difference range. Between 55% and 80% of all data fitted within ±10% relative difference range, depending on the system, except for the fan-coil cooling energy requirements model predictions which was 100% within ±10% relative difference range. Fan-coil system cooling energy requirements model also fitted more than 85% of all data within ±5% relative difference range which is tremendous, especially if it is taken into account that all other system had only between 30% and 55% of both heating and cooling energy requirements predictions within this range.

The multivariate model showed even greater accuracy predicting the heating, cooling and auxiliary energy requirements with: above 99.5% within ±20% relative difference range, above 80% within ±10% relative difference range and above 50% within ±5% relative difference range for almost all HVAC systems. Both high coefficients of determination and acceptable relative differences proved that office building HVAC systems heating, cooling and auxiliary energy requirements can be predicted with a high accuracy by simplified regression models which are function of building heating and cooling demands. Such models allow more rapid determination of HVAC systems energy requirements without the need for time-consuming (hence expensive) reconfigurations and runs of the simulation program.

Acknowledgement The authors would like to acknowledge financial support of this work which forms part of the CITYNET project funded via the Marie Curie Research Training Network.

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