Comparison of two calculation methods used to estimate cooling energy demand and indoor summer temperatures Kai Sirén and Ala Hasan Helsinki University of Technology, Finland Corresponding email: kai.siren@tkk.fi SUMMARY As a part of the Finnish implementation of the Energy Performance of Buildings Directive, a computational exercise was carried out to choose a simple method for cooling energy estimation. Three different variants of the hourly calculation method and the monthly method were implemented. A model office building was used as the object for the cooling energy predictions. The IDA-ICE building energy software was used to produce reference results. The predicted space cooling energy numbers for a three-month summer-period were compared with the reference results. The comparison shows that the simplest one-capacity variant of the hourly method is underestimating the reference results up to 25% and overestimating up to 30%. A more detailed four-capacity variant is underestimating up to 21% and overestimating up to 19%. The monthly calculation method is not underestimating but overestimating the reference up to 75%. The hourly method is able to estimate the indoor summer maximum temperatures with a deviation less than two degrees from the reference. INTRODUCTION The 2003 published Energy Performance of Buildings Directive (EPBD) [1] is calling for a methodology for calculation of the integrated energy performance of buildings. The methodology shall be set at national or regional level. The Finnish approach was to develop a simple and transparent calculation method, which could be easily implemented. The heating energy calculation was principally based on an existing, simple and standardised method [2] working with a monthly calculation period. For cooling energy demand calculation a choice between two methods had to be done. The first method, running with a time-step of one hour, is based on a simplified thermal resistance-capacitance model of the building zone. It is in principle capable to predict the cooling energy demand and to follow the daily temperature changes inside the building. The second alternative is a variant of the monthly heating energy calculation method [2] now applied to estimate cooling energy demand. Proposals of both methods for EPBD use have been published [3, 4] but with a very restricted evidence of performance. Especially the local weather conditions and the culture for implementing buildings and their heating, cooling and ventilation systems influence the calculated results. For this reason it was important to have some further evidence and comparison results. The objective of the study was to compare the two cooling energy demand calculation methods to have some facts and arguments for the Finnish EPBD methodology implementation work.
METHODOLOGY The principle of the comparison study was to calculate the cooling energy demand of a welldefined building zone using the different methods and to compare these results with the results obtained with a reference. As a reference IDA Indoor Climate and Energy 3.0 (IDA- ICE) building simulation software was used [5]. It is a detailed whole-building simulator allowing all issues fundamental to building energy calculation: shape, envelop, glazing, HVAC systems, controls, light, etc. The mathematical models are described in terms of equations in neutral-model-format (NMF), which makes it easy to replace and upgrade program modules. IDA ICE has been shown to perform well in several computational comparisons [6, 7]. The object of the computation exercise was one floor of a model office building, Fig 1. The dimensions, component properties, and load profiles of this building are described in detail in a model building report [8]. For the purpose of the implementation of the cooling energy calculation methods, four zones in the floor were selected: two office rooms (R1 and R2) with a floor area of 10.5 m 2 each and two open plan offices (O1 and O2) with a floor area of 295 m2 each, as shown by Fig. 1. N Office room R2 10.5 m 2 16 m Open plan office O1 295 m 2 Open plan office O2 295 m 2 55 m Office room R1 10.5 m 2 Figure 1. Model building floor plan and studied zones. Two different constructions were specified for the model building. Construction 1 was a standard construction according to the model building [8] with light walls and a heavy concrete floor/ceiling. A second construction, Construction 2 was defined to find out the influence of the building mass on the calculation results. In Construction 2 walls are identical with Construction 1, but the floor and ceiling are considerably lighter. Table 1 shows the ceiling/floor for Construction 2.
Table 1. Ceiling/floor thermo physical properties for Construction 2. Thickness (mm) Thermal conductivity (W/m K) Density (kg/m 3 ) Heat capacity (J/kg K) 1 floor covering 3 0.18 1390 1000 2 chipboard 22 0.14 400 1500 3 steelwork + air gap 200 4 mineral wool sound insulation 50 0.045 110 840 5 plasterboard 13 0.21 800 840 The effective thermal thickness of the construction components was defined according to the simplified calculation of heat capacity Annex A of ISO 13786 [9]. The masses and thermal capacities for the office room and the open plan office for the two constructions are shown in Table 2. C m is the effective heat capacity for the room and A floor is the floor area. Table 2. Masses and thermal capacities of construction components. Construction 1 Construction 2 Office room Open office Office room Open office Mass of external wall (kg) 96 1620 96 1620 Mass of internal walls (kg) 530 1825 530 1825 Mass of floor and ceiling (kg) 9116 256160 610 17166 C m / A floor (kj / Km 2 ) 322 294 60.0 32.5 Components for heating and cooling exist in each room of the building. Ventilation air through a mechanical ventilation system is supplied to each room. The controlled ventilation air supply temperature is a function of the exhaust air temperature, where a linear relation exists for supply between 21 C and 17 C and exhaust between 22 C and 24 C, respectively. The ventilation supply has a daily and a weekly schedule. The heating and cooling systems and the ventilation maintain the indoor air temperature between specified set limits of 21 C and 24 C around the year. A part of the input data, like internal gains, is defined in the model building description [8]. As weather data Helsinki 1979 weather was used. Other input data like solar heat gain through the window structure and infiltration are taken according to the reference software to focus on the calculation of the building zone thermal behaviour. The input data is arranged as hourly or monthly data, according to the method.
HOURLY CALCULATION METHOD The hourly calculation method for cooling is based on the conservation of energy at the temperature node points of a simple resistance-capacitance model of the building zone. The base for this model was adopted from [3]. Because the base model did not include the description of mechanical ventilation, which is the usual way of system implementation in Finland, this feature was added to the model Variant_1, Fig 2. The model runs on an hourly basis where the calculation time step is one hour and the input/output data are arranged as hourly data. The thermal mass of the calculation zone is lumped into one thermal capacitance. The heat transfer connections between the thermal nodes are described with four resistances. The mathematical solution is based on the Crank- Nicolson difference scheme. Both heating and cooling modes can be calculated, as well as variable room air temperature and variable cooling system operation. A node point and a heat capacity flow for mechanical ventilation supply are also included. Tsu Hven Ti Hinf φhc Te Hwin Ts Hsi φi heat gains φs Hms φm Hem Tm Cm, Am Figure 2. Hourly method, model Variant_1. In Fig. 2, T e is outdoor air temperature, T i indoor air temperature, T m mass temperature, T s is a star (operative) temperature, H ven ventilation heat flow, H inf the infiltration heat flow, H win the window thermal conductance, Hem the external structure thermal conductance, and H ms and H is thermal conductances between respective node points. The heating power added or cooling power removed from the room is φ hc, heat gains to the internal nodes are φ i, φ s and φ m, the effective heat capacity for the zone C m and the equivalent area for the zone capacity A m. The computation procedure [3] begins with calculation of the internal gains, including the solar heat gain. The gains are allocated to the internal node points according to certain weights. The heating/cooling power is kept equal to zero at the first stage. The mass-node temperature is determined from the Crank-Nicolson energy conservation equation for the mass-node. The star temperature and the air temperature are determined from the node energy conservation equations. If the resulting air temperature T i is in the temperature control set
limits, the need for heating or cooling is zero and the calculation can proceed to the next hour. If the resulting air temperature is above the higher set limit, the air temperature is set equal to the upper limit (24 o C) and the cooling energy needed to keep this temperature level is calculated. In case of heating the procedure is analogous. To find out whether increasing the number of the node points gives any advantage in the cooling energy demand calculation, the model Variant_1 was further modified into a fourcapacity model Variant_2, Fig 3. The star node was rejected because the model was used for energy calculations and there was no need for an operative temperature. Two capacity nodes representing the building mass (walls, ceiling, floor) in more detail were added and the air node was also given a heat capacity. The calculation procedure is in principle similar than for the previous variant. There are four differential conservation equations instead of one and no equation for star node. The solution is based on a difference scheme. To keep the mathematical manipulation as simple as possible, the usual matrix inversion is avoided by a sequential solution of the equations. The gains are identical but allocated in a slightly different way to the node points. Tsu Hven Hinf φi φhc Tiw Te Hwin Ti Hiw Cm4 Hwe Tew Hwi Cm1 Hfc Cm3 Cm2 Fig. 3. Hourly method, model Variant_2. Finally a third model Variant_3 was made out of Variant_2 by disengaging the external structure from the outdoor air point Te and engaging it to a new sol-air temperature node T sa to account for the absorbed solar radiation on the external wall structures. The determination of the sol-air temperature was based on the energy balance of the building external surface. MONTHLY CALCULATION METHOD The monthly method to calculate cooling energy demand [4] is based on earlier methods used for heating energy calculation [2]. The time period for the calculation is one month. All input
data is one-month average or cumulative values. The main principle of the method is the longterm energy balance for the building zone. Without cooling the cumulative energy from the heat gains (solar + internal) equal the heat losses. The indoor temperature is free floating and exceeds the set temperature from time to time. Introducing cooling to the zone keeps the internal temperature below or equal to the set temperature. The cooling energy is less than the gains because a part of the losses is compensating the gains: Q = Q η Q (1) c g l l where Q c is cooling energy demand, Q g is thermal energy from gains, Q l is loss term and η l is the utilization factor for heat losses. It has been shown [4] that equation (1) can be converted into Q = (1 η ) Q (2) c g g where η g is now the utilization factor for heat gains initially used for the heating demand calculations. The utilization factor η g depends on the gain-loss ratio, the time constant of the zone and two parameters a 0 and τ 0. Different values for these parameters have been used [4,10,11] depending on the application. Here the values a 0 = 1.83 and τ 0 =83.3 for cooling of non-residential buildings according to NEN 2916 standard were adopted [4]. RESULTS With the hourly method and the reference software a period of four months May August was calculated using the hourly weather data of Helsinki 1979. The first month was a preperiod to let the structure temperatures find their natural temperature levels. The three following months were for energy calculation. The monthly method was utilising the monthly average temperatures and cumulative energy values derived from the same hourly weather data. Results for the space cooling energy demand during the period June, July and August for the different calculation methods, zones and building constructions are shown in Table 3. In case of the single office rooms Table 3 shows that all three implementations of the hourly method mainly underestimate the reference values. Variant_3 seems to perform best except in case of the North facing lighter Construction 2, where it overestimates the reference value by 17 %. This is a consequence of the sol-air temperature, which is the only difference between Variant_2 and Variant_3. The monthly method predicts the cooling energy demand very close to the reference values for the south facing office rooms but overestimates up to 76% for the north facing rooms where the gains are much smaller. Both methods overestimate the reference cooling energy demand numbers for the open space office case. The percentage difference is larger for the North facing office than for the South facing office. The construction type seems not to have any significant effect on the hourly method results. The monthly method overestimates less for the light structure Construction 2.
Table 3 Predicted space cooling energy demand for the period June August. Calculation method constr. 1 constr. 2 Office room R1 facing South cooling energy cooling/ kwh reference Office room R2 facing North cooling energy cooling/ kwh reference Open office O1 facing South cooling energy cooling/ kwh reference Open office O2 facing North cooling energy cooling/ kwh reference Hourly V_1 131 0.79 38 0.75 2478 1.12 1531 1.24 Hourly V_2 132 0.79 40 0.80 2385 1.08 1471 1.19 Hourly V_3 149 0.90 49 0.98 2613 1.18 1649 1.33 Monthly 179 1.08 88 1.76 3006 1.36 2158 1.75 IDA 166 1 50 1 2211 1 1237 1 Hourly V_1 175 0.90 67 1.03 3279 1.12 2244 1.30 Hourly V_2 155 0.80 57 0.87 3104 1.07 2050 1.18 Hourly V_3 188 0.97 76 1.17 3511 1.20 2455 1.42 Monthly 194 1.00 104 1.59 3464 1.19 2614 1.51 IDA 194 1 65 1 2916 1 1732 1 In general, the rate of overestimation of the reference values is increasing with decreasing structure capacity and decreasing gains for the hourly calculation method, and vice versa. The monthly calculation method behaves in a different way. The rate of overestimation is increasing with increasing structure capacity and decreasing gains. One important factor in assessing the need for active cooling is the behaviour of the indoor air temperature during the summer period. If this temperature is exceeding the specified limits without cooling, there obviously is a need for cooling. The hourly calculation method is able to provide this information. The temperature limits, which are used for energy calculation, are inactivated and the indoor air temperature is let to float during the computation. The results for the period June August show that the hourly Variant_1 is overestimating the maximum indoor temperature by 2.2 o C compared with the reference result. The hourly Variant_2 is overestimating the maximum temperature only by 1.8 o C. The monthly method is not able to provide useful information related to temperature maximum or minimum values. CONCLUSIONS A computational exercise for the assessment of two simplified calculation methods, the hourly method and the monthly method has been carried out. The space cooling energy demand for four different zones of an office building was predicted with three variants of the hourly method and the monthly method. The IDA-ICE building energy software was used as a reference. The predicted cooling energies for a three-month period vary from 75% to 175% compared to the reference results. The hourly method implementations underestimate the reference values for a heavy structure and high gain and overestimate for a light structure and small gain values. The monthly method mainly overestimates, the more the smaller the internal gains.
As a part of the Finnish implementation for the cooling energy calculation method of the Energy Performance of Buildings Directive, a one-capacity variant of the hourly calculation method was further developed, tested and proposed for the Finnish authorities. For the Finnish implementation of the EPBD the monthly calculation method was chosen. REFERENCES 1. Directive 2002/91/EC of the European Parliament and of the Council of 16. December 2002 on the energy performance of buildings. Official Journal of the European Communities, L1, 4.1.2003, pp 65-71. 2. ISO 13790. Thermal performance of buildings Calculation of energy use for space heating. International Organisation for Standardisation, 2004. 3. J. C. Visier and J. R. Millet. Proposal for a simplified hourly calculation method, report DDD/CVA-03.132R, CSTB, Centre Scientifique et Technique du Batimont, July 2003. 4. D. van Dijk, M. Spiekman and P. de Wilde. Monthly method to calculate cooling demand for EP regulations, TNO, Building and Construction Research, Department of Sustainable Energy and Buildings, Delft, The Netherlands, February 2004. 5. http://www.equa.se/eng.ice.html 6. M Achermann and G Zweifel. RADTEST Radiant Cooling and Heating Test Cases. A report of Task 22, sub Task C. Building Energy Analysis Tools. Comparative Evaluation Tests, 2003. 7. M Achermann. Validation of IDA ICE Version 2.11.06. Hochschule Technik+Architektur Luzern. 2000. 8. J. Heinonen, J. Kurnitski and T. Tissari. RET model office building for energy calculations, Helsinki University of Technology, HVAC-laboratory, 2005. 9. ISO 13786 Thermal performance of building components - Dynamic thermal characteristics- Calculation methods, 1999.