SECOND CYCLE, 30 CREDITS STOCKHOLM SWEDEN 2019,
Development of a configurable model for temperature
distribution estimation in
multifamily houses with limited amount of sensors
FEDERICA BOZZI
KTH ROYAL INSTITUTE OF TECHNOLOGY
SCHOOL OF INDUSTRIAL ENGINEERING AND MANAGEMENT
Development of a configurable model for temperature distribution estimation in multifamily houses with limited amount of
sensors
Federica Bozzi
Master of Science Thesis
KTH School of Industrial Engineering and Management Energy Technology ITM-EX 2019:94
Division of Applied Thermodynamics and Refrigeration
SE-100 44 STOCKHOLM
Sammanfattning Århundradets största klimatutmaning innefattar att reducera CO2- utsläppen tillräckligt mycket för att begränsa den globala uppvärmningen till att vara under 2°C ökning jämfört med den förindustriella nivån. För att uppfylla 2°C-målet krävs omfat- tande insatser från alla samhällssektorer, även energisektorn. För vårt samhälle att uppnå detta mål är det viktigt att inte bara vidta åtgärder inom produktionssidan av energi, men även inom energianvändningssidan.
De senaste årtiondenas ökande ekonomiska välfärd har medfört en kontinuerlig strävan efter välbehag och trevnad. Inom byggnadssektorn har denna trend inneburit en oerhört hög energikonsumtion i byggnader. Som följd har majoriteten av företag inom byggnadssektorn i dagsläget som mål att säkerställa de boende god termisk komfort, samtidigt som byg- gnadens energikonsumtion minimeras. Den faktor som har störst påverkan på människors termiska komfort är den upplevda temperaturen. Ett flertal modeller existerar med syfte att uppskatta temperaturen i en särskild miljö, dock kännetecknas dessa av två huvudsakliga begräsningar. För det första fokuserar dessa modeller på enskilda rum eller lägenheter, inte på byggnaden som helhet. För det andra är de anpassade efter särskilda byggnadsstruk- turer och går ej att användas för andra strukturer. Syftet med detta arbete är att utveckla en övergripande modell för att uppskatta temperaturfördelningen inom en godtycklig fler- bostadshus. Den valda typologin motiveras av att den utgör en stor andel i byggindustrin.
Denna modell bör vara tillförlitlig och samtidigt ha en kort beräkningstid. Skapandet av en sådan modell kan vara första steget på vägen till att kunna kontrollera inomhusklimatet i realtid.
Vid skapandet av modellen har särskilt fokus lagts på klimatförhållandens inverkan på inomhustemperaturen.
Solens och vindens inverkan har tagits till hänsyn till olika grad. Baserat på tillvä- gagångssätten för beräkningar av de, har olika konfigurationer urskilts. Var och en av de har sedan undersökts, både med och utan optimering av effektfördelning. Root Mean Square Error (RMSE) värdet av de olika konfigurationerna har sedan jämförts för att bedöma modellens noggrannhet. Resultatet från undersökningen visade att konfigurationen för den bästa modellen var: utan optimering av effektfördelning av värmekretsen, med hänsyn till solinstrålning beroende på infallsvinkeln och med försumbar inverkan från vind.
Modellens främsta styrka är dess anpassbarhet: den kan inrätta sig till olika utformningar, riktningar och fördelningar av lägenheter för en godtycklig flerbostadshus. Modellens be-
gränsningar består bland annat av att den endast kan användas för byggnader med mekanisk ventilation, inte för gröna byggnader eller passivhus. Modeller tar inte heller hänsyn till tomma lägenheter eller värmeöverföring mellan angränsande lägenheter.
Denna rapport har utförts som följer. Det första kapitlet är en introduktion till exa- mensarbetet. Bakgrunden framlägger en tydlig bild över dagslägets temperaturmätningar i byggnader. Därefter presenteras problemformuleringen tillsammans med begränsningar vad gäller byggnadstypologin som betraktas i detta arbete. Det första kapitlet avslutas sedan med en beskrivning av den använda metoden för att skapa modellen. Arbetets an- dra del redogör de bäst tillgängliga modellerna för temperaturdistribution och placering av sensorer. Det tredje kapitlet omfattar indata för modellen, beskrivning av olika värmeöver- föring inblandade samt hur de förhåller sig till byggnadens utformning och hur lägenheterna är fördelade. Därefter beskrivs processen för att erhålla en temperaturvisualisering i 3D. I kapitel fyra presenteras resultaten från de olika modellerna och konfigurationerna. Dessa resultat analyseras, jämförs och diskuteras i det femte kapitlet, där den bästa modellen även fastställs. Examensarbete avslutas med att framföra förslag på framtida arbeten, en övergripande om den skapade modellen.
iii/ 142 Abstract The biggest environmental challenge of the current century is limiting the CO2
emissions in order to contrast the global warming and keep the temperature increase below 2.0K with respect to the pre-industrial age. For succeeding in this goal, significant changes are required in all sectors, including the energy one. For our society to reach the goal it is important to act not just on the production side of the energy, but also on the utilization one.In the last decades, the economic well-being drove people to a continuous search for comfort.
In the building sector this behavior brought to the consumption of huge amounts of energy.
Nowadays, the final target of most of the companies working in this sector is therefore to guarantee the thermal comfort desired by the inhabitants while minimizing the energy consumption. The parameter that most affects people thermal sensation is the perceived temperature. Several models have been already created with the purpose of estimating the temperature value inside a certain environment, but these are generally characterized by two main limitations. First of all the focus is on a single room or apartment and not on the building as a whole. Secondly the model is specific and cannot be applied to other structures. The purpose of the thesis is to elaborate a general model able to estimate the temperature distribution inside any Multifamily House (MFH). The reasoning behind the chosen typology is the significant share that it has in the building market. This model should be reliable enough and, at the same time, characterized by short computational time. Building this model could be the first step for being able in the future to operate a real time control on the thermal indoor conditions.
While developing the model particular attention has been given to the impact of climatic conditions on the indoor temperature. The contribution of sun and wind has been considered at different levels of detail. On the basis of the calculation approach utilized for them, different configurations have been identified. Each of them, in addition, has been analyzed with and without optimization process of the space heating power distribution. The RMSE value of the different configurations has been utilized during the comparison as a measure of the model accuracy. From the analysis the best model resulted to be the not-optimized one considering the solar radiation dependent on the incidence angle and with negligible wind effect.
The main strong characteristic of the model is its configurability: it can adapt to the geometry, orientation and apartments disposition of any MFH. The model has also some limitations such as the fact that it can be used just for buildings provided with mechanical ventilation and not one without such as green or passive houses. In addition, the model does neglect empty apartments and does not consider the heat and mass transfer between adjacent flats.
The report has been developed as follows. The first chapter is an introduction to the thesis.
The background provides insights about the actual situation regarding the temperature measurements inside a building. The addressed problem is reported together with the delimitation regarding the typology of building taken into consideration. The methodology utilized for developing the model closes the first chapter. The second one reports the state of art concerning the temperature distribution models. The third chapter contains the input data required by the model, the description of the different heat fluxes involved in it and how they are related to the building geometry and to the apartments disposition.
The equation utilized for the temperature calculation is then analyzed. The chapter ends with the description of the steps for obtaining a 3D temperature visualization and with an
overview on the whole process for evaluating the temperature distribution. In the chapter four are reported the results obtained with the different models and configurations. These are further analyzed, compared and discussed in the fifth chapter, in which is the best model is also identified. The thesis ends with the a glimpse on possible future work and a general conclusion about the developed model.
v/ 142 Acknowledgement I would first like to thank my supervisor Quirin Hamp, who gave me the great opportunity to work on this Master’s thesis project and turned out to be the best guide I could have hoped for. Thanks to his help and continuous support I managed to overcome every difficulty encountered during this journey. His teachings allowed me to grow not only as an engineer but above all as a person.
I would thank my academic supervisor at KTH Joachim Claesson that with his knowledge stimulated my interest in this subject. He is always ready to give an answer to my doubts and my curiosity.
My sincere thanks also goes to my academic supervisor at Politecnico di Torino Marco Carlo Masoero that despite the distance gave me an incredible support. His valuable advice allowed me to complete this project
I would like to express my sincere gratitude to Stockholm Exergi that accepted to have me in its team and allowed me to live a wonderful experience. I would also like to thanks to the inhabitants of "BRF Skytten 2" whose buildings have been used as test case.
Un profondo ringraziamento va alla mia famiglia, che mi ha sempre sostenuto nelle mie scelte dandomi la possibiltà di perseguire i miei sogni con ogni mezzo possibile. Un grazie ai miei genitori per avermi insegnato i veri valori. In particolare a mia madre, che mi ha dimostrato l’importanza di non arrendersi mai e con il suo amore mi guida ogni giorno attraverso la vita. A mio padre, le cui azioni sono esempio di come non ci sia ostacolo che tenga di fronte a ciò che si ama. Un grazie a mia sorella, sempre al mio fianco pronta a supportarmi e consigliarmi. A Tantiya che mi è stata vicina nei momenti più difficili dandomi la forza di andare avanti.
1 Introduction 1
1.1 Background . . . 5
1.2 Problem formulation . . . 6
1.3 Delimitations . . . 6
1.4 Methodology . . . 7
2 State of art 9 2.1 Temperature estimation models for buildings . . . 9
2.1.1 Nodal models . . . 9
2.1.2 CFD models . . . 10
2.1.3 Zonal models . . . 12
2.1.4 Artificial Neural Network models (ANN) . . . 14
3 Implementation 15 3.1 Input to model . . . 15
3.1.1 Configuration of generic model to specificities of MFH under evaluation 15 3.1.1.1 Building geometry and apartments disposition . . . 15
3.1.2 Continuous inputs to the model . . . 18
3.1.2.1 Internal heat gains: people . . . 18
3.1.2.2 Internal heat gains: electrical appliances . . . 19
3.1.2.3 Sun data . . . 20
3.1.2.4 Wind data . . . 21
3.1.2.5 Mechanical ventilation data . . . 22
3.1.2.6 Space heating data processing . . . 23
3.2 Input data processing and alignment . . . 24
3.3 Model description . . . 25
3.4 Heat losses evaluation . . . 26
3.4.1 Transmission losses . . . 26
3.4.2 Ventilation losses . . . 26
3.4.3 Infiltration losses . . . 27
3.5 Heat gains evaluation . . . 32
3.5.1 Irradiation model . . . 32
3.5.1.1 Solar gains evaluation . . . 32
3.5.2 Space Heating power . . . 36
3.5.2.1 Model A: space heating power proportional to the apart- ment surfaces areas . . . 37
Contents vii/ 142 3.5.2.2 Model B: space heating power obtained through an opti-
mization process . . . 38
3.5.3 Internal gains . . . 38
3.6 Adjustment of fluxes dependent on building configuration . . . 40
3.6.1 Apartments model . . . 40
3.6.2 Building model . . . 40
3.6.2.1 External area identification and evaluation . . . 40
3.7 Temperature distribution estimation . . . 43
3.8 3D temperature visualization . . . 45
3.8.1 3D model creation . . . 45
3.8.2 Temperature visualization . . . 46
3.9 Main process . . . 49
3.9.1 Description of the optimization procedure . . . 51
4 Results 53 4.1 Description of model configurations . . . 54
4.2 Premise to the analysis . . . 55
4.3 Model without optimization and all sensors considered . . . 57
4.3.1 Results overview . . . 57
4.3.2 Performance of not-optimized model with all sensors considered . . 59
4.3.3 Limitation of the approach with all sensors considered . . . 63
4.4 Model without optimization and one sensor excluded . . . 64
4.4.1 Results overview . . . 64
4.4.2 Reliability of model without optimization for apartments devoid of sensors . . . 66
4.5 Limitation of the approach without optimization process . . . 68
4.6 Model with optimization and all sensors considered . . . 69
4.6.1 Results overview . . . 69
4.6.2 Performance of the optimized configuration with all sensors . . . . 71
4.6.3 Limit of the approach with all sensors considered . . . 73
4.7 Model with optimization and one sensor excluded . . . 74
4.7.1 Results overview . . . 74
4.7.2 Reliability of model with optimization for apartments devoid of sensors 76 5 Discussion 79 5.1 Influence of the specificities of each apartment . . . 79
5.2 Accuracy of the interpolation method . . . 81
5.3 Magnitude of the wind effect . . . 84
5.4 Comparison optimized and not-optimized model . . . 85
5.5 Optimized redistribution of space heating power fraction . . . 87
5.5.1 Configuration with solar radiation dependent on incidence angle and without wind effect . . . 87
5.5.2 Configuration with solar radiation independent from incidence angle and without wind effect . . . 89
5.5.3 Configuration without solar radiation and without wind effect . . . 90
5.6 Optimization consequences on apartments without sensors . . . 92
5.7 Best model identification . . . 95
6 Future work 97 6.1 Improvement of presented model . . . 97 6.2 Improvement through new model . . . 98
7 Conclusion 99
A Graphs without optimization process and all sensors considered 103 A.1 Outputs of the non-optimized model with detailed solar radiation calculation
and without wind effect when all sensors are considered . . . 103 A.2 Outputs of the non-optimized model with global solar radiation and without
wind effect when all sensors are considered . . . 108 A.3 Outputs of the non-optimized model with null solar radiation and without
wind effect when all sensors are considered . . . 112 B Graphs without optimization process and one sensor excluded 116 C Graphs with optimization process and all sensors considered 117
C.1 Outputs of the optimized model with detailed solar radiation calculation and without wind effect when all sensors are considered . . . 117 C.2 Outputs of the optimized model with global solar radiation and without wind
effect when all sensors are considered . . . 122 C.3 Outputs of the optimized model with null solar radiation and without wind
effect when all sensors are considered . . . 126 D Graphs with optimization process and one sensor excluded 130
D.1 Outputs of the optimized model with detailed solar radiation calculation and without wind effect when one sensor is excluded . . . 130 D.2 Outputs of the optimized model with global solar radiation and without wind
effect when one sensor is excluded . . . 135 D.3 Outputs of the optimized model with null solar radiation and without wind
effect when one sensor is excluded . . . 139
List of Figures
1.1 Location of women aged 20 to 74. . . 1
1.2 Location of men aged 20 to 74. . . 2
1.3 Graphic Comfort Zone Method. . . 3
3.1 Global and local coordinate systems with representation of the building ori- entation. . . 17
3.2 Wind directions expressed in degree according to the chosen convention. . 28
3.3 Views of the 3D image of the analyzed building. . . 45
3.4 3D temperature visualization at 6a.m.. . . 47
3.5 3D temperature visualization at 6p.m.. . . 48
3.6 Representation of the main process. . . 49
3.7 Representation of the optimization process. . . 52
4.1 Temperature trend in the apartment 15-1103. . . 55
4.2 Comparison between outputs obtained with and without wind effect. . . . 56
4.3 Comparison of the error with and without wind effect. . . 56
4.4 Output of the model A with solar radiation dependent on incidence angle and without wind effect. . . 59
4.5 Output of the model A with solar radiation independent from incidence angle and without wind effect. . . 61
4.6 Comparison of solar gains in apartments with different external wall orientation. 62 4.7 Output of the model A with no sun radiation and without wind effect. . . 63
4.8 Model A configuration 4: comparison between apartment with and without sensor. . . 66
4.9 Model A configuration 5: comparison between apartment with and without sensor. . . 67
4.10 Model A configuration 6: comparison between apartment with and without sensor. . . 67
4.11 Output of the model B with solar radiation dependent on incidence angle and without wind effect. . . 71
4.12 Output of the model B with solar radiation independent from incidence angle and without wind effect. . . 72
4.13 Output of the model B with no sun radiation and without wind effect. . . 72
4.14 Configuration 4. Comparison between model A and B for the apartment assumed to be without sensor. . . 76
4.15 Configuration 5. Comparison between model A and B for the apartment assumed to be without sensor. . . 77
4.16 Configuration 6. Comparison between model A and B for the apartment
assumed to be without sensor. . . 78
5.1 Influence of apartment configuration on RMSE dependent on solar irraida- tion model. . . 80
5.2 Comparison between RMSE resulting from apartment 17-1203 with and without sensor in case of model A. . . 81
5.3 Comparison between RMSE variation in some of the flats when the sensors are not considered and the model A is applied. . . 83
5.4 Comparison of different configurations of optimized and not-optimized model. 85 5.5 Variation of space heating power fractions due to optimization process for configuration 4. . . 88
5.6 Variation of space heating power fractions due to optimization process for configuration 5. . . 89
5.7 Variation of space heating power fractions due to optimization process for configuration 6. . . 90
5.8 Comparison between RMSE resulting from apartment 17-1203 assumed without sensor in case of model A and B. . . 92
5.9 Configuration 5. Comparison between outputs for apartment 15-1203 in case of model A and B. . . 93
5.10 Configuration 5. Comparison between outputs for apartment 15-1301 in case of model A and B. . . 94
A.1 Temperature values obtained from model A with configuration 4. . . 107
A.2 Temperature values obtained from model A with configuration 5. . . 111
A.3 Temperature values obtained from model A with configuration 6. . . 115
B.1 Temperature values obtained with model A in the apartment 17-1203 when it is assumed to be without sensor. . . 116
C.1 Temperature values obtained from model B with configuration 4. . . 121
C.2 Temperature values obtained from model B with configuration 5. . . 125
C.3 Temperature values obtained from model B with configuration 6. . . 129
D.1 Temperature values obtained from model B with configuration 4 when one sensor is excluded. . . 134
D.2 Temperature values obtained from model B with configuration 5 when one sensor is excluded. . . 138
D.3 Temperature values obtained from model B with configuration 6 when one sensor is excluded. . . 142
List of Tables
1.1 Share of fuels in the final energy consumption in the residential sector by type of end-use. . . 4 3.1 Typical occupancy values in dwellings [21]. . . 19 3.2 Correlation between floor area and number of rooms in a general apartment. 19 3.3 Common power and utilization schedule of typical electric appliances [15]. . 20 3.4 Input data required for the calculation of wind effect. . . 28 3.5 Input data dependent on solar radiation model configuration. . . 32 4.1 Analyzed models both with and without optimization process for power
distribution. . . 54 4.2 RMSE of the analyzed configurations for model A with all sensors considered. 58 4.3 RMSE of the analyzed configurations for model A with one sensor excluded. 65 4.4 RMSE of the analyzed configurations for model B with all sensors considered. 70 4.5 RMSE of the analyzed configurations for model B with one sensor excluded. 75
ANN Artificial Neural Networks. 9, 14 CFD Computational Fluid Dynamics. 9–14 CPU Central Processing Unit. 13
DHW Domestic Hot Water. 23, 36
HVAC Heating, Ventilation and Air Conditioning. 10, 11, 14 IAQ Indoor Air Quality. 10
MFH Multifamily House. i, 5–7, 15, 43, 45, 83, 84, 97–99 OOP Object Oriented Programming. 25
PMV Predicted Mean Vote. 2
POD Proper Orthogonal Decomposition. 12 PPD Predicted Percentage of Dissatisfied. 2
RMSE Root Mean Square Error. i, ix, 54, 57–60, 62, 64–72, 74–83, 85–87, 92–95, 99 SH Space Heating. 36, 37, 50, 68, 69, 71, 73, 87–91, 95, 97
TRV Thermostatic Radiator Valve. 4–6
Chapter 1 Introduction
According to a survey [10] conducted among ten European countries between 1998 and 2002, women aged between 20 and 74 years old spend between 66% and 78% of their life at home, while for the men the correspondent range is between 60% and 69% (Fig.1.1 and Fig.1.2). Even if Sweden has in both cases the lowest percentage, the amount of time spent indoor is anyway substantial.
Figure 1.1: Location of women aged 20 to 74 ([10]).
Figure 1.2: Location of men aged 20 to 74 ([10]).
According to Jing [19] the impact of relative humidity (RH) on thermal comfort has been recognized since long time. It is anyway necessary to distinguish between two kinds of environment. In ambients with moderate climatic conditions, the effect of RH on comfort sensation can be considered negligible if the air temperature is kept within the acceptable range. In hot environments, instead, high values of RH could cause thermal discomfort.
In order to take into account the effect of RH in the identification of the comfort zone, ASHRAE has developed the concept of Standard Effective Temperature (SET). This has been used in the Standard 55 until 2010 [19]. ASHRAE standard 55-2010 [2] proposes a new graphical method for determining the conditions able to provide thermal comfort.
The definition of the comfort conditions is based on Fanger concepts of Predicted Mean Vote (PMV) and Predicted Percentage of Dissatisfied (PPD) [6]. The chart reported in Fig. 1.3 shows the indoor thermal conditions required in order to have a PPD lower than 10% in both winter (1.0 clo) and summer (0.5 clo) seasons.
3/ 142
Figure 1.3: Graphic Comfort Zone Method ([2]).
The chart 1.3 confirms that temperature and relative humidity have a different impact on the perceived thermal comfort. While the temperature must lie in a very strict range of values, the relative humidity is acceptable for every value up to 80%.
This analysis, combined with the data regarding the amount of time spent in the house, underlines the importance of a good and reliable indoor temperature control.
The temperature inside a room is directly linked with the heat or cold released by the emitters inside the zone itself. It is therefore extremely important to have a good control of the heating system. According with Eurostat [11], in the European Union the energy consumption in the residential sector in 2016 represents the 25.4% of the total.
Furthermore, as reported in Fig. 1.1, 64.7% of this amount of energy consumed in the households is utilized for space heating.
Table 1.1: Share of fuels in the final energy consumption in the residential sector by type of end-use ([11]).
According to Carbon Trust company [9], it is of primary importance to have a good control of heating not just for assuring thermal comfort and avoiding energy waste, but also for reducing the maintenance costs. A well controlled heating system could allow to reduce the fuel consumption by a percentage between 15% and 30%. There are two main types of temperature control: the wall thermostats and the Thermostatic Radiator Valve Thermostatic Radiator Valve (TRV). The first one acts directly on the main system, e.g. boiler, shutting it off or on. The second one, instead, regulates the heat output from the radiators by adjusting the water flow rate [9]. The flow rate is chosen based on the temperature perceived by the temperature sensor put on the valve itself. When the temperature is high, the liquid contained in a bellow expands, closes the valve and the water flow rate decreases. When the temperature is low, instead, the reduction in volume of the liquid allows the valve to open and a larger amount of water flows into the radiator.
1.1. Background 5/ 142
1.1 Background
Nowadays, in most cases the TRV is used for controlling indoor temperature. This proportional- temperature regulation is very simple but has some drawbacks. It is of primary importance that these sensor devices are mounted in a free-air stream and not in cavities or near any type of furniture. The presence of surfaces close to the radiator, in fact, could obstacle the convective motion of the air and cause an overheating of the air stuck nearby the emitter.
As a consequence, the temperature read by the sensor could result much higher than the effective room temperature. Also the presence of sun radiation can invalidate the sensor readings. This phenomenon TRV has been analyzed by Weker et al. [34]. According to him the most critical component of the sun radiation is the direct one. From the study, in fact, it results that this last could lead to an increment of temperature on the sensor surface of 3.3◦C. The diffuse radiation, on the other hand, affects the read values of just 0.1◦C.
A part from the problems due to the sensor positions, there are other limitations related to the TRV technology itself. A study has been conducted by Liao et al. regarding the control of heating systems in the UK [22]. According to this research, more than 95%
of analyzed radiators were controlled with TRV and more than 65% had very poor per- formance. This implies phenomena of under-heating or over-heating. There are several reasons behind this and the main one is that TRVs were not able to actually reduce the emitted heat when the room temperature increased. One of the causes is that the houses’
owners do not really know how the valves works and set them at too high values. The indoor temperature therefore exceeds 24◦C also when the outdoor one is relatively high.
Liao’s study was mainly focused on a comparison between different control strategies and showed out other limitations of the TRV technology. Among other variables, the perfor- mances of an old and a new TRV have been compared. The old TRV is characterized by a rangeability that goes from 2% with the valve completely closed to 98% in case of valve fully open. The rangeability in the new TRV reaches instead the 100%. In addition, the temperature sensor time constant drops from 8min of the old valves to just 4min in the new ones. By comparing their performances, it has been found out that the new valves are better both in terms of energy saving and thermal comfort provided in the rooms. But the study also revealed that most of the analyzed houses had the old TRV as control devices.
All these drawbacks related to the utilization of TRV as control device highlight the unreliability of this kind of solution and the necessity of finding an alternative method able to give a more realistic overview of the temperature distribution inside a building.
The presence of one or more sensors properly located in each room could provide more accurate temperature readings. By regulating the emitted heat on the base of these values, a better control on indoor thermal conditions could be achieved. The problem is that in the reality this solution cannot be applied for two main reasons. The first one is that not all buildings have sensors installed. Even when these are present, anyway, they are just in some of the rooms. The second obstacle is related to the unknown position of the sensors that makes their readings relatively useless.
Knowing the actual temperature in each apartment of a MFH could be helpful for the companies that provide the heat to the city. In the actual situation, in fact, the
heating system has a central regulation and the final users do not have any decisional power on the delivered heat. The companies, in order to avoid any kind of complaint, provide to the apartments more heat than the amount actually required for meeting the indoor comfort conditions. This makes the probability that someone complains for the too low temperature is very small and the tenants who feel hot could just use some opening for ventilation purpose. This situation is evidently negative both from an economic and environmental point of view: the users have to pay for a certain amount of delivered heat not decided by them and, at the same time, the wasted energy contributes to the air pollution without giving any beneficial effect to the indoor thermal comfort. The knowledge of the actual temperature distribution inside a building could allow to monitor the situation in each apartment. In this way just the actually required amount of heat could be delivered, assuring the thermal comfort while minimizing the energy consumption. In addition, the truthfulness of any possible complaint could be easily verified and the companies could then intervene just where there is a concrete necessity.
1.2 Problem formulation
Commonly, there is a limited amount of temperature sensors in a MFH, none or commonly at most one. Furthermore, the control of indoor climate through TRV is poor since it adjusts only to local conditions and cannot take into consideration the state of a building as a whole. Full visibility on the temperature distribution in each apartment or even room is unusual. Considering the aim of heat suppliers to provide comfort to the building in- habitants, improved observability of the indoor temperature in each apartment is a key to it.
The aim of this thesis is to build a model able to estimate the temperature distribution inside any MFH. The model shall be validated by comparing the estimated and measured temperatures. The resulting error of the estimation process should be sufficiently small thus a controller can use the estimated temperature distribution as input for determining an appropriate control action.
The development of this project, will moreover be useful for finding out which is the level of model complexity required to provide an accurate estimation of temperature distribution especially for apartments without sensors.
The full visibility on temperature distribution will allow to have an improved control strategy. The aim is to deliver the amount of heat required for satisfying the thermal comfort expectations even in apartments of MFH devoid of indoor climate sensors while minimizing the energy consumption.
1.3 Delimitations
The study is limited to the analysis of MFH. This choice is based on two reasons. First of all, most of the residential buildings in Stockholm are multi-stores: 90.3% in the 2015 according to the statistics of Stockholms Stad [28]. Secondly, the large buildings are the most difficult to control [9] due to both the high heat capacity values, which implies slow system response with delay that compromises control logics based on the linear time
1.4. Methodology 7/ 142 invariant assumption, and the variety of heat gains and loads that influence the thermal balance and are not observable.
The developed model is able to provide the temperature estimation for MFH provided with mechanical ventilation. In order to cope with green houses, passive buildings or MFH natural ventilated, some changes should be made to the model.
A further delimitation regards the building plant. The model is able to perform the analysis on MFH having a polygonal plant shape with right angles. Circular or irregular shaped buildings have not been taken into consideration during the model development.
For the analysis, in addition, it is assumed that the sensors involved in the study do not move or change their position in any way.
1.4 Methodology
The model construction starts with collecting the geometrical and geographical data about the chosen building. Information about the apartments disposition are also required. This is important in order to find out the relative position between flats and for identifying the external surfaces and their orientation. The climatic data regarding sun, wind and outdoor temperature are found in on-line databases. The amount of heat provided to the building substation for each timestamp is known.
The model is built by imposing the energy balance on each apartment. By varying the level of complexity in the calculation of solar gains and infiltration losses, six different possible approaches to the calculation of these loads are identified. The model performance is evaluated for each of them. A further analysis is carried out by developing another model configuration in which an optimization process of the space heating power distribution is performed. Also this optimized model is evaluated with all the different approaches to the calculation of sun and wind effects.
The accuracy of each model is quantitatively expressed through the Root Mean Square Error RMSE, which give an idea of how far the computed temperature is with respect to the measured values. By comparing the level of accuracy obtained with different models and configurations, the best model is identified.
The temperature distribution in the building is represented through a 3D visualization.
Before starting the study on the analyzed building, it is necessary to go through the state of art regarding the temperature modeling approach. This allows to choose the best procedure by considering the pros and cons of every existing method, together with their prerequisites and their typical field of application.
Chapter 2 State of art
2.1 Temperature estimation models for buildings
Several modeling procedure can be applied in order to calculate the temperature distribution inside a building. The most common ones are: nodal method, zonal method, Computa- tional Fluid Dynamics (CFD) models and Artificial Neural Networks (ANN). Each of these modeling methods has its own advantages and limitations, it is therefore important to analyze their application field before choosing the most appropriate to the studied case.
2.1.1 Nodal models
The nodal (or multizone) approach is most probably the most simple and intuitive one. It is built on the electrical analogy: the modeling process consists in representing a building and its components through an Resistor-Capacitor RC-circuit. The electrical resistance cor- responds to the thermal one, the thermal capacity is represented by the condenser and the temperature is treated as the voltage. The heat gains are therefore represented as current source. The nodal approach is based on the assumptions of homogeneous conditions and well-mixed air in each zone. This allows to have a lumped model of the building, in which each zone is represented by a node in the electrical circuit.
Since every building component can be represented inside the circuit, this could become extremely complex. It is therefore necessary to find out which is the model that best repre- sents the building, allowing a good trade-off between complexity and model performance.
According to Bacher and Madsen [3] the best approach for a model identification consists in starting with the simplest reasonable circuit and refine the model until when adding components does not bring further significant improvement. By applying Kirchhoff’s laws to the circuit, a set of differential equations is obtained. These, together with the bound- ary conditions regarding both the internal and external walls surfaces, are able to describe the building behavior [4]. This kind of modeling process can therefore be performed with different softwares including Matlab [5].
Prerequisites For applying this method it is necessary knowing first of all the geometry and the thermal characteristics of the analyzed building. In particular it is important to know the materials that make up the walls and the thickness of the various layers, in order to find out the total thermal resistance. In the case of dynamic simulations, the values
of thermal capacity are extremely important as well, since it influences significantly the thermal behavior of the construction. The heating loads related to the emitters must also be known. Thermal loads of secondary importance such as those due to the presence of people and electrical devices are required just in the most refined models.
Performance: advantages and limitations The simplicity of the nodal method brings with her a huge advantage: the computational efficiency [5]. According to Goyal and Ba- rooah [13], the RC-circuit is a perfect example of reduced order model, particularly suitable for the real time control of Heating, Ventilation and Air Conditioning (HVAC) systems.
From this study it results that the nodal model has a computation time of at least six orders lower than the full-scale model. This characteristic is confirmed by Foucquier [12]
that sees the power of the nodal modeling method in its ability of describing ’the behavior of a multiple zone building on a large time scale with a small computation time’.
The strong assumption of homogeneous air volume anyway influences directly the appli- cation field of the nodal model. According to Foucquier [12] it is not detailed enough to give a satisfactory representation neither of the Indoor Air Quality (IAQ) or of the pollu- tant concentration and distribution within a room. Its application is mainly related to the calculation of energy consumption, thermal loads and zonal temperature evolution in time.
The nodal approach can be also used for predicting the air flows within the building and the overall air change rate.
Application An interesting application of the nodal model is reported by Hazyuk, Ghiaus and Penhouet [16]. In the paper they deal with building dynamic models that can be used for Model Predictive Control (MPC). According to them the models deriving from spatial discretization present a huge amount of states and this implies the necessity of applying model-size reduction procedures. Another drawback is the non-linearity of this model. This feature in fact makes the model accurate just near the operating point. The alternative approach is the black-box model in which, anyway, the parameters tend to lose their physical meaning. The authors have identified in the lumped-model a way to avoid these drawbacks. In particular the RC-circuit has been utilized and they have demonstrated its accuracy. Through a comparison with a white-box model, to the authors have found a fitting above 92% for both model validation and parameters identification.
2.1.2 CFD models
The CFD models are among the most complex methods. According to Foucquier, this modeling method is able to describe a flow field with high accuracy. The level of details can be chosen through the discretization steps for both space and time. The smaller the time-steps or the mesh size, the higher will be the computational cost [12]. It is therefore necessary find a trade-off between the level of details and the Central Processing Unit (CPU) time.
This modeling approach is based on the resolution of Navier-Stokes equations and dedicated softwares, such as COMSOL Multiphysics and MIT-CFD, are required for computing the calculations.
2.1. Temperature estimation models for buildings 11/ 142 Prerequisites The CFD can be performed just by knowing the boundary conditions (BC) of each of the analyzed zones. There are three types of BC [25, 1]:
• Dirichlet BC: the temperature value on a surface is imposed;
• Neumann BC: the normal derivative of a function on a surface is imposed (air veloc- ity);
• Robin BC: the heat flux on a surface is imposed.
Performance: advantages and limitations According to Foucquier [12], the CFD modeling approach has huge potential for a detailed description of the flow pattern. This approach is therefore particularly suitable for applications such as the operating rooms, where the contaminants path is crucial, or for the study of ventilation performances [7].
Anyway, the long computation time, make this method not commonly used for the study of temperature distribution inside a large building. The detailed CFD study is in general applied just to specific components of the HVAC systems or to single construction elements [12]. Because of the high computational cost, the CFD model is not suitable for the HVAC system control since it is not able to provide information in real time.
A common solution often adopted for the study of large buildings avoiding the high com- putation cost, is coupling the CFD method with a second modeling procedure having short CPU time [12].
Another disadvantage of the CFD approach is related to the necessity of working with boundary conditions. It is fundamental to understand which BC is applicable to the studied case and to find out if that required information is known.
Application Hoffman and Schwartz have applied the CFD model to a building element, both in steady-state and transient conditions. The finite difference method has been used for the analysis. This paper shows out how accurate a CFD model can be. By comparing the temperatures resulting from the computational analysis of a ‘sandwich’ wall with the measured ones, it results that the maximum discrepancy between the values is less that 1K.
According to the authors, this type of analysis could be particularly interesting and powerful for the study of cold bridges and moisture generation inside a wall [17].
An interesting aspect of the CFD analysis is related with its ability of describing complex phenomena. An example is given by Tabarki and Ben Mabrouk’s work [29]. They have modeled a 3D combined heat transfer in a large enclosure taking into account also the effects related to the presence of a heat source with variable power and specific thermal boundary conditions. Several analysis regarding the heat transfer have been done previously but, despite their validity, none of them could be considered complete. In many cases, in fact, the convection has been studied assuming negligible the radiative heat transfer.
Other models have been built without treating the air conditioning system: usually an imposed power was considered. Sometimes the studies were limited to the 2D analysis, and therefore could not give any information regarding the presence of heterogeneous zones in the enclosure. Tabarki and Ben Mabrouk have considered the conduction through the walls as 1D heat transfer, while the natural convection has been solved using Finite Volume Method (FVM) and the surface thermal radiation with Net Radiation method. Two main
findings result from this study. First of all, it emerges how significantly the presence of a convective motion can influence the temperature field inside a room. This means that the convective heat transfer is not always negligible and that the assumption of uniform temperature distribution, that is usually at the base of a lumped model, could be very far from the real situation. Secondly, the study shows out the importance of taking into account the computational cost while building a model. In order to have a stable solution of velocity field, this model required a CPU time of two weeks [29].
The huge advantage of using an integrated approach emerges in the analysis conducted by Tan and Glicksman regarding the performance of natural ventilation [31]. In this study the CFD model has been coupled with the multizone one. For avoiding any iteration procedure between the models, the outputs of the multizone model were transferred as input data to the CFD one. The significant result is that, for the same buildings, the CPU time is more than 10 hours in the case of pure CFD simulation and less than 1 hour with the integrated solution.
Another possible example of integration model is obtained by coupling the CFD modeling method with the Proper Orthogonal Decomposition (Proper Orthogonal Decomposition (POD)) approach in order to determine in real time the temperature in a room. This procedure can be useful in order to know the actual temperature in a room where some sensors are present and there is mechanical ventilation. According to Tallet, Allery and Allard [30] this procedure is divided in two steps. The first one is an offline stage: through CFD simulation, samplings of flow configuration corresponding to different air inlet velocity and temperature are carried out. The results are used as database for the second step, the online one. This consists of several procedures: POD is used in order to decompose the velocity and temperature fields as a function of air inlet velocity and temperature and space; the readings of the sensors are used as input in an optimization algorithm that evaluates the air inlet velocity through the POD decomposition; the found velocity is used for the calculation of real temperature and air velocity inside the room itself through POD method. This model has been validated through a comparison with the measured values. A parametric study has also demonstrated that the number and position of sensor do not have a significant influence on the accuracy of the results [30]. This method could be extremely useful in order to have realistic values regarding the temperature distribution inside a room regardless the sensors positioning.
2.1.3 Zonal models
The zonal model is an approach that could be considered in a midway between the nodal and the CFD one [23]. The assumptions are in fact less strong than in the nodal models since in this case the air temperature distribution is not considered uniform. The subdivision of the analyzed room in sub-zones, allows to have detailed information regarding thermal and physical properties in each of them. The output of the simulation is a 2D map describing temperature, pressure, concentration or air velocity. Because of the relatively simplicity of the model, all these information are computed in a shorter time with respect to the CFD models [23, 12].
The model is based on the equations of both mass and thermal balance that must be satisfied in each sub-zone. The interesting aspect of this modeling procedure is that it takes into account the interaction between the system and the environment.
2.1. Temperature estimation models for buildings 13/ 142 Several softwares exist for the zonal modeling in buildings. An example is SimSPARK, that is useful for the description and visualization of indoor airflows.
Prerequisites For applying the zonal model it is required the knowledge of both the building geometry and the flows profile [12]. In the case of pressure driven flows, the pressure difference between two adjacent sub-zones creates an air flow characterized by a certain discharge velocity and discharge coefficient. Knowing the values of these last is another prerequisite for the computation of the zonal method. The discharge coefficient takes into account the viscous effect and the local contraction of the streamlines that is created when the airflow passes from one sub-zone to another. Their value is given by the ratio between the actual flow rate and the theoretical one. When it is not possible to calculate these coefficients, an approximate value of 0.8 is chosen [18].
Performance: advantages and limitations The power of the zonal model lies in its ability of giving enough detailed description of temperature distribution, pressure field and airflows path. The absence of hypotheses such as homogeneous air volumes present in the nodal model, makes this modeling approach particularly adapt to the study of indoor thermal comfort. The accuracy in the description of temperature variation in time is clearly demonstrated by Mohammedi [24]: the difference between simulated temperatures and measured ones is lower than 0.5K. On the other hand, the simplifications done with respect to the CFD method, imply limited accuracy in the description of pollutants pattern and flow field.
The computation time is shorter compared to CFD modeling approach, but anyway is two order of magnitude higher than the Central Processing Unit (CPU) time of nodal method [14]. This makes the zonal approach not really suitable for the knowledge of temperature distribution in real time.
Application Inard, Bouia and Dalicieux [18] have showed out how to build this kind of model. For each sub-zone, the mass and thermal balance must be imposed. According to them, the main problem is related with the modeling of mass transfer across the different zones and there are two possible ways to proceed. The first one is to fix air flow direction and utilize the specific flow laws in order to describe each of them. The drawback of this approach is the limited the application field due to the fixed air flow pattern. An alternative is to use a ‘degraded’ momentum equation, where the driving force of the mass transfer is the pressure gradient between different zones. These momentum equations are anyway too poor for describing the driving flows. The authors have therefore decided to use a mixed approach, describing the driving zones, having a high air momentum, with the appropriate flow laws and the zone with a small air momentum basing on the pressure field. By solving the model, both temperature and pressure fields can be found out. The importance of this paper lies in the applicability of the zonal modeling method to the dwellings. The authors have in fact validated the model comparing the numerical results with experimental data. The comparison, in addition, has not been limited to the basic cases, but it has been extended to more realistic ones characterized by convective load coming from different types of emitters. The results showed a very good matching between numerical and experimental values.
2.1.4 Artificial Neural Network models (ANN)
The Artificial Neural Network (ANN) is a ’nonlinear statistical technique principally used for the prediction’ [12]. This modeling method has an increasing importance in energy management of buildings [27]. The ANN has a much shorter computation time with respect to dynamic simulations [20], but anyway cannot be used for the real time control of HVAC systems. The ANN applications are in fact mainly related to the forecasting of energy consumption [12] and rarely to the description of temperature variation in time.
Prerequisites For the application of an ANN model, it is not required any knowledge regarding the geometry or the thermal properties of the analyzed building. What is required, instead, is to have a significant database [12].
Performance: advantages and limitations The main strong characteristic of the ANN models lies in their ability of deducing the relationship between the different data. On the other hand, there is a large amount of undetermined parameters that are utilized in the model [12] that could compromise the results reliability.
Application The paper written by Ruano regards a study for the temperature predictions in the rooms of a secondary school located in Portugal as a function of the weather condi- tions and the actuator state. The final purpose of the study is to use the predicted values in order to perform a better control on temperature regulation and energy consumption.
The ANN modeling method is very complex since for each room and for each analyzed variable is required a separate model. This method consists of two stages. In the first one the model structure is defined using a Multi-Objective Genetic Algorithm (MOGA) and the value of involved parameters is estimated through the Levenberg-Marquardt algorithm.
In the second stage, the found model is adapted on-line. The model has been validated by the author through the comparison between the calculated temperature values and the experimental ones. According to this, the simulation gives values accurate enough: the maximum discrepancy between measured and computed values is 2K, that rise up to 4K just for the window facing South. The singularity of this paper lies in its combination of detail level and completeness. A huge amount of variables in fact have been taken into account: occupation cycle, shading effect, wind components and so on. But, at the same time, the analysis is not limited at one single room or building component as it happens for CFD models. The importance of this paper is also in the evaluation of wind effect: despite the ambition of extreme accuracy, MOGA has considered the wind components irrelevant for the analysis.
Chapter 3
Implementation
In this chapter is described the implementation that was used to answer the research ques- tions presented in Sect. 1.2. The analysis of the existing temperature distribution models covered in Ch.2 allowed to have a clear picture of pros and cons characterizing each of them. Since the presented model is used for the estimation of the temperature distribu- tion in a MFH, the best option turned out to be the zonal approach with lumped-mass model per zone, i.e. apartment. The zonal model is in fact generally utilized for estimating the temperature values in different rooms or apartment taking into account their mutual influence. The air mass flows between adjacent apartments is considered negligible.
The governing equation presumes preservation of internal energy Uinternal and is a first order differential equation that can be generalized as in Eq. 3.1. The system boundary for quantifying the heat fluxes ˙Q is the outer shell of an apartment.
∆Uinternal=XQ˙in−XQ˙out (3.1)
Section 3.1 will present all required inputs to be able to calculate the heat fluxes ˙Q and configure the generic model according to the specifities of any MFH.
The resulting fluxes need to be preprocessed and aligned. The details of this processing step will be presented in Sect. 3.2.
The model used for estimating the temperature distribution in a building is described in Sect. 3.3. Several heat fluxes are considered that affect the energy balance of an apartment.
The models for the heat fluxes can be more or less complex dependent on their configuration.
At the end of this chapter in Sect. 3.8 the steps required for generating a 3D visualization of the estimated temperature distribution will be presented.
3.1 Input to model
3.1.1 Configuration of generic model to specificities of MFH under evaluation
3.1.1.1 Building geometry and apartments disposition
The final goal of the thesis is to have a configurable model of MFH. It must therefore be applicable to a building regardless its geometry and apartments disposition.
Limitations The model is applicable just to buildings characterized by polygonal plant with right angles. Constructions with unusual polygonal plant or with curved surfaces are not supported by the model. This choice was made by evaluating the characteristics that most of the buildings in Stockholm have in common. The final purpose was in fact to create a model applicable to the highest possible number of buildings.
Input data In order to give to the model the input data, a minimum of four input files are required. The first three regard the building under consideration:
1. Apartments geometry and distribution:
• Apartments identifier
• Apartments floor number
• Three main dimensions of each apartment
• Length of the two sides of the roof facing each direction
• Boolean values giving information about the presence of an external wall in each of the four directions
• Opaque ratio of the external vertical walls fext walls
• Opaque ratio of the roof froof
• Boolean values representing the presence of a sensor inside the apartment 2. Building properties:
• Building orientation Φ
• Latitude
• Longitude
• Longitude of standard time meridian
• Tilt angle of the walls
• Tilt angle of the roof facing the four main directions
• Building thermal capacity (mcp)bldg
• Heat transfer rate per unit temperature difference between indoor and outdoor, U Aext tot
• Baseload of heating power
• Solar radiation absorption factor α
• Convective heat transfer coefficient on external surface on the building hout
• cSHG factor
• Global heat transfer coefficient of the windows Uwindow
• Average opaque ratio f 3. Apartments properties:
• Fraction of opening area of each apartment ξapt
3.1. Input to model 17/ 142
• Opaque ratio of each apartment fapt
Additional files contain information for the calculation of the external area of the buildings connected to the same substation of the analyzed one. In the simplest case there are just two buildings served by the same substation. Only an additional file is therefore required. The information contained in this fourth file are reported below:
4. Secondary building geometry:
• Apartments identifier
• Three main dimensions of each apartment
• Length of the two sides of the roof facing each direction
• Boolean values representing the presence of an external wall in each of the four directions
In order to have a unique definition for the orientation of each building, Φ is defined through a correlation between local and global reference system. This last has been chosen with the Y axis in North-South direction and the X axis along West-East direction. The local reference system has instead the y axis perpendicular to the external wall facing North-East and the x axis perpendicular to the y one. The two directions on each axis are identified by the superscripts ’ and ". The building orientation Φ is defined as the angle between y0 and the North. A schematic representation is Fig.3.1.
Φ N
S
E W
y’
y"
x’
x"
Figure 3.1: Global and local coordinate systems with representation of the angle defining the building orientation Φ.
U is the global heat transfer coefficient. A is the total external area of the building. m is the mass of the building and cp,bldg its specific heat. The values UAext tot and mcp,bldg are given in output from another script able to evaluate the thermal properties of the building through the analysis of its response to the variation of space heating power supplied. This script takes as input the outdoor temperature, the indoor temperatures read by the sensors, the heating power supplied to the building and the time at which the readings are referred to. In addition it is known the time at which the power supply is switch off (2 a.m.) and the duration of this interruption (2 hours). The script gives in output the building thermal capacity, the value of UAext tot, the time constant of the building and the baseload of heating power. This last parameter will be defined and discussed in Subsec.3.1.2.6.
The tilt angle β is defined as the inclination of a surface with respect to the ground.
The solar radiation absorption factor α represents the fraction of solar radiation that is absorbed by the opaque surface of the building with respect to the total incident radiation.
This value is a function of the painting color of the external surfaces and can vary between 0 and 1.
The convective heat transfer coefficient hout is a function of the dynamic condition of the outdoor air and of its interaction with the walls of the building. An average value of this coefficient can be chosen for the calculations.
The cSHG value represents the fraction of solar radiation that is transmitted directly and indirectly inside a certain apartment with respect to the total radiation that hits the glazed surface. The value can vary between 0 and 1, depending on the type of windows. The characteristics that influence this value are: number of panes and type of glass (standard or low-emissivity).
The opaque ratio f is the ratio between external glazed and opaque surfaces. The Eq.3.3 reports the expression for the calculation of the opaque ratio for a general apartment.
fapt = Atot ext opaque, apt
Atot ext opaque, apt+ Atot ext glazed, apt
(3.2)
fapt = Atot ext opaque, apt
Aext total, apt
(3.3) The fraction of opening area ξ is defined as the ratio between the opening area and the external surface of each apartment (see Eq.3.4).
ξapt = Aopening, apt
Aext surface, apt
(3.4) In the most general case, the building structure is inhomogeneous and the ξapt values vary for each apartment. In case of homogeneous building, instead, the openings can be assumed to be uniformly distributed on the external surface. A unique ξ factor can therefore be considered for all the apartments.
3.1.2 Continuous inputs to the model
3.1.2.1 Internal heat gains: people
The occupancy of an apartment, e.g. the presence of inhabitants, gives a significant con- tribution to the internal free heat gains. In order to calculate the magnitude of this term,
3.1. Input to model 19/ 142 the information contained in the Brukarindata bostäder have been used. This article re- ports typical values that should be utilized when performing energy calculation on Swedish dwellings [21].
Assumptions and limitations The evaluation of internal gains related to the presence of people is highly uncertain. The first obstacle lies in the unknown number of tenants for each apartment. In order to solve this, the typical amount of people has been set according to what is suggested in Brukarindata bostäder [21]. The utilized values are reported in Table 3.1.
Apartment size 1 room 2 rooms 3 rooms 4 rooms 5 rooms 6+ rooms
Occupancy values 1.42 1.63 2.18 2.79 3.51 3.51
Table 3.1: Typical occupancy values in dwellings [21].
In order to utilize the approach reported above, it is required to know the number of rooms in each apartment. This information is commonly not readily available without having a structural plan of the building. To face this problem, several buildings have been analyzed through a web search. This allowed to elaborate a rule of thumb through which the number of room of a general apartment is related with its floor area. The utilized values are reported in the Table 3.2.
Apartment floor area A [ m2] A < 25 25 < A ≤ 60 60 < A ≤ 150 A > 150
Number of rooms 1 2 3 undefined
Table 3.2: Correlation between floor area and number of rooms in a general apartment.
Other limitations are related with the fact that people’s behavior can be predict and generalized just up to a certain extent. According to what reported by Levin, people use to spend at home 14 hours per week [21]. This is a value resulting from the analysis of the whole week, which means that it does not take into account the difference between weekdays and weekends. This will result in a limitation in the accuracy of the model.
Another source of error is the missing information regarding which is the actual time frame in which the occupants are inside the apartments. In order to solve this last problem, the schedule has been set according with the habits of a typical worker in Sweden. The occupancy time has therefore been set between 17:30 and 7:30.
Input data The presence of people inside the apartments in the various time steps has been given as input data. Boolean values have been used for this purpose.
3.1.2.2 Internal heat gains: electrical appliances
In order to perform a complete analysis and take into consideration all the factors that con- tribute to the energy balance, the free internal gains generated by the electrical appliances have been taken into account.
Assumptions and limitation The main assumption at the basis of the internal free heat gains calculations is that each apartment, regardless of its size, is provided with the same amount of electrical devices. The reasoning behind this choice is related with the fact that, in general, what varies between apartments having a different floor area extension is the number of bedrooms. The amount of appliances present in the kitchen and their utilization period does not change significantly.
A second assumption regards the utilization time of these appliances. The same sched- ules have been chosen for every apartment.
Taking into consideration the contribution of appliances having a low amount of hours of yearly utilization would not bring any advantage. The resulting model in fact would be characterized by an overcomplexity at which does not correspond any significant improve- ment in the output accuracy. The devices such as vacuum cleaner, oven and iron have been therefore considered negligible. This choice allows also to avoid further increment of computational time. Short computational time is in fact a key feature of any good model.
Input data The electrical appliances taken into consideration in the model development, together with the related power and schedule are reported in the Table 3.3.
Electric device Power [W] Utilization time
Freezer 200 continuously
Refrigerator 150 continuously
6:50-7:00 Cooking plates 1500 18:00-18:30
6:30-7:30
Light 60 17:30-00:00
TV 150 20:00-22:00
Table 3.3: Common power and utilization schedule of typical electric appliances [15].
The schedule for each device has been given as input data through the same file con- taining the information about the presence of people. Also in this case boolean values have been used for expressing whether the devices were operating or not.
The amount of power of each device is an input data and the utilized values have been taken from the literature [15]. The schedules have been set according with the Swedish habits and respecting the typical lengths of utilization time reported by Havtun et al. [15].
Some electrical appliances are not reported in the previous table cause, even if present in most of the apartments, they don’t contribute to the internal heat gains. This is the case of dishwasher and washing machine. The heat generate by these devices is in fact released together with the drained water.
3.1.2.3 Sun data
The solar radiation represents one of the free heat sources that, together with internal gains, contributes to the building energy balance. The relevance of this contribution depends
3.1. Input to model 21/ 142 not just on the magnitude of global radiation, but also on the relative position between the sun and the building itself. In addition to that, also the surroundings aspect can have a significant impact on the magnitude of solar gains. The presence of trees or high constructions, in particular, could decrease the amount of radiation that reaches the building surfaces.
Assumption and limitations In order to perform the calculations, it is assumed that the global radiation read in the meteorological station is measured with a pyranometer. This means that the recorded values are referred to a horizontal surface.
There are two main limitations regarding the evaluation of sun effect. First of all, the shades on the external walls, due to the presence of other walls belonging to the building itself are not taken into account. Secondly, any shading effect related to the surroundings is neglected. The main reasoning behind this choice lies in the model configurability. Each building has in fact a certain environment around it and it is not possible to generalize something characterized by a so high rate of variability.
Input data The input data required for the calculations related with the sun depend on the configuration of the model itself. All the input data are anyway given through the files regarding the building (2) and apartments (1) properties. The global radiation and the timestamp are instead taken from the meteorological data.
3.1.2.4 Wind data
The wind could have an effect more or less significant on the energy balance of a build- ing. When the wind hits a building, in fact, a condition of over-pressurization and under- pressurization is created respectively on the windward and leeward sides. The pressure difference between these pressures and the indoor one, create an air movement from the zone with higher pressure to the ambients with lower pressure. For the principle of mass balance, if a certain amount of air leaves the building, the same quantity must enter. In a cold country such as Sweden, the air coming from the outdoor environment, is always characterized by a temperature lower than the indoor one. As a consequence the infiltra- tions/exfiltrations represent always a loss in terms of energy. Part of the heat supplied by heating elements to the building, must in fact be used for rising up the temperature of infiltrated air to the desired indoor temperature.
The wind has usually a significant impact in the natural ventilated building, since in that cases the buildings themselves and some constructive elements such as chimneys are designed with the purpose of promoting the ventilation.
The analyzed building anyway does not fall into that category. It has been built between 1946 and 1953, which means that the concept of passive building was not still put into practice. At the same time the requirements reported in the Boverket’s building regulations (BBR) were already into force. According to BBR, a minimum amount of ventilation must be continuously provided. Since the amount of infiltrations/exfiltrations in case of natural ventilation is unpredictable, usually the buildings are provided with mechanical ventilation.
This last will be discussed in the subsection 3.1.2.5.
