A SIMPLE MODEL FOR THE DYNAMIC COMPUTATION OF BUILDING HEATING AND COOLING DEMAND. Kai Sirén AALTO UNIVERSITY


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1 A SIMPLE MODEL FOR THE DYNAMIC COMPUTATION OF BUILDING HEATING AND COOLING DEMAND Kai Sirén AALTO UNIVERSITY September 2016
2 CONTENT 1. FUNDAMENTALS OF DYNAMIC ENERGY CALCULATIONS Introduction Energy balance of a control volume Finite differences Euler method of solution Implicit method of solution Systems of several node points Layered structures CALCULATING THE HEATING DEMAND OF A BUILDING Time resolution A simple building model Energy balances of the node points CALCULATION PROCEDURE General progress of the computation Conductances and heat capacity flows Internal heat capacity and equivalent area Solar heat gain through windows Division of heat gains into convection and radiation WEATHER DATA LITERATURE SIMULATION SOFTWARE
3 1. FUNDAMENTALS OF DYNAMIC ENERGY CALCULATIONS 1.1. Introduction The evolution of computers has strongly influenced the development of building energy calculation methodologies. In the old times, very simple analytical steadystate methods, having a coarse time resolution like one month or one year, were preferred because there was no computation capacity available. During 1960s and 70s a revolution in energy calculation went off as the computers were offering constantly increasing computational power. This enabled first more detailed quasisteadystate implementations and finally very detailed dynamic numerical approaches which often are called simulations. Figure 1.1 Different approaches into building energy calculations There is a wide variety of modelling and computational approaches describing the building and its thermophysical behavior. Fig. 1.1 gives an idea of some physically based (whitebox) procedures which are or have been in a wide use. Time resolution (calculation time step) is one important feature of a computational implementation. Formerly when all calculation was done manually, the calculation time step was one year (steadystate calculation) or one month (quasisteadystate calculation). Now, with powerful computers the usual time resolution in energy and indoor condition calculations is one hour (dynamic calculation) or even less. The detail of modeling can also vary within wide limits. At its simplest, the whole building can be described as one thermal resistance between the indoor and outdoor air temperatures. On the other hand, on a high level of detail thousands of particulars in the building envelop, the energy and HVAC systems and their controls are accounted for. Selecting a suitable tool for energy calculations is always a compromise between the quality and information content of the results and the computational time. The higher is the time resolution and the detail of modeling, the longer is the execution time and vice versa. 3
4 The nature of the phenomena calculated plays an important role as well. Normal heating energy demand calculations do not usually call for a high time resolution. A monthly approach can be quite sufficient because the computed phenomena are rather slow and averaging over a period of time does not cause severe errors. On the other hand, computation of some faster effects like cooling load and energy, indoor temperature variations or some productions system behavior like solar PV require at least one hour resolution if not less. Modern energy simulation programs are able to work on a very detailed level of modeling as well as a very high time resolution. The calculation of energy balances is based on numerical methods. The computation is fully dynamic and the solvers can often adapt the time step to the changes going on in the computed system. The user of such a program does not see and unfortunately rather often does not know how the computation works. However, an advanced user should understand how the simulation works and what are the fundamentals the computations are based on. Only then he will be able to use the software in a progressive way and indepth understand the results which the computation is producing. To get an idea what is going on behind the scenes of a simulation, we choose the so called finite difference method for a closer examination. Finite differences actually is a general purpose mathematical method for solving differential and partial differential equations numerically. However, in ordinary language of heat transfer and energy calculations it often includes also some other principles like dividing the system under consideration into small control volumes and working based on their energy balance Energy balance of a control volume Heat transfer inside and on surfaces of the structures of buildings is in principle always a dynamic, nonstationary phenomenon. Temperatures and heat flows change constantly with fluctuating outdoor temperatures, solar radiation and internal thermal gains. In such a constantly changing situation the thermal energy charged and released in the structure mass must be taken into account in the calculation. Let's investigate the phenomenon in the light of a simple example. In Fig. 1.2 there is a brick wall which forms a system which we call control volume. The boundary of the control volume is shown in the figure. The external temperature T e = T e (t) is a function of time. As well is the internal temperature T i = T i (t). We want to calculate the heat flows from/to the wall on the external side and the internal side as a function of time. To do this following assumptions are done:  the wall is of one homogenous material  the wall has one uniform temperature T 1  the case is onedimensional (horizontal heat flows only)  all thermal mass of the wall (inside the control volume boundary) is lumped into one thermal node point (temperature T 1 ). The heat capacity of the whole wall is denoted as C 1 and the thermal resistances between the wall node point and the air node points on both sides are R 1e and R 1i. The resistances are containing the conduction of half of the wall thickness plus the convection on the wall surface and can on the external side be formulated as 4
5 / (1.1) where x is the wall thickness, k is the wall thermal conductivity, h e is the convective heat transfer coefficient on the external side and A is the wall transversal area. The resistance on the internal side is calculated in a similar way. Figure 1.2 A brick wall and its thermal model The heat capacity of the wall is based on its thermal mass and can be written as (1.2) where ρ is the density of the wall material and c p is the specific heat capacity of the wall material. Now we can write an energy balance for the control volume (wall) in the following way: (1.3) where H 1e = 1/R 1e and H 1i = 1/R 1i are the inverse of the thermal resistances and called thermal conductance. The left side of Eqn. (1.3) represents the heat flow stored or released by the wall mass and the right side represents the heat flows from or to the wall. The energy balance says that at every instant the sum of the heat flows must be equal to zero (as no heat is generated in the system). 5
6 1.3. Finite differences Euler method of solution Equation (1.3) would be easy to solve using a simple analytical treatment. However, since already in slightly more complex cases the analytical approach is useless we directly introduce a numerical method. The finite difference method, which is extremely useful and versatile, allows solving problems of practically any complexity. To this end, we discretize the differential equation (1.3). In other words we replace the time differential with a difference term as follows! " (1.4) where T 11 is the wall temperature at an earlier instant t 1 and T 1 is the wall temperature at a later instant t so that t = t 1 + t, where t is the calculation time step. Since this is an initialvalue problem, we know the solution (temperature T 11 ) at the previous time instant and we can find the solution (temperature T 1 ) at the next time instant by simply solving it from equation (1.4)! # (1.5) where the derivative term can be chosen to correspond to different instants of time: the previous, the present or some combination of them, which in turn leads to different variants of the calculation method. When we substitute the derivative from the system energy balance (1.3) corresponding to the previous instant (subscript 1) to Eqn. (1.5) we get! %!!!! & (1.6) where all temperatures at the previous time on the right side are known and the temperature of the present time can be solved. This variant is called the explicit method or the Euler method of solution. The computational procedure is to step ahead in time using t steps and by substituting the temperature of the previous time with the temperature of the present time solved from (1.6). The good feature of Euler's method is that the solution is simple to achieve even if there would be several equations to solve because the equations are not interconnected in the present time. On the other hand, the disadvantage of the Euler's solution is the tendency for instability. Especially a too long calculation time step easily leads to uncontrollable oscillations of the solution. Example 1.1 The brick wall in Fig. 1.2 has following features: A = 10 m2 x = 0.13 m k = 0.7 W/mK area of wall thickness of wall heat conductivity of the wall material 6
7 ρ = 1700 kg/m 3 c p = 840 J/kgK h e = 20 W/m 2 K h i = 4 W/m 2 K density of the wall material specific heat capacity of the wall material heat transfer coefficient on the external surface heat transfer coefficient on the internal surface. What are the heat flows on both sides of the wall during 6 hours when the external temperature is according to a sine curve (Fig. 1.3) and the internal temperature has a constant value of 22 o C.? Let's first calculate the heat resistances, conductances and the heat capacity of the wall: R 1e = K/W; H 1e = 70.0 W/K R 1i = K/W; H 1i = 29.2 W/K; C 1 = J/K. To grasp the heat flow, the temperature of the wall must first be known. To start the computation, an initial guess for the wall temperature is needed. Let's use here the value for the stationary situation during the first hour T 10 = (H 1e T e +H 1i T i )/(H 1e +H 1i ). Choosing one hour ( t = 3600 s) for the calculation time step, the solution proceeds in time as shown in Fig 1.3. When T 1 is known, the external heat flow is Φ e = H 1e (T e  T 1 ), directly from the heat balance equation (1.3) and the internal heat flow correspondingly. Figure 1.3 Temperatures and heat flow as a function of time. We notice that the temperature change of the wall has clearly smaller amplitude than the change of the external temperature. Also the phase of the wall temperature is delayed with about three hours compared with the external temperature. Further, the changes in the external heat flow are much larger than those in the internal heat flow. All these phenomena are influenced by the mass (and heat capacity) of the wall. 7
8 1.3.2 Implicit method of solution When, in place of the previous, the derivative corresponding to the present time is used, the discretized Eqn. (1.6) takes the following form:! % & (1.7) where there now the unknown temperature for the present time T 1 is on both sides of the equation. Solving for the unknown gives "' ( ) * ' ( ) *. ' ( ) * (1.8) '* This way of discretization is called the implicit method. The best feature of the implicit method is stability. The solution is not oscillating in any conditions Systems of several node points To increase the accuracy of the computation and to find out how the temperature distribution is changing inside the wall, it is divided into several smaller control volumes. One node point is placed into each control volume to characterize its temperature, Fig Writing the energy balance equation for each of the control volumes we get a set of linear differential equations. The equations are discretized and the set of algebraic equations is solved for each time step, exactly in the same way as earlier. The energy balance equations for the system in Fig are + + (1.9),   (1.10) / / . (1.11) 8
9 Figure 1.4 A system with several node points. So here the unknowns are the wall temperatures T 1, T 2 and T 3. The temperatures T 0 and T 4 are boundary conditions and must be known. Equations (1.9) (1.11) can now be discretized according to time using the Euler method, the implicit method or some other method. Let's use here the implicit method. This results in! % + + & (1.12)!, %   & (1.13)  !. %   / /  &. (1.14) By rearranging the unknowns on the left side we get ! + + (1.15), 01,, 2,  ! (1.16) /2  !. / /. (1.17) 9
10 In a matrix form the above set of equations is , 01,, 2, / ! + +! 3 (1.18) !. / / or using a shorter notation (1.19) The above equation is solved by left multiplying both sides by the inverse of matrix A to give the solution 65! 7. (1.20) The elements of matrix A consist of the physical parameters of the system. The elements of matrix B are known from the previous calculation cycle. This way the temperatures corresponding to the current time point can be calculated from equation (1.20) and passed for the temperatures of the previous time for the next calculation round. Before the calculation starts we of course need to make a first guess for the temperature vector T. Here we can see that the implicit method leads to a set of equations which then has to be solved by matrix or other equation solving methods. In case of the Euler method, there would be the same number of equations. However, as there is no cross connection between the equations in terms of the unknowns, the equations can be solved one by one, which is computationally simpler than solving a true set of equations. The downside with Euler's method is the sensitivity for unstable behavior. More broadly, the use of the finite differences to solve heat transfer problems is very well explained in Myers's book [1] Layered structures Usually the structures in a building are not made of one homogenous layer but of several different material layers each having its specific purpose, like a supporting structure, heat insulation, moisture barrier etc. When constructing a thermal model of layered structures it is advisable to place the temperature node points on the interfaces between the layers plus the external and internal surfaces. If the layer is thick also some internal node points inside the layer can be used. This is one action to minimize the error in the numerical solution. Of course the conductances and capacities have to be calculated accordingly. The conductances are always the inverse of the heat resistance between adjacent node points. To calculate the thermal capacities each node between two layers has to be allocated some material from both layers. The capacities for the external and internal nodes are containing the material towards halfway the adjacent material node point. 10
11 2. CALCULATING THE HEATING DEMAND OF A BUILDING 2.1. Time resolution Like in the introduction part was shown, the heating or cooling energy demand of a building can be calculated in many ways. The simplest methods are working on a yearly or monthly level. However, these methods are not able to satisfactorily capture rapidly changing phenomena like internal heat loads, the solar heat load coming through windows or the functioning of the control system. These kinds of effects have a crucial role in predicting the cooling power and energy as well as the internal temperatures. However, they influence the prediction of the heating energy as well. To account for the impact of the rapid phenomena, the relevant approach is to use a finer time resolution like one hour. The hourly calculation approach is representing the mainstream in energy simulation. There are few reasons for this. The weather data needed in simulations is usually available on an hourly level. Also the building is a rather slow system and the need to compute with a higher time resolution than one hour is rare. There are advanced building simulation programs using adaptive time step which can go onto a minute level but this is often not necessary. In the following an extremely simple building model is introduced. The model is used to demonstrate the principles of dynamic hourly level calculation of the indoor temperature as well as the heating and cooling power and energy A simple building model The schematic of the building and the thermal model of it are shown in Fig The heating and cooling demand are predicted with a simple model including two thermal capacities and two unknown temperatures, namely the indoor air temperature T i and the temperature of the combined building structures T m. The node points are connected either by conductances describing the routes for heat flow or heat capacity flows describing the mass (air) flow between the nodes. The computation is based on the solution of the energy balance equations hour by hour. In Fig. 2.1 T i is the temperature of the indoor air and T m the temperature of building mass. The external (outdoor) temperature T e is a boundary condition and has hourly changing values. The supply air temperature T s is known as well and based on the control of the air handling unit (AHU). H ven is the heat capacity flow of the ventilation air and H inf is the heat capacity flow of the infiltration air through the building envelop. The heat loss through the windows is described with the conductance H win and the heat flow through rest of the building envelop with H en. The internal convective connection between the indoor air and the building structure is presented by the conductance H in. The heat capacity of all structures C m is lumped and connected to the mass node. The air node is connected to the indoor air capacity C i. All convective heat gains (powers) Φ i, are directed to the air node and all radiative gains Φ m, including the solar radiation through the windows, are absorbed by the structures and thus directed to the mass node point. The space heating or cooling power Φ hc (positive heating, negative cooling) is introduced into the building through the heating or cooling system and directed to the air node. The task of the control system is to keep the indoor air temperature in specified limits by controlling the heating and cooling power. 11
12 Figure 2.1 Schematic of the building as well as the corresponding thermal model Energy balances of the node points To find out the indoor temperature and need for heating and cooling energy using the model in Fig. 2.1, the energy balances of the node points are needed. The energy balance for the air node is 89 : ; 9< =9 > 9? A. (2.1) where dt is the time differential. Accordingly the energy balance for the mass node point is? B 9? 9??. (2.2) 12
13 Let's do the discretization of the equations using the implicit method for the sake of stability! " 89 : ; 9< =9 > 9? A (2.3)? B! B" 9? 9?? (2.4) where T i and T m are the temperatures of air and mass at the present instant of time and T i 1 and T m1 are the temperatures at the previous instant of time. The computation time step t is the time between the previous and the present times. Now the behavior of the system is described with two algebraic equations (2.3) and (2.4) from which the temperatures at the present time can be solved when the temperatures at the previous time are known. The solution can in practice be achieved in few different ways. The precise solution involves the solution of a pair of equations in an ordinary way. This leads, for each of the temperatures, to one equation where the other unknown is eliminated. There is, however, another approach which leads to some extent simpler solution, especially in a case with several equations. First both unknown temperatures are solved both from their own energy balance equation. Thus the temperature of the air node becomes ) ( "'* CD E ';* DF '* GD > '* D B ' ' HI ) ( '* CD'* DF '* GD '* D (2.5) and accordingly the mass node point temperature is? )B ( B"'* D '* D " ' B )B ( '* D'* D. (2.6) As such, this pair of equations cannot provide any solution as there is the other unknown on the right side of both equations. However, by replacing the present value of the air temperature in Eqn. (2.6) by the previous value of the air temperature, we can first solve the temperature of the mass node point and thereafter the temperature of the air node point from Eqn. (2.5). In this kind of a pseudoimplicit solution one more approximation is done, which slightly affects the accuracy of the result, but not much in this case as the mass capacity is large and the temperature fluctuations of it are slow. On the other hand, the computation is easy to implement as the equations are simple and the solution is straight forward based on the previous values. In the beginning a first guess for both unknown temperatures must be done and the estimated values substituted into Eqns. (2.5) and (2.6). Here the solution of the stationary system is one good alternative which can easily be derived from the energy balance equations (2.1) and (2.2) by setting the derivative terms in both equations equal to zero. 13
14 3. CALCULATION PROCEDURE 3.1. General progress of the computation Before the hourly temperature and energy calculation, the heat conductances of the building thermal model are determined based on given input values. Also the lower and upper control limits T il and T iu for the indoor air are chosen. The (ideal) control is keeping the indoor air temperature between these values during the calculation by introducing and appropriate amount of heating or cooling energy for each hour. The temperature and energy calculation proceeds hourbyhour as follows. First the heat gains (powers) of the treated hour to different node points are computed based on solar radiation and other input data. Also the external temperature is given the value of the corresponding hour. After this the two unknown node temperatures of the building model are calculated by first setting the heating/cooling power equal to zero, Φ hc = 0 (free floating case). If now the computed indoor air temperature T i is between the set limits, no heating or cooling power is needed and the calculation can proceed for the next hour. If, however, the air node temperature remains below the lower limiting temperature, some heating is needed. The appropriate average heating power for the hour in question is solved from the air node energy balance equation to be A ; 89 9< =9 9 > ; 9< =9 > 89 : 9?! " (2.7) where the air node temperature is set equal to the lower limit T i = T il. On the other hand, if the free floating air temperature exceeds the upper limiting temperature, the air node temperature is set equal to the upper limit and the cooling power for the hour is calculated from (2.7). After solving the needed power, it is multiplied by the calculation time step (in this case one hour) to get the heating energy (positive) or cooling energy (negative) for the hour in question. For the first hour a guess for the air node and mass node temperatures must be done. One approach is to use the temperatures of the stationary case solved from the energy balance equations (2.3) and (2.4). Another approach could be to give the air node temperature a value between the upper and lower control limits and the mass point temperature a value between the air node temperature and the external temperature and then iterate few rounds using the first hour input values. After this the procedure can continue as described above by using Eqns. (2.5) (2.7) one after the other. The general calculation procedure is shown as a flow chart in Fig
15 Figure 3.1 Calculation procedure of temperatures and hourly energies. 15
16 3.2. Conductances and heat capacity flows Assuming certain values for the convective and radiative heat transfer coefficients, the conductances of the building model can be presented in following form: 9J 9 9 (3.1) 9 M 9,M M J 9,M 9,M (3.2) =9 M =9,M M J =9,M =9,M (3.3) H in is the conductance between the indoor air node and the mass node (W/K) U in is the heat transfer coefficient between the structures and the indoor air (U in = 2.0 W/m 2 K) A in is the equivalent internal heat transfer area (m 2 ) (see next chapter) H en is the conductance of the building envelop without windows (W/K) H en,j is the conductance of the part j of the envelop (W/K) U en,j is the Uvalue of the part j of the envelop (W/m 2 K) A en,j is the area of the part j of the envelop (m 2 ) H win is the total conductance of all windows (W/K) H win,j is the conductance of window j (W/K) U win,j is the Uvalue of window j (W/m 2 K) A win,j is the area of window j (m 2 ). The heat capacity flows of the ventilation air flow and the infiltration air flow are: 89NO89 P P (3.4) 9<NO9< P P (3.5) H ven is the heat capacity flow of the ventilation air flow (W/K) V ven is the ventilation air flow (m 3 /s) ρ a is the density of air (kg/m 3 ) c a is the specific heat capacity of air (J/kgK) H inf is the heat capacity flow of the infiltration air flow (W/K) V inf is the infiltration air flow (m 3 /s). 16
17 3.3. Internal heat capacity and equivalent area In a building, the heat capacity of the structures which are inside the insulation layer mainly affects the charging and discharging process of heat between the structures and indoor air. Thus this capacity is influencing both the heating and cooling energy need as well as the indoor temperature. In a simplified model where all heat capacity of the structures is lumped into one node point, we have to work with a lumped internal heat capacity of the whole building. The internal heat capacity can be calculated according to the standard ISO [2] when the structure layers are known. For cases where the detailed structures are not known, the standard gives some default values for the heat capacity and the associated equivalent heat transfer area, Table 3.1. Table 3.1 Internal heat capacity and equivalent heat transfer area [2] Structure type A in m 2 C m J/K Very light 2,5 x A f x A f Light 2,5 x A f x A f Medium 2,5 x A f x A f Heavy 3,0 x A f x A f Very heavy 3,5 x A f x A f A f is the floor area of the space in question [m 2 ] Solar heat gain through windows The sun is causing a heat gain (heat power) coming into the space both through the windows and through the other parts of the building envelop. Here we neglect the gain coming through the walls and roof and focus on calculating the gain through the windows. To further simplify the computation, we merge the direct and diffuse solar radiation components as total radiation. The heat gain through the window for each hour is the product of the radiation intensity on the outer surface of the window and the effective area of the window construction : Q = (3.6) where I t is the average total radiation intensity on the outer surface of the window during the hour and A we is the window effective area for total solar radiation. If the space in question has several windows, the heat gains through each window are calculated separately and then added together. The window effective area for total radiation is 17
18 = R S : T (3.7) where A g is the area of the window glazing, F s is the shading coefficient (0 S : 1 of the window frame and embrasure and τ t is the transmittance for total (direct plus diffuse) radiation for the entire glazingsolarshading structure. The transmission of the radiation is calculated by a simplified approach loosely according to standard EN [3]. The total transmission is dependent on the glazing itself and on the solar shading arrangement T T :: T R (3.8) where τ ss is the transmittance of the solar shading and τ g is the transmittance of the glazing. Further, the transmittance of the glazing is a function of the incident angle of the radiation and can be expressed using the following relationship T R T R9 11cosY  (3.9) where τ gn is the total normal transmittance for solar radiation (energy) coming from the direction of the normal of the glass panes and θ is the incident angle between the normal of the glass panes and the beam radiation. Typical values for the total normal transmittance according to EN [3] are shown in table 3.2. Table 3.2 Typical values for total normal solar energy transmittance Type of glazing Single clear glass 0,85 Double clear glass 0,75 Triple clear glass 0,65 Double clear glass with lowemissivity coating 0,70 τ gn 3.5. Division of heat gains into convection and radiation The internal heat gains can be classified into three groups which are: people, lighting and appliances plus equipment. The timing of internal gains during the day depends on the sequence (profile) of occupation and use of the building. A residential building has a different sequence than a school or an office. For energy calculation purposes each component of the internal gains has to be defined for each space in the building and for each hour of the year. Further, the heat power for each type of internal gains has to be divided into two parts: convective part and radiative part. This is necessary because these two modes of heat transfer are influencing the energy balance of the building in a different way. The convective part is connected to the indoor air through convection while the radiative part is connected to the structural components through thermal radiation. The proportions of the 18
19 convective and radiative parts are dependent on the type of the heat producing element. Let's denote the convective part of different gains as a portion of the total gain in the following way A Z A A[ Z A[ [ (3.10) A\ Z A\ \ where φ cpe is the convective heat power produced by people, ω cpe is the relative portion of convection and φ pe is the total heat power produced by people. Analogously for lighting as well as appliances plus other equipment. Correspondingly the radiative parts are: ] 1Z A ][ 1Z A[ [ (3.11) ]\ 1Z A\ \. In the absence of more precise information of the factors in equations (3.10) and (3.11) following default values can be used: ω cpe = 0.70, ω cli = 0.30, ω ceq = The solar gain through the windows is mainly shortwave radiation which is absorbed by the floor material and other structures in the room. A small part is absorbed by the window itself and penetrating the room as convection and longwave radiation but here this part is assumed to be included in the shortwave radiation. Summing up all convective components and radiative components we then get A A A[ A\ (3.12) ] ] ][ ]\ : (3.13) In the building model the convective part is directed to the indoor air node point, which leads to φ i = φ c and similarily the radiative part is directed to the mass node point which means φ m = φ r. 19
20 4. WEATHER DATA The most important meteorological information necessary for the calculation of building energy demand are the outdoor temperature and solar radiation data. Solar radiation is divided into two components, direct radiation and diffuse radiation. The sum of these is the total radiation. The most commonly measured meteorological radiation data is the total radiation onto the horizontal plane, as well as diffuse radiation onto the horizontal plane. For energy calculations computational transformations on differently oriented vertical or inclined surfaces are made based on this measured data. Outdoor temperature and solar radiation is needed also for determining the production of solar PV or solar thermal. Other weather information usually available is outside air humidity, and wind speed as well as wind direction. The humidity is important for calculation of different kind of air handling processes. Wind speed and direction influences the heat loss and air infiltration of the building. It is also needed for estimating the production of wind power. The time resolution of weather data is normally one hour. As the building itself is a rather slow system, this is not a problem from the point of computing the building thermal dynamics. On the other hand, there are some very fast weather connected processes like the interplay between PV production and electricity demand where the one hour time step is giving in some cases rather erroneous results. For Finnish building energy simulations a Test Reference Year (TRY 2012) has been developed. This testyear contains hourly based weather data for three locations (areas) in Finland. The data is composed of actual measured data from years by choosing data from months best representing the average weather [4]. 20
21 5. LITERATURE 1 Myers G.E., Analytical methods in conduction heat transfer (1971). McGrawHill Book Company, 508 p. 2 ISO 13790, Energy performance of buildings Calculation of energy use for space heating and cooling, 2008, 162 p. 3 EN , Solar protection devices combined with glazing. Calculation of solar and light transmittance. Simplified method, 2003, 16 p. 4 Jylhä et al, Test reference year 2012 for building energy demand and impacts of climate change. Finnish Meteorological Institute, Reports 2011:6. 6. SIMULATION SOFTWARE IDAICE (advanced, full size building energy and indoor simulation program) IDAEsbo (restricted version of IDA, freeware) Energy Plus (one of the globally best known building simulation programs, freeware) TRNSYS (a wide building and energy system simulation environment with hundreds of components) 21
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