.IBPSA.ThermalZones.ReducedOrder.RC.UsersGuide .IBPSA.ThermalZones.ReducedOrder.RC.UsersGuideThis package contains models for reduced building physics of thermal zones, where we mean by reduced order fewer numbers of wall elements and fewer numbers of RC-elements per wall (by means of spatial discretization). Such a reduction leads to fewer state variables. Reduced order models are commonly used when simulating multiple buildings, such as for district simulation, or for model predictive control, where simulation speed requirements, aggregation of multiple buildings and lack of data availability justify simpler models. However, this package allows users to choose between models with one to four wall elements, and to define the number of RC-elements per wall for each wall. The latter can be done by setting nk, which is the length of the vectors for resistances Rk and capacities Ck).
All models within this package are based on thermal networks and use chains of thermal resistances and capacities to reflect heat transfer and heat storage. Thermal network models generally focus on one-dimensional heat transfer calculations. A geometrically correct representation of all walls of a thermal zone is thus not possible. To reduce simulation effort, it is furthermore reasonable to aggregate walls to representative elements with similar thermal behaviour. Which number of wall elements is sufficient depends on the thermal properties of the walls and their excitation (e.g. through solar radiation), in particular on the excitation frequencies. The same applies for the number of RC-elements per wall.
For multiple buildings, higher accuracy (through higher discretization) can come at the price of significant computational cost. Furthermore, the achieved accuracy is not necessarily higher in all cases. For cases in which only little input data is available, the increased discretization sometimes only leads to a perceived-accuracy based on large uncertainties in data acquisition.
The architecture of all models within this package is defined in the German Guideline VDI 6007 Part 1 (VDI, 2012). This guideline describes a dynamic thermal building models for calculations of indoor air temperatures and heating/cooling power.
Each wall element uses either IBPSA.ThermalZones.ReducedOrder.RC.BaseClasses.ExteriorWall or IBPSA.ThermalZones.ReducedOrder.RC.BaseClasses.InteriorWall to describe heat conduction and storage within the wall, depending if the wall contributes to heat transfer to the outdoor environment (exterior walls) or can be considered as simple heat storage elements (interior walls). The number of RC-elements per wall is hereby up to the user. All exterior walls and windows provide a heat port to the outside. All wall elements (exterior walls, windows and interior walls) are connected via Modelica.Thermal.HeatTransfer.Components.Convection to the convective network and the indoor air.
Heat transfer through windows and solar radiation transmission
are handled separately. One major difference in the implementations
in this package compared to the guideline is an additional element
for heat transfer through windows, which are lumped with exterior
walls in the guideline VDI 6007 Part 1 (VDI, 2012). The heat
transfer element for the windows allows to model the windows
without any thermal capacity, as windows have negligible thermal
mass. Hence, it is not necessary to discretize the window element
and heat conduction is simply handled by a thermal resistance.
Merging windows and exterior walls leads to a virtual capacity for
the windows and results in a shifted reaction of the room
temperature to environmental impacts (Lauster, Bruentjen et
al., 2014). However, the user is free to choose whether keeping
windows separately (AWin) or merging them
(AExt=AExterior+AWindows, AWin=0). The window areas
can be defined separately for solar radiation (vector
ATransparent) and heat transfer (vector
AWin). For cases where the windows are kept
separately, ATransparent and AWin are
equal. When merging windows and exterior walls, AWin
can be set to zero while ATransparent still represents
the actual window area for solar radiation calculations. The
transmission of solar radiation through windows is split up into
two parts. One part is connected to the indoor radiative heat
exchange mesh network using a IBPSA.ThermalZones.ReducedOrder.RC.BaseClasses.ThermSplitter,
while the other part is directly linked to the convective network.
The split factor ratioWinConRad is a window property
and depends on the glazing and used materials.
Regarding indoor radiative heat exchange, a couple of design decisions simplify modelling as well as the system's numerics:
Instead of using Stefan's Law for radiation exchange
Q = ε σ (T14 - T24)
, the models use a linearized approach
Q = α rad (T1 - T2),
where the radiative heat transfer coefficient αrad is often set to
αrad = 4 ε σ Tm3
where Tm is a mean constant temperature of the interacting surfaces.
Indoor radiation exchange is modelled using a mesh network, each wall is linked via one resistance with each other wall. Alternatively, one could use a star network, where each wall is connected via a resistance to a virtual radiation node. However, for cases with more than three elements and a linear approach, a mesh network cannot be transformed to a star network without introducing deviations.
Solar radiation uses a real input, while internal gains utilize
two heat ports, one for convective and one for radiative gains.
Considering solar radiation typically requires several models
upstream to calculate angle-dependent irradiation or solar
absorption and reflection by windows. We decided to keep these
models separate from the thermal zone model. Thus, solar radiation
is handled as a basic RadiantEnergyFluenceRate. For
internal gains, the user might need to distinguish between
convective and radiative heat sources.
For an exact consideration, each element participating in radiative heat exchange needs to have a temperature and an area. For solar radiation and radiative internal gains, it is common to define the heat flow independently of temperature and thus of area as well, assuming that the temperature of the source is high compared to the wall surface temperatures. By using a IBPSA.ThermalZones.ReducedOrder.RC.BaseClasses.ThermSplitter that distributes the heat flow of the source over the walls according to their area, we support this simplified approach. For solar radiation through windows, the area of exterior walls and windows with the same orientation as the incoming radiation is not taken into account for the distribution as such surfaces cannot be hit by the particular radiation. This calculation is performed for each orientation separately using IBPSA.ThermalZones.ReducedOrder.RC.BaseClasses.splitFacVal.
The models in this package are typically used in combination with models from the parent package IBPSA.ThermalZones.ReducedOrder. A typical application is one building out of a large building stock for which the heating and cooling power over a year in hourly time steps should be calculated and is afterwards aggregated to the building stock's overall heating power (Lauster, Teichmann et al., 2014; Lauster et al., 2015).
The important parameters are as follows:
n... defines the length of chain of RC-elements per
wall.
R...[n] is the vector of resistances for the wall
element. It moves from indoor to outdoor.
C...[n] is the vector of capacities for the wall
element. It moves from indoor to outdoor.
R...Rem is the remaining resistance between
C[end] and outdoor surface of wall element. This
resistance can be used to ensure that the sum of all resistances
and coefficients of heat transfer is equal to the U-Value. It
represents the part of the wall that cannot be activated and thus
does not take part at heat storage.
The connector IndoorPort... adds an additional heat
port to the indoor surface of the wall element if set to
true. It can be used to add heat loads directly to a
specific surface or to connect components that distribute radiation
and have a specific surface temperature, e.g. a floor heating.
To calculate parameters of all four models, the Python package TEASER https://github.com/RWTH-EBC/TEASER can be used.
VDI. German Association of Engineers Guideline VDI 6007-1 March 2012. Calculation of transient thermal response of rooms and buildings - modelling of rooms.
M. Lauster, A. Bruentjen, H. Leppmann, M. Fuchs, R. Streblow, D. Mueller. Improving a Low Order Building Model for Urban Scale Applications. Proceedings of BauSim 2014: 5th German-Austrian IBPSA Conference, p. 511-518, Aachen, Germany. Sep. 22-24, 2014.
M. Lauster, J. Teichmann, M. Fuchs, R. Streblow, D. Mueller. Low Order Thermal Network Models for Dynamic Simulations of Buildings on City District Scale. Building and Environment, 73, 223-231, 2014. doi:10.1016/j.buildenv.2013.12.016
M. Lauster, M. Fuchs, M. Huber, P. Remmen, R. Streblow, D. Mueller. Adaptive Thermal Building Models and Methods for Scalable Simulations of Multiple Buildings using Modelica. Proceedings of BS2015: 14th Conference of International Building Performance Simulation Association, p. 339-346, Hyderabad, India. Dec. 7-9, 2015.