Annex60.ThermalZones.ReducedOrder.RC.UsersGuide

# .Annex60.ThermalZones.ReducedOrder.RC.UsersGuide

User's Guide

## Information

This 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.

#### Architecture

Each wall element uses either Annex60.ThermalZones.ReducedOrder.RC.BaseClasses.ExteriorWall or Annex60.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 Annex60.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 Annex60.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 Annex60.ThermalZones.ReducedOrder.RC.BaseClasses.splitFacVal.

#### Typical use and important parameter

The models in this package are typically used in combination with models from the parent package Annex60.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.

#### References

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.

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