.AixLib.Fluid.HeatPumps.ModularReversible.UsersGuide .AixLib.Fluid.HeatPumps.ModularReversible.UsersGuide
The packages AixLib.Fluid.HeatPumps
and AixLib.Fluid.Chillers contain
models for both reversible and non-reversible refrigerant
machines (heat pumps and chillers) based on grey-box approaches.
Either empirical data or physical equations are used to model
the refrigerant cycle. The model for a refrigerant cycle calculates
the electrical power consumption PEle,
the condenser heat flow QCon_flow,
and the evaporator heat flow QEva_flow
based on available variables of the sink and source streams.
Thus, this model does not enable closed-loop simulations of
the refrigerant cycle. However, such models are
highly demanding in terms computation time, and commercial implementations exist.
When simulating the refrigerant machine in a more complex energy system,
this modular approach enables detailed performance and
dynamic behaviour and fast computating times.
This user guide will help understand how to use the models associated with the modular approach. The approach was presented at the Modelica Conference 2021, see the section References.
Heat pumps and chillers are versatile machines:
To what extend all these effects need to be modeled depends on the simulation aim. Sometimes a simple Carnot approach is sufficient, sometimes a more detailed performance data and a realistic control behaviour is required.
The modular approach allows to disable any irrelevant features,
select readily made functional modules, and
easily add new model modules.
Relevant components are declared as replaceable.
Replaceable models are constrainedby partial models
which one is free to extend. Thus, new model approaches can be inserted
into the framework of the modular reversible model approach.
For users not familiar with replaceable models,
there are readily assembled models as well.
This section explains the inheritance and model package structure to help navigate through all options and to check out the detailed documentation of each model for further information.
All modular heat pump or chiller models base on the model AixLib.Fluid.HeatPumps.ModularReversible.RefrigerantCycle.BaseClasses.PartialHeatPumpCycle. This partial model declares all common interfaces, parameters, etc.
For heat pumps, the model
AixLib.Fluid.HeatPumps.ModularReversible.Modular extends the partial model and adds
the connector hea to choose
between the operation modes of the heat pump:
hea = true: Main operation mode (heating) hea = false: Reversed operation mode (cooling) Furthermore, the refrigerant cycle is redeclared to use the one for the heat pump AixLib.Fluid.HeatPumps.ModularReversible.BaseClasses.RefrigerantCycle. This refrigerant cycle in turn contains replaceable models for the heating and cooling operation of the heat pump. Available modules can be found in the package: AixLib.Fluid.HeatPumps.ModularReversible.RefrigerantCycle For more information on the refrigerant cycle models, refer to the section Refrigerant cycle models.
There are a number of preconfigured models provided in the package. Please check out the documentation of each approach to check if this approach is suitable.
For chillers, the model
AixLib.Fluid.Chillers.ModularReversible.Modular extends the partial model and adds
the connector coo to choose
between the operation mode of the chiller:
coo = true: Main operation mode (cooling) coo = false: Reversed operation mode (heating) Furthermore, the refrigerant cycle is redeclared to use the one for the chiller AixLib.Fluid.Chillers.ModularReversible.BaseClasses.RefrigerantCycle. This refrigerant cycle in turn contains replaceable models for the cooling and heating operation of the chiller. Available modules can be found in the package: AixLib.Fluid.Chillers.ModularReversible.RefrigerantCycle. For more information on the refrigerant cycle models, refer to the section Refrigerant cycle models.
There are a number of preconfigured models provided in the package. Please check out the documentation of each approach to check if this approach is suitable.
Simulating reversible heat pumps and chillers can get confusing, as the same heat exchanger model has to be used for both condensation and evaporation.
In most cases, heat pumps and chillers extract/exhaust heat from/to an ambient source (air, soil, ground-water, etc.), and, consuming electrical energy, provide heating or cooling on the useful or load side. For building applications, this useful / load side is inside the building. The ambient heat is outside of the building, on the ambient / source side. However, vapor compression machines can also be used to provide heating and cooling simultaneously. In this case, both sides provide utility to the energy system. Hence, both sides are useful / load sides.
What always stays the same is that there is one heated fluid, and one cooled fluid. Thus, specifying the nominal temperatures, users have to specify the temperatures of both heated and cooled fluids, for both cooling and heating operation. Note, that the heated fluid will be the cooled fluid in reversed operation, and vice versa.
Because of this, we decided on a naming scheme which is based on the main operation
of the heat pump or chiller. The main operation of a heat pump is heating, for
a chiller, it is cooling. When reversed, the condenser becomes the evaporator and
vice versa. As renaming instances after translation is not possible, users always
have to think about the names con and eva in terms of
the main operation of the device.
This applies to the instance and variable names,
such as the heat exchangers con and eva,
as well as sensors such as TConOutMea and TEvaInMea,
or nominal conditions TConHea_nominal and TConCoo_nominal.
As the nominal temperatures may be used table-based performance data
and the operational envelope model,
users also have to think about the useful / load
and ambient / source side and how they translate to
heat pumps and chillers in both main and reversed operation
when adding new datasheets.
Thinking about the heated and cooled fluid helps.
The following tables summarizes the possible options.
| Heat pump main | Heat pump reversed | Chiller main | Chiller reversed | |
|---|---|---|---|---|
| Heating / cooling? | heating | cooling | cooling | heating |
| Table-data: column 1: useful / load side | con |
con 1 |
eva |
eva 2 |
| Table-data - row 1: ambient / source side | eva |
eva 2 |
con |
con 1 |
| Operational envelope - column 1: ambient / source side | eva |
eva 2 |
con |
con 1 |
| Operational envelope - column 2: useful / load side | con |
con 1 |
eva |
eva 2 |
1 In reality, the condenser, e.g. a plate heat exchanger, of the main operation is used for evaporation. 2 In reality, the evaporator, e.g. fin-tube heat exchanger, of the main operation is used for condensation.
Aside from the aforementioned Boolean signals
hea and coo, the following
connectors are relevant to understanding how the model works:
Compressor speed and the expandable bus connector.
The ambient temperatures TEvaAmb and TConAmb are
only relevant for the heat losses.
The fluid ports are explained in more detail here:
AixLib.Fluid.UsersGuide.
The input ySet represents the relative compressor speed.
To model both on/off and inverter controlled refrigerant machines,
the compressor speed is normalised to a relative value between 0 and 1.
To model heat pumps other than inverter driven,
other signal limits can be used.
If data is in Hz or similar, consider converting
the input according to the maximum allowed value.
We use the notation Set to indicate a set value.
It may be modified by the safety control blocks which produces a signal
with the Mea notation. For example, the compressor
speed ySet is modified by the safety
control block to yMea. If no safety violations
occur, ySet equals yMea.
As the modular approach may require different information to model
the refrigerant cycle depending on configuration, all available states and outputs
are aggregated in the expandable bus connector sigBus.
For instance, in order to control both chillers and heat pumps,
both flow and return temperature are relevant.
A replaceable refrigerant cycle model for heating or
cooling calculates the electrical power consumption
PEle, condenser heat flow rate QCon_flow
and evaporator heat flow rate QEva_flow based on the
values in the sigBus.
Heat pumps models extend
AixLib.Fluid.HeatPumps.ModularReversible.RefrigerantCycle.BaseClasses.PartialHeatPumpCycle
and chiller models extend
AixLib.Fluid.Chillers.ModularReversible.RefrigerantCycle.BaseClasses.PartialChillerCycle.
Currently, two modules for refrigerant cycle are implemented. First, the AixLib.Fluid.HeatPumps.ModularReversible.RefrigerantCycle.ConstantCarnotEffectiveness model uses the same equations as the Carnot models, i.e. AixLib.Fluid.HeatPumps.Carnot_y. Second, the AixLib.Fluid.HeatPumps.ModularReversible.RefrigerantCycle.TableData2D provides performance data based on different condenser outlet and evaporator inlet temperatures using 2D-tables.
Two additional modules exist in the AixLib library. These approaches require the use of the SDF-library, as the compressor speed influences the model output as a third dimension. Currently, tables with more than two dimensions are not supported in the Modelica Standard Library. The first approach is similar to AixLib.Fluid.HeatPumps.ModularReversible.RefrigerantCycle.TableData2D approach buts adds the 3rd dimension of compressor speed. The second approach is based on white-box stationary Python models for closed-loop refrigerant cycles. The model has been empirically validated and can take up to n-dimensions. If your simulation aim requires more detailed data, be sure to check out the models in the AixLib.
The refrigerant cycle models will output varying heat flow rates and electrical power consumptions. This is based on the fact that refrigerant cycle performance depend heavily on the boundary conditions.
Still, the user needs to size the device or the system according to some reference points. Accordingly, we follow the basic AixLib concept for nominal conditions, explained in detail here: AixLib.Fluid.UsersGuide
The nominal heat flow rate of the device is distinct for
heat pumps and chillers.
For heat pumps, it is the nominal
condenser heat flow rate QHea_flow_nominal.
For chillers, it is the nominal
evaporator heat flow rate QCoo_flow_nominal (negative).
This nominal heat flow rate is only valid at the
nominal conditions. Whether parameters influence the nominal heat flow rates
depends on the model approach used to estimate the heat flow rate and efficiencies.
Typically, at least nominal source and sink temperatures will influence the
nominal conditions:
TCon_nominal,
TEva_nominal,
Depending on the model in use, this may be inlet or outlet.
Another example would be inverter driven devices.
Here, the compressor speed influences the
refrigerant mass flow rate and compressor efficiencies.
If the performance data is dependent on the compressor speed,
y_nominal influences the nominal efficiencies.
In such cases, specifying additional nominal parameters will
be nessary.
Using the nominal conditions and the specified heat flow rate,
the nominal electrical power consumption PEle_nominal is calculated.
As reversible devices have typically a four-way-valve and a single
compressor, you have to make sure that the values for PEle_nominal
are similar between heating and cooling. The pre-configured models
warn about deviations if they are too large.
To change the capacity of the model, users should change
QHea_flow_nominal for heating operation and
QCoo_flow_nominal for cooling operation. This will then also
update the electricity use PEle_nominal.
For models with table-based performance curves, changing these values will also scale
the design mass flow rates and pressure drops.
The documentation of
AixLib.Fluid.HeatPumps.ModularReversible.TableData2D
further explains the scaling.
Refrigerant machines contain internal safety controls,
prohibiting operations in possibly unsafe points.
All ModularReversible models account for those.
All options can be disabled as described in the model description
AixLib.Fluid.HeatPumps.ModularReversible.Controls.Safety.Safety
An important safety control with regard to system interaction is the operation envelope. Read the documentation of AixLib.Fluid.HeatPumps.ModularReversible.Controls.Safety.BaseClasses.PartialOperationalEnvelope for more information on this model and how it affects device operation.
The refrigerant cycle models
are based on stationary data points, any inertia
(mass and thermal) of components inside the refrigerant cycle
(compressor, pipes, expansion valve, fluid, etc.) is neglected.
To overcome this issue, replaceable SISO blocks that are connected to the
output of the refrigerant cycle (instance refCyc)
can approximate the refrigerant cycle inertia.
The package AixLib.Fluid.HeatPumps.ModularReversible.RefrigerantCycle.Inertias contains implemented inertia models. In the contribution, an empirical validation showed that a third-order critical damping element fits the inertia most closely. At the same time, models in literature often use first-order delay blocks. Additionally, higher-order elements require more computation time. At the end, the requirements on the analysis will define the required level of detail of the model.
The effect of the inertia can be removed by setting NoInertia.
If a user finds in real data that another approach might be better suited (e.g. a deadband), then the model AixLib.Fluid.HeatPumps.ModularReversible.RefrigerantCycle.Inertias.BaseClasses.PartialInertia can be extended to implement a costum model.
To simulate possible icing of the evaporator on air-source devices, the
icing factor iceFac is used to modify the outputs.
The factor models the reduction of heat transfer between refrigerant
and source. Thus, the factor is implemented as follows:
QEva_flow = iceFac * (QConNoIce_flow - PEle)
With iceFac as a relative value between 0 and 1:
iceFac = kA/kA_noIce
Finally, the energy balance must still hold:
QCon_flow = PEle + QEva_flow
Different options can be selected for the modeling of the icing factor, or a custom model can be implemented by extending AixLib.Fluid.HeatPumps.ModularReversible.RefrigerantCycle.Frosting.BaseClasses.PartialIcingFactor
Note however, that this only simulates the efficiency reduction
due to frost. If a user-provided frost module enables the simulation
of a defrost cycle, the user needs to implement the corresponding external controls.
The iceFac approach was already used by Vering et al., 2021,
to account for reverse cycle defrost based on validated literature-data.
However, as no empirical validation was performed, the model was not
added to the AixLib library.
Most refrigerant cycle models that calculate
PEle, QCon_flow, and QEva_flow
assume the device to be adiabatic, following the equation:
QCon_flow = PEle + QEva_flow
Depending on the application, one may need to model the heat losses to the ambient, as those may impact the overall efficiency of the heat pump or chiller. Thus, the heat exchangers in the models adds thermal capacities to the adiabatic heat exchanger. The parameterization may be challenging, as datasheets do not contain parameters for the required values. Besides empirical calibration, simplified assumptions (e.g. 2% heat loss) may be used to parameterize the required values. For more information, see the description of AixLib.Fluid.HeatPumps.ModularReversible.BaseClasses.EvaporatorCondenserWithCapacity
Fabian Wuellhorst, David Jansen, Philipp Mehrfeld and Dirk Müller.
A Modular Model of Reversible Heat Pumps and Chillers for System Applications.
Proceedings of 14th Modelica Conference 2021. Linköping, Sweden, September, 2021.
doi:10.3384/ecp21181561.
Christian Vering, Fabian Wüllhorst, Philipp Mehrfeld and Dirk Müller.
Towards an integrated design of heat pump systems: Application of process intensification using two-stage optimization.
Energy Conversion and Management, Volume 250, 2021.
doi:10.1016/j.enconman.2021.114888.