Grey-box model for reversible heat pumps and chillers using a
black-box to simulate the refrigeration cycle
This partial model for a generic grey-box vapour compression
machine (heat pump or chiller) uses empirical data to model the
refrigerant cycle. The modelling of system inertias and heat losses
allow the simulation of transient states.
Resulting in the choosen model structure, several configurations
are possible:
- Compressor type: on/off or inverter controlled
- Reversible operation / only main operation
- Source/Sink: Any combination of mediums is possible
- Generik: Losses and inertias can be switched on or off.
Concept
Using a signal bus as a connector, this model working as a heat
pump can be easily combined with several control or safety blocks
from AixLib.Controls.HeatPump.
The relevant data is aggregated. In order to control both chillers
and heat pumps, both flow and return temperature are aggregated.
The mode signal chooses the operation type of the vapour
compression machine:
- mode = true: Main operation mode (heat pump: heating; chiller:
cooling)
- mode = false: Reversible operation mode (heat pump: cooling;
chiller: heating)
To model both on/off and inverter controlled vapour compression
machines, the compressor speed is normalizd to a relative value
between 0 and 1.
Possible icing of the evaporator is modelled with an input value
between 0 and 1.
The model structure is as follows. To understand each submodel,
please have a look at the corresponding model information:
-
InnerCycle (Black Box): Here, the user can use between several
input models or just easily create his own, modular black box
model. Please look at the model description for more info.
- Inertia: A n-order element is used to model system inertias
(mass and thermal) of components inside the refrigerant cycle
(compressor, pipes, expansion valve)
-
HeatExchanger: This new model also enable modelling of thermal
interias and heat losses in a heat exchanger. Please look at the
model description for more info.
Parametrization
To simplify the parametrization of the evaporator and condenser
volumes and nominal mass flows there exists an option of automatic
estimation based on the nominal usable power of the vapour
compression machine. This function uses a linear correlation of
these parameters, which was established from the linear regression
of more than 20 data sets of water-to-water heat pumps from
different manufacturers (e.g. Carrier, Trane, Lennox) ranging from
about 25kW to 1MW nominal power. The linear regressions with
coefficients of determination above 91% give a good approximation
of these parameters. Nevertheless, estimates for machines outside
the given range should be checked for plausibility during
simulation.
Assumptions
Several assumptions where made in order to model the vapour
compression machine. For a detailed description see the
corresponding model.
-
Performance data 2D: In order to model inverter controlled
machines, the compressor speed is scaled linearly
-
Performance data 2D: Reduced evaporator power as a result of
icing. The icing factor is multiplied with the evaporator
power.
- Inertia: The default value of the n-th order element is
set to 3. This follows comparisons with experimental data. Previous
heat pump models are using n = 1 as a default. However, it was
pointed out that a higher order element fits a real heat pump
better in
- Scaling factor: A scaling facor is implemented for
scaling of the thermal power and capacity. The factor scales the
parameters V, m_flow_nominal, C, GIns, GOut and dp_nominal. As a
result, the vapour compression machine can supply more heat with
the COP staying nearly constant. However, one has to make sure that
the supplied pressure difference or mass flow is also scaled with
this factor, as the nominal values do not increase said mass
flow.
Known Limitations
- The n-th order element has a big influence on computational
time. Reducing the order or disabling it completly will decrease
computational time.
- Reversing the mode: A normal 4-way-exchange valve suffers from
heat losses and irreversibilities due to switching from one mode to
another. Theses losses are not taken into account.
Contents
- May 22, 2019 by Julian Matthes:
Rebuild due to the introducion of the thermal machine partial model
(see issue #715)
- November 26, 2018 by Fabian Wüllhorst:
First implementation (see issue #577)
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