Compressor cooler
(Cooler)
Model description
The model of a cooling unit is derived with the example of an air cooled heat exchanger.
For the cooling circle, theenergy efficiency ratio (EER) $\varepsilon_{cooling}$ is usedsuch that
\begin{equation}
\varepsilon_{cooling}=\frac{\dot{Q}_{th}}{P_{tot}},
\end{equation}
where $\dot{Q}_{th}$ describes the amount of thermal energy extracted by the heat exchanger. The heat exchanger has thereby a fixed operational point defined by $P_{co}$, which is given due to the dimensioning of the aggregate. The control of the heat exchanger is done by the component state $S\in\lbrace1,0\rbrace$ and the temperature state $S_T\in\lbrace1,0\rbrace$. The power consumption is thereto
\begin{equation}\label{eqn:HeatExchangerPower}
P_{tot}=\left\lbrace\begin{array}{cl}
P_{co} &\text{if }S=1\text{ and }S_T=1\\
0 &\text{else}
\end{array}\right.
\end{equation}
If the module is running, the generated heat flow can be described by
\begin{equation}\label{eqn:HeatExchangerLoss}
\dot{Q}_{th}=\epsilon_{cooling}\cdot P_{co}.
\end{equation}
The temperature state depends on the controller settings $(T_{min},\,T_{max})$:
\begin{equation}
S_{T}[i]=\left\lbrace\begin{matrix}0& \text{if }S_{T}[i-1]=1\,\wedge\,T\geq T_{max}\\
1& \text{if }S_{T}[i-1]=0\,\wedge\,T\leq T_{min}\\
S_{T}[i-1]& \text{else}\end{matrix}\right .
\end{equation}
Inputs
Parameter | Symbol | Unit | Description |
State | \(S\) | none | Component state (0=OFF, 1=ON) |
Temperature | \(T_{ctrl}\) | K | Fluid temperature |
Outputs
Parameter | Symbol | Unit | Description |
PTotal | \(P_{tot}\) | W | Total electric power demand |
PLoss | \(P_{loss}\) | W | Power loss |
PUse | \(P_{use}\) | W | Useable power |
PThermal | \(\dot{Q}\) | W | Heat sources |
Parameters
Parameter | Symbol | Unit | Description |
TemperatureHigh | \(T_{max}\) | K | Upper temperature set-point |
CompressorPower | \(P_{co}\) | W | Electrical power demand of the compressor |
TemperatureLow | \(T_{min}\) | K | Lower temeprature set-point |
EERCooling | \(\epsilon\) | none | Energy efficiency ratio of the system |