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

ParameterSymbolUnitDescription
State\(S\)noneComponent state (0=OFF, 1=ON)
Temperature\(T_{ctrl}\)KFluid temperature

Outputs

ParameterSymbolUnitDescription
PTotal\(P_{tot}\)WTotal electric power demand
PLoss\(P_{loss}\)WPower loss
PUse\(P_{use}\)WUseable power
PThermal\(\dot{Q}\)WHeat sources

Parameters

ParameterSymbolUnitDescription
TemperatureHigh\(T_{max}\)KUpper temperature set-point
CompressorPower\(P_{co}\)WElectrical power demand of the compressor
TemperatureLow\(T_{min}\)KLower temeprature set-point
EERCooling\(\epsilon\)noneEnergy efficiency ratio of the system