# Improved Solar Operation Control for a Solar Cooling System of an IT Center
## 3 Results--Model Predictive Control
### Dry-Cooler Model  
In Figure 5, the nomenclature for the dry-cooler model is depicted. A control signal \(\mathrm{C}_{\mathrm{DC}}\) is used to adjust the air flow rate \(\mathrm{V}_{\mathrm{L}}\) by changing the rotational speed of the ventilators or their motors, respectively. The necessary electrical power of the dry-cooler \(\mathrm{P}_{\mathrm{el,DC}}\) for a certain air flow rate \(\mathrm{V}_{\mathrm{L}}\) is proportional to the pressure drop and total efficiency \(\mathrm{\eta}_{\mathrm{DC,tot}}\), including all mechanical and electrical losses of the motor-ventilator assembly. In addition, a constant auxiliary power consumption \(\mathrm{P}_{\mathrm{el,DC}}^{\mathrm{aux}}\) can be considered (e.g., for a control unit). Assuming a quadratic development of the air-side pressure drop \(\mathrm{\Delta}\mathrm{P}_{\mathrm{L}}\) with respect to the pressure drop under nominal conditions (i.e., \(\mathrm{\Delta}\mathrm{P}_{\mathrm{L}}=\mathrm{\Delta}\mathrm{P}_{\mathrm{L, 0}}\big{(}\mathrm{V}_{\mathrm{L}}/\mathrm{V}_{\mathrm{L,0}}\big{)}^{2}\)), this leads to:  
\[\mathrm{P}_{\mathrm{el,DC}}=\frac{\mathrm{\Delta}\mathrm{P}_{\mathrm{L}}\cdot \mathrm{V}_{\mathrm{L}}}{\mathrm{\eta}_{\mathrm{DC,tot}}}+\mathrm{P}_{ \mathrm{el,DC}}^{\mathrm{aux}}=\frac{\mathrm{\Delta}\mathrm{P}_{\mathrm{L, 0}}}{\mathrm{\eta}_{\mathrm{DC,tot}}\big{(}\mathrm{V}_{\mathrm{L,0}}\big{)}^{ 2}}\big{(}\mathrm{V}_{\mathrm{L}}\big{)}^{3}+\mathrm{P}_{\mathrm{el,DC}}^{ \mathrm{aux}}=\mathrm{f}_{\mathrm{ric}}\big{(}\mathrm{V}_{\mathrm{L}}\big{)} ^{3}+\mathrm{P}_{\mathrm{el,DC}}^{\mathrm{aux}}. \tag{11}\]  
which can be rewritten by expanding the fraction with \(\mathrm{V}_{\mathrm{L,0}}\) as:  
\[\mathrm{P}_{\mathrm{el,DC}}=\frac{\mathrm{\Delta}\mathrm{p}_{0}\cdot\mathrm{V }_{\mathrm{L,0}}}{\mathrm{\eta}_{\mathrm{DC,tot}}\big{(}\mathrm{V}_{\mathrm{L,0}}\big{)}^{2}\cdot\mathrm{V}_{\mathrm{L,0}}}\cdot\big{(}\mathrm{V}_{\mathrm{ L}}\big{)}^{3}+\mathrm{P}_{\mathrm{el,DC}}^{\mathrm{aux}}=\mathrm{P}_{\mathrm{el,DC,0}} \cdot(\mathrm{C}_{\mathrm{DC}})^{3}+\mathrm{P}_{\mathrm{el,DC}}^{\mathrm{aux}}, \tag{12}\]  
where \(\mathrm{C}_{\mathrm{DC}}=\mathrm{V}_{\mathrm{L}}/\mathrm{V}_{\mathrm{L,0}}\) is the normalised flow rate or the control signal of the dry cooler, respectively, and \(\mathrm{P}_{\mathrm{el,DC,0}}\) is the electrical power under nominal conditions. Figure 4: Comparison of the measured and calculated values for the absorption chiller and dry-cooler model as a function of time (**a**) and for the absorption chiller as a function of the inlet characteristic temperature difference (**b**). The unknown air flow rate \(V_{L}\), which causes the electrical power, \(P_{el,DC}\) for a certain load condition, results from the reject heat flow of the absorption chiller from the absorber and condenser, \(Q_{L}=Q_{A}+Q_{C}\). It is equivalent to the negative sum of the evaporator and desorber heat flow:  
\[Q_{L}=\left(Q_{A}+Q_{C}\right)=-\left(Q_{E}+Q_{D}\right)=V_{L}\cdot\rho_{L} \cdot c_{p,L}\cdot(t_{Li}-t_{Lo}). \tag{13}\]  
To determine \(V_{L}\) (and thereby \(P_{el,DC}\)), the required air outlet temperature \(t_{Lo}\) in Equation (13) can be calculated from the dimensionless temperature glide, \(P_{L}\) of the air stream, assuming a counter flow heat exchanger (i.e., neglecting all cross-counter flow effects):  
\[P_{L}=\frac{t_{Lo}-t_{Li}}{t_{Ki}-t_{Li}}=\frac{1-\exp((R_{L}-1)\cdot NTU_{L})} {1-R_{L}\cdot\exp((R_{L}-1)\cdot NTU_{L})}. \tag{14}\]  
The required cooling water inlet temperature of the dry-cooler \(t_{Ki}\) on the left-hand side of Equation (14) is equal to the condenser outlet temperature, \(t_{Co}\) of the absorption chiller. It follows from the inlet temperature \(t_{Ai}\) plus the temperature increase in the cooling water flow of the absorption chiller due to the total reject heat flow \(Q_{E}+Q_{D}=-\left(Q_{A}+Q_{C}\right)\). Since the cooling water valve is used only for safety reasons, it is normally fully open.