# Improved Solar Operation Control for a Solar Cooling System of an IT Center
## 3 Results--Model Predictive Control
### Switchover Control Strategy
:  
\[t_{\rm Ai}=\frac{1}{1-K_{2}}\Bigg{(}(1-K_{1})\cdot t_{\rm Di}+(1-K_{3})\cdot t _{\rm Eo}^{\rm set}-\frac{Q_{\rm E}^{\rm set}}{K_{4}^{*}}\Bigg{)}. \tag{27}\]  
After inserting Equation (27) into Equation (26), it can be solved for the driving temperature \(t_{\rm Di}=t_{\rm Di}^{\rm on,SHO}\), which is necessary for a cooling load \(Q_{\rm E}^{\rm set}\) at a chilled water temperature of \(t_{\rm Eo}^{\rm set}\) and a maximum allowed control signal for the dry cooler \(C_{\rm DC}^{\rm on,SHO}\) in order to keep the specific electricity demand \(w_{\rm ACCA}\) below \(W_{\rm max}=w_{\rm CCCA}\) when the absorption chiller is operated with solar heat:  
\[t_{\rm Di}^{\rm on,SHO}=\frac{1}{K_{\rm c}^{\rm SHO}}\Bigg{(}\Big{(}K_{\rm b }^{\rm SHO}-\Big{(}K_{5}^{*}+K_{4}^{*}\Big{)}K_{\rm a}^{\rm SHO}\Big{)}Q_{\rm E }^{\rm set}/K_{4}^{*}-K_{\rm b}^{\rm SHO}\cdot(1-K_{3})\cdot t_{\rm Eo}^{\rm set }+\Big{(}C_{\rm DC}^{\rm on,SHO}\cdot a_{\rm L,0}\Big{)}\cdot t_{\rm amb} \Bigg{)}, \tag{28}\]  
where:  
\[K_{\rm a}^{\rm SHO}=C_{\rm DC}^{\rm on,SHO}b_{\rm L,0}-P_{\rm L,0}, \tag{29}\]  
\[K_{\rm b}^{\rm SHO}=\Big{(}C_{\rm DC}^{\rm on,SHO}\cdot a_{\rm L,0}-K_{6}\cdot K _{\rm a}^{\rm SHO}\Big{)}/(1-K_{2}), \tag{30}\]  
\[K_{\rm c}^{\rm SHO}=(1-K_{1})/(1-K_{2})\cdot\Big{(}C_{\rm DC}^{\rm on,SHO} \cdot a_{\rm L,0}-K_{6}\cdot K_{\rm a}^{\rm SHO}\Big{)}+K_{6}\cdot K_{\rm a}^ {\rm SHO}. \tag{31}\]  
Finally, the operating limits of the absorption chiller have to be considered. For example, to avoid crystallization of the \(H_{2}O/LiBr\) solution, a minimum cooling water temperature \(t_{\rm Ai}^{\rm min}\) is allowed. Hence, from the rearranged characteristic Equation (7) follows a minimum driving temperature for the load case \(Q_{\rm E}=Q_{\rm E}^{\rm set}\); \(t_{\rm Eo}=t_{\rm Eo}^{\rm set}\):  
\[t_{\rm Di}^{\rm min,SHO}=\frac{1}{1-K_{1}}\Bigg{(}(1-K_{2})\cdot t_{\rm Ai}^{ \rm min}-(1-K_{3})\cdot t_{\rm Eo}^{\rm set}+\frac{Q_{\rm E}^{\rm set}}{K_{4 }^{*}}\Bigg{)}. \tag{32}\]  
Consequently, the necessary driving temperature to start the solar heat operation is the maximum of the aforementioned temperatures:  
\[t^{\rm on,SHO}=\max\Big{(}t_{\rm Di}^{\rm min,SHO},t_{\rm Di}^{\rm on,SHO} \Big{)}. \tag{33}\]The cut-in condition for solar heat operation (i.e., \(\rm{SHO^{on}}\)) becomes true when the highest storage temperature \(\rm{t_{PS11}}\) and the outlet temperature of the solar heat exchanger \(\rm{t_{Ho}}\) are both higher than the necessary cut-in temperature for solar operation \(\rm{t^{on,SHO}}\):  
\[C_{\rm DC}^{\rm on,SHO}=\sqrt{\frac{w_{\rm CCCCA}\cdot Q_{\rm E}^{\rm set}-P_{ \rm el,DC,aux}}{P_{\rm el,DC,0}}}. \tag{25}\]0  
The cut-off condition for SHO consists of three aspects: Solar heat operation should be stopped when the highest temperature in the solar heat storage \(\rm{t_{PS11}}\) has decreased below the necessary driving temperature \(\rm{t_{Di}^{set}}\) to cover the load or the necessary driving temperature \(\rm{t^{on,SHO}}\) for SHO, and simultaneously, the electricity demand becomes too high or the load cannot be matched anymore. Thus, the cut-off condition reads:  
\[C_{\rm DC}^{\rm on,SHO}=\sqrt{\frac{w_{\rm CCCCA}\cdot Q_{\rm E}^{\rm set}-P_{ \rm el,DC,aux}}{P_{\rm el,DC,0}}}. \tag{25}\]1 \[C_{\rm DC}^{\rm on,SHO}=\sqrt{\frac{w_{\rm CCCCA}\cdot Q_{\rm E}^{\rm set}-P_{ \rm el,DC,aux}}{P_{\rm el,DC,0}}}. \tag{25}\]2  
Typical values for the thresholds \(\rm{\Delta t_{2}^{off,SHO}}\) and \(\rm{\Delta t_{0}^{off,SHO}}\) are 2 and 0.2 K, respectively.