## 3 Model
### Thermodynamic Model  
The thermodynamic model of SASCHCS is developed based on the following assumptions. 1. The operation of the hybrid system is considered as a quasi-static state. 2. The components of absorption subsystem and compression one are adiabatic. 3. The working fluids at the exit of evaporator and condenser in the compression subsystem are saturated. 4. There is no pressure loss in both the heat exchanger and pipeline. 5. The top layer temperature in the storage tank is equal to the generator inlet temperature. 6. The bottom layer temperature in the storage tank is equal to the collector inlet temperature. Collector model:  
The collector efficiency is calculated from the reference [15]:  
\[\eta=F_{R}[(\tau\alpha)-U_{L}(T_{c,i}-T_{a})/I] \tag{1}\]  
The heat removal factor \(F_{R}\) which relates the actual useful energy gain of a collector to the useful gain if the whole collector surface were at the fluid inlet temperature is defined as:  
\[F_{R}=\frac{mc_{p}}{A_{c}U_{L}}\Big{[}1-\exp\!\left(-\frac{U_{L}F^{\prime}A_{ c}}{mc_{p}}\right)\Big{]} \tag{2}\]  
The overall heat loss coefficient \(U_{L}\) is derived as below:  
\[U_{L}=U_{e}+U_{t} \tag{3}\]  
The edge loss coefficient of the header tube \(U_{e}\) is expressed by:  
\[U_{e}=\frac{2\pi\lambda_{ins}}{L_{T}\ln(D_{ext}/D_{\text{int}})} \tag{4}\]  
The loss coefficient from the absorber tube to the ambient \(U_{t}\) is expressed by:  
\[U_{t}=\frac{1}{\frac{1}{h_{g-a}}+\frac{1}{h_{p-g^{\prime}}+h_{p-g^{\prime}}}} \tag{5}\]  
Here, \(h_{g-a}\) is the convection heat transfer coefficient, \(h_{p-g^{\prime}}\) is the radiation heat transfer coefficient, and \(h_{p-g^{\prime}}\) is the heat transfer coefficient due to the conduction. They are calculated by the expression of the reference [25]. The collector efficiency factor \(F^{\prime}\) is also given by the reference [25]. \(F^{\prime}\) represents the ratio of the actual useful energy gain to the useful gain that would result if the collector absorbing surface had been at the local fluid temperature:  
\[F^{\prime}=\frac{1/U_{L}}{W\Big{[}\frac{1+U_{L}/C_{b}}{U_{L}[d+(W-d)F]}+\frac {1}{C_{B}}+\frac{1}{h_{f}\pi d}\Big{]}} \tag{6}\]  
Storage tank model:The energy balance of each layer with respect to the stratified storage tank is described as follows:  
\[\frac{1}{3}\rho V_{st}c_{p}\frac{dT_{st,i}}{dt}=\rho\dot{V_{c}}c_{p}(T_{st,i-1}- T_{st,i})+\rho\dot{V_{g}}c_{p}(T_{st,i+1}-T_{st,i})-h_{st}A_{st}(T_{st,i}-T_{a})/3 \tag{7}\]  
The energy change of the storage tank is equal to the heat generated by itself plus the incoming energy and the heat transfer between it and the environment. It is stated that the layer number rises in turn from top to bottom, i.e., layer 1 and layer 3 donate the top layer and bottom layer, respectively. Absorption and compression subsystems model:  
The off-design model of cooling subsystems (absorption and compression subsystems) was developed in our previous work based on the characteristic equations of the absorption subsystems and lumped parameter method of the compression subsystems [26]. The multiplication of area and heat transfer coefficient in generators for different flow rates of generator hot water is expressed as follows [27]:  
\[UA=\left(\frac{\dot{V_{g}}}{\dot{V_{g,rated}}}\right)^{0.8}(UA)_{nted} \tag{8}\]  
The cooling capacity of absorption subsystems is expressed below in terms of the model:  
\[Q_{e,as}=s\cdot\Delta t-\alpha\cdot Q_{loss,as}=s\cdot\Delta t-s\cdot\Delta t \mathrm{min} \tag{9}\]  
\(s\) accounts for the total amount of \(UA\) spent in a building machine (but for the solution heat exchanger). \(\alpha\) indicates how the distribution of the heat transfer capacity was done among the evaporator, absorber, generator and condenser.