# Multi-Objective Optimization of Hybrid Renewable Tri-Generation System Performance for Buildings
## 4 Input Parameters  
The components and system capital and installation costs are presented in Table 3. The electricity export-import cost is assumed to be the same with an average value of CAD 0.14/kWh. The emission parameters were set at CAD 25 per ton of CO\({}_{2}\) and the emission factor was 590 CO\({}_{2}\) g/kWh. There is no subsidy by the Korean Government for AWHP, PVT and GAHX. The operation and maintenance costs were 0.5-1.0% of the capital cost and the annual interest rate was set at 3.5%. Table 4 shows the boundary values of the optimization parameters, including the hybrid system components. Figure 4: AWHP heat delivery and COP at different outside temperatures and inlet water temperatures in winter and summer seasons (**a**) Heat Delivery and (**b**) COP. Table 5 presents the breakdown of the system annual cost based on the optimum parameters study. The purchased electricity from the grid has the highest cost of CAD 2106/yr., followed by AWHP capital cost with the amount of CAD 809/yr. The PVT and GAHX systems have the cost of CAD 514 and CAD 266/yr., respectively. Electrical power for fans, pumps and fan coils will cost CAD 321/yr and the emissions cost has a value of CAD 222/yr. Moreover, selling electricity back to the grids and operation and maintenance has cost values of CAD 95 and CAD 15/yr, respectively. The objective optimization cost reaches a value of CAD 4158/yr. Figure 5: Hourly heating/cooling demand load and AWHP heat delivery for hybrid trigeneration system in warmest and coldest days under optimum design conditions. Figure 6: Hourly HVAC and non-HVAC energy consumption, energy production, CO\({}_{2}\) emissions and solar radiation under Incheon weather conditions for coldest and warmest days and under optimum design conditions. \begin{table}
\begin{tabular}{c c} \hline \hline
**System** & **Cost (CAD/Yr.)** \\ \hline GAHX Capital & 265.5 \\ AWHP Capital & 809.1 \\ PVT Capital & 514 \\ Fan, Pump, Fan coil, etc. & 321.3 \\ Operation \& Maintenance & 14.6 \\ Purchase Electricity & 2105.5 \\ Selling Electricity & 94.5 \\ Emission & 222.2 \\ Subsidy & 0 \\ Objective & 4157.5 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Breakdown of the Annual Optimum Cost for a Trigeneration System. The output optimum parameters of the modules were GAHX length of 125 m and PVT surface area of 10; AHWP heating and cooling sizes from the optimization simulation are 125 m, 10 m\({}^{2}\) and AWHP size of 10 kW. A full-year dynamic simulation with a 10 s-time step was conducted using the optimum parameters under Incheon weather conditions. The analysis of thermal intensity energy delivery from each component of the tri-generation system is presented in Figure 7. The annual energy delivery from the AWHP to the fluid is 62.4 kWh/m\({}^{2}\) and 41.2 kWh/m\({}^{2}\) during the heating and cooling seasons, respectively. Moreover, the GAHX provides 17.9 kWh/m\({}^{2}\) of energy to the preheating air in the winter period and 14.7 kWh/m\({}^{2}\) of energy is extracted from the air in the summer period. The PVT system provides 1.0 kWh/m\({}^{2}\) of thermal energy to the air in the winter season, as the optimum surface area is small. There is no PVT heat contribution to the tri-generation system during the summer season. On the other hand, there is a thermal energy gain from blower fan motors with values of 2.9 kWh/m\({}^{2}\) and 1.9 kWh/m\({}^{2}\) in the winter and summer seasons, respectively. This energy gain from the blower fan motor enhances the system performance during the heating period and reduces it during the cooling season. Figure 8 presents the annual electrical energy intensity consumption by the system and imported electricity from the grid. Figure 9 shows hybrid system performance during the heating/cooling seasons and average annual system performance. The AWHP has a COP of 3.5 with PVT annual overall electric/thermal efficiency of 13.4% and 9.5%, respectively.