# ORC Optimal Design through Clusterization for Waste Heat Recovery in Anaerobic Digestion Plants
## 4 Results
### Comparison with Alternative Designs  
Despite the clear advantages in terms of additional power, the ORC operated in off-design most of the time. For this reason, the installed capacity might be underused, and an alternative design could be considered. The choice of ORC nominal power output is subjected to a trade-off between installed capacity, which should be maximized to increase the production, and the actual availability of excess thermal energy, given the mGT exhaust gas production and the digester heat requirement. The risk is to overestimate the ORC capacity and to work at low loads. Lower ORC power ratings might characterize alternative designs, which may produce less at full load, but they might be able to operate longer at higher relative loads (i.e., with better efficiencies). This possibility must be ruled out to confirm whether basing the design on the clustering of the ORC operating boundary conditions is a good strategy, or not. For the comparison with the proposed ORC design, other optimal designs related to alternative sets of boundary conditions were defined. Sensible alternative sets of boundary conditions were represented by the other clusters defined in Section 3.1.1. by the simple annual average, and by two representative seasonal averages (winter and summer). The use of the annual average conditions is a followed approach in literature. Therefore, it is of particular interest to compare the performance of the ORC designed based on the most populated cluster with the one designed based on the annual average operating conditions. The optimal ORC configurations resulting from the boundary conditions in Table 2 were derived by solving the same optimization problem of Equations (2) and (3). The \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Parameter** & \(\mathbf{\eta_{tot}}\) [–] & \(\mathbf{\Delta\eta}\) [\%] & \(\mathbf{\eta_{year,enc}}\) [\%] & \(\mathbf{E_{year,enc}}\) [MWh] & \(\mathbf{h_{eq,enc}}\) [h/y] & \(\mathbf{W_{ore,ave}}\) \\ \hline Value: & 36.6 & 10.6 & 8.0 & 397.8 & 6894.7 & 45.4 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Modified layout performance. Reference case fuel efficiency equal to 33%. Figure 9: Comparison between the net power output of the mGT reference configuration and mGT + ORC configuration. Data are related to a whole year of operation. Violet shaded areas come from the overlap of the two histograms. optimization problem constraints were the same for each case (Table 2), as the solved optimization problem is always the same. The only required adjustment is to update constraints with the new values for the boundary conditions listed in Table 2.  
As far as the off-design of such new ORC systems is concerned, the same off-design map of Figure 7 was used. Since the off-design map may be reformulated in terms of variations with respect to design conditions, this map can be used for alternative designs. These designs are centered over different values of \(\hat{m}_{f}\), \(T_{f}\), and \(\hat{Q}_{dig}\). From a physical point of view, this is a simplifying hypothesis, as the most rigorous approach would require the creation of a new off-design map for each design. However, it might be assumed that the performance of similar systems changes in the same way when their boundary conditions vary. This assumption is supported by the fact that all considered systems are of comparable sizes, and thus they share the same technologies. The power output histograms as a function of operating hours for the seven considered ORC systems (the proposed one, plus the six alternatives) are provided in Figure 10.  
The three configurations related to the discarded clusters were smaller in size than the configuration related to the most populated cluster (Cluster 3). For this reason, they may operate for a larger share of the year at nominal power output. The configuration related to the annual average was similar to that of Cluster 1, whereas the winter average and the summer average yielded the smallest and the largest configurations, respectively.