# ORC Optimal Design through Clusterization for Waste Heat Recovery in Anaerobic Digestion Plants
## 4 Results
### Comparison with Alternative Designs
Such a size distribution was due to the different seasonal operating conditions. In winter, the maximum heat flow is required by the digesters, and the minimum thermal energy content is found in the mGT five gases. Therefore, the heat flow available for the ORC is a minimum, leading to an ORC operating at high equivalent hours, but with a small power output (Figure 10 and Table 5). In summer, the situation is the opposite. Therefore, a larger ORC nominal power output may be installed. Figure 10: ORC net power output in off-design for the whole year operation. The results are related to the ORC systems built on the basis of the boundary condition sets listed in Table 2. (**a**) The four data clusters. (**b**) All the other configurations (annual, summer, and winter average) in Table 2.  
In Table 2, it may be observed how the configuration related to Cluster 3 (i.e., the most populated one) had the expected highest nominal power output among all the clusters. Cluster 3 was the cluster with the highest mGT exhaust gas mass flow rate and the lowest digester thermal requirement. As also discussed for the summer average conditions, in this case, the ORC had the highest amount of available thermal energy. Accordingly, the optimizer selected a high nominal power for the Cluster 3 ORC, and this was the reason why such ORCs are operated most often in part load, as seen in Figure 10.  
In Table 5,  
(thermal oil loop and ORC unit) was modeled, and its annual operation was simulated. Two models with different detail levels were developed. First, the system was modelled in MATLAB, with a simplified approach based on system constitutive equations and the components' constant performance parameters (isentropic machine efficiencies and heat exchanger effectiveness). Second, the system was modeled in ASPEN HYSYS, which allowed the selection of commercial components (i.e., heat exchangers). Through this detailed model, the part-load performance of the system was simulated. These two models were used to define an ORC design procedure, which considered both the design and the off-design ORC operation. Theoretically, design and off-design performance could be optimized together to maximize the annual ORC production. However, to simplify the design optimization problem, the design procedure was divided into two steps. The first step was based on the clustering of the ORC boundary conditions (i.e., the biogas facility operating conditions). Through clustering, the most representative (i.e., probable) design boundary conditions may be selected. After this, the ORC design optimization problem can be formulated more straightforwardly (i.e., by maximizing the power output ORC for the fixed set of design boundary conditions). The biogas facility operating conditions were clustered into four representative clusters. Furthermore, three additional sets of boundary conditions were considered to compare the followed design approach with a more traditional one. Annual, winter, and summer average operating conditions were considered for the comparison. By comparing the performance of the seven alternative ORC designs, it was demonstrated that the design based on the most populated cluster yielded the highest annual production. Such a result demonstrates that using the most populated cluster as design boundary conditions may help to define a design that works well for a larger share of the total cases. Therefore, clustering should be used to select the appropriate design conditions based on which the optimal ORC design was performed. The fact that the use of the most populated cluster may help to maximize the annual production suggests that the clustering should be used as a preliminary step in the design procedure. In this way, the effects due to time-varying operating conditions may be considered in the design process, without explicitly including them in the design optimization problem. This is a simplified approach, but it allows relevant increments in the produced energy.