## 3 Results and Discussion
### Coupling of biogas Engines  
Maximum efficiency is achieved when all engines are working at 100% loading. However, this is not always the case since the coupling of engines is based on biogas availability and boiler and engine demand. In addition, coupling of engines takes place after one of them reaches 100% loading. When the degree of loading slightly exceeds the nominal value, an additional engine comes into operation. Thus, the fuel is distributed between the operating set at a much lower loading, decreasing the efficiency significantly. In this way, a higher biogas availability causes an additional engine to start up and reduces the efficiency of the whole set.  
Figure 5a,b demonstrates the abovementioned behavior. In these figures, the electrical power produced and biogas consumption are represented. The steep increase in biogas consumption is associated with the incoming operation of the additional engine. This behavior is indicated in Figure 5b, where a saw-teeth diagram represents the electrical efficiency. The steep decrease in efficiency when reducing the loading is explained by how biogas is distributed between the engines. The first point of operation in these diagrams corresponds with the engine working at a 40% degree of loading, which is the minimum possible for these engines.  
The efficiency decreases as the number of operating engines increases until coupling the last one, leading to an efficiency decrease of 5.2, 2.8 and 1.9%. This is explained by the values of the engine loading moving from 50, 66.7 and 75% in each engine. This feature is a critical operational characteristic of the daily WWTP operation. For specific electrical power values, starting up a new engine may decrease the global efficiency sharply. Better efficiency is in some cases obtained by burning the excess biogas in a flare. If engines work at 90% loading, as recommended by the manufacturer, the problem may be aggravated at these so-called singular operating points.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Parameter** & \multicolumn{4}{c}{**Degree of Loading**} \\ \hline Average linear piston speed (m/s) & 100 & 80 & 60 & 40 \\ Effective torque (N m) & 3807 & 3043 & 2273 & 1502 \\ Specific electrical power (kW/t) & 84.2 & 67.3 & 50.6 & 33.7 \\ Effective specific mechanical power (kW/L) & 17.2 & 13.8 & 10.3 & 6.9 \\ Thermal load or power per unit of piston area (kW/cm\({}^{2}\)) & 3.3 & 2.6 & 2 & 1.3 \\ Efficiency and consumption & & & & \\ Specific biogas consumption (g/kWh) & 470 & 466 & 514 & 567 \\ \(\eta_{thermal-erg}\), engine thermal efficiency (\%) & 48.6 & 50.4 & 52.6 & 55.7 \\ \(\eta_{energy-eng}\), engine energy efficiency (\%) & 87.7 & 88.0 & 87.9 & 87.1 \\ _UTEF_ (\%) & 85.5 & 84.2 & 82.2 & 81.1 \\ _(W/Q)_eng, work/heat ratio & 81.1 & 75.9 & 68.5 & 57.7 \\ Combustion and emissions & & & & \\ Stoichiometric air-biogas ratio (\%) & 17.1 & & & \\ \(A\), air–biogas ratio (\%) & 10.8 & 10.9 & 10.4 & 10.4 \\ \(E_{\text{air}}\), excess air (\%) & 58.3 & 56.7 & 64.9 & 64.0 \\ \hline \hline \end{tabular}
\end{table}
Table 6: Key parameters of biogas engines calculated at different degree of loading.  
Figure 5: Coupling of the biogas engines, variation of parameters depending on the electrical power generated. (**a**) Biogas consumption; (**b**) Electrical efficiency.