## 3 Results and Discussion
### Sensitivity Analysis of biogas Engines  
The energy parameters of the engines are shown in the following figures. Values were calculated from the minimum operating point corresponding to a 40% degree of loading at working conditions established at the WWTP, until the maximum value of 100% (full load). Electrical and thermal efficiencies were obtained based on these trend lines. Figure 4a-f shows the key parameters of the engines. All curves were approximated to a linear behavior and R\({}^{2}\) (coefficient of determination) was estimated along with the resulting equation, which is indicated in each graph. The increase in the degree of loading brings with it an associated steep rise in biogas consumption, and therefore, in the input energy. However, the electrical power does not follow the same slope, experiencing a minor increase due to the engine efficiency, which increases with the degree of loading, attaining 40.3% as the maximum value. The maximum power and torque regime in this type of engine are developed at full load. The difference in rotational speed between these two parameters is zero since the engine always rotates at a constant speed to maintain synchronism, so these engines have no elasticity. Explosion ignition engines allow minimal variations of the air-fuel ratio between minimum and full load. Quantitative regulation of this ratio is necessary and this is achieved by throttling the inlet at the carburetor butterfly valve. For this reason, the pumping losses are increased at a low degree of loading as the mixture inlet pressure is reduced and therefore, the efficiency decreases. The power at a full degree of loading is generally proportional to the mass of air admitted per unit of time. The efficiency of this type of engine is a function of the filling or renewal volume into the cylinders. The engine volumetric efficiency thus decreases with the decrease in the degree of loading, as well as the power output. The turbocharger increases the mass of the mixture (air-biogas) entering into the cylinders compared to atmospheric aspirated engines, attaining a volumetric efficiency of 102.2%. However, the exhaust gas back-pressure increases the turbine inlet pressure from 140.2 to 144.7 kPa (3.2%), lowering the average effective pressure and causing a loss of power. Losses are those derived from mechanical and radiation losses. The first one corresponds mainly to those caused by friction and derived from the various auxiliary elements (oil and water pumps, fans, etc.). They present slight variations between minimum and full load because the engine rotates at constant speed. Radiation losses follow an upward trend with the degree of loading. However, they do not vary significantly because the temperature of the engine block is controlled by the cooling system. The thermal power associated with cooling circuits has different behavior. The auxiliary circuit has cooling components related to the air compression system and the lubricating oil circuits. Thus, it is not affected as much as the main circuit, which is directly linked to the performance of the engine. Increasing biogas consumption brings, as a consequence,  
Figure 4: Sensitivity analysis of the engines’ parameters as a function of the degree of loading. **(a)** Electrical power, biogas consumption and electrical efficiency; **(b)** Thermal power in cooling circuits; **(c)** Mechanical and radiation losses; **(d)** Thermal power in exhaust gases at 25 and 120 \({}^{\circ}\)C; **(e)** Mass flow of exhaust gases and air; **(f)** Exhaust gas temperature. a greater release of heat, which the main circuit should absorb to keep the crankcase and cylinders at the proper temperature. The intercooler cools down the mixture, increasing its density in an isobaric way (neglecting the small pressure losses). The compressor-turbine assembly is independent of the drive shaft, which gives a greater degree of freedom in terms of efficiency.