The model was tested for various loads and operating times. Figure 3 shows the power output and temperature of the water of the external circuit. For the simulation, the ICE displacement volume has been set to 1300cc and the external circuit water flow-rate is set to 0.15kg/s.
More specifically, Figure 3.8 (top) presents the power output for a step change in the position of the throttle valve butterfly. The power output responds fast to the step changes and reaches steady state in less than 100 seconds. The water temperature in the outlet of the external circuit is presented in Figure 3.8 (middle). The mass flow-rate of the water through the external circuit and the operation level of the internal combustion engine affect
Time (hr) 0 2 4 6 8 10 12 14 16 18 20 22 24 Valve position (u th ) 0.12 0.16 0.20 0.24 Power output (kW) (Pec) 0 1 2 3 4 Temperature ( o C) (T w,out ) 60 65 70 75 80 85
Figure 3.8: Power output for throttle valve position changes over 24 hours. The graph represents a typical hourly mean power demand satisfaction (See Figure 3.9) for a series of houses
the temperature of the water. The step changes of the two manipulating variables happen instantly which affects the response of the model in terms of both responding and reaching steady state.
It should be underlined, that the model parameters are a key feature of the CHP model that makes it ideal for describing a system of specific use such as a residential district CHP or a large scale system capable of providing electrical power and hot utility water for an
Figure 3.9: A superposition of the power demand profile (gray rectangles) with the power generation output (red line) and the valve position (blue line). The left y-axis corresponds to power demand and generation levels and the the right y-axis the valve opening position [0-1]
entire industrial plant instead.
In terms of efficiency, Figures 3.10 and 3.11 show that the behavior of (a) the internal combustion engine and (b) the combined heat and power system has been captured suc- cessfully. The efficiencies were calculated for the entire range of the throttle valve opening. More specifically, every point of Figures 3.10 and 3.11 correspond to a different throttle valve setting after the system has reached steady state. The volume of the internal combustion engine during the simulation was set to 1300cc. The flow rate of the water in the external circuit was set to 0.3kg/s, the splitter control variable was set to 50% and remained fixed. The electrical and thermal efficiencies of the engine were calculated as Effec = QP ec+P ec and
spectively, and Q the total amount of produced heat, regardless its usability. On the other hand, the efficiencies for the CHP system were calculated using only the usable produced heat.
Electrical Efficiency Thermal Efficiency
Revolutions per Minute (RPM)
0 2000 4000 6000 8000 10000 Efficiency 0 20 40 60 80 100
Figure 3.10: Internal combustion engine electrical and thermal efficiency
Revolutions per Minute (RPM)
0 2000 4000 6000 8000 10000 Efficiency 0 20 40 60 80 100
Figure 3.11: CHP electrical and thermal efficiency
More specifically, the thermal efficiency of both the internal combustion engine and the CHP system of Figures 3.10 and 3.11 are higher than the electrical efficiency by at least 60% and 20% respectively. Moreover, the efficiency difference at the maximum electrical efficiency point of the CHP system (around 8000 RPM) is 20%.
Figure 3.12 illustrates the electrical and thermal efficiency change of the CHP system, with respect to the engine volume V d. The points were acquired following the same simu- lation principles that resulted into Figures 3.10 and 3.11. The engine displacement volume between the two plotted lines differs by 100cc. Although the curves follow similar patterns, it is clear that the engine displacement volume affects the efficiency. It has been observed that for this range of displacement volume:
• The maximum electrical efficiency appears to be proportional to the displacement volumes (i.e. a higher displacement volume yields higher maximum electrical efficiency at a given operating level denoted via the revolutions per minute (RPMs) on the x- axis).
• The revolutions per minute under which maximum electrical efficiency is achieved at different volumes is proportional to the displacement volume (i.e. CHP systems with larger displacement volume engines achieve maximum efficiency at higher RPMs).
The latter is of great importance since it states that a smaller engine can achieve max- imum electrical efficiency in relatively lower revolutions per minute, compared to a larger engine. This observation implies a trade off between engine size and fuel consumption when achieving maximum electrical efficiency is regarded.
Figure 3.12: Engine displacement volume effect on system efficiency. The y-axis denotes the efficiency percentage and the x-axis denotes the operating level as revolutions per minute (RPMs)
The form of the power and torque curves versus the engine revolutions per minute shown in Figure 3.13, is of great importance since they show that the model has captured efficiently the behavior of an internal combustion engine. As the engine fuel load rises, i.e. the engine revolutions rise, the produced torque rises as well, until a maximum. The torque is progres- sively lower for higher operational. Equivalently, the power output follows a similar profile [157].
Overall, the model captures efficiently the behavior of an internal combustion CHP system both in terms of electrical and thermal output, despite the Mean Value Model assumption. The dynamic approach to the systems thermal modeling also ensures that the model is capable of predicting the thermal behavior of the system as well as being utilized for optimal control studies.