Performance evaluation and assessment of combined cycle cogeneration systems are not taught well in academia. One reason is these parameters are scattered in the literature with each publication starting and ending at different stages. In many institutions professors do not discuss or even mention these topics, particularly from a second law perspective. When teaching combined cycle cogeneration systems to undergraduates, the professor should introduce pertinent parameters in a systematic fashion and discuss the usefulness and limitations of each parameter. Ultimately for a given situation, the student should be able to determine which parameters form the most appropriate basis for comparison when considering alternative designs. This paper provides two approaches, one based on energy (the first law of thermodynamics) and the other based on exergy (the second law of thermodynamics). These approaches are discussed with emphasis on the “precise” teaching of the subject matter to undergraduates. The intent is to make coverage of the combined cycle cogeneration systems manageable so that professors can appropriately incorporate the topic into the curricula with relative ease.
The United States Department of Energy (1) lists 5267 electrical power plants operating in the United States, providing a nameplate electrical capacity of 1067 GW. Only 19.5% of this capacity is credited to the 466 power plants operating as a combined cycle, which produced , or 15.3% of the net generated total in 2006. The majority of existing power plants are not based on a combined cycle, but the majority of recently commissioned power plants are. The low capital costs and high thermal efficiency of combined cycle plants, which are fueled in 99.0% of cases by natural gas, make these power plants attractive in comparison to others listed in Figs. 1,2.
Advances in combined cycles can raise their thermal efficiency to 51% without increasing capital or operating costs (1). This helps combined cycles remain competitive even in light of recent high natural gas prices. Coal has remained relatively inexpensive and continues to fuel lower efficiency power plants.
The previous efficiencies do not include useful thermal output, as obtained from combined heat and power (CHP) plants. In 2006, CHP plants produced , or 7.9% of the United States’ total electrical output, while also producing ( Btu) of useful thermal output, mostly for industrial processes. For comparison, the total United States energy consumption in 2006 was ( Btu) (2). Hence, a combined cycle power plant that also produces useful thermal output makes more complete use of the fuel source.
Since the United States electric utility industry (1) relies more extensively on the combined cycle cogeneration system, undergraduate thermodynamics education should include introduction to such systems and the associated performance parameters. Performance parameters may be based on either the first law of thermodynamics or the second law of thermodynamics, thus many parameters may be defined to analyze a combined cycle cogeneration system. Although this type of system is comprehensive, teaching and understanding the processes are indeed very valuable. The overall intent of a combined cycle cogeneration system is to produce electrical power; process energy obtained is an added benefit.
Various thermodynamics textbooks are available to teach undergraduate thermodynamics (3,4,5,6,7,8). These textbooks provide only a simple introduction to combined cycle cogeneration systems, whereas Ref. 9 emphasizes exergo-economics in the analysis of combined cycle cogeneration systems. Most, if not all, undergraduate courses in thermodynamics introduce first law analysis; however, most programs do not introduce exergetic analysis based on the second law. This paper presents performance criteria for a combined cycle cogeneration system using both first law and second law analyses. These analyses will allow better assessment of the characteristics of a combined cycle cogeneration power plant. The intent is to provide an example that thermodynamics educators can integrate into their courses.
The sign convention, heat in positive and work in negative, is applied in this presentation consistently (10). Sign convention is not a trivial issue as consistency of its application in analysis is paramount. This is one of the points that cause confusion to the student in the classroom, as well as during tests due to the inconsistencies that exist in the textbooks mentioned above. Precision and consistency are very important and cannot be trivialized.
Technical data for the gas turbine (GT) are from Ref. 11 for the generator drive PG9351(FA) and are given in Table 1. Use of data from an actual gas turbine shows the student that real industrial gas turbines found in literature can and should be analyzed to bring reality to the classroom. This engine is a modern one on which a combined cycle cogeneration structure can be built. This is the intent of this paper so that complete first and second law analyses—energy versus exergy—can be performed to better understand the details and the meaning of the results. Should time permit, thermo-economics can also be integrated. The appropriate choices are, of course, at the discretion of the individual instructor.
Combined Cycle Cogeneration System
A typical combined cycle cogeneration system is shown in Fig. 3. The topping cycle is an open Brayton cycle consisting of a compressor, combustion chamber, and gas turbine. A generator converts output shaft power to electricity. Hot exhaust from the topping cycle provides energy to superheat steam in the Rankine cycle-based bottoming cycle. Instead of a conventional boiler that burns fuel, a heat recovery steam generator (HRSG) that includes an economizer, evaporator, and superheater converts compressed liquid water exiting the pump into superheated steam that drives the steam turbine. Within the HRSG a minimum pinch of is required to ensure proper thermal exchange. Pinch technology, its use and value are covered in the course that is presented. If this is not the case, it is suggested that it be taught by the instructor who wants to use these results. The pinch diagram for the HRSG is shown in Fig. 4. A generator connected to the steam turbine converts shaft power output into electricity. In lieu of a conventional condenser that rejects heat to the environment, heat rejection from the steam exiting the turbine in the condenser provides thermal energy for a useful purpose (process heat).
First Law-Based Performance Criteria
Based on the first law of thermodynamics, the following performance criteria may be defined. The choice is up to the instructor. Here suggestions are made as to the value or lack thereof for each so that appropriate choices can be made by the instructor for the course. If possible, all should be discussed so that the student can appreciate the importance for each and comparative value in each.
Thermal Efficiency (ηthermal)
Power to Heat Ratio (Rpower to heat)
Utilization Factor (Futilization)
Backwork Ratio (Rbackwork) for the Gas Turbine
Specific Fuel Consumption (SFC) (Gas Turbine)
The Heat Recovery Steam Generator Effectiveness (εenergy)
Power Generation Efficiency (ηpower generation)
Fuel Chargeable to Power (FCP)
Fuel chargeable to power identifies how much of the fuel actually contributes to net power generation. It compares the net heat transfer into the system on a fuel energy basis to the net power produced by the system, also known as net heat rate (13). As shown in Eq. 12, fuel chargeable to power is the reciprocal of power generation efficiency. Fuel chargeable to power is important since power generation is the primary desired output from the system
Economic Efficiency (ηeconomic)
Second Law-Based Performance Criteria
Based on the second law of thermodynamics, the following performance criteria may be defined using exergy, which is the energy that has been taxed by nature prior to use, . In these analyses, it is assumed that exergy calculations are covered in the courses taught. If this is not the case, either this section will be omitted or additional discussion will be incorporated to clarify these. Although, in general, these parameters are more meaningful, they should, nevertheless, be used judiciously to emphasize the pedagogical points that are intended.
Exergetic Turbine Efficiency (ηexergetic turbine)
Second Law Efficiency (ηII)
Exergetic Combustor Efficiency (ηexergetic combustor)
Heat Recovery Steam Generator Effectiveness (εexergy)
This paper presents a number of performance parameters relevant to industrial power generation systems. Thermodynamics educators teaching a two-semester course in thermodynamics should include these parameters in the course material. If only one semester is available, then the first law parameters should be covered in detail, particularly the thermal efficiency, power to heat ratio, utilization factor (keeping in mind that the electric power generated is the important term), and the backwork ratio for the gas turbine cycle, since a small value is desired. For the HRSG, the heat recovery steam generator effectiveness, Eq. 8, should be taught. If economic considerations are desired, then economic efficiency, Eq. 13 should be discussed. If the second law is well covered in the thermodynamics course, then exergetic turbine efficiency and the second law efficiency are the two most important terms. Additionally, heat recovery steam generator effectiveness based on the Second Law, Eq. 20, should be discussed thoroughly. The control of the pinch point and its effect on the HRSG operation and on the efficiency are also topics to be discussed. If the above is done precisely, then the student will have a better appreciation of the usefulness of the combined cycle cogeneration system. An engineering equation solver (EES) (14) is used to obtain property results given in Table 2 for analysis of the combined cycle cogeneration system in Fig. 3. The effect of the pinch point on thermal efficiency, Eq. 5, and the second law efficiency, Eq. 18, is shown in Fig. 5, and the numerical values are given in Table 3, as calculated by EES (14). For the data in Ref. 11 and other given information, as shown in Table 4, all of the parameters listed in the text are calculated using EES (14). Each term is identified by its equation number to facilitate reading. Thus the instructor and student alike can analyze a real system either using the first law or second law of thermodynamics analysis or both. It has to be decided by the individual instructor.
With the prevalence of combined cycle cogeneration systems in industry, introduction of these systems into undergraduate thermodynamics courses is important. Increasing concern with resource utilization and sustainability presents additional need for further discussion in the context of the course. This paper outlines important parameters for the complete cycle. The individual instructor should exercise discretion as to which parameters are introduced based on students’ knowledge bases, the focus of the course, and whether or not a single- or two-semester course is offered.
energy rate (kW)
exergy rate (kW)
fuel chargeable to power
lower heating value (kJ/kg)
mass flow (kg/h)
heat transfer (kJ)
heat transfer rate (kW)
specific fuel consumption (kg/kJ)