An energetic-exergetic analysis can help improve total installation performance
An energetic-exergetic analysis can help improve total installation performance
Credit: Siemens

For many readers familiar with the concept of energy balances and tools such as Sankey diagrams, background knowledge of thermodynamics is often lacking. That might not be an issue for a practical user, but such knowledge can be of utmost importance when designing installations and when promoting the benefits of cogeneration for policymakers. In a series of articles, Jacob Klimstra discusses the energy balance of cogeneration installations.

We use energy in many ways, such as powering industrial processes, heating or cooling dwellings and propelling transport. Energy is delivered to the end user as electricity, fuel, or heat and chill. Humans have always used heat to prepare food and make utensils, and the wealth level of modern society is entirely based on the extended use of energy. It is therefore entirely justified to call energy the engine of the economy. Electricity, a special type of energy, plays a key role in powering communication, data handling, tools and industry. The bulk of the world’s energy use, some 82%, is based on burning fossil fuels, but associated emissions can cause pollution and global warming. Cogeneration of electricity and heat does reduce fuel consumption and emissions compared with separate generation. Fuel is a scarce economic resource, while reduced emissions lower the burden on the environment.

Ultimately, end users of energy are primarily interested in its costs, and in a high reliability of supply. Energy supply is viewed as a service for running processes and for creating comfort. High energy efficiency and low emissions can also be priorities for interested individuals, but generally these aspects are of macroeconomic importance. Policymakers play a role in developing rules with respect to such macroeconomic issues. Fuel savings can help to improve countries’ trade balances, while the associated reduction in emissions helps to create a cleaner environment.

In this context, policymakers, civil servants, engineers and scientists do evaluate the energy savings of combined heat and power generation compared with separate generation of electricity and heat. The question is now how to judge the performance of cogeneration installations. One might undertake such an evaluation based purely on economic values, or on a more technical thermodynamic approach.

The economic value of energy differs significantly depending on the application and the moment of use. A private user easily pays €2 ($2.72) for a small battery powering her garage door remote controller, equalling some €1000/kWh. An aluminium smelter, on the other hand, is already unhappy with an electricity price exceeding 5 euro cents/kWh. For another example, the economic value of the output of a modern computer can be much more than a thousand times the cost of the energy it takes to run it. The profitability of a cogeneration installation depends very much on multiple boundary conditions, such as the prices of fuel, electricity and the required equipment and the costs of maintenance and operation.

Energy and exergy

Thermodynamics is an engineering discipline concerned with heat and temperature levels in relation to energy and work. Many former students remember with horror the days they had to learn about entropy, enthalpy, anergy and exergy. It often seemed that the theory had been made complicated on purpose. Yet thermodynamics can offer extra insight into the value of energy. Nevertheless, one has to take care to avoid seeing the thermodynamic value of energy as the absolute criterion. A person wanting a comfortable shower is very happy with a water stream of 40°C, although a thermodynamicist might say that most of the exergy of the fuel needed for the water heater is being destroyed. When viewed thermodynamically, the energy of spent fuel is not lost, but it ultimately ends up in the environment at a temperature level where it is of no use. Viewed economically, such low-temperature energy is also fully lost, hopefully after it has generated economic value at an earlier stage.

The exergy in a certain amount of energy is that part of the energy that can be, at least theoretically, completely converted into work. Work is seen as the highest-value level of energy, since it can be used to propel machines and to replace physical labour by humans and animals. Moreover, in principle, work can always be completely converted into heat. The fraction of exergy in a certain amount of energy is called the quality factor (fq) of the energy:

eq 1

The fraction of energy that cannot be converted into work is called the anergy. Therefore, anergy = energy – exergy, and

eq 2

By convention, electricity is given a quality factor of 1, since – at least in theory – it can be fully converted into work. The electric motor needed for the conversion does, however, have some losses, so in real life the quality factor of electricity is less than 1. In addition, the conversion machine – the motor – requires a capital investment and needs regular maintenance. Therefore, the conversion of electricity into work comes at a price, both thermodynamically and economically.

Heat itself can never be fully converted into work. The thermodynamic quality of heat depends on its temperature level with respect to a reference temperature. The so-called Carnot factor is used to express the exergetic quality of heat of a temperature T with respect to a reference temperature T0. This reference temperature is the temperature of the heat sink at the cold end of the process that converts the heat into work.

In this equation, the temperature is expressed in kelvin (K). Actually, the Carnot factor is the quality factor of the heat energy. Figure 1 illustrates how the quality factor of heat depends on the temperature, for a reference temperature (or heat sink temperature) T0 of 288.15 K = 15°C. For this reference temperature, the exergy fraction, i.e., the quality factor, is 0.22 for heat of 100°C, and 0.87 for heat of 2000°C.

Figure 1. The thermodynamic quality factor of heat, indicating the fraction of exergy in the amount of energy (reference temperature T0 = 15°C
Figure 1. The thermodynamic quality factor of heat, indicating the fraction of exergy in the amount of energy (reference temperature T0 = 15°C)

In real life, it is not possible to convert the exergy of heat fully into work. Machines such as steam boilers and steam turbines are needed, and such machines have their losses. And, again, these machines require capital investments as well as maintenance and repairs.

In thermodynamic theory, fuel is given a quality factor of 1. Burning the fuel can result in very high temperatures. Burning natural gas with a stoichiometric amount of air at ambient conditions gives an end temperature of close to 2000°C. Burning fuel with, e.g., pure oxygen results in temperatures approaching 10,000°C.

Thermodynamic analysis of combined heat and power

Figure 2. Electricity, fuel, and kinetic and potential energy all have a quality factor of 1, meaning that their energy equals their exergy
Figure 2. Electricity, fuel, and kinetic and potential energy all have a quality factor of 1, meaning that their energy equals their exergy

A combined heat and power plant produces electricity and heat. If we presume that the electrical efficiency of the plant is 45% and the combined efficiency is 85%, the useful heat released is 85% – 45% = 40% of the input energy. Since the electrical efficiency of the installation is 45%, the fuel input for 1 kWh of electricity equals 8 MJ, since 8 MJ • 0.45 = 3.6 MJ = 1 kWh. Figure 3 shows that, in this case, the production of 1 kWh (= 3.6 MJ) of electricity results in the useful application of 3.2 MJ of heat. If no cogeneration is applied, the 3.2 MJ of heat would have to be produced in a separate boiler with an estimated efficiency of 90%. This would require 3.2/0.90 = 3.55 MJ of fuel. Separate production would therefore require 8 MJ + 3.55 MJ = 11.55 MJ if we presume an electrical efficiency of central power equal to that of the cogeneration plant. That means that, in this case, separate production consumes 11.55/8 • 100% = 45% more fuel than cogeneration. The energetic benefit of cogeneration in this case is therefore very clear. Even if the electricity had been produced separately with 60% efficiency, production of 3.2 MJ of heat and 3.6 MJ of electricity without cogeneration would then have required 3.55 MJ + 6 MJ = 9.99 MJ of fuel. That still requires 24% more fuel than the cogeneration unit in our example. Supplying a customer with electricity from a central power plant also requires transmission and distribution of the energy, which involves losses, and therefore the presumed 60% efficiency is not realistic in practice. Cogeneration produces the electricity close to the customer, and therefore the transportation loss is low.

We will now carry out an analysis to reveal the exergy balance of the cogeneration plant in Figure 3. Viewed thermodynamically, 45% of the fuel’s exergy is converted into electricity with a quality factor of 1. If the useful heat is released at a temperature of 95 °C, the quality factor of that heat is only 0.21 (see Figure 1). Such a temperature level is common practice in district heating systems. The 3.2 MJ of heat has therefore only 3.2 MJ • 0.21 = 0.67 MJ of exergy; the rest is anergy. Thus the exergetic efficiency of the cogeneration plant in our example equals (3.6 MJ + 0.67 MJ)/8 MJ • 100% = 53.5% (see Figure 4).

Figure 3. The overall energy balance of cogeneration and separate generation
Figure 3. The overall energy balance of cogeneration and separate generation
Figure 4. Example of a cogeneration plant with a heat output of 95°C, a total energy efficiency of 85% and an exergetic efficiency of 53%
Figure 4. Example of a cogeneration plant with a heat output of 95°C, a total energy efficiency of 85% and an exergetic efficiency of 53%

If, however, the heat is used at a level of 400°C, the quality factor of the heat is 0.57 – much higher than for heat at the low temperature. But with such a high heat temperature, the system produces less useful heat than a system which produces low-temperature heat. As a rule of thumb, a 100 K higher end-user temperature reduces a system’s efficiency by five percentage points. Therefore, for a heat use temperature of 400°C, the combined cogeneration fuel efficiency would be about 70%. The exergetic efficiency of the cogeneration unit would be 45 + 0.57 • (70 – 45) = 59.3%. This is clearly higher than in the case of a low heat temperature. It actually means that high-temperature heat has great potential for being converted into work, for example with a steam generator and a steam turbine.

If the 3.6 MJ of electricity from the cogeneration plant in Figure 2 is generated in a central power plant and supplied with 55% fuel efficiency to a customer, while a separate boiler with 90% efficiency produces 3.2 MJ of heat at 95°C, the combined exergetic efficiency would be (3.6 + 3.2 • 0.21)/(3.6/0.55 + 3.2/0.90) = 42%. Therefore, the cogeneration plant in our example, with a heat output of 95°C and 53.5% exergy efficiency, is also preferable, from an exergy point of view, to central electricity generation and separate heat production.


Expressing the performance of a cogeneration installation in terms of exergy reveals how much of the fuel energy used is, theoretically, ultimately available for delivering work, the supposedly highest quality of energy. However, in real life there is also a high demand for low-temperature heat. In Germany, for example, the need for heat is 2.5 times higher than that for electricity. As long as heat demand exceeds electricity demand by such a high factor, the energy balance of a cogeneration installation offers a better insight into that installation’s performance than does its exergy balance. If, in the future, most low-temperature heat will be produced with electric heat pumps with a high performance coefficient, the emphasis of fuel applications will instead be on exergy.

Ultimately, for the owner of a cogeneration installation, only its economic performance counts. But if free market conditions do not create sufficient revenues for cogeneration, policymakers might decide to support the technology because of its macroeconomic and environmental benefits. An analysis of energetic and exergetic performance helps to reveal the benefits of cogeneration. Moreover, such an analysis can also help users to improve the total performance of their installation.

Dr Jacob Klimstra is Managing Editor of COSPP