June 1, 2010

A Proposed Definition of CHP Efficiency

By S. Can Gülen, PhD, PE

Many alternative approaches for determining a useful definition of combined heat and power fossil power plant efficiency have been proposed, although most fail to produce a universal definition. This follow-up report to our February story on plant efficiency shows how an exergy analysis supplies the elusive solution.


Combined heat and power (CHP), also known as cogeneration, describes fossil-fired power plants that generate multiple product streams, usually thermal energy and electricity. In most cases, the thermal energy product comprises one or more streams of steam at different pressures and temperatures that are used by an end-use customer for district heating and/or cooling, manufacturing process needs, or similar industrial and/or residential uses.

The key benefit of CHP is the attractive economics produced by generating electricity and useful thermal energy from a single fuel source. A quick and easy assessment of the benefits of CHP can be found in “CHP: Helping to Promote Sustainable Energy” (POWER, June 2009).

Although there is no question about the benefit of CHP’s effectiveness in fuel utilization and reduced emissions, what has been missing so far is a standardized and consistent definition of CHP efficiency that would enable industry participants to measure and rank a wide variety of cogeneration plants on a thermodynamically consistent basis. This issue was recently discussed in “Plant Efficiency: Begin with the Right Definitions” (POWER, Feb. 2010), which pointed to the fundamental error of mixing “electricity apples with thermal energy oranges.”

A Rational Explanation

The second law of thermodynamics provides an unassailable measure of each product stream of a fossil-fired power plant: exergy, also called availability.

For the electric power product from a power plant, by definition, the exergy is exactly equal to the power generated. As dictated by one of the two fundamental corollaries of the second law, the Kelvin-Planck statement, the maximum useful work generating potential of any material stream is exactly equal to its thermodynamic property exergy.

For example, the most common material stream that is a product of CHP power plants is steam or hot water at a known pressure and temperature. Using steam tables, the exergy of steam or hot water can be exactly calculated. The numerical value that is obtained is exactly equal to the power that can be generated in a Carnot engine, which utilizes that particular product stream as its heat source. According to the second law, the Carnot engine is the most efficient energy conversion device possible when operating under a given set of temperature conditions.

A simple numerical example illustrates the calculation process using data taken from the steam tables. Suppose that a combined-cycle (CC) power plant supplies an industrial customer with 25,000 pph of saturated steam at 125 psia. The enthalpy of the steam is 1,191.1 Btu/lb for a total thermal energy supply of 29.8 million Btu/h (or 8,725 kWth). The exergy of 125 psia (saturated) steam is 369.9 Btu/lb for a total thermal exergy supply of 9.25 million Btu/h or 2,710 kWth. In other words, a hypothetical Carnot engine utilizing 29.8 million Btu/h of saturated steam at 125 psia as its sole heat source, and rejecting heat to the ambient at To (59F) would generate 2,710 kW of power, which implies a maximum theoretical thermal efficiency of 31.1%. Note that these two numbers—2,710 kW and 31.1%—are not subject to any misinterpretation because they are directly derived from a fundamental law of nature. Figure 1 shows the calculated results for a range of steam pressures and temperatures in terms of β, which is the ratio of steam exergy to steam energy (that is, enthalpy).

1. Ratio of steam exergy to energy (enthalpy) for a range of steam pressures and temperatures. Exergy is given by e = (h – ho) – To · (s – so) where h is enthalpy, s is entropy, and both can be found from steam tables using p and T. The subscript denotes the reference “dead” state, which for this calculation is the ISO definition of po = 14.7 psia and To = 59F. Source: GE Energy

Obviously, it is practically impossible to design a Carnot engine. The state-of-the-art power plant engineering option available to a designer today is a steam turbine (ST). For illustrative purposes, consider what is practically possible with a ST with 85% isentropic efficiency discharging to a condenser at a pressure of 2.5 inches of mercury. Using 29.8 million Btu/h of saturated steam at 125 psia, this ST would generate 1,840 kW of shaft power for a thermal efficiency of only 21.1%. Though this seems to be a paltry number, consider that, when compared to the theoretically possible maximum of 2,710 kW (only from a hypothetical Carnot engine), the second-law or “rational” efficiency of the example steam turbine is 21.1%/31.1% = 67.9%. The term “rational” conveys the underlying concept of using a reference point that is theoretically possible instead of using a reference point that is (even theoretically) impossible.