February 1, 2010

Plant Efficiency: Begin with the Right Definitions

Dr. Robert Peltier, PE

Widely Misused Terms

These thermo fundamentals have been universally ignored on a grand scale and are a stumbling block when identifying top-performing plants.

Vattenfall is one of the largest utilities in Europe and 100% owned by the Swedish state. Vattenfall is also the largest producer of thermal energy used for district heating in Europe and is dedicated to high-efficiency coal-fired power generation. One of its most advanced district heating plants in Europe is the Nordjylland Power Station, located in Denmark’s North Jutland region, near Aalborg (Figure 3). Vattenfall states on its web site that its ultrasupercritical (USC) Nordjylland Unit 3 is "the world’s most efficient coal-fired CHP plant." The plant sells its entire electricity production on the Nordic Power Exchange and more than 90% of its heat production to Aalborg District Heating Supply.


3. Efficient but expensive. Nordjylland Power Station’s USC Unit 3 is called the most efficient coal-fired CHP plant in the world by its owner, Vattenfall. A total of six supercritical and two ultrasupercritical plants call Denmark home. Each is configured to supply thermal energy for district heating systems. Even so, Denmark also has the highest household electricity prices in the EU, with retail rates surpassing $0.32/kWh, according to the U.S. Energy Information Administration. Courtesy: Vattenfall

Vattenfall makes its case this way: "Block [Unit] 3 has the world record in the use of fuel for coal blocks. But an efficiency of up to 91 percent by combined production and 47 percent [Editor: LHV-basis, 44.9% HHV — see the "Watch Your Terminology" sidebar] by clean electricity production using fuel about 20 percent better than older coal-fired plants." Later, Vattenfall goes on to state that "this is a world’s record that remains unbeaten." The 411-MW (384 MW net) Block 3 uses low-pressure turbine extraction steam to produce district heating water at 80C to 90C (176 F to 194F) by using a condensing heater. The double reheat USC plant fires bituminous coals sourced on the world’s markets.

Given the earlier discussion, equating electricity production with the equivalent amount of low-temperature hot water is incongruous with a claim that the plant efficiency more than doubles when in CHP mode (47% without district heat and 91% when steam is extracted from the low-pressure stages of the steam turbine to heat water). Vattenfall arrives at its claimed 91% efficiency by adding the energy equivalent of the electricity with that of the low-temperature hot water and then dividing by the fuel burned.

Here’s an example of how efficiency numbers vary. Assume a large power plant operates at 38% thermal efficiency. In addition, assume that this same plant produces about 40% usable heat (as a percentage of fuel input), much as Nordjylland Unit 3 does. Using these assumptions, the First Law efficiency is quickly calculated as 78%, whereas the rational efficiency calculated using the Second Law is 55%. The difference in the calculations lies with a correction made to the thermal energy based on the ability of the thermal energy to do useful work. Similarly, your gas-fired water heater has an advertised efficiency of 90% (First Law) but actually has a rational efficiency (Second Law) of only about 18%. The rational efficiency of a power plant that only produces electricity is the same as the First Law efficiency. Also, by definition, the rational efficiency will always be less than 100%, unlike the First Law.

Similarly, the owner of a small, inefficient gas-fired reciprocating engine can produce some electricity and recover the jacket water, lube oil, and exhaust gas energy to produce low-temperature hot water and a CHP "efficiency" in the high 90s while its rational efficiency is about 40%.

PURPA also recognized the difference in the value of electricity and thermal energy. The equation used to calculate the "PURPA efficiency" of a CHP plant was to add the electricity generated to one-half (an arbitrary factor to be sure) of the equivalent thermal energy delivered to the process and then divide by the amount of fuel used. In fact, the EPA’s technical support document (TSD) prepared supporting the Clean Air Interstate Rule recognized the problem with very high plant efficiencies claimed by owners. Regulators recognized that certain CHP plants should be exempted if they met a minimum efficiency standard. The EPA first proposed using the PURPA 42.5% efficiency threshold regardless of the fuel in order to prevent units with very low efficiency from claiming the CHP exception. The TSD noted that, "Without a minimum efficiency standard, a potential loop hole would exist for units to claim the exemption by sending a nominal or insignificant amount of thermal energy to a process." This situation occurs when a low-efficiency combustion turbine (and consequently high exhaust temperatures and higher emissions) is configured to produce very large quantities of low-quality thermal energy and thus sneak in under the standard.

Let’s be clear — the efficiency calculation methods defined by the laws of thermodynamics have little to do with the actual operating economics of any particular CHP system. In fact, CHP systems usually have exceptional economics as well as other tangible benefits to society. Just be aware of exaggerated claims of plant thermal efficiency that are extraordinarily higher than those of the prime mover (typically a gas turbine or engine and steam turbine) in the plant. Chances are the plant owners and equipment suppliers have incorrectly used the First Law of Thermodynamics to further their marketing programs or because they wish to assert bragging rights for the world’s most efficient this or that plant.

To enable more rational plant comparisons and promote sound science, I propose that we, as an industry, correct our bad habit of playing fast and loose with the laws of thermodynamics and use the Second Law or rational efficiency as the proper approach to calculating plant efficiency.