February 1, 2010

Plant Efficiency: Begin with the Right Definitions

Dr. Robert Peltier, PE

"Efficiency" — A Much-Misunderstood Term

Several readers have recently suggested that our nation is missing the EEC boat by not "retrofitting" existing steam power plants to operate in CHP mode. These readers cite the "low" thermal efficiency (around 32%) of our nation’s coal-fired plants and the ease with which their efficiency could be increased to 80% or even 90% by recovering the heat energy rejected to the condensing water. What usually follows is a reference to an equipment supplier’s advertisement citing the stats on a new cogeneration project or to a European plant that boasts of 85% efficiency. Others have referenced the U.S. Environmental Protection Agency’s (EPA’s) Combined Heat and Power Partnership website (www.epa.gov/chp), which states that achievable plant efficiencies range from 70% to 80% for a diesel engine to 70% to 75% for a combustion turbine (Figure 2). The website goes on to say, "Typical CHP applications have coincident power and thermal demands that must be met. It is reasonable, therefore, to consider the values of power and thermal output from a CHP system to be equal in many situations."


2. Missed the memo. The EPA’s notes to this example of a typical CHP system explain that, to produce 75 units of useful energy, the conventional generation or separate heat and power systems use 154 units of energy—98 for electricity production and 56 to produce heat— resulting in an overall efficiency of 49%. However, the CHP system needs only 100 units of energy to produce the 75 units of useful energy from a single fuel source, resulting in a total system efficiency of 75%. However, adding electricity and thermal energy together to produce an overall plant thermal “efficiency” is technically incorrect. The calculation is flawed because the “value” of the thermal energy is far less than the value of electricity. To do so is the technical equivalent of mixing your electricity apples with your thermal energy oranges. Some correctly note the difference and use the term ”fuel utilization factor” or “fuel utilization efficiency.” Source: EPA

Regrettably, many good engineers, equipment suppliers, and the EPA make a serious mistake by quoting these pseudo-thermal efficiency numbers, perhaps because they misunderstand the science behind the calculations.

Start with the Basics

The First Law of Thermodynamics is about energy accounting — energy out of a system equals the energy entering less the energy stored. The concept is simple. Most have experienced the dreaded low fuel light when driving to work. The amount of energy stored in your gas tank (gallons of gasoline) is the difference between what you have used and what you had when you last stopped and filled up the tank. One measure of a vehicle’s efficiency is the number of miles driven divided by the net gasoline used. The same quantitative analysis is used when calculating the thermal efficiency of a power plant: Measure the amount of electricity produced (less any losses) and then divide by the amount of fuel consumed to arrive at the plant’s thermal efficiency. This calculation method works and is universally accepted because the energy produced by the "system" is homogenous — it’s all electricity.

Others have incorrectly extrapolated the First Law efficiency calculation process to CHP systems by summing the electricity and the equivalent thermal energy produced by the system (see Figure 2) and then dividing by the fuel used to arrive at system "efficiency," frequently above 80%. This calculation method is misleading.

For example, if a power plant with a First Law efficiency of 50% sends half of its electricity to a heat pump with a coefficient of performance of four, then the First Law efficiency of this plant is 125%, clearly a useless term to compare power system performance. Using the First Law to make this calculation, though it is common today, is flawed because the "thermodynamic value" of the thermal energy is far less than that of electricity — you are mixing your electricity apples with your thermal energy oranges.