# Methods for Calculating Efficiency

## Introduction

Every CHP application involves the recovery of heat that would otherwise be wasted. In this way, CHP increases fuel-use efficiency.

Two measures are commonly used to quantify the efficiency of a CHP system: total system efficiency and effective electric efficiency.

**Total system efficiency**is the measure used to compare the efficiency of a CHP system to that of conventional supplies (the combination of grid-supplied electricity and useful thermal energy produced in a conventional on-site boiler). If the objective is to compare CHP system energy efficiency to the efficiency of a site's conventional supplies, then the total system efficiency measure is likely the right choice.**Effective electric efficiency**is the measure used to compare CHP-generated electricity to electricity generated by power plants, which is how most electricity is produced in the United States. If CHP electrical efficiency is needed to compare CHP to conventional electricity production (i.e., grid-supplied electricity), then the effective electric efficiency metric is likely the right choice.

Certain assumptions are implicit in each methodology that are not appropriate in all cases. Consequently, the measure employed should be selected carefully and the results interpreted with caution.

## Key Terms Used in Calculating CHP Efficiency

Calculating a CHP system's efficiency requires an understanding of several key terms:

**CHP system**. The CHP system includes the prime mover (e.g., combustion turbine, engine, microturbine), the electric generator, and the heat recovery unit that transforms otherwise wasted heat to useful thermal energy.**Total fuel energy input (Q**. The heating value of the total fuel input. Total fuel input is the sum of all the fuel used by the CHP system. The total fuel energy input is often determined by multiplying the quantity of fuel consumed by the heating value of the fuel._{FUEL})

Commonly accepted heating values for natural gas, coal, and diesel fuel are:- 1020 Btu per cubic foot of natural gas
- 10,157 Btu per pound of coal
- 138,000 Btu per gallon of diesel fuel

**Net useful electric output (W**The gross electric output of the generator minus any parasitic electric losses. In other words, the net useful electric output is the total electric output from the CHP system that is put to a useful purpose._{E}).- Gross electric output is the total electric output of the generator.
- Parasitic electric losses are the electrical power consumed by the CHP system; for example, the electricity used to compress natural gas before it is used as fuel in a combustion turbine.

**Net useful thermal output (∑Q**The gross thermal output of the CHP system minus any thermal output that is not put to a useful purpose. In other words, the net useful thermal output is the total thermal output from the CHP system that is put to a useful purpose._{TH}).- In the case of a CHP system that produces 10,000 pounds of steam per hour, with 90 percent of the steam used for space heating and the remaining 10 percent exhausted in a cooling tower, the energy content of the 9,000 pounds of steam per hour is the net useful thermal output.
- Gross thermal output is the total thermal output of the CHP system.

## Total System Efficiency

The total system efficiency (ηo) of a CHP system is the sum of the net useful electric output (W_{E}) and net useful thermal output (∑Q_{TH}) divided by the total fuel energy input (Q_{FUEL}), as shown below:

The calculation of total system efficiency evaluates the combined CHP outputs (i.e., electricity and useful thermal output) based on the fuel consumed. CHP systems typically achieve total system efficiencies of 60 to 80 percent.

Note that this measure does not differentiate between the value of the electric output and the thermal output; instead, it treats electric output and thermal output as having the same value which allows them to be added (kWh can be converted to Btu using a standard conversion factor). In reality, electricity is considered a more valuable form of energy because of its unique properties.

## Effective Electric Efficiency

Effective electric efficiency (ℰEE) can be calculated using the equation below, where W_{E} is the net useful electric output, ∑Q_{TH} is the sum of the net useful thermal output, Q_{FUEL} is the total fuel energy input, and α equals the efficiency of the conventional technology that would be used to produce the useful thermal energy output if the CHP system did not exist:

For example, if a CHP system is natural gas-fired and produces steam, then α represents the efficiency of a conventional natural gas-fired boiler. Typical boiler efficiencies are 80 percent for natural gas-fired boilers, 75 percent for biomass-fired boilers, and 83 percent for coal-fired boilers.

The calculation of effective electric efficiency is the CHP net electric output divided by the additional fuel the CHP system consumes over and above what would have been used by a boiler to produce the thermal output of the CHP system.

Typical effective electric efficiencies for combustion turbine-based CHP systems range from 50 to 70 percent. Typical effective electric efficiencies for reciprocating engine-based CHP systems range from 70 to 85 percent.