# Power Plant Conversion Efficiencies

Quote of the Day

All of the great leaders have had one characteristic in common: it was the willingness to confront unequivocally the major anxiety of their people in their time. This, and not much else, is the essence of leadership.

— John Kenneth Galbraith

## Introduction

Figure 1: Block Diagram of a
Combined Cycle Power Plant
(Source).

While crawling around the Energy Information Administration (EIA) web page, I found some data on the energy conversion efficiencies of power plants based on the fuel that they use. I thought the data was interesting and worth going through here.

From my standpoint, the most interesting part about this information was the efficiency of electricity production using the combined cycle power generation approach (Figure 1). I had no idea that power generation using natural gas could be ~10% more efficient than traditional coal, petroleum, and nuclear generation approaches. It looks like the higher temperature exhaust available in a natural gas system can be used to generate steam to drive a secondary generator and recover some of the energy normally lost in the exhaust. In some respects, it reminds me of a turbocharger because of the focus on using the energy present in the exhaust.

## Background

### Definitions

Conversion Efficiency
Energy conversion efficiency (η) is the ratio between the useful output of an energy conversion machine and the input, in energy terms.
Combined Cycle Power Generation
A combined-cycle power plant uses both a gas and a steam turbine together to produce up to 50 percent more electricity from the same fuel than a traditional simple-cycle plant. The waste heat from the gas turbine is routed to the nearby steam turbine, which generates extra power (Source).
Theoretical Conversion Efficiency
The maximum possible efficiency from a heat engine, which is given by the formula

 $\displaystyle {{\eta }_{{\text{max}}}}=1-\frac{{{{T}_{c}}}}{{{{T}_{h}}}}$

where Th is the absolute temperature of the hot source and Tc that of the cold sink, usually measured in Kelvin (Source).

This formula tells us that having a very hot source and a very cold sink will make a heat engine more efficient. The impact on efficiency of a high-temperature source and a low-temperature sink likely drives the efficiency improvement seen with natural gas combined cycle plants.

### EIA Data

The EIA actually reports on the nominal thermal energy required (in BTU)  for every kilo-Watt (in kW) of electrical power generation by fuel type – a metric known as the operating heat rate. Observe how the natural gas operating heat rate is reducing every year. This reflects the introduction of combined cycle technology, which is more efficient.

Figure 2: EIA Efficiency Data By Year and Fuel.

I realize that "BTU/kW-hr" is a strange unit. In the US, we usually use BTU when we are talking about thermal energy and kW-hr for electrical power. This allows us to know what type of energy is being discussed just by the units being used. Unfortunately, it also means that we have a bit of unit conversion to go through in order to get the efficiency number we want.

## Analysis

### Unit Analysis

Figure 3 shows how to convert the EIA data into conversion efficiency.

Figure 3: Unit Conversions on EIA Data

### Efficiency Calculation

Figure 4 shows how the EIA data was converted to efficiencies.

Figure 4: Efficiency Calculations.

## Conclusion

I find it interesting that coal, petroleum, and nuclear have similar conversion efficiencies of ~33%. Natural gas is the outlier with 10% more efficiency than the others.

The following quote describes the rise of efficiency in electricity production using natural gas.

An aggressive buildup of high-efficiency “combined-cycle” natural gas power plants in the early 2000s began changing the game. Over the past 10 years, the average efficiency of natural gas plants has been improving continuously as more of these technologically superior systems were built and called upon to deliver power.

Although there is chatter in monthly numbers, the U.S. fleet of natural gas power plants is now achieving about 44 per cent efficiency. Rising from 32 per cent to 44 per cent is highly significant; compared to 10 years ago, an average utility today needs 27 per cent less natural gas to generate the same amount of electricity.

I can confirm the 27% reduction in fuel use for the same amount of electrical output power with the following calculation (Figure 5).

Figure 5: Reduction in Natural Gas Usage for a Given Electrical Energy Output.

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