Energy units

A primer on the units one tends to encounter in researching energy issues

The watt (W) is a measure of electric power. (Power is the rate of doing work or producing or expending energy.) One watt is equal to 1 joule (J) per second. A megawatt (MW) is one million watts.

The joule is a measure of energy, or the ability or capacity to do work. Other measures of energy are

• kilowatt-hour (kWh), a thousand watts of power produced or used for one hour, equivalent to 3.6 million joules (MJ).
  
  One quadrillion joules (PJ) = 278 million kWh.
  
  When a 1-MW [maximum rate of energy generation] wind turbine produces at 25% of that capacity as averaged over a year, its annual output is
  
  1 MW × 0.25 × 365 days × 24 hours = 2,190 MWh.


• British thermal unit (Btu), equivalent to 1,055 J or 0.293 Wh.
  
  Million (MM) Btu = 1,055 MJ = 293 kWh.
  
  Quadrillion Btu = 1,055 PJ = 293 billion kWh = 293 TWh.
  
  In the production of electricity from thermal sources, however, only a third may converted to electrical energy, the rest to heat. Therefore, 1 quad Btu may also be expressed as equivalent to only 98 billion kWh, averaging the efficiency of various generators.


• million tonne oil equivalent (mtoe), equivalent to 41,868 MJ or 11,630 GWh.

The metric system prefixes:

K (or k) means kilo, a thousand, or 10³
M means mega, a million, or 10⁶
G means giga, a billion, or 10⁹
T means tera, a trillion, or 10¹²
P means peta, a quadrillion, or 10¹⁵
E means exa, a thousand times more than peta, or 10¹⁸

Other figures and conversions

Wind speed is often expressed in meters/second (m/s) or knots.

1 m/s = 2.237 miles/hour (mph)
1 knot = 1 nautical mile [1° longitude = 1,852 meters]/hour = 1.151 mph
The sweep area of the rotor blades is usually given in square meters (m²).

1,000 m² = 0.247 acre
The sweep area A can be calculated by multiplying the square of the blade length r (or more accurately, half of the rotor diameter) by pi (π, 3.1416): A = πr²

1,000 square feet (ft²) = 0.023 acre
The speed at the blade tip in mph is: rotor diameter (in meters) × π × rpm ÷ 26.82

The area of a facility may be expressed in acres, square kilometers (km²), or square miles (mi²).

1 mi² = 640 acres
1 km² = 247 acres
Noise level is expressed in decibels (dB), using a logarithmic scale. A difference of 3 dB is the smallest that can be detected by the human ear, while a noise that is 10 dB louder than another is perceived to be twice as loud, although it is physically 10 times higher in pressure. An increase in noise level of 6 dB or more causes widespread annoyance and disruption. The usual measurement is in dB(A), which emphasizes the range of sounds easily heard (consciously) by humans. A quiet rural night may have an ambient sound level of 20-30 dB(A). Fifteen hundred feet from an industrial wind turbine, the sound level may be 45-70 dB(A), at least four to sixteen times as loud. Another measurement is dB(C), which includes lower frequencies that are not so much heard as felt and have adverse medical and psychological effects. Lower-frequency sounds more easily penetrate walls and windows and are a significant component of wind turbine noise. Yet another measurement is dB(G), which includes very-low-frequency infrasound, which recent research shows the inner ear to be sensitive to.

Noise measurements may be expressed as L₁₀, the level exceeded 10% of the time (generally taken as the level which will be found annoying), L₉₀, the level exceeded 90% of the time (generally taken as the background ambient level), and L_eq, the average level over time. The L_dn, or day-night average over 24 hours, with 10 dB added to the night-time levels, is used to compare noise levels before and after a new source is added to the environment. Following ANSI standards, 5 dB should be added to recorded levels of unfamiliar sounds and 10 dB should be added in rural areas where there is an expectation of peace and quiet. Studies of wind turbine noise find that "high annoyance" occurs at levels 20-30 dB lower than other noises. Furthermore, in predicting noise levels multiple sources must be considered (not just the nearest turbine), and "line source" decay, which is half the rate of "point source" decay, must be used for facilities in a line, as on a mountain ridge.

Note that the swishing or thumping sound of wind turbines in time with their rotation frequency, which is associated with higher annoyance, is not usually reflected in the above measures, because of the relative brevity of the peaks. This characteristic noise is called "blade swish" or "blade thump" and sometimes referred to with the nonspecific term "amplitude modulation". It is likely caused primarily by different air densities and/or wind speeds between the top and bottom of the sweep area of the blades. In the rulings allowing the Den Brook Wind Farm in England to proceed, conditions included consideration of excess amplitude modulation upon complaint as any change, outside the dwelling, in LA_eq,125ms of >3 dB in any 2-second period ≥5 times in any minute with LA_eq,1min ≥28 dB and such excess occurring in ≥6 minutes in any hour.

Emissions may be expressed in short tons (U.S.), metric tons (tonnes), or long tons (U.K.).

1 short ton = 2,000 pounds
1 metric ton (tonne) = 1,000 kilograms = 2,204.6 pounds ≈ 1.1 short tons
1 long ton = 2,240 pounds
In such figures for carbon, it should be clear if they are for carbon dioxide (CO₂) or just carbon (which may also be emitted with other compounds, such as methane). The weight of a molecule of carbon is 12/44 (0.27) that of the compound CO₂.

In 2002, according to the U.N., the U.S. and its territories emitted 5.9 billion, the E.U. 3.7 billion, and China 3.3 billion metric tons of CO₂. The worldwide total was 23.8 billion metric tons.

The greenhouse effects of methane (CH₄) and nitrous oxide (NOx) are often expressed as "CO₂ equivalence" or "global warming potential" (GWP). Thus, the effect of a ton of methane is typically considered to be equivalent to that of 25 tons of CO₂, and a ton of NOx to 300 tons of CO₂. This equivalence may vary, in part to reflect the estimated persistence of the different gases in the atmosphere: ~10 years for methane, more than 100 years for NOx, and 1000's of years for CO₂.

Capacity factor is simply the actual energy output from a generating plant over a period of time, usually a year, as a fraction or percentage of the plant's capacity. For "conventional" plants, the capacity factor generally reflects how much the plant is used and not shut down for maintenance or malfunction. For wind turbines, the capacity factor is mostly a matter of how much the wind blows, since the turbine output varies with wind speed. In North America, the capacity factor for wind is usually 20-30%.

For example, if a 1-MW wind turbine had a capacity factor of 25% for the previous year, that means that its output that year was

1 MW × 365 days × 24 hours × 0.25 × = 2,190 MWh.
Note:  It is incorrect to equate capacity factor with "efficiency" or "uptime". Wind turbines are in fact reasonably efficient (up to ~50% at the average wind speeds for which they are designed) in converting the energy from the wind and are typically "available" over 90% of the time. It's their fuel source (wind) that is fickle.

Capacity value, capacity credit, or effective capacity is how much of a generating plant's capacity is likely to be available at times of peak demand. For wind, it is virtually zero, because wind turbines respond to the wind instead of demand. Wind's low capacity value means that other sources are still required to maintain capacity and provide reliable power.

back to "A Problem With Wind Power"
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