Machine Design

# Power to the People: But in What Units?

It helps to keep a few terms straight in the discussion on alternate energy sources.

 Authored by:Robert Repas Associate Editor[email protected] Key points: • Energy and power are not interchangeable terms. • The joule is the electrical measure of energy, equal to one watt used for 1 sec. • Electrical power is measured in watts, which equals 3,600 joules/hour. Resources:U. S. Energy Information Administration, www.eia.doe.govCenter for Energy Policy and the Environment, The Manhattan Institute, www.manhattan-institute.org/html/ce.htm

Here’s an irony: Though power and energy regularly make the news, few people know what these two entities are. Discussions of alternate energy sources tend to mistakenly use the terms interchangeably. While power and energy are related, each has a specific meaning.

Readers may recall from basic physics that energy is typically defined as the ability to do work, and that two types of energy exist: potential and kinetic. Potential energy is that which is stored, ready to do work. Kinetic energy, however, is energy of motion. In many situations, potential energy is converted into kinetic energy to accomplish a task.

For example, place a rock on a sheet of horizontal glass such that the glass supports the rock above the ground. The elevated rock has potential energy due to gravity, but that potential energy isn’t enough to break the glass. Now raise the rock 3 ft above the glass surface and release it. The rock falls, probably shattering the glass on contact and continuing on to the ground. The rock sitting 3 ft above the glass has the same potential energy as when perched on the glass. But, as it fell, kinetic energy was added as its speed rose. Upon contact with the glass, the amount of kinetic energy from motion was far greater than the rock could exert by itself as potential energy. The glass couldn’t withstand the force of this applied kinetic energy, and so fractured into many pieces.

When speaking of energy sources, many times the discussion centers on the energy potential within the source. Oil, gas, and nuclear fuel all store potential energy, whereas the motion of wind, waves, and particles of light are forms of kinetic energy. To make these different forms of energy usable, they must first be converted to another form of energy — usually electricity.

Energy is typically measured in joules (J). As the idea is to accomplish some work, it’s common to define joules according to mechanical motion. Thus a common definition of a joule is the amount of energy used when a force of 1 Newton moves an object a distance of 1 m, or 1 Newton-meter (Nm). However, do not confuse this definition of a joule with that of torque, also measured in Newton-meters.

The kinetic energy equivalent is one-half of the mass times the square of the velocity (Jk = ½ mv2), so a single joule can also be defined as a mass of 2 kg moving at a velocity of 1 m/sec. In the rock example, the 1-m fall would take approximately 0.45 sec and the rock would be moving at 4.41 m/sec when it strikes the glass. As the rock mass did not change, the rock would now have kinetic energy equal to 0.5 × (4.41 m/sec)2 or almost 10× greater than its potential energy sitting on the glass. It’s no wonder the glass shattered when subjected to this stronger force.

Specific energy is the amount of energy a mass of material produces to perform a specific amount of work. For example, a barrel of oil holds about 6.12 GJ of energy. That is the total amount of potential energy in that barrel of oil. However, seldom does the amount of work done equal the full potential. Mechanical and thermodynamic losses are the culprits.

Energy density is similar, but works with the volume of the source. For example, diesel fuel has 46.2 MJ/kg of specific energy, but produces an energy density of only 37.3 MJ/l. There are 1.24 liters in a kilogram of diesel fuel, so the amount of energy in 1 liter of diesel fuel is slightly lower. Nowhere is this better shown then with hydrogen, sometimes billed as the fuel of the future for cars. Hydrogen has a specific energy of 143 MJ/kg, but its energy density is quite low and changes whether it’s a standard atmospheric-pressure gas (0.0108 MJ/l), compressed to 700 bar (5.6 MJ/l), or liquefied (10.1 MJ/l). On the other hand, gasoline has an energy density of 34.2 MJ/l. Assuming hydrogen and gasoline could move a vehicle with the same efficiency, a 700-bar hydrogen tank would still need to be over 6× bigger than a gasoline tank needed to drive the same distance on a single fill up.

Wind, waves, and solar are all forms of kinetic-energy sources. Their energy comes from some form of motion whether it’s the blowing wind, flowing water, or streaming particles of light. These systems use special devices called transducers or converters to change the kinetic energy from one form to another. (Technically, what we call a wind turbine should actually be called a wind-energy converter, but most everyone has come to call them turbines.)

It should be obvious that blowing wind has no set quantity of energy available. As long as the wind is blowing, work can be done. But the amount of work accomplished depends on how fast the wind blows and for how long. High winds can do the same amount of work faster, or more work in the same amount of time. The rate at which work is done is called power.

Power is typically measured in two forms: mechanical and electrical. Mechanical power is measured in horsepower, while electrical power is measured in watts. Both measurements come from the amount of work performed within a given period of time. For example, 1 hp equals 33,000 ft-lb of work done in 1 min. A watt represents one joule of work per second: W = J/sec. Comparing horsepower to watts, one horsepower equals 746 W.

While the joule is the electrical unit of energy, it is seldom used in electrical work because it is so small. A more common unit of electrical energy is the watt-hour (W-hr), or the number of watts multiplied by the time in use. For example, a 100-W bulb that burns for 100 hr has used 10,000 W-hr or 10 kW-hr of energy. The U.S. Energy Information Administration lists that an average U. S. home uses 920 kW-hr of electricity each month, though actual usage varies as to location and climate. For example, a home in Hawaii only averages 628 kW-hr/month, while Tennessee peaks at 1,302 kW-hr/month.

A typical wind turbine used in wind farms today can generate 2,000 kW, although several currently on the drawing board can hit 5,000 kW. Now if the 2,000-kW turbine could operate 24-hr/day at full output, it could generate 1,460,000 kW-hr/month of energy. That’s 2,000 kW multiplied by 8,760, the number of hours in a year, and divided by 12 for an average per month. However, wind doesn’t blow 24-hr-a-day every day, and equipment needs servicing from time to time. Studies of several wind-turbine sites around the world show that, on average, wind turbines seldom operate at all more than 70% of the year, and for much of that time the generator is not at full output. A more realistic number is that wind turbines typically operate at a full-output equivalency for only 25 to 30% of a year. That reduces the average energy output of the turbine to 438,000 kW-hr/month, or enough power to handle about 475 average homes.

This statement can be a bit misleading. As noted, wind turbines are intermittent power sources. As such, they can not be counted as a base-load source for utilities. The base load is the minimum continuous power level a utility must supply its customers, so this power must remain available for use 24-hr a day. Wind turbine and most other alternate energy sources can help off-load or take demand from the base-load plant, but they can not replace it.

The energy density of a wind generator takes into account the amount of land needed to erect several generators side by side. Robert Bryce, a senior fellow with the Center for Energy Policy and the Environment at the Manhattan Institute, states that a typical wind farm has an energy density of 1.2 W/m2. In a recent article in Forbes magazine, he compares the output of the wind farm to a marginal natural gas well producing 60,000 ft3/day that has an energy density of 28 W/m2.

Looking at sunlight or solar energy finds that it fares only slightly better than wind in terms of energy density. Solar cells, or photovoltaics (PV), convert the energy of arriving photons of sunlight into dc electrical energy. The dc electricity is converted to ac for use in a home using a power inverter, a device similar to an uninterruptible power source for a computer.

The amount of power available from sunlight depends upon the solar constant, or the total power per square meter that hits the earth from the sun. Satellites have measured this “constant” from 1,412 W/m2 to 1,321 W/m2 depending on the time of year. However, remember that only half the earth receives sunlight at a time, and the curvature of the earth spreads the sunlight out over a wider geographic area. The combination of these two difficult circumstances effectively reduce the usable solar energy value to about 342 W/m2. Note that this is the maximum amount of energy if PVs were 100% efficient. However, the efficiency average for most solar cells is only 15%. That means the solar cells only produce about 51 W/m2 of usable power.

That power level assumes the panels can remain pointed towards the sun. If the panels are in a fixed position, actual power output peaks only during the times the sun is directly overhead, and falls off towards mornings and evenings, effectively halving the panel’s power output. Other factors, like shadows cast on the panels and the latitude of the array, can also reduce the effective output. Mr. Bryce places the average energy density of solar panels at only 6.7 W/m2. To power the average U. S. house would need a minimum of 188 m2 of solar panels. For the 475 houses in the wind-generator example needs 89,300 m2 or about 22 acres of solar cells. This doesn’t include backup energy storage needed during the night or on days with heavy cloud cover.

TAGS: Energy