A one-kilowatt oven that is on for one hour will consume one kilowatt-hour of energy. Are energy units that easy? On rare occasions, they are. When they are not, it helps to have a fundamental understanding of power and energy. All electric loads are not created equal. Some use more energy than others, and some use the same energy less efficiently.

Energy efficiency now makes headlines, and it has become increasingly important to understand the basics of power measurement and the difference between seemingly ambiguous terms of power and energy. Moreover, it can be difficult for non EEs to grasp electrical concepts because electricity cannot usually be seen or touched. For this reason, it is often advantageous to convey electrical concepts in terms of physical and mechanical analogies.

### The units of electrical energy

There are many units used to express electrical energy components, including, most commonly, volts, amps, watts, watt-hours and frequency. Each is a unique expression with a unique role in electrical energy concepts.

Electrical power is a combination of two components: one expressed as volts and the other expressed as amperes or amps. A common analogy for the flow of electricity in a circuit is the flow of water in a pipe. In this physical analogy, water pressure represents voltage and flow volume represents current. Just as with electricity, a high value of either can perform a high level of “work.” High pressure water can cut steel with very little flow volume yet a large volume of water moving very slowly over a road can sweep away a large vehicle.

Energy is defined by the ability to do work. Work in household energy-use terms is a combination of light, heat (dryers, irons, ovens, air heaters) and motion (motors) from electrical devices. Energy bills depict how much electrical energy has been converted into work over the span of a month.

Power is a measure of rate-of-energy-conversion from one form to another. Integrating, or summing, power over time determines energy consumed in that period of time.

The relationship between power and energy may be more readily apparent using alternate units where power is expressed as a rate. One watt = 1 joule/sec. Multiplying by time in seconds yields an alternate unit for energy, the joule, where 1 joule = 3,600 watt-hours (W-hr)

Where power measures how fast an oven, say, converts electrical energy into heat, energy measures how much power was applied over a given time, or how much heat was ultimately produced. A 100-W slow-cooker can use just as much energy as a 1 kW oven. But because its rate of energy conversion is ten times slower, the slow-cooker must be on ten hours for every hour the oven is on to provide the same amount of heat energy. This is why air-conditioners typically account for the largest portion of household summertime electricity bills. They convert energy quickly (large wattage) and run for extended periods of time, especially in warmer climates.

When measured by instrumentation such as oscilloscopes, ac line voltage looks like a sine wave. The half of the sine wave above zero (positive) signifies the energy carried by the electric charge in one direction and the half of the sine wave below zero (negative) signifies the energy carried in the opposite direction. This change in direction every cycle gives ac or alternating current its name. It is caused by the alternating positive/negative poles of a magnet rotating in a generator. The frequency is a result of generator design and is based on the number of magnetic poles it contains and its rotational speed.

To simplify generation and distribution, power grids operate at specific frequencies such as 60 Hz in most parts of the Americas and 50 Hz for many other places in the world. All equipment adding energy onto the grid (generators) or pulling it off (appliances) must work at the same frequency. This is why most electrical devices sold in the U.S. will not function properly when plugged into outlets in Europe; the frequencies, and many times the line voltages, don't match. 50 Hz vs. 60 Hz is similar to any other “format war,” like VHS vs. Betamax, but with no real advantages either way. The big issue is that the cost of converting a whole electrical distribution system from one frequency to another is astronomically high.

The oscillatory nature of ac waveforms introduces complexities into measurements of their value. For example, the average value of an ordinary ac main voltage is zero, because the wave spends the same amount of time above zero as below zero. So ac signals are typically quantified as a calculated root-mean-square (RMS) value. This calculation is exactly as the name suggests. First, a single waveform is measured at a high rate of speed and broken from a smooth analog wave into hundreds of data points. The data points are then squared, averaged together, and finally the square root of that average is calculated. The result is the RMS. In the U.S., the RMS value of the voltage waveform is around 120 Vrms. This may fluctuate slightly, but it is usually within 5% of nominal.

The RMS value of voltage is used to calculate ac power. The ideal power equation, usually taught in high-school level physics, states that power equals the product of voltage and current, or *P = I×V*. Though this is true for direct current (dc) loads, it rarely holds true for ac systems. AC systems have an efficiency factor, known as the power factor. This means that given the RMS voltage and current ratings on an ac electrical device, multiplying the two together will not yield the real power. This is why appliances often list the power in watts, rather than the current.

### The Power Triangle: Real, apparent, reactive power, and power factor

Apparent power is the product of RMS voltage with RMS current yielding volt-amps (VA). Electrical outlets, extension cords, and wire installed in homes and commercial buildings are often rated in VA to account for both the real and reactive power that the system must support.

Real power is expressed in watts and as so represents the actual energy converted from electrical energy to useful work. The calculation for real power is the product of the apparent power and the cosine of the angle between the voltage and current waveforms. In the case that the current is not a true sinusoidal waveform, an alternate calculation is to take the average instantaneous power over a cycle. In other words, the average of voltage multiplied by current from each of the discrete data points measured in one cycle.

Reactive power is expressed in volt-amps reactive (VAR) and is the energy that is used to help transfer energy into usable work, but does not do any usable work itself.

A good mechanical analogy for this is a reciprocating engine as found in most cars today. The usable work (real) from the engine comes from the expansion stroke of the piston, but some energy must be used to “reset” the piston back through the compression stroke. This energy (reactive) does not perform any useful work since it does not help propel the car forward, but it is required to keep the system going. The same is true for electrical appliances.

Power Factor is the simple ratio of real power to apparent power. A power factor (PF) of 1 is the best possible and is seen on purely resistive loads. Most electrical devices are a combination of electrical load types. For example, an electric clothes dryer uses resistive elements for heat and inductive elements (motors) for the tumbling action. However, PF generally figures only into industrial uses because utilities don't monitor it for individual houses.

Together, PF, real and reactive power provide an indication of how efficiently an electrical device or load uses electrical energy. Engineers can get a “visual” indication of this efficiency by overlaying the waveform of the measured current with that of the measured voltage. If the two are in-phase such that their peaks and zero-crossings line up, then the electrical load is utilizing all energy from the grid to perform usable work. The degree to which a current waveform lags or leads the voltage waveform indicates the efficiency of the electrical device under test. Electrical loads that are purely resistive, such as incandescent light bulbs, have current waveforms that line up perfectly with the voltage waveforms. For these devices, the ideal power equation *P=I×V* applies.

Another way to visualize the three components of power is to plot them as a triangle. Reactive power is plotted perpendicular to real power because the whole portion of reactive power contributes zero to real work. Apparent power is the vector sum of real and reactive power. It should be noted that integrating any of these values over time will (respectively) yield the energy equivalents of watt-hours, VA-hours, and VAR-hours.

### Power measurement

At the core, energy savings equal cost savings. One of the simplest reasons to monitor power is to reduce energy consumption. This is true for everything from multi-billion dollar facilities all the way down to single-family residential homes. Historically, residential consumers have only had visibility into energy consumption once a month when they see their utility bills. This crude measurement makes it difficult to correlate energy consumption with power usage. Digital smart meters will likely improve this situation. The first generation of these devices reads out daily energy use in 15-minute blocks. This high-resolution view of consumption makes it easier for homeowners to target and reduce specific actions that use a lot of energy.

By monitoring power and energy, consumers can ensure the utility company is billing them properly. Today, the cost of the sophisticated monitoring equipment necessary does not make sense for most residential consumers. But the price is easily justified for office and manufacturing facilities with monthly utility bills in the tens of thousands of dollars. Smart metering is also proving to be more valuable in developing countries where the distribution of energy is less regulated or where energy is more likely to be stolen.

Large consumers of electric energy sign agreements with utility companies that limit the level of wasted energy (VAR) produced. The wasted energy is a manifestation of the facility's power factor or PF. Motors add VARs to an electrical system, so it is important that large facilities monitor the power factor to avoid fines. To boost their power factors, entities can selectively run VAR-heavy equipment so that the worst offenders don't all run at the same time, or they can install special power equipment that soaks up VARs rather than creating them. In this regard, lagging-current devices and leading-current devices will cancel out when on the same circuit.

Most people have heard of black-outs, brown-outs and power spikes. There are several other power grid phenomena that are imperceptible to ordinary power consumers yet can be harmful to expensive manufacturing, industrial or computer-based equipment. By monitoring power quality, facility managers can trigger alarms in the event of hazardous disturbances and prevent costly repairs and downtime. Problems that are systemic might call for long-term solutions such as independent on-site generators.

The cost of electric energy has risen 40% over the past ten years. If that trend continues, the process of making an informed decision about energy will increasingly demand a thorough knowledge of the units, basic calculations, and uses of electrical energy measurements.

### Resources

National Instruments Corp., Austin, Tex., www.ni.com

Smart grid energy monitoring, https://decibel.ni.com/content/docs/DOC-6071

Smart grid switching, http://www.engineeringtv.com/video/Smart-Grid-Monitoring-System;Engineering-TV-Energy-Videos

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