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Adopt a Library!

When Karen and I were living with kerosene lamps, we went to our local public library to find out if there was a better way to light up our nights. We found nothing about small scale renewable energy.

One of the first things we did when we started publishing this magazine seven years ago was to give a subscription to our local public library.

You may want to do the same for your local public library.We'll split the cost of the sub (50/50) with you if you do. You pay $11.25 and Home Power® will pay the rest. If your public library is outside of the USA, then we'll split the sub to your location so call for rates.

Please check with your public library before sending them a sub. Some rural libraries may not have space, so check with your librarian before adopting your local public library. Sorry, private or corporate libraries are not eligible for this Adopt a Library deal—the library must give free public access. — Richard Perez To Adopt a Library write or call

Home Power® PO Box 520,Ashland, OR 97520 1-800-707-6585 or 916-475-0830 or FAX 916-475-0941

Basics of Alternating Current Electricity

Part One—Sine Waves

Richard Perez

©1996 Richard Perez

Renewable energy systems have always been big users of direct current (DC) electricity. PV modules make DC electricity and DC electricity is what batteries store. With the advent of modern power inverters, however, more and more RE systems are using most of their power as alternating current (ac), just like everyone who lives on the grid. Understanding the basics of alternating current is simple—it's really just a matter of timing...


Direct current electricity is constant and consistent. Current flow is unidirectional. Voltage polarity is rigid— positive is positive and negative is negative and that's that. If you are not familiar with direct current electricity, then read Ben Root's article beginning on page 64 of this issue. You will need the concepts and terminology there to understand what you will read here.

When we enter the realm of alternating current (ac) everything changes. And I mean everything—voltage, current and even the concept known as resistance in DC electricity. The static world of direct current is lost in a sea of changes.

Fortunately the world of alternating current has its own consistencies. Sound confusing? Well, it can be. Alternating current electricity is constantly changing. Current flow and voltage vary by the millisecond. But these constantly changing electric manifestations follow a regular and repeating pattern. It is in the structure of this endlessly repeating pattern that ac electricity reveals its secrets. It's just a matter of waves and timing.


Alternating current is based on sinusoidal waves. These sinusoidal waveforms betray ac electricity's beginnings in rotational motion. Rotary ac alternators produce power with sine wave characteristics. Before understanding ac electricity, it is first necessary to understand the sine wave and how it behaves.

A sine wave is derived from angular motion. Imagine a circle with a rotating radius, exactly like a clock's face with only a minute hand. As the hand ticks off the time, the angle between the hand and the horizontal 9 o'clock axis changes. The height of the hand's pointer above the horizontal axis also changes. The sine of the angle at any point is the height of the point above the horizontal axis divided by the radius of the circle.

The left hand side of Figure 1 shows the rotational motion (like a clock face). The right hand side of this illustration shows the sine wave generated by the different values of h as the radius spins around the circle from zero to 360 degrees. There is a thin horizontal and centered line dividing both the left and right sides of the illustration. This thin line represents zero. Values above this line are considered positive while values below this line are considered negative.

Early makers of electricity used the rotary motion of water wheels and steam turbines to generate electricity. If you spin a loop of wire within a magnetic field, or conversely spin a magnetic field within a loop of wire, then electromagnetic force (EMF or voltage) is induced in the wire. This induced voltage will have a sinusoidal waveform—it will be alternating current electricity. The rotary nature of early electrical generation set the sinusoidal standard for all that was to follow.

Time and Time Again

The concept of the sine wave is familiar to anyone who stayed awake during high school math. Y=sin(x) describes a pattern that is endlessly replicated in nature as well as in alternating current electricity. Sound like mathematical mumbo-jumbo? Well, look at the sine wave shown in Figure 2. Notice a few things about this sine wave. The height of the waveform (that is, the distance from the horizontal x-axis to the curve) varies. This distance above or below the x-axis is called amplitude and it may be either positive, negative, or zero. While the amplitude varies from point to point, the pattern endlessly repeats itself. Maximum and minimum heights are always the same. The pattern has a particular wavelength and then it repeats itself over and over again. Every sine wave has a frequency. Frequency is number of times the waveform repeats itself during one second of time.

While the trigonometric equation y=sin(x) sounds like a artificial human construct, it is really our feeble attempt to understand one of nature's regular patterns. If you think this is an abstract concept just watch ocean waves, or the way a pendulum moves, or our Sun's apparent motion across the sky. Nature is into sine waves.


In the early days, before 1900, electrical pioneers realized the need of standardization of electric power. By 1900, the Battle of the Currents had been fought and won by alternating current. In the dim beginnings of commercial electricity, there was some doubt as to whether the electric power would be generated and used as direct current or as alternating current. Edison championed direct current and Westinghouse wanted an alternating current standard. Westinghouse and alternating current won out. The big reason was that alternating current could be run through transformers and have its voltage easily changed. This made long distance transmission of electric power possible.

When alternating current won out over DC, there still had to be standards set by the utilities for that current. At what voltage would it be delivered to electric power consumers? What frequency would the alternating current have? Well, in the USA, the utilities decided to deliver a sine wave voltage that varied from +164 volts to -164 volts. They decided that the frequency of this sine wave would be 60 cycles per second (60 Hz). These standards are arbitrary. In Europe for example, the voltage standard is often twice that of the USA and the frequency is 50 Hz. Figure 3 shows a graph of the American standard of ±164 volts and 60 Hz.

Figure 3 graphs the voltage of the alternating current against time. The x-axis (horizontal axis) of the graph is time and is expressed in degrees. The y-axis (vertical axis) represents voltage. Note that the voltage waveform peaks at 164 volts positive and 164 volts negative. This voltage is know as peak to peak voltage. Note that the sine wave is complete in a single 360° cycle. Since this sinusoidal waveform has a frequency

Figure 3 graphs the voltage of the alternating current against time. The x-axis (horizontal axis) of the graph is time and is expressed in degrees. The y-axis (vertical axis) represents voltage. Note that the voltage waveform peaks at 164 volts positive and 164 volts negative. This voltage is know as peak to peak voltage. Note that the sine wave is complete in a single 360° cycle. Since this sinusoidal waveform has a frequency

1 wavelength

1 wavelength

1 wavelength

1 wavelength

1 wavelength

1 wavelength

1 wavelength

1 wavelength

1 wavelength

1 wavelength

1 wavelength

Figure 2

of 60 cycles per second, the period (or duration) of each cycle is 16.666... milliseconds (or 1 cycle divided by 60 cycles per second). To find the period (or duration) of a sine wave divide its frequency into 1.

Out of Phase and In Phase

All this sine wave stuff doesn't get complicated until we start thinking about multiple sine waves. And that's what ac electric power really is: two sine wave fronts, one of EMF (voltage) and the other of electron flow (current). What were to happen if we were to graph two sine waves of the same frequency and amplitude, but we started the second wave later than the first one. If we start the second wave 45° later than the first, then the second wave is said to lag behind the first sine wave by 45°. The second wave front is said to be out of phase with the first by -45°. This out of phase situation has tremendous relevance in ac electrical circuits and is shown in Figure 4. In the later parts of this series of articles, we will see many real world situations involving ac waveforms where voltage and current become out of phase.

We can also graph two sine waves which are in phase (i.e. they have the same frequency and start at the same time), but have different amplitudes. This graphical representation fits the following real world scenario: alternating current being fed to a lightbulb. The black curve on the graph, Figure 5, represents the voltage of the ac waveform while the gray curve represents the current flowing into the lightbulb. Note that when the voltage supplied to the lightbulb reaches a maxima or minima so does the current flowing through the lightbulb. Which makes sense from Ohm's Law. When the voltage waveform is zero (at 0, 180° and 360°, etc.), the current flowing through the bulb is also zero. Which also makes sense via Ohm's Law. While these two waveforms represent different quantities (voltage and current), they are in phase (i.e. they have the same frequency and begin and end at the same time).

Figure 5 shows us the basic landscape against which alternating current electricity operates. The voltage of the waveform changes constantly and regularly. The voltage of an alternating current waveform can be either positive, negative, or zero. The current flow in an alternating current circuit is just the same—current flow can be either positive, negative, or zero. In a direct current circuit the electrons start at the negative supply voltage and move through the circuit to the positive end of the power supply. The same is not true for alternating current. Since the polarity of the current varies, so does the direction of the current. In ac electricity, an electron does not make a complete path through the circuit, but instead merely wiggles back and forth 60 times a second. In ac electricity, there is not constant voltage or even a constant direction of electron flow.

Figure 4
Figure 5

These concepts are slippery and a far cry from the gutlevel simplicity of direct current electricity. This article is the first in a series. I just want you to get a feeling for ac electricity based on its constantly changing, but repetitive, sinusoidal nature. In the articles that will follow, we will examine what happens when ac power is fed into devices like motors, transformers, and electronic lighting. We will examine and hopefully even understand abstract, yet entirely real, concepts like how power is manifested and measured in ac circuits, what happens when voltage and current are not in phase, impedance or ac resistance, power factor, and real world trivia such as why your 2500 watt inverter won't start the 1500 watt electric motor in your well pump.


Author: Richard Perez, c/o Home Power, PO Box 520, Ashland, OR 97520 • voice & FAX: 916-475-3179 • Internet EMail: [email protected]


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