# The Sign of the Sine

If one plots the speed of the pendulum as it swings back and forth, the graph would be a sine wave. At the top of the arc, the speed is zero. Then it begins to travel faster and faster until the bottom of the arc. After reaching the bottom, it begins to slow down until it hits the other top of the arc and the speed goes to zero again. The process reverses as it begins to accelerate in the opposite direction. The resulting graph shows the speed of the pendulum versus time. The same curve represents the change in electrical current induced in a coil of wire as it rotates past two magnetic poles, which is the basis for an alternating current electrical generator. Since I don’t want to restart the debate between Edison and Westinghouse over whether AC or DC is the best way to transmit electrical energy, AC is how most electrical energy is transferred between electrical suppliers and the loads. Within loads, some devices change the voltage into DC, such as those typically called electronic loads. Integrated circuits within personal computers, VCRs, or clock radios typically run off of either 5 or 12V DC (though newer circuits run on lower voltages (3.3V DC or smaller). But it is the AC voltage, or the sine wave around which most of power quality phenomena is measured. A sag or swell is determined by a variation in the amplitude of the sine wave. A sag is a reduction in the RMS value of the sine wave, typically below 90 percent of nominal, whereas a swell is an increase, typically above 110 percent of nominal. Harmonic distortion is a series of sine waves superimposed on each other. A transient, such as a power factor (PF) cap switching generated event, can be decomposed into a series of sine waves. The oscillation following the initial negative going transient usually has a frequency of between 400 and 1,500 Hz, compared to the fundamental power frequency of 50 or 60 Hz. Fourier’s Theorem states that any periodic waveshape can be represented by the sum of a series of sine waves. Even square wave and sawtooth waves are but a series of sine waves. PF is based on sine waves. The method of measuring PF in the past was based on the difference in time or phase angle between the voltage and current. This is referred to as displacement PF electrical motors, which make up 60 percent of the load in the United States, have a current sine wave that lags behind the voltage sine wave, as a motor is mostly a coil of wire, which is an inductor. Unfortunately, in today’s harmonic-rich electrical environments, this method no longer works. Today, true PF is defined as watts divided by voltage amperes, or how much work is done versus the energy transferred. Though the sine wave is really magical, most designers of equipment to be powered from the AC voltage waveform have made the assumption that the shape of the waveform will be basically sinuoidal, with the amplitude between certain limits (typically +/- 10 percent) and frequency stable. When events, such as large motor starts or downed wires, cause the sine wave to exceed these limits, it is usually a sign that a power quality event has occurred and possibly equipment malfunction has resulted. BINGHAM, manager of products and technology for Dranetz-BMI in Edison, N.J., can be reached at (732) 287-3680.