Another advantage is that AC current can be generated as a single wave form (phase) or in multiple waves (phases). We will talk more about this advantage next month. Also, its frequency (cycles per second or hertz) can be varied easily during generation or afterward. Finally, it is easy to convert AC to DC when DC is needed but more expensive to convert DC to AC.

On the downside, AC power is far more complex than DC. Fortunately, this is not a major factor as all of its complexities have been studied and understood by those before us. If we follow the known rules, we can use all of its benefits and avoid any pitfalls. We will take a look at this more complex power curve.

### The AC Power Curve

The single phase, 120 V sine wave shown in Figure 1 has several important characteristics. As it progresses through one full cycle (one 360 deg rotation of a generator), it begins at 0 V, then peaks at 170 V a quarter of the way through the cycle. It returns to zero at the halfway point and then reaches negative 170 V at 270 deg. At the end of the cycle it returns to 0 V. In the United States, this occurs 60 times each second, so one full cycle takes about 16.67 milliseconds. A full cycle is also known as a Hertz (Hz). Three complete cycles are shown in the illustration.

 Figure 1

You are probably wondering why we call this a 120 V sine wave if the actual peak is at 170 V. Could 120 V be the average? If you were to average all of the voltage values, the result would be approximately 108 V, so that must not be the answer. Why then is the value, as measured by a Volt/Ohm Meter (VOM), equal to 120 V? It has to do with something called effective voltage. It turns out that the area of the green rectangle, whose upper border is at 120 V, is equal to the sum of the actual areas under the upper and lower curves of a single AC cycle (blue areas). This area is known as the effective voltage of the sine wave. We will take a closer look at effective voltage.

If you were to measure the heat produced by a DC current flowing through a resistance, you would find it is greater than that produced by an equivalent AC current because AC does not maintain a constant value throughout its cycle. If you did this in the lab, under controlled conditions, and found that a particular DC current generated a heat rise of 100 deg, its AC equivalent would produce a rise of only 70.7 deg or 70.7 percent of the DC value. Therefore, the effective value of AC is 70.7 percent of DC. 0.707 times the peak voltage of 170 in Figure 1 equals 120 V.

Also, the effective value of an AC voltage is equal to the square root of the average of the squares of the voltage values across the cycle(√v12+v22+ •••vn2/n).  Thus, effective voltage is known as the root mean square, or RMS voltage. A simplified form of the RMS equation is vp/√2 where vp is the peak voltage. If the peak voltage were 1, the RMS calculation will also yield 0.707. It follows that the peak voltage will always be 1.414 that of the effective or RMS voltage. Remember that unless stated otherwise, all VOMs are calibrated to display RMS voltage.

Next month we will discuss the relationship between peak voltage and frequency and then move on to  three phase power.

Pumps and Systems, June 2010