# Power Factor and Harmonics

The operation of zero-cross or phase-angle SCR controllers can lower the power factor, resulting in a higher electrical cost. Harmonics can be generated which may cause radio frequency interference (RFI) or possibly affect the operation of other equipment.

#### Power Factor:

The power factor of a single-phase circuit is the ratio of true power in watts, as measured with a wattmeter, to the apparent power in volt-amperes, obtained as the product of voltage and current.

P.F. = KW / KVA

(The power factor of a balanced polyphase circuit is the same as that of the single phases. When the phases are not balanced the true power factor is indeterminate.)

Consider the supply voltage ES to be 480 volts and the load voltage EL controlled by the SCR controller to be 240 volts. The load current IL is, of course, equal to the supply current IS and is equal to EL/RL or 100 amps. The KW of the system is 24 (240 volts X 100 amps) and the KVA is of the system is 48 (480 volts X 100 amps).

P.F. = 24 / 48 = EL X IL / ES X IL = EL / ES = (% Applied power/100)0.5 = 0.5

The power factor with resistive loads controlled by either phase-angle or zero-cross control is the ratio of the load voltage to the supply voltage and is therefore proportional to (% applied power/100)0.5.

Tests have shown that most power factor meters supplied by utility companies respond correctly to phase-angle control, but provide near unity power factor for zero-cross control. Newer meters using solid state technology and which sample for a longer time period provide power factor measurements very close to the theoretical values for both phase-angle and zero-cross control.

#### Harmonics and RFI:

Harmonic wave forms are generated when electrical power is switched and are therefore generated when power is controlled by mechanical contacts, saturable core reactors, SCR controllers and all other power switching devices.

Harmonics are sinusoidal waveforms with frequencies that are integral multiples of the fundamental frequency. For example, a waveform that has twice the frequency of the fundamental frequency is called the second harmonic. All repetitive waveforms are formed by the addition of harmonics. In general, abrupt changes in the waveform or complex waveforms cause the magnitudes of the harmonics to increase, increasing the possibility of interference problems. In SCR control the magnitude of the harmonics are the greatest when the load power is controlled at 50%. The table below shows the relative magnitude and frequency for zero-cross and phase-angle control.

Although harmonics and RFI are a common concern, very few if any problems have occurred in actual application. This is because harmonics are attenuated by inductance, and because the effects of harmonics are attenuated by proper shielding and grounding of electrical equipment.

## Phase-Angle

Harmonic Frequency (Hz) Magnitude (%) Harmonic Frequency (Hz) Magnitude (%)
1 10 10.90 1 60 59.70
2 20 0.00 2 120 0.00
3 30 14.10 3 180 31.80
4 40 0.00 4 240 0.00
5 50 34.71 5 300 10.60
6 60 50.00 6 360 0.00
7 70 29.80 7 420 10.60
8 80 0.00 8 480 0.00
9 90 8.49 9 540 6.40
10 100 0.00 10 600 0.00
11 110 4.50 11 660 6.40
12 120 0.00 12 720 0.00
13 130 2.88 13 780 4.60
14 140 0.00 14 840 0.00
15 150 2.03 15 900 4.60
16 160 0.00 16 960 0.00
17 170 1.50 17 1020 3.50
18 180 0.00 18 1080 0.00
19 190 1.18 19 1140 3.50
20 200 0.00 20 1200 0.00
21 210 0.09 21 1260 2.90
22 220 0.00 22 1320 0.00