AC Power - Power Factor Explained

I originally published this on blogs.sun.com, but that site is now gone so I have published it again here.
You will need your browser's Java plugin enabled to use the interactive demos below.

From time to time, I have been asked to explain Power Factor, most commonly in connection to computer power supplies or compact fluorescent lamps. With cheap plug-in power meters now being easily available, many more people are becoming interested in this field, and trying hard to remember what (if anything) they were taught about Power Factor too many years ago! Whilst you may have remembered that PF = cos(Φ) (with Φ being the angle of phase shift of the current relative to the voltage). It's less well understood why a switched mode power supply (such as those used in a computer, or a compact fluorescent lamp), which has almost no phase shift, can still have a low Power Factor.

Well, the real definition of Power Factor is given by:

	Watts
PF =
	VA

where VA is the RMS Voltage multiplied by the RMS Current drawn by the load.

The more familiar PF = cos(Φ) formula is just a simplification for the case of a phase shift only, but phase shift isn't the only reason for low Power Factor.

Below, I investigate 3 causes for low power factor; Phase Shift, Phase Control (Light Dimmer), and Switched Mode Power Supplies. You can also see the effect low power factor has on the electricity supply. I have avoided the detailed mathematical proofs, and instead provided demos you can tweak with the mouse to see the resulting changes in Power Factor.

Phase Shift This demonstrates the effect of a phase shift in the current drawn by a load. The demonstration is a 100W load running on 240V. Initially, there is no phase shift (Phase Angle = 0). This represents a resistive load, and it can be seen that the VA is the same as the 100W Power dissipated by the load. The red area shows the energy taken from the supply. Drag the Current waveform side to side to generate a phase shift, and see what effect it has. This demonstration keeps the load dissipating 100W, but what you'll see is that the Current increases. When the current shifts, there are periods when it's flowing the wrong way for the applied voltage, and is thus feeding energy back into the supply - this is shown by the green areas. To compensate for these green areas, additional energy is taken from the supply, so the red area increases by exactly the same amount. What's happening is that the load is drawing more energy than it needs to generate 100W during the red time, storing this excess energy, and then feeding it back during the green time. This extra energy flowing back and forth between the supply and the load results in an increase in current flow, over and above that required for the 100W which the load is dissipating. Cables, fuses, and supply transformers must be sized to handle this excess current. VA If we simply estimate the power consumption by multiplying the Voltage and Current including the excess, this will be an over-estimate, but this value is useful for other purposes and is known as the VA (i.e. the product of volts and amps). The VA rating is used to calculate size of cables, fuses, and the supply, since these have to handle this excess current. True Power The True Power consumption is obtained by measuring the energy used by the load over time (which is fixed at 100W in this example). This is represented as the red area minus the green area in this demonstration. Power Factor Power Factor is defined as the True Power consumption divided by the VA. This is 1 for a resistive load where power and VA will be equal, but drops to less than 1 for a load with a phase shift.	You need to enable Java to see this applet. Drag waveform with the mouse to change phase the angle
Phase Control (Light Dimmer) This demonstrates how a Phase Control light dimmer works. This is a standard light dimmer used for filament lamps. The light dimmer uses a Triac semi-conductor switch. Each half cycle, the triac switches off when the current through it drops to zero. Later in each half cycle, the triac is switched on. By varying this switch-on position in the cycle, the RMS voltage supplied to the filament is varied, which in turn varies the light output. Drag the Current waveform left and right to change the triac switch-on position. Again, this demonstration is for a 100W light on 240V. You will see the Current waveform change as you change adjust the light level, and consequently the power consumption of the light, which is represented by the size of the red area. The Lumen output indicates how much light is given off. Notice that this falls off much faster than the power consumption reduces when you dim a light - this shows how filaments lamps become even more inefficient when dimmed. The VA and Power Factor are also shown.	You need to enable Java to see this applet. Drag waveform with the mouse to change phase control angle
Switched Mode Power Supply This shows the load generated by Switched Mode Power Supplies (SMPSU) which don't contain power factor correction. SMPSUs are used in most electronic items nowadays, such as compact fluorescent lamps, phone chargers, computers, etc. SMPSUs rectify mains into a 360V DC storage capacitor. They only draw current from the mains during the mains peaks, just to recharge the DC storage capacitor, replacing the energy consumed from it since the last mains cycle peak. Like the first example, we'll consider a load consuming a fixed 100W (typical of a computer). Since the power is the same as the first example, the energy used (the red area) will be the same. However, since the SMPSU can only draw energy during the peaks, this results in high energy demand during this small time, and no energy demand at other times. Thus the current drawn during these peaks is high. These short large current peaks result in a large RMS current draw, which in turn result in a large VA rating. Consequently, the Power Factor is well below 1. The narrower the peaks, the larger they are - you can change them by dragging left and right on the chart to see what difference this makes, but they are rarely better that a power factor of 0.5. A large number of SMPSUs has a rather devastating effect on the electricity supply infrastructure. It requires cables, transformers etc to be much bigger than the size they need to be for the True Power consumed, and it can result in flattening of the Voltage waveform. The picture shows the mains waveform at Sun's Bagshot UK site around 2002. The site consisted of a data centre containing a lot of older systems from the 1990s for handling customer support issues, drawing about 2MW. Considerable distortion of the mains waveform is clear. Consequently, regulations have been introduced in Europe and other areas which require SMPSUs over a few tens of Watts to include Power Factor correction circuits. These work by making the SMPSU draw energy through most of the mains cycle, so it looks more like a resistive load, and the power factor increases to nearly 1. Today's computer systems are much kinder to the mains supply infrastructure than those of the last century.	You need to enable Java to see this applet. Drag waveform with the mouse to change Current peak width