Got UPS? It wouldn’t hurt to have one. A power failure or a tripped breaker can be a little like playing the lottery. Most of the time nothing bad will happen, but you can almost count on losing your most important data at the worst possible time. A UPS is cheap insurance compared to the value of all that stuff on your hard drive.
Do you know which one to get? Not which brand…which size? The specs aren’t all that helpful…volt-amps, watts, amps, volts…what does it all mean? Several UPS manufacturers offer web sites that will let you check off equipment, then make a recommendation, but a better way is to understand what the numbers on the label mean.

I’m going to use my APC Back-UPS Pro 650 as an example, but what follows is applicable for any UPS on the market. A word of warning: there is a little bit of math coming your way. Nothing terribly complex and there won’t be a test later…in fact, if you skip anything that looks like math, I’ll understand.

So, when I look at the specs for my UPS, I see that it is rated at 650VA/410 watts, 120V input/120V output. Now, I know that my monitor is rated at 100 watts and I have a 400 watt power supply. How does that all relate?

In the world of battery power, there is just, well, power. We calculate it by multiplying the current by the voltage. What comes out is watts. It’s easy. In the world of AC (the stuff that comes out of your wall), things get complicated. There is **true power** (sometimes called **real power**), **apparent power** and **reactive power**. Only true power is measured in watts – it’s calculated just like battery power.

So what about the other two? Engineers use them to gain some insight into how well a power supply is working. The values for apparent power and reactive power given them an idea about what is inside the power supply, how much of the power on one side of the power supply is getting to the other side and how well the whole thing was designed. Now, you may not be an engineer, but the numbers can tell you some interesting things about your UPS.

Let’s talk about apparent power. In the case of my UPS, it is rated at 650VA. VA stands for **volt-amp**. Apparent power is a measure of the output power of the UPS, taking the impedance of the circuit into consideration. Impedance is a funny thing. It’s a lot like resistance, except that it isn’t just a simple number. Maybe you’re used to seeing resistor values expressed as **ohms**. Well, impedance is also expressed as ohms, but instead of a simple **scalar** number, it is expressed as a **complex** number. That means that it has a **real** and an **imaginary** part (a scalar number, the kind that we use every day, only has a real part). Now, I’m not going to go into complex numbers and vectors and the grief that goes with them. At this point, you can just take my word for it and, perhaps, do a little more research on your own. Suffice to say that, thanks to the wonders of trigonometry, we can express impedance as a scalar value, just a regular old number. And, also fortunately, that makes figuring out apparent power very easy.

So, now we know what impedance is. But why does it matter? What’s wrong with good old resistance? The big issue is that the heart of a UPS is a big **transformer**. And a transformer is just a couple of **inductors** (coils of wire) that are very close to each other. Inductors present an issue in that their impedance changes in response to the frequency of the power. In other words, an inductor presents a different load at 100Hz than it does at 60Hz. The other issue is the relationship between the voltage and the current in an inductor.

Try thinking about electricity as a series of waves, like the sine waves on an oscilloscope. One set of waves represents voltage, another is current. In a simple circuit with a resistor (or something that acts like a resistor), the waves line up. When voltage is at its peak, so is current. But in a coil, like the transformer of a UPS, the two waves get out of sync. That’s about as much electromagnetic theory that we’re going to get into. What’s important is to realize that, although the two waves are out of sync, it’s not necessarily a bad thing…it’s just the nature of an inductor.

Part of the effect of having voltage and current out of sync with each other is that some of the current gets reflected back from the transformer to the power source. Again, that’s not necessarily bad, but it does reduce the amount of current that is available to be converted into power on the other side of the transformer.

Now that we’ve talked about inductors and impedance, let’s put it together with apparent power. The UPS manufacturer knows how much current is available on the power supply side of the UPS. The manufacturer also knows what the impedance of the UPS is. So, just multiplying the square of the current times the impedance gives the apparent power in volt-amps.

Like I mentioned earlier, my UPS has an apparent power rating of 650VA. I don’t know what the impedance is or what the current is, but that’s OK…I know how they came up with the number. It also has a true power rating of 410 watts. But how could they come up with that number if they didn’t have a bunch of stuff hooked up to the UPS?

The true power rating is related to the apparent power rating by a number called the **power factor**. Remember the issue of current reflecting back from the transformer to the power supply? The magnitude of the reflection is measured by the power factor. A perfect transformer has a power factor of one. That means that all of the current that goes into the transformer is used to create power on the other side of the transformer. If the number is less than one, then some of the current is reflected back from the transformer and doesn’t play a role in creating the output power. So, if my UPS had a power factor of one, the real power would be 650 Watts. The apparent power multiplied by the power factor gives you the real power. Naturally, the real power divided by the power factor will give you the apparent power. And the engineers who designed the UPS measured the performance of its circuit to determine its power factor. So that’s how we know the true power output.

The power of math also tells us that we can determine the power factor by dividing the real power by the apparent power. In my case, 410 watts divided by 650 VA gives a power factor of .63. As it turns out, APC’s web site says that this series of UPS’s has a power factor of .6. What does that tell me? Well, it says that there is a lot of current on the inside of that UPS that never makes it to the outside. That doesn’t mean that it’s a cheap UPS, though. A high power factor is very expensive to achieve because of the extreme precision that is required from the transformers and supporting circuitry. **A power factor of .5 to .7 is pretty normal.**

So now we know where the numbers came from. But if you remember, I said that my monitor was rated at 100 watts and my power supply was 400 watts. If I add those values together, I get a number that is bigger than 410 watts.

As it turns out, that’s OK. Not because a monitor watt and a power supply watt is different from a UPS watt, but because neither the monitor nor the power supply are running at full power during normal operation. Those values are maximum numbers. It takes a fair amount of power to energize the electron tube of a monitor. Likewise, spinning up a hard drive requires a pretty big jolt of energy at the beginning, but once everything is running, it takes very little to keep it that way. Think of your car leaving a stop sign. You have to step on the gas to get it to accelerate to the speed limit, but once you’re there, you barely have to step on the pedal. Your computer works the same way.

Are you wondering why we’re not concerned about apparent power for the monitor and power supply? And what about reactive power?

To answer the first question, the power required by a device (which we call a “load”) is just power. We don’t get concerned about whether or not it’s apparent, real or reactive because, generally speaking, the concept of reactive and apparent power belong to power sources (like UPS’s or generators). So, basically the load draws a certain amount of current at a given voltage. That’s real power.

And to answer the second question, reactive power is just one of those topics that isn’t important to this article and would just make things a little more confusing by telling us more than we need to know. Sorry.

So how should you select a UPS? The easy way is to add up the power ratings of everything that you want to plug into it, and then purchase one with a real power rating somewhere around that number. Sure, it sounds easy, but now you know why!

I know that I threw in some math, and I’ve made some generalizations as well. If you have questions about this, feel free to email them to me. I’ll answer them and put a few of them up here to help everyone else out.

Thanks to Matthew Kidd for pointing out the glaring error in my calculation of battery power. Back to Freshman Physics for me!