AC Electrics - Introduction to AC — Page 180, Lesson 188

I want to walk you through the concept of power factor in AC circuits. This is a really important idea because it tells us how efficiently we're using the electrical power we generate on an aircraft. Let's start with the two types of power we've been discussing. We have apparent power and true power. Apparent power is the product of the RMS voltage and RMS current in one half cycle — it's what the system looks like it's delivering. True power is the power that actually does useful work, like turning a motor or heating a resistive load. Now, the relationship between these two changes depending on what's in the circuit. If you have a circuit with resistance and inductance — or resistance and capacitance — the ratio between them changes, and that changes the phase angle between voltage and current. The phase angle is the key. Here's the rule: the greater the phase angle, the greater the apparent power is compared to the true power. And the smaller the phase angle, the closer they are. This relationship has a specific name — it's called the power factor, and we calculate it as the ratio of true power to apparent power. So the formula is: Power Factor = True Power ÷ Apparent Power. Let me give you the extreme cases so you can see how this works. First, consider a purely inductive circuit — or a purely capacitive circuit. In that case, the true power is zero because no real work is being done; energy just sloshes back and forth. The phase angle is 90 degrees. If you plug that into the formula — zero divided by the apparent power — you get a power factor of zero. That's the minimum possible value. Now consider the opposite: a purely resistive circuit. Here, voltage and current are perfectly in phase — the phase angle is zero degrees. The true power equals the apparent power, so the power factor is 1. That's the maximum value. So as you decrease the phase angle, you increase the true power and you increase the power factor. As you increase the phase angle, you decrease the true power and decrease the power factor. There's another way to calculate power factor, and it's very useful. The power factor is also equal to the cosine of the phase angle. And just to remind you: cos 0° equals 1, and cos 90° equals 0. That matches perfectly with what we just said — a zero-degree phase angle gives a power factor of 1, and a 90-degree phase angle gives a power factor of zero. Let me now give you a summary of the key facts about power factor, because these are the definitions you'll need to know. Apparent power is the product of RMS voltage and current in one half cycle. It can also be called theoretical power or rated power, and it's measured in VA or kVA — volt-amperes or kilovolt-amperes. True power equals apparent power only if voltage and current are in phase. True power equals zero only if voltage and current are 90 degrees out of phase. True power can also be called real power, effective power, wattful power, or working power — the power actually consumed in the circuit. It's measured in watts or kilowatts. And here's another useful formula: Real power = voltage × current × power factor. There's also reactive power, which is measured in kVAR — kilovolt-ampere reactive. That's the power that's stored and released by inductors and capacitors, not doing useful work. Finally, the power factor formula again, this time with the units: Power Factor = True Power in kilowatts ÷ Apparent Power in kVA. That figure on screen shows you the relationship between these powers in an AC circuit — it's worth studying because it visually ties together the phase angle, the true power, and the apparent power. So to sum up: power factor is a number between 0 and 1 that tells you how efficiently your AC system is using the power it's handling. A power factor of 1 means perfect efficiency — all the power is doing useful work. A power factor near zero means most of the power is just circulating reactively, not doing useful work. In aircraft electrical systems, we want to keep the power factor as close to 1 as possible.