Mains power analysis - measuring power factor

The setup

We are going to measure the power factor of a mains-powered desk fan. This appliance was chosen because it contains a small AC motor, and is therefore likely to have an interesting current waveform and a low power factor.

The measuring equipment is as follows:

• Desk fan, rated at 25 W, 220 V to 240 V
• PicoScope 3206 PC Oscilloscope. We could have used any two- or four-channel PC Oscilloscope in the PicoScope range.
• Laptop PC to run the PicoScope software
• Pico TA009 60 A current clamp
• Pico TA041 700 V differential probe
• Modified 13 A extension lead. This has the live conductor separated from the neutral and earth conductors and formed into a loop. The cable is protected by heatshrink sleeving so that the entire assembly is safely double-insulated.
• Mains breakout box. This allows the shrouded 4 mm plugs on the differential probe’s input leads to be safely connected to the mains.

Setting up the input channels

We plugged the fan into the modified extension lead, which we then plugged into the mains. We then switched on the current clamp, pressed the ‘ZERO’ button and hooked it onto the live conductor loop in the extension lead. The BNC lead from the current clamp was connected to channel A on the oscilloscope. We then ran PicoScope on the laptop and set it to trigger on channel A, and selected the ‘60 A current clamp (20 A mode)’ custom probe from the channel A setup menu. With the fan switched on, we saw a noisy, distorted sine wave on the PicoScope display.

We then switched on the differential probe, set it to its ‘x100’ range and connected it to channel B of the oscilloscope. With a ‘x100’ custom probe selected for channel B, we saw a clean sinusoidal 240 V waveform on the display

Figure 1: Noisy, distorted sine wave

Figure 2: Clean sinusoidal 240 V waveform

Measurements and calculations

With the current and voltage traces displayed in the correct units, we then turned to the math channel feature in PicoScope. This creates a new channel, similar in appearance to an input channel but formed by a mathematical function of one or more inputs. In this experiment we wanted to calculate instantaneous power. By clicking the math channel button () to open the Math Channel dialog, we found the ‘A*B’ function listed and switched it on by ticking the check box. (The most common functions are listed, but if the one you want is not there you can type in your own equation.) This gave us a third channel showing the instantaneous power plotted against time. By default, PicoScope displays a ‘?’ as the unit symbol on the vertical axis of every new math channel, so we changed this to ‘W’, for watt, the SI unit of power. We also changed the colour of the trace to green for better contrast. The green trace (bottom) shows how the instantaneous power varies over each mains cycle, depending on both the rotation of the fan motor and the phase of the current.

The next step was to add some automatic measurements. With PicoScope, this is a simple matter of clicking the ‘Add Measurement’ button () and selecting the source channel and measurement type. We added three measurements: a DC Average of the math channel (and therefore the average power), and RMS values for the current and voltage input channels.

The measurements table shows an average power of about 19 W, which is what we expect from this fan on its low–power setting. There is a small error in our calculations here, since we have averaged the power over a period of 50 ms, which is not an integer multiple of the 20 ms cycle time. We could have improved our accuracy by setting up two rulers 20 ms or 40 ms apart on the scope view and restricting the measurement to the interval between them

Figure 3: instantaneous power varies over each mains cycle

Figure 4: Measurements table shows an average power of about 19 W

Calculating the power factor

The second and third rows in the table show the RMS current and RMS voltage. We now have enough information to calculate the power factor (pf), which is defined as follows:

pf = PR / PA

where PR is real power and PA is apparent power, both averaged over one cycle of the mains waveform.

PR = 19.32 W

PA, the apparent power, is easy to calculate. It is defined as the product of RMS current and RMS voltage, which we have in the second and third rows of the table:

PA = 0.1307 A x 246.9 V ≈ 32.27 W

So the power factor is:

pf ≈ 19.32 W / 32.27 W ≈ 0.60

Power factors are always in the range 0 to 1, with 0 indicating a purely inductive or capacitive load and 1 a purely resistive one, so 0.60 is about what we would expect for a small AC motor.