Figure 1 shows 24 hours of current consumption for a nominal experiment. The thermostat is set at position 1. The refrigerator is empty and at the set-point temperature at the beginning of the experiment. The raw signal from which figure 1 is constructed contains values. During this one day experiment, the thermostat switches the compressor on and off 68 times. The mean time for the compressor being on is 194.8 s with a standard deviation of 11.1 s. The mean off-time of the compressor is 1064.3 s with a standard deviation of 25.7 s. The duty-cycle of the refrigerator for this experiment is 15.5%.
Refrigerators exhibit oscillatory behavior: there is the main compressor on/off cycle and the electrical circuit is powered by a 60 Hz AC. Figure 2 shows a frequency plot of the signal shown in figure 1. The plot shows amplitudes in the frequency range 0-0.025 Hz. The largest non-DC amplitude is at Hz. This frequency corresponds to a period of 1269.5 s which is within 99.1% of the mean duration of the compressor on/off cycle.
Figure 3 gives us a closer look on the current signal during one compressor-on cycle. The compressor is switched-on for 172 s. In the beginning the PTC thermistor is at room temperature and has low resistance. A few seconds after that the PTC thermistor heats-up due to the current flowing through it, its resistance increases and the current that flows through the start-winding of the compressor decreases. After the start-winding of the motor is switched-off the current signal becomes a simple sinusoid of 60 Hz and constant amplitude.
If we zoom-in the current plot even further we can see the start-up of the motor as shown in figure 4. It illustrates the start-up of the compressor by running current through a special start-up winding. This particular type of refrigerator uses a Resistance Start, Induction Run (RSIR) motor. The RSIR design uses a PTC thermistor as a time delay mechanism for spinning the single-phase AC motor.
Figure 4 is important in modeling the dynamics of the PTC. The PTC is a resistor whose resistance is heavily dependent on the temperature. To emphasize the fact that it behaves similar to an ordinary (mostly linear) resistor we show the compressor voltage during the start-up of a cycle. This is done in figure 5.
The sampling of the voltage and the current is synchronized by a common clock in the power logger that we have designed and use. To verify the correct working of this power logger we compute the product of the voltage and the current signals which is the power. The resulting compressor start-up power is consistent with how this type of AC electrical motors and PTC work and is shown in figure 6.
Figure 7 shows an FFT plot of the start-up current. The 60 Hz AC mains frequency is the dominant frequency which is no surprise. The Nyquist frequency of our power logger is 250 Hz and the shape of the AC sine is well-visible. There are aliased frequencies of small amplitude at 120 Hz and 180 Hz. There are several FFT components at 80 Hz and 200 Hz which are due to the choice of the ADC (they also appear in the voltage frequency plot).
Figure 8 shows an FFT plot of the start-up voltage. The voltage is almost perfectly sinusoidal which is consistent with the working of the AC motor. In our instrumentation design we use two simultaneously clocked ADCs of the same type (LTC2440). There are small frequency components (that we can digitally filter) which are due to the ADCs. The amplitudes of these frequencies (80 Hz and 200 Hz), however, are so small that there is no need of filtering for successful diagnostic analysis. These frequencies will be filtered by the diagnostic algorithm capabilities to deal with noise and error.