I set up a simple experiment where I connected 8x680nF 450VAC polypropylene film capacitors in parallel across a 250VAC, 50Hz mains supply. The capacitors, nominally at 640nF each, have an equivalent series resistance (ESR) of 1.5 ohms at 100Hz.
simulate this circuit – Schematic created using CircuitLab
Using an oscilloscope, I monitored the voltage across one capacitor and the current through the mains input wire with a precise current probe. The setup initially drew around 570mA from a 230VAC source:
The oscilloscope captures the following:
- Blue waveform: current (current probe sensitivity at 100mV/A, 50mV per division).
- Yellow waveform: voltage across the circuit.
Plotted graph showing current usage:
An energy meter reported 421mA - 426mA with a power factor of 0, total energy consumption of 0W, indicating reactive power. However, the scope reported a peak current draw of over 500mA.
The oscilloscope indicated maximum current draw coinciding with the voltage zero crossing, aligning with the expected behaviour of the capacitors discharging.
When I introduced a big 38mH toroidal inductor (with approximately 4-ohm ESR (@100Hz)) designed to handle over 10A current without saturating in series with the capacitors, I noticed a significant current spike of over 2A at the zero crossing:
Plotted graph showing current spikes:
In this setup, the oscilloscope captures the following:
- Blue waveform: current (current probe sensitivity at 100mV/A, 100mV per division).
- Yellow waveform: voltage across the circuit as before.
An energy meter reported ~560mA, still with a power factor of 0 and a total energy consumption of 0W as well. However, the scope reported a peak current draw of over 2A!
This surge in current consumption persisted even with a reduced supply voltage of 50VAC, 50Hz from an autotransformer and when testing with other inductors rated for higher currents, as well as a common mode choke rated at 2A with a similar ESR.
Calculations for the resonant frequency of the LC circuit suggest an f0 of approximately 361Hz:
$$f_0 = \frac{1}{2 \pi \sqrt{L \cdot C}}$$
Plugging in the values:
$$f_0 = \frac{1}{2 \pi \sqrt{38 \times 10^{-3} \cdot 5.12 \times 10^{-6}}}$$
$$f_0 = \frac{1}{2 \pi \sqrt{0.038 \cdot 0.00000512}}$$
$$f_0 \approx 361.00 \ \text{Hz}$$
This is distant from the supply frequency of 50Hz, ruling out resonance as a cause for the spikes.
The question then is: What could be causing these large current spikes at the zero crossing? Intuitively, the inductor should mitigate sudden changes in current, yet the opposite is observed. What mechanisms might be at play here to cause this counter-intuitive result?
