Are DC microgrids more efficient? Calculating peak and RMS current in DC rectifiers

Question

I'm calculating the energy losses of using AC to power rectified (DC) devices.

Rectified loads have capacitor filters that demand sharp peaks of current. This increases conduction losses across the entire AC electrical installation.

We can model all rectified loads in an installation as one large rectifier, for simplicity:

• The current in this rectifier may be 20 A (or ~5 kW).

• The ripple may be 5% (Vr = 16 V).

• The capacitor will then be around 0.01 F:

  C = I / (2f * Vr) = 20 A / (2 * 50 Hz * 16 V) = 0.01 F

In a classical AC load, the RMS current is the average current. But in a rectified load, the RMS current demanded is much higher than the average current, because of the sharp peaks. This causes conduction losses.

To calculate the RMS current powering this ~5kW rectifier, I did:

• The capacitive reactance is:

  Xc = 1 / (2 * π * f * C) = 0.3 Ω

• The RMS current is:

  I_rms = V_rms / Xc = 230 V / 0.3 Ω = 770 A

Which is obviously wrong!

Can you help me understand what I should have done differently?

Answer 1

Your assumption about AC/DC PSUs have large current spikes needs some looking into.

First, at startup, AC/DC PSUs will limit inrush current, usually with a thermistor. Otherwise they would blow their fuse at startup (if not fry the rectifier too.)

Second, AC/DC PSUs devices don't discharge their capacitors completely from cycle to cycle. Instead, there will be a ripple current at the top of each cycle that 'tops off' the capacitors just before the peak. This current isn't instantaneous either, but rides the slower (near-peak) dV/dt part of the AC cycle.

Your concern about the peak rectifier currents isn't misplaced though: they can be quite large for a big (~1kW) supply with large bulk capacitance. Which leads me to...

Third, in more recent times larger devices (greater than 60W) are required or are encouraged to have some sort of power factor correction on their inputs. This mitigates the effect of peak-by-peak charging input capacitors, and thus presents a cleaner, less spiky load to the grid.

Basically, the PFC circuit is a boost-type converter interposed between the rectifier and bulk capacitor, which supplies the cap charging current locally throughout the AC cycle rather than just at the AC peak. PFC white paper from MPS: https://media.monolithicpower.com/mps_cms_document/2/0/2020-power-factor-correction-_pfc__r1.0.pdf

That said, there is some argument to using a local DC grid (12V or 48V, say). This is an emerging trend in data centers, but applies to microgrids as well. It allows better integration of a UPS, avoiding the additional DC-to-AC conversions (and losses therein) of an AC-based system.

This isn't an issue with AC-DC power factor per se, it's just basic losses inherent in any conversion step. Fewer conversions = less loss.