This is the seventh in a series of blog posts by Harry Vig, Principal Applications Engineer at Vicor. To go to *Output Line Ripple on Power Factor Corrected AC-DC Power Supply Outputs (Part 1)* click here.

**Bulk Capacitor Ripple with Missing Phases**

Perhaps seasoned three phase power engineers know this, but this was another “wow moment” for me about three phase systems. If you followed the ripple currents for single phase vs. three phase inputs, you would come to the conclusion that you can use bulk capacitors with lower ripple current ratings with a three phase input for the same amount of power.

If all three phases stay up, this is true. What if you lose one phase of your three phases?

If your load is over 2/3 power, you may have an overload on your power supply, and you may need to shut down due to overcurrent or overtemperature conditions.

But, if your load is lower, or your power supply is sized and cooled sufficiently well, you may be able to run indefinitely until the missing phase is restored, just like a redundant power supply input, but without the problems associated with safety and lockout of two independent power sources.

The question is how much ripple rating your bulk capacitors need. If you intend to allow long term operation of the power supply with a missing phase, you need to make sure the ripple current rating of the bulk capacitors is not exceeded in that state.

Removing a phase from the above simulation is easy. Change the amplitude term to 0. The two other phases need to make up the missing DC current, so multiply their amplitude by 1.5, assuming they each pick up the slack evenly:

The result can be seen in the graph below. B1 is turned off, and the ripple voltage on the bus is 4.8Vpp or 3.4Vrms, and the ripple current in the bulk capacitor ripple current is 7.2Arms. How can this be? This is almost the same ripple voltage as a single phase supply with one third the output power.

The current through the bulk capacitor has 0A DC, by definition, but the 300Hz ripple looks like… no it can’t be. It looks like it’s replacing the third missing phase. Instead of plotting –I(C2), let’s shift the waveform up by 1.5*6.9A, so that it has the same DC level as the PFM output sources:

The darker grey current has taken the place of the missing B1 phase. This isn’t an accident of course. It occurs because the impedance of the bulk cap is much lower than the load at 100Hz, or depending on the load type, it could have an even higher impedance than the resistive load.

The mystery is easy to solve if you refer back to the phasor diagram. The current of the two operating PFM output stages, B2 and B3, increased 50% in amplitude. The result will be a phasor with the same (1.5x original) amplitude along the third side of the triangle. Of course there is an offset because the DC current in the output capacitor must be zero, but it shows why it appears that the capacitor is replacing the third phase. It is because the vector sum of the two operating currents is along the axis of the source that was turned off, and of the same amplitude as the existing vectors because of the 120 degree angles forming an isosceles triangle.

The rms current of each PFM output is the average current divided by sqrt(2). That makes the vector amplitude 6.9 * 1.5 / sqrt(2) = 7.3A. The difference between this value as the 7.2A calculated by the simulator is due to the small amount of ripple current that goes through the resistive load.

Read part eight of this series: What About the Loss of Two Phases?.