Boost Inductor Design for three phase Diode Bridge Rectifier for PFC operation

Question

I am doing a simple DCM based control for power factor correction. Please see the topology below . Specifications are as below: 1.) Power 5KW 2.) Input Voltage is 415V L-L Nominal 3.) Inductor calculates 600uH 4.) Switching frequency of boost IGBT is 5KHZ Now I want to design Lia Lib and Lic one a single toroidal core. I have only designed DC inductors with EE cores before but since this will also carry 50Hz current I am slightly confused. Also since it is operating in DCM , ie the three phase currents are triangular in shape with peak reaching as high as 35Amps, the area product I am getting is quite high. If someone can guide me through the process with some application note or any reference material, I would be grateful.

Answer 1

The easiest way to approach inductor design with powdered core types, is probably to assume a design for a given part, then repeat across all parts in the product, and select the best one. This can be done incrementally, pulling core parameters from a catalog (the calculations match better, the closer you get to the ideal part), or all at once in a spreadsheet.

Basic calculations can be found here: Inductor Design with Magnetics Powder Cores | Magnetics Inc.

600µH at 35A peak is 367.5mJ, corresponding to around the 0058737A2 or similar. (I'm guessing High Flux will be more efficient/economical here, but the process is the same for other materials in any case.)

Note that lower µ is preferred, because of the high energy storage, and bias (mains AC current simply looks like DC bias here); core losses will also be lower. 40-60 \$\mu_r\$ is probably best here.

$$N = \sqrt{\frac{L}{A_L}}$$

Get the turns count. \$A_L\$ is 0.204 µH/t² so N = 54; maybe raise target inductance by 10% to allow for partial saturation, say N = 57.

80% inductance saturation point is around 1400 At for this core, or 24.6A peak. This is still pretty low for the application, and we should choose something the next few sizes up. (Depending on if the control loop is fine with inductance varying over some range, or the resulting input THD is acceptable.)

Going ahead with the same core, a 40% winding factor is 620 mm², so will fit 57t of 10.9 mm² wire, more than enough to handle 15A.

Finally, calculate core losses. This is where things get crunchy. Even at the low frequency, because the change in flux density is so high (it's in DCM), core losses dominate. I calculate about 13W core loss, plus 3.2W copper loss. Changing to MPP 60µ does reduce the core loss to 5.4W, which may be worthwhile.

The copper calculation assumes fine enough litz stranding for the frequency; probably something like 0.3mm strand dia. would suffice, 120 strand count, preferably built as a 3 x 40 'rope'.

Mind that core losses are calculated assuming sine wave excitation; harmonics generally drop off quickly so this is an acceptable assumption, but given the high content (switching harmonics) in DCM, the lower-loss material may be preferable, or a larger core (the next size up from Mag-Inc is probably the 4" part), as well as the choice of litz over solid or few-strand construction.

One would also want to check the cost and size comparison (and any other relevant parameters) between a large ferrite core (E or U shape, probably), and MPP or other materials, since MPP tends to be expensive. Core losses will almost certainly be lower; flux density in the powder core isn't terrifically high anyway (0.6T peak), so the overall size of a ferrite core (B_sat ~ 0.4T) won't be tremendously larger.

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Note the output filter capacitor must also be massive, since it's taking "100%" ripple at full load. A series-parallel combination of high performance electrolytics might be usable, but probably it should be film capacitors, at least in a sizable fraction (>10% of total value as film?). Exact calculations depend on component ratings and other circuit details.

As mentioned in comments, the inductors must be independent; simply use three cores, wound as single inductors each. This also simplifies design, no multiwinding construction needed.

Regarding distortion: saturation is quite gradual for powder cores, which will give dominant low-order odd harmonic distortion. And "low-order" and "odd" means mostly 3rd, 5th, 7th, etc. harmonics. 3rd is canceled out by symmetry: it resolves to a common-mode shift in voltage between mains and circuit neutral at 150Hz. The diagram doesn't indicate any reference to neutral or ground, so this may be irrelevant. This leaves 5th, 7th and so on (but not 9th, 15th, etc.) as current distortion; but being higher order, they will have less impact on the total (i.e. THD). So a modest change in inductance may be tolerable; perhaps a 30% swing results in only 5% THD, or even less. I don't know how much, and would need to model it to see.