# Estimate DC current from phase current in BLDC motor

I am using a BLDC motor with sinusoidal windings that I drive with FOC. The implementation uses a triple half-bridge and a DRV83 to drive the MOSFETs. I have 3 low-side amplifiers to measure the phase current Ia, Ib and Ic. The power is given by a DC power supply.

How can I estimate the instantaneous current Idc drawn from my power supply with my three phase currents Ia, Ib and Ic?

• I would expect it to be more promising to estimate $average I_{DC}$ from power than from phase current(s). $I_{DC}$ does not need to equal $\sum I_{phase}$ where the phase currents are controlled by, effectively, buck converters. Commented Oct 9, 2023 at 10:21
• @greybeard I understand this would help to get a more direct and accurate estimation but I don't have access to Idc on my system Commented Oct 23, 2023 at 12:43

Multiplying the phase currents by the cosine of the appropriate angles and summing them up with their respective weights (2/3) will give you an estimation of the DC current drawn from the power supply. Keep in mind that this formula assumes balanced three-phase currents. So, you get:

$$\text{I}_\text{dc}=\frac{2}{3}\cdot\left(\text{I}_\text{a}\cos\left(30^\circ\right)+\text{I}_\text{b}\cos\left(150^\circ\right)+\text{I}_\text{c}\cos\left(270^\circ\right)\right)\tag1$$

$$\text{I}_\text{dc}=\frac{\sqrt{3}}{3}\cdot\left(\text{I}_\text{a}-\text{I}_\text{b}\right)\tag2$$
Instantaneous $$\I_{DC}\$$ should be the sum of the phase currents