Now, I know d and q axis current can be calculated by phase current ia, ib, ic in a PMSM, via clarke transform and park transform.

ialpha = sqrt(2/3) * (ia - ib / 2 - ic / 2)

ibeta = sqrt(1/2) * (ib - ic)

id = ialpha * cos(theta) + ibeta * sin(theta)

iq = ibeta * cos(theta) - ialpha * sin(theta)

Now, if motor running at a steady state, id and iq should be in DC form.

But how to calculate RMS of phase current ia,ib,ic by id,iq.

I think RMS(ia) = RMS(ib) = RMS(ic) = K * sqrt(id^2 + iq^2)

What is the value of K.

  • \$\begingroup\$ You already have to measure them: ia, ib, ic prior to transform in d,q-coordinate system. ia, ib, ic are peak values - so a RMS value is Ia_rms = ia/sqrt(2) -> K=1/sqrt(2); \$\endgroup\$ – Marko Buršič Mar 3 at 9:56
  • \$\begingroup\$ If a motor is labeled : rated current 1A, peak current 3A. So, I should limit the value sqrt(id^2 + iq^2) <= 3 * sqrt(2) = 4.24A ? \$\endgroup\$ – Hyz Yuzhou Mar 3 at 11:58

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