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.
Best Answer
If you have your \$i_d\$ and \$i_q\$ currents, you can perform the inverse Parks-transformation (thus you obtain the \$i_\alpha\$ and \$i_\beta\$ currents) and subsequently the inverse Clarke-transformation. Then you have the three sinusoidal currents \$i_a\$, \$i_b\$, and \$i_c\$, which have the same amplitude and a phase difference of 120° to each other.
The RMS value of a sinusoidal signal is easy to derive, and it is given by \$\frac{A}{\sqrt{2}}\$, where \$A\$ is the amplitude of the signal.