I'm looking to determine the electrical power input to a 3-phase BLDC motor, driven by TI's DRV8305 motor controller. I can't use the DC power flowing into the system because I'm trying to capture the efficiency loss of the uC, gate driver, and switching MOSFETS. There are sensors on the phase voltage and phase current. For the controller, it uses a power VARIANT Clarke transform, as shown here, for BOTH the voltage and current:
Then it uses a standard Park transform to get to the DQ0 reference frame:
From my understanding, Theta is chosen such that my current and voltage will align with my D axis only, and presto, I have a DC Current and DC Voltage. However, because my Clarke Transform was power variant, I must scale my P=I*V by some factor in order to get the correct answer?
From my understanding, a solution would look like:
$$P_{ABC} = I_{DQO-INVAR}(t)*V_{DQO-INVAR}(t)$$ $$P_{ABC} = P_{\theta}I_{\alpha\beta\gamma-INVAR}(t)*P_{\theta}V_{\alpha\beta\gamma-INVAR}(t)$$ $$P_{ABC} = P_{\theta}T_{INVAR}I_{ABC}(t)*P_{\theta}T_{INVAR}V_{ABC}(t)$$ $$P_{ABC} = P_{\theta}*sqrt(3/2)*T_{VAR}I_{ABC}(t)*P_{\theta}*sqrt(3/2)*T_{VAR}V_{ABC}(t)$$ $$P_{ABC} = 3/2*P_{\theta}T_{VAR}I_{ABC}(t)*P_{\theta}*T_{VAR}V_{ABC}(t)$$
Where \$P_{\theta}\$ is the Park Matrix, \$T_{INVAR}\$ is the power invariant Clarke Matrix, and \$T_{VAR}\$ is the power variant Clarke Matrix.
This would lead me to believe that I need to scale my power variant DQ0 output by 3/2 in order to get the actual power draw? Please confirm or deny.
I've looked for a solution, but it does not seem to be a common question. I'm forced to use the power variant Clarke transformation because TI's Instaspin Library is built on it. I'm rather unfamiliar with three-phase power. If there's any other information relevant to the problem, I'll be able to provide it. A good reference would be much appreciated.