Once the test is finished, the Gen3i stores a big data file that can be easily split in N data files, where one file corresponds to one trigger, i.e. one operating point in the torque-speed plane. For each operating point, the Gen3i performs the following computations:
Input electrical power
where the vαβ and iαβ are the voltage and current (α,β) components in stationary reference frame, T is the electrical cycle (period) obtained from the electrical angle.
It must be mentioned here that no filters are applied to the acquired voltage and currents.
Copper (Joule) losses
The average stator resistance Rs,avg is calculated as
where Rs,base (Ω) is the stator resistance at base temperature (as example, θbase=20 °C) and is the average stator temperature computed as the mean value of the k measured stator temperatures.
The average resistance can be corrected to take into account the skin effects.
Mechanical shaft power
Where Tm is the measured torque and the ωm is the measured speed.
Iron and mechanical losses
where PMec are the mechanical losses that are speed dependent and that must be known in advance.
To avoid any influence of the torque ripple generated by both DM and MUT (with consequences on the speed), all the power values are saved as mean values calculated over a time interval containing a multiple number of mechanical revolutions.
Torque corresponding to the iron loss and to the total loss (iron + mechanical)
The torque calculated with (7) should be the difference between the estimated torque (by the motor controller) and the real shaft torque. The torque values calculated with (7) are provided by the Gen3i as average values over an integer number of mechanical revolutions.
MUT efficiency and inverter efficiency
The inverter efficiency can be obtained only if the DC link voltage and the DC link current are measured. In this case, the inverter efficiency will be
where is the input inverter power that must be averaged for eliminate any ripple in the DC link voltage and current.
Besides the efficiency and loss mapping, the Gen3i calculates and saves the following quantities that are extremely useful for the analysis of the MUT operation:
(A) (d,q) rotor frame flux linkages
The flux linkages are computed first in stationary (a,b) frame as time integral of the back-emf voltages:
An offset correction is necessary for each electrical period (cycle) to avoid the drifting of the computed flux linkage components. Once the (a,b) components are calculated, the (d,q) components are easily obtained with the rotational transformations; the magnitude of the flux linkage is also calculated.
where is the electrical position that is calculated from the measured mechanical position, the pole-pairs number and an offset that must be known.
Since the stator flux linkage components are calculated using the real motor voltage and a very good stator resistance, it is assumed that the precision of this computation is very good. In this case, the trajectory of the stator flux vector in the (d,q) plane can be obtained with very good precision and can be compared with the results coming from the magnetic model.
(B) (d,q) stator currents and voltages
The (d,q) rotor frame voltage and current components are calculated from the (α,β) components using the direct rotational transformation (8) that is used also for the fluxes. Since the (d,q) voltage components are affected by the PWM ripple, their mean values are extracted for each electrical cycle and also for an integer number of mechanical revolutions.
The trajectories of the stator current vector in the (d,q) plane are useful to check the MTPA trajectory below the base speed.
(C) Estimation of the electromagnetic torque
The electromagnetic (or air-gap) torque can be computed by the Gen3i as
This electromagnetic torque is computed with flux components that have been evaluated by sampling the real motor PWM voltages and with a stator resistance that takes into account the measured average stator temperature. Therefore, this torque can be defined as the best torque estimate.
The Gen3i saves the electromagnetic torque as a mean value calculated over an integer number of mechanical revolutions.