### Introduction

In a previous example (Dynamic Rapid Motor Acceleration Loss Measurements), we showed how to use the Teledyne LeCroy MDA to calculate dynamic copper and core losses during motor acceleration. This application note will extend these calculations to static and dynamic energy consumed in Joules and present results for different types of motors and control systems to understand the optimal motor and drive for a given application.

### Voltage and Current Acquisitions

Figure 1 displays a long (10-s) capture of signals for a surface-mounted permanent magnet (SPM) motor that is controlled through a loss minimization (LM), deadbeat-direct torque and flux control (DB-DTFC) algorithm. The motor is rapidly accelerated to 3000 rpm and run at constant speed for 6 seconds, after which it is shut down. We made the acquisition at a 2.5-MS/s sample rate using 25 Mpts of acquisition memory.

The displayed waveforms are described below:

- Two line-line voltage signals (V
_{RT} = C1, yellow, and V_{ST} = C2, magenta) - Two line-current signals (I
_{R} = C3, light blue, and I_{S} = C4, green) - Analog torque sensor output signal (C5, light tan)
- Analog tachometer speed sensor signal (C6, purple)
- Analog signal representing the estimated motor copper and core losses as calculated by the drive control system (C7, red)
- Analog signal representing the observed torque estimate as calculated by the drive control system (C8, orange)

We used the various voltage, current, speed, and torque signals to calculate various per-cycle three-phase electrical power, speed, and torque values, and the Numerics table reports the mean values of each of the cyclic values. From the per-cycle values, Waveforms are displayed. Figure 2 displays the acquired waveforms on the left side of the display as described previously. The waveforms on the right side of the display are zooms of those on the left to accentuate the rapid acceleration time of the motor. Additionally, the display shows the Drive Output Sync signal (third grid from the top) with transparent overlays. This is shown for easy identification of the periods over which we make the power calculations shown in the Numerics table (bottom). In this case, the MDA is being operated in Zoom+Gate mode, so the Numerics table includes data only for those power periods shown by the Drive Output Sync signal.

Figure 3 displays the zoom waveforms shown in Figure 2 with additional calculated per-cycle Waveforms (shown on the right).

- Drive Output Power in Watts (orange trace, P(ΣRST), top right) and Mechanical Shaft Power in Watts (blue trace, P(Mechanical), also top right).
- The integral of P(ΣRST) (yellow trace, F1, bottom right) and the integral of P(Mechanical) (pink trace, F2, bottom right).
- The difference of the two integrals (green trace, F8, bottom right).

In Figure 3 we placed cursors at the beginning and end of the Integral waveforms and we read the energy change in Joules (shown as N-m, and these are equivalent scientific units) from the Δy value in the F1, F2 and F8 descriptor boxes, as follows:

- F1 = 77.93 N-m (Joules)
- F2 = 67.61 N-m (Joules)
- F8 = 10.32 N-m (Joules)

We applied a similar Zoom+Gate to the ~6-second constant speed operation displayed in Figure 4. Again, we read energy loss from the integral and difference waveforms and cursors.

After proving the measurement methodology, we repeated the same experiments for a variety of different control schemes—Vector field-oriented control, or FOC; flux-intensifying, or FI control schemes; and interior permanent magnet (IPM) and surface permanent magnet (SPM) motor types. The total static and dynamic losses are compared in Figure 5.

### Conclusion

The Teledyne LeCroy MDA provides unique capabilities to measure dynamic and static power events, including the separation of these events into separate calculations from one acquisition. The ability to calculate a per-cycle power value and display it as a Waveform, and then post-process those Waveforms with the MDA’s other math toolsets provides unparalleled abilities to deeply understand system performance and the impact of control system choices.