### Introduction

In this example, we will show how the Teledyne LeCroy MDA captures three-phase drive output voltage and current signals, as well as motor shaft torque and speed signals, and uses them to calculate three-phase electrical and mechanical power during dynamic operating conditions. We will also make additional math calculations to determine total losses, and subsequently derive copper and core losses. Then we compare these measured losses to the engineering models used in the control feedback circuit. We use the rapid acceleration test condition to validate the test method because it represents the worst-case test condition.

### Voltage and Current Acquisitions

Figure 1 displays a short (500-ms) acquisition, described as follows:

- 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 observed torque estimate as calculated by the drive control system (C8, orange)
- Analog signal representing the estimated motor copper and core losses calculated by the drive control system (Z7, red)

For this acquisition (shown in Figure 1), the MDA is sampling at 1 MS/s using 500 kpts of acquisition memory. The first ~50% of the acquisition displays the voltage applied to the motor windings to align the motor for the beginning of the test. Then, applied PWM drive output signals spin the motor from 0 to 3000 rpm in 150 ms. The torque waveforms (C5 and C7) show that the motor reached a mechanical resonance condition during this rapid motor acceleration—not desirable, but a real phenomenon nonetheless. The test engineer felt that if the calculation approach worked under a worst-case resonance condition, it could be made to work in any normal operating condition.

The various acquired voltage, current, speed, and torque signals comprise the source waveforms for calculating various per-cycle three-phase electrical power, speed, and torque values. The mean values of each of the cyclic values are reported in the Numerics table. From the per-cycle values, the MDA calculates and displays Waveforms. These Waveforms are displayed on the right side of Figure 2 (for the motor-startup period only), while the originally acquired waveforms (from Figure 1) appear on the left side of Figure 2.

The per-cycle Waveforms and Math functions in Figure 2 are described below:

- Drive Output Power in Watts (blue trace, P(ΣRST), top right)
- Mechanical Shaft Power in Watts (pink trace, P(Mechanical), also top right).
- Calculated difference between Drive Output Power and Mechanical Shaft Power in Watts (yellow trace, F1, second grid from top right)
- Torque in N∙m (orange trace, Torque(Mechanical), third grid from top right), calculated from C8 (the observed torque estimate from the drive control system)
- Speed in RPM (light green trace, Speed(Mechanical), third grid from top right) calculated from C6 (the analog tachometer signal)
- Drive control system estimated copper and core losses rescaled to Watts (red trace, F6, bottom right) by applying a factor of 25 and changing units to W(atts).

The power calculations (three-phase electrical and mechanical) were made using the MDA’s Sync signal capabilities on a per-cycle basis during the machine torque resonance period only. This is shown at the bottom of Figure 2, and again (larger) in Figure 3.

We used the control system observed torque estimate (C8) from the drive control system to calculate per-cycle Torque values over time. Doing so resulted in a more accurate calculation of mechanical power (torque * speed) due to the better transient response of the observed torque estimate compared to that of the torque transducer, which is unable to measure the inertial torque that is significant during acceleration operation, and which resulted in overestimation of the losses. In this case, the test engineer compared torque calculations in the MDA using both signals to come to this conclusion.

After making the three-phase electrical and mechanical power calculations, we performed the loss calculations over the period of time defined by the motor startup and torque resonance condition. These are displayed in Figure 4, with descriptions of the waveforms below:

- Drive control system estimated energy (dark blue trace, F7, top right grid). This is an integral calculation of the F6 waveform (described below).
- Note: Both the measured (F12) and estimated (F7) energy loss have the same slope, indicating correct estimation of the motor transient power loss. The measured energy loss has a 5.5527 Joule offset, which is the energy lost during motor aligning process. We subtracted this value from the F12 waveform using a rescale function.

- Drive control system estimated copper and core losses rescaled to Watts (red trace, F6, second grid from the top right)
- Calculated difference between measured Drive Output Power and measured Mechanical Shaft Power in Watts (yellow trace, F1, second grid from top right)
- Copper (Cu, or load) losses, calculated from 3*I
_{RMS}(RST)²*R_{STATOR} (with R_{STATOR} = 0.75Ω, and I_{RMS}(RST) being the average of the three phase currents). This is the light blue trace, F3, bottom grid on the right. The per-cycle I_{RMS}(RST) trace is not shown, but is used in the calculation. - Iron (Fe, or no-load) Losses, calculated from Total Loss – Copper Loss (orange trace, F9)

We observed the following from the calculations and waveforms shown in Figure 4:

- The estimated dynamic (transient) power losses as calculated by the control system match the measured dynamic (transient) power losses during the rapid acceleration condition.
- Copper losses, which are a larger part of the total losses during motor startup, decrease after delivery of the initial startup current.
- Iron losses increase rapidly as the motor reaches steady-state speed, then decrease rapidly after delivery of the initial startup current. This is as expected because the controller uses lower flux linkage during high-speed, low-torque operation.

Note that this was a relatively small servomotor; we ignored the mechanical friction losses for the purposes of these calculations.

### Conclusion

The Teledyne LeCroy Motor Drive Analyzer is uniquely capable of measuring dynamic power events and correlating those events to control system activities. The calculation of per-cycle power values, and their display as a Waveform time-correlated to the original acquired drive system signals, makes it easy to correlate and compare various control and power system activities and gain insight into drive operation and control system models.