Introduction

Power analyzers have been manufactured for many years and are used in a wide variety of applications. Often, many settings and preferences can have significant impact on the measurements. Or, there are “legacy” capabilities that may not be well-understood. This technical brief explains the settings in the Teledyne LeCroy Motor Drive Analyzer (MDA) to achieve results consistent with a Yokogawa Power Analyzer, and to explain why the results will be different in some cases.

Measurement Period (“Sync”) Calculation

First, for proper power analysis, one must determine a measurement period within which all calculations take place. Both the Teledyne LeCroy MDA and a Yokogawa Power Analyzer use a “Sync” signal to determine the measurement period. In both cases, the Sync signal can be low-pass filtered to reduce the chances of finding an incorrect measurement period. See the images below:

For a nearly sinusoidal (e.g. low distortion) signal, both instruments should find the same measurement period with the same LPF cutoff selections, though the Teledyne LeCroy MDA offers a wider variety of selections.

The Teledyne LeCroy Motor Drive Analyzer also permits adjustment of hysteresis (band), allowing user-defined control of the software’s ignoring of non-monotonicities that interfere with the measurement period calculation. This is explained in detail in the MDA’s software instruction manual. Such control can be very useful for signals that have higher distortion (e.g. brushless DC six-step commutated signals) or signals that have high distortion during high stress or failure events.

Note that the Teledyne LeCroy Motor Drive Analyzer also permits display of the filtered Sync signal with a measurement period overlay, rendering the Sync signal settings easily understandable. See the screen image below (the Sync signal with the overlays appears at bottom).

Lastly, the Teledyne LeCroy Motor Drive Analyzer applies the Sync filter and hysteresis settings as a post-acquisition software process, while most power analyzers apply Sync filtering and hysteresis settings to the waveform during the acquisition. Thus, in the Teledyne LeCroy MDA, it is possible to make changes post-acquisition whereas this is not usually possible with a power analyzer instrument. Combined with the Sync period overlay, one may use the MDA’s post-acquisition processing to fine tune the filter and hysteresis settings for optimum results without having to take a new acquisition and lose the acquired data.

Apparent Power Formula

In Yokogawa’s Power Analyzer instrument, users may measure apparent power (S) through selection of any of the following formulas in their setup menu:

1. $$Vrms * Irms$$    Same as provided by Teledyne LeCroy, as described in this document
2. $$Vmean * Imean$$    Product of rectified mean values calibrated to the RMS values
3. $$Vdc * Idc$$     Product of simple averages of the voltage and current
4. $$Vmean * Irms$$    Product of the voltage’s rectified mean value and the current’s true RMS value
5. $$Vrmean * Irmean$$    Product of the voltage’s and current’s rectified mean values

Teledyne LeCroy only provides capability for $$Vrms*Irms$$ calculation of apparent power. To correlate power values from the Yokogawa power analyzer to the Teledyne LeCroy MDA’s results, set the selection for apparent power calculation on the Power Analyzer to $$Vrms*Irms$$.

Three-Phase (Total) Power Calculations

Teledyne LeCroy employs one method for calculation of power values whereas Yokogawa provides three different methods that return different results. The following is a simplified summary of the Teledyne LeCroy method and the Yokogawa methods for calculating power for a single power cycle – see the respective instruction manuals for complete formulaic descriptions. Note that the table below assumes use of the $$Vrms*Irms$$ formula in the Yokogawa Power Analyzer for Apparent Power calculations.

Teledyne LeCroy Yokogawa Type 1 Yokogawa Type 2 Yokogawa Type 3
Real Power “P” (in W) $$V*I$$ (instantaneous sample points)
Apparent Power “S” (in VA) $$Vrms*Irms$$ $$Vrms*Irms$$ $$Vrms*Irms$$ $$√(Q^2- P^2 )$$
Reactive Power “Q” (in VAr) $$√(S^2- P^2 )$$ $$Vrms*Irms*sin⁡φ$$ $$√(S^2- P^2 )$$ $$Vrms*Irms*sin⁡φ$$
Power Factor (λ) $$P⁄|S|$$ $$P⁄|S|$$ $$P⁄|S|$$ $$P⁄|S|$$
Phase Angle (φ) $$cos^(-1)⁡λ$$ $$cos^(-1)⁡λ$$ $$cos^(-1)⁡λ$$ $$cos^(-1)⁡λ$$

For perfectly sinusoidal (zero-distortion) waveforms, it is possible to measure the phase angle φ between the voltage and current sinusoids. However, it is not possible to measure the phase angle φ when the waveforms are distorted (e.g. PWM drive output waveform). Therefore, the Teledyne LeCroy method or Yokogawa’s Type 2 method are the only methods that demonstrably produce accurate results for reactive power (and therefore power factor and phase angle) with distorted waveforms (both also produce accurate results with sinusoidal waveforms).

Yokogawa’s Power Analyzers offer the Type 3 method on models with the harmonic measurement-mode option. This option appears to enable definition of a fundamental signal from one of the PWM signals using a PLL source. Then, the instrument determines phase angle by comparing the fundamental voltage and fundamental current waveforms, with power determined for the fundamental and each harmonic through “N” harmonics. This should provide a similar result to values provided by the Teledyne LeCroy Harmonic Filter setting = “Fundamental” or “Fundamental + N” (see below), provided that the hardware PLL response in the Yokogawa power analyzer can accommodate any change in period of the measured signal during the acquisition window.

Note that the Yokogawa power analyzer always calculates real power P correctly in all cases. If this is the only power value of interest, then all methods are suitable. However, to correctly calculate S, Q,λ, or φ, one must choose the correct Yokogawa power analyzer measurement method (if more than one is offered).

Per-Phase Power Calculations

The Yokogawa instrument calculates per-phase power using the same equations as total three-phase power, but on one phase at a time.

The Yokogawa Type 2 method with apparent power setting = $$Vrms*Irms$$ always correlates (assuming there is no problem with the Yokogawa power analyzer obtaining a proper Sync period) with Teledyne LeCroy’s MDA when using three-phase, four-wire (three voltages, three currents) wiring configurations with line-neutral or line-reference voltage probing.

However, if using line-line voltage probing, then per-phase power calculations in the Yokogawa power analyzer will be unbalanced and incorrect, even though the three-phase total will be correct. The reasons for the differences are as follows:

1. The Yokogawa three-phase, three-wire (three voltages, three currents) wiring configuration is natively defined as a two-wattmeter setup. This is beneficial in that switching from a three-voltage and three-current measurement to a two-voltage and two-current measurement requires no re-connection of wires to the power analyzer. However, it also means that the line-line voltages and currents are incorrectly associated with each other on a per-phase basis. See Figure 1 (Yokogawa) below and compare to Figure 2 (Teledyne LeCroy).
2. The Teledyne LeCroy three-phase, three-wire (three voltages, three currents) wiring configuration also uses a two-wattmeter method for total three-phase power calculations, but maintains the correct per-phase vector relationships to obtain proper per-phase calculations. Teledyne LeCroy simply inverts one of the voltage waveforms for the total three-phase power calculation.
3. The voltage associations made by Yokogawa have no impact on the total three-phase power (real, apparent, or reactive), phase angle, or power factor because the vector (voltage and current) relationships defined in their wiring setup are the correct relationships for the two-wattmeter method used to calculate their total three-phase power.
4. Both instruments can perform a line-line to line-neutral conversion (referred to as a delta-star conversion by Yokogawa, which is an extra-cost option). However, while Teledyne LeCroy’s MDA will return accurate per-phase power calculations for P, S, Q,λ, and φ with this type of conversion, the Yokogawa power analyzer instrument will only return power calculations for P.

The practical impact of the Yokogawa wiring configuration is that the voltage and current pairs all have different phase relationships (which is what leads to the incorrect per-phase power calculations). This is shown below on actual three-phase acquisitions:

 Yokogawa Teledyne LeCroy 3-phase voltage and current pairs, separated by pair 3-phase voltage and current pairs, overlaid

Calculated results appear as follows with and without a line-line to line-neutral (delta-star) conversion.

 Yokogawa Without Line-Line to Line-Neutral conversion (Delta-Star) With Line-Line to Line-Neutral conversion (Delta-Star)

 Teledyne LeCroy Without Line-Line to Line-Neutral conversion With Line-Line to Line-Neutral conversion