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 wellunderstood. 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 lowpass 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 userdefined control of the software’s ignoring of nonmonotonicities 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 sixstep 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 postacquisition 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 postacquisition whereas this is not usually possible with a power analyzer instrument. Combined with the Sync period overlay, one may use the MDA’s postacquisition 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:

\(Vrms * Irms\) Same as provided by Teledyne LeCroy, as described in this document

\(Vmean * Imean\) Product of rectified mean values calibrated to the RMS values

\(Vdc * Idc\) Product of simple averages of the voltage and current

\(Vmean * Irms\) Product of the voltage’s rectified mean value and the current’s true RMS value

\(Vrmean * Irmean\) 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 \(Vrms*Irms\).
ThreePhase (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) 
\(√(S^2 P^2 )\) 
\(Vrms*Irms*sinφ\) 
\(√(S^2 P^2 )\) 
\(Vrms*Irms*sinφ\) 
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 (zerodistortion) 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 measurementmode 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).
PerPhase Power Calculations
The Yokogawa instrument calculates perphase power using the same equations as total threephase 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 threephase, fourwire (three voltages, three currents) wiring configurations with lineneutral or linereference voltage probing.
However, if using lineline voltage probing, then perphase power calculations in the Yokogawa power analyzer will be unbalanced and incorrect, even though the threephase total will be correct. The reasons for the differences are as follows:

The Yokogawa threephase, threewire (three voltages, three currents) wiring configuration is natively defined as a twowattmeter setup. This is beneficial in that switching from a threevoltage and threecurrent measurement to a twovoltage and twocurrent measurement requires no reconnection of wires to the power analyzer. However, it also means that the lineline voltages and currents are incorrectly associated with each other on a perphase basis. See Figure 1 (Yokogawa) below and compare to Figure 2 (Teledyne LeCroy).

The Teledyne LeCroy threephase, threewire (three voltages, three currents) wiring configuration also uses a twowattmeter method for total threephase power calculations, but maintains the correct perphase vector relationships to obtain proper perphase calculations. Teledyne LeCroy simply inverts one of the voltage waveforms for the total threephase power calculation.

The voltage associations made by Yokogawa have no impact on the total threephase 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 twowattmeter method used to calculate their total threephase power.

Both instruments can perform a lineline to lineneutral conversion (referred to as a deltastar conversion by Yokogawa, which is an extracost option). However, while Teledyne LeCroy’s MDA will return accurate perphase 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 perphase power calculations). This is shown below on actual threephase acquisitions:

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


3phase voltage and current pairs, overlaid 


Calculated results appear as follows with and without a lineline to lineneutral (deltastar) conversion.

Yokogawa 
Without LineLine to LineNeutral conversion (DeltaStar) 

With LineLine to LineNeutral conversion (DeltaStar) 


Teledyne LeCroy 
Without LineLine to LineNeutral conversion 

With LineLine to LineNeutral conversion 

SteadyState vs. Dynamic Events
The Yokogawa power analyzer calculates a mean value over a normally short acquisition time (several cycles). An option exists for increasing the update rate for the meanvalue calculations, but it is still a meanvalue calculation over a defined period of time or number of cycles. The Sync period is determined through a PLL circuit programmed into an FPGA, which has a limited ability to lock onto widely varying speeds, dependent on the PLL loop bandwidth. In general, there is no practical limitation on a steadystate signal with a slowly changing measurement Sync period. Thus, a Yokogawa power analyzer is very good for measuring mean values of power in steady state (constant load, torque, speed, etc.) operating conditions.
The Teledyne LeCroy MDA can acquire short records and calculate mean power values for display in a table. As described earlier, the Sync period is determined using a software algorithm. However, it can also make accurate measurements under dynamic operating conditions or loads because it lacks the operating limitations of a power analyzer instrument.
If the load is dynamic, it is quite possible that a power analyzer instrument cannot provide a meaningful result. First, ensure correlation on a simple, static, steadystate load condition, and then attempt correlation with something more dynamic. If one cannot correlate results during dynamic operation, it is likely because the power analyzer instrument cannot accurately determine or verify Sync period, which is not typically a limitation of the Teledyne LeCroy MDA.
Summary
It is easy to correlate a Yokogawa power analyzer instrument to a Teledyne LeCroy MDA. The Teledyne LeCroy MDA does provide more visual feedback on its operation, especially in accurate calculation of the Sync measurement period, which is vital to accurate power measurements. In some cases, a Yokogawa power analyzer instrument has different settings or makes different wiring assumptions that lead to different results, which can be easily understood once they are known.