LAB WM428 - Power - Real And Apparent - Teledyne LeCroy

LeCroy Application Brief No. LAB_WM 428Power - Real And ApparentA Tutorial On Basic Line Power MeasurementsOscilloscopes measure currentand voltage and, through themagic of mathematics, calculatepower. Unfortunately, powercomes in a large number ofguises: instantaneous, real, apparent,and reactive. This plethoraof power terms often leads toconfusion. The Power MeasureAnalysis (PMA2) software packagesimplifies these measurementsand eliminates the necessityof setting up the proper mathoperations.Oscilloscopes, whether analog ordigital, are voltage respondinginstruments. Current is measuredusing a suitable transducer,usually a current probe or resistiveshunt. The oscilloscope displayis the instantaneous functionof voltage or current vs.time. The product of these quan-Figure 1 The elements of a power measurement (instantaneous voltage, current, and power)show on a WavePro 7300 using PMA2. Real and apparent power are automatically computed usingparameters.

LeCroy Application Brief No. LAB_WM 428tities is instantaneous power.A basic line power measurementis shown in Figure 1. The productof the instantaneous voltageand current is the instantaneouspower shown in the lower trace.Note that the power waveformconsists of a waveform at twicethe frequency of the current orvoltage, and a DC offset. ThisDC offset represents the averagepower being delivered to theload. The average or realpower, represented by the symbolP, is measured in units ofWatts. In Figure 1 the realpower is determined automaticallyby determining the mean oraverage value of the instantaneouspower waveform. Realpower is displayed as the parameterrpwr and has the value9.2 W in this example.The product of the effective(rms) current and effective (rms)voltage is called the apparentpower. Apparent power is representedby the symbol S and ismeasured in units of Volt-Amps(VA). In our example above theapparent power is:S =114.7 * 0.1501= 17.2 VAApparent power is automaticallycomputed and displayed as theparameter apwr. For resistiveloads, the apparent and averagepower are equal.phase angle between the currentand voltage waveforms. It ismore generally computed as theratio of real to apparent power.In our example the power factoris also computed automaticallyand displayed using the parameterpf(V,I). The value of thepower factor is 0.535.The reactive power, N, can bederived from the real and apparentpower, using the followingequation:N = (S 2 - P 2 ) 1/2The units of reactive power areVolt Amperes Reactive or VAR.Most users have an interest inreal power and power factor, soreactive power is not calculatedautomatically.The PMA2 software is useful inanalyzing line power. It simplifiesthe determination of realpower, apparent power, andpower factor by eliminating theneed to set up math traces andparameter math. It is even moreconvenient to use than dedicatedline power analyzers. The scopeis already on your bench and theanswers are only a button pushaway.The ratio of average to apparentpower is the power factor. In thesinusoidal case, the power factoris equal to the cosine of the