Active power measurement in nonsinusoidal environments

1142 IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 15, NO. 3, AUGUST 2000

Active Power Measurement inNonsinusoidal Environments

Larry G. Durante, Member, IEEE,and Prasanta K. Ghosh, Senior Member, IEEE

Abstract—A comparative study of the measurement capabilitiesof solid state watthour meters and other commercially availablemeasurement instruments was performed. This study included theuse of both theoretically developed harmonically distorted test sig-nals and “real world” waveforms. Results indicate a general agree-ment between observed measured data and calculated values ex-cept when the test signals contained a high current crest factor.

I. INTRODUCTION

W ITH the present day proliferation of nonlinear loads onthe power grid the effects on, and measurement of, the

associated energy is an issue gaining substantial concern andawareness. The number of components, capable of producingconsiderable harmonic distortion, introduced to the power gridis increasing rapidly. The increased use of static power con-verters, adjustable speed drives, electronic instrumentation, per-sonal computers and other nonlinear loads will very likely con-tinue to worsen waveform distortion on the power system. Thesefacts have triggered a growing interest worldwide in the devel-opment of method(s) which enable accurate harmonic assess-ment for both the individual components and the power deliverysystem. This paper contributes to research published to date ad-dressing the issue of the accurate measurement of the total activepower associated with nonsinusoidal current and voltage wave-forms. The term total active power is used by the authors to referto the active power ( ) as defined by the IEEE Standard Dictio-nary [1] which contains, in addition to the fundamental activepower component, harmonic active power components as a re-sult of distorted current and voltage waveforms.

The effects of nonsinusoidal waveforms on the delivery andconsumption of electrical energy have been clearly indicatedby many researchers [2], [3] however, as far as we know, theengineering community has not yet reached a consensus for auniversally accepted definition for the powers in electrical net-works with nonsinusoidal waveforms. The IEEE working groupon nonsinusoidal situations has suggested some basic resolu-tions addressing these issues [3].

The following primary questions and concerns were the cata-lyst of this power quality project: First, are there currently com-mercially available measurement devices with the capability toaccurately measure, or its associated watthours, in nonsinu-soidal situations? Second, if available, what are the measure-ment response limitations of these devices? That is, how dis-

Manuscript received December 27, 1996.L. G. Durante is with Meter and Test Laboratories, Niagara Mohawk Power

Corporation, Syracuse, NY 13202.P. K. Ghosh is with the Department of Electrical & Computer Engineering,

Syracuse University, Syracuse, NY 13244.Publisher Item Identifier S 0885-8950(00)08282-1.

torted can the electrical signal become and still be measuredaccurately? Finally, how can the general response of these mea-surement devices be tested?

Efforts to address these questions lead to this experimentaltesting of the registration capabilities of several measurementdevices concerning the value ofand its associated watthours.The devices under test (DUT’s) included a wideband power an-alyzer, an industry standard watthour reference instrument, andfour (4) Form 9S solid state watthour meters.

After reviewing available literature [4]–[6] we selected thephantom loading concept for our experiments. However, webelieve that the test currents and voltages should consist of bothfield captured waveforms and mathematically designed testsignals. We feel that the results from the exclusive use of fieldcaptured waveforms provides only a specific portion of theDUT performance information. It is hoped that this experimen-tation with both “real world” waveforms and mathematicallydesigned test signals is the catalyst of, and contributes to, thedevelopment of generalized testing procedures, incorporating aset of standard test signals, capable of probing and predictingthe general performance of instruments expected to measurethe or watthours of “real world” waveforms in nonsinu-soidal situations.

To date, no National Institute of Standards and Technologytraceable or otherwise traceable benchmark instrument existswhich can be referenced for measuring correctly total activepower or its accumulated watthours in nonsinusoidal situations.Many scientists including those of the National ResearchCouncil of Canada are presently researching benchmarkingand traceability standards [6], [7]. However, with no referenceavailable at present, it seems logical to present the experi-mental results as observations and facts rather than in percenterror. In the results section we will present measurementsof accumulated total active power or watthours by differentinstruments. The independent measurements have different anddistinct energy sensing and resolution methods. The authorsbelieve that a certain degree of engineering confidence inthe measurement results can be achieved by comparing theconsistency and correspondence of measurements between theindependent devices.

II. EXPERIMENTAL DESCRIPTION

A. Experimental System

The block diagram of the experimental system used tosynthesize the test signals and make the total active power andwatthour measurements is shown in Fig. 1. The system’s maincomponents and operational characteristics are conceptually

0885–8950/00$10.00 © 2000 IEEE

DURANTE AND GHOSH: ACTIVE POWER MEASUREMENT IN NONSINUSOIDAL ENVIRONMENTS 1143

Fig. 1. Experimental system.

similar to those previously reported by other researchers[4]–[6].

The amplitude and phase spectral information for three inde-pendent voltage signals and three independent current signalsare used as inputs to the system. The computer calculates theFourier Series representation of the voltages(1) and cur-rents (2) for three phases (, , and ). The ArbitraryWaveform Generators (AWG’s) convert the Fourier Series rep-resentation into three analog currents and three analog voltages.The signals are then amplified independently by three currentand three voltage amplifiers. The amplified currents and volt-ages then become the inputs to the measurement devices usingthe phantom loading technique. The system is capable of sup-plying up to 200 A per phase and up to 600 V per phase.Up to fifty (50) harmonics are programmable for current andvoltage waveform synthesis.

The system incorporates several independent measurementinstruments to monitor, control, and record test results. Thesystem’s components with their generic descriptions are listedbelow with reference to the block diagram in Fig. 1:

• Computer System: 486 DX4 100 MHz• Six Arbitrary Waveform Generators (AWG’s)• Three Wideband Current (I) Amplifiers• Three Wideband Voltage (V) Amplifiers• IEEE 488.2 GPIB Interface Bus• Electronic Registers (accumulate and store results)• WWV Receiver [precise test time window (ttw)]• Digitizing Signal Analyzer (DSA) Scope [provides two

giga samples per second real time monitoring of andduring the ttw]

• Wideband Power Analyzer (PA)• Three industry watthour standard (Whr S) instruments

solid state watthour meter

Fig. 2. Test signal 1: current amplitude spectra.



B. Test Signal Design

The test signals used in this experiment were developed usinga mathematical approach employing the Fourier Series repre-sentation for periodic voltage (1) and periodic current(2). For our purposes: ; Hz, and .Since the Fourier Series builds only periodic and all ofour test signals are periodic and steady state during the test timewindow (ttw). In conjunction with the Fourier Series our pri-mary consideration in the design of the test signals was the IEEEstandard definition for the total active powerof nonsinusoidalwaveforms (3). Additional pertinent IEEE standard definitionsof signal characteristics (e.g.: rms, crest factor, %THD) werealso considered when building the test signal currents and volt-ages. Further, the test signals were designed focusing on theirfrequency domain parameters (Figs. 2–4) while simultaneouslyconsidering their resulting time domain shapes (Figs. 5–7). Thedesign and synthesis of test signals using this approach allowsfull control over the test signal parameters and facilitates the de-velopment of a myriad of possible testing criteria.


Fig. 5. Test signal 1: time shapes.



The experimental test criteria and test signals were designedin an attempt to explore the DUT’s capabilities of measuring adesired electrical quantity (e.g.: or watthours) of a test signalwith “hand-picked” spectral content under “laboratory test con-ditions.” Based on this response information the authors believethat it should then be possible to characterize, with some degreeof engineering confidence, the capabilities of the DUT’s to mea-sure the same electrical quantity of “real world” signals with lessor similarly demanding spectral content.

There are a number of interrelated variables that must be con-sidered to develop meaningful current and voltage test signals.The essential equations relating these variables are as follows:

(1)

(2)

TABLE ITEST SIGNAL CHARACTERISTICS

(3)

Notice that each of these equations are a function of all or partof the current and voltage amplitude spectra (and ) and thecurrent and voltage phase spectra (and ). Therefore thedesign of the test signals is implemented by a prudent choice ofthe values of , , and . These values are chosen withcareful consideration given to all of the interrelated test signalparameters (Table I) and their effects.

Experimentation included both field captured “real world”waveforms and a large variety of test signal candidates. Theexperimental results and observations for this population wereconsistent. Due to the space limitations of this paper only threerepresentative test signals were chosen for this presentation.Only phase of the three phase test signals is shown in Figs. 2–7, as these figures are intended only to give the reader a feel forhow the test signals were developed. The authors’ philosophywas to identify the current as the fundamental parameterand consider all other parameters the result of. With this inmind the shapes of and were decided upon first. The ’sin Figs. 2 –4 were designed to contain primarily consistent spec-tral components to build a “frequency response” test signal. Thechoice of distribution for is discussed on the following page.

The next step is to design the shape of and . Theseshapes are designed to support the current spectra thus givingrise to the total active power in the test signals as defined by(3).

C. Test Signal Characteristics

Figs. 2 and 3 show that test signals 1 and 2 have essentiallythe same amplitude spectral content. That is; odd harmonics upto the 25th are 30% of the fundamental, with the exception thatthe harmonic frequencies 5th thru 15th were set at 35% in signal1. A similar harmonic distribution is followed for the voltageamplitude spectra of test signals 1 and 2. That is; odd harmonicsup to the 25th are 5% of the fundamental with the harmonicfrequencies 5th thru 15th at 4.5% in signal 1. Notice that thetime shape of signal 1 (Fig. 5) has a current crest factor (CCF)of 4.375 while that of signal 2 (Fig. 6) has a CCF of only 2.555.The difference in the time shapes is due primarily to the currentphase spectral distributions (i.e.: ).


TABLE IITEST RESULTS: MEASUREMENTS INWATTHOURS

In signal 1 the distribution of , was chosen to provide themaximum CCF. The authors believe this to be the one of themost stringent current test signal from the time domain aspect.

Table I lists further characteristics of the test signals. Notethat the test signals are the same for phase, , and fortest signals 1 and 2. In addition, a substantial amount of %THD, % THD, and % were designed into the test signalsto provide rigorous testing demands. The % is defined asthe percentage of total harmonic active power compared to thefundamental active power.

Fig. 4 shows the current amplitude spectral distribution of testsignal 3 for phase . The odd harmonics up to the 25th are 30%and 50% of the fundamental with four even harmonics at 10%. Asimilar harmonic distribution is again followed for the voltagespectra. The odd harmonics up to the 25th are 3% and 5% ofthe fundamental with the evens at 1% of the fundamental. Thecurrent and voltage spectral contents were redistributed for bothphase and . Table I shows that test signal 3 provides a totallyunbalanced test condition.

III. EXPERIMENTAL RESULTS

A. Measurement Details

The experimental results for the three test sequences per-formed on each of the DUT’s including the four watthour me-ters, tested in turn, is shown in Table II. All measurements are inwatthours and are the sum of the watthours in each of the threephases. Prior to the run of each Test Sequence shown in Table IIa 60 Hz sine wave current and voltage test was performed andrecorded to insure test system equipment integrity.

The column headings represent five independent quantifica-tion’s of the test signal watthours: 1) The Meter #, Watthourscolumn lists the quantity of watthours that each of the metersmeasured during the test time window (ttw). The ttw or lengthof the test period is determined by both the pulse rate, whichis a function of signal strength or, and the number of meterpulses programmed to be accumulated before terminating thetest. The number of pulses times the meter constant determines

the watthours accumulated during the ttw by the meter. The ttwswere not chosen to be equivalent, however, they were all chosento be greater than one minute in duration. 2) The Math columnis the theoretical value of the test signal watthours. This valueis determined by first calculating the theoretical watts in the testsignal, as defined by (3) using the designed parameters shownin Figs. 2–7. Then the test signal watts are multiplied by thettw to arrive at the signal watthour value shown. 3) The PowerAnalyzer’s Discrete Fourier Transform (DFT) watthour valueis arrived at as follows: The PA performs the DFT algorithm toprovide current and voltage amplitude and phase information foreach of fifty (50) harmonics. This spectral information is thenused to calculate the total active powerin watts. Then ismultiplied by the ttw resulting in a third independent look at thetest signal’s watthours.

It is essential to point out here that this measurement methodwas used by the authors as an additional “check” on thewatthours. This method of using the spectral information fromthe DFT for calculation of and subsequent multiplicationby the ttw is considered to be the least reliable of the methodsused to arrive at watthours. The uncertainties involved withthe DFT calculation of individual spectral components, asper manufacturers specifications, coupled with the number ofcomponents ( ) in the calculation of make this methodthe most susceptible to deviation. However, the DFT algorithmwas sufficiently accurate to provide the actual system outputcurrent and voltage spectral information needed for comparisonwith the designed spectra of the test signals. These spectralcomparisons, along with the real time waveforms traced bythe DSA scope, provided the information needed to insureconfidence that the experimental system was indeed generatingcurrent and voltage waveforms representing the mathematicallydesigned test signals. 4) In addition the PA has an algorithmthat uses four hundred simultaneous samples (per fundamentalcycle) of the current and voltage to arrive at the average wattsfor the duration of the ttw. This value is then multiplied by thettw resulting in the test signal watthour value shown in columnsPA Test 1 and PA Test 2. Two consecutive tests were performed


to insure consistency. 5) The watthour standard column Whr STest 1 and Whr S Test 2 shows the test signal watthour valuesaccumulated during the ttws, of the two consecutive tests, bythree (one per phase) widely used industry standard watthourreference instruments.

B. Measurement Observations

The intent of the authors, as discussed in the introduction,is to present the facts/results of this experiment in a mannerthat facilitates the reader’s own observations and conclusions.Therefore we have excluded references to benchmarking and% error. The following observations were made by the authorsconcerning the experimental results presented, however, theyare not intended to be an exhaustive treatment.

In Test Sequence #1 the expected Math watthours trackedclosely with the PA watthours and the Meter watthours for allfour meters tested. The DFT watthours were also very similar.However, the Whr S watthours differed considerably from theother measurements. In Test Sequence #2 the expected Mathwatthours tracked closely with the PA watthours, the Meterwatthours for all four meters tested, and in addition the WhrS watthours. The DFT watthours were again very similar. InTest Sequence #3 the expected Math watthours tracked closelywith the PA watthours, the Meter watthours for all four meterstested, and the Whr S watthours. The DFT watthours wereagain very similar but suffered the largest deviation of the threetest sequences.

We believe that the anomalies in the measurements observedare the result of the demands designed into the test signals cou-pled with the operating limitations of the measurement devices.The first anomaly is that the Whr S did not track the other mea-surements for test signal 1 (Fig. 5). The operating limitations ofthe Whr S and the CCF of 4.375 is believed to have caused thisdifference in measurement. Further evidence of this is that whenthe CCF was relieved to 2.555 in test signal 2 (Fig. 6) by ad-justing the current phase spectra only, while maintaining a sim-ilar current amplitude spectral content (Figs. 2 and 3), all mea-surement results tracked very closely. With the CCF maintainedat or close to 3 in test signal 3. the same tracking consistencybetween measurements was observed. Further, close scrutiny ofTable I will show that the demands of test signal 3 exceed thoseof test signals 1 and 2 for selected parameters including unbal-anced phase conditions. Even with the demanding test signal 3characteristics all the measurement devices tracked watthourswith consistency and close agreement between measurementsand calculations as shown in Table II.

IV. CONCLUSIONS

Evaluation of solid state watthour meters along with othermeasuring instruments was performed using the phantomloading technique. Experimentation was designed to do a com-parative analysis of the watthours measured by independentinstrumentation and calculated watthours using the IEEE def-inition of active power. The comparative method was adoptedto gain engineering confidence in the measured data because,to date, no standard testing procedures or traceable reference

instruments exist. The mathematical test signals were used fortheoretical comparison and to broaden the scope of this study.

In conclusion we address the questions posed in the intro-duction. First, are there currently commercially available mea-surement devices with the capability to accurately measure,or its associated watthours, in nonsinusoidal situations? If onedefines capability as the consistency and agreement of measure-ments between independent devices and in addition agreementwith the theoretically calculated value of the desired parameter,then based on the experimental evidence of this study our ob-servations lead us to believe that such measurement devices arecommercially available. In fact, the DUT’s of this study meetthese capability requirements under the conditions exposed toin this experimentation. The exceptions are the results recordedby the Whr S with respect to test signal 1. However, it is essen-tial to note that the demands of all the test signals far exceed theWhr S’s manufactures’ specifications.

This study was not able to answer the second question as moreexhaustive testing is needed to fully address the device responselimitations. However, we do believe that the test signal parame-ters chosen for these experiments were sufficiently demandingto provide very interesting information.

To address the last question concerning the evaluation of thegeneral response of the DUT’s, their watthour registration ofseveral “real world” waveforms of less demanding, but substan-tial, spectral content was also tested. The measurement resultsusing the “real world” waveforms were consistent with the re-sults using the designed test signals of this experiment. There-fore, the authors believe that the concept of using mathemati-cally devised test signals is a viable one and could be helpful inthe development of generalized performance testing criteria. Wehope these experiments motivate further study and contributesto the development of this much needed standardized perfor-mance testing of measurement devices expected to operate innonsinusoidal environments.

ACKNOWLEDGMENT

The authors would like to thank General Electric, ABB,Process Systems and Transdata for their cooperation in thisstudy. Special thanks to General Electric for providing the useof their Somersworth, NH, Engineering Laboratory Facilities.In addition the continued support of Niagara Mohawk manage-ment and staff in these efforts is greatly appreciated.

REFERENCES

[1] IEEE Standard Dictionary of Electrical and Electronics TermsANSI/IEEE Std. 100-1992, Fifth Edition ed. New York, NY: The Inst.of Electrical and Electronics Engineers, Inc., 1992, p. 983.

[2] V. E. Wagner, J. C. Balda, D. C. Griffith, A. McEachern, T. M. Barnes, D.P. Hartmann, D. J. Phileggi, A. E. Emmanuel, W. F. Horton, W. E. Reid,R. J. Ferraro, and W. T. Jewell, “Effects of harmonics on equipment,”IEEE Trans. Power Delivery, vol. 8, no. 2, pp. 672–680, April 1993.

[3] R. Arseneau, Y. Baghzouz, J. Belanger, K. Bowes, A. Braun, A. Chiar-avallo, M. Cox, S. Crampton, A. Emanuel (Chairman), P. Filipski, E.Gunther, A. Girgis, D. Hartmann, S.-D. He, G. Hensley, D. Iwanusiw,W. Kortebein, T. McComb, A. McEachern, T. Nelson, N. Oldham, D.Piehl, K. Srivinivasan, R. Stevens, T. Unruh, and D. Williams, “Prac-tical definitions for powers in systems with nonsinusoidal waveformsand unbalanced loads: A discussion,” inIEEE Working Group on Non-sinusoidal Situations: Effects on Meter Performance and Definitions ofPower.


[4] R. Arseneau and P. S. Filipski, “Application of a three phase nonsinu-soidal calibration system for testing energy and demand meters undersimulated field conditions,”IEEE Trans. Power Delivery, vol. 3, no. 3,pp. 874–879, July 1988.

[5] A. Domijan Jr., E. Embriz-Satander, A. Gilani, G. Lamer, C. Stiles, andC. W. Williams Jr., “Watthour meter accuracy under controlled unbal-anced harmonic voltage and current conditions,” in IEEE Power SystemInstrumentation & Measurements Committee of the IEEE Power Engi-neering Society, 1995 IEEE/PES Winter Meeting, New York, NY, Jan-uary 29–February 2, 1995, 95WM039-8 PWRD, pp. 1–7, submitted forpublication.

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Larry G. Durante received his B.S.E.E. degree from Syracuse University in1989. He began working for Niagara Mohawk Power Corporation in 1990. Heis presently Supervisor of Niagara Mohawk’s System Standards Laboratory.

Prasanta K. Ghoshreceived his Ph.D. degree in solid state science in 1986from Pennsylvania State University. He is currently an Associate Professor ofElectrical and Computer Engineering, Syracuse University. His research interestincludes nonlinear dielectric and optical devices, microelectronics, VLSI andpower quality of power distribution.

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Active power measurement in nonsinusoidal environments