Ieeepro techno solutions 2013 ieee embedded project study of the accuracy requirements of the instrumentation for efficiency measurements in power conversion systems

2154 IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 62, NO. 8, AUGUST 2013

Study of the Accuracy Requirements of theInstrumentation for Efficiency Measurements in

Power Conversion SystemsGaetano Pasini, Member, IEEE, Lorenzo Peretto, Senior Member, IEEE, Roberto Tinarelli, Senior Member, IEEE

Abstract—Efficiency of power conversion apparatus must usu-ally be measured with very low uncertainty, and depending onthe kind of apparatus under test and on the measurement methodapplied, more or less accurate instrumentation is required.The main issues to be faced, once the target uncertainty isfixed, concern the choice of the measurement method as wellas the instruments to be used for fulfilling such requirement.This paper investigates by means of both theoretical analysisand experimental results on the relationship between targetuncertainty and instrumentation accuracy in the measurementof uninterruptible power supply efficiency. The results show,amongst other things, that the measurement method allowsobtaining very low uncertainty values by means of low accuracyinstrumentation.

Index Terms—Attenuation measurement, communicationequipment testing, communication systems, power system com-munication, power system measurements.

I. Introduction

THE measurement of the efficiency is probably the firstkind of measurement that comes to mind when thinking

about the characterization of power apparatus like transform-ers, uninterruptible power supply (UPS), converter, speeddrives, rotating machinery, and so on. Nowadays, this attentionis even more justified, if it was necessary, by the increasingcost of electricity that has lead to a continuous growth ofstudies and investments for improving and maximizing theenergy efficiency of systems used in power networks. As aconsequence, there is need of measuring this parameter withincreasing accuracy, with the sake of comparing different appa-ratus for choosing the one to be installed, and experimentallyanalyze the effect of a new solution aimed at improving theefficiency performance.

International standards define the methods for performingsuch measurement according to the kind of apparatus con-sidered, e.g., [1] for UPS and [2] for power transformers,and specify if it is a routine or type test. Moreover, severalpapers can be found in literature dealing with this topic.

Manuscript received December 11, 2012; revised March 5, 2013; acceptedMarch 8, 2013. Date of current version July 10, 2013. The Associate Editorcoordinating the review process was Dr. Carlo Muscas.

The authors are with the Department of Electrical, Electronic and Informa-tion Engineering “Gugliemo Marconi,” Alma Mater Studiorum, University ofBologna, Bologna, Italy (e-mail: [email protected]).

Color versions of one or more of the figures in this paper are availableonline at http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TIM.2013.2264864

For example, in [3] an automatic system for efficiency mea-surement on variable speed drives is presented along with acriterion for its optimization. In [4] a method for power lossesmeasurement in real working condition is proposed, whichfeatures an uncertainty lower than that of the other approaches.The problem of efficiency and power losses measurement ofsaturated magnetic devices under nonsinusoidal condition isfaced in [5], whereas in [6] a procedure for a high accurateefficiency measurement of bi-directional DC–DC converter isshown. Also UPS efficiency has been tackled off in [7].

Despite the huge number of methods for efficiency measure-ment that can be chosen for a specific application, the basicquestion to be answered is: “I have to provide the efficiencywith a given number of significant digits. Which methodshould I use? And then, which uncertainty should feature theinstruments to be used?” In other words, from a practicalpoint of view, once the target measurement uncertainty isfixed (“measurement” uncertainty specified as an upper limitand decided on the basis of the intended use of measurementresults,” according to the VIM [8]), the main problem is toapply a measurement method and to choose the instrumentsthat allow fulfilling such requirement. The problem is nottrivial given that an inappropriate choice will produce uselessresults and lead to carrying out new measurements, thusleading to a waste of time and an increasing of costs.

Therefore, in this paper, the attention is focused on theanalysis of the accuracy performance that must be featuredby an instrument to get, for a given measurement method,a prefixed target uncertainty on the efficiency. For the sakeof simplicity, the study is limited to UPS that, due to thevery high efficiency value, are the most critical from theuncertainty point of view. In this connection, the paper isorganized as in the following. Section II recalls the mainapproaches for efficiency measurement of UPS, whereas astudy on the propagation of the uncertainty sources in suchmethods is reported in Section III. Section IV shows the resultsof the analysis of the instrument requirements, and Section Vdeals with some experimental tests. Lastly, final remarks aredrawn in Section VI.

II. Measurement Methods for the Efficiency

Evaluation in UPS

The procedure for the measurement of the UPS efficiencyis defined by the standard IEC 62040-3:2011 “Uninterruptible

0018-9456/$31.00 c© 2013 IEEE

PASINI et al.: STUDY OF THE ACCURACY REQUIREMENTS OF THE INSTRUMENTATION FOR EFFICIENCY MEASUREMENTS 2155

Fig. 1. Scheme for the standard method for efficiency measurement.

Power Supply (UPS)—Part 3: Method of specifying the per-formance and test requirements” [1] and classified as type test.

The standard specifies that the tests must be performed witha reference test load of unitary power factor (PF) capable ofbeing adjusted so that the UPS delivers 25%, 50%, 75%, and100% of the active power (W) for which it is rated. Moreover,for each test the following conditions must be met.

1) Energy transfer to the energy storage system shall beprevented, for example, by disconnecting it.

2) UPS and load must be in steady-state conditions, whichmeans that their temperature variations, measured everygiven time intervals, should not exceed a specified value.

3) Each load condition must be within the range 95%–105% of the fixed value and the PW must be greaterthan 0.99.

4) The input voltage must be within 97%–103% of its ratedRMS and within 99%–101% of its nominal frequency.

As for the instruments and transducers are concerned, thestandard [1] requires that they are able to perform simulta-neous measurements of the input and output active powerswith an uncertainty at full rate load less than or equal to0.5% with 95% confidence level. Such requirements must befulfilled even in presence of harmonic components.

The so-called standard method for the efficiency measure-ment refers to the very simple scheme in Fig. 1, where WA andWB are the two wattmeters, transducers included, connected toport 1 (input) and port 2 (output) of the UPS under test, respec-tively. The circuit in the figure is single-phase, but, of course,it can be easily extended to a three-phase configuration. Insuch a case, it is assumed that WA and WB directly provide theoverall active power. Let use denote by PX,y is the active powermeasured by the generic wattmeter X (i.e., A or B) at port y(i.e. 1 or 2). The procedure to be applied is the following [1].

1) 100% reference load is applied to the UPS output asuitable stabilization time is allowed to reach steady-state conditions.

2) The input and output active powers PA,1 and PB,2 aresimultaneously measured in three successive readingsP

(1)A,1, P

(1)B,2, P

(2)A,1, P

(2)B,2, P

(3)A,1, and P

(3)B,2, taken at not more

than 15-min apart.

3) The efficiencies η(1) =P

(1)B,2

P(1)A,2

, η(2) =P

(2)B,2

P(2)A,2

, and η(3) =P

(3)B,2

P(3)A,2

are computed.4) The arithmetic mean η̄(st) = 1

3 (η(1)+η(2)+η(3)) is computedand taken as efficiency value.

5) Steps from 1) to 5) are repeated for 75%, –50%, and25% reference load conditions.

The standard [1] states that instruments and transducersmeeting the above uncertainty requirements may not be com-mercially available, and, therefore, it describes an alternative

method for efficiency evaluation, which allows using lessaccurate instrumentations. Such a method differs from the so-called standard one for points 3) and 4), which become thefollowing.

3) Step 2) is repeated by exchanging wattmeters A and B,thus measuring P

(4)B,1, P

(4)A,2, P

(5)B,1, P

(5)A,2, P

(6)B,1, and P

(6)A,2.

The efficiencies η(4) =P

(4)A,2

P(1)B,2

, η(5) =P

(5)A,2

P(1)B,1

, and η(3) =P

(6)A,2

P(6)B,2

η(4) =P

(4)A,2

P(1)B,1

, η(5) =P

(5)A,2

P(5)B,1

, η(3) =P

(6)A,2

P(6)B,1

are then computed.4) The arithmetic mean η̄(alt) = 1

6 (η(1) + η(2) + η(3) + η(4) +η(5) + η(6)) is computed and taken as efficiency value.

According to [1], the result must be expressed in % androunded at the first decimal digit. Of course, the exchange ofwattmeters A and B is allowed that the electrical quantities inports 1 and 2 are in the same range. This does not occur forall the power conversion systems (e.g., transformer).

Lastly, as a further proof of the importance of efficiencyfor UPS, the standard also reports minimum efficiency valuesthat the manufacturer has to guarantee depending on the loadcondition and UPS size. For example, for a certain kind ofUPS with nominal power greater than 200 kVA and at 100%of the load, the minimum efficiency must be 98.1%.

III. Propagation of the Effects of

Uncertainty Sources

The evaluation of the uncertainty must be performedaccording to the ISO “Guide to the Expression of Uncertaintyin Measurement” [9] or to its Supplement 1 “Propagation ofDistributions Using a Monte Carlo Method” [10]. As it iswell known, the first approach provides exact results onlyunder specific conditions, whereas the latter gives alwaysapproximated values but it is applicable to all the measurementalgorithms.

For the sake of simplicity, but without loss of generality, letus consider only uncertainty sources located in the instrumentsand in the transducers, so that averaging becomes useless.Under this assumption, the expressions for computing theefficiency turn into the following ones:

η(st) =PB,2

PA,1. (1)

η(alt) =1

2

(PB,2

PA,1+

PA,2

PB,1

). (2)

Let u(Px,y) the uncertainty affecting the active power Px,y.According to [9], the analytical expression of the uncertaintyu(η(st)) on η(st) is

u(η(st)) =

√√√√(−PB,2

P2A,1

)u2(PA,1) +

(1

PA,1

)2

u2(PB,2). (3)

It should be underlined that (3) is not totally correct giventhat (1) is nonlinear so that the application of the procedure


endorsed in [9] might require the use of a higher-order termsin the Taylor series expansion.

As for the uncertainty u(η(alt)) on η(alt), it must be firstnoted that PA,1, PA,2 and PB,1, PB,2 are correlated quanti-ties with unitary correlation coefficient given that they aremeasured with the same instrument. Therefore, according to[9], a covariance term containing only the expressions inu(PA,1)u(PA,2) and u(PB,2)u(PB,1) appears in the formula forestimating u(η(alt))

u(η(alt)) =1√2

√√√√√√√√√√√√

(− PB,2

P2A,1

)u2(PA,1) +

(1

PA,1

)2u2(PB,2)

+(−PA,2

P2B,1

)u2(PB,1) +

(1

PB,1

)2u2(PA,2)

+2(− PB,2

P2A,1

1PB,1

u(PA,1)u(PA,2)

−PA,2

P2B,1

1PA,1

u(PB,1)u(PB,2))

.

(4)

The same consideration as (3) holds for its nonlinearity.If the efficiency is very high as it is usual for UPS, it isreasonable taking u(PA,1) ∼= u(PA,2) = u(PA) and u(PB,1) ∼=u(PB,2) = u(PB). This way, (4) turns into

u(η(alt)) =1√2

√√√√√[

1P2

B,1+

(− PB,2

P2A,1

)− 2 PB,2

PB,1P2A,1

]u2(PA)

+[

1P2

A,1+

(−PA,2

P2B,1

)− 2 PA,2

PA,1P2B,1

]u2(PB).

(5)

As stated in previous section, standard [1] requires that theefficiency is provided with three significant digits, and this isin accordance with the minimum efficiency values reported inthe same publication. From an uncertainty point of view, thismeans that the uncertainty affecting η, no matter the methodused to measure it, must be about 0.1%, given that η is veryclose to 1. In the same section, it was recalled that the standard[1] allows employing instruments and transducers featuringan “overall” uncertainty not greater than 0.5% with 95%confidence level. If η = 0.980 is assumed, and, for the purposeof easiness, it is taken u(PA,1)% ∼= u(PA,2)% ∼= u(PB,1)% ∼=u(PB,2)% = 0.5%, (3) provides u(η(st))% ∼= 0.7%, whereas(4) gives u(η(alt))% ∼= 0.01%. Therefore, it is confirmedthat the so-called alternative method allows getting, with thesame instrumentation and for the same efficiency degree, anuncertainty lower than that it is obtained with the standard one.But, at the same time, it highlights that the standard [1] makesa mistake when it states that the efficiency can be measuredwith the standard method by using instruments and transducershaving uncertainties up to 0.5%. In fact, as shown, it turnsinto u(η(st))% ∼= 0.7%, which is much greater than 0.1% thatallows to express the efficiency with three significant digits,as required by [1].

IV. Analysis of the Accuracy Requirements

In this section the accuracy requirements of the instru-mentations used to carry out efficiency measurements areinvestigated. In particular, aim of this paper is to relate it withthe target uncertainty as well was the measurement method.

The main issue to be tackled is how to express the accuracyinformation of the wattmeters and the voltage and currenttransducers. As a matter of fact, with the exception of the

Fig. 2. 3-D representation of the relationship between instrumentation un-certainty ∞, target uncertainty ∞ and efficiency η when the standard methodis applied. ui% is expressed as percentage of the measured power, whereasui(η)% is a percentage of η.

IEC 60044 series [11] that defines the accuracy specificationof instrument transformers, there is still a lack of standardsdealing with the way the nominal uncertainty of an instrumentor a transducer for the measurement of electrical quantitiesmust be expressed in the device manual or datasheet. There-fore, each manufacturer provides such critical informationin an arbitrary manner, thus determining a sort of junglewhere sometimes the same parameter has different meaningsdepending on the company that has built the device. Of course,this problem has major practical implications that the scientificcommunity is trying to address with the project “Standardfor Measurements on Electric Power Systems: UncertaintyEvaluation and Expression” [12] sponsored by the TC39Measurements in Power Systems of the IEEE Instrumentationand Measurement Society. Given that such project is still inprogress and proposing solution for the above-illustrated issueis outside the purpose of this paper, it has been decided to usea single value to represent the minimum accuracy that mustbe guaranteed, on the whole, by a wattmeter and the relevanttransducers, if used. In detail, such a value is an uncertaintyrepresenting the bounds of rectangular probability distributionwith zero mean. Let us refer to this value as instrumentationuncertainty.

A numerical approach based on a Monte Carlo method hasbeen adopted [10] (10 000 iterations) in which efficienciesranging from 0.900 to 0.999 with step of 0.001 (100 values)were considered. As for the instrumentation uncertainty, valuesranging from 0.01% to 2.00% with step of 0.01% (200 values)were used. For every combination of the above values, andfor each measurement method, the Monte Carlo simulationprovided an estimate of the uncertainty (95% confidence level)on the efficiency, which was taken as target uncertainty. Thisway, 100 × 200 = 20 000 terns are obtained, each of them madeby a target uncertainty, an efficiency, and an instrumentationuncertainty. From these, the searched relationship is easilyachieved.

A. Standard Method

Fig. 2 is a 3-D plot representing the variation of the instru-mentation uncertainty uI% versus both the target uncertainty


Fig. 3. Trend of the instrumentation uncertainty ui% versus the targetuncertainty ur(η)% for three different values of the efficiency η.gr3

Fig. 4. Zoom of the plot in Fig. 3. It clearly shows that it is impossibleobtaining target uncertainty below 0.03%.

uT(η)%, and the efficiency η when the standard method isapplied. The uI% is expressed as percentage of the measuredpower, whereas uT(η)% is a percentage of η. It can be notedthat, as it was obviously expected, the required instrumenta-tion uncertainty decreases as the target uncertainty decreases.Moreover, it seems that uI% is substantially independent of theefficiency value. From a numerical point of view, for uT(η)%equal to about 1%, that allows expressing the efficiency withtwo significant digits only, instrumentation accuracy around0.3% is needed. Better consideration can be carried out byusing a 2-D plot, such as the one shown in Fig. 3, whichreports for three different efficiency values (0.900, 0.940, and0.990), the trend of uI% versus uT(η)%. First of all, it confirmsthat the instrumentation uncertainty does not depend on theefficiency value, at least for the considered values. Moreover,the relationship between uI% and uT(η)% is practically linear.For the reason discussed in Section III, uT(η)% values ofpractical interest are in the order of few part per thousandthat, in Fig. 3, cannot be seen due to the scale adopted.To this purpose, in Fig. 4 a zoom of Fig. 3 in the interval[0,0.2] of uT(η)% is shown. It clearly highlights that it isimpossible obtaining target uncertainty below 0.03% and thatinstrumentation featuring an uncertainty lower than one partper thousand is needed to achieve the above uT(η)% values.

B. Alternative Method

Fig. 5 is a 3-D plot representing the variation of theinstrumentation uncertainty uI% versus both the target un-certainty uT(η)% and the efficiency η when the alternativemethod is applied. As in the previous case, uI% is expressedas percentage of the measured power, whereas uT(η)% is apercentage of η. It was assumed that both instruments A andB featured the same nominal accuracy, and, hence, they mustensure an uncertainty not greater than uI%. Apart the differentshape of the surface, the main difference with respect to Fig. 2is in the scale of the target uncertainty that shows values abouttwo orders of magnitude lower than those depicted for thestandard method case. Fig. 6 plots for three different efficiencyvalues (0.900, 0.940, and 0.990), the trend of uI% versusuT(η)%. The first evident observations are the instrumentationuncertainty does not depend on the efficiency value also whenthe alternative measurement method is applied (at least forthe considered value) and that the relationship between uI%and uT(η)% is no more linear, mainly for low values ofuI%. However, the most important information arising fromFig. 6 is about the possibility to get very low values oftarget uncertainty by using “low accuracy” (and hence “lowcost”) instrumentation. For example, from Fig. 6 it can bedrawn that a target uncertainty of about 1/10 000 can beachieved by using instrumentation featuring accuracy justbelow 1%.

C. Instrumentation Uncertainty Estimation

The plots presented in the previous subsections providesvery interesting information, but from a practical point ofview, their usage is not so easy if the aim is to choosethe proper instrumentation to perform efficiency measurementwith a given target uncertainty. In this light of fact, it willbe very useful having an analytical expression relating uI%and uT(η)%. Unfortunately, due to the nonlinearity of both(1) and (2), deriving such expression from (3) or (4) maylead to significant errors. Therefore, given that it has beenpreviously shown that for the standard as well as the alternativemethod, uI% is independent of the efficiency value (at leastfor the ones considered, that is for η ≥ 0.9), quite simpleanalytical expressions can be derived from the results ofthe Monte Carlo simulations by applying regression tech-niques.

As far as the standard method is concerned, Fig. 3 highlightsthe linearity of the searched relationship that therefore can beeasily expressed as follows (R2 = 0.9999):

uI% = 0.3218 × uT (η)% + 0.0009526. (6)

Fig. 7 compare the regression curve (continuous line) withthe Monte Carlo results (circular markers) for η = 0.900.

As for the alternative method, it has found that the followingsimple expression allows fitting very well (R2 = 0.9999) theMonte Carlo results:

uI% = 8.403 × uT (η)%0.4989 − 0.003428. (7)

Fig. 8 compare the regression curve (continuous line) withthe Monte Carlo results (circular markers) for η = 0.900.


Fig. 5. 3-D representation of the relationship between instrumentation uncertainty ui%, target uncertainty uT (η)% and efficiency η when the alternativemethod is applied. ui% is expressed as percentage of the measured power, whereas uT (η)% is a percentage of η.

Fig. 6. Trend of the instrumentation uncertainty ui% versus the targetuncertainty uT (η)% for three different values of the efficiency η.gr6

Fig. 7. Relationship between instrumentation uncertainty ui% and the targetuncertainty uT (η)% when the standard method is applied. Comparison be-tween regression curve (continuous line) and the Monte Carlo results (circularmarkers) the trend of the for η = 0.900.

Equations (6) and (7) are simple tools that estimate themaximum value of the relative uncertainty affecting both thewattmeters (and the relevant transducers, if used) that allowto reach the target uncertainty on the efficiency.

Fig. 8. Relationship between instrumentation uncertainty ui% and the targetuncertainty uT (η)% when the alternative method is applied. Comparisonbetween regression curve (continuous line) and the Monte Carlo results(circular markers) the trend of the for η = 0.900.

V. Experimental Activity

Aim of the experimental activity was to verify if the alter-native method allows obtaining very low uncertainty valuesby using “lower accuracy” instrumentation as discussed inthe previous sections. To this purpose, the efficiency of anUPS Trust mod. PW-4060T was measured by applying thestandard as well as the alternative method. In the former case(Fig. 9), two different channels of a wattmeter Yokogawamodel WT2030, which features the following nominal accu-racy specifications: percentage of reading 0.04%, percentageof range 0.04%, selected range 1500 VA, were used. This way,the uncertainty affecting the efficiency is very low also whenit is measured with the standard method and can be comparedwith that achieved by applying the alternative one. In thelatter case (Fig. 10), two different channels of a wattmeterDucati model DUCA47 were used. Its nominal accuracyspecifications are: percentage of reading 1%, percentage ofrange 0.1%, and selected range 1500 VA. As shown in Figs. 9and 10, a 600-W electric heater was taken as load.


TABLE I

Efficiency η and Relevant Relative Uncertainty u(η)% (95%-Confidence Level) of an insulating Transformer

Instrument used Instrument accuracy PA,1 (W) PB,2 (W) PB,1 (W) PA,2 (W) η u(η)%Standard Method Yokogawa WT2030 0.04% rdg + 0.04%range 652.87 609.78 - - 0.9340 0.32%Alternative Method Elcotronic EM3 1% rdg + 0.1%range 658.3 614.5 647.9 605.8 0.9343 0.041%

Fig. 9. Schematic representation of the application of the standard methodto the measurement of the efficiency of a UPS Trust mod. PW-4060T.

Fig. 10. Schematic representation of the application of the alternativemethod to the measurement of the efficiency of a UPS Trust mod. PW-4060T.

Table I summarizes the obtained results, reporting, forboth the measurement methods, the reading of the pow-ers PA,1, PB,2, PB,1, and PA,2, the computed efficiency η

and the estimated relative uncertainty u(η)%. The latter onewas evaluated by applying a Monte Carlo simulation [10]with 10,000 iterations and then by determining, accordingto [10], the shortest 95% coverage interval. Fig. 11 showsthe estimated probability density functions relevant to thestandard method (black bars) as well as the alternative one(white bars). The gray bars highlight the area shared by boththe pdfs.

From Table I, it can be concluded that the alternative methodallows to measure the efficiency with a very high accuracy byusing “lower accuracy” instrumentation given that the obtained

Fig. 11. Estimated pdfs of the efficiency measured by applying the standardmethod (black bars) and the alternative method (white bars). The grey barsrepresent the area shared by both the pdfs.

confidence interval overlaps (as shown in Fig. 11) the oneprovided by an high performance wattmeter that contains theunknown “true” value of the efficiency.

The results obtained can also be used to prove the correct-ness of expressions (6) and (7). To this purpose, let us assumethat the values of uT(η)% reported in Table I are the targetuncertainties uT(η)% of such equations. The application of (6)provides uI% = 0.10% that is correct by considering that thenominal accuracy specifications of the considered wattmeter(percentage of reading 0.04%, percentage of range 0.04%,and selected range 1500 VA) leads to an uncertainty on themeasured power of about 0.13% (that is about 0.8 W, sum of0.6 W due to uncertainty on the full scale, and 0.2 W due tothe uncertainty on the reading). As far as (7) is concerned, itestimates uI% = 1.70% against about 1.3% obtained by usingthe wattmeter accuracy specification (that is about 8 W, sumof 1.5 W due to uncertainty on the full scale, and 6.5 W dueto the uncertainty on the reading). In both cases, the smalldifferences between the values provided the (6) and (7) and theactual uncertainties on the measured powers can be explainedby considering that the model developed in Section IV [andfrom which (6) and (7) are derived] relies on the simplifiedassumption that uI% takes the same value for all the powersappearing in the efficiency equation. Of course, this is notstrictly true and may leads to the above approximations. How-ever, it should be kept in mind that the aim of (6) and (7) is toprovide an indication of the accuracy class of the instrumentsto be used and such differences does not affect the choice.

VI. Conclusion

The efficiency measurement of power conversion apparatusmay be a critical task because of the very high accuracythat is usually required. Depending on the kind of apparatus,international standards define specific measurement methods,and, hence, the uncertainty sources located in the measurementchain propagates in diverse way, thus leading to different


values of the uncertainty affecting the efficiency even if thesame instruments are used. From a practical point of view, themain problem to be tackled is, once the target measurementuncertainty is fixed, how measurement method can apply, andwhat instruments choose to fulfill such requirement.

In this connection, in this paper a study on the relationshipbetween target uncertainty and instrumentation uncertaintyin measurement of UPS efficiency was performed. First ofall, it was shown that the requirements on the instrumentaccuracy endorsed by the international standard may notbe sufficient for achieving an uncertainty that allowed toexpress the efficiency with three significant digits, as itis intrinsically required by the standard itself. Moreover,surfaces relating the values of the instrumentation uncertaintyto both the target uncertainty and the efficiency were providedfor both the measurement method defined by the standard.In addition, two simple and easy-to-use expressions forestimating the maximum value of the relative uncertaintyaffecting both the wattmeters (and the relevant transducers,if used) from the target uncertainty were derived. Finally,experiments were realized to demonstrate that the so-calledalternative method for efficiency measurement allowed toobtain very low uncertainty values by means of low accuracyinstrumentation.

References

[1] Uninterruptible Power Supply (UPS)—Part 3: Method of specifying theperformance and test requirements, IEC 62040-3:2011, 2011.

[2] Power Transformer—Part 1: General, IEC 60076-1:2011, 2011.[3] C. De Capua and C. Landi, “Measurement station performance optimiza-

tion for testing of high efficiency variable speed drives,” IEEE Trans.Instrum. Meas., vol. 48, no. 6, pp. 1149–1154, Dec. 1999.

[4] E. Arri, N. Locci, and F. Mocci, “Measurement of transformer powerlosses and efficiency in real working conditions,” IEEE Trans. Instrum.Meas., vol. 40, no. 2, pp. 384–387, Apr. 1991.

[5] E. F. Fuchs and R. Fei, “A new computer-aided method for the efficiencymeasurement of low-loss transformers and inductors under nonsinusoidaloperation,” IEEE Trans. Power Del., vol. 11, no. 1, pp. 292–304, Jan.1996.

[6] W. Yu, H. Qian, and J.-S. Lai, “Design of high-efficiency bidirectionalDC–DC converter and high-precision efficiency measurement,” IEEETrans. Power Electr., vol. 25, no. 3, pp. 650–658, Mar. 2010.

[7] A. Ariatta, G. Pasini, and L. Peretto, “Measurement of the efficiencyand uncertainty evaluation in UPS,” in Proc. 2nd IEEE Energy Conf.Exhibition, Sep. 2012, pp. 1080–1084.

[8] International Vocabulary of Metrology—Basic and General Conceptsand Associated Terms (VIM), 3rd ed., JCGM, 2008.

[9] Uncertainty of Measurement—Part 3: Guide to the Expression of Un-certainty in Measurement, ISO Guide 98-3:2008, 1995.

[10] Evaluation of Measurement Data—Supplement 1 to the ‘Guide to the Ex-pression of Uncertainty in Measurement’—Propagation of DistributionsUsing a Monte Carlo Method, ISO Guide 98-3/Suppl.1:2008, 2008.

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evaluation and expression, IEEE P1878, active project approved by theIEEE Std. Assoc.

Gaetano Pasini (M’97) received the Laurea degreein electronic engineering from the University ofBologna, Bologna, Italy, in 1991.

In 1993, he joined the Electrical and ElectronicMeasurement Group, Electrical Engineering De-partment (now Department of Electrical, Electronicand Information Engineering “Guglielmo Marconi”),University of Bologna as an Assistant Professor, andthen in 2001 he became an Associate Professor.From 1999 to 2009, he was a co-founding partnerof TechImp srl (now TechImp HQ SpA), a spin-

off with academic partner the University of Bologna; for this company,he worked to design tools and algorithms for medium and high voltagedevices diagnostic. His current research interests include digital-signal pro-cessing, nonconventional-sampling strategies, modeling and characterizationof nonlinear devices (specifically ADC and Sample and Hold), distributedmeasurement systems, and design and implementation of instrumentation forpartial-discharge measurements.

Mr. Pasini is an AEIT member and a member of the Italian Association ofElectrical and Electronic Measurement.

Lorenzo Peretto (M’98–SM’03) received the M.S.and Ph.D. degrees in electronic engineering andelectrotechnical engineering from the University ofBologna, Bologna, Italy, in 1993 and 1997, respec-tively.

He joined the EE Department, University ofBologna, as an Assistant Professor and then becamean Associate Professor. He has authored or co-authored more than 150 scientific papers and is a co-inventor of 21 patents. His current research interestsinclude digital signal processing and measurements

for the analysis of power quality, novel techniques for the characterization ofvoltage and current transducers instrumentation design for flicker measure-ment, prediction of reliability, and reliability tests.

Dr. Peretto has participated in the IEEE Working Group for the revision ofStandard 1459-2000 and has worked in the IEC TC 25, “on the new definitionof the Ampere.” He is an IEC representative in the BIPM Joint Committeefor Guides in Metrology. He is the Chair of the IMS TC 39.

Roberto Tinarelli (S’02–M’05) was born inBologna, Italy, in 1974. He received the M.S. andPh.D. degrees in electrical engineering from theUniversity of Bologna, Italy, and the Polytechnic ofMilan, Italy, in 2000 and 2004, respectively.

He is an author or co-author of more than 100scientific papers and co-inventor of 12 patents. In2000, he joined the EE Department, University ofBologna, where he is currently an Assistant Profes-sor of electrical measurements. His current researchinterests include design and metrological characteri-

zation of instruments for measurement under nonsinusoidal conditions; designand development of new instrumentation for flicker measurement; and designof new electromagnetic-fields sensors and instrumentation.