measuring electric power quality problems and perspectives

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Measurement xxx (2006) xxx–xxx

www.elsevier.com/locate/measurement

Measuring electric power quality: Problems and perspectives

Alessandro Ferrero *

Dipartimento di Elettrotecnica, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133 Milano, Italy

Received 21 January 2006; accepted 6 March 2006

Abstract

The proliferation of non-linear and time-variant loads is causing a number of disturbances on the electric network, froma more and more significant distortion of both currents and voltages, to transient disturbances on the supply voltage. Inthis respect the electric network behaves as an ‘‘healthy carrier’’ of disturbances, so that a disturbance generated by onecustomer can be distributed to other customers, causing possible damage to their equipment. The measurement of the qual-ity of the electric power in a network section is therefore becoming an impelling need, especially in a deregulated electricitymarket, where each actor can be responsible for the injection of disturbances. However, there are still some respects ofpower-quality measurement, from both the methodological and instrumental point of views, that are still unsolved andrequire to be carefully analyzed. The paper gives a survey of these problems and some indications about the present trendsof the research work in this field.� 2006 Elsevier Ltd. All rights reserved.

Keywords: Electric power quality; Non-sinusoidal systems; Measurement of distorted quantities

1. Introduction

The ‘‘power-quality problem’’ has been knownsince the beginning of the ac energy transmissionand distribution, although this term is relativelyrecent. It was soon clear that, for a given supplyvoltage and a given active power, the current mightbe higher than the value associated with that voltageand power and, consequently, voltage drops on thesource equivalent impedance might be higher thanexpected and even outside the allowed limits. Theconcepts of apparent and reactive power and that

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of power factors were introduced in order to quan-tify this phenomenon: the first ‘‘quality index’’ wasdefined.

As far as the sinusoidal conditions are kept andthe supply is considered ideal, the power-qualityconcept is confined to a ‘‘loading-quality’’ concept,since the responsibility for decreasing the power fac-tor is fully assigned to the load. However, as soon asthe electric energy has been employed to feed thegreat industrial applications, a different phenome-non called for attention, as the power of some loadsbecame comparable with the power of the supplyingsystem: changes in the load consumption reflectedinto voltage drops on the equivalent source imped-ance that were no longer negligible with respect tothe supply voltage.

.

mailto:[email protected]

Fig. 2. Basic representation of the way a disturbance injected bya load is distributed to all other loads. L2 is the disturbing loadand draws a distorted current (dashed line). When these currentcomponents reach the source equivalent impedance (dotted line)are converted in voltage disturbances and distributed to all loadsconnected to the PCC (dash-dotted line).

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If the loads are slowly variable, the supply volt-age variations can be easily controlled with the volt-age regulators. On the contrary, when the loadsbecome rapidly variable (arc furnaces, solderingplants, . . .) new phenomena arise on the supply volt-age, such as sags, swells, notches, flicker. The prob-lem is no longer a ‘‘loading-quality’’ problem, butturns into a ‘‘supply-quality’’ problem.

Until the loads injecting disturbances were few,known, generally large-power loads, it was possibleto filter out the disturbances at the load site, andprevent them to travel along the network.

In more recent years, the development of high-quality, low-cost power electronic components hasled to a very rapid diffusion of non-linear, time-var-iant loads, spreading from low-power domesticappliances to low and high-power industrial appli-cations. New steady-state disturbances, such as har-monic and inter-harmonic components, andtransient disturbances appeared on the line-current,causing several phenomena, ranging from anincrease in the losses and voltage drops to EMI bothon the other loads and the communication systems.

The overall power of such distorting loads con-nected to the supply network may be once againcomparable with the power of the supply system(that does not generally show a source equivalentimpedance constant with frequency) and thereforethe supply voltage is distorted too by harmonicand inter-harmonic components, and disturbed bysags, swells, notches. Again, a ‘‘loading-quality’’problem becomes a ‘‘supply-quality’’ problem.

In a typical network structure like the one shownin Fig. 1, where different loads, belonging to differ-ent customers are connected to the same point ofcommon coupling (PCC), the disturbances injected

Fig. 1. Single-phase representation of a power system withmultiple loads connected to the same point of common coupling(PCC) fed by a sinusoidal non-ideal generator.

by one load are distributed to all other loads bythe disturbances that arise on the supply voltage,as schematically shown in Fig. 2. A linear, time-invariant load may be forced to consume a distortedcurrent, some flicker may appear on the lighting sys-tem, interference may appear on the electronic con-trol apparatus and so on. The electric network isnow behaving as an ‘‘healthy carrier’’ of load-gener-ated disturbances: the ‘‘loading-quality’’ problems,together with the ‘‘supply-quality’’ problems, arenow causing ‘‘power-quality’’ problems.

As far as the ‘‘loading quality’’ and the ‘‘supplyquality’’ are concerned, recommendations havebeen issued by the Standard Organizations both tolimit the injection of harmonics [1–4] and to definethe characteristics of the voltage supplied by publicnetworks [5–7]. Definitions of power-quality relatedterms are also given [8]. However, these recommen-dations appear to be still insufficient to ensure thesolution of the ‘‘power-quality’’ problems. In fact,it should be considered that, when the supply volt-age is distorted (and possibly unbalanced, in three-phase systems), a customer may not be totallyresponsible for the harmonic and unbalance currentcomponents flowing in its loads. Ethical and legalissues, other than technical ones, are involved, whensetting allowable limits [9], since the source respon-sible for injecting the disturbances should be first ofall detected.

Moreover, the same amount of disturbancesinjected by a load may have different impact onthe power quality, according to the short-circuit

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power granted by the Utility at the PCC: the higheris the short-circuit power, the lower is the impact ofthe injected disturbances.

The main issue, when dealing with ‘‘power qual-ity’’, is therefore not only that of limiting theamount of injected disturbances, but also that ofdetecting the source, or the sources, injecting thedisturbances and quantifying the effect of such dis-turbances on the power quality. The next sectionswill discuss the technical respects of this problem,both from the methodological point of view andthat of the measuring equipment.

2. Theoretical background

The power theory of the ac electric systems andcircuits has developed, during the last century, underthe strong constraint of sinusoidal waveforms. Whendisturbances are superimposed to the sinusoidal volt-age and current waveforms, and particularly whensuch disturbances are steady-state disturbances, thatconstraint cannot be considered any longer. Conse-quently, all conventional quantities and factors usu-ally employed to analyze the energy flow in theelectric systems under sinusoidal conditions, suchas the reactive and apparent powers and the powerfactor, lose most of the properties they have undersinusoidal conditions. This leads to a dramatic andmisleading loss of information [10] when they areused in power-quality assessment.

In order to avoid these problems, the non-sinu-soidal conditions should be theoretically reconsid-ered, starting from the mathematical bases of theelectromagnetism and circuit theory, in order todescribe the physical behaviour of an electric systemunder non-sinusoidal conditions in terms of a suit-able set of equations and mathematical relation-ships that relate voltages, currents and physicalproperties of the system elements. At the Author’sknowledge, very few attempts have been publishedthat try to give a general answer to this basic prob-lem [11–13].

Nevertheless, several attempts were made, in thepast, to extend to the non-sinusoidal systems con-cepts and definitions typical of the sinusoidal systems[14–18]. These attempts were mainly concerned withthe solution of particular problems, typically thecompensation of non-active current componentsand, in some cases, have been proved to be not totallycorrect from the physical point of view [19].

More recently, a more in-depth investigation intothe power phenomena has been proposed by several

Authors [12,13,20–31], so that these phenomena arenow more clearly described than in the past,although a generally accepted, comprehensive the-ory of the power phenomena under non-sinusoidalconditions is not yet available. A good, extensivesurvey of the scientific work done in this field is rep-resented by the issues of the ETEP and L’EnergiaElettrica journals [32–37] dedicated to the contribu-tions presented during six ‘‘International Workshops

on Power Definitions and Measurements under Non-

Sinusoidal Conditions’’ (Como, Italy, 1991, Stresa,Italy, 1993, Milano, Italy, 1995, 1997, 2000 and2003).

A second critical point that must be consideredwhen discussing about power-quality measurementis concerned with the evaluation of the measure-ment uncertainty in the presence of heavily distortedsignals. Up to a recent past, only the behaviour ofthe active and reactive energy meters in the presenceof distorted waveform conditions was widely dis-cussed [38–40]. However, the power-quality indicesthat have been more recently proposed require com-plex measuring systems for their measurement. Theevaluation of the measurement uncertainty, accord-ing to the recommendation of the ISO Guide [41], isstill an open problem.

All above referenced contributions represent atheoretical background wide enough, if properlyapplied, to allow a correct approach to power-qual-ity definition and measurement.

3. Power-quality indices

The first, obvious, though not easy step towardpower-quality measurement is the definition ofpower-quality indices able to quantify the deviationfrom an ideal reference situation, quantify the detri-mental effects of this deviation and identify thesource generating these detrimental effects.

A quite natural way seems to be the extension tothe non-sinusoidal conditions of the indicesemployed under sinusoidal conditions, such as thepower factor and the total distortion factor (THD),together with a discussion of their limits when thesinusoidal conditions are left.

In order to extend the definition of the power fac-tor, the apparent power must be considered too. Itsextension to the non-sinusoidal conditions is quiteimmediate for single-phase systems; on the con-trary, several different definitions are available inthe literature [42] when three-phase systems are con-sidered. The following one, due to Buchholz [43], is


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receiving increasing acceptance in the scientific com-munity, though it is not endorsed by severalstandards:

SR ¼ URIR ð1Þwhere UR and IR are the voltage and current collec-tive rms values, respectively and are defined as

UR ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiXn

j¼1

U 2Lj

vuut and IR ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiXn

j¼1

I2Lj

vuutULj and ILj being the rms values of the zero-sum linevoltages and the line currents, respectively, n thenumber of wires of the system.

If the total active power is defined as

PR ¼Z

T

Xn

j¼1

uLjðtÞiLjðtÞdt ð2Þ

where T is the period of the voltage and currentwaveforms, the power factor can be still defined asthe ratio between the active power and the apparentpower (1):

k ¼ PR

SRð3Þ

The power factor (3) can be still considered apower-quality index, though it loses the propertyof fully qualifying the load. Under non-sinusoidalconditions it only represents an index of conformityof the line current waveforms to the line voltagewaveforms. It can be easily proven that also the dis-tortion factors only show the conformity of the linevoltages and currents to sinewaves. In fact, for thethree-phase systems, the global voltage and currentTHD factors can be defined as

GTHDU ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiU 2

R

U 2R1

� 1

sand GTHDI ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiI2R

I2R1

� 1

s

ð4Þwhere UR1

and IR1are the collective rms values of

the fundamental frequency components of the linevoltages and currents, respectively. According tothe given definition, factors (4) act as non-confor-mity indices of the line voltage and current wave-forms to sinewaves, no matter if these sinewavesare balanced or not.

Since it has been proven that the harmonic com-ponents and the sequence components, in three-phase systems, have similar effects from the power-quality point of view and can be considered as thecomponents of a generalized Fourier decomposition

[28], the factors defined in (4) can be modified, inorder to keep into account the effects of the unbal-ance components too, as

GTHDþU ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiU 2

R

U 2Rþ1

� 1

sand GTHDþI ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiI2R

I2Rþ1

� 1

s;

ð5Þ

where URþ1and IRþ1

are the collective rms values ofthe fundamental frequency, positive sequence com-ponents of the line voltages and currents, respec-tively. It can be readily checked that the factorsdefined in (5) act as non-conformity indices of theline voltage and current waveforms to positive se-quence sinewaves.

The comparison between the values assumed by(4) and (5) allows to establish whether the responsibil-ity for the electrical pollution is mostly due to thepresence of distortion or to the presence of unbalance.

All above quantities, however, are not useful inestablishing whether the load or the supply areresponsible for the power-quality deterioration,since they can only provide an estimate of confor-mity to given reference conditions, where, accordingto [1–9], the term ‘‘conformity’’ denotes ‘‘the fulfill-ment of specified requirements’’.

An attempt to find more useful indices has beenproposed by the IEEE Working Group on Non-sinusoidal Situations [40] with the following resolu-tion for the apparent power (1):

S2R ¼ ðURIRÞ2

¼ ðUR1IR1Þ2 þ ðUR1

IRHÞ2 þ ðURH

IR1Þ2 þ ðURH

IRHÞ2

ð6Þ

where URHand IRH

are the collective rms values ofthe harmonic components of voltage and current,respectively.

Although the quantities:

S2R1¼ ðUR1

IR1Þ2

and

S2RN¼ ðUR1

IRHÞ2 þ ðURH

IR1Þ2 þ ðURH

IRHÞ2

are introduced, it can be immediately checked that:

SRN

SR1

� �2

¼ ðGTHDIÞ2 þ ðGTHDU Þ2

þ ðGTHDI �GTHDU Þ2

This approach, therefore, does not provide anyadditional information to the one associated with


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the THD factors and is useless in identifying thesources producing distortion.

Some information about the location of thesource producing distortion is provided by the ratio:

gþ ¼ GTHDþIGTHDþU

; ð7Þ

since a linear, balanced load is expected not to am-plify the distortion of the current, with respect tothat of the voltage, whilst a non-linear or unbal-anced load is expected to. However index (7) is sen-sitive to resonance too, so it cannot discriminatebetween distortion and resonance effects.

The search for more effective approaches has led,recently, to focus on the analysis of the energy flow-ing in a network section [22,44]. This analysis showsthat, under distorted conditions, active power com-ponents associated with the harmonic and negativesequence components of voltages and currents arisethat flow backward from the load to the generator,and dissipate in the generator source impedance.This phenomenon can be explained by consideringthat the non-linear loads behave as ‘‘converters’’,which draw active power at the fundamental fre-quency and positive sequence, and return part ofit back at different frequencies and sequences.

According to the above considerations, the activepower PR, in the metering section of a three-phasecircuit can be resolved as

PR ¼ PRþ1þ PR�1

þXk 6¼�1

PRk ð8Þ

PRþ1is the active power generated by the sinusoidal,

balanced ideal supply. The other terms in (8) repre-sent active powers delivered to the load and gener-ally dissipated if the supply is distorted and/orunbalanced, or reflected backward and dissipatedin the equivalent source impedance if the load isnon-linear, time-variant and/or unbalanced. A firstsupply- and loading-quality index can be hence de-fined as [45]

nslq ¼PR

PRþ1

ð9Þ

It can be readily checked that, when the distortionand/or unbalance of the supply prevail over the loaddistorting and unbalancing effects, nslq > 1. On thecontrary, when the load distorting and/or unbalanc-ing effects prevail over the supply voltage distortionand/or unbalance, nslq < 1.

A second power-quality index has been proposed[46]:

nHGI ¼kIRLk2

kIRSk2

ð10Þ

where IRLis the vector of the collective rms values of

the harmonic and sequence components associatedwith active powers reflected backward from the loadto the source, and IRS

is the vector of the collectiverms values of the harmonic and sequence compo-nents associated with active powers flowing fromthe source towards the load. The higher is the valueassumed by (10), the higher is the load contributionto distortion. Both indices (9) and (10) may provideincorrect information under practical conditions[47] when compensation effects arise between theharmonic power components injected by the supplyand those reflected by the load and when the har-monic active powers are close to zero, due to aphase shift close to p/2 between the harmonic com-ponents of voltage and current, despite the presenceof large harmonic current components. Providingincorrect indications is a common flaw of all syn-thetic indices obtained from measurements done ina single metering section. These indices are some-how doomed to fail, since an electric system undernon-sinusoidal conditions has a theoretically infinitenumber of freedom degrees [11], and therefore itsstate cannot be fully determined by means of a sin-gle index or quantity.

In order to overcome this problem, new methodsand indices have been recently proposed in the liter-ature, based on the measurement of suitable quanti-ties and indices in different metering sections of thenetwork.

In particular, a first index has been proposed in[48,49], based on multi-point measurements of indi-ces (7), (9) and (10). For each line k leaving a PCC,this index can be defined as

tk ¼1

3

n�1slqk

n�1slqs

þ nHGIk

nHGIs

þ gþkgþs

!ð11Þ

where subscript k refers to a line leaving the PCCand subscript s refers to the line supplying the PCC.

This index is based on the consideration that, whenindices nHGI and g+ are evaluated for each line con-nected to the same PCC, the ratio of one index mea-sured on one of the lines leaving the PCC with thesame index measured on the line supplying the PCCincreases if the disturbances are injected by the loadconnected to the line, while it decreases if the distur-bances are injected by the supply. The oppositeoccurs when the ratio of indices nslq is considered.


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Index (11) averages the above ratios, and isexpected to compensate the different reasons thatcause each single index to fail in assessing theresponsibility for the injection of disturbances.When tk > 1, the load connected to line k is injectingdisturbances in the network. When tk < 1, line k isdisturbed.

A different approach has been proposed in [50],based on an estimate of a cost function v of theeffects of the harmonic current components as

v ¼ FXn;n6¼1

ðwnInÞ2" #

where wn are suitable weights that depend on theharmonic order n and the characteristics of thesource impedance.

In the approach proposed by [50], the consideredcost function considers the loss on the source equiv-alent impedance. In order to evaluate this loss, eachharmonic component Isn of the current flowing inthe source equivalent impedance is obtained bycomposing the corresponding harmonic compo-nents of all currents drawn from the PCC. Thesecurrent components are then divided into the twosubsets P and N. Subset P contains all harmoniccomponents IþðkÞ;n of the current flowing in load k

that cause an increment in current Isn , while subsetN contains all harmonic components I�ðkÞ;n of thecurrent flowing in load k that cause a decrementin current Isn . A graphical example of this classifica-tion of the current components is reported in Fig. 3.

The evaluation, for each single load k connectedto the PCC, of the contribution given by each har-monic component of current to the loss in thesource impedance allows to state whether that loadis increasing or mitigating the disturbances.

IS,n

I+(1),n

I+(k),n

I -( j),n

I -(2),n

Re

Im

Fig. 3. Load harmonic current components contributing to theharmonic components of the current flowing in the sourceequivalent impedance.

The two above approaches, based on multi-pointmeasurements, have been tested by means of simu-lations on the IEEE industrial test system and theirperformance have been compared in [51]. Bothmethods provided satisfactory results, and appearto deserve further, in-field evaluation.

4. The measurement problems

Up to the present days, the discussion aboutpower quality in the electric systems under non-sinu-soidal conditions has dealt mainly with the definitionof suitable theoretical approaches and indices.

When the practical issues of measuring thedefined quantities and indices began to be consid-ered, it was soon clear that the traditional instru-ments (mainly active and reactive energy meters)used under sinusoidal conditions to evaluate theenergy consumption, both from a quantitative and‘‘qualitative’’ point of view, were inadequate[38,39]. This inadequacy involves also the traditionalelectromagnetic current and voltage transformers, aswell as the capacitive voltage transformers, used inHigh Voltage systems, whose bandwidth is too nar-row to allow a correct transduction of the distortedsignals.

This problem can be overcome, if the electronictransducers are used, based on zero-flux currenttransformers for the current transducers, and elec-tro-optical techniques for the voltage transducers[52–54]. Several solutions have been proposed andare already commercially available.

As far as the measurement method is concerned,most of the newly defined indices, such as (7), (9),(10) and (11), require an extensive processing ofthe input signals to be determined: index (10), forinstance, requires a Fourier Transform of both volt-ages and currents, and the evaluation of the activepower associated with each voltage and currentcomponent. This kind of processing can be obtainedonly if the new, modern, DSP-based instruments areemployed.

From a mere technical point of view, this is not aproblem, since the available DSP-based structuresperform the Analog-to-Digital conversion and thesubsequent digital processing fast enough to allowa real-time evaluation of all above mentioned indi-ces with the required resolution. Distributed mea-surement systems can be also implemented in arelatively simple way, so that the evaluation of indi-ces based on multi-point measurements, such as(11), can be obtained [48].


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The most critical problem, with the DSP-based,distributed systems that process complex measure-ment algorithms, is the uncertainty estimation. Atthis stage of the research on the electric systemsunder non-sinusoidal conditions, this is not only amere metrological problem, but has also a largeimplication on the theoretical analysis. In fact, itshould be always kept into account that no informa-tion can be obtained about the practical utility ofany proposed theory until the defined quantitiescan be measured and the measurement uncertaintyis known. In other words, the validity of any theo-retical approach that is aimed at identifying a phys-ical phenomenon and providing quantitativeinformation about it is limited by the uncertaintywith which the quantities employed to describe thatphenomenon can be measured.

The reference document for expressing the uncer-tainty in measurement is the well known ISO Guide[41]. The Guide follows a probabilistic approach touncertainty, where uncertainty itself is expressedas a standard deviation. In the recent years, thisapproach has been more and more questioned, sinceits application may become quite troublesome whenthe uncertainty of measurement based on complexDSP algorithms has to be estimated.

Several proposals are available in the recent liter-ature to overcome this kind of problems. Some ofthem are still based on a probabilistic approach[55–58], while some others are looking for different,innovative mathematical approaches, such as thetheory of evidence and the fuzzy mathematics [59–61].

Moreover, the use of distributed measurementsystems is also posing a number of new problems,related to the synchronization requirements betweenthe different remote units of the system [62].

All the mentioned approaches are too complex tobe considered in this short survey. It is howeverworth while to note that the research activity inthe measurement field is eagerly considering thepower-quality measurement problems and the char-acterization of the power-quality instruments as achallenging problem, and several answers havealready been provided.

5. Conclusions

The considerations reported in the above sectionsallow for drawing a few conclusions about the pres-ent achievements and the future trends in the field ofpower-quality monitoring.

• The theoretical background is wide enough toallow a good analysis of the power quality inthe presence of non-sinusoidal conditions,although a generally accepted approach fordescribing the behaviour of the electric systemsunder non-sinusoidal conditions has not yet beendeveloped.

• Several indices have been proposed to detect thedeviations from the reference ideal conditionsthat lead to power-quality problems.

• The analysis of the direction of the active powercomponents associated with the harmonic andsequence components of voltages and currentshas been proposed as the most effective tool forthe identification of the sources producing distor-tion and unbalance.

• The use of a single index was proved to be notsufficient for power-quality assessment. The mostrecent developments of the research activity areoriented towards the use of indices obtained frommulti-point measurements performed in differentmetering sections of the electric system.

• The presently available digital instrumentation,including the new generation of electronic volt-age and current transducers, is suitable for mea-suring the newly defined quantities and indiceswith good accuracy and at a reasonable cost.

• The true present challenge is making the mea-surement uncertainty evaluation of the DSP-based instrument less troublesome than it pres-ently appears if the recommendations of theISO Guide [41] are strictly applied.

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