201: Voltage Measurement

Halit ErenCurtin University 01 Technology, Perth, Western Australia, Australia

1 INTRODUCTION

The output signal fonTI to be measured in the majority ofsensors will require the measurement of either a voltage(this article), a current (Artide 202, CorreDi Measure-meni, Volume 3), or a resistancelimpedance (Artide 203,Resistance Measurement, Volume 3). Thus, their expla-nation is fundamental to most measurements.

So far as voltage measuring devices are concerned, volt-age measurement can be classified as

1. low-voltage measurements, such as those generated by

sensors;2. medium-voltage measurements, such as those that

exist in the power mains, laboratories, and industriaIoperations;

3. bigh-voltage measurements, sue h as a rise in power

generators, transmission lines. and with plasma effects.

- , ;"./ ' 'èi~~! ,.Handbook 01 Measuring System Design. edited by Peter H. Sydenham and Ricbard 'l'borA, . .. ,'.;:;

e 2005 Jobo Wiley & Soo8. Ltd. ISBN: 0-470-02143-8. ' ,,' .

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Consequently, there is a wide range of voltage measuringtechniques and devices in use. This article concentrates onmedium-voltage and high-voltage measurements.

Low-voltage measurements for sensors require sophisti-cated signal processing schemes - see Artide 121, Signalsin the Presence or Noise, Volume 2; Artide 176, Signalsand Signal-to-noise Ratio, Volume 3; Artide 178, NoiseMatching and Preamplifier Selection, Volume 3; Arti-de 179, Input Connections; Grounding and Shielding,Volume 3; and Artide 181, Amplitude Modulated Sig-nals: The Lock-in Amplifier, Volume 3.

Common to alI techniques are three major aspects thatcharacterize the measurements:

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1. Amplitude: li the voltage is smaller than a few milli-volts. we may'òeed to use suitable electronic compo-nents to amplify the' signals. li the voltage is large. inthe kilovolts and megavolts region. we may need toattenuate the magnitude in order to bring it to manage-able levels.

2. Frequency: The frequency of a voltage signal plays animportant role in configuring the appropriate compo-nents of a voltage measuring device. The frequencyof interest can range from DC to a few gigahertz.If digital techniques of measuring afe used. samplingof the voltage signals must conCorro to the Nyquistsampling criteria. The signal frequency waveform alsoneeds careful consideration test errors be generated.

3. Duration: The duration of a signal is significant indeterrnining the appropriate technique to use for themeasurement. Duration may vary from continuous sig-nals; as in the case of power supplies. to impulsesappearing for a few microseconds; as in the cases ofsurges. and corona effects in power transmission anddistribution.

1354 Common Measurands ..~,'.J~.!

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2 BASIC THEORY

Voltage measurement is essential in electrical engineeringas well as in many other disciplines of engineering andscience. Voltage measurement involves determination ofthe electric potential difference between two points. Thepotential difference is the amount of work needed to movea unit charge located in an electric field from a referencepoint to another point. Hence, the potenti al difference isalways relative to some reference point such as the Earth.

The potential difference is taken as the work per unitcharge and the volt is related to the unit of work (joule -J) and the unit of charge (coulomb - C) by

lvolt = ljou1ecou1omb (1)

Although the concepì of electric potential is useful inunderstanding electrical phenomena, it is worth I\Oting thatonly the differences in potential energy are measurable.Therefore, it is commonly understood that the term voltagerefers to potential differences. The measurement unit farthe voltage is, in the International System of Units (SI), thevolt (symbol: V).

Measurement of voltage is of utmost importance andextensively used in the electrical and electronic engineering,especia1ly in the power industry. Moreover, when electronicdevices far signal processing are involved, such as thoseused in telecommunication systerns, control systems, andinformatics, the majority of signals are in the voltage andcurrent formo Therefore, voltage measurement constitutesan important area in industriai and scientific measurements,and in a diverse range of sensors of chemical, biological,and physical variables.

3 MEASURING NETWORKS

Since most common signals afe in voltage fonTI, there afemany different techniques for processing the signals gen-erated by a particular variable. However, some instrumentscalled voltmeters afe deliberately designed to measure volt-ages. There are five common types of voltmeters; these are

1. electromechanical instruments,2. thennal type instruments,3. electronic instruments,4. Cathode Ray Oscilloscopes (CRO) or vacuum tube

instruments (VTI),5. virtual instruments.

1. Electromechanical instruments: These instruments afe

based on the mechanical interaction between variouscurrents. between currents and magnetic fieJds. or

between eIectri~ed conductors. Such interactions

generate mechamcal torque proportional to the voltage

or to the square of the voltage under investigation.

The generated torque is then balanced by a restraining

torque, usually obtained by the use of suitably arrange4

mechanical springs. The balancing action causes the

instrument pointer to be dispiaced by an angle

proportional to the driving torque, and hence indicates

the voltage to be measured. The value of the input

voltage is therefore given by the reading of the pointer

dispiacement on a graduated scale.

Thermal type instruments: These instruments afe based

on the thermal effects of a current ftowing in a con-

ductor. The reading is proportional to the square of the

input voltage. These instruments afe not used as wideIy

as the others bui afe suitabie for high frequency voltage

measurement.

Electronic instruments: These

on pureIy eIectronic circuits, and attain the required

measurement by processing the input signal by means

of eIectronic semiconductor devices. The method

employed to process the input signal can be ei' .

analog or digital. In the first case, analog electr<.

instruments are obtained, while in the second .

digital eIectronic instruments afe obtained.Oscilloscopes or vacuum tube instruments: These .'"

truments afe basically voltrneters, and their main

acteristic is to allow a graphic representation,

Cathode Ray Tubes (CRTs), or liquid crystal dispia

(LCDs). The time and amplitude characteristics of

signal can be determined directly from the dispi

signal.

Vlrtual instruments: These afe computer-based

that can be programmed to function Iike voI

ammeters, oscilloscopes, spectrum analyzers,

so OD. They afe equipped with AnaIog-Di

Analog, converters - see Artide 139, Analog

Digital (A/D) Converters, Volume 3 and Artide

Digital-to-Analog (DIA) Converters, Volume 3

afe supported with software programs such

the LabView from National Instruments-

Artide 105, Modeling with LabVIEWT>l, Volume

and Artide 106, Virtual Instrumentation in Ph.

Volume 2.

These five basic types of voltrneters can be used for lo

voltage, medium-voltage, and high-voltage measure

In some cases, suitabie arrangements such as amplifi

attenuation, and conversions may be necessary to '

the signals for measurement.

In addition, the voltage, current, resistance

can be made by a single instrument termed as multimet~

2.

3.

4.

5.

or volt-ohm-multimeters(VOMs). The VOM is a combi-nation of the necessary circuits of a DC ammeter, DCvoltmeter, AC ammeter, AC voltmeter, and a multirangeohmD1eter. The typical DC voltage range of a commonVOM is O to lOOOV, although with extemaI resistor net-works and voltage transformers, the range can be increasedfurther, to say 5000 V. The DC current range is usua11ylO A but with the use of externa1 resistive shunt networks,or current transformers the range can be extended to muchhigher levels.

Particularly in power generation and transmission net-works, precise, and adequate system measurements at thecontrai centers are criticai far high quality of operationaIdecision making. The measurements talcing piace in remotelocations are made available to the controllers by networkssuch as the Rea! TIme Supervisory Control and Data Acqui-sition systems SCADA. The digital devices that collect thevoltage measurements from the substation instruments andtransducers afe called remote terminaI units (RTUs). TheRTIJs communicate with the SCADA aver dedicated tele-phone lines, sometimes the transmission line itself and/ormicrowave channels.

The collection of anaIog measurements and the status ofthe circuit breakers from remotely monitored and controlledsubstations are telemetered by means of the cyclic scans ofSCADA system. TypicaIly, each scan lasts from 1 sto tOsoThis information has to be sufficient in number and evenlydistributed across the network so that the observability ofthe system can be ensured.

4 VOLTAGE TRANSFORMERS

Transformers afe extensively used in high-voltage measure-ments primarily to step the voltage down to a lower levelthat can be less expensively measured.

Transfonners are devices tbat change tbc voltage levelin tbe process of energy transfer from ODe AC systemto another. The transfonner has two coils, primary andsecondary, botb of which are wound on an iron core asshown in Figure l.

Tbe magnetic ftux generated by tbe primary current linkstbe secondary windings to generate a secondary voltage.Assuming 100% magnetic coupling, tbe ratio of tbe primaryvoltage (VI) and secondary voltage (V2) can be expressedby tbe turns ratio NI and N2 as

VI - N) (2)V2 - N2

This means the secondary voltage can be stepped up ordown depending on the turos carlo. For example, if N l is

Voltage Measurement 1355

Figure 1. Transformer conStructioD.

lO times greater tban N2' tbe secondary voltage is lO timessmaller tban primary voltage.

Voltage measurement instruments afe used throughouttbe electric power system for monitoring and control pur-poses. Instrurnentation components required to accomplishtbe measurements are tbe transducers, signal condition-ers, and tbe analysis and monitoring equipment. Voltagetransducers convert tbe system voltage to an acceptablelevel needed as tbe input to tbe signal conditioning equip-mento The transducers are required to produce a scaleddown replica of tbe input voltage to the accuracy expectedfor a particular measurement. Commonly used transduc-ers afe electromagn~tic voltage transformer (VT), capac-itive voltage transfonner (CVf), and tbe cascade volt-age transfonner.

Voltage measurement transfonners need to be speciallydesigned to ensure tbe ratio is constant. Voltage transform-ers are much like small power transformers but tbey neroto operate witb secondary winding operating close to opencircuito The winding voltage drops are made small, and tberated ftux density in tbe core is designed to be well belowsaturation density. These conditions maintain tbe calibratedvoltage ratio.

Measuring very high frequency components in tbe volt-age requires eitber a capaciti ve divider, or pure resistivedivider. Special-purpose capacitor dividers can be obtainedfor accurate characterization of transients and hannonics upto at least l MHz. A disadvantage of such dividers is tbattbey do not provide electrical isolation between tbe highvoltage and tbe measuring systems and so impose specialconditions for tbeir use.

The cost of tbc electromagnetic VT tends to increaseat an exponential rate witb tbe rated voltage increase. An

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alternative, more economie solution has been found in theCVT. This combines a capacitive potential divider with anauxiliary electromagnetic voltage transformer. This com-bination enables the insulation requirements of the electro-magnetic unit to be reduced with associated savings in costo

The CVT was developed to reduce the high così ofconventional VT by compromising on the frequency andtransient response. Another possible solution to the problemis to use the cascade VT that is formed by connectingtWo or more electromagnetic transformer units in cascade.The primary windings of these transformers are connectedin series and in this way the primary voltage is brokendown in several distinct and separate stages. This sol vesthe insulation problem and reduces costs. The secondarywinding consists of a single winding on the last stage only.

Optical voltage sensors afe also under development asreplacements for VTs. They lower the costs compared toconventional CTs and VTs when mass produced.jIowever,questions remain about their stability, sensitivity, and lin-earity. The sensitivity of the optical sensors to vibration and . . '" . .' ,.

temperatureeh t be .. . edb ' th d . battery emf, R IS the regulatrng reslstance; I IS the slide~.anges mus ID1D1ID1Z y el er eslgn or. . . . .

signal processing. The long-term stability of these sensors Wlre c~nt at bal~ce c~ndiUon~; r ~s the reslstance '"

is under study in field trials, but techniques for calibrat- per urnt length of.slide-wlre; E) IS the battery ernf to ,::ing them in the field and in the test laboratory bave yet to be measored; ~2 IS ~e emf of standar~. batte~; l) is :;

be developed, the len.gth of slide-wlre ~t bal~e conditions Wl~ ~~.:.An important branch of voltage measurement is the deter- E! ; 12 IS the length of slide-wlre at balance COndltiO~ ..

mination of harmonics of such pararneters as the fundamen- Wlth standard ernf E2.

tal power-frequency voltage, voltage dips, spikes, sorgesti.,and sags, and other transient behaviors. A battery of unknown emf E1 is inserted in the circui~

Specific reasons for taking harmonic measurements in- at a point shown in Figure 2. The galvanometer switch S is,"elude confirming the presence of harmonics, evaluating the elosed and the contact B moved along the slide-wire unti1%severity of the problem relative to acceptable limits, estab- the balance condition (zero reading on the galvanomete'i' c,

lishing compliance with standards and guidelines, harmonic is achieved. In this condition, no current ftows through th~,filter design, providing input data for harmonic software galvanometer circuito The current j supplied by battery E'\analysis program, and designing an analytical model of ftows tbrough the slide-wire. By Ohm's Law: ,"

the problem.Instruments and systems for power quality measurements

can help identify the sources of power quality degradationand protect customer equipment. Many power quality mon-itoring instruments are designed for input voltages up to600 V rms and current inputs up to 5 A rms. In measure-ments, appropriate voltage transducers must be selected toprovide these signal levels. ,

5 POTENTIOMETERS

There afe many applications in which voltage measure-ments must be performed without drawing any current fromthe circuit to which the measurement device is connected.A typical case is the measurement of the electromotive LC2jrocce (emf), or no-load voltage, of a source with high inter-naI resistance. Figure 2. Slide-wire potentiometer.

1356 Common Measurands;~ -,,",,;iti

AD important device that is capable of measuring volt-ages without drawing currents is the potentiometei. Thisdevice is not actually an instrument. but a set of electri-cal networks that afe suitably arranged for the purpose.This arrangement also inciudes a galvanometer or indica-toro The main purpose of the potentiometer is to perforroan accurate comparison of an unknown emf against a stan-dard oDe. There afe many different types of potentiometersthat can suit the requirements of a particular measurement,such as the slide-wire De, slide-wire AC, Gall- TinsleyAC, and Drysdale- Tmsley AC Potentiometers. Owing tolimited space. as an example. only the slide-wire DC poten-tiometer will be explained bere.

1. The slide-wire DC potentiometer: The principle ofoperation of a slide-wire potentiometer can bestbe described by the slide-wire variety illustratedin Figure 2. The description of the various tennsemployed in this figure is as follows: E is the supply

EI = irll

-

Single-phase voItage controllar1.0

With purely resistive load, from (6), the rms value outputvoltage can be determined to be

/1 Ot sin2aV. =v. ---+- (7)o,. 111 2 21Z' 41Z'

Equation (7) indicates that the output voltage is a functionof the firing angle of the thyristors. The nonnalized nns loadvoltage versus firing angle far a single-phase controller isillustrated in Figure 4.

7 RECTIFIERS

For AC measurements, most instruments contain AC-to-DC conversion (or rectificatiòn), which afe made fromgermanium or silicon diodes so that the voltages can beexpressed in rms values. Depending on the signals, therectification can be performed by transistor or operationalamplifier circuits or by the SCRs.

AC/DC converters (rectifiers) operate on similar prin-ciples as the voltage controllers. These rectifiers can beconfigured in uncontrolled, semicontrolled, or fully con-trolled forms. Some of the configurations afe

. single-phase half-wave rectifiers,

. single-phase full-wave rectifiers,

. polyphase half-wave rectifiers,

. polyphase full-wave rectifiers.

Rectifiers can be configured by using center-tapped trans-former arrangements or by bridge forms. Since there afe avariety of techniques available, bere, as an example, we will

The DC average value is then

l 1"+. 2VVi) = - Vm sin(wt) d(wt) = -2!. cosa

K a K

The amplitude of the AC terms can be calculated from

v" = J a: + b2.

where

2Vma =-Il 11:

b = 2V",Il 11:

[cos<n + 1)(1- cos(n - 1)(1

]n+l n-l

[Sin(n + l)a - sin(n -l)a] for n = 2,4,6...

n+l n-l

The Fourier series for the current is determined by super-position

where

The outputs of the controlled rectifiers can be improved bysuitable arrangements of capacitive-inductive (L-C) filterS..;

tbe moving-coil electromagnetic volbneters (D'Arson-vaI GaIvanometer);the moving-iron electromagnetic voltmeters;the electrodynamic voltmeters;the electrostatic voltmeters;electromechanicaI multimeters or VOMs.

Figure 6. Schernatic of a spring control1ed voltage indicator.

Voltage Measuremem 1359

The spring has a large number of turns greatly reduc-ing the deformation per unit length and giving an angleof deftection (9) directly proportional to the deftectingtorque. Occasionally. a long helical SPrÌng replaces thespiraI spring. In some instrurnents. a single strip of phos-phor-bronze provides tbe necessary spfing control. Oftentwo springs. wound in opposite directions are employed.This method is employed in order to reduce the read-ing errors.

Although tbe electromechanical instruments represent0100 tecbnology in comparison to tbe electronic techniques.and the digital ones. in particular. they are stilI extensivelyused in many areas such as Panel displays in industry.dashboard displays in motor vehicles. general-purpose lowcost measurements and laboratories.

9 DIGITAL VOLTMETERS

The basic structure of a digital voltmeter (DVM) consistsof the following three main stages:

I. analog signal processing,2. analog-to-digital (AID) converter,3. digital signal processor (DSP).

The first stage of the device conditions the input signal,adapting it to the dynamics of the AID. The AID converteris responsible for sampling of the input signal and convert-ing each sampled value into a digital formo The sequenceof digital values obtained~after the sampling and conver-sion operations is stored into the memory of the DSP andprocessed in order to attain the desired measured values.The detailed structure of a digital multimeter is given inFigure 7.

9 DIGITAL VOLTMETERS

I

1360 Common Measurands

o

Figure 7. Block diagram of a typical digital multimeter.

DVMs may differ from each other in the following ways:

number of measurement ranges,number of digits,

.

....accuracy,speed of readings,

operating principles.

In a modero DVM, the basic measurement ranges toobtain fun-scale vaIues are as low as 0.111 V. If an appro-priate voltage divider is used, it is aIso possible to obtainfun-scale vaIues as high as lOOOV. The DVM, with a suit-able input stage, can be used as an ammette having verybroad measurement ranges from I nA to lO A.

When the measurement result is displayed on the instru-ment front panel, it is usualIy presented in decimaI numbers,with a number of digits that typica11y range from 3 to 6.When the measurement result is sent to a DSP system,its representation takes the form of a binary-coded outputsignaI. The number of bits of this representation typicaIlyranges from 8 to 16, though 18-bit and 24-bit AID convert-ers are available.

The accuracy of a DVM is usuaIly coITelated to its reso-lution. This is quite obvious, since assigning an uncertaintylower than 0.1 % of the range to a three-digit DVM makesno sense, since this is the displayed resolution of the instru-mento Similarly, a poorer accuracy makes the three-digitresolution quite useless. Presently, a six-digit DVM canfeature an uncertainty, for short periods of time in con-troned environment, as low as the 0.0015% of reading or0.0002% of the full range.

The spero of reading of a DVM can be as high as1000 readings per secondo When the AID conversion isconsidered, the conversion rate is taken into account insteadof the speed of reading. Presently, the conversion rate for12-bit, successive approximation AID can be as high asnominalIy lO MHz. The conversion rate can be on theorder of 1 GHz for lower resolutions when flash AID

~J---K:> ..!lQ.

RIV

converters afe used - see Artide 139, Analog-to-Digital(AID) Converters, Volume 3.

lO VOLTAGE AND VOLTAGEMEASUREMENT STANDARDS

Voltage is an important property in electrica! engineeringand measurement technology. Hence. strict standards afédeveloped in two major areas:

l.

2.

by its own standards suchstandard - see Artide 43,

techniques afe standardized. t~:suit specific areas of application, such as the IEEE S~1122 for digital recorders, IEC 60060 for high-voltagl:impulse calibrations.

The primary voltage standard is, today, the Josephso~junction standard. Other voltage standards are nevertheles~'employed in the metrologicallaboratories as they afe mo~convenient and, far example, afe the lime honored standar~:cells, although their accuracy is lower than that of th~

Josephson junction. .The Josephson junction standard describes the quantum

standard of voltage. A Josephson junction consists of tW°o

super conductors separated by a thin insulation barrier:The junction is supercooled in belium cryostat and whelf'it is irradiated by microwave energy (in the frequencyrange 10-100 GHz), the voltage-current characteristics get~broken to the stepped formo The height of each voltage stepcan be found from ...

(12):

where h is the Plank constant, f is the frequency at wbicbthe junction is irradiated, and e is the electron charge. . .<

..

. The standard cells are made from saturated electrochem-ical Weston cells, which consist of electrodes of mercury(positive) and mercury cadmium amalgam (negative) placedin an electrolyte of saturated cadmium sulfate solution con-tained in an H-shaped glass container. There afe two typesof Weston cells - the saturated celI and the unsaturated celI.

The saturated celI has a voltage variation of approx-imately -40 ~ V per 1 K, whereas the unsaturated celIhas a negligible temperature coefficient at normal roomtemperatures. .

By using precision potentiometers, the standard-cell volt-age can be compared with better than 1 part in 107 accuracy.However, the saturated cells afe very sensitive to environ-menta! conditions and the current they supply introducesfurther uncertainty in calibrations.

The various national standard IAboratories refer to theJosephson junction standard as their primary standard forvoltage. However, since the standard cells are much easierto employ, they also maintain a number of saturated cells,referred to by the Josephson junction standard, as theprimary standards for voltage. Cells afe kept in an oH bathto control their temperature within :i:0.01 K. The voltageof the Weston saturated celI at 293.5 K is 1.01858 V. Theyremain satisfactory as voltage standards for a period of 15to 20years with a drift voltage of about 1 ~V per year.

Electronic voltage standards, also known as the trans-fer standards, afe based on electronic components such asdiodes. When the voltage across a diode rises above a cer-tain level, a current starts ftowing (e.g. Zener breakdown)through it and the diode acts as a constant voltage device.When these diodes afe fed by well-stabilized sources, theycan provide a reference voltage that is stable by l partin l rI'. Ofren, they are used together with other electronic

components such as transistors, operational amplifiers, andintegrated circuits for stability and compensation of theenvironrnental factors like temperature. They afe widely

used sioce they afe oot affected by environmental coodi-tioos, as is the case with standard censo

Numerous standards define the procedures and methodsfor voltage determinatioos, particularly in power circuits.Some of these standards afe -uncertainty. IEC Std 60060-2 standard for high-voltage impulse

calibrations;. IEEE Std 519-1992 standard for harmonic control in

electrical power systems;. IEEE Std 4-1995 standard for high-voltage testing;. IEEE Std 181-2003 standard for transition. pulses, and

related waveforms;. IEEE Std 1122 standard for digital reeorders used with

measurements in high-voltage impulse tests;. IEEE Std 1451-1999 standard for smart sensors;. IEEE Std 1459-2000 standard for the Measurement of

Electric Power Quantities Under Sinusoidal, Nonsinu-soidal, Balanced, or Unbalanced Conditions.

FURTHER READING

Dyer. S.A. (ed) (2001) Instruments. Survey oflnstrumentation andMeasurement. Wiley. New York.

Eren, H. (2002) Analogue and Discrete InputlOutput, Costs, andSignal Processing, Chapter 1.9, in lnstrumentation EngineersHandbook, 4th edn (ed. B. Liptak), CRC Press, Boca Raton,FL (pp. 123-141).

&eo, H. (2003) Electronic Portable Instrument s- Design andApplications, CRC Press, LLC, Boca Ratoo, FL.

&en, H. and Fernro, A. (2003) Galvanometers and Electrome-chanical Voltmeters entI Ammeters in Encyclopedia oJ LiJe Sup-pOrI Systems. EOLSSIID{ESCO, URL: http://www.eolss.netlE6-39A-toc.aspx. "I

Eren, H. and Ferraro, A. (2003) Electronic Voltmeters and Amme-ters in Encyclopedia 01 Lile Support Systems, EDLSSIUNES-eD, URL: http://www.eolss.netlE6-39A-toc.aspx.

Hoeschelle, D.F. (1994) Analog-to-Digital and Digital-to-AnalogConversion Techniques, ISBN: 0-4715-7147-4 Wiley, NewYork.

SchIabbach, J. (2001) Voltage Quality in Electrical Power Sys-tems, ISBN: 0-8529-6975-9, IEE, Stevenage.

Webster, J.G. (ed) (1999) The Measurements,/nstnunentation andSensors Handboo/c, ISBN: 0-8493-8347-1, CRC, IEEE Press,New York.

202: Curreot Measuremeot

Halit ErenCurtin University oJ Technology, Perth,

J . ". I.~:, ..~. .

1 Introduction2 Basic Theory3 Measuring Networks4 Current Transducers5 Current Shunts6 Converters7 Rectifiers8 Indicators

9 Digital InstrumentsIO Standards

Furtber Reading

INTRODUCTION

KnowIedge of the voltage Iocated at the terminaI of eachcircuit element as well as the current ftowing in eachelement gives full knowIedge of the circuit behavior. More-over, when eIectronic devices for signal processing areinvolved, such as those used in measuring systems, telecom-munication systems, control systems, and informatics, themajority of involved signals afe in the voltage and currentforms. Therefore, the voltage and CUITent measurementsconstitute an important area in industriaI and Iaboratorymeasurements, sensors, and systems.

Electrical CUITents can be measured in many differentways. Once the current is converted to voltage form, theoscilloscope (strictly a voltage measuring device) is a typ-ical device that can be used to measure currents. There afe

many analog and digital ammeters and multimeters that areoffered by many vendors. In some applications, special cur-renI measurement techniques may bave to be designed by

Handbook oJ Meosuring System Design, edited by Peter H.e 2005 John Wiley & Sons, Ltd. ISBN: 0-470-02143-8.

1

.

Western Australia, Australia

using carefully selected transducers to meet the particul~,characteristics and specifications of the processo In this arti-

",lde, the operation of ammeters and multimeters is explained,current transducers afe discussed, and examples afe give,!:"

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2 BASIC THEORY

A charged body in an electric field is subject to a force.'!f'the body is not restrained, it will start moving in the electlC-'field. The result of the movement of charged bodies fròhl;ODe point to another point in the space is the electric curreqiCIn the metallic conductors used in the electric circuits,ffi~,;,charged bodies that can llow through the conductors' a1~.,the electrons. A basic property of an electron is its chargei(1.603 x 10-19 C). 1\".

Electric eurrent is the rate of eharge llowing in a eroseetion of the eondueting element in a second ancbi 'l'' measurement unit is, in the SI, the ampere (symbol: A).<)

Sinee the current is taken as the eharge llow per UDÌtLlime. ils measurement unit is related to Ibe uoil of C""

.,..I

. .'~.".. ..' and the unit of rime (second s) by~1~:

1 ampere = 1 coulombjsecond (1)1",~,

A current will flow in any medium in which there aree fr~'\charges to move. These conduction charges may be el~;-:',,,"-trons, positively charged 'holes', or positive or negativ~~ions, depen~ing on the ~ate~al. They afe in cont~uoN~;i'random mobon and collide wlth each other and Wlth m~,

atomic structure of the material. When a conducting ma~riaI is placed in an electric field, the conducting chargèfare accelerated in the direction of the field. The velocity:acquired is small compared with the average value of~random velocity (typically in the arder of 106 m çl). .;ì~

Sydenham and Richard Thorn.

.. .. ...

~

~ "",."c,.. "'..CU.uucrncnl .I.:JO.)

: The correDI ftowing through a circuit element is relatedto tbe properties of tbe circuit element and to tbe vol.

ss its terminals by tbe well-known Ohm's law:

V=Rl (2)

. where R is a quantity representing tbe electric bebavior of

me circuit elemento Under DC cooditions this quantity iacalled resistance and its measurernent uniI is, in tbc SI, tbe

I,

'obm (O)." In mogI of tbc usually met applications of electrical

, ìmd electronic engineering, voltages and currents exist in

continuous forms. This means tbat a generic voltage v and, a generic corrent ; can be represented as functions of Urne ,:

v = ve,) and ; = jet) (3)

,In tbc DC systems, voltages and correDI! are constant, tbatis

v = v(t) = Voc, const. and ; = jet) = IOCt const.

. ~)The voltmeters and ammeters for DC systerns afe realizcdin order to measure Voc and loc respectively.

In AC systems, the voltage and current are defined witb, . respect to time as

~t v(t) = Vmax sin(CL!t + a) (5),l"

. where V max is tbe maximal value of tbc sinusoidal voltageand a is tbe phase angle of tbe voltage:

; (t) = lmax sin(CL!t + fJ) (6)

where lmax is tbe maximal value of tbe sinusoidal current, and fJ is the phase angle of the current. CL! represents angular

. frequency and t is tirne in (5) and (6). Quantities tbat afe~ used to characterize sinusoidal voltage and corrent afe

I

.

,~II..,=

v=

1363

1 (TT lo ;(1)2 dt = (8)-]./2JDaX

where T is tbe periodo -In tbe case of a circuit containing only a resistive load, tbe

single frequency current wave is entirely symmetrical witbtbe voltage wave. Tbe current wave lags behind tbe voltagewave in tbe case of inductive loads. In a purely capacitiveload. tbe current wave leads tbe voltage wave. In generaI,circuits contain elements of resistance, inductance, andcapacitance in varying amounts and tbey must, tberefore,assume some intermediate condition of phase ansie betweenvoltage and current.

Ammeters far AC systems afe realized primarily byusing AC-to-OC conversion techniques or by using suit-able transducers, botb of which will be explained in tbefollowing sections.

Different kinds of signals, such as pulse, random, anddiscrete signals can also be found in nature, especially attbe atomic scale. Such signals, however, require measure-ment witb different kinds of instruments, which are notcovered bere.

3 MEASURING NETWORKS

Tbere exists a diverse range of metbods and instrumentsavailable far current measurements, and some of tbese afe

. electromechanìcal ammeters

. tbermal type ammeter,

. multimeters

. oscilloscopes

. virtual instruments.

Electromechanical ammeters provide readings in analogform by moving a pointer tbat indicates tbe measuredvalue on a scale. The scale is a linear scale if tbe pointerdisplacement is proportional to tbe measured quantity. Tbeenergy required to dispiace the pointer is taken direcdyfrom tbe circuit to which the instrument is connected. Thisenergy is tbe so-called instrument self-consumption and,in electromechanical instruments, can be nonnegligible.Electromechanical ammeters can be c1assified according totbeir deftecting movements as

I. moving-iron electromagnetic ammeters,2. electrodynamic ammeters,3. moving-coil electromagnetic ammeters (D'Arsonval

galvanometers),4. electromechanical multimeters or VOM.

(2)

(3)

3

(5)

'...'

I-"

..

-"

(6)

(1)

(D'Arsonval

~

Although electromechanical ammeters stili find extensiveapplications, they are not used as much as their elec-tronic counterparts, so they will not be explained further.However, because of its special features, the D'Arsonvalgalvanometers will be visited in Section 8 of this artic1e.

Thermal type ammeters are based on the thermal effectproduced by a corrent ftowing in a conductor. These amme-ters are also known as the thermo-instruments or true rmsdevices. Irrespective of the shape of the input signal wave-Corro, the active power dissipated in the heated conductoris equal to the heat generated and is proportional to the truerms value of the input current.

A simplified construction of this kind of ammeters, alsocalled the 'hot-wire instrument' is shown in Figure 1. Theheated element has a negligible temperature coefficient ofresistance (that is, its resistance will remain essentially con-stant over its operating range) and a constant temperaturecoefficient of expansion. Since the heating effect is pro-portional to the square of the current, àccurate effective(rrns) values of AC currents afe measurable irrespectiveof frequency and waveform. Also, since no magnetism isinvolved in providing scale deftection, stray magnetic fieldsbave no effect on the operation.

The hot-wire element is made of platinum-iridium, whichhas a constant resistance and temperature coefficient ofexpansion over its operating range. The element is about0.1 mm in diameter. Platinum-iridium has the added ben-efit of being able to withstand high temperatures withoutoxidation. Attached to the hot wire is a phosphor-bronze'magnifying' wire. A silk thread, connected to the magni-fying wire, passes around a pulley before being tìxed to aspring, which keeps the system under tension. When the

Figure 1. A hot-wire voltmeter.

hot-wire element expands, its slack and that in the magifying wire is taken up by the tension in the spring and tsilk thread causing the pulley to rotate and the pointerdeftect on the scale.

Multimeters are instruments that can measure voltaglcurrents, and resistances. These instruments afe also knO\as volt-ohm-multimeters (VOMs). The VOM is a combÙJtion of a DC ammeter, a DC voltmeter, an AC anuneter,AC voltmeter, and a multirange ohmmeter with a switcbselect the ODe to use. The DC voltage range of a COtnm.VOM is O to lOOOV, although with an external resistor trange can be increased to 5000 V. The DC current rangeusua11y up to lO A, although with an external sbunt it cbe extended to 20 A or more.

For AC measurements, the instrument contains a rectifing circuit made from germanium or silicon diodes. Becauof the inertia of the moving coil, the meter indicates a stealdeftection proportional to the average value of the CurrelSince AC currents and voltages afe expressed in rms valU(the meter is scaled to read the nns values of sinusoidal voages through the form factor 1r /2./2. The indicated readilof a nonsinusoidal voltage may be erroneous, since its av(age value may differ considerably from the average ValIof a pure sinusoidal voltage.

Owing to the fact that tbe internai structure of tiVOM cannot be optimized for a single measurement, titemperature and frequency ranges can be limiting factolFor example, a deterioration of 0.5% in the readings m.be expected for every l-kHz rise in frequency.

Further information on multimeters is providedSection 8.

Qscilloscopes are probably the most versatile instrments for ali forms of pbysical investigation, since a1mcany physical phenomenon can be converted into a corrsponding electric voltage and the oscilloscope makes tJwavefonn versus time visible for buman observation. Mesurements afe performed on the borizontal axis and verticaxis since the screen features a graduated grido Nowadaydigital storage oscilloscopes DSO are commonly usedvoltage and current measurements. They sample the inpsignal and convert it into a sequence of data. whicb astored in the DSO memory and displayed on cathode-ntubes CRT or liquid-crystal displays (LCD). A typical stnJtUTe of a digital oscilloscope is shown in Figure 2.

Virtual instruments use computers, interface electronicand software to emulate the operational features of motraditional instruments. In this technology, plug-in daacquisition (DAQ) boards, PCMIA cards, and parallel poUO devices are used to interface sensors and transduceof the system under investigation with computers. ODIthe signal is interfaced, the computer can be programm(to act just lite a stand-alone instrument; but it can al!

I

,,:

~ ;~.': ~'J"

.~,?f.

::l

;~

,

in

CURRENTTRANSDUCERS

Current transformers (CT),HalI-effect transducers, and.

~

Current Measurement 1365

Dataout

. Rogowski Coils,

. optical current transducers (0CTs), and

. current shunts (explained in detail in Section 4).

Current transformers bave two windings, designated asprimary and secondary, which afe insulated from eachother. The pJimary winding is connected in series with thecircuit carrying th~ line current to be measured, and the sec-ondary winding is"i; connected to instruments or protectivedevices. The secondary winding supplies a secondary cur-rent in direct proportion to the primary current aImost with-out any difference in phase angle. Hence, the CT transformsline current into values suitable for measuring instruments,meters, protective relays, and other similar apparatus. CTalso isolates the instruments and the relays from line volt-ages. The four common types of CT design are

. wound type

. bar type

. window type

. bushing type.

The current in any system changes more often and withgreater magnitude than the voltage. Hence, selecting propertransducer for currents could be difficult. The right CTcurrent rating and tums ratio to be used depends on themeasurement objective.

In the case of disturbance recorders or protective devices,where fault or inrush currents afe of concem, the CT

~

must be sized in the range of 20 to 30 times of normalload current. This will result in low resolution of theload currents and inability to accurately characterize loadcurrent harmonics.

Conventional current transformers afe designed to oper-ate within a frequency range from 15 to 100Hz. With theneed to measure harmonic content of the primary current,the frequency response of current transformers is essen-tial to the measurement processo The frequency response ofcurrent transformers is e"ffectively determined by the capac-itance present in the transformer and its relationship withthe transformer inductance. The standard metering class CTis generally adequate for frequencies up to 2 kHz. Phaseangle shift between primary and secondary currents maystart to become significant when the frequency is close to2 kHz. For higher frequencies than 2 kHz, a window-typeCf with a high ratio should be used. Desirable attributesfor a CT, when harmonics are measured, include large ratio,small remanent flux, large core area (the mor~ steel usedin the core, the better the frequency response of the Cf),secondary winding resistance and leakage impedance (assmall as possible).

Rogowski Coi/s afe more specialized transducers usuallyused for the measurements of very large currents, whichlast for a very short duration (hundreds of kiloamperes inless than a microsecond). The Rogowski Colli is a solenoidair core winding of a small cross-section looped around aconductor carrying the large primary current. The voltageinduced on the terrninals of the coil is proportional to thederivative of the primary transient current and number ofturns. The coil is connected to an integrator. Integratedinduced voltage gives a measure of the current in theprimary conductor. The Rogowski Coils bave the advan-tage of being free from saturation problems and bave fastresponse tinte.

Hall-effect sensors operate on voltage difference acrossa thin conductor carrying current. The current depends onthe intensity of the magnetic field applied perpendicularto the direction of current flow, as shown in Figure 3.AD electron moving through a magnetic field experiencesLorentz rocce perpendicular to the direction of motion andto the direction of the field. The response of electrons to the

eml t

A Hall-effect sensor.

.Lorentz force creates a voltage known as tbe Hall Voltage.If a current l ftows through tbe sensor. tbe Hall voltage canmatbematically be found by

v = RH! H/t (9),

where RH is the Hall coefficient (cubic meters per degree ofCelsius), B is the flux density (Tesla), and t is the thickness,of the sensor (meters). .'.'

The value of RH depends on the material used, tem::.perature, and field magnitude. Its characteristics can 00.control1ed to a certain extent by doping the base mate-~riai with some impurities. For example, doping gennaniW:

,'o

with arsenic can reduce the temperature dependence at the:expense of magnitude.

Semiconductor materials, such as gallium arsenide(GaAs), indium antimonide (InSb), and indium arsenid~.(InAs), produce the high est and most stable Hall.coefficients. Because of its combined low temperature',coefficient of sensitivity «0.1 %/ °C), low resistance and,relatively good sensitivity, InAs is the material favored b~,commerciai manufacturers of Hall-effect devices. ,~

Optical transducers represent ODe possible solution to th~need for reliable and economical sensors in high-voltagc;:measurement systems. Conventional transducers for volt;4age and current afe expensive and require large volum~iof electrical insulation when used on high-voltage lines;'~Optical current transducers afe designed with all solid ins~~lating materials and afe therefore intrinsically gare. Becau~iOCT is an electronic device, it differs fundamentally fro~Cf with respect to the signal power involved. In a ~the secondary signal has a power level of severa! watts~while p()wer in theOCT secondary signal is typically ~few microwatts. .:

A number of quite different OCTs are available. Diversitiis present in alI elements of the system. The sensor ma~be optical or electronic. The insulator may be ceramicipolymer and it may be used to support OCT or it may ~"suspended from it. All types of ocr use optics to isola~a high-voltage part of the system from a secondary sid~that carries information. The current being measured by ari.OCT is represented as modulated light. Typically, the linkbetween sensor and user device (measuring instrument) isan optical fiber.Magnetic field

5 CURRENT SHUNTS

Apart from CUlTent transformers, cfs, and Hall-effect seni. "

sors, cUITent shunts are a most common and cost-effecUV~JfolTO of transducers that are used for CUlTent sensing. '

It consists of a low-value resistor connected to the currenfpath of the circuit, as shown in Figure 4. The wavefortn

FuI! current

across

Sleeve shunts can be used for measuring impulse cur-rents up to 500 A. The ohmic value of shunts can bechanged by replacement of the active parts.Cage shunts can be used for currents up to lO kA. Thehousing is usually filled with special sand to enhanceoperations and thermal characteristics.Tubular coaxial shunts can handle currents up to 100 kAfor short durations.Special high current shunts are used for high currents inhigh-voltage applications, such as the arrestor testing.

Current Measurement 1367

.In applications where curreot shunts are selected for cur-

rent measurements, attention must be paid to the inductiveeffects on shunts, terminaI resistances of connections, andthe types of leads used. This is especially so as the fre-quency content of the sigttal rises.

6 CONVERTERS

In many applications, signals afe deliberately converted tocurrents for transmission of information (e.g. the 4-20 mAtransmission method) to be connected back to voltage atthe receiving end. Voltage-to-current (V-I) and current-to-voltage (I-V) converters afe used extensively in theprocess industry to transmit information from ODe locationto another. Current transmission is convenient becauseof its good immunity to electromagnetic interference andnoise.

the of Figures 5(a) and (b) show how such converters are imple-mented using op-amp circuits. In the case of a V - I con-verter, the output is a current lo proportional to the inputvoltage ~. Note that the portion of circuit between pointsA and B acts as a current source controlled by the inputvoltage ~. In the case of the I-V converter, the outputis a voltage Vo proportional to the input current li' Also,note that whatever the load resistor placed at the output, theentire input current li will flow through resistor R). Thus,the portion of the circuit between point S and ground actsas a voltage source controlled by the input current li'

In some applications, it is important to note that thecurrent-to-voltage converter can simply be a suitable ter-minating resistor thatp1akes use of Ohm' s Law to generatea voltage. '-Cf

7 RECTIFIERS

In many applications, AC voltages and currents are mea-sured by means of DC voltmeters and ammeters with anadditioo of a rectifyiog circuit in the input stage. Rectifiers

VI10= R Vo'" -~/I

(b)

Figure 5. (a) Voltage and (b) current converters based on oper-ational amplifiers.

..

1368 Common Measurands

Figure 6. Rectifier-based AC ammeter.

can be classified as controlled or uncontrolled rectifiers, tbemajority of which Me controlled types, which are obtainedusing tbyristors and triacs.

Controlled rectifiers can vary tbe average value of tbevoltage applied to tbe load. They are suitable for usein rectification of single-phase or tbree-phase voltagesand currents from constant AC supplies. A typical basicstructure for a rectifier used in ammeters is shown inFigure 6.

1be rea1ized meter becomes an average voltage detectorthat can be used as an rms ammeter by labeling tbescale to measure currents, provided tbat tbe input signalis a sinewave.

8 INDICATORS

Indicators are base<! OD electromagnetic ammeter princi-ples; ODe typical ex ampie is the O' Arsonval galvanome-ter. This galvanometer is an iDstrument specially designedfor the measuremeDt of very Iow currents (in the orderof 10-8 A) and is therefore employed as null indicatorin a majority of balance measurement methods (like thebridge and potentiometer methods). Because of the inter-naI resistance of its coil, it can be alSO used to mea-sure very Iow voltages, in the order of 10-7 V or evenlesso

The galvanometer structure comprises a rectangular coilof fine copper wire suspended between the pole faces ofa permanent magnet. The magnet pole faces are curved toprovide a radiaI flux. A fixed cylindrical iron core providescontinuity of the magnetic circuito The amplitude of the airgap between the fixed CyliDdrical iron core and the per-manent magnet is about 3 rom. Each coil side lies. halfway

~sphor~'sIIfp -

suspen8lan

. N . i

!

/ :i

Perm8nent ~PoIe '

Figure 7. O' Arsonval galvanometer structure.

between tbc core and corresponding pole tace. 1be suspen-sion is a single fine strip of pbosphor bronze and serves as alead to tbc upper eod of the coil. 1be lower end is connectedto a lead consisting of a spirai spring. In the most accurateexecutions, tbe restraining torque is given by tbe torsionof the suspension strip. In this way, the friction torque isalso practically removed. A small minor, fixed to the sus-pension, reftects a narrow beam of light through a glasswindow in tbe outer case surrounding tbe galvanometer00 to a scale placed a meter away, on wbich tbe deftec-tion is measured. Simply winding tbc coil on aluminiumframe provides eddy curreot damping. Resistive dampingmay also be obtained by connecting a variable resistor inparallel witb tbe deftection coil. Proper adjustment of thisresistance gives criticai damping, tbereby reducing mea-surement time. A typical galvanometer structure is shownin Figure 7.

9 DIGITAL INSTRUMENTS

Digital ammeters (multimeters) obtain tbe required mea-surements by converting tbe analog input signal into asequence of digital samples uniformly spaced in time intbe early stages of tbc signal processing. The input sig-nals are tberefore processed in tbc discrete-ti me domainand tbe measurement results afe displayed in a digi-tal formo It is worthwhile to note tbat tbe distinctionbetween analog and digital meters is not because of tbcway tbc measurement results are displayed. but because of

Currenti(t) -

Figure 8. Structure of a modero digital meter.

the domain (continuous-time or discrete-ti me domain) inwhich the input signals are processed in the main body ofthe devices.

A more modero approach to this type of measure-meni exploits the capability of a fully digital structureas shown in Figure 8 that represents a voltmeter. Thesame structure can be adapted to an ammeter operation,provided that a current-to-voltage conversion input stageis inserted.

This structure samples the input signal Vj(t) at constantsampling rate fs and converts each sampled value into adigital code. The whole sequence of converted codes isstored in the memory of the DSP and then processed forthe evaluation of information.

Assume that the input signal is periodic, with period T,and that the frequency spectrum is by theupper-limitedharmonic component of order N. Digital signal processingtheory, and in particular tbe sampling theorem, ensures tbatthe inforrnation associated witb tbe input signal can betota1ly retrieved from tbe sequence of tbe sampled data ifat least (2N + l) samples are taken over a period T in sucha way tbat (2N + I)Ts = T, where the sampling period Tsbeing Ts = li/s'

If vi (kTs) is the kth sample, tbe rms value of tbe inputsignal is given by

1 2NV = 2N 1 L vf(kTs)

+ 1=0

As an example, a true rrns AC ammeter based on tbisapproach can feature an uncertainty as low as the 0.1 % ofthe CulI-scale value with a 12-bit resolution analog-to-digitalconverter (ADe). According to the sampling theorem, theinstrument bandwidth is limited to half the sampling fre-quency. This means that a 500-kHz bandwidth can beattained with modero devices. Although wider bandwidthscan be obtained, this is paid for in terrns of a lower reso-lution of the ADC devices.

In many cases, such as current measurements in high-voltage and power quality applications, special arrange-ments can be made by using appropriate current trans-ducers and supporting equipment. In these cases, care-fuI consideration is needed when sizing the transducers(e.g. cfs) required so that they take advantage of the

Current Measurement 1369

Digitaloutput

~S&H DSP

full resolution of the instrumenttorting the measured signal. Torepresentation of the signal beingtant to use as much of the fun

possible.

without clipping or dis-obtain the most accurate

monitored, it is impor-range of the ADe as

lO STANDARDS

The unit of current is defined as, 'the ampere is thatconstant current which, if maintained in two straight parallelconductors of infinite length, of negligible circular cross-section, and placed l meter apart in vacuUID, would producebetween these conductors a rocce equal to 2 x 10-7 Newtonper meter of length' .

There is no defined standard for electrical current as suchas it is mainly derived from existing electrical standards ofresistance and voltage, which are based on the quantumHall effect and the Josephson effect respectively.

However, there exist numerous document standards forthe current generation, harmonic contents, durations of cur-rents in high-voltage applications, electrical and electroniccircuits, batteries, grounding and safety aspects, circuitbreakers ana fuses, and so OD. Some examples are

.". IEEE C37.09-1979 for eircuit breakers;. ASTM 0495-99 for test method for high-voltage. low-

eurrent, dry are resistanee of solid electrieal insula-tion;

. mc 60255-8 for high-voltage eurrent-limiting fuses;

. AS 2024-1991 for high-voltage AC switehgear.

(10)

FURTHER READING

Dyer, S.A. (ed.) (2001) Survey of lnstrumentation and Measure-ment, Wiley, New York.

Eren, H. (2003) Electronic Portable Instrumems-Design andApplications. CRC Press LLC, Boca Raton, FL.

Eren, H. and Ferraro, A. (2003) Electronic Voltmeters and Amme-ters, Encyclopedia oJ liJe Support Systems, EOLSSIUNESCO,http://www .eolss.netlE6-39 A-toc.aspx.

Eren, H. and Ferraro, A. (2003) Galvanometers and Electrome-chanical Voltmeters and Ammeters, Encyclopedia oJ LiJe Sup-pOrI Systems, EOLSS/UNESCO, http://www.eolss.netlE6-39A-toc.aspx.