Analysis of transfer touch voltages in low-voltage electricalinstallationsM Barretta BSc, K O’Connella BSc MSc CEng and ACM Sungb BSc MSc PhD CEngalecturer in the department of Electrical services Engineering, DIT, Dublin, IrelandbHead of the Department of Electrical services Engineering, DIT, NG Bailey Ltd.

Protection against electric shock in our homes and work places is one of the most importantpriorities for electrical services engineers who are now designing electrical installations toconform to the requirements of the 17th edition IEE Wiring Regulations (BS7671: 2008).Now Chapter 41 of BS7671: 2008 requires that additional protection by means of a 30mA40ms residual current protection device be provided for final circuits supplying generalpurpose socket outlets that are intended for use by ‘Ordinary persons’. However, there arefew publications and little information available on the theory describing how touch voltageof a dangerous magnitude could be transferred from a faulty circuit onto the exposed-conductive-parts of Class 1 equipment of another healthy circuit. This paper summarises thetheory of transfer touch voltage calculations and expands on it to show how to carry out asensitivity analysis in relation to the design parameters that are being used by designers andinstallers. Based on the results of a real case study, it appears that there is sufficientevidence to show that it may not be sufficiently safe to use the nominal external earthfault loop impedance quoted by the electricity utility companies for adopting a low touchvoltage design.Practical application: The touch voltage sensitivity equation derived in this paper is apowerful tool for designers and installers of electrical installations to investigate and identifythe sensitivity of resulting touch voltages of any electrical circuits.

Nomenclature

Ut= touch voltage

Uoc= open circuit voltage of the mains supply

R2= circuit protective-conductor resistance

R1= phase conductor resistance

Ze= earth fault loop impedance external to

the faulty circuit

Usource= the potential drop ofZe

MET= the main earthing terminal (or main

earth bar) of the electrical installation

Uo= the nominal declared voltage of the

mains supply

1 Introduction

Statistically it has been shown that electricshock is one of the main causes of fatality inthe workplace1 and homes.2 To ensure anegligibly small risk of electric shock in thebuilt environment, designers and installersadopt good wiring practices and abide bythe relevant national wiring rules, e.g. NEC2008,3 BS7671: 20084 or IEC 60364,5 to enablethem to produce a safe electrical installation.It has been agreed universally that for

Address for correspondence: M Barrett, Department ofElectrical Services Engineering, Dublin Institute ofTechnology, Kevin St., Dublin 8, Ireland.E-mail: martin.barrett@dit.ieFigures 1, 2 and 4–8 appear in color online:http://bse.sagepub.com

Building Serv. Eng. Res. Technol. 31,1 (2010) pp. 27–38

� The Chartered Institution of Building Services Engineers 2010 10.1177/0143624409351796

general applications, an earthed and poten-tially equalised (i.e. main-bonded) system willafford protection against electrical shockhazards. The circuit-protective-conductor(cpc) of a final circuit provides a dedicatedlow resistance and high efficiency earth faultcurrent return path to the supply source. Aneffective low impedance earth-fault currentreturn path ensures an almost guaranteedoperation of the overcurrent and/or shockprotection device thus disconnecting the elec-tric shock energy source under earth-faultconditions, limiting the duration of the touchvoltage. In addition the main bonding willlimit the magnitude of the touch voltage6 onecan receive across two simultaneously acces-sible bonded conductive parts. Therefore, theuse of proper earthing (i.e. grounding) andbonding techniques remains the best way toprotect people and equipment against electricshock hazards. However, when an installationhas a large number of interconnectedcircuits and exposed-conductive-parts, afault in another circuit can result in a touchvoltage of a dangerous magnitude andduration being transferred onto a circuitfeeding healthy equipment with exposed-conductive-parts.

2 Theory of touch voltage

For the purpose of this paper, we shall define‘touch voltage’ as a difference in voltagepotential being experienced by a person whomakes contact simultaneously with more thanone conductive part, which is not normallyenergised.

By this definition, we have excluded the‘direct contact’ electric shock hazard which isdefined as the hazard of electric shock arisingfrom making an unimpeded contact withnormally live parts and we explicitly restrictour discussions to touch voltage arising fromcontact with exposed-conductive-parts andextraneous/exposed-conductive-parts.

The touch voltage Ut of the faulty equip-ment circuit shown in Figure 1 can becalculated using a simple voltage dividercircuit:7

Ut ¼ UocR2

Ze þ R1 þ R2

� �ð1Þ

From the above formula (1) for touchvoltage, it is evident that in practice themagnitude of touch voltage Ut is dependentupon four values Uoc, Ze, R1 and R2.

(1) The Uoc value will be higher than thedeclared nominal supply voltage Uo.

Usource

Uoct

Dist. board

MET

R2

Ut

R1

Faultyequipment

Ze

240V

Figure 1 Touch voltage concept of a single faulty equipment circuit

28 Analysis of transfer touch voltages

(2) The external earth fault loop impedanceZe will depend on the system earthingtype,

(3) R1 will depend on the final chosen size ofthe phase conductor (which mainlydepends on the size of the overcurrentprotective device – overload protection inparticular), and

(4) R2 will depend of the final installedsize of the cpc (which depends on thestandard twin-with-cpc cable if notsingle-core conductor cables).

It can be seen from Figure 1 that R2

governs Ut and the size of the cpc of a circuitcan be designed or selected to provide a touchvoltage that is restricted by the designer orinstaller intentionally. By assigning a bound-ary value to each of Ut, Uoc, Ze, R1 and R2,the size of cpc can be designed using thefollowing expression:

Ut ¼ UocR2

Ze þ R1 þ R2

� �

Ut

Uoc¼

R2

Ze þ R1 þ R2

� � ð2Þ

In the UK and Republic of Ireland, forlocations where low body resistance is notexpected (i.e. normal dry locations) the fol-lowing boundary values are used by designersand installers:

� Safe touch voltage value: Ut� 50V� Utility supply voltage:

Uoc¼ 240V (16th edition IEE WiringRegulations) or

Uo¼ 230V (17th edition IEE WiringRegulations) where Uo is the declared nom-inal voltage of the mains supply.

For simplicity, this paper assignsUoc¼ 240V and a safe touch Ut¼ 48V, alimiting value of R2 is found to be:

R2 ¼1

4Ze þ R1ð Þ ð3Þ

From IEC 60479 part 18 (Effects of currenton human beings and livestock), when thetouch voltage is 50V a.c. or less under normaldry conditions, the body impedance of aperson is high enough to prevent a touchcurrent of high enough magnitude to causeany injury. Based on this assumption,Table 41C of the 16th edition of IEE WiringRegulations9 permits the extending of thedisconnection time from 0.4 to 5 s maximum.The use of a safe touch voltage is limited bythe types and rating of a protection deviceand the associated maximum impedance ofthe cpc.

It will be a simple design procedure for thedesigner or installer to apply Equation (3) andthe appropriate value of Tables 41C and 41Dto the required circuit to adopt a safe touchvoltage design with an extended 5 s discon-nection time.

In the UK and Republic of Ireland, R1 andR2 are normally dictated by economics andstandard practice. The standard combinationsof conductor size in twin-with-cpc cables are:16mm2/6mm2, 10mm2/4mm2, 6mm2/2.5mm2, 4mm2/1.5mm2, 2.5mm2/1.5mm2

and 1.5mm2/1.0mm2. These are general pur-pose wiring cables used for final circuits indomestic type properties. These would beunder the control of the designer and installer.

However, during the design stage, theearth-fault-loop impedance that is externalto the electrical installation (Ze) is normallyan estimated figure. The exact value cannotbe ascertained until the supply is actuallyinstalled and energised by the utility com-pany. In most cases at the enquiry stage ofa project the utility company will onlyprovide the designer and installer with aworst case nominal Ze of 0.35X for a TNC-S supply or 0.8X for TN-S supply.However, the actual installed Ze could becompletely different and it is outside thecontrol of the designer and installer. Usingthe typical nominal value quoted by theutility supplier and assigning a boundary

M Barrett et al. 29

value of Ut¼ 50V, Equation (2) will give theresult of:

Ut ¼ 50 ¼ Uoc �R2

0:35þ R1 þ R2ð Þ

It can be seen that the final circuit wasoriginally based on a Ze¼ 0.35X to provide atouch voltage of 50V under an earth faultcondition, but the actual resulting touchvoltage will be higher than 50V should theactual Ze be lower than 0.35X. Hence, theconsequence of not knowing the exact valueof Ze means that the actual touch voltageresulting from a faulty circuit could not beaccurately calculated using a nominal Ze

indicatively quoted by the electricity supplier.The indicative Ze is only useful in providingthe designer or installer a frame of referenceto check if the overall fault-loop impedance(Zs) of the circuit is designed correctly toensure operation of the overcurrent or shock

protection device promptly. Unfortunately itwill err on the unsafe side for the touchvoltage value.

To illustrate the deficiency of an indicativeworst case maximum Ze, the results of touchvoltage variations with a decrease in theactual value of Ze and increasing circuitlengths were produced using an Excel spread-sheet for a typical TNC-S supply withZe� 0.35X. The outcomes are plotted inFigure 2 for final circuits wired in 1.5mm2/1.0mm2 twin-with-cpc cables.

It can be seen from Figure 2 that the touchvoltage Ut will rise from a safe-to-touch value(45V) to an unsafe value (450V) withdecreasing Ze and increasing circuit length.It should be noted that Ut, will be at itsmaximum or worst case when Ze is at itsminimum value. (The minimum valueexpected for each situation was calculatedusing the prospective short circuit current (Ipf)value of the incoming supply.) irrespective of

Touch voltage sensitivity to Zefor a general TNC-S system, pscc 16kA at 230Vusing a 1.5mm twin and earth cable cpc 1mm

Touc

h vo

ltage

160

140

120

100

80

60

40

20

0

12.44%

0.04

3555

0.05

25

0.07

0.10

5

0.14

0.17

5

0.21

0.24

5

0.28

0.31

5

0.35

15% 20%

Touch voltage at 5M from dist. boardTouch voltage at 10M from dist. board

Touch voltage at 20M from dist. boardTouch voltage at 25M from dist. boardTouch voltage at 30M from dist. boardTouch voltage at 35M from dist. boardTouch voltage at 40M from dist. board

Touch voltage at 15M from dist. board

30% 40% 50% 60% 70% 80% 90% 100%

External impedance Ze (Ω)

Figure 2 Touch voltage plot of 1.5mm2/1.0mm2 twin-with-cpc cable circuits

30 Analysis of transfer touch voltages

the actual circuit length. Most of the resultsplotted indicate a value of Ut well above 50V.

The new BS7671:20084 was introduced inJanuary 2008, replacing the 16th edition IEEWiring Regulations and Table 41C removed.However, additional protection by means of a30mA 40ms residual current protectiondevice (RCD) will have to be provided forfinal circuits supplying general purpose socketoutlets that are intended for use by ordinarypersons. It should be noted that the use ofRCDs can help to reduce the risk of a hightouch voltage and touch current of theassociated circuit in the event of an earthfault, but it is unable to provide protectionagainst any touch voltage transferred from afault arising from another circuit not pro-tected by an RCD within the sameinstallation.

3 Touch voltage transferred from afaulty circuit to a healthy circuit

The above analysis was applied to a singlecircuit. However, within the same buildingwhere a number of circuits with mixeddisconnection times exist, as illustrated inFigure 3,10 it has been shown that theresulting touch voltage from an earth faultof another defective circuit will be transferredto the exposed-conductive-part of a healthycircuit. Clearly, unless every circuit within thesame installation is protected by an individualRCD or the whole distribution panel byone main RCD, touch voltage of an unsafevalue could appear on exposed-conductive-parts for a short duration until it has beencleared by the associated overcurrentprotection device.

230 V

L

N

E

Earth

Distributionboard

Circuit AExposed-conductive-part

Circuit BFixedload B

Protectiveconductorin cord

Load A(indoors)

Main earthingterminal

Extraneous-conductive-part

Main equipotentialbondingconductor

Further equipotentialbonding conductor(if necessary)

Rc

Uf

If

Figure 3 Transferred touch voltage appearing on healthy equipment (source: IEE Guidance Note 5)

M Barrett et al. 31

Figure 4 is a generic diagram illustratingthe concept of how touch voltages Vtouch1 andVtouch2 can appear on healthy equipment. Thediagram illustrates three separate electricalcircuits of an electrical distribution system,which at some point defaulted to utilising acommon earthing riser as part of its earthreturn path. As equipment B develops anearth fault, an earth fault current Ifault flowsin the cpc resistances, and by Ohm’s law,results in transfer touch voltages Vtouch1 andVtouch2 appearing on the exposed-conductive-parts of equipment in locations A and C.

4 Touch volatge practical case study – adomestic property

This section outlines a method of simulatingan electrical fault in the built environment.50Hz a.c. currents up to 20A were circulatedthrough the cpc of several electrical circuits in

a domestic property to simulate earth faultconditions. The resulting transfer touch vol-tages in the dwellings were measured andrecorded.

The electrical installation tested is a domes-tic property in Dublin built around 1980.The supply is single-phase 230V 50Hz a.c.TNC-S. A new consumer unit has recentlybeen installed to meet ET10111 (equivalent toBS7671: 2008). The meter board has recentlybeen re-housed outside the dwelling for easeof access. At the meter board the measured Ze

was 0.37X at a Uo of 233V and frequency of50.1Hz.

The practical measurements were carriedout as illustrated in Figure 5. A variac acted asthe source of supply. One of the outputterminals of the 225VA Variac, which can bevaried from 0 to 14V was connected to theassociated cpc at the chosen fault locations andthe other terminal was connected to the mainearth terminal at the main distribution board.

MET.

Extraneous-conductive-parts

Vtouch1

Vtouch2

Rcpc2

Rcpc4Rcpc3

Rcpc1.2Rcpc1.1Rcpc1.3

Vtouch2Ifault

Ifault

Healthyequipmentlocation A

Healthyequipmentlocation C

Faultyequipmentlocation B

Figure 4 Touch voltage is transferred from location B to locations A and C in the same building

32 Analysis of transfer touch voltages

The characteristics of the simulated fault wererecorded using a voltmeter and ammeter. Thetemperature of the associated cpc wasrecorded using a digital thermometer beforeand during each simulated fault.

Figure 6 illustrates the circuits present inthe test dwelling. During the simulation of thefault, transferred touch voltages thatappeared in various locations were recorded.The test was setup to study in particular whatmagnitude of transfer touch voltage can existin a location (i.e. bathrooms) where low bodyresistance would be commonly encountered.

There are a number of countries wheresupplementary bonding in bathrooms maynot be required but the main equipotentialbonding should be correctly installed. It is forthis reason that the new 17th edition of IEEWiring Regulations requires that all electricalcircuits supplying appliances or equipment inthe bathroom be protected by RCDs so thatany touch voltage originating from within thebathroom will be automatically disconnectedwithin 40ms.

This particular test has deliberately discon-nected the supplementary bonding in the

bathroom to study the magnitude of transfertouch voltage in the particular location.

For such a case, the results are shown inFigure 7 with an earth fault in the light fittingin the attic.

Simulation results – At the faulty light priorto simulation, the impedance of the cpc wasrecorded at 0.18 X. Under test conditions, thevoltage and current were recorded at 6.4Vand 15A, respectively. Using the recordedvalues (6.4V/15A¼ 0.4266X) and subtract-ing the impedance of the variac/ammetercombination and the earth wire from thevariac to the MET, the impedance of the cpccan be calculated to be 0.196X. The increaseof resistance is due to copper having apositive temperature coefficient.

Under test conditions, the touch voltagerecorded between the light and earth in theattic was 2.95V, while in the bathroom thetouch voltage was 2.95V between the heaterand the cold-water copper pipe and shower.

Hence, under true fault conditions, if afault occurred at the light in the attic and atouch voltage developed, a voltage of thesame magnitude would develop on the heater

Ammeter

Voltmeter

Distributionboard

Variac

PhaseNeutral

Earth

E N P

Figure 5 Circuit diagram of the test setup

M Barrett et al. 33

in the bathroom where there was no supple-mentary bonding present.

Using the recorded values an approximatedvalue for the touch voltage can be calculated.

Fault loop impedance at distributionboard¼ 0.42 X

Resistance of R1 is approximately 0.12 XResistance of R2 is approximately 0.1966 X

(both R1 and R2 will vary depending on the

temperature of the copper under fault condi-tions). Using Equation (1):

Ut ¼ 64V ¼ 2400:1966

0:42þ 0:12þ 0:1966

� �

It was found that a touch voltage istransferred into the bathroom where theexposed-conductive-part of a heater, although

Faul

t 2 d

owns

tairs

soc

kets

no.

8

Dow

nsta

irs s

ocke

ts n

o. 5

Ups

tairs

soc

kets

no.

5

Imm

ersi

on h

eate

r

Faul

t 5 a

ttic

Ligh

ts

Ligh

ts

Ups

tairs

Dow

nsta

irs

Dow

nsta

irs s

ocke

ts n

o. 7

Faul

t 1

Fault 4 bathroom

Bar heater

Fault 3 oven

Hob

Oven

20A MCB B type

30mA RCD

boardDistribution

63A switch

Fuse

Main incomingsupply

33A MCB Btype

Main earth bar

10A MCB B type

Main gasEarthelectrode

Figure 6 Single-line diagram of the test dwelling

34 Analysis of transfer touch voltages

it was not switched on, has attained a value of64V, which is considered a dangerous voltagefor people with low body resistance.

In addition to using ‘Earthed EquipotentialBonding by Automatic Disconnection ofSupply (EEBADS)’ as the primary methodof protection against electric shock faults,IEE Guidance note 510 suggests that addi-tional supplementary equipotential bondingconductors can be installed at strategiclocations so that any touch voltage Ut

originating from outside the particular loca-tion is lowered to a safe-touch-value. This was

implemented as a control comparison and theresults are shown in Figure 8.

Simulation results, supplementary bondingrestored – With a fault simulated on the lightin the attic, touch voltages were recorded atthe fault location and in the bathroom. Thevoltage and current were recorded at 4.35Vand 15A, respectively. The reduction in thevoltage required to drive 15A through thecircuit dropping to 4.35V due to the parallelpaths back to the MET as shown in Figure 8.

10A of the 15A was recorded flowingtowards the bathroom and the remaining

Bathroom

MET

Fault at light in attic-Nosupplementary bonding in bathroom

AtticFault location

Consumer unit

Light

Heater

Cold watercu. pipe

Showers earthSocket

Extraneous conductive part

Ut=64 V Ut=64 V

Figure 7 Presence of dangerous touch voltage in bathrooms with no supplementary bonding

Bathroom

MET

Fault at light in attic–supplementary bondingin bathroom restored

Consumer unit AtticFault location

Light

Heater

Cold watercu. pipe

Showers earthSocket

Extraneous conductive part

Ut=24 V

Ut=3.6 V

Ut=1.56 V

Figure 8 Elimination of presence of transfer touch voltage in bathrooms by mandatory supplementary bonding

M Barrett et al. 35

5.0A was recorded flowing from the faulttowards the distribution board. In the bath-room the 10A split in two directions, 7Aflowed through the electric showers earthcircuit and 3A flowed through the copperpipes.

The touch voltages recorded under simula-tion were as follows, 0.96V at the faulty lightin the attic, 0.144V between the heater andelectric shower in the bathroom and 0.066Vbetween the heater and cold-water copperpipes.

From the recorded values it was possible tocalculate the resistance R2, 4.35/15A¼0.29X¼ resistance of circuit under fault con-ditions. 0.29–0.23X (impedance of earth wireand variac)¼ 0.06X¼R2. Also, the resis-tances of the supplementary bonding in thebathroom could be calculated, 0.144V/7A¼ 0.02X and 0.066V/3A¼ 0.02X.

Using the recorded values an approximatedvalue for the various touch voltages can becalculated. Using Equation (1):

Touch voltage at faulty light ¼ Ut ¼ 24V

¼ 240 ð0:06=0:42þ 0:12þ 0:06Þ

To determine the touch voltages developedin the bathroom, the prospective fault current(Ipf) at the fault location was calculated:

Ipf ¼233V

0:6�¼ 388A

Two-thirds (259A) of the total faultcurrent flows towards the bathroom underfault conditions. The current that would flowto earth via the cold water copper pipes isgiven by (3/10)� 259A¼ 78A. Hence thetouch voltage between the heater and coldwater copper pipe would be approximately78� 0.02 X¼ 1.56V.

Therefore the touch voltage between heaterand the shower would be approximately be259A (7/10)� 0.02 X¼ 3.6V.

The findings demonstrate that with supple-mentary bonding, the transfer touch voltagewas reduced to less than 4V within thebathroom. Therefore it appears that there issufficient evidence to show that with supple-mentary bonding in place, even in the event of adefective RCDa or a sluggish overcurrentprotection device such that the faulty circuitmight remain in an energised state for quitesome time, a person in the bathroom wouldonlybe exposed toa touchvoltageof 4Vor less.

Alternatively, a designer or installer can optfor making sure that all the circuits within thesame dwelling will have a very low safe touchvoltage value in the event of a fault. Forexample, to have a transfer touch voltage notexceeding 12V4 maximum to provide protec-tion against electric shock for a person withvery low body resistance in the special loca-tion. This requires the designer and installer tohave a good understanding of the sensitivity ofthe resulting touch voltage in relation topercentage changes of Uoc, Ze, R1 and R2

between design and as-installed phases.

5 Touch voltage sensitivity analysis

In this section, the technique of partial dif-ferentiation for small percentage changes wasused to determine the sensitivity of touch vol-tage in relation to the four design parameters:

Equation (4) is obtained by applyingpartial differentiation to Equation (1):

�Ut ¼@f

@Uoc�Uoc þ

@f

@Ze�Ze

þ@f

@R1�R1 þ

@f

@R2�R2 ð4Þ

aFrom the ERA Technology Report ‘In-service reliability ofRCDs’ published in Italy in May 2006 – electromechanicalRCDs have an average failure rate of 7.1%. If RCDs are testedregularly this figure falls to 2.8%. RCD reliability is improvedif the test button is operated regularly. However, the report hasindicated that RCDs with an inadequate IP rating subjected todust and moisture could have a 20% failure rate.

36 Analysis of transfer touch voltages

where f ¼ Ut ¼ Uoc � ðR2=Ze þ R1 þ R2Þ

and �Ut is the small change in touch voltage,giving the result of (For simplicity, we havelet Ze, R1 and R2 be summed directly. Theactual �Ut can vary significantly when com-plex quantities are used.):

�Ut¼R2

ZeþR1þR2�Uoc

þ�Uoc�R2

ZeþR1þR2ð Þ2�Ze

þ�Uoc�R2

ZeþR1þR2ð Þ2�R1

þ�Uoc�R2

ZeþR1þR2ð Þ2þ

Uoc

ZeþR1þR2ð Þ

� ��R2

�Ut ¼R2 ��Uoc þUoc ��R2

Zs� w ��Zs ð5Þ

whereZs ¼ Ze þ R1 þ R2,w ¼ ðUoc � R2=Z2s Þ,

and �Zs ¼ �Ze þ�R1 þ�R2

U0t ¼ Ut þ�Ut ð6Þ

where Ut0 is the final touch voltage after

changes of Uoc, Ze, R1 and R2 been accountedfor.

Equations (5) and (6) allow the designerand installer to investigate the resulting mag-nitude of the change in touch voltage Ut forany combination of percentage changes of thefour design parameters Uoc, Ze, R1 and R2.

As an example: for a final circuit with aUo¼ 230V, Uoc¼ 240V TNC-S system,R1¼ 0.1X and R2¼ 0.15X, during thedesign stage Ze¼ 0.35X and Ipf¼ 16 kAwere obtained from the electricity supplierby enquiry.b Using Equation (1), the esti-mated touch voltage Ut can be evaluated

equal to 60V. However, the actual touchvoltage will change due to the percentagevariation of the four parameters for reasonsbeyond the control of the designer as below:

� Uoc changes by þ6%c due to the variation

of the utility supply, �Uoc ¼ 240�ðþ6%Þ ¼ þ14:4 V� Ze changes by �35% due to the location ofthe utility supply transformer, �Ze ¼

0:35� ð�35%Þ ¼ �0:1225�� R1 changes by �15% due to shorter cableruns in the construction stage,�R1 ¼ 0:1� ð�15%Þ ¼ �0:015� and� R2 changes by �15% due to shorter cableruns in the construction stage,�R2 ¼ 0:15� ð�15%Þ ¼ �0:0225�

Using Equation (5), the change of touchvoltage will be:

�Ut ¼ ð3:6þ ð�9ÞÞ � ð�16ÞV ¼ 10:6V

Hence, U0t ¼ ð60þ 10:6ÞV ¼ 70:6V,approximately. The actual Ut is 73.72V ifthe exact value of R1¼ 0.085X, R2¼

0.1275X, Ze¼ 0.2275X and Uoc¼ 254.4Vwere applied to Equation (1). The discrepancyof (73.72�70.6) V¼ 3.12V is mainly due tothe large percentage change of Ze but theoverall result is still within an acceptablemargin.

It can be seen from the above, the touchvoltage sensitivity equation (5) derived in thispaper is thus a powerful tool for designersand installers of electrical installations toinvestigate and identify the sensitivity ofresulting touch voltages of any electricalcircuits.

bBS7671: 2008, Regulation 434.1 suggests determinationof prospective short circuit current (Ipf) at the relevant pointof the installation may be done by calculation, measurement orenquiry.

cThe UK ESQC Regulations state that the declared nominalvoltage on LV networks is 230V� 10%, the open circuitvoltage at the DNO supply transformer is normally set at240V, hence 240Vþ 6% is used in the analysis.

M Barrett et al. 37

6 Conclusion

� The underpinning basic theory of thesafe touch voltage design equation hasbeen explained and illustrated with anexample.� A generic circuit diagram is presentedillustrating how a touch voltage of adangerous magnitude could be transferredfrom a faulty circuit onto healthyequipment located elsewhere within anelectrical installation.� A touch voltage case study has been used todemonstrate that a dangerous touch voltagecould be present in locations where extremelow body resistance may exist.� It has been demonstrated that by the use oflocal supplementary bonding, the danger ofany touch voltage transferred from a faultarising from outside the bathroom canalmost be completely eliminated even inthe event of a fault of long duration.

A set of touch voltage sensitivity calcula-tion equations has been developed and usingan example, the authors have demonstratedthat the equations can be used by installationdesigners and installers to investigate andidentify the range of resulting touch voltagevalues that might be the consequence ofvariation of the four main design parametersUoc, Ze, R1 and R2.

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38 Analysis of transfer touch voltages