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Energy 65 (2014) 145e151

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Energy

journal homepage: www.elsevier .com/locate/energy

Influence of cable losses on the economic analysis of efficientand sustainable electrical equipment

J.A. Lobão a, T. Devezas b, J.P.S. Catalão b,c,d,*

a Polytechnic Institute of Guarda, Av. Dr. Francisco Sá Carneiro 50, 6300-559 Guarda, PortugalbUniversity of Beira Interior, R. Fonte do Lameiro, 6201-001 Covilha, Portugalc INESC-ID, R. Alves Redol, 9, 1000-029 Lisbon, Portugald IST, University of Lisbon, Av. Rovisco Pais, 1, 1049-001 Lisbon, Portugal

a r t i c l e i n f o

Article history:Received 14 May 2013Received in revised form7 November 2013Accepted 6 December 2013Available online 24 December 2013

Keywords:Energy efficiencyDecision supportElectricity consumptionCable losses

* Corresponding author. University of Beira Interior6201-001 Covilha, Portugal. Tel.: þ351 275 329914; fa

E-mail addresses: catalao@ubi.pt, catalao@ieee.org

0360-5442/$ e see front matter � 2013 Elsevier Ltd.http://dx.doi.org/10.1016/j.energy.2013.12.022

a b s t r a c t

Increasing energy needs are accompanied by environmental responsibilities, since nowadays electricitycompanies operate in a competitive and sustainable energy framework. In this context, any proposal foraction on energy efficiency becomes important for consumers to minimize operational costs. In electricalinstallations, electricity consumption can be decreased by reducing losses in the cables, associated withthe overall efficiency of the equipment, allowing a better use of the installed power. The losses must beanalysed in conjunction with all loads that contribute to the currents in the sections of an electricalinstallation. When replacing equipment in output distribution boxes with more efficient ones, the cur-rent in those sections is reduced in association with the decrease in power losses. This decrease, oftenforgotten, is taken into account in this work for the economic analysis of efficiency and sustainableelectrical equipment. This paper presents a new software application that compares and chooses the bestinvestment in the acquisition of electrical equipment. Simulation results obtained with the new softwareapplication are provided and are then validated with experimental results from a real electricalinstallation.

� 2013 Elsevier Ltd. All rights reserved.

1. Introduction

In power production, transport, and distribution for final con-sumption, various aspects have been particularly highlighted:environmental and economically efficient dispatch [1,2], distrib-uted generation and impacts on the operational characteristics ofnetworks [3], customer satisfaction and profit making of the pro-ducer and distributor of energy [4], dimensioning of the section ofcables to reduce energy consumption and optimize operating dis-tribution systems [5e7], reduction of distribution losses byreducing reactive power optimization with capacitors placed in thedistribution lines [8e10], layout optimization for radial distribution[11], and the use of superconducting power transmission [12,13].

Also noteworthy are the study and development of efficient andsustainable electrical equipment, in particular industrial inductionmotors [14e16], which are responsible for a large share of elec-tricity consumption, as well as efficient lamps [17,18] for industrialand domestic use.

, R. Fonte do Lameiro,x: þ351 275 329972.(J.P.S. Catalão).

All rights reserved.

At a time when global energy consumption is predicted to in-crease by 38.6% by the year 2030 [19], in association with growingenvironmental pressure around the industry, there is a need for themost efficient use of energy.

Moreover, in the near future the consumer is expected to stopbeing passive and to become an active element throughout thechain of production and consumption of energy. This requires thatthe consumer have action tools available that will help him or hermake decisions taking into account the characteristics of the dataand the installation.

In order to reduce the energy consumption in a domestic orindustrial installation, the efficiency of real loads and all losses inthe cables of the installation should be thoroughly studied toimprove the energy efficiency. Indeed, energy efficiency andreduction of consumption in electrical installations and equipmentrepresent an important line of research.

Hence, this paper provides consumers with a new softwareapplication that allows them to compare options and choose thebest investment in the acquisition and installation of electricalequipment, aiming for both efficiency and sustainability. Tworesearch aspects are connected in an original way: the influence ofequipment and the losses caused by it in the installation, on the onehand, and the associated economic analysis, on the other hand.

Nomenclature

J!

S current density vectorJ!

ei eddy current density vectorsV volumeT period of the currentPskin losses due to skin effectPprox losses due to proximity effectd skin depthR conductor radiusD conductor diameterRac AC resistance for the conductorRdc DC resistance of the conductorIrms current (true rms)Q distribution boxess electric conductivityRR profitII new investmentd monthly operating days

m months of annual operationl price of electricityDP difference in cable lossesP powerDP[k,i] difference in cable losses of the conductor of the

output i of the distribution boxes KR[k,i] resistance of the conductor of the output i of the

distribution boxes KI[k,i] current of the conductor of the output i of the

distribution boxes KNi initial investmentOi mean annual savingsSPBT simple payback timeVAL net present valueIRR internal rate of returnI currentDD operation costa annual interest rate

J.A. Lobão et al. / Energy 65 (2014) 145e151146

The equipment choice focuses on multiple factors: cost/price,energy consumption, reduction of losses in the cables, useful life,and interest rate. The consumer can then make a decision in thelight of all the parameters of the equipment and its electricalinstallation. The power losses in the conductors must be consideredtogether with all loads that contribute to the current in the sectionsof an installation, which makes a real difference in the choice ofefficient and sustainable equipment.

This study is based on a new way of thinking: from minimalinvestment cost to minimal life cycle cost. The connection betweenoptimal cables selection and the influence of efficient/sustainableequipment is also experimentally validated, in addition to thesimulation results obtained using the new software application.

This paper is structured as follows. Section 2 presents theproblem formulation. Section 3 explains the economic evaluation.Section 4 illustrates the software application. Section 5 provides thesimulation results, validated with experimental results. Finally,concluding remarks are given in Section 6.

2. Problem formulation

The losses in electrical installations are a known problem thatcannot be eliminated, but it may and should be reduced. Theobjective of this study is to present a new software application thatallows analysing the influence of cable losses on the economicanalysis of efficient and sustainable electrical equipment, validatingsimulation results with experimental data.

The methodology used to develop this work shows how tocalculate the losses in electrical conductors, identifying first theparameters of an electrical installation with the respective loads.The calculation methods used in the software application and therespective outputs are provided. An analysis is presented based onreal laboratory measurements, with a wattmeter at the beginningand at end of the conductors to obtain the respective losses. Finally,the simulation results are compared with experimental results tovalidate the software application.

An electrical installation, whether large or small, produces heatin the conductors when in operation, which is associated withpower losses. Industrial and domestic electrical systems operatemostly on alternating current, for which the influence of the skineffect and proximity of conductors should be considered, due to thecreation of eddy currents and magnetic fields caused by theneighbouring conductors. The skin effect is the tendency of an AC

current to become distributed within a conductor such that thecurrent density is largest near the surface of the conductor andsmaller at greater depths in the conductor. The electric currentflows mainly at the “skin” of the conductor between the outersurface and a level called the skin depth. The skin effect causes theeffective resistance of the conductor to increase at higher fre-quencies where the skin depth is smaller. Skin depth is due to thecirculating eddy currents arising from a changing H field, cancellingthe current flow in the centre of the conductor and reinforcing it inthe skin.

If currents are flowing through one or more nearby conductors,the distribution of current within the first conductor will be con-strained to smaller regions, so the resulting current crowding istermed the proximity effect. The proximity effect can significantlyincrease the AC resistance of adjacent conductors when comparedto its resistance to a DC current. The losses in the conductors of aninstallation should thus consider the skin effect and the proximityto other conductors. Due to the nonlinearity of configurations anddiversity of types of cables, the problemmay become very complexin terms of analysis. Multiple studies have been done using pro-grams for finite element analysis, simplification, and verification ofsemi-empirical formulae that allow valid results and facilitate ananalytical and computational analysis.

In an installation as referred to in Refs. [20], it is assumed thatthe multiple phase conductors can be treated as infinitely longparallel wires, so the resulting magnetic field wraps around theconductors in the plane perpendicular to the conductor axis andthe resulting eddy currents flow parallel or anti-parallel to the netphase current. The source current density vector J

!S and the

induced eddy current density vectors J!

ei from various phaseconductors can be added in each infinitesimal area of the conductorcross-section of interest, after which Eq. (1) can be applied over thecross-sectional area of the conductor to determine the total loss perunit length:

Ptotal ¼1T

ZT0

12s

ZVolume

hJ!

S þXN

i¼1J!

ei

i2dVdt (1)

where V is the volume variable, t is the time variable, s is theelectric conductivity of the conductor, and T is the period of thecurrent wave.

Fig. 1. Connection matrix.

J.A. Lobão et al. / Energy 65 (2014) 145e151 147

The total losses are the sum of two components, the skin effectand the proximity effect, as given by:

Ptotal ¼ Pskin þ Pprox (2)

The total losses can be analysed separately, making the overlapat the end.

The loss associated with the proximity effect results from theinteraction of conductors that occurs when they are transversed byan electric current, which creates magnetic fields, changing thetotal distribution of current in the straight section in all conductors.This interaction is a function of the distance between conductors,the amplitude of the current, the phase angle, and the frequencyand distribution of induced current.

For instance, in two adjacent conductors carrying AC currentflowing in opposite directions, such as the ones found in powercables and bus bars pairs, the current in each conductor isconcentrated into a strip on the side facing the other conductor.Since the current is concentrated into a smaller area of the wire, theresistance is increased. The additional resistance increases powerlosses, which can generate undesirable heating.

To determine the proximity effect losses of multi-conductorthree-phase cables, several solutions have been presented as sug-gested in Refs. [20], proposing that when the conductor radius islarger than the skin depth, the power dissipation from the prox-imity effect is proportional to the conductor radius (Eq. (3)). As theconductor radius becomes less than the skin depth, the loss can beexpressed by Eq. (4).

Pprox ¼ ðcRþ dÞ�m0mrI2pr

�2

; R � d (3)

Pprox ¼ aRb�m0mrI2pr

�2; R < d (4)

where a¼ 2.605E6, b¼ 3.968, c¼ 10.192, and d¼�0.074 for copper,a ¼ 1.485E6, b ¼ 3.951, c ¼ 13.222, and d ¼ �0.125 for aluminium,Ris the conductor radius, and d is the skin depth, given by:

d ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

2sum0mr

s(5)

The contribution of skin effect losses can be calculated usingfinite element or analytical methods and semi-empirical randomconfigurations for conductors. One approach to three-phase cablesystems is presented in Ref. [20].

The skin effect increases conductor resistance with frequency asa result of the reduced cross-section through which the currentflows. The AC resistance for a conductor with a diameter muchgreater than the skin depth can be computed from Eq. (6), where Dis the conductor diameter:

Rac ¼ lpsdðD� dÞ (6)

The skin effect losses Pskin can be calculated by:

Pskin ¼ I2rmsRac (7)

In cases where the conductor diameter is comparable to or lessthan the skin depth, the exact skin effect loss calculation formula,Eq. (8), should be applied, where Rdc is the DC resistance of theconductor, and I0 and I1 are themodified Bessel functions [21] of thefirst kind in the zero and first orders, respectively.

Pskin ¼ I2rmsRdc Re�gI0ðgÞ

�(8)

2 I1ðgÞ

with:

g ¼ ð1þ jÞD2d

(9)

Thispaper introduceshereafteranewanalysisofexistingelectricalconsumers, integrating the losses of conductors, the investmentanalysis, and the choice of efficient/sustainable equipment.

2.1. Identification of parameters

Three types of parameters are considered: physical, load, andoperating parameters. The physical parameters correspond to:

� Distribution boxes (Q): The distribution boxes are numberedfrom number 1 (initial distribution boxes) to the total number ofdistribution boxes for the installation.

� Connections between distribution boxes: The connection of thedistribution boxes is saved in a matrix that identifies theconnection courses. The number contained in the matrix [k,i]indicates the number of the respective output, where k indicatesthe distribution boxes that provide energy, and i indicates thedistribution boxes that receive energy. Fig. 1 shows an exampleof a connection matrix, where distribution box k 1 providesenergy to distribution box i 2.

� Length and section of the output conductors in the distributionboxes: From the length and section, the resistance of the con-ductors is determined for all outputs. The values are saved in aresistances matrix, as illustrated in Fig. 2.

The load parameters correspond to:

� The power of the loads connected to the electrical installation.� The efficiency and power factor of the loads.� The daily load diagram.

The operating parameters correspond to:

� The operating time of the electrical installation.� Monthly operating days (d).� Months of annual operation (m).� The price of electricity (l).

2.2. Calculations

After the input of the parameters and load diagrams, thefollowing calculations are made:

Fig. 2. Resistances matrix.

J.A. Lobão et al. / Energy 65 (2014) 145e151148

� Determination of the load diagram associated to the outputdistribution boxes, adding the corresponding load diagrams.

� Determination of the currents in all conductors of the electricalinstallation.

� Difference in cable losses (DP) in the conductors affected by thechanged equipment:

� Profits from the variation of cable losses (G1), given by:

G1 ¼Xnj¼1

hR½k; i��I½k; i�1�2 � R½k; i��I½k; i�2�2ijdml (10)

� Profits from the variation of power equipment (G2), given by:

G2 ¼Xn h

P1½k; i�j � P2½k; i�ji

dml (11)

J¼1

Fig. 3. Flowchart of the software application.

� Total profits, given by:

R ¼Xn h

R½k; i��I½k; i�1�2 � R½k; i��I½k; i�2�2i dml

Fig. 4. Scheme of installation A.

j¼1j

þXnj¼1

hP1½k; i�j � P2½k; i�j

idml

(12)

3. Economic evaluation

The economic evaluation is conducted in accordance with therational selection of a solution to be taken during the investmentdecision, which should be based on a number of comparisons andanalyses. The methods can be grouped into static and dynamicmethods, to be described hereafter.

3.1. Static methods

Static methods are applied for the assessment of the efficiencyduring the initial stage when the economic justification of an in-vestment is examined. One of the most popular methods involvesthe payback period.

SPBT (SimplePaybackTime) refers to amethod that enables one todetermine the overall periodnecessary for the costof the expenditureto be returned and is expressed as the length of time needed for aninvestment to make enough to recoup the initial investment:

SPBT ¼ Ni

Oi(13)

whereNi is the initial investment, andOi is themean annual savingsresulting from an investment.

3.2. Dynamic methods

Dynamic methods result in the verification of the credibility ofthe calculations due to the application of a discount account,considering the change in the time value of money and the totalcash flow associated with an investment.

The following methods have found most extensive application:VAL (Net Present Value), IRR (Internal Rate of Return), and PP(Payback Period).

Fig. 5. Results of the new software application for installation A. Fig. 7. Results of the new software application for installation B.

J.A. Lobão et al. / Energy 65 (2014) 145e151 149

In this paper the VAL is used, which is computed from the sumof the annual cash-flows for a given annual interest rate.

The interest rate is indicated by the investor according to thedesired profitability:

VAL ¼Xnk¼0

RRk � DDk � IIkð1þ aÞk

þ V0ð1þ aÞn (14)

where RR is the net profit, DD is the operation cost, II is the newinvestment, n is the number of years of useful life, V0 is the residualvalue of the old equipment, and a is the annual interest rate.

4. Software application

The software is structured using matrices and vectors that allowthe characterization of the electrical installations and respectiveloads. The loaddiagramandparametersof the installationareenteredvia thekeyboardormaycarryoutdataacquisitionautomatically.Afterthe installation is characterized (physical parameters, load parame-ters, operating parameters), updating the data in all sections, it startswith the distribution boxes that do not feed other distribution boxes,with the diagram loads being the set of outputs.

Fig. 6. Scheme of installation B.

Fig. 3 provides a flowchart of the software application.Fig. 5 presents the results of the new software application for

the installation shown in Fig. 4. The results compare an initial sit-uation of a normal induction motor with two more efficient in-ductionmotors, towork 5 h a day, providing the power losses in thecables, the VAL, and the best investment. These results are illus-trative of the capabilities of the software application developed.

5. Case study

5.1. Simulation results

Fig. 6 shows the scheme of a real installationwith the respectiveparameters: heater [2,1]: 1000W; lamps [2,2]: 3�100W, 3� 72W,or 3 � 20 W; lamp [3,1]: 100 W; inductor motor [3,2]: 1000 W, towork 8 h a day.

Fig. 7 presents the results of the new software application forthe real installation shown in Fig. 6. The results compare an initialsituation of a normal 3�100W incandescent lampwith a 3� 72Whalogen lamp and another 3 � 20 W fluorescent compact one.

5.2. Experimental validation

The experimental setup can be seen in Fig. 8, which correspondsto the scheme shown in Fig. 6.

Fig. 8. Experimental setup.

Fig. 9. Initial measure in cable B (begin).

Fig. 10. Initial measure in cable B (end).

Fig. 12. Measure in cable B (end), option 2.

J.A. Lobão et al. / Energy 65 (2014) 145e151150

Laboratorymeasurements were performed at the beginning andend of the cables identified in Fig. 6 as A and B. With 3 � 100 Wlamps, losses of 6 and 1.4 W were obtained in cables A and Brespectively. Considering themore efficient 3� 20W lamps (option2), losses of 4 and 0.2 W were obtained in cables A and Brespectively.

Fig. 11. Measure in cable B (begin), option 2.

Figs. 9 and 10 shows the measurements made at the beginningand end of cable B, respectively, considering the less efficientlamps. Figs. 11 and 12 show the measurements made at thebeginning and end of cable B, respectively, considering the moreefficient lamps (option 2).

From the experimental results a 43.2% decrease in total losseswas observed, which is considerable. Thus, option 2 represents thebest investment, validating the simulation results, which providedcomparative VAL results.

Considering the operation over a year and large-scale electricalinstallations, the software application developed represents avaluable tool for assessing different alternatives, indicating themost efficient and sustainable ones.

6. Conclusions

The losses in electrical installations can make a considerabledifference in the economic evaluation supporting the investmentdecision. The results presented confirm that the VAL is superiorwhen the losses are included, and may even switch from negativeto positive. The importance of the application of software in realsituations was also demonstrated and validated with experimentalresults, making it possible to analyse and choose effective solutionsfrom the point of view of economic profitability, making energy usemore efficient and sustainable. The analysis of energy efficiency inindustrial systems should include the whole life cycle and all thecomponents and losses of the system for a proper assessment.

Acknowledgements

This work was supported by FEDER funds (European Union)through COMPETE and by Portuguese funds through FCT, underProjects FCOMP-01-0124-FEDER-020282 (Ref. PTDC/EEA-EEL/118519/2010) and PEst-OE/EEI/LA0021/2013. Also, the researchleading to these results has received funding from the EU SeventhFramework Programme FP7/2007-2013 under grant agreement no.309048.

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