Cyclic and Emergency Rating Factors of Distribution Cables in Presence

of Non Linear Loads P. Caramia G. Carpinelli, Member, IEEE A . La Vitola P. Verde, Member, IEEE

Abstrocl: - The paper proposes procedures which allow to know, lor assigned harmonic pronle of non linear loads, the cable cyclic and emergency ratings in non sinusoidal operating conditions. The proposed procedures refer to distribution cables and employ simplified expressions very similar to those adopted by IEC Standard 853 for the sinusoidal conditions; the harmonic presence is taken into account by a new proper definition of the load-loss factor and by the introduction of harmonic coefficients easily to be predicted. Numerical applications to low voltage and medium voltage cables nre developed and discussed considering typical non linear load scenarios, in order to furnish practical indications regarding the derating lactors to be introduced lor the harmonic preSe"Ce.

Index Terms: Cables. Rating, Harmonic distortion,

1. INTRODUCTION

The presence of current and volrage harmonics in electrical energy systems is well known: the harmonics are due to non linear loads and can damage the system components. In the case of cables. current and voltage harmonics can cause so relevant additional losses in the conducting and in the insulating materials that unacceptable cable life reduction arises if they are neglected in the cable sizing [l-5].

The evaluation of the cable ratines in non sinusoidal - operating conditions has been analyzed in literature [6-91. All the procedures mainly refer IO steady-state non sinusoidal currents, that is assuming 100% load factor. Maximum load is based on the continued application of a constant distorted current.

In practice, the maximum load is usually applied only for a limited time, and the maximum current may then be increased without the maximum permitted conductor temperature rise being exceeded. Such increases in current rating are given by cyclic rating factor. when the applied load is cyclic, and by emergency rating factor. when the applied load is an emergency load current [ 10-131.

P. Cunmia. G. Carpineili. A. La Vitola. P. Verdc arc with thc Depnnmcnl of lndusrial Enginemin) of the tinivcrriry of Carrlno. Via Di Biasio. 43 ~ 03043 Cassino (FR) loly (c-mail: anniin6umcns.it. Eominellil~~unicas.iI vcrde@unicas.il)

The problem of cyclic current rating was analyzed in sinusoidal operating conditions at beginning of 1950. Then, in [14] a simplified approach was proposed, based on the use of the 100% load factor steady-state rating equations; the cyclic load is taken into account by a proper modification of the external thermal resistance of the cable. Another simplified approach was proposed in [I51 and later adopted by IEC Standard [12-131; the permissible peak value of current during a daily cycle is obtained multiplying the 100% load factor steady-state rating equations by a proper computed cyclic rating factor. Finally, in [I61 some considerations about the cyclic rating in non sinusoidal conditions were done.

The problem of emergency rating was analyzed only in sinusoidal operating conditions. In [ 171 formulas for calculating the emergency loading of cables taking into account the variation of the electrical resistivity of the conductor with temperature were proposed and later adopted by IEC Standard [13]; the emergency load current is obtained multiplying the 100% load factor steady-state rating equations by a proper factor which takes into account the maximum permissible temperature rise above ambient at the end of emergency period and the current applied before the beginning of emergency period.

In this paper the approaches adopted by IEC Standards 853 [IZ-131 are extended to the case in which the cyclic or emergency currents are non sinusoidal as a consequence of the presence of non linear loads such as static converters. The current rating equations derived for both cyclic and emergency conditions refer only to distribution cables and need only to know the form of the fundamental current of the cycle and the nature of the non linear loads which the cable feeds. As in the IEC Standard 853, only balanced three phase loads are considered: moreover, the voltage dependent losses such as charging current and dielectric losses are not taken into account because these losses can be neglected for most distribution class cables [ 181.

Numerical applications to low voltage and medium voltage cables are developed and discussed considering typical non linear load scenarios. The aim is to furnish practical indications regarding the derating factors to be introduccd in calculation of thc cyclic and emergency ratings when cables feed non linear loads.

0-7803-7611-41021S17.W 02WZ IEEE 716

I

I, 11. CYCLIC RATING M NON SNUSOIDAL CONDmlONS

In sinusoidal conditions [12-131, the cyclic rating of ' " ~ cables refers to the current rating of cables carrying a load

O b . which vanes cyclically over a 24 h period (the shape of each daily cycle being substantially the same). It generally 4 0 ~ requires computation of a cyclic rating factor M by which the permissible steady-state rated current I, (100% load 0 4 - factor) is multiplied to obtain the permissible peak value of oI: current I,, during a daily cycle (I,,,%, = M In) such that the

T l m ofman" ,e--

conductor temperature attains, but does not exceed, the o 1 standard permissible maximum temperature during the ..---,-..., 6 4 2 0 T n " n o r l o b g h s cycle. The standard permissible maximum temperature is usually the one associated to steady-state (100% load factor) current.

As well known [12,13,15] the expression of the cyclic rating factor M is obtained assuming that the maximum conductor temperature caused by the actual cyclic daily load current may be approximated by the maximum conductor temperature caused by the actual current applied for a time T hours prior the expected time of maximum temperature, and

Fiz. I Equivalenl stcp function cyclic lorr-load

Then, the simplified expression ( I ) has to be properly modified to take into account harmonics 1161.

Lei be the RMS value of the hth harmonic o f the non sinusoidal current at time i, I-,, be the highest value of the fundamental of non sinusoidal current during the daily cycle, Rh be the cable ac equivalent resistance at frequency corrennondine to the h" harmonic and obtained initiallv ~ ~~~~~ I . . ~ ~ ~ ~ ~ ~ ~. ~~~ ~~ ~~

a constant current applied for all earlier times, its amplitude being an average provided by loss-load factor. It results in:

neglecting variation with Assuming that the temperature rise is proportional to the

joule losses (fundamental plus harmonics), the temperature rise 9(0), obtained considering the cable subjected for a long time before t = 0 to joule losses equal to the average value of the losses during the day Wd, can be computed as:

(1) I M =

with the load-loss factor p given by:

V . 2

23 I 23 H and with 5 usually equal to 6 hours. In ( I ) the scaled

current stepped cume ordered for the six hourly periods before the occurrence of the highest temperature (fig. I). e&) is the conductor temperature rise above ambient at time t after application of the sustained (100% load factor) w, I 23 H R h 2 resistance, I j is the RMS value of the applied sinusoidal current at time i of the equivalent step function cyclic loss- load and I,, is the highest value of current during the daily cycle.

= L x W i = - x xR,,l;h

A new load-loss factor in non sinusoidal conditions I&,, quantities Yo, Y , . ..., Ys are the ordinates of the squared 24i=0 2 4 i = 0 h=l

can be introduced as':

(4) rated current I, with neglected variation in conductor l h =-=- xYi.1 1 - Y i . h 3 Ri1Lm,1 24i,o h = l R I

being:

The temperature rise ratios in ( I ) are furnished by IEC

In non sinusoidal conditions. the presence of the joule

1:I

1 i 3 X . I

y. = _ Standard [ 12-13] for the various cable configurations. 1.1

losses due to current harmonics has to be taken into account. In fact, because the resistance ratios. and hence the joule

consideration of the effect of harmonics on cable losses is clearly justified [ I I ] . On thc other hand, the growing

high level in a distribution system.

l i .h Y , , ~ =-

losses, increase dramatically at higher frequencies, Ii.1

and with H maximum order of harmonics. presence of non linear loads and capacitors can cause very 1 shown in 1191. load-losr factor i n sinusoidal condllioilr should

be m m formally defincd assuming as refcrencc the highest Y ~ I U C oflowl losses (fundamental plus harmonics) dwmg the cyclc in spire afthc hiehcsi value of IOSSES at fundamenwl. However. thc definition given by 141 rimplifier the following cxprc~sionr IO bc tahn into account in cyclic rating cvrlumon in non rmusoidrl conditions.

7 1 1

It should be noted that the 'is,, coefficients have the same structure of the Yi coefficients in ( I ) with the only difference that they now refer to the fundamental of the non sinusoidal current waveform. The coefficients Y , . ~ , that are the ratios of the current harmonics to the fundamental, represent the harmonic mark linked to the fed non linear loads.

Having in mind (4), the relation (3) becomes:

The temperature rise at t = I hour. 8( I) , arising for the subsequent application at t = 0 of a single step We of joule losses lasting I hour, can he computed as:

( 6 )

with the position that e,(O) = 0. By iterating the above procedure likely in the sinusoidal

case (12-131, with the same ordering technique and with the formal substitution of the currents with the losses (fundamental plus harmonics), the maximum conductor temperature rise at time t = T hours is:

(7)

where the scaled quantities Ye.,. Y,,,, ... are the ordinates of the squared current stepped curve at fundamental ordered for the T hours before t = T, expected time of the highest temperature.

The relation (7) is very useful to introduce the cyclic rating factor M,, in non sinusoidal conditions. For assigned harmonic mark linked to the fed non linear loads, this quantity can be defined as the factor by which the permissible steady-state rated current I n (100% load factor) has to be multiplied to obtain the permissible highest value of the fundamental of non sinusoidal currcnt durinz the daily cycle I,,,, (I-,, = M., IRj such that the conductor temperature attains but does nor exceed. the standard permissible maximum temperature during the cyclc. Having in mind (7) i t results:

( 8 )

where the temperature ratios are the same as in (1 I . It should be noted that also in non sinusoidal conditions

the maximum conductor temperature caused by the actual non sinusoidal cyclic load current may be approximated by the maximum conductor temperature caused by the actual non sinusoidal current applied for a time 7 = 6 hours prior the expected time of maximum temperature, ana a constan1 current applied for all earlier times. its amplitude being an average provided by the new loss-load factor (41. This has been numerically verified comparing in several cases the cyclic rating factors (8) obtained with 7 = 6 hours with the one obtained considering the whole daily cycle. as shown in [lo]; in all the examined cases the difference between the two procedures always resulted less than 2%.

The applicability of the proposed expression for the cyclic rating in non sinusoidal conditions requires, like in the sinusoidal cases, the knowledge of the form of the fundamental current of the cycle; this knowledge allows to calculate the coefficients Y,,. In addition, the nature of the non linear loads which the cable feeds has to be known; this knowledge allows to calculate the ratio of the current harmonics to the fundamental Y, .~. No additional time temperature variations have to be calculated.

We note that in applying (8) the ac cable equivalent resistances at harmonic frequencies have to be calculated. Both skin and proximity effects and losses in other metallic parts of the cable have to he taken into account properly; the hest results have been obtained making total joule losses equivalent to conductor joule losses. In [ I l l how to calculate all the needed coefficients is illustrated.

Let us now consider the variation of the resistances with temperature, initially neglected. Strictly speaking. all the resistances of the relations (8) or (10) should be calculated at proper temperature values: in fact the resistances Rh assume different values versus time in dependence on the transient that characterizes the cable temperature during the load cycle. As already known, to rigorously take into account this dependence is not trivial, because the resistance values depend on temperature and, in turn, the temperature values depend on resistances: it follows that an iterative procedure should be employed to solve the problem, but this is neither a simple nor practical solution. Fortunately, no1 many noteworthy errors in cyclic rating factor M,, evaluation have been numerically evidenced if all resistances are calculated at thc same temperature. In particular, as later seen in the numerical applications, a cautious evaluation can be done assumins as reference temperature for ali resistances the standard maximum permissible temperature; the errors evidenced in several numerical applications have ric; bccn more than 3;.

111. EMERGENCY RATING W NON SIAIJSOIDAL CONDITIONS

In sinusoidal conditions [13]. the emergency rating of cables refers to cables carrying an emergency current following a constant current (less than the rated current) or a cyclic current. The emergency rating is sometime called short time rating [ I I ] and requires computation of an emergency rating factor N by which the permissible steady- state rated current In (100% load factor) is multiplied to obtain the emergency load current IE (IE = N In) which may be applied so that the conductor temperature rise above ambient at the end of the period of emergency loading attains, but does not exceed, the maximum permissible temperature rise emay. The maximum temperature rise in emergency conditions is in excess of or equal to the maximum standard permissible temperature associated with sustained 100% rated current.

As well known [13], the expression of the emergency rating factor N is obtained assuming that the cable prior the emergency load is canytng a constant current I, for a sufficiently long time for steady-state conditions and that the temperature rise is proportional to the joule losses; if a cyclic load with the highest value of current equal to I,, amperes has been applied for a long time , then I, = (p)"zlm where p is the load-loss factor of the cyclic load [ I I]. The emergency rating factor N is obtained as:

where:

and being R, the ac resistance of conductor before application of emergency current. RR the ac resistance at standard maximum permissible temperature. RE the ac resistance at the end of the assigned period TE of emergency loading and eR(TE) the conductor temperature rise at time t = TE follouing application of losses Wn due to the steady- state rated current. The temperature rise ratio in (9) - like the temperature ratios present in ( I ) - is furnished by IEC Standard [12-13] for the various cable configurations.

In non sinusoidal conditions, the presence of the joule losses due to current harmonics has to be taken into account once again so that the simplified expression (9) has to be properly modified.

Let lE.h and IE., be, respectively. the RMS value of the h" harmonic and of the fundamental of the emergency non sinusoidal current, RE., the cablc ac equivalent resistance a1 frequency corresponding to the hlh harmonic and at the end of the period TE of emergency loading.

Assuming once again that the temperature rise is proportional to the joule losses (including the harmonic losses), the following relation can be written:

where WE are the Joule losses (fundamental plus harmonics) in emergency conditions, W. are constant Joule losses before application of emergency non sinusoidal current, ea(-) is the steady-state conductor temperature rise following application of losses W,.

The expression of the emergency rating factor No, in non sinusoidal conditions depends on the load applied before the application of the emergency current.

If a constant sinusoidal current I, is applied before the emergency loading, the expression (I 0) with trivial manipulations becomes:

The relation (11) is very useful to introduce the emergency rating factor Nns in non sinusoidal conditions. For assigned harmonic mark linked to the non linear loads fed in emergency conditions, this quantity can be defined as the factor by which the permissible steady-state rated current In (100% load factor) has to be multiplied to obtain the permissible highest value of the fundamental of non sinusoidal current II.E = N., In) which may be applied so that the conductor temperature rise above ambient at the end of the period of emergency loading attains, but does not exceed, the maximum permissible temperature rise e,-. Bearing in mind ( I I ) it results:

If the cable is subjected for a long time before the application of the emergency current to joule losses W, equal to the average Yalue of the losses during a daily cyclic non linear load W,, = RlpnsI~ax, l (see relation (4)). the expression (IO) with trivial manipulations becomes:

where: I E.h

7E.h =I E. I

I t should be noted that the coeficients that is thc ratios of the current harmonics to the fundamental. are the

719

harmonic mark linked to the non linear loads fed in emergency conditions. It should be noted. moreover, that the ratio RI& disappears in (13) since both resistances are evaluated at fundamental frequency and at standard permissible maximum temperame.

Bearing in mind (13) it results: r ,112

(14)

where:

The applicability of the proposed expressions for the emergency rating in non sinusoidal conditions requires, like in the sinusoidal cases, the knowledge of the current applied before the beginning of emereency period; this knowledge allows to calculate the coefficients h, a n d i t . In addition, the n a m e of the non linear loads which the cable feeds has to be known; this knowledge allows to calculate the ratio of the current harmonics to the fundamental No additional time temperature variations have to be calculated.

IV. NUMERICAL APPLICATIONS

Numerical applications have been developed to evaluate the derating of low voltage and medium voltage cables in presence of harmonics and in cyclic or emergency conditions.

The low voltage and medium voltage cables analyzed are:

. cable type N. I : I O kV single conductor XLPE cable under ground in flat formation (cable model N. I of

cable type N. 2: IO kV three-core XLPE cable under ground (cable model N. 2 of [ I I]); cable type N. 3: 0.75 kV four conductor EPR cable under ground (cable model reported in Appendix);

The XLPE cables have copper screen while EPR cable

[ I l l ) ;

does not have it

A. Cyclic raring in non sinusoidal condirions

Various load cycles with harmonics have been considered, typical of low voltage and medium voltage level. However, since to report all them i t is impossible. in the following. we only refer about some cascs in which we have assumcd that thc Y,,, coefficients - which detail the form of the fundamental current of the daily cycle - are coincident with the Y: corfficienl shown in thc IEC Standard 853 [12-13] for the sinusoidal operating conditions.

With reference to the harmonic profile. both the case in which the shape of non sinusoidal current waveforms

remains unchanged during the cycle and the case in which the shape changes are considered. In particular. the following harmonic profiles have been considered:

profile N. I : the shape remains unchanged and it is characterized by the yh coefficients reported under cavital letter A in Tab. I: profile N. 2 : as in profile N. I , but with the yh coefficients reported under capital letter B in Tab. I; profile N. 3: as in profile N. I but with the yh coefficients reported under capital letter C in Tab. I; profile N. 4: the shape changes during the cycle with the profiles I , 2 and 3 that cyclically repeat every three hours.

Profile N. 1 is taken from IEEE Standard 519 [20] and it is the profile given for AC-DC converters as described in Table 13.1 of the Standard. The profile N. 2 takes the value for the first scenario and attenuates all harmonics so that the THD reaches I O %. The profile N. 3 takes the values for the first scenario and attenuates all the harmonics so to represent a combination of linear and non linear loads.

The values of the cyclic rating factor hl,, in non sinusoidal conditions for the three cable types and for the considered four profiles are reported in Tables II and 111, compared to the cyclic rating factor M in sinusoidal condition, reported in the Tables as profile 0. The cyclic rating factors of Table II have been calculated with 7 = 6 hours and assuming for all resistances the same temperature: the standard maximum permissible temperature: the cyclic rating factors of Table Ill have been calculated considering the whole cycle and applying the iterative procedure outlined at the end of Section 11.

Tablc I Harmonic profilcr.

Yh [P.".] A B C

h

I 5

7

I1

13

17

I 9

2 3

25

29

31

35

37

4 1

4;

47

49

I

0.192

0.132

0.073

0.057

0.035

0.027

0.020

0.016

0.014

0.012

0.01 I

0.010

0.009

0.00s

0.008

I

0.050

0.0s0

0.035

0.035

0.030

0.027

0.012

0.012

0.012

0.0 I2

0.007

0.007

0.007

0.007

0.007

I 0 . l 2 l

0.083

0.046

0.036

0.022

0.017

0.013

0.010

0.009

0.00s

0.007

0.006

0.006

0.005

0.00s

0.007 0.007 0.004

THD 1 25.7'X 10% 16.270 72u

Table II Cyclic raring facton for vanoms cable types and profiles (-6 hours and all resistances calculated st standard maximum permissible tempetatun)

Cable Cable TypcI Type2

Profile Cable Type3

Tablc 111 Cyclic rating factors far various cable wee and pmfilcs (whole cycle

and a11 rcsistanccs calculatcd with an ilcrative praccdurc)

Profile

1.245 1.211 1.152 1.102 1.115 1.108

1.209 1.187 1.144

1.182 1.170 1.134

4 1.141 1.139 1.117

From the analysis of the Tables I1 and III it should be

the harmonics may create a significant change in the cyclic rating factor values; as foreseeable, the most critical harmonic profile is the N.I while the less critical one is the N.2, so that a positive influence of the attenuation of the harmonics to meet 10% limit ofTHD can be revealed; the influence of the change of the non sinusoidal current waveforms during the cycle (profile 4) is not particularly pronounced, being the maximum temperature during the cycle mainly constrained by the hour in which the harmonic content attains the highest value; the cable type N. I and N. 2 are the most subjected to the harmonic influence due to significant additional harmonic losses in metallic parts of the cable other than conductor; this is particularly the case of cable type N. 1 ; the errors between the cyclic rating factors evaluated with I = 6 hours and with all resistances calculated at the maximum standard temperature and the ones evaluated with the whole cycle and with all resistances calculated at the actual temperatures are always less than I ,3%.

Eventually, in order to show the strong influence that may have the harmonics on the cyclic rating of low voltage and medium voltage cables, the Table IV shows the actual

noted that:

maximum temperatures that cables reach if the harmonics are neglected in the sizing stage and the profile N. I is the actual operating condition. These values are compared with the maximum standard permissible temperature associated with sustained 100% rated current.

B. Emergency rating in non sinusoidal conditions

Various emergency loads with harmonics have been considered, typical of low voltage and medium voltage level. However, since to report all them it is impossible, in the following, we only refer about some cases in which the three cable type 1 , 2 and 3 of the above Section A are subjected to:

constant sinusoidal current I. equal to 0.7 In or non sinusoidal cyclic load characterized by the four harmonic profiles considered in Section A, before the beginning of the emergency period; non sinusoidal emergency conditions characterized by the four harmonic profiles considered in Section A.

Moreover, the maximum temperature rise in emergency conditions 0- is assumed to be equal to 105 C for cable types 1 and 2 and equal to 100 C for cable type 3. The period TE of emergency loading is assumed to be 6 hours.

The values of the emergency rating factor N., in non sinusoidal conditions for the three cable types are reported in Table V, compared to the emergency rating factor N in sinusoidal condition, reported also in Table V as profile 0. Constant sinusoidal current before the emergency conditions was assumed.

Table VI reports the same factors of Table V, but assuming non sinusoidal cyclic load before the emergency conditions.

From the analysis of Tables V and VI the same considerations as for cyclic loads arise regarding both the most critical harmonic profile (the profile N.1) and the most sensitive cable (the cable type N.l).

Moreover, it should be noted that the emergency rating factors obtained starting from constant sinusoidal current are greater than the ones obtained starting from cyclic non sinusoidal load. This is not a general rule, because it is due to the fact that the cable temperature just before the emergency condition is lower for the cases of Table VI than for the ones ofTable V. As obvious, other cases can arise in which the behavior is opposite.

Tablc IV Cable maximum ~cmperaturc dunng cyclic non sinusoidal

load ( profileN. I)

cable Actual maximum Maximum scandad tempcrarure lCmpEratUrC

[Cl . r y

. . 107.5 90

3 I 99.3 85 72 I

Table V Emergency rating fastars far various cable t y p and pmfila. staniag

hnm sinusoidal constant c m t

Pmfils before

E m e r g "

N,

Cable Cable Cable Type1 Typc2 Type3

Emergency

1.496 1.357 1.272 I i I 1.333 1.260 1.223 1.454 1.333 1.263

1.424 1.316 1.252

0 4 1.401 1.302 1.246

I

2

3

4

Table VI Emergency rating factor for various csblc types and profilcs. rming

I 1.201 1.187 1.185

2 1.314 1.256 1.223

3 1.286 1.239 1.213 4 1.278 1.233 1.210

f" cyclic non sinusoidal c m t

Conductor

s (mot')

before Emergency

1.353 1.211 1.232

C"

95

In (A) TI ( K - W

h ( K . W

T, ( K . W

Table Vn Csblc maximum tcmperaturc during emergency non sinusoidal

load ( profile N. 1)

296

0.3895

0.2270

0.657

CablE A C N ~ m i m u m Maximum emergency temp cram ImperaNE

rc1 ["Cl type

125.1 105

112.4 105

3 105.4 100

Eventually, in order to show the strong influence that may have the harmonics on the emergency rating of low voltage and medium voltage cables, the Table VI1 shows the actual maximum temperatures that cables reach if the harmonics are neglected in the sizing stage and the profile N. 1 is the actual emergency operating condition. These values are compared with the maximum permissible temperature in emergency conditions.

1 12.86 EPR l n s u l at ion

D.h" I 16.51

Cameuted Pammncrs 1Hotte~t Cablc)

V. CONCLUSIONS

In this paper the problem of the cable cyclic and emergency ratings in non sinusoidal operating conditions has been analyzed. The drawn expressions guarantee a practical and immediate application of the approach. In fact, the derived cyclic and emergency rating equations need only

VI. REFERENCES

[ I ] A. Cavallini. D. Fabiani, G . M-mi. G.C. Montanan and A. Contin. "Voltagc endurancc of cleeirical components supplied by distoncd voltage wsvcforms ". Prw. 2000 lntcmational Symposium an Elmmeal Insulation. DO. 73-76. Anahcim. California (USA). . . . .. April 2000. P. Caramia. G . Carpinclli. E. Di Vito. A. Losi and P. Vcrdc. "Probabilistic Evaluation of thc Economical Damage duc to

121 122

141

I51

Harmonic Losses in Industrial Encrgy Systems. IEEE Trans. Powcr Delivery. Val. II. No. 2.pp. 1021.1031. 1996. A. Cavallini. 0. Mananti. G.C. Montanari and D. Fahiani. The cffect of powcr system hamonie on cable endurance. A entical nviov to IEEE std. 5 I9 voltagc distortion limiu. hoc. IAS Annual Meeting, Roma (Italy), Cktobcr Zoo0 P. Caramia. 0. Carpinclli, A. Losi. A. Rusro and P. Vcrde. A Simplified Method for thc Probabilistic Evaluation o f the Economical Damage duc to Harmonic Lossn. h c . of 8 International Conference on harmonies and Quality o f Powcr, pp. 767-776, Athens. 1998 P. Csramia, G. Carpinclli, P. Vcrde, G. Mananti, A. Cavallini. G.C. MontanariAn approach to Lifc Estimation of Electrical Plant Components in thc Pnscncc of Harmonic Distortion. Pmc. of Ninth Intmional Conference on Harmonics and Quality of Powcr, pp. 887-891. Orlando. Florida. 2000. S. Meliopaulos. M.A. Manin: Coldot ion of Secondory Cable LDsres and Ampoclry in the Prerence of Honnonics . IEEE Trans. on Powcr Deliwry. n. 22, April 1992, pp. 45 I- 459. G.Hiranandani: Colculorion 91 Cable Ampocilies Including the &Is o/ Hormonicr - IEEE Industry Applications Mag&ne. MarchJApril 1998. pp. 42-51. J.A. Palmcr. R.C. Dcgcncff. T.M. McKcman. T.M. Halleran: b e - typc Cablc Ampacity in the Prcscncc o f Harmonics - IEEE Trans. on Power Delivery. n.4, 1993. pp. 1689-1695. G.CarpinclB. F. Donaui, D. Valcnra: On rhe Low Voltage ond Medium Volioge Cables Sizlng Problem in Presence of Current and Voltage Non Slmnusoidal Waveform - LEncrgia Elemica, n. 5 , 1987,pp. 181 -187. H. Goldberg: The Colculorion of Cyclic Rating Foctor~ for Cables Laid Direct or in Ducts - IEE Procecdings Pan C. vol. 104. 1956. pp.154-166. G. J . Andcn: Raring q{Elecrric Power Cable3 - EEE Pres. New York (USA). 1997. Colculorion of the Cycllc ondEmmergency Cvrrcnr R ~ i l n g o/Cables. Port I: Cyclic Raring FaerorJor Cables up IO and Including 18/30 (36) k V - IEC Publication 851-1. 1985 Colcularion of the Cyclic ond Emergencv Currenr Raring o/Cabies. Pa? /I: Cyclic Roling Faclor qf Cables p x r e r than 18/30 (36) I l l and Emmergcncy Ratings for Cables o/ all Voltages - IEC Publication 853-2. 1989 M.H. MeGrath Discussion Contribution to Neher, 1964, IEEE Trans. on Powcr Apparatus and Symms, vol. 83, 1964. p.111. H. Goldbcrg: The Colculotion o/ Cyclic Rating FoNors and Emergency Looding/or one or more Cobler Laid Direcr or in DUCIJ - IEE Praceedingr Pan C . vol. 105. 1957. pp.46-54.

1161 P. Caramia. G. Carpindli, A. LaVitola. P Vmddc: Simplitid Expression of the Evaluation of thc Cyclic Ratings of Low and Medium Voltage Cabln in Nan Sinusoidal Conditions, IEEE Wintcr Meeting, Singapom. 2000, pp. 686-2909.

[I71 H. Goldhcrg: Emergency hading of Buried Cable with TPmperorure-d~pendenr Conductor Rerirtmce - IEE Pmccdings.

G. J. Andcn, M. Vainbcrg, D. I. Harroeks, S. M. Fory. and J. Mollis. Parametcm affecting economic selection of cahlc iizcs, IEEE Tms. PowcrDclivcry,vol 8.pp.1661-1667.Oct. 1993. P. Caramia, G. Carpinclli, A. La Vitala. P. Verde: On the Economic Selection of Medium Voltage Cable S i z e in non Sinnusoidol Conditions - IEEE Transactions on Power Dcl ivw. vol. 17. N.I. 2002. pp. 1-7. IEEE Recommended Practices and require men^^ /or Harmonic Control in Electrical Power Systems, IEEE Std 519-1992, IEEE. New York. NY, A p d 1993.

MI. 118,1971,pp. 1807-1810. [I81

[I91

[20]

VI[. BIOGRAPHIES

Guido Cnrpinolll (M91) was bom in NPPICS. Italy. in 1953. He rcceived his degree in Elcctrical Engineenng from the Univcrsita dcgli Siudi di Napoli in 1978. Hc bccamc Professor in Industrial Energy Systems in 1990 at Univerrita degli Studi di Cassino. Italy. H i s rcsearch inlcmt concerns clcctlical power systcms and power quality. Guido Carpinelli i s mcmbcr of IEEE and componcnt of the IEEE Working Group on Powcr System narmonicr. Pierluigl Carsmi. was ham in Naples. Italy. in 1963. Hc ohtaincd his dcgnc in Elccnical Engineenng from thc Univenita degli SNdi d i Cassino. Italy, in 1991. Currently. hc is Arrociatc Professor o f Eleftrical Power System a1 UniveniIi degli Studi di Cassino. His research int~rcsl ConcEms mainly POWU clectronics in power systems. Paoln Verdc was bom in Bencvento. Italy. in 1964. She rcceivcd her dcgrcc in Electrical Engineering from the Univcrsitd d q l i Studi di N~poI i . Italy, in 1988. Currently. shc is Associalc Professor of Electrical Powcr Systems at Univeriitb dfgli Studi di Cassino. Italy. Hcr rcscarch interest conccms mainly powcr clccwonics in power systems. Pnola Vcrdc is a mcmbcr of EEE and component of the IEEE Working Gmup on Powcr S y s m Harmonics. La Vitols Alfredo was born in Sora (FR). Italy. in 1973. Hc ohtaincd his dcgrec in Elcctrical Enginccnng from thc Univcrsild dcgli Studi di Cassino, Italy. in 1997. Currently. he i s PHD student at Univcnitb degli Studi d i Cassino. His research interest conccms mainly power clmtronics in power systems.

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