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Overvoltage attenuation in power cable lines—A simplified estimation method
Electric Power Systems Research 80 (2010) 506–513
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Electric Power Systems Research journal homepage: www.elsevier.com/locate/epsr
Overvoltage attenuation in power cable lines—A simplified estimation method M. Marzinotto ∗ , C. Mazzetti Electrical Engineering Department, Sapienza University of Roma, Via Eudossiana 18, 00184 Roma, Italy
a r t i c l e
i n f o
Article history: Received 28 April 2008 Received in revised form 6 August 2009 Accepted 24 October 2009 Available online 4 December 2009 Keywords: Cable lines Insulation coordination Lightning surges Switching surges Overvoltages
a b s t r a c t Cable lines impart attenuation and distortion to overvoltages coming from overhead lines. In particular the attenuation is an important factor for the insulation coordination of a cable line and consequently for its reliability. The evaluation of such attenuation needs the utilization of numerical programs and their utilization, although it becomes an obliged step, is not an easy task without a specific skill. In this paper a simplified method is proposed which is based on the results of a specific numerical program, in order to evaluate the overvoltage attenuation introduced from cable lines for both the conductor screen (insulation stress) and screen to ground (jacket stress) modes of propagation. Although such method introduces some approximation, it is a useful tool in order to have both a first and conservative evaluation of the overvoltage stressing the cable line insulation when the impinging overvoltage to the cable line is known. © 2009 Elsevier B.V. All rights reserved.
1. Introduction Insulation coordination of cable lines requires the knowledge of the overvoltages stressing the cable insulation and the probability of the insulation breakdown to such stresses [1–9]. The estimation of the overvoltages can be assessed via numerical programs [10] that require a skill for the their utilization. The IEC 60071 standard [11] gives a method for a statistical approach to switching surges. Breakdown voltages of cable line can be estimated via dielectric strength test on short cable samples before the installation [12–22]. Existing standards [11,23] approach the insulation coordination of cable lines through deterministic methods which are based on the knowledge of the maximum overvoltage that stresses the cable line insulation and its withstand voltage level for both lightning and switching surges. Aim of this paper is the evaluation, through a simplified method, of the overvoltage stressing the cable insulation when the overvoltage, in terms of amplitude and wave shape, coming from an overhead line and impinging a cable line is known. Typical power system configurations, cable ratings and power cable formations are considered. Overvoltages coming from overhead lines when they impinge cable lines are attenuated and distorted. Attenuation and distortion rates are due to cable features (formation, length, burial disposition, etc.), impinging voltage wave shape, equipment connected at both ends (e.g. transformer, overhead line). While cable length
and impinging voltage shapes strongly influence the overvoltage attenuation rate [13,24–27], boundary conditions (e.g. ground impedance value of cable screen, etc.) and power cable formation play a secondary role [27]. In this paper the overvoltage attenuation rate of a cable line is quantified through an “overvoltage reduction factor” as the ratio of the peak value of the overvoltage stressing the cable line insulation and the peak value of the overvoltage impinging the cable line. Such overvoltage reduction factor is then dependent on all the aforementioned variables, which play a part in the attenuation of the overvoltage. Thus, the overvoltage reduction factor is not only useful for the estimation of single overvoltage event stressing the cable line when the impinging overvoltage is known, but it is also useful for the estimation of the statistical distribution parameters of the overvoltages stressing the cable line insulation when the statistical distribution of the impinging overvoltages is known [27]. The paper is framed in different sections. In Section 2 the cable and power systems configuration considered here are illustrated. Cable line model and ground return model used for the simulations are mentioned in this section too. In Section 3 the three considered stressing modes of propagation of the overvoltages in a power cable line are illustrated. In Section 4 the results of the simulations are presented and discussed. Concluding remarks are reported in Section 5, while Section 6 closes the paper.
2. Analyzed configurations and cables ∗ Corresponding author. Tel.: +39 06 44585544; fax: +39 06 4883235. E-mail addresses: [email protected] (M. Marzinotto), [email protected] (C. Mazzetti). 0378-7796/$ – see front matter © 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.epsr.2009.10.027
Cable lines are usually connected between overhead lines or transformers or between a combination of both. Cable lines
M. Marzinotto, C. Mazzetti / Electric Power Systems Research 80 (2010) 506–513
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Table 1 Cable lines characteristics taken into account for the simulations.
Fig. 1. The two analyzed configurations: (a) overhead line/cable line/transformer; (b) overhead line/cable line/overhead line.
connected at overhead lines are subjected to a higher number of dangerous events. In fact, overhead lines work as collectors of lightning strokes and then they can transfer harmful overvoltages to the cable line. Due to the high value of transformer surge impedance [24,25], an overvoltage travelling along a cable line connected between an overhead line and a transformer can double its peak value when it reaches the transformer side end. Thus, the most critical configuration for a cable line for the insulation coordination point of view is usually the mixed configuration with an overhead line at one end and a transformer at the other end. On the other hand, cable lines connecting two overhead lines can experience higher number of dangerous events due to lightning strokes. In this paper two configurations only are considered: “overhead line/cable line/transformer” and “overhead line/cable line/overhead line” as reported in Fig. 1. Overhead lines have been considered of infinite length on both configurations and the space distribution of the overhead line conductors has been appropriately chosen if a medium voltage (MV), a high voltage (HV) or an extra high voltage (EHV) line has been taken into account. In the case of Fig. 1a), transformer has been simulated with a capacitance connected between the cable conductor and ground [23]. Values of 1 nF and 4 nF have been selected for the MV transformer and for the HV and EHV transformers, respectively; such values are in accordance with [23]. In this case, the approximation usually suggested in standards is able to take into account even the open line end configuration that represents the worst condition for the cable line insulation. Bays capacitance have more or less the same order of magnitude [28] considering typical voltage transformers and bays length. Power transformer surge response has been the object of several studies [29–33] and different and complex representation have been proposed in literature in order to take into account its frequency-dependent input impedance. The adopted transformer representation here is a first approximation of its input impedance model. Cable screens have been considered grounded at both ends of the cable line with a surge impedance of 30 at the overhead/cable line transitions end and with a surge impedance of 10 at the transformer side end. Such values have been chosen in accordance with [8,11,23]. In fact, the CIGRE formula [23,34,35], highlights that the surge impedance value (with high injected current) of a rod electrode is always smaller than the value measured at 50/60 Hz (with low current) [34]. In low resistivity soils as 100 m considered in this paper, tower footing resistance value measured at 50/60 Hz are usually never higher than 30 . Furthermore in both medium voltage and especially high voltage transformer stations the ground resistance measured at 50/60 Hz is lower than 1 . Consequently a surge impedance of 30 at the overhead/cable line transitions end and a surge impedance of 10 at the transformer side end for the grounding of the cable screen represent conservative values for the estimation of overvoltages along a cable line. No surge arrester are considered at both ends of the cable line of both configurations. The stressing wave shape impinging the cable line has been considered coming from the overhead line as a phase-to-ground
20 kV cable Conductor cross-section Inner semicon thickness Insulation thickness Outer semicon thickness Inner semicon resist. Insulation tan ı Screen cross-section Conductor material Jacket thickness Jacket material Disposition type
150 mm2 0.7 mm 5.5 mm 0.5 mm 10 m 2 × 10−3 25 mm2 Aluminum 2 mm PVC Trefoil
Conductor radius Inner semicon Insulation ε Outer semicon ε Outer semicon resist. Insulation type Screen type Screen material Jacket ε Soil resistivity Burying depth
7.1 mm 1000 2.6 1000 10 m EPR Wires Copper 5 100 m 1m
150 kV cable Conductor cross-section Inner semicon thickness Insulation thickness Outer semicon thickness Inner semicon resist. Insulation tan ı Screen cross-section Conductor material Jacket thickness Jacket material Disposition type
1600 mm2 2 mm 20 mm 1 mm 10 m 2 × 10−3 85 mm2 Aluminum 4 mm PE Flat
Conductor radius Inner semicon ε Insulation ε Outer semicon ε Outer semicon resist. Insulation type Screen type Screen material Jacket ε Soil resistivity Burying depth
26 mm 1000 2.6 1000 10 m EPR Wires Copper 2.3 100 m 1.2 m
400 kV cable Conductor cross-section Inner semicon thickness Insulation thickness Outer semicon thickness Inner semicon resist. Insulation tan ı Screen cross-section Conductor material Jacket thickness Jacket material Disposition type
2500 mm2 4 mm 28 mm 2 mm 10 m 0.4 × 10−3 393 mm2 Copper 5 mm PE Flat
Conductor radius Inner semicon ε Insulation ε Outer semicon ε Outer semicon resist. Insulation type Screen type Screen material Jacket ε Soil resistivity Burying depth
28 mm 1000 2.3 1000 10 m XLPE Sheath Alum. 2.3 100 m 1.2 m
overvoltage with the same amplitude and the same wave shape for each phase. Overvoltages due to lightning are the most harmful in MV systems, while for EHV levels switching surges can even be more critical. In the HV level switching surges are not negligible, although lightning surges are usually higher. Four different types of voltage wave shapes impinging the cable line have been selected in order to take into account events of lightning and switching surges. In particular the standard lightning and switching wave shapes have been considered. Although flashover and back-flashover of insulator strings due to a lightning stroke on overhead line give rise to tail in the range of 10–20 s [35], the standard 1.2/50 s wave has been selected because of, as it will be illustrated later on, gives higher values (and then conservative values) of the overvoltage reduction factor. A non-standard short wave shape has been also considered in order to take into account likely truncated waves. Finally a 10/350 s wave have been also considered in order to take into account direct strokes to phase conductor without subsequent flashovers on insulator string (possible scenarios in HV and EHV overhead line only). Such wave is the standard lightning current first stroke [36–40]. In fact, when a direct stroke to overhead line phase conductors occurs and no flashover on insulator strings takes place the corresponding overvoltage wave is similar to the stroke current wave [35]. The wave shapes have been simulated by Heidler function [36,39,40] with adequately selected parameters, which is more realistic than the typical double exponential function. In fact, the first derivative of Heidler function is zero at the foot of the wave in spite of the double exponential wave. Three types of cable ratings have been selected for the analysis: a 20 kV MV cable, a 150 kV HV cable and a 400 kV EHV cable. Their characteristics are reported in Table 1. In the same table the soil
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resistivity and the burying characteristics considered in the simulations are also reported. HV and EHV cable lines are usually buried in flat formation; here the minimum distance between the jackets of two adjacent cores has been considered of 30 cm for both the 150 kV and the 400 kV cable lines. A Matlab program implementing the Shelkunoff theory (frequency-dependent cable model) [41,42], that takes into account also the effect of the semiconductive layers [36–38] has been used for the estimation of the overvoltages stressing the cable line insulation starting from a known wave shape travelling on the overhead line and impinging the cable line. Impedance and admittance of the semiconductive layers have been considered taking into account the last developments performed by Ametani et al. [43–45]. The ground return has been considered using the Wedepohl–Wilcox’s approximation [46,47] of the Pollaczek’s formula [48]. 3. Overvoltage stressing modes for power cable lines The propagation of overvoltage along a cable line is strictly influenced if a flashover occurs at the transition point overhead line—cable line. When surge arresters are not used in an overhead line—cable line transition point, the insulation of the tower at the transition point has usually a reduced withstand value to voltage surges in respect of the insulation of the other towers. Consequently, when a voltage surge travelling along an overhead line, reaches the overhead line—cable line junction two conditions are possible: the voltage surge may be high enough to cause a flashover along the external insulation (along the cable termination or along the insulator string of the last tower), or the voltage surge is not high enough and the external insulation withstands. Considering a flashover along the cable termination, conductor and screen of the cable are stressed (neglecting the arc voltage) by the same voltage wave (Vc = Vs in Fig. 2). On the contrary, if no flashover occurs, only the conductor is directly stressed by the surge coming from the overhead line: the external stressing voltage is V only. Beside this two case, a third case should be considered: lightning struck to the last tower (at the overhead line—cable line transition point). In this case again two conditions are possible: the lightning current is high enough to cause back-flashover on the external insulation, or the lightning current is not high enough and back-flashovers does not occur. In the former it is possible to consider again Vc ∼ = Vs in
Fig. 2. In the latter, the screen is directly stressed only, and then Vs is the external stressing voltage only. Thus, taking into account Fig. 2 which shows the overhead line—cable line transition point: three are the external stressing conditions for a cable line that are considered here: • the external voltage stress is applied to the conductor only (referred from now on as “stressing mode” #1 (SM #1)); • the external voltage stress is applied to the screen only (referred from now on as “stressing mode” #2 (SM #2)); • the external voltage stress is simultaneously applied to the conductor and the screen (referred from now on as “stressing mode” #3 (SM #3)). Finally, it is possible to assert that a voltage surge coming from the overhead line can give rise to SM #1 or SM #3, while a voltage surge due to stroke to the last tower (at the overhead line—cable line transition) can give rise to SM #2 or SM #3. Actually different stressing modes are possible with / Vs = / 0, but they are not considered here. The aforeVc = mentioned three SMs are in any case those more representative of the possible scenarios. The maximum conductor screen stressing overvoltage (VCS ) and the maximum screen-ground stressing overvoltage (VSG ) are strictly dependent on the SM. Furthermore, VCS and VSG are mainly dependent on cable length due to the effect of the successive reflections of voltage waves at cable ends and to the impinging voltage shapes. In order to take into account the attenuation of the impinging voltage shape, an “overvoltage reduction factor” has been introduced for both the conductor screen (hc ) mode of propagation and for the screen-ground (hs ) mode of propagation: hc =
VCS VH
(1)
hs =
VSG VH
(2)
where VH is the peak value of the voltage surge (voltage-to-ground) impinging the cable line. Factors hc and hs depends on several variables and their analysis is performed in the next section. The utilization of the overvoltage reduction factor (hc and hs ) becomes a powerful tool for a quick estimate of the overvoltage stressing a cable and it bypasses heavy numerical analysis. Thus, the estimation of the overvoltage reduction factor once for all for different wave shapes, cable formations and typical system configurations can help in a first step the engineer to address the insulation coordination of a cable line. 4. Analysis of results 4.1. General considerations
Fig. 2. Sketch of the overhead line—cable line transition point.
Taking into account the three selected cables, a sensitivity analysis on variation of inner and outer semiconductive layers, semiconductive dielectric constant ε, soil resistivity has been considered here and in [26,27,49] showing negligible differences. For the 20 kV MV cable a parametric analysis on conductor crosssection and insulation thickness variations has been also carried out showing weak influence on both hc and hs values. On the contrary, cable length, the wave shape of the impinging overvoltage, the cable rating (e.g. MV, HV or EHV), the termination type of the cable line (transformer or overhead line) and the SM have not negligible effect on the attenuation of the overvoltage. In order to simplify the discussion of results, they are reported and commented separately for the three different SMs. Furthermore for each SM, the two
M. Marzinotto, C. Mazzetti / Electric Power Systems Research 80 (2010) 506–513
Fig. 3. Overvoltage reduction factor hc vs. cable length for the three considered types of cables when the impinging voltage shape is a 1.2/50 s with reference to SM #1 and Fig. 1a.
types of terminations of the cable line, e.g. transformer (Fig. 1(a)) or overhead line (Fig. 1(b)), are also considered. 4.2. Stressing mode #1 Fig. 3 shows the hc variation with cable length with SM #1 and a 1.2/50 s wave shape, for 20 kV, 150 kV and 400 kV cables when the cable line is terminated on a transformer. In this figure it is possible to note the effect of successive reflection: for short cable length the overvoltage stressing the insulation may even reach the ≈70–75% of the impinging one. The same considerations can be made for the Figs. 4–6 where the overvoltage reduction factor is reported vs. cable length for 250/2500 s, 0.5/6 s and 10/350 s impinging wave shapes respectively. These figures highlight that the hc decrease is as weaker as longer the tail of the surge wave. Consequently, for a fixed cable length, the longest is the tail of the wave shape the heaviest is the stress for the cable insulation. For long cable lines the overvoltage reduction factor tends to be asymptotically constant. The cable length value in which such factor becomes constant depends on the impinging wave duration and in particular to the time to half value. For very long cables when the
Fig. 4. Overvoltage reduction factor hc vs. cable length for the three considered types of cables when the impinging voltage shape is a 250/2500 s with reference to SM #1 and Fig. 1a.
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Fig. 5. Overvoltage reduction factor hc vs. cable length for the three considered types of cables when the impinging voltage shape is a 0.5/6 s with reference to SM #1 and Fig. 1a.
successive reflections at cable ends have no further effect in increasing the voltage shape stressing the cable insulation [13,24–27], the overvoltage reduction factor can be estimated as twice the coefficient of transmission (3) where Z1 and Z2 are the surge impedance of the overhead line and the cable line, respectively: =
2Z2 Z1 + Z2
(3)
It is important to outline that (3) does not take into account the losses in the propagation of the waves along the cable leading to a conservative estimation of the peak value of the overvoltage stressing the cable insulation. The curves reported in Figs. 3–6 are well fitted with the following mathematical expression:
x
h = A exp −
B
x
+ C exp −
D
(4)
where x is the cable length and A, B, C and D are constant. The values of such constants are reported in Table 2 for the examined types of cables and impinging wave shapes. Figs. 7–10 show the hc values vs. cable length for the four considered impinging wave shapes and for the three considered cable ratings when the cable line is terminated on an overhead line. It can
Fig. 6. Overvoltage reduction factor hc vs. cable length for the three considered types of cables when the impinging voltage shape is a 10/350 s with reference to SM #1 and Fig. 1a.
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Table 2 A, B, C and D constant values to use in Eq. (4) for the estimation of hc for different types of cables, different impinging wave shapes and stressing mode #1. System configuration as reported in Fig. 1a. Impinging wave shape [s]
A
B [km]
C
20 kV cable 0.5/6 1.2/50 10/350 250/2500
0.3662 0.5611 0.4855 1.024
0.1351 0.3952 0.8787 13.642
0.0767 0.2195 0.4997 0.0107
14.775 5.6274 9.7087 −4.9164
0.1–10 0.1–10 0.1–10 0.4–10a
150 kV cable 0.5/6 1.2/50 10/350 250/2500
0.361 0.6108 0.5959 0.5829
0.1532 0.6373 1.5537 9.6525
0.0801 0.1215 0.3522 0.4485
60.569 40.7000 23.9980 101.28
0.1–50 0.1–50 0.1–50 0.3–50b
400 kV cable 0.5/6 1.2/50 10/350 250/2500
0.4131 0.6206 0.5622 0.5774
0.1634 0.7745 2.0145 14.961
0.1174 0.1631 0.4054 0.4528
95.785 73.800 34.1180 157.60
0.1–50 0.1–50 0.1–50 0.5–50c
a b c
D [km]
Range of validity [km]
For cable length shorter than 0.4 km, hc = 1 (hc % = 100). For cable length shorter than 0.3 km, hc = 1 (hc % = 100). For cable length shorter than 0.5 km, hc = 1 (hc % = 100).
Fig. 7. Overvoltage reduction factor hc vs. cable length for the three considered types of cables when the impinging voltage shape is a 1.2/50 s with reference to SM #1 and Fig. 1b.
Fig. 8. Overvoltage reduction factor hc vs. cable length for the three considered types of cables when the impinging voltage shape is a 250/2500 s with reference to SM #1 and Fig. 1b.
be noted that for each case the variation of hc with increasing cable length is very similar to that of cable line terminated on a transformer except for short cable lengths in which the hc values are about halved. For impinging wave shapes with short tail (0.5/6 s and 1.2/50 s waves: Figs. 7 and 9, respectively) and 10 km of cable length, the hc values reach the same value reported in Figs. 3 and 5, respectively. This fact confirms the aforementioned assertions in which the effect of successive wave reflections at cable ends can be disregarded for very long cables. As for the case of cable line terminated on a transformer, the hc values vs. cable length for cable lines terminated on overhead line well fit the Eq. (4) and the relevant A, B, C and D values for the considered impinging wave shapes are reported in Table 3. The hs values are substantially constant with the cable length and they are quite independent on the impinging voltage shape and on the type of termination of the cable length (transformer or overhead line). The greatest variation of hs value with cable length has been highlighted with the 250/2500 s in which the hs value is less than 1% for short cable lengths and it reaches some per cent for long cable lengths. In Table 4 the values of hs for the three considered cables and for the different impinging wave shapes are reported. When ranges of variation of hs values are reported, the smaller values refer to shorter cable lengths and larger values to longer cable
Fig. 9. Overvoltage reduction factor hc vs. cable length for the three considered types of cables when the impinging voltage shape is a 0.5/6 s with reference to SM #1 and Fig. 1b.
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Table 5 hc values for different types of cables, different impinging wave shapes for stressing mode #2. hc values valid for both system configurations reported in Fig. 1. Impinging wave shape [s]
hc
20 kV cable (cable length between 0.1 and 10 km) 0.5/6 1.2/50 10/350 250/2500 150 kV cable (cable length between 0.1 and 50 km) 0.5/6 1.2/50 10/350 250/2500 400 kV cable (cable length between 0.1 and 50 km) 0.5/6 1.2/50 10/350 250/2500 Fig. 10. Overvoltage reduction factor hc vs. cable length for the three considered types of cables when the impinging voltage shape is a 10/350 s with reference to SM #1 and Fig. 1b.
Table 3 A, B, C and D constant values to use in Eq. (4) for the estimation of hc for different types of cables, different impinging wave shapes and stressing mode #1. System configuration as reported in Fig. 1b. Impinging wave shape [s]
A
B [km]
C
20 kV cable 0.5/6 1.2/50 10/350 250/2500
0.2382 0.2788 0.1816 0.5128
0.1408 0.5885 0.8779 25.627
0.0710 0.1386 0.3251 0.00007
150 kV cable 0.5/6 1.2/50 10/350 250/2500
0.2439 0.3061 0.2513 0.1936
0.1506 0.8539 1.8053 11.896
0.0777 0.1013 0.2405 0.3205
63.816 55.401 30.656 100.84
0.1–50 0.1–50 0.1–50 0.5–50a
400 kV cable 0.5/6 1.2/50 10/350 250/2500
0.2991 0.2924 0.2267 0.1863
0.1377 1.0278 2.6652 19.940
0.1139 0.1372 0.2608 0.3214
94.339 105.08 48.590 156.17
0.1–50 0.1–50 0.1–50 0.4–50b
a b
D [km]
16.2416 8.7183 11.9005 −1.9557
Range of validity [km] 0.1–10 0.1–10 0.1–10 0.5–10a
For cable length shorter than 0.5 km, hc ≈ 0.5 (hc % ≈ 50). For cable length shorter than 0.4 km, hc ≈ 0.5 (hc % ≈ 50).
Table 4 hs values for different types of cables, different impinging wave shapes for stressing mode #1. hs values valid for both system configurations reported in Fig. 1.
<0.01 0.01 0.01 0.025 0.02 0.045 0.05 0.05 0.03 0.06 0.06 0.06
lengths. The variation of hs with cable length can be considered substantially linear. Furthermore due to the small variation in the hs range, the highest value can be considered for any cable length, leading in this way to a conservative estimation of the stressing overvoltage. 4.3. Stressing mode #2 In Table 5 the hc values for different cables and impinging wave shapes are reported for the SM #2. Such results can be extended for both the analyzed system configurations, e.g. cable line terminated on a transformer and cable line terminated on an overhead line. In fact no differences have been revealed regardless of cable termination. For a given cable length, the highest is the cable rating and the highest is the hc value. Furthermore for a given cable rating, the longest is the impinging wave shape the highest is the hc value. The hc values reported in Table 5 highlight that the overvoltage stressing the insulation reduces to less than 6% in respect of the peak value of the impinging wave shape. Table 6 shows the hs values for SM #2 for different types of cables and with different impinging wave shapes. Also in this case such results can be extended for both the analyzed system configurations, e.g. cable line terminated on a transformer and cable line terminated on an overhead line. When ranges of variation of hs values are reported, the smaller values refer to shorter cable lengths and larger values to longer cable lengths. In such cases the Table 6 hs values for different types of cables, different impinging wave shapes for stressing mode #2. hs values valid for both system configurations reported in Fig. 1.
Impinging wave shape [s]
hs
20 kV cable (cable length between 0.1 and 10 km) 0.5/6 1.2/50 10/350 250/2500
0.05 0.06 0.05–0.06 0–0.05
20 kV cable (cable length between 0.1 and 10 km) 0.5/6 0.16 1.2/50 0.21 10/350 0.22 250/2500 0.16–0.22
150 kV cable (cable length between 0.1 and 50 km) 0.5/6 1.2/50 10/350 250/2500
0.06 0.07 0.04–0.07 0–0.07
150 kV cable (cable length between 0.1 and 50 km) 0.5/6 0.32 1.2/50 0.36 10/350 0.33–0.36 250/2500 0.25–0.39
400 kV cable (cable length between 0.1 and 50 km) 0.5/6 1.2/50 10/350 250/2500
0.07 0.08 0.04–0.08 0–0.08
400 kV cable (cable length between 0.1 and 50 km) 0.5/6 0.33 1.2/50 0.37 10/350 0.33–0.36 250/2500 0.25–0.38
Impinging wave shape [s]
hs
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M. Marzinotto, C. Mazzetti / Electric Power Systems Research 80 (2010) 506–513 Table 7 hs values for different types of cables, different impinging wave shapes for stressing mode #3. hs values valid for both system configurations reported in Fig. 1. Impinging wave shape [s]
hs
20 kV cable (cable length between 0.1 and 10 km) 0.5/6 1.2/50 10/350 250/2500
0.055 0.06 0.06 0.07
150 kV cable (cable length between 0.1 and 50 km) 0.5/6 1.2/50 10/350 250/2500
0.065 0.07 0.07 0.08
400 kV cable (cable length between 0.1 and 50 km) 0.5/6 1.2/50 10/350 250/2500
0.075 0.085 0.085 0.09
variation of hs with cable length can be considered substantially linear. Furthermore due to the small variation in the hs range, the highest value can be considered for any cable length, leading to a conservative estimation of the stressing overvoltage. 4.4. Stressing mode #3 It is interesting to note that for SM #3 the hc values are below 1% except for the 250/2500 s impinging wave shape in which it reaches about 2%. Such results are valid for both the analyzed terminations, i.e. transformer and overhead line. Table 7 shows the hs values for SM #3 with different impinging wave shapes. hs values are practically constant with cable length. The wave shape weakly influences the hs value: the largest values are those for longer time to half value of the surge wave. 5. Final remarks The utilization of hc and hs factors is useful for an estimation of the stresses on the insulation and on the jacket of a cable line. The former is much more important than the latter due to the fact that a failure in the insulation leads to an outage. In fact damage of the jacket leads to a breakdown between the screen (or the metallic sheath) and the soil, consequently, a punctured thermoplastic jacket can be a risk for moisture entrance and it may be a threat for the cable life itself [13,50]. From the analysis of results reported in the previous section it is possible to conclude that: • SM #1 is the most critical for the insulation and furthermore cable length play a relevant role: the stress due to the impinging overvoltage significantly reduces with cable length and it is also influenced from the type of cable termination (overhead line or transformer). • SM #2 is the most critical for the cable jacket; it is independent on cable length and on the type of cable termination (overhead line or transformer). • SM #2 gives rise to a cable insulation stress that is only some percent of the impinging overvoltage, while the stress due to SM #3 can be even disregarded for the cable insulation. • The peak amplitude of the overvoltage transferred to the jacket for both SM #1 and SM #3 is only some percent. As a first step, in the reliability analysis of a cable line, only the SM #1 and the SM #2 can be taken into account for a first estimation
of the maximum stressing overvoltage for the cable insulation and the cable jacket, respectively. 6. Conclusions Cable lines reduce overvoltage coming from overhead lines. Such reduction is due to different parameters which have different influence in the attenuation. Furthermore their weight is different regarding what type of stressing mode is considered, i.e. overvoltage stressing the conductor only, the screen only or both. Cable length, impinging overvoltage wave shape, cable termination type have the largest weight for the overvoltages stressing the cable insulation, while only the impinging overvoltage wave shape has the largest weight for overvoltage stressing the cable jacket. The utilization of an overvoltage reduction factor for both conductor screen and screen-soil modes of propagations becomes a useful method for the assessment of power cable reliability. It is then possible to assess the insulation coordination itself and the evaluation of jacket failure too. Although the utilization of such overvoltage reduction factors leads to a simplified method of overvoltage estimation, it can be a powerful way to predict with a conservative approach the reliability of power cable lines. References [1] L.O. Barthold, L. Paris, The probabilistic approach to insulation coordination, CIGRE Electra (May (13)) (1970 May) 41–58. [2] L. Paris, Insulation coordination, in: High Voltage Engineering Research Proceedings ENEL R&D Management, Italy, 1970. [3] A. Taschini, Insulation coordination on high voltage systems, in: High Voltage Engineering Research Proceedings ENEL R&D Management, Italy, 1970. [4] P. Reggiani, Insulation coordination on medium voltage systems, in: High Voltage Engineering Research Proceedings, ENEL R&D Management, Italy, 1970. [5] G. Carrara, E. Occhini, L. Paris, F. Reggiani, Contribution to the study of insulation coordination from the probabilistic point of view, in: CIGRE International Conference, 1966. [6] L. Paris, A. Taschini, Results of recent investigation on switching surges in EHV networks, in: CIGRE International Conference, 1968. [7] L. Paris, R. Cortina, Switching and lightning impulse discharge characteristics of large air gaps and long insulator strings, IEEE Transactions on Power Apparatus and Systems PAS–87 (April) (1968). [8] A.R. Hileman, Insulation Coordination in Power Systems, Marcel Dekker, New York, USA, 1999. [9] W. Diesendorf, Insulation Co-ordination in High-voltage Electric Power System, Butterworth & Co. Ltd., London, England, 1974. [10] TransEnergiesTechnologies Simulation of power network with EMTP-RV, Tome 1 and 2, Hydro Québec, 2004. [11] EN Insulation co-ordination Part 2: Application guide, EN 60071-2 Standard, 1998. [12] M. Marzinotto, On the application of the enlargement law to cable lines, in: Proceedings of IEEE Power Tech 2005, St. Petersburg, Russia, June 27–30, 2005. [13] M. Marzinotto, Insulation coordination of extruded power cable lines, Ph.D. Thesis, Roma, Italy. Padis Ed.—pub. no. 1148369693 31587, 376 pages, September 2006. [14] A. Borghetti, M. Marzinotto, C. Mazzetti, C.A. Nucci, M. Paolone, Insulation coordination of MV cables against lightning-induced overvoltages generated by LEMP-coupled overhead lines, in: Proceedings of 28th International Conference on Lightning Protection ICLP 2006, Kanazawa, Japan, September 18–22, 2006. [15] M. Marzinotto, C. Mazzetti, M. Pompili, P. Schiaffino, Impulsive strength of power cables with different XLPE compounds, in: Proceedings of IEEE Conference on Electrical Insulation and Dielectric Phenomena IEEE–CEIDP 2006, Kansas City, MO, USA, October 15–18, 2006. [16] M. Marzinotto, G. Mazzanti, C. Mazzetti, Comparison of breakdown performances of extruded cables via the enlargement law, in: Proceedings of IEEE Conference on Electrical Insulation and Dielectric Phenomena IEEE–CEIDP 2006, Kansas City, MO, USA, October 15–18, 2006. [17] M. Marzinotto, C. Mazzetti, M. Pompili, P. Schiaffino, AC strength test data of unaged and water tank aged XLPE compounds for transmission and distribution power cables, in: Proceedings of 19th International Conference on Electricity Distribution CIRED 2007, Vienna, Austria, May 21–24, 2007. [18] M. Marzinotto, Experimental Validation of the Volume Effect in the Statistical Enlargement Law for Cable Lines, in: Proceedings of the Nordic Insulation Symposium NORDIS 07, Lyngby, Copenhagen, Denmark, June 11–13, 2007. [19] M. Marzinotto, G. Mazzanti, C. Mazzetti, The effect of conductor radius and insulation thickness in the application of the enlargement law for comparing power cable breakdown performances, in: Proceeding of International Conference on Solid Dielectrics ICSD 2007, Winchester, UK, July 8–13, 2007.
M. Marzinotto, C. Mazzetti / Electric Power Systems Research 80 (2010) 506–513 [20] M. Marzinotto, G. Mazzanti, C. Mazzetti, A new approach to the statistical enlargement law for comparing the breakdown performances of power cables—Part 1: Theory, IEEE Transactions on Dielectrics and Electrical Insulation 14 (October (5)) (2007) 1232–1241. [21] M. Marzinotto, G. Mazzanti, C. Mazzetti, A new approach to the statistical enlargement law for comparing the breakdown performances of power cables—Part 2: Application, IEEE Transaction on Dielectrics and Electrical Insulation 15 (June (3)) (2008) 792–799. [22] M. Marzinotto, G. Mazzanti, C. Mazzetti, Crossing quantities: how to compare electrical strength performances of insulation compounds for power cables, Energy 34 (March (3)) (2009) 245–253. [23] IEEE Guide for the Application of Insulation Coordination, IEEE Std. 1313.2, 1999. [24] A. Morello, Extra high voltage cables and impulse reflections, L’Elettrotecnica 43 (12) (1956) (in Italian). [25] E.W. Greenfield, Transient behaviour of short and long cables, IEEE Transactions on Power Apparatus and Systems PAS-103 (11) (1984). [26] M. Marzinotto, C. Mazzetti, P. Schiaffino, Statistical approach to the insulation coordination of medium and high voltage cable lines, in: Proceedings of IEEE Power Tech 2005, St. Petersburg, Russia, June 27–30, 2005. [27] M. Marzinotto, Relationship between statistical distributions of impinging and stressing overvoltages in power cable lines, in: Proceedings of IEEE Power Tech 2007, Lausanne, Switzerland, July 1–5, 2007. [28] A. Greenwood, Electrical transients in power systems, Wiley–Interscience, USA, 1971. [29] T. Funabashi, T. Ito, T. Sugimoto, K. Miyagi, T. Sano, T. Ueda, J.A. Martinez, A. Ametani, Generalized generator transformer model for transient studies, IEEE Transactions on Energy Conversion 19 (September (3)) (2004) 526–531. [30] A. Piantini, C.V.S. Malagodi, Modelling of three-phase distribution transformers for calculating lightning induced voltages transferred to the secondary, V SIPDA, May 1999. [31] D.J. Wilcox, T.P. McHale, Modified theory of modal analysis for the modelling of multiwinding transformers, IEE Proceedings-C 139 (November (6)) (1992) 6. [32] M.J. Manyahi, Characteristics of surge transfer through transformers: study of conventional distribution transformer and XLPE cable winding transformer (dryformer), Ph.D. Thesis, Uppsala, Sweden. Acta Universitatis Upsaliensis Ed., ISBN 91-554-5398-8, 2002. [33] M.J. Manyahi, Response of transformers to lightning transients and their transfer between the transformer circuits, Thesis in Electricity, Uppsala, Sweden. Uppsala University Ed., ISSN 0349-8352, 2000. [34] CIGRE Working Group 01 (Lightning) of Study Committee 33 (Overvoltages and Insulation Coordination), Guide to procedures for estimating the lightning performance of transmission lines, CIGRE Brochure no. 63, 1991.
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[35] IEEE Guide for the Application of Metal-Oxide Surge Arresters for AlternatingCurrent Systems, IEEE Std. C62.22, 1997. [36] IEC Protection against lightning—Part 1: General principles, IEC 62305-1, 2006. [37] K. Berger, R.B. Anderson, H. Kroninger, Parameters of lightning flashes, CIGRE Electra (41) (1975) 23–37. [38] R.B. Anderson, A.J. Eriksson, Lightning parameters for engineering applications, CIGRE Electra (69) (1980) 65–102. ´ B.V. Stanic, ´ Calculation of lightning current parameters, [39] F. Heidler, J.M. Cvetic, IEEE Transactions on Power Delivery (April (2)) (1999). [40] F. Heidler, J. Wieisenger, W. Zischank, Lightning currents measured at a telecommunication tower from 1992 to 1998, in: Proceedings of the 14th International Symposium on Electromagnetic Compatibility, Zurich, Switzerland, 2001. [41] S.A. Shelkunoff, The electromagnetic theory of coaxial transmission lines and cylindrical shields, Bell Syst. Tech. J. 13 (1934). [42] A. Ametani, A general formulation of impedance and admittance of cables, IEEE Transactions on Power Apparatus and Systems PAS-99 (3) (1980) 189– 197. [43] A. Ametani, Y. Miyamoto, N. Nagaoka, Semiconducting layer impedance and its effect on cable wave-propagation and transient characteristic, IEEE Transactions on Power Delivery 19 (October (4)) (2007) 1523–1531. [44] N. Amekawa, N. Nagaoka, Y. Baba, A. Ametani, Derivation of semiconducting layer impedance and its effect on cable wave propagation and transient characteristics, IEE Proceedings-Generation Transmission and Distribution 150 (July (4)) (2003) 434–440. [45] Y. Baba, N. Tanabe, N. Nagaoks, A. Ametani, Transient analysis of a cable with low conducting layers by a finite time-domain method, IEEE Transactions on Electromagnetic Compatibility 46 (August (3)) (2004). [46] L.M. Wedepohl, D.J. Wilcox, Transient analysis of underground powertransmission systems, IEEE Transactions on Electromagnetic Compatibility 120 (2) (1973). [47] J.P. Bickford, N. Mullineux, J.R. Reed, Computation of Power-System Transients, Peter Peregrinus Ltd., London, 1980. [48] F. Polaczek, Sur le champ produit par un conducteur simple infiniment long parcouru par courant alternatif, Revue Generale de Thermique 29 (1931). [49] M. Marzinotto, C. Mazzetti, Propagation of transients in extruded MV and HV cables considering typical thickness and resistivity values of commercial semiconductive compounds, in: Proceedings of the International Power System Transients Conference IPST 2007, Lyon, France, June 4–7, 2007. [50] R. Bartnikas, K.D. Srivastava, Power and Communication Cables—Theory and Applications, IEEE Press Series on Power Engineering, John Wiley & Sons, Inc., Hoboken, NJ, USA, 2000.
Contents lists available at ScienceDirect
Electric Power Systems Research journal homepage: www.elsevier.com/locate/epsr
Overvoltage attenuation in power cable lines—A simplified estimation method M. Marzinotto ∗ , C. Mazzetti Electrical Engineering Department, Sapienza University of Roma, Via Eudossiana 18, 00184 Roma, Italy
a r t i c l e
i n f o
Article history: Received 28 April 2008 Received in revised form 6 August 2009 Accepted 24 October 2009 Available online 4 December 2009 Keywords: Cable lines Insulation coordination Lightning surges Switching surges Overvoltages
a b s t r a c t Cable lines impart attenuation and distortion to overvoltages coming from overhead lines. In particular the attenuation is an important factor for the insulation coordination of a cable line and consequently for its reliability. The evaluation of such attenuation needs the utilization of numerical programs and their utilization, although it becomes an obliged step, is not an easy task without a specific skill. In this paper a simplified method is proposed which is based on the results of a specific numerical program, in order to evaluate the overvoltage attenuation introduced from cable lines for both the conductor screen (insulation stress) and screen to ground (jacket stress) modes of propagation. Although such method introduces some approximation, it is a useful tool in order to have both a first and conservative evaluation of the overvoltage stressing the cable line insulation when the impinging overvoltage to the cable line is known. © 2009 Elsevier B.V. All rights reserved.
1. Introduction Insulation coordination of cable lines requires the knowledge of the overvoltages stressing the cable insulation and the probability of the insulation breakdown to such stresses [1–9]. The estimation of the overvoltages can be assessed via numerical programs [10] that require a skill for the their utilization. The IEC 60071 standard [11] gives a method for a statistical approach to switching surges. Breakdown voltages of cable line can be estimated via dielectric strength test on short cable samples before the installation [12–22]. Existing standards [11,23] approach the insulation coordination of cable lines through deterministic methods which are based on the knowledge of the maximum overvoltage that stresses the cable line insulation and its withstand voltage level for both lightning and switching surges. Aim of this paper is the evaluation, through a simplified method, of the overvoltage stressing the cable insulation when the overvoltage, in terms of amplitude and wave shape, coming from an overhead line and impinging a cable line is known. Typical power system configurations, cable ratings and power cable formations are considered. Overvoltages coming from overhead lines when they impinge cable lines are attenuated and distorted. Attenuation and distortion rates are due to cable features (formation, length, burial disposition, etc.), impinging voltage wave shape, equipment connected at both ends (e.g. transformer, overhead line). While cable length
and impinging voltage shapes strongly influence the overvoltage attenuation rate [13,24–27], boundary conditions (e.g. ground impedance value of cable screen, etc.) and power cable formation play a secondary role [27]. In this paper the overvoltage attenuation rate of a cable line is quantified through an “overvoltage reduction factor” as the ratio of the peak value of the overvoltage stressing the cable line insulation and the peak value of the overvoltage impinging the cable line. Such overvoltage reduction factor is then dependent on all the aforementioned variables, which play a part in the attenuation of the overvoltage. Thus, the overvoltage reduction factor is not only useful for the estimation of single overvoltage event stressing the cable line when the impinging overvoltage is known, but it is also useful for the estimation of the statistical distribution parameters of the overvoltages stressing the cable line insulation when the statistical distribution of the impinging overvoltages is known [27]. The paper is framed in different sections. In Section 2 the cable and power systems configuration considered here are illustrated. Cable line model and ground return model used for the simulations are mentioned in this section too. In Section 3 the three considered stressing modes of propagation of the overvoltages in a power cable line are illustrated. In Section 4 the results of the simulations are presented and discussed. Concluding remarks are reported in Section 5, while Section 6 closes the paper.
2. Analyzed configurations and cables ∗ Corresponding author. Tel.: +39 06 44585544; fax: +39 06 4883235. E-mail addresses: [email protected] (M. Marzinotto), [email protected] (C. Mazzetti). 0378-7796/$ – see front matter © 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.epsr.2009.10.027
Cable lines are usually connected between overhead lines or transformers or between a combination of both. Cable lines
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Table 1 Cable lines characteristics taken into account for the simulations.
Fig. 1. The two analyzed configurations: (a) overhead line/cable line/transformer; (b) overhead line/cable line/overhead line.
connected at overhead lines are subjected to a higher number of dangerous events. In fact, overhead lines work as collectors of lightning strokes and then they can transfer harmful overvoltages to the cable line. Due to the high value of transformer surge impedance [24,25], an overvoltage travelling along a cable line connected between an overhead line and a transformer can double its peak value when it reaches the transformer side end. Thus, the most critical configuration for a cable line for the insulation coordination point of view is usually the mixed configuration with an overhead line at one end and a transformer at the other end. On the other hand, cable lines connecting two overhead lines can experience higher number of dangerous events due to lightning strokes. In this paper two configurations only are considered: “overhead line/cable line/transformer” and “overhead line/cable line/overhead line” as reported in Fig. 1. Overhead lines have been considered of infinite length on both configurations and the space distribution of the overhead line conductors has been appropriately chosen if a medium voltage (MV), a high voltage (HV) or an extra high voltage (EHV) line has been taken into account. In the case of Fig. 1a), transformer has been simulated with a capacitance connected between the cable conductor and ground [23]. Values of 1 nF and 4 nF have been selected for the MV transformer and for the HV and EHV transformers, respectively; such values are in accordance with [23]. In this case, the approximation usually suggested in standards is able to take into account even the open line end configuration that represents the worst condition for the cable line insulation. Bays capacitance have more or less the same order of magnitude [28] considering typical voltage transformers and bays length. Power transformer surge response has been the object of several studies [29–33] and different and complex representation have been proposed in literature in order to take into account its frequency-dependent input impedance. The adopted transformer representation here is a first approximation of its input impedance model. Cable screens have been considered grounded at both ends of the cable line with a surge impedance of 30 at the overhead/cable line transitions end and with a surge impedance of 10 at the transformer side end. Such values have been chosen in accordance with [8,11,23]. In fact, the CIGRE formula [23,34,35], highlights that the surge impedance value (with high injected current) of a rod electrode is always smaller than the value measured at 50/60 Hz (with low current) [34]. In low resistivity soils as 100 m considered in this paper, tower footing resistance value measured at 50/60 Hz are usually never higher than 30 . Furthermore in both medium voltage and especially high voltage transformer stations the ground resistance measured at 50/60 Hz is lower than 1 . Consequently a surge impedance of 30 at the overhead/cable line transitions end and a surge impedance of 10 at the transformer side end for the grounding of the cable screen represent conservative values for the estimation of overvoltages along a cable line. No surge arrester are considered at both ends of the cable line of both configurations. The stressing wave shape impinging the cable line has been considered coming from the overhead line as a phase-to-ground
20 kV cable Conductor cross-section Inner semicon thickness Insulation thickness Outer semicon thickness Inner semicon resist. Insulation tan ı Screen cross-section Conductor material Jacket thickness Jacket material Disposition type
150 mm2 0.7 mm 5.5 mm 0.5 mm 10 m 2 × 10−3 25 mm2 Aluminum 2 mm PVC Trefoil
Conductor radius Inner semicon Insulation ε Outer semicon ε Outer semicon resist. Insulation type Screen type Screen material Jacket ε Soil resistivity Burying depth
7.1 mm 1000 2.6 1000 10 m EPR Wires Copper 5 100 m 1m
150 kV cable Conductor cross-section Inner semicon thickness Insulation thickness Outer semicon thickness Inner semicon resist. Insulation tan ı Screen cross-section Conductor material Jacket thickness Jacket material Disposition type
1600 mm2 2 mm 20 mm 1 mm 10 m 2 × 10−3 85 mm2 Aluminum 4 mm PE Flat
Conductor radius Inner semicon ε Insulation ε Outer semicon ε Outer semicon resist. Insulation type Screen type Screen material Jacket ε Soil resistivity Burying depth
26 mm 1000 2.6 1000 10 m EPR Wires Copper 2.3 100 m 1.2 m
400 kV cable Conductor cross-section Inner semicon thickness Insulation thickness Outer semicon thickness Inner semicon resist. Insulation tan ı Screen cross-section Conductor material Jacket thickness Jacket material Disposition type
2500 mm2 4 mm 28 mm 2 mm 10 m 0.4 × 10−3 393 mm2 Copper 5 mm PE Flat
Conductor radius Inner semicon ε Insulation ε Outer semicon ε Outer semicon resist. Insulation type Screen type Screen material Jacket ε Soil resistivity Burying depth
28 mm 1000 2.3 1000 10 m XLPE Sheath Alum. 2.3 100 m 1.2 m
overvoltage with the same amplitude and the same wave shape for each phase. Overvoltages due to lightning are the most harmful in MV systems, while for EHV levels switching surges can even be more critical. In the HV level switching surges are not negligible, although lightning surges are usually higher. Four different types of voltage wave shapes impinging the cable line have been selected in order to take into account events of lightning and switching surges. In particular the standard lightning and switching wave shapes have been considered. Although flashover and back-flashover of insulator strings due to a lightning stroke on overhead line give rise to tail in the range of 10–20 s [35], the standard 1.2/50 s wave has been selected because of, as it will be illustrated later on, gives higher values (and then conservative values) of the overvoltage reduction factor. A non-standard short wave shape has been also considered in order to take into account likely truncated waves. Finally a 10/350 s wave have been also considered in order to take into account direct strokes to phase conductor without subsequent flashovers on insulator string (possible scenarios in HV and EHV overhead line only). Such wave is the standard lightning current first stroke [36–40]. In fact, when a direct stroke to overhead line phase conductors occurs and no flashover on insulator strings takes place the corresponding overvoltage wave is similar to the stroke current wave [35]. The wave shapes have been simulated by Heidler function [36,39,40] with adequately selected parameters, which is more realistic than the typical double exponential function. In fact, the first derivative of Heidler function is zero at the foot of the wave in spite of the double exponential wave. Three types of cable ratings have been selected for the analysis: a 20 kV MV cable, a 150 kV HV cable and a 400 kV EHV cable. Their characteristics are reported in Table 1. In the same table the soil
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resistivity and the burying characteristics considered in the simulations are also reported. HV and EHV cable lines are usually buried in flat formation; here the minimum distance between the jackets of two adjacent cores has been considered of 30 cm for both the 150 kV and the 400 kV cable lines. A Matlab program implementing the Shelkunoff theory (frequency-dependent cable model) [41,42], that takes into account also the effect of the semiconductive layers [36–38] has been used for the estimation of the overvoltages stressing the cable line insulation starting from a known wave shape travelling on the overhead line and impinging the cable line. Impedance and admittance of the semiconductive layers have been considered taking into account the last developments performed by Ametani et al. [43–45]. The ground return has been considered using the Wedepohl–Wilcox’s approximation [46,47] of the Pollaczek’s formula [48]. 3. Overvoltage stressing modes for power cable lines The propagation of overvoltage along a cable line is strictly influenced if a flashover occurs at the transition point overhead line—cable line. When surge arresters are not used in an overhead line—cable line transition point, the insulation of the tower at the transition point has usually a reduced withstand value to voltage surges in respect of the insulation of the other towers. Consequently, when a voltage surge travelling along an overhead line, reaches the overhead line—cable line junction two conditions are possible: the voltage surge may be high enough to cause a flashover along the external insulation (along the cable termination or along the insulator string of the last tower), or the voltage surge is not high enough and the external insulation withstands. Considering a flashover along the cable termination, conductor and screen of the cable are stressed (neglecting the arc voltage) by the same voltage wave (Vc = Vs in Fig. 2). On the contrary, if no flashover occurs, only the conductor is directly stressed by the surge coming from the overhead line: the external stressing voltage is V only. Beside this two case, a third case should be considered: lightning struck to the last tower (at the overhead line—cable line transition point). In this case again two conditions are possible: the lightning current is high enough to cause back-flashover on the external insulation, or the lightning current is not high enough and back-flashovers does not occur. In the former it is possible to consider again Vc ∼ = Vs in
Fig. 2. In the latter, the screen is directly stressed only, and then Vs is the external stressing voltage only. Thus, taking into account Fig. 2 which shows the overhead line—cable line transition point: three are the external stressing conditions for a cable line that are considered here: • the external voltage stress is applied to the conductor only (referred from now on as “stressing mode” #1 (SM #1)); • the external voltage stress is applied to the screen only (referred from now on as “stressing mode” #2 (SM #2)); • the external voltage stress is simultaneously applied to the conductor and the screen (referred from now on as “stressing mode” #3 (SM #3)). Finally, it is possible to assert that a voltage surge coming from the overhead line can give rise to SM #1 or SM #3, while a voltage surge due to stroke to the last tower (at the overhead line—cable line transition) can give rise to SM #2 or SM #3. Actually different stressing modes are possible with / Vs = / 0, but they are not considered here. The aforeVc = mentioned three SMs are in any case those more representative of the possible scenarios. The maximum conductor screen stressing overvoltage (VCS ) and the maximum screen-ground stressing overvoltage (VSG ) are strictly dependent on the SM. Furthermore, VCS and VSG are mainly dependent on cable length due to the effect of the successive reflections of voltage waves at cable ends and to the impinging voltage shapes. In order to take into account the attenuation of the impinging voltage shape, an “overvoltage reduction factor” has been introduced for both the conductor screen (hc ) mode of propagation and for the screen-ground (hs ) mode of propagation: hc =
VCS VH
(1)
hs =
VSG VH
(2)
where VH is the peak value of the voltage surge (voltage-to-ground) impinging the cable line. Factors hc and hs depends on several variables and their analysis is performed in the next section. The utilization of the overvoltage reduction factor (hc and hs ) becomes a powerful tool for a quick estimate of the overvoltage stressing a cable and it bypasses heavy numerical analysis. Thus, the estimation of the overvoltage reduction factor once for all for different wave shapes, cable formations and typical system configurations can help in a first step the engineer to address the insulation coordination of a cable line. 4. Analysis of results 4.1. General considerations
Fig. 2. Sketch of the overhead line—cable line transition point.
Taking into account the three selected cables, a sensitivity analysis on variation of inner and outer semiconductive layers, semiconductive dielectric constant ε, soil resistivity has been considered here and in [26,27,49] showing negligible differences. For the 20 kV MV cable a parametric analysis on conductor crosssection and insulation thickness variations has been also carried out showing weak influence on both hc and hs values. On the contrary, cable length, the wave shape of the impinging overvoltage, the cable rating (e.g. MV, HV or EHV), the termination type of the cable line (transformer or overhead line) and the SM have not negligible effect on the attenuation of the overvoltage. In order to simplify the discussion of results, they are reported and commented separately for the three different SMs. Furthermore for each SM, the two
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Fig. 3. Overvoltage reduction factor hc vs. cable length for the three considered types of cables when the impinging voltage shape is a 1.2/50 s with reference to SM #1 and Fig. 1a.
types of terminations of the cable line, e.g. transformer (Fig. 1(a)) or overhead line (Fig. 1(b)), are also considered. 4.2. Stressing mode #1 Fig. 3 shows the hc variation with cable length with SM #1 and a 1.2/50 s wave shape, for 20 kV, 150 kV and 400 kV cables when the cable line is terminated on a transformer. In this figure it is possible to note the effect of successive reflection: for short cable length the overvoltage stressing the insulation may even reach the ≈70–75% of the impinging one. The same considerations can be made for the Figs. 4–6 where the overvoltage reduction factor is reported vs. cable length for 250/2500 s, 0.5/6 s and 10/350 s impinging wave shapes respectively. These figures highlight that the hc decrease is as weaker as longer the tail of the surge wave. Consequently, for a fixed cable length, the longest is the tail of the wave shape the heaviest is the stress for the cable insulation. For long cable lines the overvoltage reduction factor tends to be asymptotically constant. The cable length value in which such factor becomes constant depends on the impinging wave duration and in particular to the time to half value. For very long cables when the
Fig. 4. Overvoltage reduction factor hc vs. cable length for the three considered types of cables when the impinging voltage shape is a 250/2500 s with reference to SM #1 and Fig. 1a.
509
Fig. 5. Overvoltage reduction factor hc vs. cable length for the three considered types of cables when the impinging voltage shape is a 0.5/6 s with reference to SM #1 and Fig. 1a.
successive reflections at cable ends have no further effect in increasing the voltage shape stressing the cable insulation [13,24–27], the overvoltage reduction factor can be estimated as twice the coefficient of transmission (3) where Z1 and Z2 are the surge impedance of the overhead line and the cable line, respectively: =
2Z2 Z1 + Z2
(3)
It is important to outline that (3) does not take into account the losses in the propagation of the waves along the cable leading to a conservative estimation of the peak value of the overvoltage stressing the cable insulation. The curves reported in Figs. 3–6 are well fitted with the following mathematical expression:
x
h = A exp −
B
x
+ C exp −
D
(4)
where x is the cable length and A, B, C and D are constant. The values of such constants are reported in Table 2 for the examined types of cables and impinging wave shapes. Figs. 7–10 show the hc values vs. cable length for the four considered impinging wave shapes and for the three considered cable ratings when the cable line is terminated on an overhead line. It can
Fig. 6. Overvoltage reduction factor hc vs. cable length for the three considered types of cables when the impinging voltage shape is a 10/350 s with reference to SM #1 and Fig. 1a.
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Table 2 A, B, C and D constant values to use in Eq. (4) for the estimation of hc for different types of cables, different impinging wave shapes and stressing mode #1. System configuration as reported in Fig. 1a. Impinging wave shape [s]
A
B [km]
C
20 kV cable 0.5/6 1.2/50 10/350 250/2500
0.3662 0.5611 0.4855 1.024
0.1351 0.3952 0.8787 13.642
0.0767 0.2195 0.4997 0.0107
14.775 5.6274 9.7087 −4.9164
0.1–10 0.1–10 0.1–10 0.4–10a
150 kV cable 0.5/6 1.2/50 10/350 250/2500
0.361 0.6108 0.5959 0.5829
0.1532 0.6373 1.5537 9.6525
0.0801 0.1215 0.3522 0.4485
60.569 40.7000 23.9980 101.28
0.1–50 0.1–50 0.1–50 0.3–50b
400 kV cable 0.5/6 1.2/50 10/350 250/2500
0.4131 0.6206 0.5622 0.5774
0.1634 0.7745 2.0145 14.961
0.1174 0.1631 0.4054 0.4528
95.785 73.800 34.1180 157.60
0.1–50 0.1–50 0.1–50 0.5–50c
a b c
D [km]
Range of validity [km]
For cable length shorter than 0.4 km, hc = 1 (hc % = 100). For cable length shorter than 0.3 km, hc = 1 (hc % = 100). For cable length shorter than 0.5 km, hc = 1 (hc % = 100).
Fig. 7. Overvoltage reduction factor hc vs. cable length for the three considered types of cables when the impinging voltage shape is a 1.2/50 s with reference to SM #1 and Fig. 1b.
Fig. 8. Overvoltage reduction factor hc vs. cable length for the three considered types of cables when the impinging voltage shape is a 250/2500 s with reference to SM #1 and Fig. 1b.
be noted that for each case the variation of hc with increasing cable length is very similar to that of cable line terminated on a transformer except for short cable lengths in which the hc values are about halved. For impinging wave shapes with short tail (0.5/6 s and 1.2/50 s waves: Figs. 7 and 9, respectively) and 10 km of cable length, the hc values reach the same value reported in Figs. 3 and 5, respectively. This fact confirms the aforementioned assertions in which the effect of successive wave reflections at cable ends can be disregarded for very long cables. As for the case of cable line terminated on a transformer, the hc values vs. cable length for cable lines terminated on overhead line well fit the Eq. (4) and the relevant A, B, C and D values for the considered impinging wave shapes are reported in Table 3. The hs values are substantially constant with the cable length and they are quite independent on the impinging voltage shape and on the type of termination of the cable length (transformer or overhead line). The greatest variation of hs value with cable length has been highlighted with the 250/2500 s in which the hs value is less than 1% for short cable lengths and it reaches some per cent for long cable lengths. In Table 4 the values of hs for the three considered cables and for the different impinging wave shapes are reported. When ranges of variation of hs values are reported, the smaller values refer to shorter cable lengths and larger values to longer cable
Fig. 9. Overvoltage reduction factor hc vs. cable length for the three considered types of cables when the impinging voltage shape is a 0.5/6 s with reference to SM #1 and Fig. 1b.
M. Marzinotto, C. Mazzetti / Electric Power Systems Research 80 (2010) 506–513
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Table 5 hc values for different types of cables, different impinging wave shapes for stressing mode #2. hc values valid for both system configurations reported in Fig. 1. Impinging wave shape [s]
hc
20 kV cable (cable length between 0.1 and 10 km) 0.5/6 1.2/50 10/350 250/2500 150 kV cable (cable length between 0.1 and 50 km) 0.5/6 1.2/50 10/350 250/2500 400 kV cable (cable length between 0.1 and 50 km) 0.5/6 1.2/50 10/350 250/2500 Fig. 10. Overvoltage reduction factor hc vs. cable length for the three considered types of cables when the impinging voltage shape is a 10/350 s with reference to SM #1 and Fig. 1b.
Table 3 A, B, C and D constant values to use in Eq. (4) for the estimation of hc for different types of cables, different impinging wave shapes and stressing mode #1. System configuration as reported in Fig. 1b. Impinging wave shape [s]
A
B [km]
C
20 kV cable 0.5/6 1.2/50 10/350 250/2500
0.2382 0.2788 0.1816 0.5128
0.1408 0.5885 0.8779 25.627
0.0710 0.1386 0.3251 0.00007
150 kV cable 0.5/6 1.2/50 10/350 250/2500
0.2439 0.3061 0.2513 0.1936
0.1506 0.8539 1.8053 11.896
0.0777 0.1013 0.2405 0.3205
63.816 55.401 30.656 100.84
0.1–50 0.1–50 0.1–50 0.5–50a
400 kV cable 0.5/6 1.2/50 10/350 250/2500
0.2991 0.2924 0.2267 0.1863
0.1377 1.0278 2.6652 19.940
0.1139 0.1372 0.2608 0.3214
94.339 105.08 48.590 156.17
0.1–50 0.1–50 0.1–50 0.4–50b
a b
D [km]
16.2416 8.7183 11.9005 −1.9557
Range of validity [km] 0.1–10 0.1–10 0.1–10 0.5–10a
For cable length shorter than 0.5 km, hc ≈ 0.5 (hc % ≈ 50). For cable length shorter than 0.4 km, hc ≈ 0.5 (hc % ≈ 50).
Table 4 hs values for different types of cables, different impinging wave shapes for stressing mode #1. hs values valid for both system configurations reported in Fig. 1.
<0.01 0.01 0.01 0.025 0.02 0.045 0.05 0.05 0.03 0.06 0.06 0.06
lengths. The variation of hs with cable length can be considered substantially linear. Furthermore due to the small variation in the hs range, the highest value can be considered for any cable length, leading in this way to a conservative estimation of the stressing overvoltage. 4.3. Stressing mode #2 In Table 5 the hc values for different cables and impinging wave shapes are reported for the SM #2. Such results can be extended for both the analyzed system configurations, e.g. cable line terminated on a transformer and cable line terminated on an overhead line. In fact no differences have been revealed regardless of cable termination. For a given cable length, the highest is the cable rating and the highest is the hc value. Furthermore for a given cable rating, the longest is the impinging wave shape the highest is the hc value. The hc values reported in Table 5 highlight that the overvoltage stressing the insulation reduces to less than 6% in respect of the peak value of the impinging wave shape. Table 6 shows the hs values for SM #2 for different types of cables and with different impinging wave shapes. Also in this case such results can be extended for both the analyzed system configurations, e.g. cable line terminated on a transformer and cable line terminated on an overhead line. When ranges of variation of hs values are reported, the smaller values refer to shorter cable lengths and larger values to longer cable lengths. In such cases the Table 6 hs values for different types of cables, different impinging wave shapes for stressing mode #2. hs values valid for both system configurations reported in Fig. 1.
Impinging wave shape [s]
hs
20 kV cable (cable length between 0.1 and 10 km) 0.5/6 1.2/50 10/350 250/2500
0.05 0.06 0.05–0.06 0–0.05
20 kV cable (cable length between 0.1 and 10 km) 0.5/6 0.16 1.2/50 0.21 10/350 0.22 250/2500 0.16–0.22
150 kV cable (cable length between 0.1 and 50 km) 0.5/6 1.2/50 10/350 250/2500
0.06 0.07 0.04–0.07 0–0.07
150 kV cable (cable length between 0.1 and 50 km) 0.5/6 0.32 1.2/50 0.36 10/350 0.33–0.36 250/2500 0.25–0.39
400 kV cable (cable length between 0.1 and 50 km) 0.5/6 1.2/50 10/350 250/2500
0.07 0.08 0.04–0.08 0–0.08
400 kV cable (cable length between 0.1 and 50 km) 0.5/6 0.33 1.2/50 0.37 10/350 0.33–0.36 250/2500 0.25–0.38
Impinging wave shape [s]
hs
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M. Marzinotto, C. Mazzetti / Electric Power Systems Research 80 (2010) 506–513 Table 7 hs values for different types of cables, different impinging wave shapes for stressing mode #3. hs values valid for both system configurations reported in Fig. 1. Impinging wave shape [s]
hs
20 kV cable (cable length between 0.1 and 10 km) 0.5/6 1.2/50 10/350 250/2500
0.055 0.06 0.06 0.07
150 kV cable (cable length between 0.1 and 50 km) 0.5/6 1.2/50 10/350 250/2500
0.065 0.07 0.07 0.08
400 kV cable (cable length between 0.1 and 50 km) 0.5/6 1.2/50 10/350 250/2500
0.075 0.085 0.085 0.09
variation of hs with cable length can be considered substantially linear. Furthermore due to the small variation in the hs range, the highest value can be considered for any cable length, leading to a conservative estimation of the stressing overvoltage. 4.4. Stressing mode #3 It is interesting to note that for SM #3 the hc values are below 1% except for the 250/2500 s impinging wave shape in which it reaches about 2%. Such results are valid for both the analyzed terminations, i.e. transformer and overhead line. Table 7 shows the hs values for SM #3 with different impinging wave shapes. hs values are practically constant with cable length. The wave shape weakly influences the hs value: the largest values are those for longer time to half value of the surge wave. 5. Final remarks The utilization of hc and hs factors is useful for an estimation of the stresses on the insulation and on the jacket of a cable line. The former is much more important than the latter due to the fact that a failure in the insulation leads to an outage. In fact damage of the jacket leads to a breakdown between the screen (or the metallic sheath) and the soil, consequently, a punctured thermoplastic jacket can be a risk for moisture entrance and it may be a threat for the cable life itself [13,50]. From the analysis of results reported in the previous section it is possible to conclude that: • SM #1 is the most critical for the insulation and furthermore cable length play a relevant role: the stress due to the impinging overvoltage significantly reduces with cable length and it is also influenced from the type of cable termination (overhead line or transformer). • SM #2 is the most critical for the cable jacket; it is independent on cable length and on the type of cable termination (overhead line or transformer). • SM #2 gives rise to a cable insulation stress that is only some percent of the impinging overvoltage, while the stress due to SM #3 can be even disregarded for the cable insulation. • The peak amplitude of the overvoltage transferred to the jacket for both SM #1 and SM #3 is only some percent. As a first step, in the reliability analysis of a cable line, only the SM #1 and the SM #2 can be taken into account for a first estimation
of the maximum stressing overvoltage for the cable insulation and the cable jacket, respectively. 6. Conclusions Cable lines reduce overvoltage coming from overhead lines. Such reduction is due to different parameters which have different influence in the attenuation. Furthermore their weight is different regarding what type of stressing mode is considered, i.e. overvoltage stressing the conductor only, the screen only or both. Cable length, impinging overvoltage wave shape, cable termination type have the largest weight for the overvoltages stressing the cable insulation, while only the impinging overvoltage wave shape has the largest weight for overvoltage stressing the cable jacket. The utilization of an overvoltage reduction factor for both conductor screen and screen-soil modes of propagations becomes a useful method for the assessment of power cable reliability. It is then possible to assess the insulation coordination itself and the evaluation of jacket failure too. Although the utilization of such overvoltage reduction factors leads to a simplified method of overvoltage estimation, it can be a powerful way to predict with a conservative approach the reliability of power cable lines. References [1] L.O. Barthold, L. Paris, The probabilistic approach to insulation coordination, CIGRE Electra (May (13)) (1970 May) 41–58. [2] L. Paris, Insulation coordination, in: High Voltage Engineering Research Proceedings ENEL R&D Management, Italy, 1970. [3] A. Taschini, Insulation coordination on high voltage systems, in: High Voltage Engineering Research Proceedings ENEL R&D Management, Italy, 1970. [4] P. Reggiani, Insulation coordination on medium voltage systems, in: High Voltage Engineering Research Proceedings, ENEL R&D Management, Italy, 1970. [5] G. Carrara, E. Occhini, L. Paris, F. Reggiani, Contribution to the study of insulation coordination from the probabilistic point of view, in: CIGRE International Conference, 1966. [6] L. Paris, A. Taschini, Results of recent investigation on switching surges in EHV networks, in: CIGRE International Conference, 1968. [7] L. Paris, R. Cortina, Switching and lightning impulse discharge characteristics of large air gaps and long insulator strings, IEEE Transactions on Power Apparatus and Systems PAS–87 (April) (1968). [8] A.R. Hileman, Insulation Coordination in Power Systems, Marcel Dekker, New York, USA, 1999. [9] W. Diesendorf, Insulation Co-ordination in High-voltage Electric Power System, Butterworth & Co. Ltd., London, England, 1974. [10] TransEnergiesTechnologies Simulation of power network with EMTP-RV, Tome 1 and 2, Hydro Québec, 2004. [11] EN Insulation co-ordination Part 2: Application guide, EN 60071-2 Standard, 1998. [12] M. Marzinotto, On the application of the enlargement law to cable lines, in: Proceedings of IEEE Power Tech 2005, St. Petersburg, Russia, June 27–30, 2005. [13] M. Marzinotto, Insulation coordination of extruded power cable lines, Ph.D. Thesis, Roma, Italy. Padis Ed.—pub. no. 1148369693 31587, 376 pages, September 2006. [14] A. Borghetti, M. Marzinotto, C. Mazzetti, C.A. Nucci, M. Paolone, Insulation coordination of MV cables against lightning-induced overvoltages generated by LEMP-coupled overhead lines, in: Proceedings of 28th International Conference on Lightning Protection ICLP 2006, Kanazawa, Japan, September 18–22, 2006. [15] M. Marzinotto, C. Mazzetti, M. Pompili, P. Schiaffino, Impulsive strength of power cables with different XLPE compounds, in: Proceedings of IEEE Conference on Electrical Insulation and Dielectric Phenomena IEEE–CEIDP 2006, Kansas City, MO, USA, October 15–18, 2006. [16] M. Marzinotto, G. Mazzanti, C. Mazzetti, Comparison of breakdown performances of extruded cables via the enlargement law, in: Proceedings of IEEE Conference on Electrical Insulation and Dielectric Phenomena IEEE–CEIDP 2006, Kansas City, MO, USA, October 15–18, 2006. [17] M. Marzinotto, C. Mazzetti, M. Pompili, P. Schiaffino, AC strength test data of unaged and water tank aged XLPE compounds for transmission and distribution power cables, in: Proceedings of 19th International Conference on Electricity Distribution CIRED 2007, Vienna, Austria, May 21–24, 2007. [18] M. Marzinotto, Experimental Validation of the Volume Effect in the Statistical Enlargement Law for Cable Lines, in: Proceedings of the Nordic Insulation Symposium NORDIS 07, Lyngby, Copenhagen, Denmark, June 11–13, 2007. [19] M. Marzinotto, G. Mazzanti, C. Mazzetti, The effect of conductor radius and insulation thickness in the application of the enlargement law for comparing power cable breakdown performances, in: Proceeding of International Conference on Solid Dielectrics ICSD 2007, Winchester, UK, July 8–13, 2007.
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