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Journal of Information, Control and Management Systems, Vol. 12, (2014), No. 2 113 CALCULATION OF INDUCED SHEATH VOLTAGES IN POWER CABLES – SINGLE CIRCUIT SYSTEM VERSUS DOUBLE CIRCUIT SYSTEM Stanislaw CZAPP, Krzysztof DOBRZYNSKI, Jacek KLUCZNIK, Zbigniew LUBOSNY Gdansk University of Technology, Faculty of Electrical and Control Engineering, Gdansk, Poland e-mail: [email protected] Abstract This paper presents comparison of values of induced sheath voltages in power cable metallic sheaths when one or two cables per phase are used. Calculation of voltages is performed for various phase sequences of the power cables. Three types of the sheaths bonding and earthing are considered. Shock hazard and voltage stress of non-metallic outer sheath of cables are evaluated. The proposed, optimal configuration of the power cable system is indicated. Keywords: electromagnetic coupling, electrical safety, power engineering, power system analysis computing 1 INTRODUCTION In concentric metallic sheaths of single-core high voltage power cables induced voltages occur. In the steady state, these voltages may reach value of several hundred volts and electric shock risk exists then. In case of earth fault, induced sheath voltages are much higher, even several kilovolts, and breakdown of non-metallic outer sheath of cables may occur [1–7]. For a conductor k lying parallel with a three phase system (three conductors) a voltage gradient Uk induced along its length can be calculated as follows 1 m m U k j I 2 10 7 ln Ak Ck 2 mBk 3 mCk , j ln 2 mAk (1) where: I – load current in the reference cable conductor (phase B), mAk – axial spacing of the parallel k conductor and phase A conductor, mAk – axial spacing of the parallel k conductor and phase B conductor, mAk – axial spacing of the parallel k conductor and phase C conductor. A high voltage cable system can be represented by the structure drawn in Fig. 1 [1]. 114 Calculation of Induced Sheath Voltages in Power Cables – Single Circuit System… U1 I1 R1 Conductor 1 X1 U2 I2 R2 Conductor 2 X2 Un In Rn Conductor n Xn Local earth Local earth Uepr1 RLE1 IE RE Uepr2 RLE2 UE Earth return path (remote earth reference) XE Fictitious covering cylinder (free of current) Figure 1 Equivalent scheme of a high voltage cable system: R1,2,n – resistance of the conductors, X1,2,n – reactance of the conductors, RLE – resistance to earth, I1,2,n – current in the conductors, IE – earth current, Uepr – earth potential rise [1] A cable sheath may be considered as a special parallel concentric conductor. When in the vicinity of the system is no other current-carrying conductors, voltage gradients of the sheaths for a group of cables in any formation are given by [8] 2 1 2mAB 3 2mAC , j U As j I 2 10 7 ln ln 2 d 2 d mAC 1 4m m U Bs j I 2 10 7 ln AB BC d2 2 (2) 3 mBC , j ln 2 mAB (3) 2 1 2mBC j 3 ln 2mAC , U Cs j I 2 10 7 ln 2 d m 2 d AC (4) where: UAs, UBs, UCs, – induced sheath voltages in phase A, B and C respectively, I – load current in the reference cable conductor, d – geometric mean sheath diameter, mAB – axial spacing of phases A and B, mBC – axial spacing of phases B and C, mAC – axial spacing of phases A and C. For trefoil formation in single circuit, induced sheath voltages are calculated according to the following equations 1 3 2m U As j I 2 10 7 j ln 2 2 d 2m , U Bs j I 2 10 7 ln d , (5) (6) Journal of Information, Control and Management Systems, Vol. 12, (2014), No. 2 1 3 2m , U Cs j I 2 10 7 j ln 2 2 d 115 (7) where: UAs, UBs, UCs, – induced sheath voltages in phase A, B and C respectively, I – load current in the reference cable conductor, d – geometric mean sheath diameter, m – axial spacing of adjacent cables. When flat formation in single circuit is applied, induced sheath voltages are calculated according to the following equations 1 m 3 4m , U As j I 2 10 7 ln j ln 2 d 2 d (8) 2m , U Bs j I 2 10 7 ln d (9) 1 m 3 4m . U Cs j I 2 10 7 ln j ln 2 d 2 d (10) Permissible touch voltage (V) For multiple-circuit system the calculations are more complicated and a computer model of the power cable system must be designed. The more parallel circuits the more complicated calculation is. Induced sheath voltages exist during normal operating condition (long time duration of induced voltages) and in case of earth fault (short time duration of induced voltages). These voltages should not exceed values described by the standards. Figure 2 presents permissible values of touch voltage as a function of fault duration [9]. For normal operating condition, 80 V is assumed as a permissible value. 800 700 600 500 400 300 200 80 V 100 0 0,05 0,1 0,2 0,5 1 2 5 10 >> 10 Fault duration (s) Figure 2 Permissible touch voltage as a function of the fault duration The paper considers induced sheath voltages in the 110 kV power cable system. The total length of the power line is 1000 m (two sections of 500 m length each, flat formation). Required power transfer capability is equal to 330 MW. Arrangements of the power system with one cable per phase (cross-section of conductor is equal to 2000 mm2) and two cables per phase (for equivalent power transfer capability cross-section of each conductor is equal to 800 mm2) are compared. For the each mentioned case, 116 Calculation of Induced Sheath Voltages in Power Cables – Single Circuit System… single point bonding or, for sheath voltages limiting purpose, cross-bonding is applied and analysed. The proposed configuration of the power cable system is indicated. COMPARED POWER CABLE SYSTEMS Induced sheath voltages were analyzed with the use of DIgSILENT PowerFactory® software. The following general arrangements of the power cable system were considered: 1) One cable per phase (single circuit system) – Distance between adjacent cables (C1-C2 and C2-C3) inside the section is equal to the outside diameter of the cable (D in Fig. 3). The number of analysed configurations is equal to 6. 2) Two cables per phase (double circuit system) – Distance between adjacent cables (C1-C2 and C2-C3) inside the section is equal to the outside diameter of the cable (D in Fig. 4). Distance to adjacent cables between circuits is equal to twice of the outside diameter of the cable (2D in Fig. 2). The number of analysed configurations is equal to 36. Configurations: W5a, W6a, W6b 2 C1 Sh1 C2 Sh2 C3 Sh3 Cross-bonding T1 (A), 500 m T1 (B), 500 m D ECC ECC D Ush E1 E2 A B C A B C Figure 3 The power cable system with one cable per phase C1 Sh1 C2 Sh2 T1 (B), 500 m D ECC C3 Sh3 Configurations: W3a, W4a, W4b Cross-bonding T1 (A), 500 m ECC D Ush 2D E1 C1 Sh1 C2 Sh2 C3 Sh3 E2 Cross-bonding T2 (A), 500 m T2 (B), 500 m D ECC ECC D Ush E1 A B C E2 A B C Figure 4 The power cable system with two cables per phase Journal of Information, Control and Management Systems, Vol. 12, (2014), No. 2 117 The cable systems described above are equipped with an earth continuity conductor (ECC). Various configurations of earthing and bonding of cables were assumed (Table 1). Table 1 List and symbols of the analyzed configurations Symbol of analysed configuration One cable per Two cables per phase phase Type of bonding and earthing Sheaths bonding and earthing in E1, crossbonding in E2 Single-point bonding; sheaths bonding and earthing in E1 Single-point bonding; sheaths bonding and earthing in E2 W5a W3a W6a W4a W6b W4b 3 NORMAL OPERATING CONDITION A first step of the analysis is to find the values of induced sheath voltages Ush, at the unearthed end, in normal operating condition, when current-carrying capacity of cables (maximum power transfer for each configuration) is achieved. Figures 5 and 6 present groups of results of the computer calculations – each point represents voltage for particular configuration of the system. When two cables per phase are used (configurations W3a, W4a, W4b), total number of results is 336 = 108, some results overlap themselves and give one point in particular diagram. The range of power transfer capability varies from about 302 MW to only 315 MW. Only for configuration W4a (Fig. 5b) the results reach values higher than 80 V. Configurations W3a (Fig. 5a) and W4b (Fig. 5c) are acceptable. a) Induced sheath voltage (V) 75 70 65 60 55 50 45 1 Loa d cu 315 0.9 rre nt u 0.8 nifo rmi ty ( IIm in /I ma ) x 310 305 0.7 300 Powe sfer c r tran ility (M apab W) 118 Calculation of Induced Sheath Voltages in Power Cables – Single Circuit System… b) Induced sheath voltage (V) 130 120 110 100 90 80 1 Loa d cu 315 0.9 rre nt u nifo rmi 0.8 ty ( IIm in /I ma ) x 310 305 0.7 300 s r tran Powe fer ca ) W ity (M pabil c) Induced sheath voltage (V) 65 60 55 50 45 40 1 Loa d cu rre 0.9 nt u nifo rmi 0.8 ty ( IIm 315 310 305 in /I ma ) x 0.7 300 y (M it pabil f er c a s r tran Powe W) Figure 5 Induced sheath voltages in normal operating conditions as function of power transfer capability and uniformity (Imin/Imax) of load current – configurations: a) W3a, b) W4a, c) W4b; two cables per phase; Imin – current in the lowest loaded conductor, Imax – current in the highest loaded conductor Unfortunately, for an arrangement of the power system with one cable per phase (configurations W5a, W6a, W6b – with total number of result 36 = 18; overlapped too) all results are above the line indicating 80 V (Fig. 6). In some cases the voltage exceeds even 200 V. The calculation results indicate that the arrangement with two cables per phase is better than with one cable per phase. A second step of the analysis is to find such a type of bonding and earthing in two cable power system which gives maximum power transfer capability, acceptable induced sheath voltages (not higher than 80 V) and high uniformity of load current in Journal of Information, Control and Management Systems, Vol. 12, (2014), No. 2 119 Induced sheath voltage (V) the cable conductors. Figure 7 presents induced sheath voltages for the most favourable configurations. a) 110 105 100 95 90 85 80 0 50 100 150 200 250 300 350 300 350 300 350 Power transfer capability (MW) b) Induced sheath voltage (V) 200 180 160 140 120 100 80 0 50 100 150 200 250 Power transfer capability (MW) c) Induced sheath voltage (V) 105 100 95 90 85 80 0 50 100 150 200 250 Power transfer capability (MW) Figure 6 Induced sheath voltages in normal operating conditions as function of power transfer capability – configurations: a) W5a, b) W6a, c) W6b; one cable per phase Calculation of Induced Sheath Voltages in Power Cables – Single Circuit System… 120 These are the configurations: W3a (sheaths bonding and earthing in E1, crossbonding in E2) and W4b (single-point bonding; sheaths bonding and earthing in E2). Figure 7 also includes detailed information about phase sequence in particular circuit (e.g. ABC/CBA – phase sequence in circuit T1 is ABC, phase sequence in circuit T2 is CBA) and induced sheath voltage in particular cable metallic sheath (e.g. W3a(T1C1) – induced voltages in circuit T1 and conductor C1 for configuration W3a). a) Phase sequence in section Induced sheath voltage (V) ABC/CBA ACB/BCA BAC/CAB BCA/ACB CAB/BAC CBA/ABC 80 70 60 50 40 30 20 10 0 W3a(T1C1) W3a(T1C2) W3a(T1C3) W3a(T2C1) W3a(T2C2) W3a(T2C3) Type of configuration and symbol of section b) Phase sequence in section ABC/CBA ACB/BCA BAC/CAB BCA/ACB CAB/BAC CBA/ABC Induced sheath voltage (V) 80 70 60 50 40 30 20 10 0 W4b(T1C1) W4b(T1C2) W4b(T1C3) W4b(T2C1) W4b(T2C2) W4b(T2C3) Type of configuration and symbol of section Figure 7 Induced sheath voltages in normal operating conditions for the preferred configurations of cables: a) configuration W3a – sheaths bonding and earthing in E1, cross-bonding in E2, b) configuration W4b – single-point bonding; sheaths bonding and earthing in E2 Journal of Information, Control and Management Systems, Vol. 12, (2014), No. 2 4 121 PHASE TO EARTH SHORT-CIRCUIT Induced sheath voltages in case of short-circuit (single phase to earth) were calculated as well. The value of short-circuit current is assumed to be 50 kA. In order to avoid installing sheath voltage limiters (SVL), induced voltages should not exceed 5 kV. It is important to find such configurations of power cables that give value of induced voltages not higher than 5 kV. In the considered cases, earth continuity conductor (ECC) was implemented (see Fig. 3 and 4). This conductor provides a return path of fault current and allows limiting induced sheath voltages significantly with comparison to the arrangement without ECC [1, 10]. Induced sheath voltages are presented as a function of number of power cables configuration (phase sequence) – Fig. 8 and 9. a) Induced sheath voltage (V) 10000 9500 9000 8500 8000 7500 7000 6500 6000 5500 5000 1 2 3 4 5 6 Variant number of phase sequence b) Induced sheath voltage (V) 12000 11000 10000 9000 8000 7000 6000 5000 1 2 3 4 5 Variant number of phase sequence 6 122 Calculation of Induced Sheath Voltages in Power Cables – Single Circuit System… c) Induced sheath voltage (V) 5700 5600 5500 5400 5300 5200 5100 5000 1 2 3 4 5 6 Variant number of phase sequence Figure 8 Induced sheath voltages in case of short-circuit, as function of variant number of phase sequence – configurations: a) W5a, b) W6a, c) W6b; one cable per phase a) Induced sheath voltage (V) 6600 6400 6200 6000 5800 5600 5400 5200 5000 0 6 12 18 24 30 36 30 36 Variant number of phase sequence b) Induced sheath voltage (V) 8000 7500 7000 6500 6000 5500 5000 0 6 12 18 24 Variant number of phase sequence Journal of Information, Control and Management Systems, Vol. 12, (2014), No. 2 123 c) Induced sheath voltage (V) 3950 3900 3850 3800 3750 3700 3650 3600 3550 3500 0 6 12 18 24 30 36 Variant number of phase sequence Figure 9 Induced sheath voltages in case of short-circuit, as function of variant number of phase sequence – configurations: a) W3a, b) W4a, c) W4b; two cables per phase Comparison of Fig. 8 and Fig. 9 allows to state that the arrangement with one cable per phase (configurations W5a, W6a, W6b) gives the values of induced sheath voltages higher than 5 kV. The worst case is for the arrangement W6a (Fig. 8b), where induced voltages exceed 11 kV. Sheath voltage limiters are necessary then. For the arrangement with two cables per phase one configuration – W4b (Fig. 9c) – gives induced voltages not higher than 5 kV. This is the preferred configuration of cables. Figure 10 includes detailed information about phase sequence in particular circuit and induced sheath voltage in particular cable metallic sheath. In case of short-circuit the most favourable configuration is W4b – the same as in normal operating condition. Phase sequence in section ABC/CBA ACB/BCA BAC/CAB BCA/ACB CAB/BAC CBA/ABC Induced sheath voltage (V) 5000 4500 4000 3500 3000 2500 2000 1500 1000 500 0 W4b(T1C1) W4b(T1C2) W4b(T1C3) W4b(T2C1) W4b(T2C2) W4b(T2C3) Type of configuration and symbol of section Figure 10 Induced sheath voltages in case of earth fault for the most favourable configuration of cables: configuration W4b – single-point bonding; sheaths bonding and earthing in E2 124 Calculation of Induced Sheath Voltages in Power Cables – Single Circuit System… 5 CONCLUSIONS Computer-aided calculation of the induced sheath voltages in power cable system allows finding the optimal configuration of the system, with covering technical and economic aspects. In the considered cases the preferred configuration is the configuration W4b (two cables per phase, single-point bonding; sheaths bonding and earthing in E2). This configuration gives acceptable values of induced sheath voltages and the highest power transfer capability. Power system with two cables per phase, instead of single cable system with large cross-section of conductor, should be recommended. REFERENCES [1] CIGRE, Working group B1.18, Special bonding of high voltage power cables, October 2005. [2] CZAPP, S.: Principles of protection against electric skock in high voltage power lines (Zasady ochrony przeciwporazeniowej w liniach elektroenergetycznych wysokiego napiecia). Journal Automatyka Elektryka Zaklocenia, vol. 13, no. 3, pp. 8–22, 2013, http://epismo-aez.pl/, (in Polish). [3] CZAPP, S., DOBRZYNSKI, K., KLUCZNIK, J., LUBOSNY, Z.: Computeraided analysis of induced sheath voltages in high voltage power cable system. The 10th International Conference on Digital Technologies 2014, Zilina, Slovakia, 9–11.07.2014, pp. 44–50, IEEE Catalog Number CFP14CDT-USB. [4] JUNG, C. K., LEE, J. B., KANG, J. W., WANG Xinheng, SONG Yong-Hua: Characteristics and reduction of sheath circulating currents in underground power cable systems. International Journal of Emerging Electric Power Systems, vol. 1, no. 1, pp. 1–17, 2004. [5] de LEON, F.: Major factors affecting cable ampacity. IEEE Power Engineering Society General Meeting (PES), 2006. [6] TZIOUVARAS, D. A.: Protection of high-voltage AC cables. Power Systems Conference: Advanced Metering, Protection, Control, Communication and Distributed Resources PS '06, pp. 316–328, 2006. [7] LI, Zhonglei, DU, B. X., WANG, L., YANG, C., LIU, H. J.: The calculation of circulating current for the single-core cables in smart grid. Innov. Smart Grid Technologies, ISGT, Asia, 21–24 May, 2012. [8] ANSI/IEEE Std 575-1988, IEEE Guide for the application of sheath-bonding methods for single-conductor cables and the calculation of induced voltages and currents in cable sheaths. [9] EN 50522:2010 Earthing of power installations exceeding 1 kV a.c. [10] LEE, J. B., JUNG, Ch. K.: Technical review on parallel ground continuity conductor of underground cable systems. Journal of International Council on Electrical Engineering, vol. 2, no. 3, pp. 250–256, 2012.