applied sciences Article Safety Issues Referred to Induced Sheath Voltages in High-Voltage Power Cables—Case Study Stanislaw Czapp * and Krzysztof Dobrzynski Faculty of Electrical and Control Engineering, Gdańsk University of Technology, Narutowicza 11/12, PL-80-233 Gdańsk, Poland; krzysztof.dobrzynski@pg.edu.pl * Correspondence: stanislaw.czapp@pg.edu.pl Received: 20 August 2020; Accepted: 23 September 2020; Published: 25 September 2020 Abstract: Load currents and short-circuit currents in high-voltage power cable lines are sources of the induced voltages in the power cables’ concentric metallic sheaths. When power cables operate with single-point bonding, which is the simplest bonding arrangement, these induced voltages may introduce an electric shock hazard or may lead to damage of the cables’ outer non-metallic sheaths at the unearthed end of the power cable line. To avoid these aforementioned hazards, both-ends bonding of metallic sheaths is implemented but, unfortunately, it leads to increased power losses in the power cable line, due to the currents circulating through the sheaths. A remedy for the circulating currents is cross bonding—the most advanced bonding solution. Each solution has advantages and disadvantages. In practice, the decision referred to its selection should be preceded by a wide analysis. This paper presents a case study of the induced sheath voltages in a specific 110 kV power cable line. This power cable line is a specific one, due to the relatively low level of transferred power, much lower than the one resulting from the current-carrying capacity of the cables. In such a line, the induced voltages in normal operating conditions are on a very low level. Thus, no electric shock hazard exists and for this reason, the simplest arrangement—single-point bonding—was initially recommended at the project stage. However, a more advanced computer-based investigation has shown that in the case of the short-circuit conditions, induced voltages for this arrangement are at an unacceptably high level and risk of the outer non-metallic sheaths damage occurs. Moreover, the induced voltages during short circuits are unacceptable in some sections of the cable line even for both-ends bonding and cross bonding. The computer simulations enable to propose a simple practical solution for limiting these voltages. Recommended configurations of this power cable line—from the point of view of the induced sheath voltages and power losses—are indicated. Keywords: power cables; high-voltage; induced sheath voltages; electric shock hazard; overvoltages; power losses 1. Introduction High-voltage transmission and distribution power lines are usually used overhead with bare conductors. The main reason for the widespread use of overhead power lines, instead of cable lines, is their lower investment cost. However, there are cases in which the application of overhead lines is precluded. These refer mainly to urban areas but also to rural areas when an increased risk of electric shock hazard or exposure to electromagnetic fields exists [1]. With many undoubtable advantages, the utilization of high-voltage cable lines is associated with some problems. One of the main problems is the induced voltage generated in the power cable’s metallic concentric sheath. With reference to this voltage, power cables may operate as single-point bonded, both-ends bonded or cross-bonded. Recommendations for the performance of power cables bonding and earthing are mainly included Appl. Sci. 2020, 10, 6706; doi:10.3390/app10196706 www.mdpi.com/journal/applsci Appl. Sci. 2020, 10, 6706 2 of 16 Appl. Sci. 2020, 10, x 2 of 16 in the standards [2,3] as well as the report [4]. Figure 1 presents the three aforementioned cable mainly included in the standards [2,3] as well as the report [4]. Figure 1 presents the three bonding arrangements. aforementioned cable bonding arrangements. aluminium conductor copper sheath XLPE insulation PE outer sheath L1 L1 L2 L2 L3 L3 (a) (b) L1 L2 L3 (c) Figure 1. 1. High-voltage High-voltage power power cables cables arrangements: arrangements: (a) (a) single-point single-point bonding; bonding; (b) (b) both-ends both-ends bonding; bonding; Figure (c) cross bonding. (c) cross bonding. The simplest cable sheath bonding arrangement is single-point bonding. In such a solution The simplest cable sheath bonding arrangement is single-point bonding. In such a solution (Figure 1a) the load current in the cable conductor (core) induces a voltage in the sheath, which value (Figure 1a) the load current in the cable conductor (core) induces a voltage in the sheath, which value is the highest at the unearthed end of the power cable line. The induced sheath voltages for any cables’ is the highest at the unearthed end of the power cable line. The induced sheath voltages for any formation in a single-circuit system can be calculated (in simplified form) as follows [2]: cables’ formation in a single-circuit system can be calculated (in simplified form) as follows [2]: √ ! 2 1 1 2D 2L1−L2 2D 3 L1−L3 −7− DL1-L3 7− ln 2 DL1-L2 + 3j 2ln VL1−sh jωI 2 · 10 (1) L1 VL1= j I j 2 10 + ln ln ω = ⋅ − (1) -sh L1 DL1−L3 2 2 D DCu 2 2 D DCu ⋅· D Cu L1- L3 Cu √ ! !# " · D 3 D DL2−L3 1 4D L1−L2 L2−L3 −7 1 D D ⋅ 4 3 VL2−sh = jωI 2 · 10 ln + j ln − 7 L1 L2 L2 L3 L2 L3 + j VL2-sh = jωL2I L2 2 ⋅ 10 2 ln ln DCu22 L1−L2 2 2 DL1D 2 DCu -L2 √ ! 1 2D2L2−L3 2D 3 L1−L3 −7 VL3−sh = jωIL3 2 · 10 − ln ln − j 2 21 D 2 D· DL1−L3 − j 32ln 2 D L1D - L3 Cu = jωI 2 ⋅ 10 −7 − ln Cu L2-L3 V (2) (2) (3) (3) L3-sh L3 2 D ⋅ D 2 D Cu L1-L3(V/m) Cu sheath and L3, respectively; where: V L1-sh , V L2-sh , V L3-sh are the induced voltages in phases L1, L2 IL1 , IL2 , IL3 , are the load currents in the cable conductor (core) of phases L1, L2 and L3, respectively; where: VL1-sh, VL2-sh, VL3-sh are the induced sheath voltages (V/m) in phases L1, L2 and L3, respectively; D is the geometric mean sheath diameter; DL1-L2 is the axial spacing of phases L1 and L2; DL2-L3 is IL1cu , IL2, IL3, are the load currents in the cable conductor (core) of phases L1, L2 and L3, respectively; the axial spacing of phases L2 and L3; DL1-L3 is the axial spacing of phases L1 and L3. Dcu is the geometric mean sheath diameter; DL1-L2 is the axial spacing of phases L1 and L2; DL2-L3 is the For more accurate calculation of the voltages, especially taking into account the electromagnetic axial spacing of phases L2 and L3; DL1-L3 is the axial spacing of phases L1 and L3. couplings, computer-based tools should be employed. The computer-aided modelling of the induced For more accurate calculation of the voltages, especially taking into account the electromagnetic sheath voltages with the use of the PSCAD/EMTDC software is presented in [5], whereas [6] presented couplings, computer-based tools should be employed. The computer-aided modelling of the the calculation by the Pearson Correlation. Multiple-circuit systems require the application of induced sheath voltages with the use of the PSCAD/EMTDC software is presented in [5], whereas [6] advanced computer-based tools to calculate these voltages, as presented by the authors in [7] or presented the calculation by the Pearson Correlation. Multiple-circuit systems require the other researchers in [8,9]. application of advanced computer-based tools to calculate these voltages, as presented by the To avoid electric shock, the induced voltage-to-earth at the unearthed end should not exceed authors in [7] or other researchers in [8,9]. permissible values determined by the standard [10]. For a long-time of touch voltage duration, To avoid electric shock, the induced voltage-to-earth at the unearthed end should not exceed permissible values determined by the standard [10]. For a long-time of touch voltage duration, the permissible value is equal to 80 V. When the load current is relatively low or a cable line is not long, Appl. Sci. 2020, 10, 6706 3 of 16 the permissible value is equal to 80 V. When the load current is relatively low or a cable line is not long, values of the induced voltages are usually below the permissible limit. A more serious problem occurs in the case of a line-to-earth fault at the unearthed end. If the value of the short-circuit current is high, this current produces a high-value induced voltage, which may damage the cables’ non-metallic polyethylene (PE) outer sheath. It is assumed in the engineering practice that during the short-circuit conditions the induced voltage should not exceed 5 kV. To limit values of the induced voltage, an earth continuity conductor (ECC) is buried in the ground, parallel to the cables, what was widely studied in [11]. The extensive analysis conducted in [12] shows that in special cases the ECC may reduce the induced voltages by even over 60% compared to a system without the ECC. Despite this, the induced voltages may still exceed the acceptable level. Moreover, the study results presented in [13] indicate that in the case of the uninsulated ECC, dangerous touch voltages may appear around this parallel cable. For these reasons or when the voltages are too high in normal operating conditions, both-ends bonding of cables is used as an alternative (Figure 1b). When both-ends bonding is used, metallic sheaths are bonded and earthed in the accessible points in substations and no risk of electric shock occurs in normal operating conditions. Moreover, in the case of a line-to-earth short circuit, the current distribution through the earthing system is more favourable [14], especially when a global earthing system exists in the analyzed area [15]. The most unfavourable effect of the both-ends bonding is the presence of sheath circulating currents. These currents produce additional power losses in the cables and hence decrease the current-carrying capacity. Such power losses, due to the induced voltages, may occur even in HVDC power cable systems, as underlined in [16]. Therefore, it is important to evaluate sheath circulating currents with relatively high accuracy [17], taking into account different geometries of the cables [18], sheath resistance, phase rotation and cable armouring [19] as well as varied load conditions [20]. High circulating currents and high power losses resulting from them are required to be reduced [21–24]. The most effective method of sheath currents suppression, but relatively complicated, is the implementation of the cross-bonded cable system (Figure 1c). Broad studies of this method are included in [25–30]. Transposition of the cables’ sheaths in particular phases compensates induced voltages and theoretically, no production of the sheath circulation currents occurs. The literature study leads to the conclusion that methods of the induced sheath voltages and sheath circulating currents reduction should be applied very carefully. Any given cable system, especially a complicated one, should always be analyzed individually. Unfortunately, the selection of the type of bonding in the particular case of the cable system is not an easy task. In practice, a compromise between technical and economic aspects should be reached. This paper presents a comprehensive study of the induced voltages in the 110 kV power cable line. The power cable line is relatively long (12 km) but the power transferred via this line is very low (approx. 12% with reference to max permissible power transfer via the cables) due to a specific type of the industrial consumer at the end of the line. Such a low transferred power suggests the application of the single-point bonding in the analyzed power cable line because the induced sheath voltages at the unearthed end are clearly below the permissible limit equal to 80 V, hence no electric shock hazard exists. However, the short-circuit analysis has shown that the single-point bonding is excluded—very high values of the induced voltages are dangerous for the non-metallic PE outer sheath. The results of the calculations suggest to apply both-ends bonding or cross bonding, but detailed analysis for these arrangements has shown that the risk of outer sheath damage still exists in some sections of the power cable line. A solution for the elimination of too high induced voltages during a short circuit is indicated. As an extension of the analysis related to induced voltages, power losses in the cable system, including in cables’ sheaths, have been calculated for all types of bonding. In some cases, values of the power losses may be a decisive factor in selecting the type of the bonding system. The presented results of the analysis of the induced voltages and power losses in the example high-voltage power cable line can be useful for practical applications, especially for the designers of parameters of the cable/cable line are as follows [31]: • • nominal voltage of the cable: 110 kV (line-to-line), 64 kV (line-to-earth); nominal cross-sectional area of the aluminium conductor (core): 240 mm2; (external diameter DAl2020, = 17.9 Appl. Sci. 10, mm); 6706 4 of 16 • resistance of the aluminum conductor (core): 0.125 Ω/km (DC in 20 °C), 0.161 Ω/km (AC in max temp. 90 °C); the cable lines.cross-sectional The analysis has the possible points in such lines, which • nominal areaindicated of the copper sheath:critical/weak 95 mm2 (mean diameter DCu = 58.5 mm);could be overlooked at the design stage. • resistance of the copper sheath: 0.192 Ω/km (DC in 20 °C); • inductive reactance of the cable line in the trefoil formation: 0.143 Ω/km; 2. Description of the Analyzed 110 kV Cable Line • XLPE insulation external diameter: DXLPE = 52.9 mm; The power cable external system under analysis connects a 110 kV power substation (supply • PE outer sheath diameter (the outer diameter of the cable): DPE = 66.6 mm; service) and a• dedicated consumer/load (Figure 2). in Thethe total lengthformation: of the single-circuit three-phase cable line is approx. the current-carrying capacity trefoil 421 A (single-point bonding), 409 A 12 km. The manufacturer’s (both-ends bonding); length of the cable (minor section) is equal to approx. 1 km and the points with connections of the consecutive sections are marked • short-circuit power at the supply service point: 1120p.0–p.12 MVA. in Figure 2. In some of these points, earthing and bonding (including cross bonding) of the cables’ sheaths are possible. Generally, cables are On the base of the nominal parameters of the cable/cable line, it can be stated that the maximum laid in trefoil formation without spacing. Some spacing, as well as short sections with flat formation, permissible power transmitted via this line is approx. 80 MW. However, the consumer’s demand is are applied in the cable ducts, what is included in the computer model. only 10 MW and the connection of other loads to this 110 kV cable line is not planned. Power system 110 kV Supply service Load 10 MW tgφ = 0.4 Consumer p.0 p.12 p.1 p.11 ~3 km ~3 km p.2 ~1 km p.10 p.5 p.4 p.6 p.7 p.8 p.3 ~3 km p.9 ~3 km Figure 2. General data of the analyzed power cable system; p.0–p.12—possible points for earthing Figure 2. General data of the analyzed power cable system; p.0–p.12—possible points for earthing and bonding. and bonding. The type of cable used in this line is presented in Figure 3 (a simplified view). The nominal parameters of the cable/cable line are as follows [31]: • • • • • • • • • • nominal voltage of the cable: 110 kV (line-to-line), 64 kV (line-to-earth); nominal cross-sectional area of the aluminium conductor (core): 240 mm2 ; (external diameter DAl = 17.9 mm); resistance of the aluminum conductor (core): 0.125 Ω/km (DC in 20 ◦ C), 0.161 Ω/km (AC in max temp. 90 ◦ C); nominal cross-sectional area of the copper sheath: 95 mm2 (mean diameter DCu = 58.5 mm); resistance of the copper sheath: 0.192 Ω/km (DC in 20 ◦ C); inductive reactance of the cable line in the trefoil formation: 0.143 Ω/km; XLPE insulation external diameter: DXLPE = 52.9 mm; PE outer sheath external diameter (the outer diameter of the cable): DPE = 66.6 mm; the current-carrying capacity in the trefoil formation: 421 A (single-point bonding), 409 A (both-ends bonding); short-circuit power at the supply service point: 1120 MVA. Appl. Sci. 2020, 10, 6706 5 of 16 Appl. Sci. 2020, 10, x 5 of 16 Figure 3. A view ofofthe analyzedcase. case. Figure 3. simplified A simplified view thepower powercable cableused used in in the the analyzed On the of the nominal of the line, with it canthe be use stated thatPowerFactory the maximum Thebase power cable system parameters under analysis hascable/cable been modelled of the permissible transmitted this takes line isinto approx. 80 MW. However, thebyconsumer’s demand softwarepower [32]. The computervia model account all data delivered the investor, among is onlyother: 10 MW and the connection of other loads to this 110 kV cable line is not planned. cable technical parameters, cable line layout (including the arrangement with cable ducts), The power cable system under analysis The has entire been modelled with the use ofofthe possible points of the bonding or earthing. model of the line consists 161PowerFactory sections, of software Thecable computer model takes into account all data delivered investor, among which[32]. 61 are ducts with different cable arrangements. Two typesby of the cable ducts are used:other: the cableflat technical parameters, cable line layout The (including the arrangement with cableducts ducts), points formation and the trefoil formation. participation of the flat formation in possible the length of the line is 1.7%, and the participation of the trefoil formation ducts is 8.2%. Thus, 90% of the cable of the bonding or earthing. The entire model of the line consists of 161 sections, of which 61 are cable line length is the cable trefoilarrangements. formation without without rough of the ducts with different Twospacing types ofand cable ductsducts—for are used: the flatcalculations formation and the induced voltages, is acceptableof to the assume such a formation along the entire length line.and the trefoil formation. Theitparticipation flat formation ducts in the length of the lineofisthe 1.7%, Figure 4a trefoil presents a cable ducts route,iswhich is reflected the computer model—small dots participation of the formation 8.2%. Thus, 90% ofinthe cable line length is the trefoilblue formation indicate a change in cable spacing (due to ducts application). The cables’ joints are marked as big redto without spacing and without ducts—for rough calculations of the induced voltages, it is acceptable dots. assume such a formation along the entire length of the line. The PowerFactory software allows for modelling cable lines, including cable spacing, which Figure 4a presents a cable route, which is reflected in the computer model—small blue dots indicate means that the software automatically determines the selected power line electrical parameters. a change in cable spacing (due to ducts application). The cables’ joints are marked as big red dots. Impedance Z and admittance Y of cables are defined in two matrix equations presented in [33] and The PowerFactory software allows for modelling cable lines, including cable spacing, which means implemented in the software as well as described in its guide [34]: that the software automatically determines the selected power line electrical parameters. Impedance Z and admittance Y of cables are defined in two ∂matrix presented in [33] and implemented V = −equations Z⋅I (4) in x ∂ the software as well as described in its guide [34]: ∂ (5) ∂ ∂x I = − Y ⋅ V V =−Z · I (4) ∂x where: |V| and |I| are the voltage and current vectors respectively, at distance x along the cable line; ∂ |Z| and |Y| are square matrices of the impedance and admittance respectively. I =−Y · V (5) ∂x The complexity of |Z| and |Y| matrices depends on the number of cables and the number of layers The impedance and vectors admittance matrices can be described in the where: |V| per andsingle |I| arecable. the voltage and current respectively, at distance x along thefollowing cable line; way: |Z| and |Y| are square matrices of the impedance and admittance respectively. The complexity of |Z| and |Y| matrices the number of cables and the number of layers [ Z ] = depends [ Z i ] + Z on (6) p + [Z c ] + [Z 0 ] per single cable. The impedance and admittance matrices can be described in the following way: h i [Y h] = is ⋅ [Ch ] i h i (7) [Z] = Zi + Zp + Zc + Z0 (6) [C ] = [Ci ] + C p + [Cc ] + [C0 ] (8) [Y] = s · [C]−1 (7) where: the matrices with subscript i include cable (core, sheath and armour); the matrices h parameters i with subscript 0 include parameters outer [C]of=the [Ccable [Cc ] +(air, [C0 ]earth); the matrices with subscripts p(8) p +media i] + C and c include parameters of a pipe (an enclosure—if applied); C is a potential coefficient matrix; s = jω. where: the matrices with subscript i include cable parameters (core, sheath and armour); the matrices Detailed information on the calculation of individual components of the impedance and withadmittance subscript 0matrices includecan parameters cable outer media (air, earth); the matrices with subscripts be found of in the [33,34]. p and c include parameters of a pipe (an enclosure—if applied); C is a potential coefficient matrix; s = jω. Detailed information on the calculation of individual components of the impedance and admittance matrices can be found in [33,34]. −1 Appl. Appl.Sci. Sci.2020, 2020,10, 10,6706 x 6 6ofof1616 (a) point p.0 p.0(c) point p.1 ~1 km ... Core L2 ... Core L3 Electric circuit of cores (c) ... 9m 68 m p.0(sh) p.1(c) p.0.3(c) p.0.4(c) p.0.2(c) p.0.1(c) Core L1 Sheath L1 p.0.1(sh) 22 m p.0.2(sh) 3m p.0.3(sh) p.0.4(sh) p.1(sh) ... Sheath L2 ... Sheath L3 ... Electric circuit of sheaths (sh) Cable arrangement Cables directly buried in the ground (trefoil formation) 160 mm Cables in ducts (flat formation) in consecutive sections Cables in ducts (trefoil formation) (b) Figure cable route of the cablecable system reflected in the PowerFactory software software (a); an example Figure4.4.Real Real cable route of analyzed the analyzed system reflected in the PowerFactory (a); an part of the computer model of the cable system (minor section between point p.0 and point p.1) (b). example part of the computer model of the cable system (minor section between point p.0 and point p.1) (b). Appl. Sci. 2020, 10, x 7 of 16 Appl. Sci. 2020, 10, 6706 7 of 16 In the considered case, the cable line model consists of two electromagnetically coupled circuits: cores electric circuit (c) and sheaths electric circuit (sh) (Figure 4b). The results of the multi-variant computer analysis included the next show theoflevels of voltages induced incoupled the cables’ In the considered case, theincable line sections model consists two electromagnetically circuits: risks(c) referred to them, as wellcircuit as the(sh) power losses4b). influencing the current-carrying coressheaths electricand circuit and sheaths electric (Figure The results of the multi-variant capacity of the cables. computer analysis included in the next sections show the levels of voltages induced in the cables’ sheaths and risks referred to them, as well as the power losses influencing the current-carrying capacity 3. Results of the Induced Voltages Computer Simulations of the cables. 3.1. Induced Voltages for Single-Point Bonding 3. Results of the Induced Voltages Computer Simulations In the first stage of the analysis, the induced sheath voltages in normal operating conditions, in case of the single-point bonding, Bonding have been analyzed. The load current flow in the cable cores, as 3.1. Induced Voltages for Single-Point well as the induced voltages, are calculated by the software taking into account the electromagnetic In the firstAll stage ofpresenting the analysis, the induced sheath voltages in normal operating conditions, couplings. charts the induced voltages include the highest rms values among phases in case of the single-point bonding, have been analyzed. The load current flow in the cable cores, L1, L2, L3. as well asThe theanalyses inducedhave voltages, are calculated the software taking into account the electromagnetic been conducted for thebyfollowing variables: couplings. All charts presenting the induced voltages include the highest rms values among phases L1, • the transferred power equal to 1 MW (an example very low power), 10 MW L2, L3. (contracted/declared consumed power), 80 MW (maximal permissible power in terms of the The current-carrying analyses have been conducted for the followingvalue, variables: capacity of the cables; a theoretical used for the comparison purposes); • • • • the single-point-bonding at the 110 kV supply service substation (p.0 in Figure 2) or at the the transferred power equal to 1 MW (an example very low power), 10 MW (contracted/declared consumer substation (p.12 in Figure 2); consumed power), 80 MW (maximal in terms of the current-carrying capacity • the reactive-to-active power ratio: tgpermissible φ = Q/P = 0 orpower tgφ = Q/P = 0.4 (contracted). of the cables; a theoretical value, used for the comparison purposes); Figure 5 presents the induced sheath voltages for the case with the tgφ = 0. When the the single-point-bonding at the 110 kV supply service substation (p.0 in Figure 2) or at the single-point bonding is performed at the 110 kV supply service substation (Figure 5a), the induced consumer (p.12 in Figure 2); limit 80 V indicated in the standard [10], both for the voltages aresubstation significantly below the assumed the reactive-to-active power ratio: = Q/P = 0value or tgφ =isQ/P = 0.4 (contracted). power 1 MW and the contracted powertgφ 10 MW. The 80 V many times exceeded in the case of the 80 MW (approx. 330 V), but it is presented only for the comparison purposes. When the Figure 5 presents theisinduced sheath forsubstation the case with the5b), tgφthe = 0. Whenvoltages the single-point single-point bonding performed at thevoltages consumer (Figure induced are bonding is performed at the 110 kV supply service substation (Figure 5a), the induced voltages generally higher than for the case presented in Figure 5a. For the transferred power 10 MW, it is are significantly below the assumed 80 unearthed V indicated close to the permissible limit 80 limit V at the endinofthe the standard line (point[10], p.0). both for the power 1 MW and the contracted power 10 MW. Thevoltages value 80 V is many the case ofnatural the 80 MW The differences in the induced (Figure 5a vs. times Figureexceeded 5b) are theineffect of the load 330 of the line (capacitive),only which a capacitive purposes. current flow of a changing value along (approx. V),cable but it is presented forforces the comparison When the single-point bonding the length of the cable line. It indicates that the location of the point of the earthing (reference point) is performed at the consumer substation (Figure 5b), the induced voltages are generally higher than for is important. Note, that for5a. theFor case presented in Figure 5a,10 the induced voltages at the unearthed limit the case presented in Figure the transferred power MW, it is close to the permissible end are practically the same for the power 1 MW and 10 MW. In the case of Figure 5b, the respective 80 V at the unearthed end of the line (point p.0). voltages at the unearthed end differ about two times. 80 V 400 350 80 MW 300 250 200 induced voltage (V) induced voltage (V) 400 150 100 80 V 50 0 2 4 6 length (km) (a) 300 250 200 150 100 10 MW 50 1 MW 0 80 MW 350 8 10 10 MW 12 0 1 MW 0 2 4 6 8 10 12 length (km) (b) Figure 5. Induced sheath voltages as a function of the cable line length, for three values of the Figure 5. Induced sheath voltages as a function of the cable line length, for three values of the transferred power (1 MW, 10 10 MW, 8080MW), 0:(a) (a)single-point single-point bonding at point in Figure 2; transferred power (1 MW, MW, MW),tgφ tgφ = = 0: bonding at point p.0 inp.0 Figure 2; (b) single-point bonding at point p.12 in Figure 2. (b) single-point bonding at point p.12 in Figure 2. The differences in the induced voltages (Figure 5a vs. Figure 5b) are the effect of the natural load of the cable line (capacitive), which forces a capacitive current flow of a changing value along the length of the cable line. It indicates that the location of the point of the earthing (reference point) is important. Note, that for the case presented in Figure 5a, the induced voltages at the unearthed end are Appl. Sci. 2020, 10, 6706 8 of 16 practically the same for the power 1 MW and 10 MW. In the case of Figure 5b, the respective voltages at the unearthed end differ about two times. Appl. 88 of Appl. Sci. Sci. 2020, 2020, 10, 10, xx of 16 16 Similar general conclusions flow from the analysis of the results presented in Figure 6 (tgφ = 0.4). However,Similar the variations of the induced voltages along the length ofpresented the cablein line are slightly different general flow the of results Figure 66 (tg Similar general conclusions conclusions flow from from the analysis analysis of the the results presented in Figure (tgφφ == 0.4). 0.4). thanHowever, for the tgφ = 0, especially if one compares Figure 5a vs. Figure 6a for 1 MW and 10 MW. However, the the variations variations of of the the induced induced voltages voltages along along the the length length of of the the cable cable line line are are slightly slightly than one Figure MW MW. different than for for the the tg tgφφ == 0, 0, especially especially one compares compares Figure 5a 5a vs. vs.power Figure 6a 6a for MW and and 10well MW.as the Thus,different the reactive-to-active power ratioifif tgφ, natural Figure capacitive of for the11 cables as10 Thus, power tg capacitive power the as as the Thus, the reactive-to-active power ratio ratio tgφφ,, natural natural capacitive power of the cables cables as well wellin asthe thesafety location ofthe thereactive-to-active point of the single-point bonding and earthing should beof taken into account location of the point of the single-point bonding and earthing should be taken into account in the location of the point of the single-point bonding and earthing should be taken into account in the analysis. In the light of the aforementioned investigation, it can be concluded that for the contracted safety In the of the investigation, itit can that for the safety analysis. analysis. In MW, the light light of 0.4), the aforementioned aforementioned can be be concluded concluded that the transferred power (10 tgφ = the single-pointinvestigation, bonding is acceptable, whether in p.0for (preferred) contracted contracted transferred transferred power power (10 (10 MW, MW, tg tgφφ == 0.4), 0.4), the the single-point single-point bonding bonding is is acceptable, acceptable, whether whether in in or in p.12. p.0 p.0 (preferred) (preferred) or or in in p.12. p.12. 80 80 VV 400 400 80 80 MW MW 350 350 300 300 250 250 200 200 150 150 100 100 80 80 VV 50 50 00 induced voltage voltage (V) (V) induced induced voltage voltage (V) (V) induced 400 400 00 22 44 66 length length (km) (km) 88 10 10 300 300 250 250 200 200 150 150 100 100 10 10 MW MW 50 50 10 10 MW MW 11 MW MW 80 80 MW MW 350 350 00 12 12 11 MW MW 22 00 44 (a) (a) 66 length length (km) (km) 88 10 10 12 12 (b) (b) Figure 6. Induced sheath function thecable cable line length three values Figure 6. sheath voltages as line length for three values of Figure 6. Induced Induced sheathvoltages voltages as as aaa function function of ofofthe the cable line length for for three values of the theof the transferred power (1 MW, 1010 MW, 8080 MW), 0.4:(a) (a)single-point single-point bonding at point in Figure 2; bonding at p.0 Figure 2; transferred power (1 MW, MW), tg = 0.4: 0.4: (a) single-point bonding at point point p.0 in inp.0 Figure 2; transferred power (1 MW, MW, 10 MW, 80 MW),tgφ tgφφ == (b) single-point bonding at at point p.12 (b) bonding p.12 in Figure (b) single-point single-point bonding at point point p.12in inFigure Figure 2. 2. The The next step step of theof is to evaluate the induced sheathsheath voltages in casein of case the line-to-earth the is the voltages of The next next step ofanalysis the analysis analysis is to to evaluate evaluate the induced induced sheath voltages in case of the the fault the Like previous the bonding faultline-to-earth at the unearthed Like in end. the previous the single-point bonding was was assumed line-to-earth fault at at end. the unearthed unearthed end. Like in in the thescenarios, previous scenarios, scenarios, the single-point single-point bonding was assumed at supply substation 7a) at assumedatalternatively alternatively at the the 110 110 kV kV substation supply service service substation (Figure 7a) or or substation at the the consumer consumer alternatively the 110 kV supply service (Figure 7a) or at(Figure the consumer (Figure 7b). substation (Figure 7b). In the short-circuit analysis, the induced voltages have been calculated for substation (Figure 7b). In the short-circuit analysis, the induced voltages have been calculated for the earth In the short-circuit analysis, the induced voltages have been calculated for the cases without the an cases without an earth continuity conductor (ECC) or with this conductor. The ECC was laid parallel cases without an earth continuity conductor (ECC) or with this conductor. The ECC was laid parallel continuity conductor (ECC) or with this conductor. The ECC was laid parallel to the cable line at to at 20 of to the the cable cable line at aa distance distance of 20 cm cm (Figure (Figure 8a). 8a). An An insulated insulated cable cable with with aa copper copper conductor of the the a distance of 20 line cm (Figure 8a). of An insulated cable with a copper conductor of theconductor cross-sectional area 22 was assumed as the ECC. Halfway along the cable line (in p.6), the cross-sectional area of 120 mm cross-sectional area of 120 mm was assumed as the ECC. Halfway along the cable line (in p.6), the 2 of 120 mm was assumed as the ECC. Halfway along the cable line (in p.6), the ECC was transposed to ECC ECC was was transposed transposed to to the the other other side side of of the the line line (Figure (Figure 8b), 8b), according according to to the the recommendations recommendations the other sideinofthe theguide line [2]. (Figure 8b), according to the recommendations included in the guide [2]. included included in the guide [2]. 25 25 without without ECC ECC 20 20 15 15 with with ECC ECC 10 10 55 00 without without ECC ECC 20 20 induced voltage voltage (kV) (kV) induced induced voltage voltage (kV) (kV) induced 25 25 00 22 44 66 length length (km) (km) (a) (a) 88 10 10 12 12 15 15 with with ECC ECC 10 10 55 00 00 22 44 66 length length (km) (km) 88 10 10 12 12 (b) (b) Figure 7. Induced sheath voltages as as aasfunction ofof the cable line Figure 7. sheath voltages aa function the cable line length, in case of the line-to-earth Figure 7. Induced Induced sheath voltages function of the cable linelength, length,in incase caseof ofthe theline-to-earth line-to-earth fault fault at end; bonding supply service (point p.0 Figure 2); fault at the the unearthed unearthed end; single-point single-point bonding at: (a) supplyservice service substation substation (point p.0 in in Figure 2); 2); at the unearthed end; single-point bonding at: at: (a)(a) supply substation (point p.0 in Figure (b) substation (point p.12 in (b) consumer consumer substation (pointp.12 p.12in in Figure Figure 2). 2). (b) consumer substation (point Figure 2). Appl. Sci. 2020, 10, 6706 Appl. Sci. 2020, 10, x Appl. Sci. 2020, 10, x 9 of 16 9 of 16 9 of 16 p.6 p.6 p.0 p.0 20 cm 20 cm ECC ECC p.12 p.12 ECC ECC ECC ECC (a) (a) (b) (b) Figure 8. 8. Arrangement Arrangementofof earth continuity conductor (ECC): a distance the line; cable(b) line; Figure thethe earth continuity conductor (ECC): (a) a(a) distance to theto cable its Figure 8. Arrangement of the earth continuity conductor (ECC): (a) a distance to the cable line; (b) its (b) its transposition. transposition. transposition. Induced sheath end of of thethe lineline reach values overover 22 kV the ECC Induced sheathvoltages voltagesatatthe theunearthed unearthed end reach values 22without kV without the Induced sheath voltages at the unearthed end ofare thesimilar, line values oversingle-point 22 the kV without the and approx. 12 kV12 with ECC. All respective values regardless, the bonding ECC and approx. kVthe with the ECC. All respective values arereach similar, regardless, single-point ECC and and approx. 12 kVare with the All respective values arehigh similar, regardless, the between single-point and earthing are performed in p.0ECC. or inin p.12. Such values of thevalues induced voltages the bonding earthing performed p.0 or in high p.12. Such of the induced voltages bonding and earthing are performed in p.0 or in p.12. Such high values of the induced voltages copper sheath and the earth may be a source of the damage of the non-metallic outer sheath of the between the copper sheath and the earth may be a source of the damage of the non-metallic outer between copper sheath and the be Ita is source of thedesign damage of the non-metallic outer cable (PE outer sheath in Figure 3). earth ItinisFigure a may common design practice to assume that this non-metallic sheath ofthe the cable (PE outer sheath 3). a common practice to assume that this sheath of the cable (PE outer sheath in Figure 3). It is a common design practice to assume that outer sheath will not be damaged if the induced voltage does not exceed 5 kV. As it is seen in Figure 7, non-metallic outer sheath will not be damaged if the induced voltage does not exceed 5 kV. As this it is non-metallic outer sheath will5 not be damaged if the induced voltage does not exceed 5 kV. As itthe is the value 5 kV is7,not exceeded only the length ofonly the cable linelength (from thethe earthing point) approx. seen in Figure the value kV isfor not exceeded for the of cable line (from seen in Figure 7, the value 5 kV is not exceeded only for the length of the cable line (from the 2.5 km without the ECC and approx. 5 km with the ECC. Thus, in the considered power line of the earthing point) approx. 2.5 km without the ECC and approx. 5 km with the ECC. Thus, in the earthing approx. km without the acceptable—too ECCsingle-point and approx. 5 km with ECC. Thus, inhigh the length 12point) km, the single-point bonding not high values induced voltages in considered power line of2.5the length 12iskm, the bonding is of nottheacceptable—too considered power line of the length 12 (despite km, theshort-circuit single-point bonding isexist not acceptable—too high case of of thethe short-circuit conditions the possibleconditions application of sheath voltage limiters values induced voltages in exist case of the (despite the possible values of the induced voltages in case of the short-circuit conditions exist (despite the possible (SVL); a high-level margin of reliability and safety is required). application of sheath voltage limiters (SVL); a high-level margin of reliability and safety is required). application of sheath voltage limiters (SVL); a high-level margin of reliability and safety is required). 3.2. Induced Voltages for Both-Ends Bonding or Cross Bonding 3.2. Induced Voltages for Both-Ends Bonding or Cross Bonding 3.2. Induced Voltages for Both-Ends Bonding or Cross cable Bonding Since single-point bonding in the analyzed line is not acceptable, both-ends bonding is Since single-point bonding in the analyzed cable line is not acceptable, both-ends bonding is considered as an alternative solution. For the both-ends bonding, the induced sheath voltages in the Since single-point bonding in theFor analyzed cable line is not the acceptable, bonding is considered as an alternative solution. the both-ends bonding, induced both-ends sheath voltages in the normal operating conditions solution. (10 MW) For are close to 0 V. Therefore, they are not presented in the form of considered as an alternative the both-ends bonding, the induced sheath voltages in the normal operating conditions (10 MW) are close to 0 V. Therefore, they are not presented in the form the chartoperating in this paper. However, the induced voltages areare very interesting inincase of the normal (10 MW) close tovoltages 0 V. distributions Therefore, they thecase form of the chart in thisconditions paper. However, theare induced distributions are not verypresented interesting in of line-to-earth fault. The cable line comprises straight-joints approx. every 1 km. After discussion with of chart in thisfault. paper. However, induced straight-joints voltages distributions very interesting in case of thethe line-to-earth The cable linethe comprises approx. are every 1 km. After discussion the industrial partner involved inline the cable line project, it was decided toevery analyze the induced voltages the fault. The cable comprises 1 km. Afterthe discussion withline-to-earth the industrial partner involved in the cablestraight-joints line project, itapprox. was decided to analyze induced distribution in case of the earth fault in the selected joints. The line-to-earth fault was consecutively with the industrial partner involved the cable project, it was decided analyze thefault induced voltages distribution in case of the in earth fault line in the selected joints. The to line-to-earth was assumed distribution in the following points (Figure 9): fault in the selected joints. The line-to-earth fault was voltages in case of the earth consecutively assumed in the following points (Figure 9): consecutively assumed in the following points (Figure 9): p.3: quarter of of the the line line length; length; •• p.3: aa quarter ••• p.3: a quarter of the line length; p.6: half of the line length; p.6: half of the line length; ••• p.6: of the line length; p.9: three-quarters of the p.9: half three-quarters of the line line length; length; ••• p.9: three-quarters of the line p.12: the consumer substation.length; • p.12: the consumer substation. Power system Power 110system kV 110service) kV (supply (supply service) p.0 p.1 p.0 p.1 p.2 p.2 p.3 p.3 p.4 p.4 p.5 p.5 p.6 p.6 p.7 p.7 p.8 p.8 p.9 p.9 p.10 p.10 p.11 p.11 p.12 p.12 Figure 9. Simplified diagram of the cable system presenting points of the assumed consecutive line-to-earth faults. diagram of the cable system presenting points of the assumed consecutive Figure 9. Simplified Figure 9. Simplified line-to-earth faults. diagram of the cable system presenting points of the assumed consecutive line-to-earth faults. of the induced voltages for the aforementioned points of the fault are presented The distributions in Figure For the both-ends 10a)for thethe line-to-earth-fault at point induced The 10. distributions of the bonding induced(Figure voltages aforementioned pointsp.12 of gives the fault are The distributions of the induced voltages for the aforementioned points of the fault are voltage practically to 0the V. Itboth-ends is obviousbonding because(Figure this point is the located at the consumer presented in Figureequal 10. For 10a) line-to-earth-fault at substation, point p.12 presented in Figure 10. practically For the both-ends 10a)because the line-to-earth-fault at pointatp.12 gives induced voltage equal tobonding 0 V. It (Figure is obvious this point is located the gives induced voltage practically equal to 0 V. It is obvious because this point is located at the induced voltage (kV) induced voltage (kV) sheaths are performed in p.4 and p.8; see Figure 10b), the induced voltages in the characteristic points are only slightly lower compared to the both-ends bonding. Unfortunately, the voltages still exceed the assumed permissible level of 5 kV. To decrease the induced voltages below the permissible 5 kV, an additional earthing in point p.6 has been proposed. The earthing is relatively easy to perform in this place—the cables’ metallic Appl. Sci. 2020, 10, 6706 of 16 sheaths are accessible. With this additional earthing, the power cable system is composed of10three earthing points it Appl. Sci. 2020, 10, x (p.0, p.6 and p.12) and the induced voltages distributions are as in Figure 11.10As of 16 was expected, in the case of the line-to earth fault in p.6, for the both-ends bonding (Figure 11a), the which contains an earthing system. An earth fault in points p.3, p.6 or p.9 gives the induced voltages consumervoltage substation, which contains an earthing system. An earth fault in points p.3,see p.6that or p.9 gives induced in this point is reduced 0 V. the higher than the assumed permissible limit 5practically kV (at theto point ofHowever, the fault). one Thecan highest valuefor of the the induced voltages higher than the assumed permissible limit 5 kV (at the point of the fault). The arrangement with the cross bonding (Figure 11b), in the case of the line-to earth fault in p.6, the voltage is in p.6 (over 7 kV) mainly because it is located at the farthest distance from the earthed points highest value of between the voltage isand in p.6 7 kV) mainly it is locateddistribution at the farthest distance induced voltage p.6 (over reaches approx. 250because V. Similar is observed (p.0 and p.12). In the case p.0 of the cross bonding (transpositions of thevoltage cable sheaths are performed in from the earthed points (p.0 and p.12). In the case of the cross bonding (transpositions of the cable between p.6see and p.12, 10b), in the of thevoltages line-to in earth p.12. For both arrangements (both-ends p.4 and p.8; Figure thecase induced the in characteristic points are only slightly lower sheaths are performed in p.4the andhighest p.8; see Figure 10b), the induced voltages in the characteristic bonding and cross bonding), value of the around 4 kV in p.3), compared to the both-ends bonding. Unfortunately, the voltage voltagesisstill exceed the (line-to-earth assumed permissible pointsisare onlybelow slightly lower compared to (5 thekV). both-ends bonding. Unfortunately, the voltages still what clearly the permissible value level of 5 kV. exceed the assumed permissible level of 5 kV. To decrease the induced voltages below the permissible 5 kV, an additional earthing in point p.6 p.6 p.6 has The earthing is relatively easy to8 perform in this place—the cables’ metallic 8 been proposed. p.3 p.9 p.9 p.3 7 power cable system is composed of three 7 are accessible. With this additional earthing, the sheaths 6 6 earthing points (p.0, p.6 and p.12) and the induced voltages distributions are as in Figure 11. As it 5 was expected, in the case of the line-to earth fault in p.6,5for the both-ends bonding (Figure 11a), the 4 4 induced voltage in this point is reduced practically to 0 V. However, one can see that for the 3 3 p.12 arrangement with the cross bonding (Figure p.1211b), in the 2 case of the line-to earth fault in p.6, the 2 induced voltage between p.0 and p.6 reaches approx. 250 V. Similar voltage distribution is observed 1 1 between p.6 and p.12, in the case of the line-to earth 0in0 p.12.2 For both arrangements10(both-ends 0 4 6 8 12 0 2 4 10 8 6 12 c-b 4 kV (line-to-earth c-b bonding and cross bonding), the highest value of the voltage is around in p.3), length (km) length (km) what is clearly below the(a)permissible value (5 kV). (b) induced voltageinduced (kV) voltage (kV) induced voltageinduced (kV) voltage (kV) Figure 10. Induced sheath voltages as a function of the cable line length, in case of the line-to-earth line-to-earth p.6 p.6 in the the characteristic characteristicpoints points(p.3, (p.3,p.6, p.6,p.9 p.9ororp.12): p.12):(a) (a)both-ends bonding; cross bonding (c-b) fault in bonding; (b)(b) cross bonding (c-b) in 8both-ends 8 p.3 p.9 p.9 p.3 in7 p.4 and p.4 and p.8.p.8. 7 6 6 p.3 in case of the line-to-earth Figure 11. Induced sheath voltages as a function of the cable line length, p.3 4.5 4.5 p.9 fault in characteristic points (p.3, p.6, p.9 or p.12); additional earthing in p.6: (a) both-endsp.9 bonding; 4.0 4.0 3.5 (b) cross bonding (c-b) in p.2, p.4 as well as in p.8, p.10. 3.5 3.0 induced voltage (kV) induced voltage (kV) To the induced voltages below the permissible 5 kV, anp.3additional earthing in point p.6 5 5 decreasep.3 4.5 4.5 p.9 4 p.9 4 proposed. The earthing is relatively has been easy to perform in this place—the cables’ metallic sheaths 4.0 4.0 3 3 are accessible. With this additional earthing, the power3.5 cable system is composed of three earthing 3.5 p.12 p.12 2 2 3.0 points3.0 (p.0, p.6 and p.12) and the induced voltages distributions are as in Figure 11. As it was expected, 1 1 2.5 in the2.5case of the line-to earth fault in p.6, for the both-ends bonding (Figure 11a), the induced voltage 0 0 2.0 2.0 0 0 2 4 10 6 8 12 2 4 10 8 6 12 in this point is reduced practically to 0 V. However, one can the arrangement 1.5 see that for c-b c-b with the cross 1.5 length (km) length (km) p.12 p.6 p.6case of the line-to bonding (Figure 11b), in the earth fault1.0in p.6, the induced voltage between p.0 and p.12 1.0 (a) (b) 0.5 p.6 reaches approx. 250 V. Similar voltage distribution is observed between p.6 and p.12, in the case of 0.5 0 0 0 bonding 2length, 4 incross 10 highest the line-to earth in p.12. For both arrangements (both-ends and bonding), the 6 of 8 line-to-earth 12 Figure 10.2 Induced voltages as10a function of the cable linec-b case thec-b 6 0 4 sheath 8 12 c-b c-b valuefault of the voltage is around 4 kV (line-to-earth in p.3), what is clearly below the permissible value in the characteristic points (p.3, p.6, p.9 or p.12): (a) both-ends bonding;length (b) cross (km) bonding (c-b) length (km) (5 kV). in p.4 and p.8. (b) (a) 3.0 2.5 2.5 Thus, the additional earthing in p.6 eliminates in a simple way the problem of too high induced 2.0 2.0 sheath voltages in case of the short-circuit conditions. The 1.5 both-ends bonding, as well as the cross 1.5 p.6 1.0 p.12 0.5 0.5 0 p.12 p.6 1.0 0 0 2 4 6 length (km) (a) 8 10 12 0 2 c-b 4 c-b 6 8 c-b 10 c-b 12 length (km) (b) Figure 11. 11. Induced Induced sheath sheath voltages voltages as as aa function function of of the the cable cable line line length, length, in in case case of of the the line-to-earth line-to-earth Figure fault in in characteristic characteristic points points (p.3, (p.3, p.6, p.6, p.9 p.9 or or p.12); p.12); additional additional earthing earthing in in p.6: p.6: (a) (a) both-ends both-ends bonding; bonding; fault (b) cross cross bonding bonding (c-b) (c-b) in in p.2, p.2, p.4 p.4 as aswell wellas asin inp.8, p.8,p.10. p.10. (b) Thus, the additional earthing in p.6 eliminates in a simple way the problem of too high induced sheath voltages in case of the short-circuit conditions. The both-ends bonding, as well as the cross Appl. Sci. 2020, 10, 6706 11 of 16 Thus, the additional earthing in p.6 eliminates in a simple way the problem of too high induced sheath voltages in case of the short-circuit conditions. The both-ends bonding, as well as the cross bonding, can be employed (with additional earthing in p.6) but the latter is a more complicated solution. 4. Power Losses for the Analyzed Types of Bonding During the selection of the type of bonding, which is to be used in a high-voltage cable system, an analysis of the power losses in this system is recommended to be performed. In the total power losses in the cable system, additional losses produced in the cable sheaths should be included. Generally, power losses ∆P3sh generated in three cables’ sheaths and power losses ∆P3c generated in three cables’ conductors (cores) can be calculated according to the following expressions: 2 2 2 ∆P3sh = Rsh Ish−L1 + Ish−L2 + Ish−L3 (9) 2 2 2 ∆P3c = Rc IL1 + IL2 + IL3 (10) where: ∆P3sh represents the power losses in three cables’ sheaths; ∆P3c represents the power losses in three cables’ conductors (cores); Ish-L1 , Ish-L2 , Ish-L3 are the currents flowing through the sheath of the cable in phases L1, L2 and L3, respectively; IL1 , IL2 , IL3 are the currents flowing through the conductor (core) of the cable in phases L1, L2 and L3, respectively; Rsh is the resistance of the cable’s sheath; Rc is the resistance of the cable’s conductor (core). One of the main problems in the power losses calculation is to evaluate the real current distribution in each cable sheath (currents Ish-L1 , Ish-L2 , Ish-L3 ). It is relatively difficult to calculate analytically, especially when the arrangement of the cable line is varied or the cross bonding is applied. In this investigation, all the parameters have been calculated on the base of the data obtained from the PowerFactory software, taking into account the arrangement of the cables in every of 161 sections of the cable line. Power losses in the cables’ sheaths can be very high in the case of both-ends bonding. Relatively high circulating currents may give a significant heat flux generation across the sheath’s resistance, which increases the temperature of the cables. However, in the power cable line under consideration, the contracted transferred power is relatively low compared to the transmission capacity of the line, so the selection of the type of the bonding system, from the point of view of the power losses, is not obvious. The power losses have been evaluated with the use of the aforementioned computer model of the cable system. Figure 12a presents power losses in the cable sheaths (all three phases) for the contracted transferred power (10 MW, tgφ = 0.4) and the cable system arrangements, which are to be implemented in practice. The both-ends bonding gives, in fact, the highest value of the power losses, but it is only slightly higher than for the single-point bonding. Generally, for these two aforementioned types of bonding, the power losses are on the low and acceptable level. This is not a typical phenomenon. The almost equal power losses for these two arrangements are the effect of the natural capacitive power of the line. Since the consumer load (active power) in the cable line is at the low level, the natural power forces a reactive (capacitive) current circulation in the system, which gives observable losses. When the cross bonding is used, power losses in the copper sheaths are negligible, due to the compensation of the induced voltages in the consecutive minor sections. The comparison of all the analyzed types of losses (in cores, in sheaths, total; for 10 MW, tgφ = 0.4) is presented in Figure 12b. The total power losses (in copper sheaths + aluminium cores) are almost the same, both for the single-point bonding and both-ends bonding. They are within the range 15.4–15.8 kW, whereas for the cross bonding they are at the level of 13 kW. Power losses in the cores are the same for every type of bonding. Appl. Sci. 2020, 10, x 12 of 16 reactive/capacitive current coming from the natural power of the line is not the same along its whole 12 of 16 length—it is a normal phenomenon of the current flowing via capacitance-to-earth of the cables. Appl. Sci. 2020, 10, 6706 Losses (sheath) power losses (kW) 3.0 2.5 2.0 1.5 1.0 0.5 0 s-p in p.12 s-p in p.0 b-e c-b b-e +earthing in p.6 c-b +earthing in p.6 bonding type (a) Losses (core) Losses (sheath) Losses (total) 18.0 power losses (kW) 16.0 14.0 12.0 10.0 8.0 6.0 4.0 2.0 0 s-p in p.12 s-p in p.0 b-e c-b b-e +earthing in p.6 c-b +earthing in p.6 bonding type (b) Figure12. 12. Power Power losses losses in in the the analyzed analyzed three-phase three-phase cable cable system system for for the the transferred transferred power power 10 MW, MW, Figure tg φ = 0.4: (a) losses in the metallic sheaths; (b) comparison of the losses in the metallic sheaths, cores tgφ = 0.4: (a) losses in the metallic sheaths; (b) comparison of the losses in the metallic sheaths, cores and and losses; total losses; s-p: single-point bonding; b-e: both-ends bonding; c-b: cross bonding. total s-p: single-point bonding; b-e: both-ends bonding; c-b: cross bonding. The effect the transfers natural reactive power ofto the especially in Figure 13a when If the cableofline the power equal 80cable MW,line tgφ is = 0seen (Figure 13b), giving practically the the transferred power only 1current MW, tgφ = 0 (for theA), simplicity of the analysis, the is active max permissible loadis(load approx. 420 the value of the poweronly losses two power orders transfer is modelled). Theresults natural reactive power of thewas analyzed line the of the length 12 km is approx. higher, compared to the from Figure 13a. What expected, highest value of the power 6losses Mvarisand exceeds the In transferred (1 MW). In suchislow-load conditions forsignificantly the both-ends bonding. this case,active when power the transferred power many times higher (active load current in thepower, cable core is approx. A; reactive/capacitive current in the cable core is than the natural reactive the effect of the 5latter power is negligible. approx. A), the of single-point gives losses the highest total power losses. It should be noted The30analysis the resultsbonding of the power calculations shows that all types ofalso bonding are that the reactive/capacitive current coming fromtothe power of thethe linecross is notbonding the same gives along the its acceptable for the transferred power equal 10natural MW. Admittedly, whole length—it is a normal phenomenon of the current flowing via capacitance-to-earth of the cables. lowest losses but introduces the most complicated technical solution to the power line. If the cable line transfers the power equal to 80 MW, tgφ = 0 (Figure 13b), giving practically the max permissible load (load current approx. 420 A), the value of the power losses is two orders higher, compared to the results from Figure 13a. What was expected, the highest value of the power losses is for the both-ends bonding. In this case, when the transferred power is many times higher than the natural reactive power, the effect of the latter power is negligible. The analysis of the results of the power losses calculations shows that all types of bonding are acceptable for the transferred power equal to 10 MW. Admittedly, the cross bonding gives the lowest losses but introduces the most complicated technical solution to the power line. Appl. Sci. Sci.2020, 2020,10, 10,x6706 Appl. 13 of of 16 16 13 Losses (core) Losses (sheath) Losses (total) power losses (kW) 10.0 8.0 6.0 4.0 2.0 0 s-p in p.12 s-p in p.0 b-e c-b bonding type b-e +earthing in p.6 c-b +earthing in p.6 (a) Losses (core) power losses (kW) 1000 Losses (sheath) Losses (total) 800 600 400 200 0 147 2 2 s-p in p.12 s-p in p.0 147 <1 b-e bonding type c-b <1 b-e +earthing in p.6 c-b +earthing in p.6 (b) Figure Figure 13. 13. Power Power losses lossesin inthe theanalyzed analyzedthree-phase three-phasecable cablesystem: system:(a) (a)for forthe thetransferred transferredpower power11MW, MW, tg φ ==0;0; (b)(b) forfor thethe transferred power 80 MW, tgφ =tgφ 0; s-p: single-point bonding;bonding; b-e: both-ends bonding; tgφ transferred power 80 MW, = 0; s-p: single-point b-e: both-ends bonding; c-b: cross bonding. c-b: cross bonding. 5. Conclusions Conclusions 5. Most of of the the high-voltage high-voltage power power cable cable lines lines are are significantly significantly loaded loaded in in practice, practice, so so in in normal normal Most operating conditions the induced sheath voltages or power losses may be high. In order to exclude the operating conditions the induced sheath voltages or power losses may be high. In order to exclude risk of the electric shock and the negative effect of the power losses in the long cable lines, during such the risk of the electric shock and the negative effect of the power losses in the long cable lines, during load load conditions, crosscross bonding of theofcable sheaths is most oftenoften indicated as theasbest such conditions, bonding the cable sheaths is most indicated thesolution. best solution. However, if the cable line carries a relatively low load, as in the analyzed case, choice of However, if the cable line carries a relatively low load, as in the analyzed case, the the choice of the the best of the bonding system is not obvious. For the analyzedcable cableline, line,aacomparison comparisonof of the the best typetype of the bonding system is not obvious. For the analyzed possible bonding and earthing solutions is presented in Table 1. possible bonding and earthing solutions is presented in Table 1. Table 1. A summary of the properties of the bonding systems in the analyzed cable line. Table 1. A summary of the properties of the bonding systems in the analyzed cable line. Criterion Single-Point Bonding Both-Ends Bonding Cross Bonding Single-Point Cross Criterion Both-Ends Bonding Bonding Bonding Induced voltages in normal (0) (0) (0) 1 operating condition Induced voltages in normal operating 1 (0) (0) (0) Induced voltages in the case of (+) (+) condition (-) short circuit with earthing with earthing Inducedthe voltages in the case of the short (+) in p.6 (+) in p.6 (-) Power losses circuit with earthing in p.6 with earthing (0) (0) (+) in p.6 in the cable system Power losses Simplicity of the solution and (+) (0) (0) (+) (+) (0) in the aspects cable system economic (0) with ECC Simplicity of the solution and economic (+) 1 Markings: (+) preferred solution; (0) acceptable solution; (-) (+) (0) excluded solution. aspects (0) with ECC 1 Markings: (+) preferred solution; (0) acceptable solution; (-) excluded solution. Appl. Sci. 2020, 10, 6706 14 of 16 When the risk of electric shock in normal operating conditions is considered, the values of the induced sheath voltages are acceptable in every case—for single point-bonding the highest value is below the permissible 80 V and for both-ends bonding or cross bonding the voltages are close to 0 V. In case of the line-to-earth fault, the single point-bonding is excluded in this cable line, due to very high induced voltages. For the system without ECC, the voltage reaches 22 kV. When the ECC is installed, it decreases only to 12 kV. In the light of the assumed permissible level being equal to 5 kV, these high-value voltages are dangerous for the outer non-metallic sheath of the cable. It should also be noted that, due to the induced voltages in the case of the earth fault, the both-ends bonding, as well as the cross bonding, requires an additional earthing in the middle of the power cable length (point p.6). Without this additional earthing, the voltages may exceed 7 kV but with the earthing, they are reduced to approx. 4 kV. A comparison of the power losses shows that the best solution is the cross bonding but two other solutions are acceptable as well—the total losses in the cable system are within the range 15.4–15.8 kW for the single-point bonding and both-ends bonding, whereas for the cross bonding they are equal to 13 kW. Such low and comparable power losses are the effect of the relatively low transferred power (10 MW). Considering the economic aspect and simplicity of the solution, the single-point bonding without ECC (no additional parallel cable is installed) or both-ends bonding (no equipment for transpositions of the sheaths is required) are recommended. Taking into account all the aforementioned aspects, the both-end bonding or cross bonding can be used in the analyzed cable line. For each of the two solutions, the additional earthing in p.6 is required. To achieve safe operation of relatively long high-voltage cable lines, which are loaded in a low percentage, special attention must be given to the study of short-circuit currents. The induced sheath voltages coming from high-value currents can give unacceptably high-voltage stress, not only in the case of single-point bonding, but also in the case of both-ends bonding. In the latter case, this stress applies to points located close to the centre of the cable section between the earthing arrangements. In such a cable system, shorter distances between the earthing arrangements should be used. Author Contributions: Conceptualization, S.C.; software, K.D.; validation, S.C. and K.D.; formal analysis, S.C.; investigation, S.C. and K.D.; resources, S.C.; writing—original draft preparation, S.C. and K.D.; writing—review and editing, S.C.; supervision, S.C. All authors have read and agreed to the published version of the manuscript. 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