Zero-Sequence Current in Cable Systems: A Study Zero-Sequence Current in Cable Systems: A Study

Large zero-sequence current is not a new phenomenon for cable bus duct systems; the question is what in ﬂ uences its magnitude. It was found that the zero-sequence currents were circulating between different circuits in the cable system and that they were being generated by induction between phases in the same cable route. It was determined that the zero-sequence currents could be greatly reduced in a twin circuit by a symmetrical con ﬁ guration of the cables. However, in a four-circuit system, no signi ﬁ cant reduction could be achieved even by the symmetrical con ﬁ guration. Therefore, in this paper, this phenomenon will be analyzed and discussed. ATPDraw is used to simulate and analysis this kind of study. Also, the effect of sheath cross-bonding is explained and analyzed. It is found that the currents are changed dramatically according to the arrangement of each cable. When reducing zero-sequence currents, various layouts are examined in light of their underlying physical causes. Also, It is determined that the zero-sequence current is hardly affected by any unbalanced crossbondig


Introduction
W ith the power consumption in cities increasing continuously, the capacities of single-core cables need to be extended. At present, two schemes were widely used: one was to directly replace the previous cables with larger-capacity cables; another was to added cables in the same phase to put into operation in parallel. As the replacement scheme needed longer outage time and greater investment, the parallel scheme was always seen as the optimum scheme in practice. However, after been applied, the current distribution in parallel single-core cables was not even as expected. This phenomenon may cause the overheating problem in parts of the cables. It had been estimated that an increase of 8 Ce10 C in insulation temperature was lead to a 50% reduction of insulation life expectancy (Petty, 1988;Li et al., 2015).
High-power DC rectifier/converter design is a key focus of electrochemical applications. Due to the high current magnitudes involved, additional cable geometry considerations are made to achieve the necessary current balance in parallel rectifier cells (Bernadelli et al., 1997). The majority of industrial rectifiers employ l2-pulse converters, which phase shift one converter with regard to the other by 30 (Tambe and Frisch, 2004).
Despite the high-current secondary windings not being grounded, depending on the input cable geometry and the converter's operational characteristics, a zero-sequence ground current (I ZS ) may flow (Skibinski et al., 2006). In industrial and commercial power distribution networks, underground cables are increasingly used for power transmission. In many cases, one substation will send out two or more transmission lines, and one line may include double circuits. Therefore, in some cases, cables from two or more circuits are put in ducts side by side along the same route for several kilometres. When numerous circuits are built on one tower, it is also known that each circuit of overhead transmission cables is saturated with I ZS . The zero-sequence currents are an issue because they can occasionally make safety relays malfunction. However, it has not been well understood that systems with many cables deployed along the same path generate I ZS . Depending on the cable configuration, such as that of an untransposed overhead line, the impedance imbalance between the phases cannot be ignored (Nakanishi et al., 1991).
On a single-core cable, the impacts of earthing, cross-bonding, and transposition procedures are investigated, along with the number of joint sites. It was found that the produced voltages and currents were related to cable length and that, in addition to neutralizing the cable ends, cross-bonding and transposition processes were the only ways to lower them Kaloudas et al., 2011;Shokry et al., 2019;Ledari and Mirzaie, 2020;Salem et al., 2022).
In this paper, a cable system was recently found, where a very large amount of I ZS flows. For this study in a test power system, the Alternative Transients Program (ATP) analyses the I ZS . Typical twoand four-circuit cable systems are examined to show that large I ZS are induced in the cable systems. It is shown that the currents are changed dramatically according to the arrangement of each cable. In light of their physical sources, several arrangements are tested to lower I ZS . Also highlighted are certain issues with zero-sequence circulating current cabling. Therefore, the paper organization is give as follows. An introduction to the problem is given in section 1. The test system description and simulation is explained in section 2, and in section 3 the system is analyzed in fault and abnormal operating conditions. Then, induced zero-sequence currents are simulated and modeled in section 4. In section 5, the effect of sheath cross-bonding is discussed.
Finally, the conclusions and future work are given in section 6.

Test system description and simulation
The test system is picked from reference (Nakanishi et al., 1991). Fig. 1 illustrates the configuration of the test system. The main substation S is linked to a 154 kV line. Transformers lower the voltage to 77 kV, and the power is distributed to substations SA, SB, and S1 to S4 via cables and overhead lines. Transformers at each substation further lower the incoming 77 kVe6.6 kV, which is subsequently supplied to customers via distribution lines.

Transformers description
A computation that takes into account the impact of the earth return current and transformer inductance includes the transformer in the main substation. The transformer is connected starestar, and its neutral point is grounded by connecting a 200 U resistor in parallel to a series circuit made up of 260 mH inductors and a 15 U resistor. For distribution in the substations at the load side, the voltage is reduced to 6.6 kV. Although a resistor grounds the main substation transformer's neutral point when using a staredelta connection, the neutrals of the transformers S1eS4 are not earthed (Nakanishi et al., 1991).   Table 2. Every section of routes A and B has two cables, and each section of a PI equivalent circuit with 24 conductors simulates the changing cable configurations and sheath terminating conditions. Table 3 shows the lines parameters (Cable, 2009;'Indian Standard for Hard, 1982). A PI equivalent circuit's single section is used to represent the lines. The placement of the overhead lines along routes A and B is depicted in Table 4.

Load description
During the calculation, star connection load resistance is simulated. Not earthed is the load neutral. The measured load flow via each circuit of examples (a) to (d) led to the calculation of the load resistance linked to each circuit, which is given in Table 5 (Nakanishi et al., 1991).

Test system simulation by ATPDraw
ATP is used to analyze the current distribution in the system with several scenarios of the fault and abnormal operating conditions (Rifaldi and Lastra, 2001). The test system is simulated using ATPDraw as shown in Fig. 2.
An AC (type 14) three-phase, the voltage source is selected for source simulation. The Hybrid three-   phase transformer model is used for transformer simulation. Also, the three-phase time-controlled switch is used for switch simulation. The three-phase single-core cables are modeled using LCC (line cable constant) model as shown in Fig. 3. The number of phases is 6 to simulate sheath circuits, (1, 2, 3) number of cable phases and (4, 5, 6) number of sheath circuits. Also, the three-phase overhead lines are modeled using LCC model of PI equivalent circuit.
A PI equivalent circuit's single section with 24 conductors is used to simulate each section of the route A and B cables when the cable arrangement and sheath terminating condition change. A PI equivalent circuit's single section is used to simulate the overhead lines as well. The load RLC-Y, three-phase is used for load simulation.

Analysis of the test system for fault and abnormal operating conditions
Power flow through each circuit is calculated via the following scenarios of the system; case (a) to (d).
In case (a), there are two circuits connected. Bus 2 is connected with route A. While route B are separated from the bus and the cable separated from the line. Fig. 4a and b illustrate the output current waveform in route A. It is shown that the current is about 260 A through cable (L1) and about 330 A through cable (L2). Fig. 4c illustrates the output current waveform in route B. It is shown that the current is 0 A through cables (L3&L4).
In case (b) three circuits are connected. Route A is connected to Bus 2. While (L3) is connected to Bus 1 and (L4) is separated from the bus. Also, the cable separated from the line, and the remote end is separated from SB. Fig. 5a and b illustrate the output current waveform in route A. It is shown that the current is 250 A through cable (L1) and 350 A through cable (L2). Fig. 5c and d illustrate the output current waveform in route B. It is shown that the current is 400 A through cable (L3) and 0 A through cable (L4).
In case (c) three circuits are connected. Route A is connected to Bus 2. While (L3) is separated from the    bus also, the cable separated from the line, and (L4) is connected to Bus 1. Farther end of the overhead line separated from SB. Fig. 6a and b illustrate the output current waveform in route A. It is shown that the current is 250 A through cable (L1), and 350 A through cable (L2). Fig. 6c and d illustrate the output current waveform in route B. It is shown that the current is 0 A through cable (L3) and 430 A through cable (L4).
In case (d) four circuits are connected. Bus 2 is linked to Route A (L1, L2). Bus 1 is also connected to route B (L3, L4), but SB is separated from the receiver end of the overhead transmission line. Fig. 7a and b illustrate the output current waveform in route A. It is shown that the current is 250 A through cable (L1), and 350 A through cable (L2). Fig. 7c and d illustrate the output current waveform in route B. It is shown that the current is 230 A through cable (L3) and 200 A through cable (L4).
It is found that the results confirm the model validity by comparing with (Nakanishi et al., 1991).
The above observations indicate that the ATP-Draw simulation provides great accuracy in comparison to the measured data, despite using PI equivalence for the simulation's cables to be represented. Therefore, it may be sufficient to analyze the I ZS using the ATPDraw with PI equivalent model of the cables. Table 6 shows the measured results of I ZS for cases (a) to (d). A large I ZS of 40e80 A was observed on route A (Nakanishi et al., 1991).
The following conclusions are drawn about I ZS based on the data in Table 6 Case (a) only has two    circuits, route A (L1, L2). Here, an I ZS is generated between L1 and L2, with the currents having the same amplitude but an opposite direction. The loop circuit of the main source, S, L1, SA, L2, and then back to the main source, S, is shown to be circulating the I ZS . Cases (b) and (c) are systems that have three circuits of route A (L1 and L2), and route B (L3 or L4). L3 and L4 of route B do not carry any I ZS . The neutrals of the transformers S1 to S4 are not earthed, however, the neutral of the main S transformer is through a resistor. As a result, it is impossible to complete the loop circuit using the earth as the return path, and no I ZS is produced in one circuit. A multi-circuit system's I ZS is observed to be the vector sum of the I ZS in both its own circuit and those induced by the other circuit (Nakanishi et al., 1991).

Calculation of I ZS in ATPDraw
The information in this section is a summary of research on parallel-two and parallel-four circuits that create I ZS . After that, this knowledge is expanded upon to explain the I ZS in a parallel six   Table 7 shows this cable parameters (Nexans, 2009). While taking conductor and sheath into account, each minor section is represented by a PI equivalent circuit's single section. Both of the cable's sheaths are grounded by a 10 U resistor and are short circuited at both ends. The load is represented by 44.5 U, three-phase, and star-connections. The load is balanced, star-connection resistor. The neutral point of the load is not earthed.
An extraction of the fundamental I ZS can be performed according to equations (1)e(3) (Badran and Abdel-rahman, 2010 Fig. 11. System model in ATPDraw for four circuits. Where i a , i b , and i c are the measured phase currents for phase A, B, and C, respectively. Also, i ap , i bp , and i cp are three-phase positive sequence components; i an , i bn and i cn are three-phase negative sequence components, and i a0 , i b0 , and i c0 are three-phase zerosequence components for the three-phases, respectively. The ATPDraw model of the current's calculations given in equations (1)e(3) is illustrated in Fig. 8.

Analysis of I ZS in a twin-circuit
In a nine-duct configuration test system with twin parallel circuits, the change of cable arrangements is discussed (Nakanishi et al., 1991). The test system is model using ATPDraw as shown in Fig. 9. Zerosequence current is the vector sum of the I ZS in its own circuit and the currents generated by the other parallel circuits in zero-sequence. Different cable configurations in the model system of Fig. 9, twin circuits in parallel in a nine duct layout, are given as shown in Table 8 (case 1 to case 11) as follow: (1) Low Reactance Phasing (LR Phasing) is a type of phasing arrangement where cases (1) and (2) are inversely arranged, and case 1 is an arrangement where there is no conduit between L1 and L2.
(2) Super-Bundle Phasing (SB Phasing) is used to describe Cases (3) and (4), and Case (3) is the arrangement where the conduit line between L1 and L2 is left empty of Cases (4). (3) Case 5 and 6 are defined as triangular arrangement of L1 and L2 and point symmetrical to the center of 6 cables. (4) In case (7), a diagonal-shaped empty conduit line is formed by the arrangement of L1 and L2, which are triangularly arranged and axially symmetrical to it. (5) Cases (8) to (10) are the asymmetrical arrangements of the cables between circuits L1 and L2. (6) In cases 10 and 11, an underground cable that is directly buried and axially symmetrical is assumed. Fig. 10 shows the results of I ZS flows at cable L1 and L2 in cases (1) to (11). Table 9 gives the I ZS in all cases. It is noted from Table 9 that low I ZS flows with symmetrical arrangements (1) to (7) and (11). However, for the asymmetrical arrangements (8) to (10), I ZS of 144e178 A flow for the same load currents. Math analysis of the parallel two-circuit cases proves the required condition to insure no I ZS is to have all mutual impedance's between conductors balanced (Nakanishi et al., 1991). Proper conductor phasing arrangements can accomplish this. A zero I ZS condition corresponds to point or axial symmetry of the six-conductors in the two parallel circuits and indicates an asymmetrical arrangement of cable is the cause of I ZS generation. That is to say, the mutual impedance unbalance generates the I ZS in the twin circuit.

Analysis of I ZS in a four-circuit system
The test system is represented using ATPDraw as illustrated in Fig. 11 in order to investigate I ZS in a four-circuit system. In the system, a loop is formed by circuits L1 and L2 on route A and L3 and L4 on route B, respectively. Routes A and B are shortcircuited at the opposite end for each phase. Table 10 gives the various cable arrangements of twelve phases (case 1 to case 5) in a model system of Fig. 11; four circuits in parallel as follows: (1) Super-Bundle Phasing (SB Phasing) arrangements are used in Cases (1) and (5), but route B is arranged in opposition to route A.   Table 11 gives the I ZS in all cases. As can be seen from Table 11, unlike in the cases of two circuit systems, the I ZS does not decrease to almost zero even with SB phasing or LR phasing design. At least 20 A of I ZS must flow in addition to the conductor current of 500 A. With a triangular configuration, I ZS can move at a maximum rate of 83 A. Zero-sequence currents vary with conductor phasing arrangement. The results show I ZS generated due to unbalanced mutual coupling between the four parallel circuits. Four parallel circuits are unlike parallel two-circuit arrangements; I ZS cannot be reduced to zero in parallel four-circuits, even with point or axial symmetry conductor configurations. The results show a minimum (I ZS / I load ) ratio of 4% can be expected. Conductor transposition is required to reduce I ZS in a four-circuit cable duct system.

Effect of sheath cross bonding
The arrangements of Case (4), which has no I ZS flowing, and Case (8), which has the maximum zerosequence current flowing, are taken from Table 9 in order to analyse the effect of sheath cross bonding over I ZS in twin-circuit systems. Additionally, calculations were done for two scenarios: balanced cross-bonding (each minor section was 250 m long) and unbalanced cross-bonding (length of minor section at 300 m-250 me200 m). This section   analyses and discusses the findings of a study on how sheath cross-bonding affects I ZS in twin-circuit systems.
In case of balanced cross-bonding; Fig. 13a shows the result of the I ZS flows at cables L1 and L2 in case (4) and Fig. 13b shows the result of the I ZS flows at the sheath. Also, Fig. 14a shows the result of the I ZS flows at cables L1 and L2 in case (8) and Fig. 14b shows the result of the I ZS flows at the sheath.
In case of unbalanced crossbonding, Fig. 15a shows the result of the I ZS flows at cables L1 and L2 in case (4) and Fig. 15b shows the result of the I ZS flows at the sheath. Also, Fig. 16a shows the result of the I ZS flows at cables L1 and L2 in case (8) and Fig. 16b shows the result of the I ZS flows at the sheath.
The calculated results for I ZS in twin-circuit systems for different cable configurations are shown in Table 12. The table shows that, assuming balanced cross bonding is used, the sheath current at the arrangement of case (8) of big I ZS is approximately ten times greater than that by configuration of case (4) of no I ZS . However, the I ZS in the circuit of unbalanced cross-bonding is not affected by the cable arrangement. However, in the design of case (8) where the I ZS is considerable, the sheath circulation current between circuits is practically constant, at roughly 24 A, and irrespective of the imbalance ratio. While no sheath current circulates in the configuration of case (4).

Conclusions
By using ATPDraw analysis, an I ZS produced in cable networks is investigated. It is obvious from the estimated findings that cable networks' unusually big I ZS generation is caused by an unbalanced mutual coupling of two circuits. In order to decrease the mutual coupling unbalance, which in turn reduces the I ZS , cable layouts are studied. The best cable configuration is determined to be effective in reducing the I ZS . The conclusions are as follows: (1) In a twin-circuit system, a I ZS circulates between two circuits of cables and is lowered to almost zero with a symmetrical phase configuration.
(2) In a four-circuit system, unlike a twin-circuit system, even with symmetrical phase arrangement, the I ZS cannot be lowered to zero. (3) The I ZS is not significantly affected by any unbalanced crossbonding.

Authors contribution
Shimaa A. F. Salem: data curation, resources, writing-original draft preparation; Rabab R. M. Eiada: conceptualization, investigation; Ebrahim A. Badran: review and editing the manuscript. All authors have read and agreed to the published version of the manuscript.

Conflicts of interest
The author declared that there are no potential conflicts of interest with respect to the research authorship or publication of this article.