Accurate Evaluation of Steady-State Sheath Voltage and Current in HVDC Cable Using Electromagnetic Transient Simulation

: The current and voltage in High Voltage DC (HVDC) line is not pure DC but contain superimposed ripple components. The current ripple in core of HVDC cable magnetically induces a voltage in the sheath, whereas the voltage ripple causes the ﬂow of charging current from core to sheath. The knowledge of sheath voltage is necessary to ensure compliance with the speciﬁcation of utility companies. In this work, we have reported that the models available in commercial Electromagnetic Transient (EMT) simulation software erroneously introduce a DC bias in steady-state sheath voltage and sheath current. We have also demonstrated that by removing the DC bias accurate steady-state evaluation of sheath voltage and sheath current is possible. Additionally, we have analyzed the sheath voltage and currents in HVDC cable considering di ﬀ erent cable lengths and sheath grounding schemes. It has been found that grounding the sheath at the terminal of HVDC cable can limit the sheath voltage to acceptable levels without causing substantial joule loss in the sheath.


Introduction
As of today, over one hundred and fifty HVDC transmission projects are in operation or under construction worldwide. Amongst them more than eighty-five projects have transmission lines partly or entirely based on underground or submarine cables. The earlier HVDC cable technologies, i.e., self-contained oil filled (SCOF), high-pressure oil filled (HPOF) and gas filled (GF) have low service temperature, limited installation length and complex manufacturing process [1,2]. However, gradual improvements have allowed cross linked polyethylene (XLPE) cables to be satisfactory for operation in HVDC projects where polarity reversal can be avoided [3][4][5]. Owing to their higher allowable conductor temperature, more compact cables can be used for same power rating. Due to these breakthrough improvements in DC insulation technologies, the use of longer HVDC cables is expected to grow substantially [6].
The underground HVDC cable is composed of a central power conductor, surrounded by a layer of insulator, metallic sheath and outer polyethylene (PE) jacket. Purpose of metallic sheath is to mechanically strengthen the cable while at the same time confine the electric field entirely within the insulation. Outer jacket safeguards the sheath from corrosion due to galvanic and electrolytic action and provides a barrier against moisture ingress [7].
A twelve-pulse Line Commutated Converter (LCC) HVDC system converts three-phase AC to a pulsating DC with high magnitude voltage ripples. The resulting current flow in the DC line also contains ripples. However, the magnitude of the current ripples is much lower than the voltage ripples due to the presence of large reactors on DC side of converters [8]. The flow of current ripples in the core conductor of DC cable magnetically induces voltage whereas the voltage ripple causes flow of charging currents from core to sheath. The utility companies specify the maximum limit of sheath voltage to ensure safe operation of cable and prevent operating personnel from shock hazard. Moreover, the circulating current flow in sheath causes joule heating. The knowledge of joule heating is important for accurately calculating the ampacity of cable [9].
Several analytical formulations have been recommended in literature to estimate the sheath voltage and currents in AC cable systems for most common bonding and grounding schemes [10], [11]. For asymmetrical and unusual circuits and bonding configurations Finite Element Method (FEM), Electromagnetic Transient (EMT) and Complex Impedance Matrix (CIM) based calculation techniques have been shown to calculate the sheath voltage and currents accurately [12][13][14][15][16][17]. However, for DC cables no analytical or numerical simulation-based solution has been presented in literature so far. A frequency dependent (phase) model implementation of cable in PSCAD based on Universal Line Model (ULM) can take into account the inductive and capacitive coupling between sheath and core conductor for a very wide range of frequencies. However, it is well known that rational function approximations of admittance and propagation matrices are imprecise at frequencies close to DC. To overcome this problem, [18] has proposed to modify the functional form of rational function by specifying a known DC value or by adding a low order pole. Both methods have been demonstrated to reduce the error significantly. The DC correction of frequency dependent line models continues to be a topic of interest with aim to improve the precision of DC response [19,20].
The allowable sheath voltage is decided by the utility companies to prevent jacket from overvoltage stress and limit the shock hazard for personnel who may come in contact with any exposed conducting parts such as sheath interrupts, bonding leads and grounding leads. The sheath bonding and grounding is applied to maintain the sheath voltage within an allowable limit. Several bonding and grounding schemes have been applied to suppress the sheath voltage in AC cables. Cross bonding is one of the most efficient bonding schemes for three phase AC cables. In this technique the sheath is sectionalized into minor section and cross connected in such a way that net induced voltage in three consecutive sections is neutralized. It has been successfully applied in three phase AC cables to suppress circulating currents in the sheaths [11,[21][22][23]. In DC cables, sheath grounding at terminals is applied to suppress the sheath voltage in [7,[24][25][26]. However, the steady state sheath voltage and losses have not been discussed by any of these papers. The need for investigating steady state sheath voltage and losses in DC cable considering various sheath grounding schemes has been emphasized in [1,26,27].
In this work, we have reported that even after application of DC correction procedure of [18], the error in calculated values of sheath voltage and circulating currents in HVDC cables is substantial. A procedure for removing the error has been proposed. It has been demonstrated that after applying the proposed procedure exact values of sheath voltage and circulating currents can be obtained. Using this approach, we have evaluated the sheath voltage and circulating currents in cable considering several sheath grounding schemes.
The sheath grounding schemes along with power system model used for this study are described in detail in Section 2. The simulation setup and evaluation method has been explained in 3. The detailed analysis of electromagnetic transient (EMT) model has been presented in Section 4, where limitations of the existing DC correction procedure along with proposed accurate evaluation procedure has been demonstrated. Sheath voltage, circulating current and losses considering different sheath grounding schemes and variable cable lengths have been presented in Section 5. The discussion on results has been presented in Section 6. Finally, in Section 7 we have presented the conclusion of this study.

System Description
A 500-kV monopolar LCC HVDC transmission system with a rated power of 1000 MW based on the CIGRE benchmark model (CBM) is used in this study [28]. The lumped parameter line used

HVDC Converter Model
The AC sources, LCC HVDC system and its controls are modelled in detail. The AC supply network with nominal frequency of 50 Hz is composed of Thevenin equivalent voltage sources, with equivalent source impedance. AC filters are present to absorb the harmonics generated by converters and supply the reactive power required by the HVDC system.
LCC HVDC system consists of 12-pulse converters on rectifier and inverter side. Each 12-pulse converter is comprised of two serially connected 6-pulse converters. The damping angles of AC network, converter configuration and controls are based on first CIGRE benchmark model [28].

Cable Model
The 500 kV, 2000 mm 2 single core cable with layout shown in Figure 2a is based on [25]. The structure, dimensions and electrical parameters of cable used in PSCAD model are shown in Figure  2b. A frequency dependent (phase) model of PSCAD is used to model the cable. This model can account for capacitive and inductive coupling caused by a ripple current composed of range of high frequency harmonic components. However, the rational function approximations of admittance and propagation matrices used by this model are not accurate at frequencies close to DC. This results in a large DC error in the calculations [20,30]. In this work a DC correction procedure [18] available in PSCAD is enabled. This procedure corrects the DC response of the line by factoring out the theoretical DC response of the propagation and admittance matrices and replacing it with known DC response. The resultant corrected line model improves the accuracy in calculation of voltage and current in the core as well as sheath of HVDC cable.

HVDC Converter Model
The AC sources, LCC HVDC system and its controls are modelled in detail. The AC supply network with nominal frequency of 50 Hz is composed of Thevenin equivalent voltage sources, with equivalent source impedance. AC filters are present to absorb the harmonics generated by converters and supply the reactive power required by the HVDC system.
LCC HVDC system consists of 12-pulse converters on rectifier and inverter side. Each 12-pulse converter is comprised of two serially connected 6-pulse converters. The damping angles of AC network, converter configuration and controls are based on first CIGRE benchmark model [28].

Cable Model
The 500 kV, 2000 mm 2 single core cable with layout shown in Figure 2a is based on [25]. The structure, dimensions and electrical parameters of cable used in PSCAD model are shown in Figure 2b. A frequency dependent (phase) model of PSCAD is used to model the cable. This model can account for capacitive and inductive coupling caused by a ripple current composed of range of high frequency harmonic components. However, the rational function approximations of admittance and propagation matrices used by this model are not accurate at frequencies close to DC. This results in a large DC error in the calculations [20,30]. In this work a DC correction procedure [18] available in PSCAD is enabled. This procedure corrects the DC response of the line by factoring out the theoretical DC response of the propagation and admittance matrices and replacing it with known DC response. The resultant corrected line model improves the accuracy in calculation of voltage and current in the core as well as sheath of HVDC cable.

HVDC Converter Model
The AC sources, LCC HVDC system and its controls are modelled in detail. The AC supply network with nominal frequency of 50 Hz is composed of Thevenin equivalent voltage sources, with equivalent source impedance. AC filters are present to absorb the harmonics generated by converters and supply the reactive power required by the HVDC system.
LCC HVDC system consists of 12-pulse converters on rectifier and inverter side. Each 12-pulse converter is comprised of two serially connected 6-pulse converters. The damping angles of AC network, converter configuration and controls are based on first CIGRE benchmark model [28].

Cable Model
The 500 kV, 2000 mm 2 single core cable with layout shown in Figure 2a is based on [25]. The structure, dimensions and electrical parameters of cable used in PSCAD model are shown in Figure  2b. A frequency dependent (phase) model of PSCAD is used to model the cable. This model can account for capacitive and inductive coupling caused by a ripple current composed of range of high frequency harmonic components. However, the rational function approximations of admittance and propagation matrices used by this model are not accurate at frequencies close to DC. This results in a large DC error in the calculations [20,30]. In this work a DC correction procedure [18] available in PSCAD is enabled. This procedure corrects the DC response of the line by factoring out the theoretical DC response of the propagation and admittance matrices and replacing it with known DC response. The resultant corrected line model improves the accuracy in calculation of voltage and current in the core as well as sheath of HVDC cable.  The rational functions of admittance and propagation matrices for non-DC components are derived in the range of 0.5 Hz to 5 kHz with the fitting accuracy of 0.2% using PSCAD Line Constant Program.

Sheath Grounding Schemes
Following outcomes are desired from sheath grounding of HVDC cable.

•
Minimize the sheath voltage.

•
Minimize the circulating currents in sheath.

•
Minimize the sheath loss.
The following sheath grounding schemes have been evaluated in this work.

Terminal Grounding (TG)/ Multipoint Grounding (MPG)
In a TG scheme the sheath of cable is directly grounded at the terminals via sheath grounding electrodes as shown in Figure 3a. In an MPG scheme, the cable is divided into several segment of equal length. The sheath is grounded via grounding electrodes at terminals of each segment as shown in Figure 3b.
In both cases the sheath is continuous along the length of cable. The rational functions of admittance and propagation matrices for non-DC components are derived in the range of 0.5 Hz to 5 kHz with the fitting accuracy of 0.2% using PSCAD Line Constant Program.

Sheath Grounding Schemes
Following outcomes are desired from sheath grounding of HVDC cable.
• Minimize the sheath voltage.
• Minimize the circulating currents in sheath.
• Minimize the sheath loss.
The following sheath grounding schemes have been evaluated in this work.

Terminal Grounding (TG)/ Multipoint Grounding (MPG)
In a TG scheme the sheath of cable is directly grounded at the terminals via sheath grounding electrodes as shown in Figure 3a. In an MPG scheme, the cable is divided into several segment of equal length. The sheath is grounded via grounding electrodes at terminals of each segment as shown in Figure 3b.
In both cases the sheath is continuous along the length of cable.

Single Point Grounding (SPG)/ Multiple Single Point Grounding (MSPG)
In an SPG scheme, the sheath of cable is grounded at the sending end terminal via a ground electrode, whereas the receiving end terminal is grounded via a sheath voltage limiter (SVL). The HVDC cable with SPG scheme is shown in Figure 4a. MSPG scheme is a variation of SPG scheme. In multiple SPG scheme the sheath of the cable is divided into several equal segments. Sheath is then interrupted at each segment. One end of each

Single Point Grounding (SPG)/ Multiple Single Point Grounding (MSPG)
In an SPG scheme, the sheath of cable is grounded at the sending end terminal via a ground electrode, whereas the receiving end terminal is grounded via a sheath voltage limiter (SVL). The HVDC cable with SPG scheme is shown in Figure 4a. The rational functions of admittance and propagation matrices for non-DC components are derived in the range of 0.5 Hz to 5 kHz with the fitting accuracy of 0.2% using PSCAD Line Constant Program.

Sheath Grounding Schemes
Following outcomes are desired from sheath grounding of HVDC cable.
• Minimize the sheath voltage.
• Minimize the circulating currents in sheath.
• Minimize the sheath loss.
The following sheath grounding schemes have been evaluated in this work.

Terminal Grounding (TG)/ Multipoint Grounding (MPG)
In a TG scheme the sheath of cable is directly grounded at the terminals via sheath grounding electrodes as shown in Figure 3a. In an MPG scheme, the cable is divided into several segment of equal length. The sheath is grounded via grounding electrodes at terminals of each segment as shown in Figure 3b.
In both cases the sheath is continuous along the length of cable.

Single Point Grounding (SPG)/ Multiple Single Point Grounding (MSPG)
In an SPG scheme, the sheath of cable is grounded at the sending end terminal via a ground electrode, whereas the receiving end terminal is grounded via a sheath voltage limiter (SVL). The HVDC cable with SPG scheme is shown in Figure 4a. MSPG scheme is a variation of SPG scheme. In multiple SPG scheme the sheath of the cable is divided into several equal segments. Sheath is then interrupted at each segment. One end of each MSPG scheme is a variation of SPG scheme. In multiple SPG scheme the sheath of the cable is divided into several equal segments. Sheath is then interrupted at each segment. One end of each segment is directly grounded via a grounding electrode whereas the opposite end is grounded via an SVL. The HVDC cable with MSPG scheme is shown in Figure 4b.

Simulation Setup & Evaluation Method
The detailed EMT model of converters and cable is implemented in graphical environment of PSCAD (X4, Version 4.6.2). In PSCAD, current and voltage of cable can be evaluated at its terminals only. To evaluate the values of sheath voltage and circulating currents along the length, the cable must be divided into several sections.
In this work we have evaluated sheath voltage and losses in cable considering four different lengths i.e., 10, 20, 40 and 80 km. The cable is divided into 40 equal sections regardless of the overall length. The length of a section in each case along with the simulation time steps are listed in Table 1. The simulation time step is chosen in such a way that it is 1/10th of the travel time of one section [31].
The sheath voltage and circulating current reaches its steady state well before 5 s. However, the duration of simulation run is set as 10 s to ensure accurate steady state results.
The instantaneous values of voltage and current in the sheath are evaluated at the terminals of each section as shown in Figure 5. The instantaneous values are converted to rms values using (1) & (2). segment is directly grounded via a grounding electrode whereas the opposite end is grounded via an SVL. The HVDC cable with MSPG scheme is shown in Figure 4b.

Simulation Setup & Evaluation Method
The detailed EMT model of converters and cable is implemented in graphical environment of PSCAD (X4, Version 4.6.2). In PSCAD, current and voltage of cable can be evaluated at its terminals only. To evaluate the values of sheath voltage and circulating currents along the length, the cable must be divided into several sections.
In this work we have evaluated sheath voltage and losses in cable considering four different lengths i.e., 10, 20, 40 and 80 km. The cable is divided into 40 equal sections regardless of the overall length. The length of a section in each case along with the simulation time steps are listed in Table 1. The simulation time step is chosen in such a way that it is 1/10th of the travel time of one section [31].
The sheath voltage and circulating current reaches its steady state well before 5 s. However, the duration of simulation run is set as 10 s to ensure accurate steady state results.
The instantaneous values of voltage and current in the sheath are evaluated at the terminals of each section as shown in Figure 5. The instantaneous values are converted to rms values using (1) & (2).
The joule loss in the sheath will be evaluated using (3).

Analysis of Electromagnetic Transient (EMT) Model: Limitations and Proposed Solution
Before proceeding with the analysis of steady state sheath voltage and currents, we will verify the interaction of converters and cable, analyze the sources of sheath voltage and currents in steady state and the accuracy of proposed model for analysis of steady state sheath voltage and currents.

Ripple Current & Voltage Analysis
The flow of current ripples in the core conductor of DC cable magnetically induces voltage (4) in the sheath whereas the voltage ripple causes flow of charging currents (5) from core to sheath. where, i ripple : ripple current in core conductor V ripple : ripple voltage in DC line i c : charging current.
The currents and voltage ripples on DC side are composed of harmonic components that are predominantly multiple of 12th harmonic component i.e., at the frequency 12, 24, 36 and 48 times of the nominal AC side frequency i.e., 50 Hz in CBM [8].
The magnitude and phase of ripple components depends on the cable characteristics i.e., its length, dimensions and layout. The ripple current and voltage at the sending end of the cable, according to the length of cable section is shown in Figure 6. Figure 6a shows the current ripple in time domain and its frequency spectrum. Figure 6b shows the voltage ripple in time domain and its frequency spectrum. It should be noted that not only the magnitude, but the relative phase angle of harmonic components at the sending end also changes with the changing length of the cable.

Limitations of ULM in Evaluation of Steady State Sheath Voltage and Currents
The sheath voltage of a ULM with and without DC correction procedure of [18] are compared to verify the efficacy of correction procedure.
A system of 10 km cable with TG sheath as shown in Figure 7a is developed in PSCAD. A unit step voltage is applied at the sending end whereas the receiving end is grounded with the resistance of 1 ohm. The sheath voltage is evaluated at the receiving end. A current inrush occurs upon the application of unit step voltage at 1 s, which soon reaches its steady state value. At the same instant i.e., at 1 s a large voltage transient occurs at the receiving end of sheath as can be seen in Figure 7b. In an uncorrected ULM, the voltage continues to increase even after the current reaches its steady state value. However, in the corrected ULM, the sheath voltage appears to settle at zero in steady state. However, a closer observation shows the steady state value to be slightly higher than zero i.e., 143 µV. This error albeit small, indicates that even the corrected ULM can have a DC voltage in sheath during steady state which is contrary to the physical nature of HVDC cables.

Limitations of ULM in Evaluation of Steady State Sheath Voltage and Currents
The sheath voltage of a ULM with and without DC correction procedure of [18] are compared to verify the efficacy of correction procedure.
A system of 10 km cable with TG sheath as shown in Figure 7a is developed in PSCAD. A unit step voltage is applied at the sending end whereas the receiving end is grounded with the resistance of 1 ohm. The sheath voltage is evaluated at the receiving end. A current inrush occurs upon the application of unit step voltage at 1 s, which soon reaches its steady state value. At the same instant i.e., at 1 s a large voltage transient occurs at the receiving end of sheath as can be seen in Figure 7 (b). In an uncorrected ULM, the voltage continues to increase even after the current reaches its steady state value. However, in the corrected ULM, the sheath voltage appears to settle at zero in steady state. However, a closer observation shows the steady state value to be slightly higher than zero i.e., 143 µV. This error albeit small, indicates that even the corrected ULM can have a DC voltage in sheath during steady state which is contrary to the physical nature of HVDC cables.

Limitations of ULM in Evaluation of Steady State Sheath Voltage and Currents
The sheath voltage of a ULM with and without DC correction procedure of [18] are compared to verify the efficacy of correction procedure.
A system of 10 km cable with TG sheath as shown in Figure 7a is developed in PSCAD. A unit step voltage is applied at the sending end whereas the receiving end is grounded with the resistance of 1 ohm. The sheath voltage is evaluated at the receiving end. A current inrush occurs upon the application of unit step voltage at 1 s, which soon reaches its steady state value. At the same instant i.e., at 1 s a large voltage transient occurs at the receiving end of sheath as can be seen in Figure 7 (b). In an uncorrected ULM, the voltage continues to increase even after the current reaches its steady state value. However, in the corrected ULM, the sheath voltage appears to settle at zero in steady state. However, a closer observation shows the steady state value to be slightly higher than zero i.e., 143 µV. This error albeit small, indicates that even the corrected ULM can have a DC voltage in sheath during steady state which is contrary to the physical nature of HVDC cables. To verify the extent of this error in an HVDC setup, we have modelled a cable based on ULM with corrected DC response as shown in Figure 8a. A step voltage of 500 kV is applied at 1 s and the steady state sheath voltage and currents are evaluated along its length. It can be seen in Figure 8b and Figure 8c that DC voltage and currents in sheath become substantial in HVDC application and increase proportionally with increase in length of cable. To verify the extent of this error in an HVDC setup, we have modelled a cable based on ULM with corrected DC response as shown in Figure 8a. A step voltage of 500 kV is applied at 1 s and the steady state sheath voltage and currents are evaluated along its length. It can be seen in Figure 8b,c that DC voltage and currents in sheath become substantial in HVDC application and increase proportionally with increase in length of cable.
(b) Figure 7. (a) A unit step voltage is applied on the sending end, while the receiving end is grounded via a low resistance ground electrode. Sheath voltage is measured at the receiving end. (b) Comparison of measured sheath voltage with and without the DC correction of ULM.
To verify the extent of this error in an HVDC setup, we have modelled a cable based on ULM with corrected DC response as shown in Figure 8a. A step voltage of 500 kV is applied at 1 s and the steady state sheath voltage and currents are evaluated along its length. It can be seen in Figure 8b and Figure 8c that DC voltage and currents in sheath become substantial in HVDC application and increase proportionally with increase in length of cable.

Proposed Method for Accurate Evaluation of Sheath Voltage and Current in Steady State
As it has been demonstrated in the previous subsection, the application of pure DC voltage to core conductor causes a substantial amount of sheath voltage and current in steady state. Therefore, this evaluation method is erroneous and would not be appropriate for evaluation of sheath voltage and current in HVDC cable.
Since, in the actual HVDC cables the only cause of sheath voltage and current during steady state operation are the alternating component in DC line, the sheath voltage and current should also be alternating. Therefore, if the DC component is removed from the evaluated values of sheath voltage and currents the accurate values of steady state sheath voltage and currents can be obtained.
To verify and demonstrate this approach, we have prepared a simulation setup as shown in Figure 9. The DC and harmonic sources applied to the line are based on steady state analysis of  Table 2. Instantaneous values of sheath voltage and current are evaluated along the length of the cable in Figure 9. The instantaneous values are then converted to rms values using (1) and (2) and plotted in Figure 10. and current in HVDC cable.
Since, in the actual HVDC cables the only cause of sheath voltage and current during steady state operation are the alternating component in DC line, the sheath voltage and current should also be alternating. Therefore, if the DC component is removed from the evaluated values of sheath voltage and currents the accurate values of steady state sheath voltage and currents can be obtained.
To verify and demonstrate this approach, we have prepared a simulation setup as shown in Figure 9. The DC and harmonic sources applied to the line are based on steady state analysis of coreground voltage at the sending end of line using Cigre Benchmark Model and listed in Table 2. Instantaneous values of sheath voltage and current are evaluated along the length of the cable in Figure 9. The instantaneous values are then converted to rms values using (1) and (2) and plotted in Figure 10.   Table 2. Instantaneous values of sheath voltage and current are evaluated along the length of the cable in Figure 9. The instantaneous values are then converted to rms values using (1) and (2) and plotted in Figure 10.    1-In Figure 9a the dominant harmonic voltage sources are applied at the sending end of the cable. The resulting rms values of sheath voltage and currents can be seen in Figure 10. Figure 9b the DC source in addition to dominant harmonic voltage sources are applied at sending end of the cable. It can be seen in Figure 10 that resulting rms values of sheath voltage and current are significantly higher than that obtained from harmonic sources alone. This indicates a DC bias introduced to the sheath voltage and current. 3-In Figure 9c the DC component is subtracted from the sheath voltage obtained in Figure 9b. It can be seen in Figure 10; the resulting values of sheath voltage is exactly equal to that obtained in Figure 9a. The correct value of sheath current can also be obtained in the same manner.

2-In
Hence, it has been proved that accurate values of sheath voltage and currents in HVDC cables can be obtained by subtracting the DC component from the obtained values.

Results
We have evaluated steady state sheath voltage and circulating currents in HVDC cable considering varying cable lengths and sheath grounding schemes.

TG/MPG Scheme
The steady state sheath voltage and circulating currents along the length of cable section for a single segment terminal grounded (TG) along with 2 and 4 segments multipoint grounded (MPG) schemes is shown in Figures 11 and 12 respectively.
The maximum sheath voltage in cable with TG scheme increases initially with increase in length from 10 km to 20 km, but upon further increase in length the maximum sheath voltage begins to decrease. The maximum sheath voltage is highest in 40 km and 80 km cables in 2 segment and 4 segment MPG respectively. The maximum sheath current decreases with increasing number of segments.
The relation between the sheath voltage/current and cable length or number of segments is not consistent.

SPG/MSPG Scheme
The steady state sheath voltage and circulating currents along the length of cable section for a single point grounded (SPG) along with 2 and 4 segments multiple single point grounded (MSPG) schemes is shown in Figures 13 and 14 respectively.
In SPG, the maximum sheath voltage occurs at the receiving end of 10 km cable, whereas in MSPG the maximum sheath voltage occurs at the receiving end of 20 and 40 km cable respectively as shown in Figure 13. The maximum sheath current decreases with increasing number of segments in most of the cases.
Maximum sheath voltage along with average energy dissipation per km according to cable length and sheath grounding strategy are shown in Tables 3 and 4 respectively on the subsequent pages.

Discussion
In the previous section the maximum sheath voltage in SPG/MSPG cables is seen to be much higher than TG/MPG. Energy dissipation in SPG/MSPG is also higher than TG/MPG in most of the cases.
The maximum sheath voltage does not relate linearly to the length of cable segment which can be attributed to the changing magnitudes and relative phase angle of dominant harmonic components in the power conductor with changing cable length as shown in Figure 6. The lack of pattern in results can be attributed to the very complex nature of phenomenon in which inductive as well as capacitive coupling plays its role. Following reasons can be attributed to the lack of pattern in results.

1.
The magnitudes of dominant harmonic component of current in DC line changes with the changing length of line. This is because the harmonic components face the series reactance and shunt admittance as opposed to the DC component.

2.
As per faradays law the voltage is induced in the sheath due to changing current and depends upon the rate of change of current. Therefore, 24th harmonic current component can induce the same amount of voltage in sheath as 12th harmonic component which is twice its magnitude.

3.
The relative phase angle of harmonic component keeps on changing along the length of cable. Therefore, along the length of cable, the two harmonic currents for instance 12th and 24th may be additive in certain regions and subtractive in others.

4.
Shunt admittance between core conductor and sheath and between sheath and ground will be higher for the higher frequency harmonic components. Therefore, the charging current flow caused by different harmonic components will be different.

5.
Despite the open circuit sheath in SPG/MSPG, the current flow does not stop. It is contradictory to the concept of single point grounding in AC cable where the sheath current flow is assumed to be limited to zero by open circuiting the sheath. This behavior in DC cable can be attributed to the very high admittance offered to the high frequency harmonic components, resulting in high charging currents from sheath to ground.