1. Introduction
There is increasing attention being paid to the significance of high voltage direct current (HVDC) interconnections in bulk power transmission, driven by their lower power losses, capacity, resilience to power outages, power flow controllability, and association with green energy sources [
1]. Previously, overhead lines (OHLs) and cable systems were separately designed and established for transmission. Underground cables (UGCs) have lower environmental and visual effects compared to OHLs and can cover large distances in metropolitan areas [
2]. However, the high economical and technical installation requirements associated with them cannot be overlooked. This led to the advent of more prevalent mixed HVDC links, containing both OHL and UGC sections. Therefore, the effect of lightning overvoltages on OHLs in such links can easily traverse to the UGC section [
3].
Fast front overvoltages on OHLs due to lightning is a subject of major interest, especially with the trends of improving power quality [
4]. Bipolar lightning strokes are less frequent, and overall bipolar flashes constitute 6% to 14% of summer lightning in Switzerland, Russia, and the USA. Many bipolar current waveforms have been observed in winter lightning studies in Japan, with the reported frequency of occurrence ranging from 5% to 33% [
5]. Transients due to bipolar strokes have usually asymmetrical magnitude characteristics and have several zero crossings. Moreover transients in transmission lines due to a unipolar direct lightning stroke with multiple flashovers and changing contact points within the riser section pertain to similar surge characteristics as that of the transients produced due to bipolar lightning strokes [
6]. However, to date, there is little understanding of bipolar lightning flashes, especially compared to positive and negative lightning strokes [
7]. Analysis of how the overvoltage stress affects surge arresters (SAs) due to bipolar lightning on AC distribution transmission systems has been performed, and the influences of channel impedance and footing resistance on SA energy have been discussed [
8,
9,
10]. However, the effect of multi-component flashes on high voltage (HV) transmission lines is not well understood. Transmission lines that carry high power over long distances usually pass through various terrain configurations, which can lead to the footing resistance of towers not remaining constant throughout the line length [
11]. The higher soil resistivity of rocky terrains along with the effective height (i.e., the height of the rocky terrain from the plain level + height of the tower) of tower structures are adept at catching bipolar lightning strokes.
Early studies on the growth of over voltages in mixed transmission lines that consider the cable insulation level are accounted for [
12,
13]. Some studies [
14,
15,
16] have provided parametric analysis and formulations to explain the traveling wave behavior. Nonetheless, bipolar lightning is a multi-flash phenomenon, and transient overvoltages due to subsequent lightning strokes and the response of traveling waves in a mixed HVDC link have been overgeneralized in the literature.
The limitations found in the literature survey above are as follows: (a) in the case of HV transmission lines, the behavior of bipolar strokes is unaddressed, as most cloud-to-ground lightning events consist of negative polarity; (b) the impact of voltage surges at the OHL and cable intersection in a multi-flash lightning stroke is not considered; consequently, (c) there is a gap in modeling the response of traveling waves along the line as multi-flash lightning strokes hit the OHL section several times with short, no-current intervals in between.
Unlike a unipolar lightning stroke, when a bipolar lightning stroke hits the OHL section, it can cause overvoltage and polarity reversal simultaneously inside the cable section. Therefore, the aim of this paper is to highlight the serious threats that multi-flash strokes with different polarities can cause. The transient responses of a mixed HVDC line for direct lightning strokes to the overhead pole conductor (OHPC) and ground wire are considered. Lightning currents for shielding failure are calculated using the electrogeometric model (EGM). We have analyzed the reasons for the high-risk positive pole insulator flashover of adjacent and subsequent towers. Moreover, the impacts of the tower grounding resistance, the riser section length, and the cable length are discussed.
This paper is laid out as follows:
Section 2 explains the underlying modeling strategy and choices. Case studies and simulation results on the effects of direct bipolar lightning strokes hitting the HVDC transmission link are given in
Section 3. Final remarks and recommendations for future prospects of this work are presented in
Section 4.
2. Modeling Methodology
The overvoltage withstand capability of HVDC system due to bipolar lightning strokes can be examined by modeling the detailed tower and cable structures with footing resistances, insulators and conductors.
The frequency dependence of conductors and ground wires result in the nonlinear behavior of the transmission lines. The frequency-dependent phase model (FDPM) quantifies the frequency dependence of all distributed parameters of the line, and its PSCAD implementation is given by [
17,
18]. This model is the most accurate choice for analyzing the maximum cable core to ground overvoltages in the case of shielding failure (SF). This model is also appropriate for understanding the BFO of subsequent and adjacent towers with varying footing resistance, the riser section length, and the cable section length. Lightning is a high frequency phenomena, which brings the HVDC transmission system from a steady to transient state. Thus, the frequency used for the transformation matrix in this study is 1 MHz. Wave propagation theory is used to understand the behavior of the voltage and current along the conductor, and the line constant program (LCP) of PSCAD was used to quantify various parameters. Considering the fact that it is a very long transmission line, the impedance at both ends is matched using terminating impedance. A total length of 2 km on each side of the cable section has been modeled, which constitutes 10 DC bipolar towers of a 500 kV rating, five on each side, with a 485 m span between towers (see
Figure 1).
2.1. Line Insulation
Power line conductors are suspended by means of insulators and are thus isolated electrically from the tower. The insulators used in this study are modeled using stray capacitance, parallel to the circuit breaker. This circuit breaker is operated using volt time characteristics as defined by the leader progression model (LPM) [
19,
20,
21]. Here,
is the time taken to break down, given by Equation (
1):
where
is the corona inception time (which is approximated as 0), and
and
are the streamer propagation time and leader propagation time, respectively. A streamer begins to grow and crosses the gap after
if the voltage still increases after the inception of corona.
is given as (
2):
For negative polarity voltage,
and for positive polarity voltage,
is the voltage on the insulator in kV, and
g is the gap length in m.
The leader will start to grow from both sides after
until the voltage gradient across the un-bridged gap is larger than the critical leader inception gradient
. The leader progression velocity
v in ms
proposed by CIGRE is given by Equation (
5):
where
l is the leader length in m,
is the leader coefficient, and
and
are the arc horns and cap pin insulator, respectively, as given in
Table 1 [
21].
2.2. Line Design
The line material and size are selected for a power rating of 1.5 GW per pole. In this study, high strength steel is used to model the overhead ground wire (OHGW), and an 806-A4-61 all-aluminum alloy conductor (AAAC) is used to model the OHPC. The same conductor geometry is applied to model the riser section, as there are no standard guidelines available in the literature for its modeling. However, the span of transmission lines adjacent to cable terminals is set to 100 m, which is different from the rest of the line.
2.3. Tower Representation
The tower structure and geometry are mostly site-dependent factors and have a minute impact on the simulation results [
22]. Each major section of the ±500 kV HVDC tower is modeled in
Figure 2, as a combination of four short transmission lines using FDPM.
The wave propagation velocity along the tower is 85% of the velocity of the light. A single shielding wire tower is selected to cater the worst case scenario. Further details of the tower geometry are given in
Table 2.
The surge impedance of the tower at its base, top, and cross arms is measured using Equations (
6)–(
8), respectively, given by [
23].
2.4. Tower Footing Resistance
A voltage surge was produced due to the lightning partially running along the OHGW, while the rest of it propagated towards the ground via the tower structure. Low values for tower footing impedance are desired in grounding of the tower. This parameter is strongly influenced by seasonal variations, geography, and the conduction properties of the soil [
21]. As explained in [
24], the current-dependent resistance model has been used herein, given by Equations (
9) and (
10).
is the footing resistance in
, and the footing resistance at a low frequency and current is
, given by 10
.
is the limiting current to start soil ionization, and
I is the lightning current from the footing resistance. Both are measured in A.
is the soil ionization gradient given by 300 kV/m, and the typical grounding resistance used in this study is 10
. The soil resistivity
is 300
m, where this parameter is directly related to the footing impedance. In this study, this parameter is kept high to consider the effect of the increased effective height of the tower structure due to rocky terrain.
2.5. Cable Line
In between the two sections of OHLs, an extruded HVDC underground cable section of copper core and steal sheath with a cross-sectional area of 3000 mm
, as described in [
25], is inserted, considering the effect of lightning overvoltage. The cables are laid horizontally 0.75 m apart from each other, at a depth of 1 m from the ground level. The lightning impulse withstand level (LIWL) of the cable is 2.7 pu. Further specifications of the UGC are listed in
Table 3.
2.6. Surge Arrester Model
In the case of a mixed HVDC transmission line, excessive lightning overvoltage stress on the OHL section can cause permanent failure of the cable insulation, as the cable insulation is more fragile compared to the OHL insulators. To prevent such failure, the cable section should be protected by SAs. As per the instructions for cable overvoltages in [
2], a frequency-dependent surge arrester with a maximum continuous operation voltage (MCOV) of 1.5 pu for the rated system voltage is modeled in this work, as shown in
Figure 3a. An inductance of 6.55
H is connected in series with the surge arrester to represent the connection leads [
26]. The lightning impulse protective level (LIPL) is 2.25 pu for 10 kA, an
20
s discharge current impulse, offering a protective margin of 20%. The surge arrester is 7 m in height and has one parallel-connected metal oxide block, composed of an RLC circuit and two nonlinear resistances,
and
. The desired VI characteristic of the metal oxide surge arrester is given using nonlinear resistors, as illustrated in
Figure 3b, and the lumped parameter values are given in
Table 4, using [
27].
2.7. Bipolar Lightning Stroke Parameters
The bipolar lightning source model presented in this research abide by the parametric values and the pattern of data available on the subject in the literature. The positive peak current was found to be comparatively higher than the negative peak current in most cases and 76% of bipolar lightning strokes change their polarity from positive to negative [
28]. Bipolar lightning flashes have been divided into a four-step process (see
Figure 4).
For the dimensioning of the modeled bipolar lightning stroke, the following parameters are of prime significance, which are as follows:
two peak current magnitudes of lightning strokes (positive and negative);
two rise and decay times;
the mid-interval between the first and the subsequent stroke;
After the modeled HVDC system reached its steady state value of ±500 kV, at 6.5 ms the first positive stroke of the bipolar lightning is initiated, which is then followed by a negative stroke that is 3 ms apart from the previous stroke. As shown in
Figure 5, a time delay is created, representing the mid-interval.
Lightning strokes are modeled conventionally as current sources. Two Hiedler functions [
29] have been used to simulate two strokes of bipolar lightning sequentially, as given by Equation (
11):
controls the amplitude of the peak current,
is the correction factor,
and
define the current rise and decay times, respectively, and n is the concave factor, which controls the waveform steepness. The values of these constants for stroke on the OHPC and OHGW are listed in
Table 5.
The current correction factor
has been chosen as equivalent to 1 because it is a function of the current time parameters, and the ratio between the time constants (
) is set such that it is greater than 10. These sets of values reduced the error rate to less than 1%, demonstrating the validity of the selection criteria. The modeled bipolar lightning waveform has coherence with a naturally recorded one, as is evident from [
30]. The lightning channel impedance is estimated by connecting a resistance of 400
in parallel to the lightning source [
31].
4. Conclusions
Insulation coordination strategy for underground cables is based upon the standard industry test waveshape (10 kA, 8/20
s), and in adverse situations at an unprotected cable terminal, the surge doubles. As shown in our previous research work, for an exceptionally high-magnitude unipolar lightning stroke, the overvoltage exceeded the LIPL of only unprotected shorter cables [
35]. In case of bipolar lightning strokes even with minimal lightning stroke parameters, the voltage surge at the cable terminals exceeds the assumed margin of the worst-case scenario for cable insulation.
This work outlines the transient response of a mixed HVDC transmission line due to a bipolar lightning stroke and provides a critical assessment of the vulnerabilities. A detailed investigation of overvoltages produced by the multi-flash lightning strokes is essential before proposing a coherent strategy for insulation coordination. The insulator flashover of OHLs produces lightning overvoltages, which originate multiple reflecting waves from the base of towers and cable entrance, leading to an increase in the risk of cable insulation failure, due to dual polarity reversal along with the strokes of bipolar lightning. The following are the findings of this research.
- (1)
In the case of a bipolar stroke on OHGW, the voltage stress caused insulator flashover of the positive pole due to the subsequent lightning stroke and the contribution of reflected waves from the first stroke. For unipolar lightning strokes, BFO occurs only under exceptional lightning and grounding conditions. Meanwhile, in this work, it is obvious from
Table 5 that extreme lightning parameters are not selected; hence, there is a high likelihood of insulator flashover for bipolar lightning strokes.
- (a)
BFO occurred at the adjacent tower due to the subsequent stroke when the footing resistance of the tower and the riser section length were both large. At smaller riser section lengths, no BFO took place despite the varying footing resistance due to reflection waves from the cable entrance, the adjacent tower, and its neighboring tower base. Strong backward reflected waves from the cable entrance at shorter riser section lengths compensate for the effect of increased footing resistance of the adjacent tower, and no BFO occurred despite the rising footing resistance. Similarly, no BFO took place with a smaller tower footing resistance and varying riser section lengths.
- (b)
At the subsequent tower with riser section lengths greater than 150 m, no BFO occurred due to sufficient attenuation of the backward reflected waves from the cable entrance.
- (2)
The SF of the positive OHPC caused overvoltage at the cable terminals, which was above the LIPL of the cable, and the energy dissipated by SA increased with decreasing cable lengths.
- (3)
The small propagation time in shorter cables enabled the constructive superposition of the forward and backwards traveling waves, particularly in cables shorter than 10 km, and the voltage at the receiving end of the cable was greater than that at the sending end.
- (4)
No BFO took place under normal conditions after applying the SA on the cable terminals for the adjacent and subsequent towers. However, for the worst choices of tower footing and riser section lengths for the adjacent tower, insulator failure occurred despite the application of SA.
This work analyzes the risks of damage caused by bipolar strokes to the mixed HVDC links instead of proposing a complete insulation coordination strategy. Future discussions can propose cost-effective lightning protective solutions with a nominal rating of SAs to avoid overvoltage and polarity reversal due to multiple strokes in short cable sections.