Analysis of Lightning Transient Characteristics of Short-Length Mixed MMC-MVDC Transmission System

Medium voltage direct current (MVDC) transmission system are growing due to their assistive quality in conventional grid and compatibility with renewable power network. MVDC distribution links with “Mixed” overhead (OH) & underground (UG) sections could be devised based on urban planning. UG Cables or substations are indirectly exposed to lightning strikes due to adjacent tower sections. In case of MVDC converter or cable, present researchers do not specify lightning voltage impulse level for related system voltage. Therefore, preluding electromagnetic (EM) transient investigation are required to determine the maximum lightning overvoltages for system peripherals i.e. cable & Modular Multilevel Converter (MMC) substation. This research focuses on analyzing lightning performance of OH transmission towers-cable junction & tower-substation link in case of a shielding failure (SF) and back flashover (BF) for a ±35kV short-length mixed MMC-MVDC transmission scheme. This article provides broad-band modeling method for MMC substation for lightning investigation. In addition, based on a detailed time-domain parametric evaluation in PSCAD/EMTDC program, lightning impulse voltage across the transmission line’s pole insulator and embedded cable section are estimated along with numerical validation relying on travelling wave theory. Effect of project parameters such as tower grounding resistance, riser section surge impedance (which connects cable & OH line) and cable length on lightning overvoltage impacting the cable and connected tower section has been demonstrated.


I. INTRODUCTION
Commercial application of DC transmission systems has increased drastically over the past few decades. As compared to AC power systems, electronic power converters offer better integration with unconventional/low footprint power resources and more efficient power management. This has led to the construction of medium voltage DC links by energy subsidies and research consortiums across the globe [1], [2] i.e., ANGLE DC project in Europe, ±10 kV MVDC The associate editor coordinating the review of this manuscript and approving it for publication was Sinisa Djurovic. distribution project in Zhangbei, Zhuhai and Guizhou and HVDC Light (Denmark-Sweden).
As reported, most MVDC projects are point-to-point links or based on underground (UG) power cables [2], [3]. However, recent proposals for the conversion of MVAC transmission lines to DC have paved the development of mixed MVDC lines [3], [4]. These transmission corridors could pass through urban or suburban regions. Where availability of space, visual impact, and city planning could influence transmission infrastructure. Thus, MVDC projects with partial overhead (OH) and UG transmission segments would be constructed worldwide like HVDC projects. In such a scenario UG cable and MVDC substation are exposed to indirect lightning strike. Overvoltages caused by such events are important to be investigated for insulation coordination of cable system & substation. Consequently, lightning overvoltage on cable-overhead line (OHL) junction has been studied for MVAC system [5]. Methods to calculate lightning overvoltage surge along a DC cable in a mixed transmission system have been demonstrated in few researches [6], [7].
Currently, significant lightning research has been conducted on ''Line Commutated Converter'' (LCC) DC transmission lines at HVDC level including ''Mixed'' transmission Links [8]. Contrary to MVDC projects which are 10-100km in length, HVDC systems have long-length transmission lines thus reflection and refractions from the converter substation are not taken into consideration for lightning studies. Usually, insulation coordination of few towers and cable sections with varying length are studied [9]. Latest MVDC corridors are composed of modular multilevel converter (MMC) along with DC specialized switchgear and DC circuit breakers (CB); standards for such power projects are being evolved i.e., PROMOTioN Project in Europe. Some research articles had shed light on high-frequency MMC lightning study. Gao et al. [10] depicts MMC converter station by representing the electronic switches as open/closed switches depending on their state. A detailed model of submodule (which is building block of MMC converter) has been defined in reference [11]. This is done by representing stray capacitance and inductances in an IGBT of submodule. Zhu et al. has done a thorough electromagnetic investigation (EMI) of MMC converter station by representing the structural capacitances of submodules housed in a vertical configuration [12].
The scope of this paper is to derive lightning impulse voltage across the UG Cable, adjacent overhead transmission line (OHTL) tower's as well as DC substation in a mixed MMC-MVDC grid. In order to obtain a general statement about the occurring voltage stresses, parametric evaluation and time-domain analysis has been performed. A variety of system parameters like transmission tower grounding conditions, cable length & riser surge impedance is evaluated under shielding failure and back flashover lightning current. It is not intended to conduct entire insulation coordination studies within this research. However, compared to [5] understanding and concept about the lightning surge waveform across cable and transitioning tower insulators have been broadened for MVDC system. Additionally, modelling depth and scope regarding wide-band MMC converter & substation for lightning study has been fundamentally extended from previous research [10].
This article is further structured as follows. Section II provides a description of ±35kV Mixed symmetric monopolar MMC-VSC transmission with a brief explanation of wide-band converter station & transmission line model for lightning investigation in PSCAD/EMTDC program. Project specifications for transmission infrastructure from articles examining MVAC to MVDC distribution system are utilized and interpolated [7], [14]. Section III provides an overview of shielding failure (SF) and backflash-over (BF) lightning intrusion waveform for system under considered. Subsequently, a method to include steady state DC system voltage at the converter station for accurate lightning analysis is also reported. Section IV portrays a scenario in which lightning strike at a tower adjacent to cable connected transmission tower. Peak lightning transient overvoltage at various location of OHTL, riser and cable section are estimated in PSCAD. Furthermore, equations are formulated to validate the following contribution: • Recognized and explained the superior flashover performance of transitioning tower under the influence of SF.
• Identified the role of tower footing resistance on farthest tower insulators' flashover.
• Investigated the variance in BF overvoltage waveform at tower insulator w.r.t pole's polarity and explained higher flashover probability of -ve/+ve pole insulator at transitioning and adjacent towers as compared to SF.
• The highest lightning peak intrusion voltage across the cable length has been estimated with regards to location & variation in length. • Proved that hypothetical DC voltage source introduced in section III appropriately adds the steady-state system voltage in PSCAD/EMTDC for lightning studies. Finally, section VI & VII provide a general evaluation and conclusion respectively.

A. TRANSMISSION LINK PARAMETERS
A half-bridge MMC converter Monopolar ±35kV point to point link is considered for the manuscript which is connected to a 22.9kV AC system on both sides. Two 10km OHL section are connected with underground cable section in PSCAD model. Where sheath of the cable is solidly bonded to OHGW. Cable length is taken as variable in this study to investigate the worst-case scenario. The MMC converter station is composed of 6 arms, each comprising of 28 half-bridges. The detail of fundamental components of converter stations is given in Table. 1 along with the basic structure of the transmission structure, shown in Fig. 1.
Based on the relatively small size of the MVDC converter station as compared to higher voltage levels, the substation is considered to be confined indoors. As switchgear for DC systems are being developed isolated till now i.e., DC circuit VOLUME 11, 2023  breaker topologies devised are independently built or other disconnectors/earthing equipment are incorporated according to converter topology [15], [16]. For a short-length transmission line, one DC interrupter on each pole could be enough for current fault protection. Thus, a DCCB is installed on positive pole of one substation & negative pole of the other substation.

B. CONVERTER STATION MODELING
To evaluate the response of MMC substation under highfrequency surge, each part must be modelled appropriately. For steady state study, converter station sub-modules are represented as a voltage source with equivalent resistance [18], [19]. For any instance, during normal operation, the capacitor voltage in submodules face insignificant change as shown in Fig. 2.
Additionally, lightning surges have a very high frequency (more than 10MHz), much large than the switching frequency of converter station. Computation for such a small time period doesn't require conventional MMC converter models in PSCAD. Thus, voltage source in PSCAD with converter surge impedance is used to represent MMC for this investigation.
The MMC converter station arms are taken to be a vertical pile of connected submodules. Each submodule (SM) is in a half-bridge configuration with 2 IGBT (1200G450350) [20]. The stray capacitance & inductance of them are used to model the SM [11]. Although the submodule tower structure has no electrical connection with the MMC power-electronic equipment, for high surge overvoltage evaluation, the stray capacitance of the metallic MMC tower must be accounted. Zhu et al. [12] discuss a set of stray capacitances subjected to converter station. The housing capacitance between the submodules could be convolved into just two types i.e., terminal to ground and SM parallel stray capacitance (Fig. 3). For instance, C (n−27) and C (n−28) are the terminal to ground stray capacitance of sub-module 28, while C 28 represent stray capacitor across the SM. For such structures, stray elements must be calculated exclusively. Here, 10pF is utilized for both types of SM's stray capacitances. Thus, accounting for internal & external stray elements of SM's.

C. SWITCHGEAR
The use of special type of DC interrupter in an MVDC grid is eminent for grid protection. A lot of DC CB have been proposed and evaluated but only few of them have been physically developed and tested i.e. offshore HVDC system on Nan'ao island in China [24]. A ±27kV Forced Oscillating interrupter has been developed in the PROMOTioN project [25]. The stray components of Vacuum interrupter (VI) and other electronic parts of that DC CB has been considered for the supposed substation. Detailed information about additional elements of DC breaker is presented in Table. 2 and Fig. 4. VI is in closed condition with a resistance of 80µ . Wideband modelling of DC CB's surge arrester is done as explained in section VI-F.
Disconnector or breakers are required for energizing and protection of any general power network. The number and type of switchgear in a practical MVDC link could vary. Thus, derived configuration of substation is utilized [15]. Disconnecting switches and measurement transformers are represented as their parasitic ground capacitances [21], [22], [23], [24] (as depicted in Table. 3). Necessary elements like Converter Disconnector switch (CD), Pole Line Earthing switch (PLES) or Electrode Line Disconnector switch (ELD), etc. are incorporated ( Fig. 5(a)). Typical Air Insulated Substation (AIS) busbar has a self-surge impedance of 350 [29]. To consider the effect of mutual surge impedance between busbars, they are represented as frequency-dependent line model in PSCAD/EMTDC [21]. Dimensions of busbar are presented in Fig. 5(b). The total length of AIS busbar is 25m per pole. Additionally, Surge retardation of 20% has been added to account the presence of bushings, supporting insulators & measurement equipment in substation. Finally, the interconnection between the transmission line and substation are modelled as lumped inductance of 4m (1µH/m) [9].

D. TOWER AND LINE STRUCTURE
For this study, experimented AC transmission equipment for DC compatibility is chosen [4]. Compact tower structure reduces carbon footprint and electrical interference in line [13]. However, audible corona and insulator flashover limits the tower compactness. For ±35kV line, the Electric field strength model of Austrian 30kV AC tower has been interpolated [4] (Fig. 6(b)), similar tower model has been utilized in other studies [26]. The considered tower is a conical 'T' shaped galvanized steel pole. The tower is grounded using a 2m lead wire with a 0.05m radius. Also, a ground wire is placed 1.545m above the pole conductors.
In PSCAD/EMTDC Frequency-Dependent phase model has been incorporated that can represent transmission lines over a wide range of frequencies with a DC Correction factor. The line is divided into multiple sections in PSCAD to  transmission line model with 15% surge retardation [27]. (1) where, R avg (2) is a ratio composed of height from base to midspan of tower h1 (m) and midspan to top h2 (m), 4.5m each, while r1, r2 & r3 are the top, midsection and bottom radius of the tower structure which are 0.1m, 0.25m and 0.5m repeatedly for 9m conical tower structure [27]. Z T calculated by this scheme is equal to 209 . Short length grounding rod and tower portion between the OH power cable (PC) & ground wire (GW) are presented as RLC lumped model (for earth resistivity ρ 100 .m) and inductance respectively as shown in Fig. 6(a) [22], [28].

E. INSULATOR MODELING
Pin type ceramic insulator VHD 35-G based on Austrian standards have been utilized for this study [30], DC evaluation of similar insulators has been done before [4]. For the insulator under consideration, the overall capacitance is 100pF which is installed in parallel with the ideal switch [31]. The inductance of the insulator path can be modelled as a lumped inductance (1µH/m) in series with the switch as depicted in Fig. 6(a). Although there are multiple methods to evaluate insulator flashover under the influence of fast front transients. However, for insulator of length shorter than 1.2m 'Disruptive effect method' could be utilized [32]. This technique evaluates breakdown process as a function of voltage applied across the insulator and time duration of the applied voltage. In case, the insulator voltage exceeds a certain value X (kV), the breakdown of air gap can be evaluated, mathematically formulated as: where ''D'' is Disruption effect/Area criteria specific for a certain length of insulator. Evaluated by the integral of difference between instantaneous voltage across the insulator V (t) and the triggering voltage X, starting from the lightning triggering instance t o . Once the integral value increase above D the above-mentioned ideal switch is closed in the simulation to emulate insulator flashover. The constants (X, K, D) for 0.29m long insulator are given in Table. 4 [17].

F. UNDERGROUND CABLE
Like PSCAD transmission line representation, the underground cable could be modelled as frequency-dependent (phase) model. The cable sections for both the poles are designed as 1-core XLPE Cable [26], 0.5m apart from each other and 1.5m deep underground. The core diameter, insulation, and sheath thickness along with the single cable depth are depicted in Fig. 7(a). The cable poles are divided into several sections to evaluate the voltage in separated sections of the cables. The lightning-withstand-level (LIWL) of cable core insulator is 170kV [33] (IEC 60071-1) that means if the cable overvoltage, due to lightning, surpasses this value the inner insulation of cable may rapture. Similarly, the cable sheath LIWL is 60kV. The sheath of cable sections can be grounded in multiple ways to reduce any stress on outer jacket of insulator under transient conditions [34]. Here, analysis is done by considering multi-terminal grounding as shown in Fig. 7(b). The sheath is grounded with 10 (R g ) resistance at each subsection of the UG transmission section. However, R g is also varied to study its impact on cable & sheath overvoltages (section IV-D).

G. OTHER TRANSMISSION EQUIPMENT
''Mixed'' transmission line requires riser section (which is tower with underground cable connection) between overhead power cable (OHPC) and underground cable ( Fig. 7(c)).
Since there are no proper guidelines for riser section modelling. Asif et al. [8] has modelled it like an OHL (i.e., similar speed of wave propagation, geometry, and surge impedance).
However, practically riser section should have a geometry transitioning from tower section to cable. For example, the separation between the poles and ground conductors reduces gradually and riser sections conductors must have an appropriate insulation jacket. This suggests that surge impedance of riser section might be approximately average of OHPC & underground cables. Thus, the impact of riser surge variation has been studied in this manuscript.

III. LIGHTNING SURGE INSTIGATION
The lightning surge waveshape impact transients on transmission equipment. For this study, CIGRE single lightning stroke is utilized with varying magnitude [22]. Lightning channel impedance of 1000 and 400 (Z c ) is added in PSCAD for SF and back flashover (BF) respectively as suggested in previous literature [35].

A. LIGHTNING SIGNAL WAVEFORM
In the presence of a ground wire, the lightning strokes reaching directly to the phase wire are relatively of lower magnitude. The first lightning stoke can be mathematically depicted as: where, at & bt n form the front portion while I 1 e A & I 2 e B compose the tail portion of the CIGRE lightning model.
While t represents the instantaneous time after the initiation of lightning current. Similarly, t f & S m are the front time and maximum steepness of CIGRE lightning stroke. (see Fig. 8) The maximum shielding failure lightning stroke current I MSF is calculated by conducting Electro geometric modelling of the overhead transmission structure (proposed by IEEE Std. 1243) [36]. The geometric constraint of tower structure, in this paper, suggests an I MSF of 10kA. Elements of I MSF are tabulated in Table. 5 and depicted in Fig. 8.
Lightning strokes of higher values could strike at overhead ground wire (OHGW) causing BF. However, cumulative probability of very large magnitude is low i.e., chances of worst-case lightning amplitude of 200kA is less than 1% [36] which in case of an urban/sub-urban area might not directly strike a short length MVDC transmission system. In addition, occurrence of certain lightning impulse along an OHTL is estimated using project specific ground stroke density. Gao et al. [10] utilized 118kA BF lightning magnitude estimated for a period of 20 years based on the length & average ground lightning density (N g ). For a 35kV mixed AC transmission line a 150kA BF lightning current is chosen in [5]   which is supposed to be rare. Here, 110kA OHGW lightning have been considered for BF analysis.
Although, for lightning insulation coordination maximum BF lightning current should be chosen based on the service life of the MVDC system peripherals i.e. cable section. However, the aim of this research is to assess the general BF lightning transients of the transmission link. Thus, a more frequent and rounded-off magnitude of 110kA has been utilized for it, which accounts for the maximum BF occurrence in a 12-year period for the OHTL tower as shown below.
Average ground lightning density (N g ) of 6.7 flashes/km 2 /year is taken here (as done in appendix of [37] for a 35kV tower).
The number of lightning strokes N L (flashes/100 km/year) on the considered line is calculated using (9). H T and W are the total tower height and width respectively. S f is the shielding factor taken to be 0.5 [37]. The total exposed transmission segment is 20km (L).   (7) and (8). Thus, considering the random nature and relatively similar waveform of large magnitude lightning, 110kA surge can be utilized to analysis the behavior of OHTL in case of back flashover. Indirectly Induced-voltage flashovers on the transmission equipment are not studied here.

B. STEADY-STATE VOLTAGE ACROSS MVDC LINE TERMINATION
To appropriately add the DC side voltage into the system and significantly reduce any reflection from the hypothetical voltage sources, Electromagnetic wave propagation theory is exploited. Kirchhoff's laws are valid for characteristic impedance of any electrical system [37]. For the studied MVDC link, DC voltage source is connected in parallel configuration adjacent to one of the converter station equivalent models in PSCAD/EMTDC. A Bergeron lossless line with surge impedance 10 times higher than OHTL line is placed in series with voltage sources to avoid unnecessary reflection from DC source, as depicted in Fig. 9. Thus, impact of the emulated DC voltage source is negligible, and the cumulative characteristic impedance of the converter station is not impacted significantly. In addition, the reflection coefficient of the substation busbar & transmission line tends to reflect 26.06% of substation intruding surge. While the remainder of it would be refracted into the MMC substation. Reflection & transmission coefficient between substation busbar and OHPC are shown in (12) & (13) respectively [37].
where, OHPC→busbar & OHPC→busbar are reflection and refraction coefficient for surge transmitting from OHPC to substation. Z OHPC and Z busbar are the surge impedances of transmission OHPC & substation busbar in equation (12) & (13). Characteristic impedance of components of transmission link are given in Table. 6. AC line surge impedance is added at the ends to eliminate reflections from model endings.

IV. LIGHTNING STROKE ON TRANSMISSION SYSTEM
The most vulnerable sections of MVDC system from lightning overvoltage's are the line transition areas i.e., the cable section adjacent to the overhead transmission segment and the substation region [8]. Thus, lightning impact on them has been studied based on I MSF (10kA) on positive power conductor and 110kA BF lightning on OHGW.

A. SHIELDING FAILURE AT OHPC ADJACENT TO CABLE
A scenario is considered where negative polarity lightning strikes a positive (+ve) polarity pole due to SF at tower (T ), 60m away from the riser tower (T r ) as shown in Fig. 9.
To study the influence of surge, overvoltage at four other transmission segments opposite to T r section is considered (T 1 , T 2 , T 3 & T 4 ). Length of each (voltage measured) tower section considered is double of its predecessor i.e., T 1 is 120m away from T while T 4 is 960m.
Lightning strike will initiate a forward voltage surge (e f ) towards the cable section and reverse voltage surge (e r ) towards the transmission line/substation. Initially, total surge voltage at +ve pole of T(location x) is a sum of e f & e r : e r will travel across OHPC which is connected to towers via insulators. e will result in negative voltage surge across the +ve polarity pole insulators. Meanwhile, part of the forward surge e f will reflect from riser section x r and remaining of it will be refracted into the cable: The reflected riser surge e r (x r , t) will be 40% of the initial e f value with opposite polarity as estimated from travelling wave theory [37], equipment surge impedance in Table. 6 and (15). Remaining 60% percent surge will refract towards cable entrance x ce . Part of the refracted riser surge e f (x r , t) will reflect from the boundary x ce and ultimately reach the impacted tower section, (depicted as third term in Eq. (16) & (17). Equation (16) shows, initially, reflected surges retards the growth of overvoltage (V T ) at +ve insulator of tower T . However, as the steeper part of the lightning surge arrives at the tower, positive insulator breaks down. Reflection from the cable end x ct is not accounted for in (16) as it doesn't reach instantly due to relatively large cable length. The insulation breakdown is represented as a close switch in PSCAD, governed by equal area criterion model (3).
Overvoltage V Tn (n = 1 to 4) at further towers opposite to riser section (T 1 , T 2 , T 3 & T 4 ) experience similar lightning overvoltages along with surge retardation due to OHTL length & towers base. This surge retardation can be accounted using attenuation constant k n as stated in (17).  However, steeper portion of lightning surge (at 5.5µs) results in breakdown of +ve tower insulator. Fig. 11 depicts the growth of Insulation disruption coefficient of the considered tower sections insulators. Once this coefficient goes above the disruptive area criteria ''D'', as recommended for VHD 35-G pin type insulators in Table 4, the insulators of tower experience breakdown. In case of further tower i.e., T 3 & T 4 surge retardation is imminent as expressed in (17). Due to relatively short arrival time of reverse travelling surge and smaller half time (t h ) at T r 's positive insulator, it doesn't experience breakdown.
Once the tower insulator breaks down, surge is transmitted into tower & ground. Tower surge impedance Z T and grounding impedance Z R is lower than OHPC this results in opposite polarity reflected wave e rR to reach the tower top, retarding the further insulator surge voltage. The simulation is also done using 200 .m to 800 .m ground resistivity. Increment in lumped ground resistance (R g from 64 to 260 ) significantly raise the insulation breakdown probability on farthest towers i.e., T 3 & T 4 due to lower surge reflections from the base of adjacent towers as shown in Fig. 12.

B. LIGHTNING SURGE ON OHGW ADJACENT TO CABLE
This section discusses the backflash-over on OHTL adjacent to UG cable section. Lightning strikes the ground wire of the tower ''T '' for the same configuration of tower as previous section. Part of the lightning surge traverse along the impacted tower as well as forward and reverse direction on OHGW.  Fig. 13 that the positive pole insulator flashover at T occurs before the negative pole under 110kA lightning impact. This is due to fact that tower insulator with opposite polarity w.r.t tower -ve polarity lightning overvoltage (U T ), experience largest voltage stress i.e., |35kV −U T | > |−35kV −U T |. Initially, the +ve insulator at T do not experience any breakdown as the surge reflected from tower base (e rR ) and riser/cable sheath hinders the growth of flashover until steeper portion of lightning occur at 4.5µs ( Fig. 13(a)). After which +ve insulator flashover occur and part of the surge is injected into the OHPC of +ve pole which escalate as forward & reverse voltage (e +f and e +r ). Part of the forward surge reflects back from the cable/ riser section to tower section. In case of negative (-ve) pole insulator, although there is surge attenuation at first due to positive pole flashover, the large surge half time (t h ), eventually leads to flashover occurring at the -ve insulator of tower T at 9.8µs. This generates a forward/reverse voltage surge (e −f and e −r ) on OHPC at -ve pole.

It can be observed in
V +Tn = k n e + (x, t) + e +r (x r , t) + e +r (x ce , t) Initially, direct OHGW surge do not cause severe tower overvoltages at adjacent tower i.e., T 1 , T 2 & T 3 . However, secondary negative polarity reflected surge from impacted tower (T ) poles and riser/cable section arrive at insulator of these tower section. Voltage surge V +Tn (n = 1 to 4) at +ve insulator for adjacent tower T 1 , T 2 , T 3 & T 4 can be formulated as (18). Similar voltage stress could be observed on -ve pole insulators as seen in Fig. 13(b). It is seen that larger half time of CIGRE 110kA lightning strike result in longer duration of voltage surge at subsequent tower. Thus, even attenuation constant k n , due to transmission line length, do not result in significant reduction of disruptive criterion coefficient of +ve/-ve insulator (as shown in Fig. 14), except at tower T 4 . Large surge t h also influence the surge overvoltages at riser tower T r . The immediate reflection & refraction at T r cause oscillations at the riser insulators but larger duration of surge result in insulator flashovers.
The maximum lightning stroke over the transmission line may vary during its service period. For instance, more frequent and less prevalent, 31kA & 200kA lightning surge may strike. Thus, these lightning strikes along with maximum lightning surge in 20 & 25 years have been studied. Fig. 15 depicts the peak overvoltages at positive pole of incident tower, and 18.75km cable entrance and ending for 31kA, 110kA, 128kA, 137kA & 200kA OHGW lightning stroke. It can be noticed that under the influence of lightning intrusion, incident tower insulator experience breakdown. However, for cable section voltage peak are higher for higher lightning current i.e., for 200kA CIGRE lightning stroke, cable entrance experiences a voltage impulse above -1000kV while for 31kA strike, its -178kV. It is expected that increase in half-time and S m have resulted in a higher cable entrance overvoltage.

C. SHIELDING FAILURE LIGHTNING SURGE ACROSS CABLE
In case of SF, lightning surge partially refract into the cable section. Positive transmission coefficient generates negative forward voltage surge at the cable entrance which is similar in overvoltage polarity as the impacted tower. (19) represent the forward voltage surge at x ce in terms of e f (x r , t) and transmission coefficient at cable junction.
The surge e f (x ce , t) travels and attenuates across the length of cable section. At cable termination x ct (as depicted in fig. 9) a reflected backward surge is developed. Positive reflection coefficient from cable and riser junction produces backward voltage surge with same voltage polarity as e f (x ce , t). Superpositioning of these multiple travelling waves might result in higher initial overvoltage at cable termination, if surge attenuation (k) of cable isn't significant as depicted in (20).
For 18.75km +ve cable pole, 10kA MSF lightning overvoltages are shown in Fig. 16. The voltages at the cable entrance, entrance of sections II, III and cable termination are presented. Propagation time of cable (τ ) is large as compared to lightning surge half time (t h ) thus initial surge at cable entrance subsides before any superposition occur due to reflections/refractions from cable junctions [6], [7]. As depicted in fig. 16 the first overvoltage surge at cable termination is higher than at cable entrance due to immediate constructive interference between forward and reflected waves, resulting in -205kV peak voltage surge.

D. LIGHTNING VOLTAGE AS A FUNCTION OF CABLE LENGTH
The impact of cable length on SF lightning voltage has been studied by considering varying length of the cable from 10km, 5km, 2.5km and 1.25km respectively. It is evident    from Fig. 17 that as the length of the cable decrease (from Fig. 17 (a) to (d)) there is a significant increase in the cable termination overvoltage because a shorter cable will not dampen the surge as much as the bigger segment. This can be verified using (20) as attenuation constant (k) decrease for shorter cables. For instance, variation in cable length (from 18.75km to 1.25km) cause peak cable termination overvoltage reaches up to -300kV breaching the cable breakdown limit [33]. While peak cable entrance overvoltage remains same. With short cables, propagation time (τ ) for surge gets smaller than surge half time (t h ) which makes multiple superposition of reflected waves eminent [6], along any point of cable, before the first impulse subside i.e., for 10km cable initial lightning surge reach x ct at 57.1µs as estimated using Table. 6 or depicted in fig. 17 (a). With reduced length subsequent overvoltage maxima & minima become more prominent. (See fig. 17 (c) & (d)). Cable's sheath grounding resistance may vary during its service period. It is observed that 18.75km cable entrance, under I MSF , endure 6.3% increase in overvoltage when grounding resistance vary from 10 to 100 . Whereas cable sheath peak overvoltage drastically rises up to 62% (Table. 7).

E. EFFECT OF RISER SURGE IMPEDANCE ON LIGHTNING IMPACT
As described in II-G the riser section surge impedance (Z riser ) was taken to be 230 for the above considered case. But it can widely vary between overhead transmission surge impedance and cable surge impedance owning to the fact that not much research has been conducted on high-frequency riser section modelling.
Change in riser characteristic impedance cause variation in surge refraction & transmission coefficient which impact e f (x r , t) and e r (x r , t). In fig. 18, it can be observed that for tower sections other than T r , lower riser section surge impedance doesn't account to significant change in disruption coefficient for +ve insulator under 10kA lightning strike. This can be explained based on IV-A, reflections from riser section have lesser impact on flashover of OH tower insulators adjacent to T r as compared to the steeper portion of lightning surge. Significant increase in disruption coefficient at riser section doesn't cause flashover but may influence the cable overvoltages.

F. INCORPORATION OF SURGE ARRESTERS AND SURGE MITIGATION
Usually, for 35kV insulation lightning-withstand-voltage is about 145 to 170 kV [33]. Recent research papers recommend a higher insulation level for DC cables as compared to AC cable of same voltage [2], [14]. PSCAD result show that cable might experience breakdown due to SF or back flashover lightning strikes on OHTL. Thus, an appropriate surge mitigation scheme is required for the cable section. A maximum continuous operating voltage (MCOV) of 39kV is chosen for the surge arrester (1.12 p.u.) [39]. Station low surge arrester (PVI-LP) has been incorporated for the protection of underground cables [40]. The arresters lightning Impulse Protection Level (LIPL) is 148kV while the Switching Impulse Protection level is 105kV. The protection margin (PM) of the arrester can be calculated as: PM is calculated to be 15% for the case under consideration. High-frequency model of a MOSA has been shown in Fig. 19(a) & (b) along with surge arrester's I-V characteristic. The nonlinear attributes of the surge arrester are represented as A o and A 1 , shown in Fig. 19(a). In case of a slow front (switching impulse), low pass filter in fast front model allows the current to pass through A 1 as well as A o , manifesting the character of arrester for low-frequency surge. However, in case of a fast front surge only A 1 is suppressed resulting high-frequency response of the arrester. Arrester's V-I characteristic conversion into A o and A 1 has been performed according to [40] and parameters of single surge arrester model with a height of 0.5842m are evaluated as given in Table. 8. On the bases of lightning overvoltage maxima across the cable section. The most vulnerable part i.e., boundaries of the cable, are connected with surge arrester. The resultant forward voltage at the cable entrance e f (x ce , t) as a function of arrester current i SA and initial riser forward voltage e f (x ce , t) can be formulated as (done in [6]): (21) Equation (21) portrays the influence of cable entrance's arrester on e f (x ce , t). i SA govern the surge overvoltage across the cable. As depicted in Fig. 20 (a), in case of 10kA shielding failure overvoltage impulse is clipped at each portion of the 1.25km long cable. Due to low half-time of I MSF initial overvoltage surge subsides within 50µs. For OHGW lightning ( Fig. 20 (b)), this arrester configuration limits the cable overvoltage below LIWL of cable. It is seen that for 1.25m cable surge residual voltage is dictated by lightning wave-shape/half-time and location of surge.

V. LIGHTNING STROKE ON MMC SUBSTATION
Most likely, the converter & substation are heavily protected against any direct lightning strokes. However, lightning overvoltages could traverse through a nearby connected OHTL. To emulate worst-case scenario, lightning fault on tower, 60m away from the converter station is considered.

A. LIGHTNING IMPACT ON SUBSTATION SWITCHGEAR
High-frequency MMC substation modelling (as described in section II-C) suggest that AIS busbar might experience multiple reflection/refraction across it due to difference in characteristic impedance as compared to OHTL and short length (25m). In addition, impact of mutual surge impedance between poles and Earth metallic return have been considered which implies that lightning surge on one pole would also impact the remaining busbars. Fig. 21 shows the lightning overvoltages waveform across PLD and smoothing reactor in case of 10kA SF current on nearby +ve pole. The initial oscillating voltage surge at pole line disconnector remains till 15µs due to small half-time  of I MSF . For smoothing reactor, the oscillating surge is low because of its parallel stray capacitance in high-frequency model. Other switchgear equipment like DC circuit breaker, LD, and SD would experience similar overvoltage due to short length and symmetrical modelling in PSCAD.
To observe the maximum peak overvoltage, no converter station arrester has been added. As converter station switchgear are interconnected with each other by balancing capacitors & electronic converter structure. The 10kA tower surge also traverses through negative and ground/earth pole switchgear. Fig. 22 shows the response of negative and earth switchgear under the influence of lightning surge at +ve pole.

B. IMPACT OF VOLTAGE SOURCE ON LIGHTNING SURGE AT MMC CONVERTER
In-order to validate the placement of hypothetical voltage source, lightning overvoltages at MMC poles with and without it are needed. Ideally, voltage source across the converter shouldn't alter the voltage waveform at its poles except shifting the surge to nominal voltage of +ve/-ve pole. Fig. 23 shows the lightning voltage waveshape at converter poles under above discussed scenario for 10kA lightning strike. Thus, validating the method to incorporate DC voltage source alongside MMC converter, described in section III-B.

C. LIGHTNING TRANSIENTS ON MMC SUBSTATION DUE TO BF
Low probability OHGW lightning impact is critical to measure the maximum overvoltage that could ever be endured by MMC converter station. 110kA lightning surge is injected into the OHGW adjacent to the substation. The peak overvoltages experience by different converter station sections are illustrated in Fig. 24.

D. LIGHTNING SURGE REDUCTION USING ARRESTER AT CONVERTER SWITCHGEAR
It is quite clear that substation peripherals could be damaged due to high magnitude lightning strike or being in close contact to I MSF. To mitigate the risk of insulation damage surge arresters are installed at the switchgear entrance adjacent to tower model in PSCAD along with other arresters (i.e. DR) specified in Fig. 5. The resulting voltage waveform at +ve pole disconnector could be noticed in Fig. 25. The peak overvoltage at other converter station portions has been depicted in table. 9. It is tabulated that earthing switchgear still have surge overvoltage above lightning impulse withstand level (170kV) due to direct impact from BF.

VI. GENERALIZED EVALUATION
To assess the overvoltage surge along an MVDC transmission line, extensive time domain simulation & travelling wave theory based numerical analysis have been carried out and broad range of parameters have been estimated. Following are the assessments regrading main characteristics of MVDC system's lightning behavior: • SF lightning strike might superimpose a -ve polarity overvoltage surge on positive pole of the tower • BF on such tower results in insulator breakdown at each of its pole insulators. However, insulator with higher voltage stresses experience flashover first i.e., +ve insulator at the impacted tower experience flashover first due to higher voltage stress from the -ve polarity lightning surge.    • In an event of BF on the tower adjacent to riser section, lightning surge on OHGW do not cause immediate back flashover on adjoining towers. This is because part of the surge is retarded by reflection from tower base. However, steeper portion of surge from impacted tower's poles results in flashover of adjoining tower's insulator.
• In case of shielding failure and BF, immediate surge reflections from cable/riser section suppress the flashover of riser pole insulators. However, due to large surge half-time (h f ) of BF lightning, riser tower poles ultimately experience flashover.
• Likeliness of +ve pole insulators at farthest tower increase with higher footing resistance due to SF on tower adjacent to the cable.
• A previous study on mixed HVDC transmission line had shown that riser connected tower is highly resistant to insulator flashover in case of SF/BF lightning incident on it [8]. However, it has been identified in this research that for BF on mixed MVDC transmission line, riser tower poles are prone to insulator flashover. It is expected that installing surge arresters on riser/adjacent tower poles could improve its performance against back flashover lightning.
• Higher riser section characteristic impedance increases the likelihood of insulator disruption at riser tower.
• Without surge arresters at cable joint, it experiences initial surge overvoltage above its Lightning-withstandlevel due to shielding failure current at adjacent tower section. Shorter cables tend to have higher terminal overvoltage as well as secondary maxima/minima due to reduction in surge retardation factor and lower propagation time.
• Surge arresters at cable terminal clips the lightning overvoltage across the cable. The surge voltage waveform at cable entrance is dependent on surge arrester current i SA , lightning waveform parameters (S m & t h ) & transmission/reflection coefficients of cable.
• Lightning surge on MMC substation due to SF on nearby tower's +ve pole results in oscillating overvoltage at impacted busbar pole. Although, overvoltages are observed at -ve pole and earth pole line switchgear but are less severe as compared to the impacted pole switchgear.
• A comprehensive method has been proposed in Section III-B to introduce steady-state system voltage, alongside the MMC converter, in PSCAD simulations for the lightning study of short transmission lines. The validity of this method is demonstrated in V-B by comparing the voltage waveform at the converter poles with and without the hypothetical voltage source. The results show that adding the voltage source shifts the voltage at the converter terminal to the nominal voltage without altering its waveshape.
• Substation without surge arrester show extremely high overvoltage on all poles because of BF on nearby tower. The surge overvoltages are mitigated by surge arresters' configuration across the substation. However, lightning overvoltages still exceed the LIWL at the earth pole switchgear.
Finally, it is emphasized that general lightning impulse levels w.r.t rated system voltage doesn't seem to be a beneficial measure. As they are dictated by project specific parameters i.e. tower structure, grounding condition or cable etc. Additionally, BF resultant overvoltages are estimated for 110kA lightning current amplitude. However, more severe lightning might occur at tower adjacent to cable depending on project specific ground stoke densities, stroke probabilistic nature [36], [37]. Nevertheless, it is deduced that OHGW do not prevent insulator breakdown on impacted towers sections locally in cases of SF/BF. Therefore, in sensitive transitioning regions of MVDC systems where permanent current faults due to lightning strike are need to be avoided, such as OHTL connecting to cables adjacent to a substation, a few adjoining towers should be equipped with both OHGW and tower surge arresters [10].

VII. CONCLUSION
As worldwide number of MVDC projects realized with ''Mixed'' transmission structure rises continuously, a profound understanding of lightning stresses affecting the cable-tower or tower-converter station conjunction are of major importance. This contribution determines the absolute maximum lightning impulse voltage waveforms along the tower section & adjoining underground cable which ranges from 1.25km to 18.75km. Particularly with regards to the lightning surge reflection/refractions from overhead power line, cable and riser section, thorough electromagnetic transient studies have been carried out for backflash over and shielding failure lightning. In addition to that overvoltages at the converter station peripherals have been investigated. Future studies must focus on devising strategies to suppress tower insulator breakdown at critical locations of tower-cable or substation junctions to prevent lightning surge from resulting in current faults. Future discussions need to clarify whether standard lightning impulse test practice should be extended to include superimposed steady-state DC voltages for tower insulators and cables, considering different DC voltage levels. The results obtained within this paper are valuable for insulation coordination of mixed MMC-MVDC transmission system.

A. ESTIMATION OF MAXIMUM BF OVER OHTL FOR RANGE OF YEARS
Maximum lightning magnitude across the overhead transmission line (OHTL) for a certain period can be evaluated using its back flashover rate (BFR). Highest BFR (flashes/100km/year) for a certain lightning magnitude I , at overhead ground wire directly above tower, is a product of its cumulative probability P (I ) and average number of flashes on the OHTL per 100km per year (N L ) [22]. Thus, 20km air exposed OHTL experiences a 110kA magnitude lightning strike once in 11.92 or 12 years due to an N L of 39.624 flash/100km/year.