Reliability and Cost-oriented Analysis, Comparison and Selection of Multi-level MVdc Converters

—DC technology has gained considerable interest in the medium voltage applications due to the beneﬁts over the AC counterpart. However, to utilize the full capacity of this development, the selection of a suitable power electronic converter topology is a key aspect. From the pool of voltage source converters (VSC’s), it is unclear which topology is suitable for multi-megawatt applications at medium voltage dc (MVdc) levels. To address this, the paper proposes a selection guideline based on reliability and optimum redundancy levels of VSCs for MVdc applications. This will be combined with other functional factors such as operational efﬁciency and return-on-investment. Three candidate multi-level topologies namely three-level neutral point clamped converter (3L-NPC), modular multi-level converter (MMC) and cascaded 3L-NPC (which is being used for the ﬁrst MVdc link in the UK) have been evaluated over two-level-VSC from ± 10 kV to ± 50 kV. Results show that with the increase of MVdc voltage level MMC shows better performance whereas at low MVdc voltage levels 3L-NPC is the prominent topology.


I. INTRODUCTION
M EDIUM voltage dc (MVdc) technology is becoming an attractive solution for distribution networks thanks to its high power transfer capability, excellent controllability and operational flexibility [1].With the increased penetration of distributed generation and electric vehicles, active control of the state-of-the-art ac distribution system has become challenging than before.Thus, MVdc network can act as an additional layer between ac transmission and distribution networks to enhance the overall system efficiency and transfer capability.
Potential applications of voltage source converter (VSC) based MVdc range from the integration of renewable energy sources [2], [3], traction and shipboard power systems [4], [5], smart distribution systems [6] and future offshore dc collection grids [7], [8].In particular, the use of VSC technologies at MVdc voltage level is beneficial in terms of their applicability in weak rural and complex urban distribution networks.
Among the VSC technologies, for low voltage (LV) applications, the two-level (2L) VSC has been considered as one of the simplest and cost-effective solutions [9].Another This work was supported by the European Commission's Horizon 2020 Research & Innovation Programme (Marie Skłodowska-Curie Actions) through the project "Innovative Tools for Offshore Wind and DC Grids (InnoDC)", under grant agreement no.765585 and the EPSRC "Sustainable urban power supply through intelligent control and enhanced restoration of AC/DC networks", Grant No.: EP/T021985/1.(Corresponding author: Gen Li) G. Abeynayake, G. Li, T. Joseph, J. Liang and W. Ming are with the the School of Engineering, Cardiff University, Cardiff, CF24 3AA, United Kingdom.(e-mail: AbeynayakePA@cardiff.ac.uk;LiG9; JosephT; LiangJ1; MingW{@cardiff.ac.uk}).candidate topology is the three-level neutral point clamped converter (3L-NPC), which offers higher efficiency and better harmonic performance compared to the 2L-VSC [10]- [12].Due to lower switching frequencies required to maintain the harmonic levels defined in standards such as IEEE 519 [13], 3L-NPC is relatively more efficient than 2L-VSC.However, for high-voltage dc (HVdc) applications, the modular multilevel converter (MMC) has been the most favored choice due to its exceptional waveform quality, compact and modular design [14], [15].
To this end, the assessment of VSC topologies at different dc voltage levels has been a key research area that received interest recently [9], [16], [17].This is also evidenced in the several demonstration projects that have been or being implemented around the globe.The first AC to DC conversion MVdc link demonstration project in the UK, the "ANGLE-DC" project, aims to demonstrate the application of MVdc by converting an existing 33 kV ac double-circuit to a rigid bipolar dc circuit at ±27 kV [18].Due to the technological maturity of the 3L-NPC and lower cost compared to MMC, a special designed cascaded 3L-NPC (C3L-NPC) has been deployed in the "ANGLE-DC" project.However, the first multi-terminal MVdc project in China used MMCs to demonstrate and supply reliable and quality power to the distribution networks [19].The voltage of this multi-terminal MVdc project is ±10 kV.Other MVdc demonstration projects include the underground MVdc grid within the campus infrastructure in Aachen, Germany [20] and the MVdc system in an industrial area of Shenzhen, China [21].
Although the above projects demonstrate different MVdc technologies, the selection of VSCs for these applications were largely project dependent and varies case by case.A general MVdc converter design and optimal selection principle considering reliability, efficiency and economics are not yet considered in the open literature.
Very few researches were focused on the selection of VSC on MV applications with dc solutions.In [22], the feasibility of utilizing MMC and 3L-NPC for battery energy storage applications at 10 kV dc has been evaluated based on efficiency and capital investment.However, the long term investment benefits or redundant designs have not been investigated.Redundant designs are required for the secure and economic operation of converters [23].At LV levels, topology reliability is not much of a concern due to lower repair times and financial loss is comparatively minimal.Thus, the n+1 redundant design approach is used [9].However, at HVdc levels, the unavailability of converters may cause high revenue losses and redundancy is an important aspect.The benefits of using active redundant sub-modules (SMs) for improving the reliability of MMCs have been discussed in [24], [25].However, the optimal redundancy level has not been considered in any of these studies.
In the converter topology assessment, redundancy level needs to be considered due to higher repair times and capital investment.Thus, the identification of the optimal redundancy level is important.To bridge this research gap and identify the suitable VSC topology for MVdc voltage levels, this paper proposes a selection criterion based on the optimal redundancy level with the consideration of the VSC reliability, preventive maintenance interval, operational efficiency, the total cost of ownership (TCO) and return on investment (ROI).The primary motivation of this paper is to investigate the feasibility of utilizing suitable multi-level VSC topologies at different MVdc voltage levels.Following the proposed selection criterion, the voltage crossover points which the candidate VSCs are suitable to have been identified for the MVdc spectrum from ±10 kV to ±50 kV.Finally, the practicality of the proposed selection methodology is applied to the ANGLE-DC case and tested.

A. MVdc Converter Topologies 1) MVdc Converter Topologies:
For 2L-VSC and 3L-NPC at MVdc voltage levels, the poleto-pole voltage cannot be withstood by a single IGBT.Thus, series-connected IGBTs are required.Press-pack IGBTs are used for series connection of IGBTs with active redundancy where all the IGBTs are sharing the load [26].In this paper, active redundancy is chosen considering industry practice and concerns over the passive scheme.In this paper, the seriesconnected IGBT group in the arms of 2L-VSC and 3L-NPC is defined as switch position (SP), as shown in Fig. 1.Considering the 2L-VSC and 3L-NPC shown in Figs.1(a) and (b), the minimum number (k) of the required IGBT modules per SP can be calculated as where V dc is the converter pole-to-pole voltage, α is the number of SPs per arm with α=1 and α=2 refer to 2L-VSC and 3L-NPC, respectively.The IGBT nominal voltage V IGBT is defined as where η and V D are IGBT module de-rating factor and withstand voltage, respectively.The dc-link capacitor C dc is estimated by where S V SC is the converter MVA rating, E S is the energyto-power ratio which is normally between 10-50 kJ/MVA [27].
The converter reliabilities can be obtained using the Reliability Block Diagrams (RBDs) [16].Fig. 1(c  the two converters, all components are required to be in a healthy state for the normal operation.Therefore, all the blocks are in series from the reliability point of view. 2) Cascaded 3L-NPC: Such as cascaded 2L-VSC (used in HVdc applications), 3L-NPC can also be connected in cascaded configuration as shown in Fig. 2. One of the practical examples of such configuration is the ANGLE-DC project.It comprises of 12 cells (pole-topole), each of which is a 3L-NPC.Each cell is rated for 2.55 MVA with the dc-link voltage of 4.5 kV [28].
A high impedance dc grounding is applied at the converter mid-point to protect the C3L-NPC from earth faults [29].Therefore, this is a rigid bipolar system without a monopolar operation mode.The required number of components and dclink capacitance of each cell can be calculated using (1)-(3).The hierarchical structure of the RBD of the C3L-NPC is shown in Fig. 2. Fig. 2. Cascaded 3L-NPC topology and corresponding RBD.

3) MMC:
The use of MMC at MVdc voltage level needs to be further justified in terms of reliability, efficiency and return on investment.As the capital cost and power losses of the full-bridge (FB) MMC are higher than the half-bridge (HB) MMC, the FB-MMC may not be an optimal option for MVdc applications.Therefore, only the HB-MMC is investigated in this paper, as shown in Fig. 3.As illustrated in the RBD of the HB-MMC, the redundant SMs are added at the arm level.To model the reliability of the HB-SM, the reliability blocks of the IGBTs and SM capacitor are connected in series irrespective of the physical configuration.The minimum number of SMs (k SM ) required per arm can be calculated as where V dc is the MMC pole-to-pole voltage and V SM is the SM nominal voltage.As defined in [30], the SM capacitance C SM can be calculated as where S M M C is the nominal capacity of the MMC; E M M C is the nominal energy per MVA stored in the MMC; n is the number of SMs in each arm.

B. Reliability Modelling
In converter level reliability analysis, the stochastic failure nature of power electronic (PE) devices can be represented by the well-known "bathtub" curve [17], [25], [31].In this paper, the intrinsic failure period is assumed considering the typical project lifetime of MV distribution networks.Mathematically, the reliability function R(t) of any PE device with a failure rate λ(t) is defined as ) Assuming the useful life period is characterized by a constant value, the reliability function is calculated Unscheduled outages are associated with high costs due to the long repair time and the high amount of energy not served.These uncertain outages can be reduced with redundant designs.However, more redundant modules will increase capital investment.Therefore, an optimal redundancy level for a specific project is required.There are two main redundancy schemes which can be utilized in PE converters: the active and passive (standby) mode [32].In the passive redundancy, redundant modules are kept idle and disconnected (or bypassed) until an operating module fails.Whereas in the active redundancy, the total dc bus voltage is shared by all the n IGBTs/modules until k minimum required modules are in operation.In this paper, active redundancy is chosen from a practical point of view.
According to the RBDs shown in Figs.1∼3, the reliability R a (t) of an SP (2L-VSC, 3L-NPC) or an arm (MMC) or pole (C3L-NPC) can be calculated with the probability theory applied for k-out-of -n systems [17].
In ( 8) R y (t) is defined as where In ( 9), R IGBT (t) is the IGBT module reliability and R cell (t) is the reliability of the 3L-NPC which is used for the C3L-NPC.In (10), R IGBT,1 (t) and R IGBT,2 (t) are the reliabilities of IGBTs within the SM.R cap,SM (t) is the MMC SM capacitor reliability.Once R a (t) is calculated, the phaselevel R ph (t) and converter level R V SC (t) reliabilities can be calculated as below.
) where R cap (t) and R npc-d (t) are the reliabilities of dc-link capacitor and NPC diode respectively.The term α is the number of SPs.At present, no single dc capacitor or NPC diode is able to withstand the MVdc voltage levels discussed in this study.Thus, series connections of dc capacitors are required.The terms γ and µ stand for the number of series-connected dc capacitors and NPC diodes.To obtain the reliability of the MMC, ( 12) can be used with γ = µ = 0 and α = 1 since the failure rate of the SM capacitor has already been included in (10).The reliability R C3L (t) of the C3L-NPC can be obtained once the cell level reliability R cell (t) is obtained following the same methodology discussed for the 3L-NPC.

C. Availability and Maintenance Requirements of MVdc Converters
The availability of a converter relies on the frequency of maintenance and repair time.At HVdc levels, periodic preventive maintenance is performed to keep operational costs low because planned outages attract much lower penalty payments than unplanned outages [33].For example, the Crown Estate licenses for offshore wind farms around the UK require that the HVdc converter availability must be above 98% (including planned maintenance) [34].The same maintenance approach can be used for MVdc applications.
In this paper, the analysis is mainly confined to the comparison of MVdc converter topologies.The availability of the cooling system and the power supply system are assumed to be the same.Further, compared to the failure rate of a converter topology which comprises of a large number of power electronics devices, the failure rate of the interfacing transformer is very low [35].Hence, the converter transformer is assumed failure-free for the lifetime considered in this analysis.A stringent availability level of 99.99% is maintained for the SP (2L-VSC, 3L-NPC), arm (MMC) and pole (C3L-NPC) level so that the total converter availability can be maintained above 99.99% as of [32].
To calculate the availability of a converter SP/arm/pole A a using the individual availability of IGBTs/SMs/cells, the kout-of -n model is used as shown in (13), where A b is the base availability of the arm/pole with no redundancy, N is the total number of IGBTs/SMs within an SP/arm/pole and M is the number of redundant modules.
The parameter T M in ( 14) is defined as the preventive maintenance interval (in years).In reliability theory, the base failure rate is defined as the system failure rate without redundancy.The base failure rate of converter SP/arm/pole λ b is calculated as shown in (15) following ( 9) and (10) with n = k in (8).

D. VSC Availability and Redundancy Analysis with Different Maintenance Intervals for ±27 kV
The base failure rates of candidate VSCs for ±27 kV MVdc voltage level can be calculated using (15) with the parameters given in Table I.The IGBT used for this analysis is ABB 5SNA 1300K450300 with a de-rating factor of 56% [26].The gate drive unit SCALE-1SC0450E and dc capacitor of 2.7 kV and 1.5 mF from EPCOS-B25750H2448k004 with the failure rates given in [32] are used.The selected NPC diode is ABB-5SDF13H45014 with the nominal dc voltage of 2.8 kV [36].The calculated minimum required components and base failure rates of converters are given in Table II.Due to the higher number of components MMC shows the highest base failure rate.The C3L-NPC shows the lowest failure rate due to its lower component count.However, due to the inclusion of NPC diodes in 3L-NPC configuration, its failure rate is higher than that of 2L-VSC even though the same number of IGBTs and dc-link capacitors are used in both.
After obtaining the base failure rates of VSCs, the availability is calculated over different redundancy levels and maintenance intervals for half-year and one-year as shown   in Figs. 4 and 5.The required redundant modules (which corresponds to 99.99% availability) for each topology can be obtained using the same and summarized in Table III.It can be noted that even though the base failure rate of C3L-NPC is the lowest, it requires a higher number of redundant cells to keep the same availability level (> 99.99%) because its per-pole availability is the lowest amongst these VSCs due to its physical configuration.Notably, with the increase of preventive maintenance interval, the redundancy level should also be increased to maintain the same availability level.Hence, the capital investment and power losses of converters may increase unnecessarily.Therefore, T M =0.5 year has been selected as the best preventive maintenance interval in the analysis.The variation of VSC reliability for half-year maintenance interval is shown in Fig. 6.To compare VSC reliabilities on a common ground the B 10 life can be used [25].In reliability engineering calculations, the B 10 life is defined as the time taken to reach 90% of the reliability of a system.It can be noted that B 10 life of MMC is the highest with 5.9 years which is more reliable compared to other topologies.The 2L-VSC and 3L-NPC have lower B 10 life values with 0.68 years and 0.64 years respectively.Although the MMC has the highest base failure rate, its B 10 life is the highest after redundancy is added.The reason is, due to the cascaded structure of MMC, the capacitors are placed at SM level.When redundant SMs are added it provides additional redundancy compared to 2L-VSC and 3L-NPC which makes MMC more reliable.Fig. 7 shows the variations of failure rate for the four topologies with different redundancy levels.It is notable that, even though the number of redundant modules is increased after the selected redundancy level, the failure rate does not increase significantly before the B 10 life.For instance, consider the failure rates of MMC with different redundant SMs in Fig. 7(d).The failure rates correspond to B 10 life show that below the selected optimal redundancy level (in here R SM <5) the MMC is more prone to fail.

III. ANALYSIS OF OPERATIONAL EFFICIENCY, TOTAL COST OF OWNERSHIP AND RETURN ON INVESTMENT
Apart from reliability and redundancy, the efficiency and lifetime cost of the VSC (i.e.TCO) are two main factors should be considered in the selection of VSCs.In [11], two types of 3L-NPC topologies are compared with the 2L-VSC for the grid integration of the type-4 wind turbine considering capital investment and operational efficiency.However, depending on the application, voltage and powers level, the associated VSC losses will change.For example, the accumulated annual energy losses of a converter utilized in MVdc distribution networks may differ from an MVdc converter applied in the offshore dc collection system.

A. Operational Efficiency
To analyze the VSCs on common ground with the general grid code requirements defined by IEEE 519 Std., the switching frequencies have been adjusted to meet the maximum current harmonic distortion limits defined in [13].Thus, the switching frequencies of the VSCs considered for this analysis are 2.5 kHz/2L-VSC, 2 kHz/3L-NPC, 1 kHz /C3L-NPC and 100 Hz/MMC.
To evaluate the switching and conduction losses of each VSC, the PLECS software tool has been used which is based on multi-dimensional lookup tables on manufacturer information at various semiconductor junction temperatures [37].For all the losses analysis conducted, the ambient temperature was maintained at 25 • C. Fig. 8 shows the percentage losses of VSCs at its rated power for ±27 kV with different maintenance intervals for selected redundancy levels.When the maintenance interval is increased, the losses are also increased due to the utilization of more redundant modules.At T M =0.5 years, the C3L-NPC (1.52%) shows lower losses compared to 3L-NPC (1.81%) which is notable.However, due to the utilization of a greater number of redundant cells (to maintain the same availability) at T M =1 year, the losses are slightly higher than 3L-NPC.The 2L-VSC shows the highest power losses with P l 2L−0.5 =2.95% and P l 2L−1 =3.17%.MMC presents the lowest power losses, P l M M C−0.5 =0.69% and P l M M C−1 =0.61% for both maintenance intervals.
From the perspective of mitigating converter power losses, having a lower preventive maintenance period is beneficial.Thus, for the rest of the analysis, the VSC redundancy level corresponds to T M =0.5 years has been selected.

B. Annual Energy Production
Due to variations in the demand profile of distributed loads, VSCs connected to MVdc systems may not always operate at their rated power.Thus, efficiency evaluation only at rated power may not reflect the actual efficiency of the VSC.The converter efficiencies related to different loading conditions have been obtained by varying the load current of each VSC.Obtained PLECS simulation results are shown in Fig. 9.According to Fig. 9, MMC shows the highest efficiency (above 99%) at all the loading conditions.Notably, the C3L-NPC has higher efficiency than 3L-NPC.However, at low load conditions, the converter efficiency is lower compared to the rated power due to relatively higher turn-on and turn-off losses.To obtain a reasonable value for annual energy produced by each VSCs, a method based on the normalized load duration curve is proposed.Fig. 10 shows the normalized load duration curve for Great Britain (GB) electricity sector in 2019 [38] and its discretized 6-segment step graph.This discretized 6segment load duration curve illustrates the average loading of each 6 segments and each segment divided according to the percentage of hours during a year [39], as shown in Fig. 10.
In the operational efficiency analysis of VSCs, instead of using a single average value, this normalized 6-segment load duration curve method provides accurate information to calculate the annual energy produced.The corresponding efficiencies with respect to the loading of the VSCs can be obtained by referring to Figs. 8 and 9. Accordingly, the annual energy losses E l X (in kWh) of each VSC (where x defines the corresponding VSC) is calculated.
where η (b i ) and t (b i ) define the efficiency and time (in hours) of the VSC related to the corresponding segment b i = 1, 2 . . .6.The term P V SC (in MW) is the rated power of the converter.Table IV shows the cumulative energy losses for each VSC per annum for T M = 0.5 years.Due to the lower efficiency of 2L-VSC, the energy losses of each segment is relatively higher than other VSCs.

C. Total Cost of Ownership (TCO)
Depending on the VSC topology, the capital cost, and the operation and maintenance (O&M) costs are varying.The term TCO includes initial investment costs and the O&M cost.However, in this paper, the O&M cost is assumed the same for each VSC considering the same preventive maintenance interval and simplicity.
To perform cost calculations, up-to-date market prices have been obtained through cross-referencing via various manufacturers and distributors [40].The IGBT unit price is roughly $2104 for a minimum order quantity of 25 units and the 3L-NPC diodes are $93/unit.Moreover, the gate drive unit cost of $189 is accounted per channel and the capacitor energy price is around $128/kJ [40].The average exchange rate of 1.277 USD = 1 GBP in 2019 has been considered [41].Table V summarizes the TCO of each VSC including redundant components.
It should be mentioned that this analysis mainly focuses on the selection of a suitable VSC topology which is the core component in an MVdc converter station.The converter associated plant equipment in a typical VSC substation or MMC SM, such as the cooling plant and interfacing transformers and SM mechanical switch and structural parts, can be further added in the TCO calculation with reliable data (price) input.

TABLE V TOTAL COST OF OWNERSHIP OF VSCS (FOR T
The cost of the 3L-NPC is higher than the 2L-VSC due to the additional NPC diodes.Due to more redundant cells in C3L-NPC, (to maintain the same availability) the cost is 69% higher than that of 3L-NPC.The TCO of the MMC is the highest among the four VSCs due to higher part counts.
It is worth mentioning that the actual cost of these VSCs may deviate from the above values due to various nontechnical reasons such as confidentiality of cost data and pricing strategies of different manufacturers, time-dependency of component costs due to varying raw material prices and economies of scale.However, project engineers can use their know-how to include more precise component cost factors.

D. Return on Investment (ROI)
In any industrial application, the investment decision is made on how much profit can be gained over its capital investment.This is equally valid in the selection of VSCs which provides a quantitative implication for the financial investment made.The ROI is a quantitative indication of how much profit each dollar invested into that VSC is producing.Thus, a higher ROI is preferred.The topology which shows the highest ROI is selected as the optimal one.To measure the performance of VSCs in terms of ROI, accumulated cost savings relative to 2L-VSC is determined first.The present value of the future cost savings due to energy saving of a VSC can be calculated by where S n is the accumulated cost savings in present value for a period of n years.The term S i is the cost-saving in year i and k is the annual interest rate.The parameter ∆E bi (kWh) in (18) defines as the relative energy saving of segment b i compared to the 2L-VSC.The term P t ($/kWh) is the unit of the electricity selling price.For this analysis, P t =0.198 $/kWh in the UK for the year 2019 has been used [38].Finally, the ROI is used (19) to measure the VSC investment return (over 2L-VSC), relative to their capital cost.
Table VI shows the calculated ROI of each VSC with respect to operational years n=1,5 and 10 assuming a constant annual interest rate of 5% [11].The topology which shows the highest ROI is selected as the optimal one.Table VI shows that MMC has the highest ROI at ±27 kV.Even though the initial investment is nearly double of 2L-VSC (as shown in Table V), MMC accounts for the highest energy saving compared to other VSCs.Following the MMC, 3L-NPC shows the second most suitable VSC to be used at ±27 kV.However, the sensitivity analysis carried out for C3L-NPC shows that, instead of 5 redundant cells, 4 redundant cells are used (at the expense of lower availability) the ROI=0.66 for n=1.By doing so, the TCO of C3L-NPC can be reduced by 23% which is significant and competitive compared to the MMC.

A. Impact of DC Voltage Level
As discussed in Section II, the selection method of redundant modules for a VSC (to keep the availability above a certain level) is a non-linear process.The required minimum modules and level of redundancy are also different depending on the dc voltage.Thus, the ROI will be different due to variations in TCO and operational efficiencies.In order to observe the impact of dc voltage on topology selection, analyses have been performed from ±10 kV to ±50 kV with a fixed rated current of 500 A. Thus, the power rating varies from 10 MVA to 50 MVA.
Table VII shows the required minimum (k min ) and redundant modules (k R ) for each VSC for some selected MVdc voltage levels with the consideration of the target availability level of 99.99%.It can be noted that with the increase of dc voltage level the redundancy level also increases to keep the same availability.However, as k min is increased the reliability of the VSC decreases over time due to the stochastic failure nature of PE devices.At low voltage levels, the B 10 life is high due to the utilization of a few components.To observe the voltage ranges in which a particular VSC is the most suitable, variations of ROI against the MVdc voltage are shown in Fig. 11.According to Fig. 11, between ±10 kV and ±24.2 kV (R-1) use of 3L-NPC VSC is more economical than the use of other VSCs.This is because, within these power levels (10 -24 MVA), and dc voltage levels 3L-NPC require only a few redundant modules and capital costs do not increase significantly.This makes the increase in capital cost of 3L-NPC does not depend on the redundancy level.Between ±10 kV and ±15 kV the ROI of all the VSCs increase due to the use of the same k R as of ±10 kV level.However, at ±15 kV the ROI difference between 3L-NPC over C3L-NPC and MMC is relatively higher.This indicates if C3L-NPC or MMC are used at this dc voltage level it will take much longer time to recover the investment.Notably, after ±15 kV the ROI values of C3L-NPC and MMC decrease due to the increase of k R and relative energy saving is less significant.
Finally, beyond ±24.2 kV (R-2) MMC shows the highest ROI compared to other VSCs owing to the fact that improved efficiencies.This is because at higher MVdc voltage levels more MMC SMs are available to select in the switch selection algorithm.Further, after about ±34 kV C3L-NPC also shows better performance than 3L-NPC, but still inferior to MMC.It should be mentioned that these intersection points may vary depending on the sensitivity of the data.
Table VIII and Fig. 12 summarize the characteristic comparisons of multi-level VSCs based on multiple functional factors discussed above at some selected MVdc voltage levels.The B 10 life comparison shows that the MMC has better reliability over the other three VSCs even though the percentage redundancy difference is not much significant compared to 2L-VSC and 3L-NPC.However, with the increase of the dc voltage level, the B 10 life decreases irrespective of the VSC due to higher number of components.

B. Impact of Rated Current
The selection of VSC topologies at different MVdc voltage levels for a fixed rated capacity has been discussed in the above section.Further analysis in identifying a suitable VSC topology with the variation of its rated current has been carried out in this section.In this study, the 3L-NPC, C3L-NPC and MMC are selected as the candidates.As shown in Fig. 13, the converter rated current has been changed from 100 A to 1000 A and the same MVdc voltage class (from ±10 kV to ±50 kV) has been considered.This corresponds to a broader spectrum of analysis of converter power ratings which ranges from 2 MVA to 100 MVA.
From Fig. 13, it can be observed that irrespective of the MVdc voltage level, the ROI increases with the increase of converter rated current.This is due to the fact that, at higher current levels converter exports more energy than at lower current levels.This results in higher accumulated cost savings for the period considers.The general trend for 3L-NPC is that the ROI decreases with the increase of the voltage level irrespective of the converter rating.On the contrary, the ROI of MMC and C3L-NPC shows an increasing trend.For the current range considered in this analysis, between ±30 kV and ±35 kV, C3L-NPC crosses over 3L-NPC.However, as mentioned in Section IV-A, its ROI is still lower compared to MMC.Fig. 14 summarizes different MVdc crossover voltage levels in which a candidate VSC topology is suitable under a specific rated current.At current levels below 400 A and voltage level below ±28 kV, the use of 3L-NPC is more beneficial.Beyond 900 A, the use of MMC is more economical for the whole MVdc voltage spectrum discussed here.

V. CONCLUSION
To obtain overall techno-economic benefits from MVdc technology, a suitable converter topology is required.This paper presents a systematic criterion to select multi-level VSC for MVdc applications taking the reliability, redundancy, efficiency and economic feasibility factors such as TCO and ROI into account.To obtain the optimum redundancy level for VSCs, a preventive maintenance based approach is used with a pre-defined availability level.A method based on normalized six-segment load duration curve is introduced to assess the operational efficiencies and thereby to evaluate feasibilities of VSCs at different MVdc voltage levels.
The analysis performed here reveals that below 400 A and ±28 kV MVdc voltage level, use of 3L-NPC VSC is much more cost-effective since it provides higher investment return (due to lower capital cost and redundancy).Between 500 A and 700 A and above ±23 kV, the use of MMC is more economical.However, the study suggests that with the increase of MVdc voltage level and higher current levels, the use of MMC is financially beneficial and is also more reliable than other converter topologies.Additionally, beyond about ±35 kV, C3L-NPC can also be considered as an alternative option for MMC.
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Fig. 11 .
Fig. 11.Variation of ROI with MVdc voltage level (at the rated current of 500 A).

Fig. 14 .
Fig. 14.Variation of voltage crossover points with the change of rated currents.
) shows the hierarchical RBD models of the two topologies.There are different hierarchical levels in the RBDs: SP level, arm-level, phase-level and converter-level.According to the topology of

TABLE I SYSTEM
PARAMETERS AND BASE FAILURE RATES.

TABLE II REQUIRED
MIN. NUMBER OF COMPONENTS AND BASE FAILURE RATES.

TABLE IV CUMULATIVE
ANNUAL ENERGY LOSSES OF EACH VSC (IN M W h).

TABLE VIII CHARACTERISTICS
COMPARISON OF MULTI-LEVEL VSCS AT DIFFERENT DC VOLTAGE LEVELS.