# Rapid Evaluation Method for Modular Converter Topologies

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Topology Assessment Methodology

#### 2.1. Definition of the PQ Operating Domain

#### 2.2. Definition of Constraints and Degrees of Freedom

- Degrees of freedom—parameters used to optimize the overall sizing.
- Constraints or constant parameters—parameters that must be the same for all the converter topologies in order to allow for a fair comparison between them.

- Typical degrees of freedom:
- Transformer secondary side voltage.

- Typical constant parameters:
- Submodule rated voltage;
- Maximum stack voltage ripple;
- Maximum DC voltage ripple.

#### 2.3. Definition of the Steady-State Characteristic Equations Guaranteeing the Converter Energy Balance

#### 2.4. PQ Domain Sweeping, Sizing Work Point Identification, and KPI Calculations

## 3. Converter KPI Identification

**Transformer number and their sizing power (${\mathit{N}}_{\mathit{T}}\mathbf{,}{\mathit{S}}_{\mathit{T}}$).**these parameters are related to the cost and volume of the transformers. In HVDC applications, single-phase transformers are usually preferred over three-phase transformers (due to transportation constraints) and, as long bushings and clearance distances are needed, the number of transformers has a significant impact on the station footprint. This KPI is highlighted here; even if the standard number of transformers is three for AC/DC HVDC converters, it can be different for other topologies.**Submodule (SM) number (${\mathit{N}}_{\mathit{S}\mathit{M}}$).**In the set of the KPIs proposed, this represents the footprint of the converter to the highest degree. It is related to the number of interconnections between the submodules and mechanical assemblies, the number of capacitor voltages to measure, and the number of discharge circuits (as well as the number of bypass circuits, depending on the manufacturer’s technical choices). As the submodules correspond to the major cost of the converter, they also relate to the cost, but other KPIs provide a better representation of the cost.**Semiconductor switch total sizing power (${\mathit{S}}_{\mathit{S}\mathit{W}}$).**This is related to the “quantity of silicon” (voltage the semiconductors must withstand and the current passing through them), and therefore is related to the converter cost. In simple terms, it represents the sum of the sizing power of all the switches.**DC voltage ripple (${\mathit{R}}_{\mathbf{02}\mathit{p}\mathit{k}}$).**This is related to the converter’s cost and volume, as it indicates whether an additional filter is needed on the DC side.**Submodule cell capacitance (${\mathit{C}}_{\mathit{S}\mathit{M}}$).**This is mainly related to the SM size (which is important regarding its ability to handle it during the construction phase and during replacement operations for faulty ones). It is also related to the energy stored in an individual submodule, which is a constraint for the devices in the fault current path in the case of an SM internal short-circuit.**Stored energy (${\mathit{W}}_{\mathit{s}\mathit{t}\mathit{o}\mathit{r}\mathit{e}\mathit{d}}$).**This parameter quantifies the energy stored in the converter, which is mainly due to the SM capacitors (but it also takes into account the energy stored in the inductors), which represent the major part of the SM volume. Therefore, this parameter is linked to the converter volume.**Switch number (${\mathit{N}}_{\mathit{S}\mathit{W}}$).**This has a main influence on cost.**Power loss (${\mathit{P}}_{\mathit{L}}$).**This is related to the converter’s efficiency and then the operation costs, but also to the constraints on the thermal-management system (impacts on cost and footprint).

#### 3.1. Per Unit System

- The DC voltage ${V}_{DC}$;
- The maximum DC current ${I}_{DC,max}$;
- The power base, which is given by: ${P}_{DC,max}={V}_{DC}{I}_{DC,max}$.

#### 3.2. Submodule Capacitance Calculation

#### 3.3. Total Semiconductor Switch Sizing Power

#### 3.4. Power Loss

## 4. Definition of Case Studies

#### 4.1. MMC

- The voltage drop determined by the transformer was negligible.
- The voltage drop on the arm inductance was negligible.
- The DC current source was ideal.

#### 4.2. Open-Delta CLSC

#### Equation Definition

- The series connection of the capacitor ${C}_{s}$ and the transformer inductance ${L}_{T}$ determined a perfect series-resonance.
- An ideal DC current source.

## 5. Sizing Results

#### 5.1. MMC

#### 5.2. Open-Delta CLSC

## 6. KPI Comparison

## 7. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

- Bahrman, M.P.; Johnson, B.K. The ABCs of HVDC transmission technologies. IEEE Power Energy Mag.
**2007**, 5, 32–44. [Google Scholar] [CrossRef] - Bresesti, P.; Kling, W.L.; Hendriks, R.L.; Vailati, R. HVDC connection of offshore wind farms to the transmission system. IEEE Trans. Energy Convers.
**2007**, 22, 37–43. [Google Scholar] [CrossRef] - Qin, X.; Zeng, P.; Zhou, Q.; Dai, Q.; Chen, J. Study on the development and reliability of HVDC transmission systems in China. In Proceedings of the 2016 IEEE International Conference on Power System Technology (POWERCON), Wollongong, Australia, 28 September–1 October 2016; pp. 1–6. [Google Scholar]
- Xie, H.; Bie, Z.; Li, G. Reliability-oriented networking planning for meshed VSC-HVDC grids. IEEE Trans. Power Syst.
**2018**, 34, 1342–1351. [Google Scholar] [CrossRef] - Orths, A.; Hiorns, A.; van Houtert, R.; Fisher, L.; Fourment, C. The European North seas countries’ offshore grid initiative—The way forward. In Proceedings of the 2012 IEEE Power and Energy Society General Meeting, San Diego, CA, USA, 22–26 July 2012; pp. 1–8. [Google Scholar]
- Gomez, D.; Páez, J.D.; Cheah-Mane, M.; Maneiro, J.; Dworakowski, P.; Gomis-Bellmunt, O.; Morel, F. Requirements for interconnection of HVDC links with DC-DC converters. In Proceedings of the IECON 2019-45th Annual Conference of the IEEE Industrial Electronics Society, Lisbon, Portugal, 14–17 October 2019; pp. 4854–4860. [Google Scholar]
- Lesnicar, A.; Marquardt, R. An innovative modular multilevel converter topology suitable for a wide power range. In Proceedings of the 2003 IEEE Bologna Power Tech Conference Proceedings, Bologna, Italy, 23–26 June 2003; Volume 3, p. 6. [Google Scholar]
- Merlin, M.; Green, T.; Mitcheson, P.D.; Trainer, D.R.; Critchley, R.; Crookes, W.; Hassan, F. The alternate arm converter: A new hybrid multilevel converter with DC-fault blocking capability. IEEE Trans. Power Deliv.
**2013**, 29, 310–317. [Google Scholar] [CrossRef][Green Version] - Hao, Q.; Li, G.; Ooi, B. Approximate model and low-order harmonic reduction for high-voltage direct current tap based on series single-phase modular multilevel converter. IET Gener. Transm. Distrib.
**2013**, 7, 1046–1054. [Google Scholar] [CrossRef] - Hao, Q.; Ooi, B.-T.; Gao, F.; Wang, C.; Li, N. Three-phase series-connected modular multilevel converter for HVDC application. IEEE Trans. Power Deliv.
**2015**, 31, 50–58. [Google Scholar] [CrossRef] - Feldman, R.; Tomasini, M.; Amankwah, E.; Clare, J.; Wheeler, P.; Trainer, D.R.; Whitehouse, R.S. A hybrid modular multilevel voltage source converter for HVDC power transmission. IEEE Trans. Ind. Appl.
**2013**, 49, 1577–1588. [Google Scholar] [CrossRef] - Amankwah, E.; Costabeber, A.; Watson, A.; Trainer, D.; Jasim, O.; Chivite-Zabalza, J.; Clare, J. The series bridge converter (SBC): A hybrid modular multilevel converter for HVDC applications. In Proceedings of the 2016 18th European Conference on Power Electronics and Applications (EPE’16 ECCE Europe), Karlsruhe, Germany, 5–9 September 2016; pp. 1–9. [Google Scholar]
- Patro, S.K.; Shukla, A.; Ghat, M.B. Hybrid series converter: A DC fault-tolerant HVDC converter with wide operating range. IEEE J. Emerg. Sel. Top. Power Electron.
**2019**, 9, 765–779. [Google Scholar] [CrossRef] - Adam, G.P.; Abdelsalam, I.A.; Ahmed, K.H.; Williams, B.W. Hybrid multilevel converter with cascaded H-bridge cells for HVDC applications: Operating principle and scalability. IEEE Trans. Power Electron.
**2014**, 30, 65–77. [Google Scholar] [CrossRef][Green Version] - Kaya, M.; Costabeber, A.; Watson, A.J.; Tardelli, F.; Clare, J.C. A Push–Pull Series Connected Modular Multilevel Converter for HVdc Applications. IEEE Trans. Power Electron.
**2021**, 37, 3111–3129. [Google Scholar] [CrossRef] - HITACHI. Static Compensator (STATCOM). Available online: https://www.hitachienergy.com/offering/product-and-system/facts/statcom (accessed on 15 June 2021).
- Schön, A.; Bakran, M.-M. Comparison of modular multilevel converter based HV DC-DC-converters. In Proceedings of the 2016 18th European Conference on Power Electronics and Applications (EPE’16 ECCE Europe), Karlsruhe, Germany, 5–9 September 2016; pp. 1–10. [Google Scholar]
- Kung, S.H.; Kish, G.J. Multiport modular multilevel converter for DC systems. IEEE Trans. Power Deliv.
**2018**, 34, 73–83. [Google Scholar] [CrossRef] - Camurca, L.; Langwasser, M.; Zhu, R.; Liserre, M. Future MVDC Applications Using Modular Multilevel Converter. In Proceedings of the 2020 6th IEEE International Energy Conference (ENERGYCon), Gammarth, Tunisia, 28 September–1 October 2020; pp. 1024–1029. [Google Scholar]
- Alvarez, J.P. DC-DC Converter for the Interconnection of HVDC Grids. Ph.D. Dissertation, Université Grenoble Alpes, Greenoble, France, 2019. [Google Scholar]
- Steckler, P.-B. Convertisseur de Tension AC/DC Triphasé Comprenant Uniquement deux Modules de Conversion Electrique. EU Patent FR3112042A1, 28 April 2020. [Google Scholar]
- Farr, E.M.; Trainer, D.R.; Idehen, O.E.; Vershinin, K. The series bridge converter (SBC): AC faults. IEEE Trans. Power Electron.
**2019**, 35, 4467–4471. [Google Scholar] [CrossRef] - ANGLE-DC. 2015 Electricity Network Innovation Competion. Available online: https://www.ofgem.gov.uk/2015 (accessed on 15 June 2021).
- Evans, N.; Dworakowski, P.; Al-Kharaz, M.; Hegde, S.; Perez, E.; Morel, F. Cost-performance framework for the assessment of Modular Multilevel Converter in HVDC transmission applications. In Proceedings of the IECON 2019-45th Annual Conference of the IEEE Industrial Electronics Society, Lisbon, Portugal, 14–17 October 2019; pp. 4793–4798. [Google Scholar]
- Merlin, M.; Green, T.; Mitcheson, P.; Moreno, F.; Dyke, K.; Trainer, D. Cell capacitor sizing in modular multilevel converters and hybrid topologies. In Proceedings of the 2014 16th European Conference on Power Electronics and Applications, Lappeenranta, Finland, 26–28 August 2014; pp. 1–10. [Google Scholar]
- Li, R.; Fletcher, J.E.; Williams, B.W. Influence of third harmonic injection on modular multilevel converter-based high-voltage direct current transmission systems. IET Gener. Transm. Distrib.
**2016**, 10, 2764–2770. [Google Scholar] [CrossRef][Green Version] - ABB Research Ltd Switzerland, ABB Research Ltd Sweden. AC/DC Converter with Series Connected Multicell Phase Modules Each in Parallel with a Series Connection of DC Blocking Capacitor and AC Terminals. EU Patent EP2569858B1, 1 May 2010.
- Amankwah, E.; Costabeber, A.; Watson, A.; Trainer, D.; Jasim, O.; Chivite-Zabalza, J.; Clare, J. The series bridge converter (SBC): Design of a compact modular multilevel converter for grid applications. In Proceedings of the IECON 2016-42nd Annual Conference of the IEEE Industrial Electronics Society, Florence, Italy, 23–26 October 2016; pp. 2588–2593. [Google Scholar]
- ABB. 5SNA 1800G330400 HiPak IGBT Module, Data Sheet, Doc. No. 5SYA 1471-00 11-2019. Available online: https://search.abb.com/library/Download.aspx?DocumentID=5SYA1471&LanguageCode=en&DocumentPartId=&Action=Launch (accessed on 6 November 2021).
- Judge, P.D.; Chaffey, G.; Wang, M.; Dejene, F.Z.; Beerten, J.; Green, T.C.; Van Hertem, D.; Leterme, W. Power-system level classification of voltage-source HVDC converter stations based upon DC fault handling capabilities. IET Renew. Power Gener.
**2019**, 13, 2899–2912. [Google Scholar] [CrossRef][Green Version]

**Figure 2.**Typical PQ domains for grid-connected converters: (

**a**) rectangular profile; (

**b**) butterfly profile; (

**c**) reactive power only; (

**d**) zero-Q load.

**Figure 4.**Collector current–collector emitter voltage curves for the IGBT (

**left**); forward current–forward voltage curves for the associated freewheeling diode (

**right**).

**Figure 11.**Upper a arm current and voltage waveforms at p = 1, q = −0.3, R

_{v}= 0.866 (

**a**); max and min arm voltage and current (

**b**).

**Figure 19.**KPI spider plot. The notation “$1\to x$” means that 1 in the spider plot corresponds to the value $x$.

Name | Symbol | Value |
---|---|---|

DC voltage | ${V}_{DC}$ | $640\mathrm{kV}$ |

Rated power | ${P}_{DC,max}$ | $1\mathrm{GW}$ |

Max reactive power | ${Q}_{max}$ | $\pm 0.3{P}_{DC,max}=\pm 330\mathrm{MVar}$ |

Transformer impedance | ${X}_{cc\%}$ | $10\%$ |

IGBT collector–emitter forward voltage | ${V}_{CE0}$ | $1.3\mathrm{V}$ |

Freewheeling diode forward voltage | ${V}_{DE0}$ | $1.3\mathrm{V}$ |

IGBT on resistance | ${R}_{CE0}$ | $0.79\mathrm{m}\mathsf{\Omega}$ |

Freewheeling diode forward voltage | ${R}_{DE0}$ | $0.46\mathrm{m}\mathsf{\Omega}$ |

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Lanzarotto, D.; Morel, F.; Steckler, P.-B.; Vershinin, K.
Rapid Evaluation Method for Modular Converter Topologies. *Energies* **2022**, *15*, 3492.
https://doi.org/10.3390/en15103492

**AMA Style**

Lanzarotto D, Morel F, Steckler P-B, Vershinin K.
Rapid Evaluation Method for Modular Converter Topologies. *Energies*. 2022; 15(10):3492.
https://doi.org/10.3390/en15103492

**Chicago/Turabian Style**

Lanzarotto, Damiano, Florent Morel, Pierre-Baptiste Steckler, and Konstantin Vershinin.
2022. "Rapid Evaluation Method for Modular Converter Topologies" *Energies* 15, no. 10: 3492.
https://doi.org/10.3390/en15103492