# Rapid Evaluation Method for Modular Converter Topologies

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## 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

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**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 | ${R}_{DE0}$ | $0.46\mathrm{m}\mathsf{\Omega}$ |

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**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