# Modeling and Enhanced Control of Hybrid Full Bridge–Half Bridge MMCs for HVDC Grid Studies

^{*}

## Abstract

**:**

## 1. Introduction

## 2. MMC Description

## 3. MMC Control

**Arm energy control**

- °
- Total converter energy control. This control regulates the total converter energy by setting the DC power if the MMC is in power control mode or the AC active power if the converter is in DC voltage mode.
- °
- Leg energy control. This control regulates the overall leg energy by means of the DC circulating current.
- °
- Common energy difference control. This control regulates the total energy difference between the upper and lower arms by using positive AC circulating currents.
- °
- Differential energy control. This control regulates the individual leg energy differences between the upper and lower arms by means of negative AC circulating currents.

**Capacitor balancing control**

#### 3.1. Enhanced Control

## 4. Hybrid MMC Modeling

#### 4.1. SM Equivalent Circuit

#### 4.2. Simplified Arm Thévenin Equivalent Model

## 5. Results

#### 5.1. Control Validation

#### 5.2. Verification of the Simplified Model

#### 5.2.1. Normal Operation

#### 5.2.2. DC Faults

#### 5.2.3. AC Faults

#### 5.2.4. Simulation Efficiency

#### 5.2.5. Comparison with Other Models

## 6. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## Abbreviations

AC | Alternating current |

DC | Direct current |

HVDC | High voltage direct current |

EMT | Electromagnetic transient |

MMC | Modular multilevel converter |

SM | Submodule |

HB-SM | Half-bridge submodule |

FB-SM | Full-bridge submodule |

CBA | Capacitor balancing algorithm |

AVM | Averaged value model |

PI | Proportional-Integral |

PIR | Proportional-Integral-Resonant |

FPGA | Field-programmable gate array |

IGBT | Insulated gate bipolar transistor |

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**Figure 6.**States and current paths for half-bridge submodules (HB-SMs): (

**a**) bypassed; (

**b**) inserted; (

**c**) blocked.

**Figure 8.**Current path for the inserted state of the FB-SMs: (

**a**) positive voltage; (

**b**) negative voltage.

**Figure 10.**Output MMC voltage and its reference. (

**a**) MMC voltage and its reference; (

**b**) zoom in of the MMC voltage and its reference.

**Figure 17.**Comparison between the conventional and proposed enhanced control. (

**a**) Conventional control; (

**b**) enhanced control.

**Figure 18.**Zoom in of the conventional and proposed enhanced controls. (

**a**) Conventional control; (

**b**) enhanced control.

**Figure 19.**External variables of the MMC during normal operation. (

**a**) Detailed model; (

**b**) simplified model.

**Figure 20.**Internal variables of the MMC during normal operation. (

**a**) Detailed model; (

**b**) simplified model.

**Figure 21.**External variables of the MMC during normal operation (reduced switching modulation). (

**a**) Detailed model; (

**b**) simplified model.

**Figure 22.**Internal variables of the MMC during normal operation (reduced switching modulation). (

**a**) Detailed model; (

**b**) simplified model.

**Figure 23.**Response of the MMC (${N}_{HB}=300$ and ${N}_{FB}=100$) to a DC fault when the MMC is blocked 2 ms after the fault onset. External variables. (

**a**) Detailed model; (

**b**) simplified model.

**Figure 24.**Response of the MMC (${N}_{HB}=300$ and ${N}_{FB}=100$) to a DC fault when the MMC is blocked 2 ms after the fault onset. Internal variables. (

**a**) Detailed model; (

**b**) simplified model.

**Figure 25.**Response of the MMC (${N}_{HB}=150$ and ${N}_{FB}=250$) to a DC fault when the MMC is blocked 2 ms after the fault onset. External variables. (

**a**) Detailed model; (

**b**) simplified model.

**Figure 26.**Response of the MMC (${N}_{HB}=150$ and ${N}_{FB}=250$) to a DC fault when the MMC is blocked 2 ms after the fault onset. Internal variables. (

**a**) Detailed model; (

**b**) simplified model.

**Figure 27.**Response of the MMC (${N}_{HB}=150$ and ${N}_{HB}=250$) to a DC fault when the MMC is blocked 25 ms after the fault onset. External variables. (

**a**) Detailed model; (

**b**) simplified model.

**Figure 28.**Response of the MMC (${N}_{HB}=150$ and ${N}_{HB}=250$) to a DC fault when the MMC is blocked 25 ms after the fault onset. Internal variables. (

**a**) Detailed model; (

**b**) simplified model.

**Figure 29.**Response of the MMC (${N}_{HB}=150$ and ${N}_{HB}=250$) to an AC fault. External variables. (

**a**) Detailed model; (

**b**) simplified model.

**Figure 30.**Response of the MMC (${N}_{HB}=150$ and ${N}_{HB}=250$) to an AC fault. Internal variables. (

**a**) Detailed model; (

**b**) simplified model.

**Figure 32.**SM capacitor voltage errors. Upper graphs: half-bridge submodules (HB-SMs). Lower graphs: FB-SMs. (

**a**) Normal operation; (

**b**) DC fault; (

**c**) AC fault.

${\mathit{i}}_{{}_{\mathit{SM}}}$ | Bypassed | Inserted | Blocked | |
---|---|---|---|---|

${v}_{SM}$ | >0 | ${V}_{F}^{IGBT}$ | ${v}_{c}+{V}_{F}^{diode}$ | ${v}_{c}+{V}_{F}^{diode}$ |

<0 | $-{V}_{F}^{diode}$ | ${v}_{c}-{V}_{F}^{IGBT}$ | $-{V}_{F}^{diode}$ | |

${R}_{SM}$ | >0 | ${R}_{ON}^{IGBT}$ | ${R}_{ON}^{diode}$ | ${R}_{ON}^{diode}$ |

<0 | ${R}_{ON}^{diode}$ | ${R}_{ON}^{IGBT}$ | ${R}_{ON}^{diode}$ |

${\mathit{I}}_{\mathit{SM}}$ | Bypassed | Inserted + | Inserted − | Blocked | |
---|---|---|---|---|---|

${V}_{SM}$ | >0 | ${V}_{F}^{IGBT}+{V}_{F}^{diode}$ | ${V}_{c}+2{V}_{F}^{diode}$ | $-{V}_{c}+2{V}_{F}^{IGBT}$ | ${V}_{c}+2{V}_{F}^{diode}$ |

<0 | $-{V}_{F}^{IGBT}-{V}_{F}^{diode}$ | ${V}_{c}-2{V}_{F}^{IGBT}$ | $-{V}_{c}-2{V}_{F}^{diode}$ | $-{V}_{c}-2{V}_{F}^{diode}$ | |

${R}_{SM}$ | >0 | ${R}_{ON}^{IGBT}+{R}_{ON}^{diode}$ | $2{R}_{ON}^{diode}$ | $2{R}_{ON}^{IGBT}$ | $2{R}_{ON}^{diode}$ |

<0 | ${R}_{ON}^{IGBT}+{R}_{ON}^{diode}$ | $2{R}_{ON}^{IGBT}$ | $2{R}_{ON}^{diode}$ | $2{R}_{ON}^{diode}$ |

Parameter | Value | Parameter | Value | Parameter | Value |
---|---|---|---|---|---|

Active power | 1200 MW | ${R}_{ON}^{diode}$ | 0.5 mΩ | AC grid voltage | 400 kV |

Reactive power | 415 MVAr | ${R}_{ON}^{IGBT}$ | 1 mΩ | ${T}_{R}$ power | 1300 MVA |

Levels | 401 | ${V}_{F}^{diode}$ | 1.15 V | ${T}_{R}$ | $333/400$ kV |

Arm inductance | 41.7 mH | ${V}_{F}^{IGBT}$ | 1.15 V | ${L}_{{T}_{R}}$ | 0.18 pu |

${C}_{SM}$ | 14.5 mF | ${v}_{c}$ | 1.6 kV | ${R}_{{T}_{R}}$ | 0.01 pu |

Case | Detailed Model | Simplified Model | Ratio |
---|---|---|---|

Normal operation | 480 s | 10 s | 48 |

DC fault | 418 s | 9 s | 46.4 |

AC fault | 691 s | 12 s | 57.5 |

© 2020 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 (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Vidal-Albalate, R.; Forner, J. Modeling and Enhanced Control of Hybrid Full Bridge–Half Bridge MMCs for HVDC Grid Studies. *Energies* **2020**, *13*, 180.
https://doi.org/10.3390/en13010180

**AMA Style**

Vidal-Albalate R, Forner J. Modeling and Enhanced Control of Hybrid Full Bridge–Half Bridge MMCs for HVDC Grid Studies. *Energies*. 2020; 13(1):180.
https://doi.org/10.3390/en13010180

**Chicago/Turabian Style**

Vidal-Albalate, Ricardo, and Jaume Forner. 2020. "Modeling and Enhanced Control of Hybrid Full Bridge–Half Bridge MMCs for HVDC Grid Studies" *Energies* 13, no. 1: 180.
https://doi.org/10.3390/en13010180