# Multiterminal HVDC System with Power Quality Enhancement

^{1}

^{2}

^{3}

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## Abstract

**:**

^{TM}/EMTDC

^{TM}(Power System Computer-Aided Design; Electromagnetic Transients including Direct Current), where the AC grids associated with the terminals suffer from voltage imbalances and voltage harmonics owing to the connection of unbalanced loads and nonlinear loads. The obtained simulation results show the performance of the complete system in terms of active power flow, voltage regulation, and harmonic distortions of the grid current and the grid voltage.

## 1. Introduction

#### Main Contributions

^{TM}/EMTDC

^{TM}(Power System Computer-Aided Design; Electromagnetic Transients including Direct Current) are presented in Section 4. Finally, the main conclusions are provided in Section 5.

## 2. Model of the Multiterminal VSC–HVDC

## 3. Proposed Control Topology

#### 3.1. Regulation of the DC Voltage across the DC Bus

#### 3.2. Regulation of the Voltage at the PCC

#### 3.3. Compensation of Imbalances and Harmonics of the Grid Current

## 4. Case Study

^{TM}/EMTDC

^{TM}. Four AC grids are interconnected by means of the HVDC system. The main features of these networks are as follows:

- AC Grid 1: 11 kV and 50 Hz, inductance of the line ${L}_{{g}_{1}}=2$ mH.
- AC Grid 2: 13.8 kV and 50 Hz, inductance of the line ${L}_{{g}_{2}}=1$ mH.
- AC Grid 3: 13.8 kV and 50 Hz, inductance of the line ${L}_{{g}_{3}}=1.5$ mH.
- AC Grid 4: 11 kV and 50 Hz, inductance of the line ${L}_{{g}_{1}}=1.2$ mH.

- AC grid 1.
- Balanced load 1: active power 20 MW and reactive power 11 MVAr; connected at instant $t=0.25$ s.
- Balanced load 2: active power 30 MW and reactive power 15 MVAr; connected at instant $t=0.4$ s.
- Unbalanced load 1 (resistive load): consumption of 8 MW in phase A, consumption of 8 MW in phase B, and consumption of 1.6 MW in phase C; connected at instant $t=0.8$ s.

- AC grid 2.
- Balanced load 1: active power 25 MW and reactive power 12 MVAr; connected at instant $t=0.25$ s.
- Balanced load 2: active power 35 MW and reactive power 15 MVAr; connected at instant $t=0.4$ s.
- Unbalanced load 1 (resistive load): consumption of 1.6 MW in phase A, consumption of 20 MW in phase B, and consumption of 20 MW in phase C; connected at instant $t=0.8$ s.

- AC grid 3.
- Balanced load 1: active power 15 MW and reactive power 8 MVAr; connected at instant $t=0.25$ s.
- Balanced load 2: active power 25 MW and reactive power 16 MVAr; connected at instant $t=0.4$ s.
- Unbalanced load 1 (resistive load): consumption of 2 MW in phase A, consumption of 8 MW in phase B, and consumption of 2 MW in phase C; connected at instant $t=0.8$ s.

- AC grid 4.
- Balanced load 1: active power 25 MW and reactive power 15 MVAr; connected at instant $t=0.25$ s.
- Balanced load 2: active power 35 MW and reactive power 10 MVAr; connected at instant $t=0.4$ s.
- Unbalanced load 1 (resistive load): consumption of 1.4 MW in phase A, consumption of 10 MW in phase B, and consumption of 1.4 MW in phase C; connected at instant $t=0.8$ s.

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## Abbreviations

HVDC | High Voltage Direct Current |

VSC | Voltage Source Converter |

CSC | Current Source Converter |

PCC | Point of Common Coupling |

PQ | Power Quality |

PI | Proportional–Integral |

DC | Direct Current |

AC | Alternating Current |

HVAC | High-Voltage Alternating Current |

NPC | Neutral-Point Clamped |

FC | Flying Capacitor |

MMC | Modular Multilevel Converter |

FTS | Flexible Transmission Systems |

SRF | Synchronous Reference Frame |

THD | Total Harmonic Distortion |

Brk | Breaker |

SPWM | Sinusoidal Pulse-Width Modulation |

RMS | Root-Mean Square |

PR | Proportional Resonant |

IGBT | Insulated-Gate Bipolar Transistor |

PSCAD | Power System Computer-Aided Design |

EMTDC | Electromagnetic Transients including Direct Current |

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**Figure 1.**Scheme of a four-terminal high-voltage direct current (HVDC) system. VSC—voltage-source converter.

**Figure 3.**Single-phase equivalent circuit of the m-th terminal of the HVDC connected to the grid. PCC—point of common coupling.

**Figure 4.**Proposed control scheme of the VSC that regulates the DC voltage across the DC bus. SPWM—sinusoidal pulse-width modulation.

**Figure 5.**Proposed control scheme of the VSC without regulation of the DC voltage across the DC bus.

**Figure 6.**Proposed control scheme for the compensation of imbalances and harmonics in the grid current together with the inner control loop for the control of the current injected by the VSC.

**Figure 8.**Evolution of the voltages at the four PCCs in p.u: (

**a**) ${V}_{{\mathrm{PCC}}_{1}}$, (

**b**) ${V}_{{\mathrm{PCC}}_{2}}$, (

**c**) ${V}_{{\mathrm{PCC}}_{3}}$, and (

**d**) ${V}_{{\mathrm{PCC}}_{4}}$.

**Figure 10.**Evolution of the active powers injected/absorbed by each terminal into/from its respective AC grid and the total active power flow in each AC grid: (

**a**) active power of terminal 1 ${p}_{1}$ (blue color) and active power of AC grid 1 ${p}_{{g}_{1}}$ (red color); (

**b**) active power of terminal 2 ${p}_{2}$ (blue color) and active power of AC grid 2 ${p}_{{g}_{2}}$ (red color); (

**c**) active power of terminal 3 ${p}_{3}$ (blue color) and active power of AC grid 3 ${p}_{{g}_{3}}$ (red color); (

**d**) active power of terminal 4 ${p}_{4}$ (blue color) and active power of AC grid 4 ${p}_{{g}_{4}}$ (red color).

**Figure 11.**Time responses of the d component (blue color) and q component (red color) of the current through each terminal of the HVDC system: (

**a**) ${i}_{{d}_{1}}$ and ${i}_{{q}_{1}}$, (

**b**) ${i}_{{d}_{2}}$ and ${i}_{{q}_{2}}$, (

**c**) ${i}_{{d}_{3}}$ and ${i}_{{q}_{3}}$, and (

**d**) ${i}_{{d}_{4}}$ and ${i}_{{q}_{4}}$.

**Figure 12.**Waveforms obtained from AC grid 1 for different time intervals: (

**a**) grid line currents ($1.15\phantom{\rule{4pt}{0ex}}\mathrm{s}\le t\le 1.35\phantom{\rule{4pt}{0ex}}\mathrm{s}$), (

**b**) line-to-neutral voltages at PCC${}_{1}$ ($1.15\phantom{\rule{4pt}{0ex}}\mathrm{s}\le t\le 1.35\phantom{\rule{4pt}{0ex}}\mathrm{s}$), (

**c**) grid line currents ($1.45\phantom{\rule{4pt}{0ex}}\mathrm{s}\le t\le 1.65\phantom{\rule{4pt}{0ex}}\mathrm{s}$), (

**d**) line-to-neutral voltages at PCC${}_{1}$ ($1.45\phantom{\rule{4pt}{0ex}}\mathrm{s}\le t\le 1.65\phantom{\rule{4pt}{0ex}}\mathrm{s}$), (

**e**) grid line currents ($1.95\phantom{\rule{4pt}{0ex}}\mathrm{s}\le t\le 2.15\phantom{\rule{4pt}{0ex}}\mathrm{s}$), (

**f**) line-to-neutral voltages at PCC${}_{1}$ ($1.95\phantom{\rule{4pt}{0ex}}\mathrm{s}\le t\le 2.15\phantom{\rule{4pt}{0ex}}\mathrm{s}$), (

**g**) grid line currents ($2.45\phantom{\rule{4pt}{0ex}}\mathrm{s}\le t\le 2.65\phantom{\rule{4pt}{0ex}}\mathrm{s}$), and (

**h**) line-to-neutral voltages at PCC${}_{1}$ ($2.45\phantom{\rule{4pt}{0ex}}\mathrm{s}\le t\le 2.65\phantom{\rule{4pt}{0ex}}\mathrm{s}$).

**Figure 13.**Waveforms obtained from AC grid 2 for different time intervals: (

**a**) grid line currents ($1.15\phantom{\rule{4pt}{0ex}}\mathrm{s}\le t\le 1.35\phantom{\rule{4pt}{0ex}}\mathrm{s}$), (

**b**) line-to-neutral voltages at PCC${}_{2}$ ($1.15\phantom{\rule{4pt}{0ex}}\mathrm{s}\le t\le 1.35\phantom{\rule{4pt}{0ex}}\mathrm{s}$), (

**c**) grid line currents ($1.45\phantom{\rule{4pt}{0ex}}\mathrm{s}\le t\le 1.65\phantom{\rule{4pt}{0ex}}\mathrm{s}$), (

**d**) line-to-neutral voltages at PCC${}_{2}$ ($1.45\phantom{\rule{4pt}{0ex}}\mathrm{s}\le t\le 1.65\phantom{\rule{4pt}{0ex}}\mathrm{s}$), (

**e**) grid line currents ($1.95\phantom{\rule{4pt}{0ex}}\mathrm{s}\le t\le 2.15\phantom{\rule{4pt}{0ex}}\mathrm{s}$), (

**f**) line-to-neutral voltages at PCC${}_{2}$ ($1.95\phantom{\rule{4pt}{0ex}}\mathrm{s}\le t\le 2.15\phantom{\rule{4pt}{0ex}}\mathrm{s}$), (

**g**) grid line currents ($2.45\phantom{\rule{4pt}{0ex}}\mathrm{s}\le t\le 2.65\phantom{\rule{4pt}{0ex}}\mathrm{s}$), and (

**h**) line-to-neutral voltages at PCC${}_{2}$ ($2.45\phantom{\rule{4pt}{0ex}}\mathrm{s}\le t\le 2.65\phantom{\rule{4pt}{0ex}}\mathrm{s}$).

**Figure 14.**Waveforms obtained from AC grid 3 for different time intervals: (

**a**) grid line currents ($1.15\phantom{\rule{4pt}{0ex}}\mathrm{s}\le t\le 1.35\phantom{\rule{4pt}{0ex}}\mathrm{s}$), (

**b**) line-to-neutral voltages at PCC${}_{3}$ ($1.15\phantom{\rule{4pt}{0ex}}\mathrm{s}\le t\le 1.35\phantom{\rule{4pt}{0ex}}\mathrm{s}$), (

**c**) grid line currents ($1.45\phantom{\rule{4pt}{0ex}}\mathrm{s}\le t\le 1.65\phantom{\rule{4pt}{0ex}}\mathrm{s}$), (

**d**) line-to-neutral voltages at PCC${}_{3}$ ($1.45\phantom{\rule{4pt}{0ex}}\mathrm{s}\le t\le 1.65\phantom{\rule{4pt}{0ex}}\mathrm{s}$), (

**e**) grid line currents ($1.95\phantom{\rule{4pt}{0ex}}\mathrm{s}\le t\le 2.15\phantom{\rule{4pt}{0ex}}\mathrm{s}$), (

**f**) line-to-neutral voltages at PCC${}_{3}$ ($1.95\phantom{\rule{4pt}{0ex}}\mathrm{s}\le t\le 2.15\phantom{\rule{4pt}{0ex}}\mathrm{s}$), (

**g**) grid line currents ($2.45\phantom{\rule{4pt}{0ex}}\mathrm{s}\le t\le 2.65\phantom{\rule{4pt}{0ex}}\mathrm{s}$), and (

**h**) line-to-neutral voltages at PCC${}_{3}$ ($2.45\phantom{\rule{4pt}{0ex}}\mathrm{s}\le t\le 2.65\phantom{\rule{4pt}{0ex}}\mathrm{s}$).

**Figure 15.**Waveforms obtained from AC grid 4 for different time intervals: (

**a**) grid line currents ($1.15\phantom{\rule{4pt}{0ex}}\mathrm{s}\le t\le 1.35\phantom{\rule{4pt}{0ex}}\mathrm{s}$), (

**b**) line-to-neutral voltages at PCC${}_{4}$ ($1.15\phantom{\rule{4pt}{0ex}}\mathrm{s}\le t\le 1.35\phantom{\rule{4pt}{0ex}}\mathrm{s}$), (

**c**) grid line currents ($1.45\phantom{\rule{4pt}{0ex}}\mathrm{s}\le t\le 1.65\phantom{\rule{4pt}{0ex}}\mathrm{s}$), (

**d**) line-to-neutral voltages at PCC${}_{4}$ ($1.45\phantom{\rule{4pt}{0ex}}\mathrm{s}\le t\le 1.65\phantom{\rule{4pt}{0ex}}\mathrm{s}$), (

**e**) grid line currents ($1.95\phantom{\rule{4pt}{0ex}}\mathrm{s}\le t\le 2.15\phantom{\rule{4pt}{0ex}}\mathrm{s}$), (

**f**) line-to-neutral voltages at PCC${}_{4}$ ($1.95\phantom{\rule{4pt}{0ex}}\mathrm{s}\le t\le 2.15\phantom{\rule{4pt}{0ex}}\mathrm{s}$), (

**g**) grid line currents ($2.45\phantom{\rule{4pt}{0ex}}\mathrm{s}\le t\le 2.65\phantom{\rule{4pt}{0ex}}\mathrm{s}$), and (

**h**) line-to-neutral voltages at PCC${}_{4}$ ($2.45\phantom{\rule{4pt}{0ex}}\mathrm{s}\le t\le 2.65\phantom{\rule{4pt}{0ex}}\mathrm{s}$).

Coupling Transformer | Resistance ${\mathit{R}}_{\mathit{m}}$ | Inductance ${\mathit{L}}_{\mathit{m}}$ |
---|---|---|

Coupling transformer 1 | ${R}_{1}=6\phantom{\rule{4pt}{0ex}}\mathrm{m}\mathrm{\Omega}$ | ${L}_{1}=1.5\phantom{\rule{4pt}{0ex}}\mathrm{mH}$ |

Coupling transformer 2 | ${R}_{2}=5\phantom{\rule{4pt}{0ex}}\mathrm{m}\mathrm{\Omega}$ | ${L}_{2}=1.2\phantom{\rule{4pt}{0ex}}\mathrm{mH}$ |

Coupling transformer 3 | ${R}_{3}=3\phantom{\rule{4pt}{0ex}}\mathrm{m}\mathrm{\Omega}$ | ${L}_{3}=1.0\phantom{\rule{4pt}{0ex}}\mathrm{mH}$ |

Coupling transformer 4 | ${R}_{4}=4\phantom{\rule{4pt}{0ex}}\mathrm{m}\mathrm{\Omega}$ | ${L}_{4}=1.2\phantom{\rule{4pt}{0ex}}\mathrm{mH}$ |

Terminal 1 | Terminal 2 | Terminal 3 | Terminal 4 | |
---|---|---|---|---|

${k}_{p}$ | 3.594 | 2.876 | 2.397 | 2.876 |

${k}_{i}$ | 2160 | 1728 | 1440 | 1728 |

Terminal 1 | ||||
---|---|---|---|---|

${R}_{{a}_{1}}\left(s\right)$ | ${R}_{{a}_{2}}\left(s\right)$ | ${R}_{{a}_{3}}\left(s\right)$ | ${R}_{{a}_{4}}\left(s\right)$ | ${R}_{{a}_{5}}\left(s\right)$ |

${k}_{{h}_{1}}=26.76$ | ${k}_{{h}_{2}}=943.48$ | ${k}_{{h}_{3}}=3.76\times {10}^{3}$ | ${k}_{{h}_{4}}=1.97\times {10}^{3}$ | ${k}_{{h}_{5}}=3.50\times {10}^{3}$ |

${a}_{1}=-3.4\times {10}^{-3}$ | ${a}_{2}=-1\times {10}^{-3}$ | ${a}_{3}=-5.1\times {10}^{-4}$ | ${a}_{4}=-4.1\times {10}^{-4}$ | ${a}_{5}=-2.9\times {10}^{-4}$ |

${b}_{1}=-1.7\times {10}^{-4}$ | ${b}_{2}=-5.1\times {10}^{-5}$ | ${b}_{3}=-2.5\times {10}^{-5}$ | ${b}_{4}=-2.0\times {10}^{-5}$ | ${b}_{5}=-1.5\times {10}^{-5}$ |

Terminal 2 | ||||

${R}_{{a}_{1}}\left(s\right)$ | ${R}_{{a}_{2}}\left(s\right)$ | ${R}_{{a}_{3}}\left(s\right)$ | ${R}_{{a}_{4}}\left(s\right)$ | ${R}_{{a}_{5}}\left(s\right)$ |

${k}_{{h}_{1}}=19.74$ | ${k}_{{h}_{2}}=754.10$ | ${k}_{{h}_{3}}=3.01\times {10}^{3}$ | ${k}_{{h}_{4}}=1.57\times {10}^{3}$ | ${k}_{{h}_{5}}=2.80\times {10}^{3}$ |

${a}_{1}=-3.4\times {10}^{-3}$ | ${a}_{2}=-1\times {10}^{-3}$ | ${a}_{3}=-5.1\times {10}^{-4}$ | ${a}_{4}=-3.9\times {10}^{-4}$ | ${a}_{5}=-2.9\times {10}^{-4}$ |

${b}_{1}=-1.7\times {10}^{-4}$ | ${b}_{2}=-5.1\times {10}^{-5}$ | ${b}_{3}=-2.6\times {10}^{-5}$ | ${b}_{4}=-1.9\times {10}^{-5}$ | ${b}_{5}=-1.5\times {10}^{-5}$ |

Terminal 3 | ||||

${R}_{{a}_{1}}\left(s\right)$ | ${R}_{{a}_{2}}\left(s\right)$ | ${R}_{{a}_{3}}\left(s\right)$ | ${R}_{{a}_{4}}\left(s\right)$ | ${R}_{{a}_{5}}\left(s\right)$ |

${k}_{{h}_{1}}=16.43$ | ${k}_{{h}_{2}}=628.07$ | ${k}_{{h}_{3}}=2.51\times {10}^{3}$ | ${k}_{{h}_{4}}=1.31\times {10}^{3}$ | ${k}_{{h}_{5}}=2.33\times {10}^{3}$ |

${a}_{1}=-3.4\times {10}^{-3}$ | ${a}_{2}=-1\times {10}^{-3}$ | ${a}_{3}=-5.1\times {10}^{-4}$ | ${a}_{4}=-3.9\times {10}^{-4}$ | ${a}_{5}=-2.9\times {10}^{-4}$ |

${b}_{1}=-1.7\times {10}^{-4}$ | ${b}_{2}=-5.1\times {10}^{-5}$ | ${b}_{3}=-2.5\times {10}^{-5}$ | ${b}_{4}=-1.9\times {10}^{-5}$ | ${b}_{5}=-1.5\times {10}^{-5}$ |

Terminal 4 | ||||

${R}_{{a}_{1}}\left(s\right)$ | ${R}_{{a}_{2}}\left(s\right)$ | ${R}_{{a}_{3}}\left(s\right)$ | ${R}_{{a}_{4}}\left(s\right)$ | ${R}_{{a}_{5}}\left(s\right)$ |

${k}_{{h}_{1}}=19.74$ | ${k}_{{h}_{2}}=754.10$ | ${k}_{{h}_{3}}=3.01\times {10}^{3}$ | ${k}_{{h}_{4}}=1.57\times {10}^{3}$ | ${k}_{{h}_{5}}=2.80\times {10}^{3}$ |

${a}_{1}=-3.4\times {10}^{-3}$ | ${a}_{2}=-1\times {10}^{-3}$ | ${a}_{3}=-5.1\times {10}^{-4}$ | ${a}_{4}=-3.9\times {10}^{-4}$ | ${a}_{5}=-2.9\times {10}^{-4}$ |

${b}_{1}=-1.7\times {10}^{-4}$ | ${b}_{2}=-5.1\times {10}^{-5}$ | ${b}_{3}=-2.5\times {10}^{-5}$ | ${b}_{4}=-1.9\times {10}^{-5}$ | ${b}_{5}=-1.5\times {10}^{-5}$ |

AC Grid 1 | AC Grid 2 | AC Grid 3 | AC Grid 4 | |
---|---|---|---|---|

$TH{D}_{i}$ (%) | 0.49 | 0.43 | 0.87 | 0.39 |

$TH{D}_{v}$ (%) | 1.8 | 1.7 | 2.1 | 1.9 |

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## Share and Cite

**MDPI and ACS Style**

Roncero-Sánchez, P.; Parreño Torres, A.; Vázquez, J.; López-Alcolea, F.J.; Molina-Martínez, E.J.; Garcia-Torres, F. Multiterminal HVDC System with Power Quality Enhancement. *Energies* **2021**, *14*, 1306.
https://doi.org/10.3390/en14051306

**AMA Style**

Roncero-Sánchez P, Parreño Torres A, Vázquez J, López-Alcolea FJ, Molina-Martínez EJ, Garcia-Torres F. Multiterminal HVDC System with Power Quality Enhancement. *Energies*. 2021; 14(5):1306.
https://doi.org/10.3390/en14051306

**Chicago/Turabian Style**

Roncero-Sánchez, Pedro, Alfonso Parreño Torres, Javier Vázquez, Francisco Javier López-Alcolea, Emilio J. Molina-Martínez, and Felix Garcia-Torres. 2021. "Multiterminal HVDC System with Power Quality Enhancement" *Energies* 14, no. 5: 1306.
https://doi.org/10.3390/en14051306