# Sequence Control Strategy for Grid-Forming Voltage Source Converters Based on the Virtual-Flux Orientation under Balanced and Unbalanced Faults

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## Abstract

**:**

## 1. Introduction

## 2. System Description

## 3. Spanish Grid Code Requirements under Balanced and Unbalanced Faults Review

## 4. Sequence Control Strategy

#### 4.1. Sequences Extraction Algorithm

#### 4.2. Positive Sequence Control Scheme

#### 4.3. Negative Sequence Control Scheme

#### 4.4. Converter Voltage Setpoints Calculation

## 5. Real-Time HIL Simulation Results

#### 5.1. Balanced Three-Phase Faults

#### 5.2. Unbalanced Phase-to-Phase Faults

#### 5.3. Converter Response to Unbalanced Phase-to-Phase Faults for Different Values of ${K}_{1}$ and ${K}_{2}$

#### 5.4. Comparison between the Original and the Proposed Model

## 6. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Appendix A. RSCAD Parameters

Parameters | Value | Units |

DC voltage of the VSC, ${V}_{dc}$ | 1200 | V |

Converter rated power, ${S}_{n}$ | 2 | MVA |

Line to line rated voltage (RMS), ${V}_{n}$ | 690 | V |

Filter inductance, ${L}_{f}$ | 0.113 | mH |

Filter resistance, ${R}_{f}$ | 0.714 | mΩ |

Filter capacitance, ${C}_{f}$ | 0.5 | mF |

Nominal frequency, ${f}_{n}$ | 50 | Hz |

Switching frequency, ${f}_{sw}$ | 3 | kHz |

Grid inductance, ${L}_{g}$ | 56.5 | µH |

Grid resistance, ${R}_{g}$ | 0.357 | µΩ |

Short-circuit ratio, SCR | 2 | |

X/R ratio | 10 | |

${T}_{t}$: power rating, ${S}_{N}$ | 2 | MVA |

${T}_{t}$: rated line–line voltage primary, ${V}_{1N}$ | 20 | kV |

${T}_{t}$: rated line–line voltage secondary, ${V}_{2N}$ | 0.69 | kV |

${T}_{t}$: frequency | 50 | Hz |

## Appendix B. Control System Parameters

Parameters | Value | Units |

Inertia, ${T}_{m}$ | 15 | s |

Damping constant, $D$ | 50 | p.u. |

PSS time constant,$\text{}{T}_{w}$ | 1.2 | s |

PSS constant,$\text{}{K}_{w}$ | 0.01 | |

PI Gain, $AC{C}^{+}$ | 0.12 | |

PI Time constant, $AC{C}^{+}$ | 0.01 | s |

PI Gain, $RC{C}^{+}$ | 0.3 | |

PI Time constant, $RC{C}^{+}$ | 0.04 | s |

PI Gain, $AC{C}^{-}$ | −0.5 | |

PI Time constant, $AC{C}^{-}$ | 0.085 | s |

PI Gain, $RC{C}^{-}$ | −0.5 | |

PI Time constant, $RC{C}^{-}$ | 0.085 | s |

PI Gain, $VFOC$ | 1 | |

PI Time constant, $VFOC$ | 0.16 | s |

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**Figure 2.**(

**a**) Positive sequence reactive current injection/absorption additionally required proportional to the positive sequence voltage error; (

**b**) positive sequence total reactive current injection/absorption limitation; (

**c**) negative sequence reactive current injection/absorption additionally required proportional to the negative sequence voltage error [38].

**Figure 15.**GFM converter instantaneous voltage and currents during a balanced fault with 0.22 p.u. depth.

**Figure 16.**GFM converter positive sequence voltage and currents during a balanced fault with 0.22 p.u. depth.

**Figure 17.**GFM converter instantaneous voltage and currents during a balanced fault with 0.95 p.u. depth.

**Figure 18.**GFM converter positive sequence voltage and currents during a balanced fault with 0.95 p.u. depth.

**Figure 19.**GFM converter instantaneous voltage and currents during an unbalanced fault with 0.23 p.u. depth.

**Figure 20.**GFM converter positive sequence voltage and currents during an unbalanced fault with 0.23 p.u. depth.

**Figure 21.**GFM converter negative sequence voltage and currents during an unbalanced fault with 0.23 p.u. depth.

**Figure 22.**GFM converter instantaneous voltage and currents during an unbalanced fault with 0.5 p.u. depth.

**Figure 23.**GFM converter positive sequence voltage and currents during an unbalanced fault with 0.5 p.u. depth.

**Figure 24.**GFM converter negative sequence voltage and currents during an unbalanced fault with 0.5 p.u. depth.

**Figure 25.**GFM converter positive sequence voltage and currents during the unbalanced fault for ${K}_{1}^{\text{}}$ and ${K}_{2}^{\text{}}$ different values.

**Figure 26.**GFM converter negative sequence voltage and currents during the unbalanced fault for ${K}_{1}^{\text{}}$ and ${K}_{2}^{\text{}}$ different values.

**Table 1.**Power generating module types according to the Spanish grid code [38].

Power Generating Module Type | Voltage at the Connection Point | Maximum Capacity |
---|---|---|

Type A | ${V}_{PCC}<110\text{}\mathrm{kV}$ | $0.8\text{}\mathrm{kW}\le {P}_{max}110\text{}\mathrm{kW}$ |

Type B | ${V}_{PCC}<110\text{}\mathrm{kV}$ | $100\text{}\mathrm{kW}\le {P}_{max}5\text{}\mathrm{MW}$ |

Type C | ${V}_{PCC}<110\text{}\mathrm{kV}$ | $5\text{}\mathrm{MW}\le {P}_{max}50\text{}\mathrm{MW}$ |

Type D | ${V}_{PCC}\ge 110\text{}\mathrm{kV}$ | ${P}_{max}\ge 50\text{}\mathrm{MW}$ |

Cases | ${\mathit{I}}_{\mathit{a}\mathit{c}\mathit{t}}^{+}$ | ${\mathit{I}}_{\mathit{r}\mathit{e}\mathit{a}\mathit{c}\mathit{t}}^{+}$ | ${\mathit{K}}_{1}^{\text{}}$$\text{}\mathbf{and}\text{}{\mathit{K}}_{2}^{\text{}}\text{}\mathbf{Set}\text{}\mathbf{Value}$ | ${\mathit{K}}_{1}^{\text{}}$$\text{}\mathbf{and}\text{}{\mathit{K}}_{2}^{\text{}}\text{}\mathbf{Real}\text{}\mathbf{Value}$ |
---|---|---|---|---|

$\Delta {\mathit{v}}^{+}=\mathbf{0.22}\text{}p.u.$ | $0.9\text{}\mathrm{p}.\mathrm{u}.$ | $0.44\text{}\mathrm{p}.\mathrm{u}.$ | $2$ | $2$ |

$\mathit{\Delta}{v}^{+}=\mathbf{0.95}\text{}p.u.$ | $0\text{}\mathrm{p}.\mathrm{u}.$ | $1\text{}\mathrm{p}.\mathrm{u}.$ | $2$ | $1.05$ |

Cases | ${\mathit{I}}_{\mathit{a}\mathit{c}\mathit{t}}^{+}$ | ${\mathit{I}}_{\mathit{r}\mathit{e}\mathit{a}\mathit{c}\mathit{t}}^{+}$ | ${\mathit{I}}_{\mathit{a}\mathit{c}\mathit{t}}^{-}$ | ${\mathit{I}}_{\mathit{r}\mathit{e}\mathit{a}\mathit{c}\mathit{t}}^{-}$ | ${\mathit{K}}_{1}^{\text{}}$$\text{}\mathbf{and}\text{}{\mathit{K}}_{2}^{\text{}}\text{}\mathbf{Set}\text{}\mathbf{Value}$ | ${\mathit{K}}_{1}^{\text{}}$$\text{}\mathbf{and}\text{}{\mathit{K}}_{2}^{\text{}}\text{}\mathbf{Real}\text{}\mathbf{Value}$ |
---|---|---|---|---|---|---|

$\Delta {\mathit{v}}^{-}=\mathbf{0.23}\text{}p.u.$ | $0.28\text{}\mathrm{p}.\mathrm{u}.$ | $0.46\text{}\mathrm{p}.\mathrm{u}.$ | $0\text{}\mathrm{p}.\mathrm{u}.$ | $0.46\text{}\mathrm{p}.\mathrm{u}.$ | $2$ | $2$ |

$\Delta {\mathit{v}}^{-}=\mathbf{0.5}\text{}p.u.$ | $0\text{}\mathrm{p}.\mathrm{u}.$ | $0.5\text{}\mathrm{p}.\mathrm{u}.$ | $0\text{}\mathrm{p}.\mathrm{u}.$ | $0.5\text{}\mathrm{p}.\mathrm{u}.$ | $2$ | $1$ |

**Table 4.**Summary of the results obtained for different values of ${K}_{1}^{\text{}}$ and ${K}_{2}^{\text{}}$.

${\mathit{K}}_{1}^{\text{}}$$\text{}\mathbf{and}\text{}{\mathit{K}}_{2}^{\text{}}\text{}\mathbf{Set}\text{}\mathbf{Value}$ | ${\mathit{I}}_{\mathit{a}\mathit{c}\mathit{t}}^{+}$ | ${\mathit{I}}_{\mathit{r}\mathit{e}\mathit{a}\mathit{c}\mathit{t}}^{+}$ | ${\mathit{I}}_{\mathit{a}\mathit{c}\mathit{t}}^{-}$ | ${\mathit{I}}_{\mathit{r}\mathit{e}\mathit{a}\mathit{c}\mathit{t}}^{-}$ | ${\mathit{K}}_{1}^{\text{}}$$\text{}\mathbf{and}\text{}{\mathit{K}}_{2}^{\text{}}\text{}\mathbf{Real}\text{}\mathbf{Value}$ |
---|---|---|---|---|---|

${\mathit{K}}_{\mathbf{1}}^{\text{}}={\mathit{K}}_{\mathbf{2}}^{\text{}}=\mathbf{1}$ | $0.72\text{}\mathrm{p}.\mathrm{u}.$ | $0.24\text{}\mathrm{p}.\mathrm{u}.$ | $0\text{}\mathrm{p}.\mathrm{u}.$ | $0.24\text{}\mathrm{p}.\mathrm{u}.$ | $1$ |

${\mathit{K}}_{\mathbf{1}}^{\text{}}={\mathit{K}}_{\mathbf{2}}^{\text{}}=\mathbf{2}$ | $0.28\text{}\mathrm{p}.\mathrm{u}.$ | $0.46\text{}\mathrm{p}.\mathrm{u}.$ | $0\text{}\mathrm{p}.\mathrm{u}.$ | $0.46\text{}\mathrm{p}.\mathrm{u}.$ | $2$ |

${\mathit{K}}_{\mathbf{1}}^{\text{}}={\mathit{K}}_{\mathbf{2}}^{\text{}}=\mathbf{3.5}$ | $0\text{}\mathrm{p}.\mathrm{u}.$ | $0.5\text{}\mathrm{p}.\mathrm{u}.$ | $0\text{}\mathrm{p}.\mathrm{u}.$ | $0.5\text{}\mathrm{p}.\mathrm{u}.$ | $2.17$ |

${\mathit{I}}_{\mathit{a}\mathit{c}\mathit{t}}^{+}$ | ${\mathit{I}}_{\mathit{r}\mathit{e}\mathit{a}\mathit{c}\mathit{t}}^{+}$ | ${\mathit{I}}_{\mathit{a}\mathit{c}\mathit{t}}^{-}$ | ${\mathit{I}}_{\mathit{r}\mathit{e}\mathit{a}\mathit{c}\mathit{t}}^{-}$ | |
---|---|---|---|---|

Original Model | $0\text{}\mathrm{p}.\mathrm{u}.$ | $0.75\text{}\mathrm{p}.\mathrm{u}.$ | $-0.02\text{}\mathrm{p}.\mathrm{u}.$ | $1.28\text{}\mathrm{p}.\mathrm{u}.$ |

Proposed Model | $0.28\text{}\mathrm{p}.\mathrm{u}.$ | $0.46\text{}\mathrm{p}.\mathrm{u}.$ | $0\text{}\mathrm{p}.\mathrm{u}.$ | $0.46\text{}\mathrm{p}.\mathrm{u}.$ |

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## Share and Cite

**MDPI and ACS Style**

Dolado Fernández, J.; Eloy-Garcia, J.; Arnaltes, S.; Rodríguez-Amenedo, J.L. Sequence Control Strategy for Grid-Forming Voltage Source Converters Based on the Virtual-Flux Orientation under Balanced and Unbalanced Faults. *Energies* **2023**, *16*, 3056.
https://doi.org/10.3390/en16073056

**AMA Style**

Dolado Fernández J, Eloy-Garcia J, Arnaltes S, Rodríguez-Amenedo JL. Sequence Control Strategy for Grid-Forming Voltage Source Converters Based on the Virtual-Flux Orientation under Balanced and Unbalanced Faults. *Energies*. 2023; 16(7):3056.
https://doi.org/10.3390/en16073056

**Chicago/Turabian Style**

Dolado Fernández, Juan, Joaquín Eloy-Garcia, Santiago Arnaltes, and Jose Luis Rodríguez-Amenedo. 2023. "Sequence Control Strategy for Grid-Forming Voltage Source Converters Based on the Virtual-Flux Orientation under Balanced and Unbalanced Faults" *Energies* 16, no. 7: 3056.
https://doi.org/10.3390/en16073056