# Fault Analysis Method Considering Dual-Sequence Current Control of VSCs under Unbalanced Faults

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## Abstract

**:**

## 1. Introduction

## 2. Fault Analysis Method

#### 2.1. Dual-Sequence Current Control

#### 2.2. Algorithm

#### 2.3. Verification

## 3. The Impact of Dual-Sequence Current Control on the System

#### 3.1. Problem Description

#### 3.2. Problem Formulation Using the Proposed Fault Analysis Method

#### 3.3. Investigation and Discussion

## 4. Application on the Western Danish Power System

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**Boundary conditions for faulted networks: (

**a**) single-phase-to-ground fault; (

**b**) two-phase fault; (

**c**) two-phase-to-ground fault.

**Figure 5.**Dual-sequence current control block diagram of the VSC in Real Time Digital Simulator (RTDS).

**Figure 6.**Sequence voltages from the RTDS simulation of a fault at bus 4: (

**a**) S3, A–g fault. (

**b**) S4, A–B fault. (VP: positive-sequence voltage; VN: negative-sequence voltage; the number refers to the bus number).

**Figure 7.**VSC short circuit current (measured from the delta winding side) from the RTDS simulation of a fault at bus 4. (IP: positive-sequence current; IN: negative-sequence current).

**Figure 8.**Sequence voltages from RTDS simulations subject to an A–B fault at bus 4: (

**a**) a stable scenario. (

**b**) an unstable scenario. (VP: positive-sequence voltage; VN: negative-sequence voltage; the number refers to the bus number).

**Figure 12.**The values of min(Z) under different scenarios for an A–B fault at IDU: (

**a**) the original system. (

**b**) with three SGs (ESVB3, SKVB3 and NJVB3) phased out.

Scenario | ${\mathit{a}}_{1}$ | ${\mathit{c}}_{1}$ | Share of Sequence Powers |
---|---|---|---|

S1 | 1 | 1 | ${P}^{+}$(100%), ${P}^{-}$(0%), ${Q}^{+}$(100%), ${Q}^{-}$(0%) |

S2 | 1 | 0.5 | ${P}^{+}$(100%), ${P}^{-}$(0%), ${Q}^{+}$(50%), ${Q}^{-}$(50%) |

S3 | 1 | 0 | ${P}^{+}$(100%), ${P}^{-}$(0%), ${Q}^{+}$(0%), ${Q}^{-}$(100%) |

S4 | 0.5 | 1 | ${P}^{+}$(50%), ${P}^{-}$(50%), ${Q}^{+}$(100%), ${Q}^{-}$(0%) |

A–B Fault | A–g Fault | |||||||
---|---|---|---|---|---|---|---|---|

Bus | $\left(\right)$ (p.u.) | $\left(\right)$ (p.u.) | $\left(\right)$ (p.u.) | $\left(\right)$ (p.u.) | ||||

Cal | RTDS | Cal | RTDS | Cal | RTDS | Cal | RTDS | |

4 | 0.636 | 0.645 | 0.636 | 0.645 | 0.721 | 0.726 | 0.551 | 0.558 |

6 | 0.692 | 0.699 | 0.619 | 0.625 | 0.773 | 0.780 | 0.536 | 0.542 |

10 | 0.817 | 0.821 | 0.591 | 0.599 | 0.886 | 0.893 | 0.512 | 0.520 |

Converter | $\left(\right)$ (p.u.) | $\left(\right)$ (p.u.) | $\left(\right)$ (p.u.) | $\left(\right)$ (p.u.) | ||||

1 | 0.263 | 0.260 | 0 | 0 | 0.223 | 0.228 | 0 | 0 |

2 | 0.320 | 0.317 | 0 | 0 | 0.279 | 0.282 | 0 | 0 |

A–B Fault | A–g Fault | |||||||
---|---|---|---|---|---|---|---|---|

Bus | $\left(\right)$ (p.u.) | $\left(\right)$ (p.u.) | $\left(\right)$ (p.u.) | $\left(\right)$ (p.u.) | ||||

Cal | RTDS | Cal | RTDS | Cal | RTDS | Cal | RTDS | |

4 | 0.599 | 0.605 | 0.599 | 0.605 | 0.684 | 0.690 | 0.513 | 0.519 |

6 | 0.640 | 0.646 | 0.564 | 0.570 | 0.723 | 0.727 | 0.477 | 0.485 |

10 | 0.785 | 0.792 | 0.554 | 0.563 | 0.854 | 0.859 | 0.473 | 0.480 |

Converter | $\left(\right)$ (p.u.) | $\left(\right)$ (p.u.) | $\left(\right)$ (p.u.) | $\left(\right)$ (p.u.) | ||||

1 | 0.276 | 0.271 | 0.044 | 0.041 | 0.235 | 0.238 | 0.050 | 0.058 |

2 | 0.332 | 0.034 | 0 | 0 | 0.298 | 0.297 | 0 | 0 |

A–B Fault | A–g Fault | |||||||
---|---|---|---|---|---|---|---|---|

Bus | $\left(\right)$ (p.u.) | $\left(\right)$ (p.u.) | $\left(\right)$ (p.u.) | $\left(\right)$ (p.u.) | ||||

Cal | RTDS | Cal | RTDS | Cal | RTDS | Cal | RTDS | |

4 | 0.549 | 0.556 | 0.549 | 0.556 | 0.634 | 0.641 | 0.460 | 0.468 |

6 | 0.571 | 0.580 | 0.491 | 0.499 | 0.658 | 0.666 | 0.394 | 0.401 |

10 | 0.742 | 0.750 | 0.504 | 0.510 | 0.812 | 0.817 | 0.420 | 0.428 |

Converter | $\left(\right)$ (p.u.) | $\left(\right)$ (p.u.) | $\left(\right)$ (p.u.) | $\left(\right)$ (p.u.) | ||||

1 | 0.306 | 0.301 | 0.102 | 0.096 | 0.269 | 0.264 | 0.114 | 0. 115 |

2 | 0.351 | 0.350 | 0 | 0 | 0.328 | 0.326 | 0 | 0 |

A–B Fault | A–g Fault | |||||||
---|---|---|---|---|---|---|---|---|

Bus | $\left(\right)$ (p.u.) | $\left(\right)$ (p.u.) | $\left(\right)$ (p.u.) | $\left(\right)$ (p.u.) | ||||

Cal | RTDS | Cal | RTDS | Cal | RTDS | Cal | RTDS | |

4 | 0.645 | 0.651 | 0.645 | 0.651 | 0.725 | 0.732 | 0.558 | 0.564 |

6 | 0.704 | 0.710 | 0.626 | 0.634 | 0.779 | 0.787 | 0.541 | 0.546 |

10 | 0.834 | 0.838 | 0.599 | 0.605 | 0.890 | 0.899 | 0.518 | 0.525 |

Converter | $\left(\right)$ (p.u.) | $\left(\right)$ (p.u.) | $\left(\right)$ (p.u.) | $\left(\right)$ (p.u.) | ||||

1 | 0.143 | 0.142 | 0.140 | 0.138 | 0.123 | 0.124 | 0.152 | 0.149 |

2 | 0.317 | 0.312 | 0 | 0 | 0.278 | 0.282 | 0 | 0 |

$\left(\right)open="|"\; close="|">{\dot{\mathit{V}}}^{+}$ (p.u.) | $\left(\right)open="|"\; close="|">{\dot{\mathit{V}}}^{-}$ (p.u.) | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

Bus | IDU | EDR | TJE | FER | TRI | LAG | IDU | EDR | TJE | FER | TRI | LAG |

Cal | 0.524 | 0.664 | 0.627 | 0.689 | 0.736 | 0.765 | 0.524 | 0.374 | 0.424 | 0.338 | 0.288 | 0.274 |

RTDS | 0.518 | 0.658 | 0.622 | 0.681 | 0.730 | 0.758 | 0.518 | 0.368 | 0.416 | 0.329 | 0.279 | 0.265 |

$\left(\right)open="|"\; close="|">{\dot{\mathit{V}}}^{+}$ (p.u.) | $\left(\right)open="|"\; close="|">{\dot{\mathit{V}}}^{-}$ (p.u.) | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

Bus | IDU | EDR | TJE | FER | TRI | LAG | IDU | EDR | TJE | FER | TRI | LAG |

Cal | 0.630 | 0.738 | 0.706 | 0.747 | 0.786 | 0.817 | 0.354 | 0.278 | 0.280 | 0.220 | 0.184 | 0.168 |

RTDS | 0.624 | 0.731 | 0.701 | 0.738 | 0.778 | 0.810 | 0.346 | 0.267 | 0.272 | 0.211 | 0.196 | 0.175 |

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## Share and Cite

**MDPI and ACS Style**

Jia, J.; Yang, G.; Nielsen, A.H.
Fault Analysis Method Considering Dual-Sequence Current Control of VSCs under Unbalanced Faults. *Energies* **2018**, *11*, 1660.
https://doi.org/10.3390/en11071660

**AMA Style**

Jia J, Yang G, Nielsen AH.
Fault Analysis Method Considering Dual-Sequence Current Control of VSCs under Unbalanced Faults. *Energies*. 2018; 11(7):1660.
https://doi.org/10.3390/en11071660

**Chicago/Turabian Style**

Jia, Jundi, Guangya Yang, and Arne Hejde Nielsen.
2018. "Fault Analysis Method Considering Dual-Sequence Current Control of VSCs under Unbalanced Faults" *Energies* 11, no. 7: 1660.
https://doi.org/10.3390/en11071660