# Single-Ended Protection Scheme for VSC-Based DC Microgrid Lines

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Pole-to-Pole Fault Characteristics of DC Microgrids

#### 2.1. Structures of DC Microgrids

#### 2.2. Fault Transient Stages

_{a}, u

_{b}, u

_{c}represent the AC voltage connected point. Under this fault condition, the capacitor discharges through the fault point (i

_{C}). As for the AC system, it is collapsed to a three-phase short-circuit because of the low impedance of DC lines. The converter is then blocked by its overcurrent protection. Therefore, the AC power would feed in the fault point through the parallel diodes in the VSC (i

_{VSC}) [18,19]. Because the equivalent circuit is nonlinear, it can be divided into four stages in detail for the mathematical analysis, as shown in Figure 4.

#### 2.3. DC Fault Analysis of VSC

_{0}and I

_{0}, the fault voltage and current can be solved as follows:

^{2}< 1/LC in Equation (4) if a metallic fault occurs, indicating $\omega ={\omega}_{0}$. The DC fault current of Equation (4) can therefore be rewritten simply as follows:

_{0}= 1 s, with the four stages each labeled.

## 3. Single-Ended Protection Scheme

#### 3.1. Requirements for Protection

_{1}suggests an internal fault, f

_{4}and f

_{5}suggest external forward faults, and f

_{2}and f

_{3}suggest backward DC faults. The role of protection at CB1 is to ensure the power transfer security and stability of the system under DC fault conditions. This is achieved by isolating the faulty segments in such way that the remaining healthy part operates normally. The characteristics of the terminal fault f

_{1}on line 12 are very similar to those of the terminal fault f

_{5}on line 24. In this aspect, the protection should be selective enough, sufficiently fast, reliable, and robust. In general, the transient characteristics of DC capacitors and inductors are important for designing a single-ended protection scheme. The scheme should satisfy the selectivity, speed, sensitivity, and reliability simultaneously. The action of protections should be made in 2 ms at stages 1 and 2.

#### 3.2. Startup Component

_{k}indicates the measured current, and k = 1, 2, …, N. N is the total number of sampling points in the time window. I

_{op_set}indicates the setting value, where normally I

_{op_set}= K

_{rel}I

_{rate}K

_{rel}, the reliability coefficient, is equal to 1.3–1.5, and I

_{rate}is the DC current rating.

#### 3.3. Directional Criterion

_{dc}. For the backward fault in Figure 8, however, the inductor current flows in the other direction. This paper proposes a practical directional criterion utilizing the voltage over the supplemental inductor to distinguish the forward faults from the backward faults, formulated as follows:

_{L}is the voltage of inductance L, and i

_{dc}is the reference current through the inductor as labeled in Figure 7 and Figure 8.

_{0}of less than zero, that is, $-\frac{\pi}{2}<\delta <0$, then $-\pi <\delta -\theta <0$ can hence be derived, which means the changing rate (Equation (10)) is greater than zero.

_{0}of greater than 0, the relationship between these two angles in Equation (11) should be further determined. Here some simulations using parameters from the projects were investigated, as shown in Figure 9. A typical group of parameters from a DC microgrid were chosen: U

_{0}= 1000 V, L

_{0}= 0.56 mH/km, R

_{0}= 0.078 Ohm/km, L

_{r}= 1 mH, and C = 2 mF. The fault distance varied from 0 to 30 km, and the initial current varied from 50 to 500 A. The mathematical analysis results show that the angle was always around −69° to −70°.

#### 3.4. Faulted Pole Selection

^{+}and CRU

^{−}represent the change rate coefficients of positive and negative pole voltages, respectively; K

_{U}is the ratio of CRU

^{+}to CRU

^{−}; u

^{+}(k) and u

^{−}(k) represent the kth samples of positive and negative pole voltages, respectively; u

_{0}

^{+}and u

_{0}

^{−}represent the initial voltages; N represents the number of samples in the time window of 2 ms; and the corresponding N is equal to 100 for the sampling frequency of 50 kHz.

^{+}coefficient is much greater than CRU

^{−}for a positive-pole-to-ground fault, ${K}_{\mathrm{U}}\gg 1$; on the other hand, CRU

^{+}is much smaller than CRU

^{−}for a negative-pole-to-ground fault, $0<{K}_{\mathrm{U}}<1$. When a pole-to-pole fault happens, ${K}_{\mathrm{U}}=1$ can be concluded theoretically. The ratio K

_{U}, therefore, can be taken as a faulted pole selection criterion in Equation (14). This criterion was generally useful in the various simulations, as an adequate margin was considered. To guarantee its reliability in industrial project usage, a further field test with project parameters is recommended.

#### 3.5. Identification of Fault Areas

_{2}and f

_{5}have similar features, as explained above. This section proposes a criterion to identify an internal fault on the basis of the idea of distance protection. For a pole-to-pole fault, at a distance x from CB1 on line 12, the time-domain equation containing the distance is Equation (15):

_{0}and R

_{0}are the inductance and resistance per kilometer of lines, respectively; L

_{r}is the supplemental inductance; and u

_{t}is the local measured voltage. The shunt capacitor of the line has been omitted for its limited contribution. The fault distance can then be solved for as follows:

## 4. Verification

#### 4.1. Simulation of Directional Criterion

_{1}at the terminal end (fault distance x = 900 m) of line 12, and the external fault f

_{5}at line 24 close to VSC2. The backward fault f

_{3}was located at line 13, which was near VSC1. As is seen from the results, the directional criterion could selectively distinguish the forward faults and backward faults by the threshold of 0.5 kV, the dashed line in Figure 13.

#### 4.2. Simulation of Faulted Pole Selection

_{U}values were all greater than 1.3 for positive-pole faults-smaller than the setting value of 0.7 and around 1.0 for pole-to-pole faults, which is demonstrated by Equation (14). The proposed faulted pole selection criterion works properly, regardless of the fault resistance and fault distance.

#### 4.3. Simulation of Fault Area Identification

#### 4.4. Sensitivity Analysis

#### 4.4.1. Influence of Signal Noise

_{U}was still greater than 1.3 for PG faults and smaller than 0.7 for NG faults even with the high level of additive noise. Meanwhile, the ratio for PP faults did not exceed either of the two thresholds. The results demonstrate that the proposed protection scheme has a high robustness to additive noise.

#### 4.4.2. Influence of Sampling Frequency

_{U}value calculated by the pole voltages at CB1 are presented in Figure 15. It is seen that K

_{U}was greater than 1.3 for PG faults and less than 0.7 for NG faults, even with a low level of sampling frequency. Meanwhile, the ratio for PP faults did not exceed either of the two thresholds. Therefore, the proposed protection scheme performs well, undisturbed by the sampling frequency.

## 5. Conclusions

## Author Contributions

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 4.**Four successive stages of transient response to pole-to-pole faults: (

**a**) Stage 1: Capacitor discharges through the line with diodes off. (

**b**) Stage 2: Capacitor discharges through the line with diodes on. (

**c**) Stage 3: Inductor discharges through the line with diodes on. (

**d**) Stage 4: Grid current feeds the DC link through the diodes.

**Figure 7.**The voltage of inductor for forward faults for CB1 in the multi-terminal system, taking a pole-to-pole fault as an example: f

_{1}on line 12 and f

_{5}on line 24. The DC faults i

_{2}and i

_{5}suggest the fault current through local sensors at CB1.

**Figure 8.**The voltage of inductor for the backward fault f

_{3}for CB1 in the multi-terminal system; i

_{3}suggests the fault current through local sensors at CB1.

**Figure 10.**Features of DC voltage of positive and negative poles during different fault types: (

**a**) Positive-pole-to-ground fault; (

**b**) Negative-pole-to-ground fault; (

**c**) Pole-to-pole fault.

**Figure 14.**Simulation results for the influence of signal noise: (

**a**) Positive-pole-to-ground (PG) fault; (

**b**) Negative-pole-to-ground (NG) fault; (

**c**) Pole-to-pole (PP) fault.

**Figure 15.**Simulation results for the influence of sampling frequency: (

**a**) Positive-pole-to-ground (PG) fault; (

**b**) Negative-pole-to-ground (NG) fault; (

**c**) Pole-to-pole (PP) fault.

Fault Type | x/m | R_{fault}/Ω | K_{U} | Fault Type | x/m | R_{fault}/Ω | K_{U} |
---|---|---|---|---|---|---|---|

Internal PG fault ^{1} | 100 | 0.1 | 29.8425 | Internal PP fault ^{1} | 100 | 0.1 | 1.0492 |

1 | 18.6964 | 1 | 1.0772 | ||||

500 | 0.1 | 17.9425 | 500 | 0.1 | 1.0375 | ||

1 | 12.1508 | 1 | 1.0575 | ||||

900 | 0.1 | 13.6224 | 900 | 0.1 | 1.0541 | ||

1 | 10.0290 | 1 | 1.0887 | ||||

Internal NG fault ^{1} | 100 | 0.1 | 0.0177 | External PP fault | 100 | 0.1 | 1.0832 |

1 | 0.0434 | 1 | 1.1373 | ||||

500 | 0.1 | 0.0131 | 500 | 0.1 | 1.0816 | ||

1 | 0.0421 | 1 | 1.1258 | ||||

900 | 0.1 | 0.0220 | 900 | 0.1 | 1.1132 | ||

1 | 0.0608 | 1 | 1.1763 |

^{1}PG (NG) fault: positive (negative)-pole-to-ground fault; PP fault: pole-to-pole fault.

Fault Type | x/m | R_{fault}/Ω | Results |
---|---|---|---|

Internal PG, NG, and PP faults | 100 | 0.1 | Internal |

1 | Internal | ||

500 | 0.1 | Internal | |

1 | Internal | ||

900 | 0.1 | Internal | |

1 | Internal | ||

External PG, NG, and PP faults | 100 | 0.1 | External |

1 | External | ||

500 | 0.1 | External | |

1 | External | ||

900 | 0.1 | External | |

1 | External |

^{1}PG (NG) fault: positive (negative)-pole-to-ground fault; PP fault: pole-to-pole fault.

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## Share and Cite

**MDPI and ACS Style**

Lv, C.; Zheng, X.; Tai, N.; Chen, S.
Single-Ended Protection Scheme for VSC-Based DC Microgrid Lines. *Energies* **2018**, *11*, 1440.
https://doi.org/10.3390/en11061440

**AMA Style**

Lv C, Zheng X, Tai N, Chen S.
Single-Ended Protection Scheme for VSC-Based DC Microgrid Lines. *Energies*. 2018; 11(6):1440.
https://doi.org/10.3390/en11061440

**Chicago/Turabian Style**

Lv, Cheng, Xiaodong Zheng, Nengling Tai, and Shi Chen.
2018. "Single-Ended Protection Scheme for VSC-Based DC Microgrid Lines" *Energies* 11, no. 6: 1440.
https://doi.org/10.3390/en11061440