# Research on multi-terminal traveling wave fault location method in complicated networks based on cloud computing platform

- Feng Deng
^{1}Email author, - Xiangjun Zeng
^{1}and - Lanlan Pan
^{2}

**2**:19

https://doi.org/10.1186/s41601-017-0042-4

© The Author(s) 2017

**Received: **31 December 2016

**Accepted: **13 March 2017

**Published: **10 May 2017

## Abstract

Cloud computing technology is used in traveling wave fault location, which establishes a new technology platform for multi-terminal traveling wave fault location in complicated power systems. In this paper, multi-terminal traveling wave fault location network is developed, and massive data storage, management, and algorithm realization are implemented in the cloud computing platform. Based on network topology structure, the section connecting points for any lines and corresponding detection placement in the loop are determined first. The loop is divided into different sections, in which the shortest transmission path for any of the fault points is directly and uniquely obtained. In order to minimize the number of traveling wave acquisition unit (TWU), multi-objective optimal configuration model for TWU is then set up based on network full observability. Finally, according to the TWU distribution, fault section can be located by using temporal correlation, and the final fault location point can be precisely calculated by fusing all the times recorded in TWU. PSCAD/EMTDC simulation results show that the proposed method can quickly, accurately, and reliably locate the fault point under limited TWU with optimal placement.

## Keywords

## 1 Introduction

With the development of smart grid, safe and reliable control and operation of the complicated grid have become more and more important. However, the existing fault location technology and massive data processing capacity cannot meet the demand of smart grid.

Traveling wave fault location has a fast response speed and is immune to distributed capacitance, system oscillation, and current transformer saturation, etc. Thus, compared to other kinds of fault location methods, it has obvious theoretical advantages. With the advancement of modern traveling wave theory and related technologies, traveling wave fault location has had significant development [1–5] and has a good prospect in practical applications.

Currently, traveling wave fault location method can be divided into two categories: local-based [6, 7] and network-based [8–14]. The local-based traveling wave fault location method is executed on a single line, which can be significantly affected by the operating status of the locating devices and interference signals. The method has high risk of miss-trip or mal-operation, and thus the reliability of fault location can’t be guaranteed. Network-based traveling wave fault location method collects large amount of data from TWU installed in all the substations, and fuses all the information to determine the exact fault position. This significantly improves the fault location reliability and guarantees high accuracy. Traveling wave fault location method based on the graph theory was presented in [8]. The complicated network can be simplified by using Floyd algorithm, and the initial traveling wave arrival times are uniquely matched with the transmission path. The exactly fault point is then calculated by information fusion technology. On this basis, the transmission path for the initial traveling wave is found by using adjacent point optimization algorithm in [9]. Based on the positive proportional relationship between transmission distance and transmission time, linear fitting is executed and the fault location is realized. However, all these methods need massive data pre-processing for each single fault, and loop simplification, data matching, and information fusion, which are complicated and unfeasible.

Based on the technical condition of smart grid and cloud computing, a multi-terminal traveling wave fault location algorithm for complicated networks is proposed based on cloud computing platform. According to the topology structure, the complicated loop can be divided into several sections, in which the shortest traveling wave transmission path is determined, and multi-objective optimal TWU configuration is realized based on network full observability. Because of the correlation of the initial traveling wave arrival times, fault section can then be defined. Finally, the exactly fault position is determined by converting all the recorded initial traveling wave arrival times and fusing converted ones. The proposed method determines the fault section and realizes optimal TWU configuration. It can directly obtain the shortest transmission path, which omits network simplification and the matching process for the shortest transmission path. The method guarantees accurate fault location and improves reliability, and only requires to install a portion of TWU in the complicated network.

## 2 Methods

### 2.1 Multi-terminal traveling wave fault location network based on cloud computing platform

Cloud computing [15–17] has the advantages of flexible service, resource pooling, service on demand, generalization access, which can satisfy the large-scale and parallel computation characteristics for power systems. It makes use of dispersive resources in different regions and unites the management by resources pooling. The way of management can also meet the uncertainty of computation. In the cloud computing platform, it allocates calculation resources base on the scale of the terminal load, thus avoiding the decrease of service quality. There is no need for precise understanding of the computing equipment, which significantly reduces operation complexity for users.

### 2.2 Analysis the relationship between topology structure and shortest transmission path

_{M}、 t

_{N}and the shortest transmission path L

_{MN}must be known.

_{MN}is the length of M-N. However, in a complicated network, L

_{MN}cannot be directly determined. As shown in Fig. 3, TWU is not installed in substations M and N. Thus, the initial traveling wave-front will pass through both ends of the substations and then transmit to the TWU installed in the distant substations X and Y (called detection point in the paper). L

_{XY}must satisfy the following condition: L

_{XY}= L

_{fX}+ L

_{fY}, where, L

_{fX}and L

_{fY}represent the shortest transmission path from the fault point f to the detection points X and Y, respectively. L

_{fX}、 L

_{fY}cannot be determined directly because of the existence of the loop. When a fault occurs in section O

_{2}N, the shortest transmission path is L

_{fX}= k

_{1}. While for a fault occurring in section MO

_{2}, the shortest transmission path is L

_{fX}= k

_{2}. Thus, in the loop, the shortest transmission path of the initial traveling wave-front varies with the fault section.

In addition, if the fault occurred within section O_{i}N, the initial traveling wave-front transmits to the detection point X via path k_{1} and to another detection point Y via the path k_{3}. Consequently, the calculated fault position is substation N, thus the fault location method is failed due to the blind spot.

- (1)
The transmission path for initial traveling wave is determined by network topology structure, and varies with difference fault section.

- (2)
In complicated network, based on double-terminal traveling wave fault location method, at least a pair of TWU in X and Y must be installed. The corresponding shortest transmission path L

_{fX}and L_{fY}must from f via substation M or N to the TWU located at X or Y. In this condition, the complicated network has full observability

### 2.3 Multi-objective optimal TWU configuration method

#### 2.3.1 Searching section connecting point

The key point of the Eq. (2) is on the determination of whether the initial traveling wave-front will pass through via fault starting point M or N, which must meet the following relationships:

_{i}is the section connecting point of the line M-N corresponding to the detection point X. It can divide the line M-N into several sections: [O

_{M}, O

_{1}], [O

_{1}, O

_{2}], ……, [O

_{N-2}, O

_{N-1}], [O

_{N-1}, O

_{N}]. For a fault within section [O

_{i-1}, O

_{i}], the shortest transmission path of the initial traveling wave-front can be uniquely determined.

- (1)
When

*l*_{ NX }=*l*_{ MN }+*l*_{ MX }, \( {l}_{M{ O}_i}={\mathrm{l}}_{M N} \). The section connecting point O_{i}is located at substation N. If a fault occurs within section [O_{N-1}, O_{N}], the shortest transmission paths are all via substation M. The area [O_{N-1}, O_{N}] is a fault location blind spot, as seen in Fig. 3. - (2)
When

*l*_{ MX }=*l*_{ MN }+*l*_{ NX }, \( {l}_{M{ O}_i}=0 \). The section connecting point O_{i}is located at substation M. If a fault occurs within section [O_{M}, O_{1}], the shortest transmission paths are all via substation N. The area [O_{M}, O_{1}] is thus a fault location blind spot, as seen in Fig. 3.

Thus, the area [O_{1}, O_{N-1}] is observable, but the areas [O_{M}, O_{1}] 、 [O_{N − 1}, O_{N}] are the blind areas. Therefore, if a line is fully observable, the section connecting point should both have O_{N} and O_{M}.

#### 2.3.2 Multi-objective optimal configuration method

Based on the above analysis, TWUs can be optimally configured by setting up multi-objective models.

_{M}] or [G

_{N}] stand for the initial traveling wave transmission path via starting fault point M or N to the remote TWU. Substation array [T

_{i}] is then set up, indicating substations with installed TWU. Binary coding for [G

_{M}] 、 [G

_{N}] and [T

_{i}] are listed in Tables 1 and 2.

Initial traveling wave-front transmission path array [G]

Array | Binary code | Explanation |
---|---|---|

[G | 1 | Initial traveling wave transmission path via starting fault point M to remote TWU |

0 | Initial traveling wave transmission path via starting fault point N to remote TWU | |

[G | 0 | Initial traveling wave transmission path via starting fault point M to remote TWU |

1 | Initial traveling wave transmission path via starting fault point N to remote TWU |

Substation array [T]

Array | Binary code | Explanation |
---|---|---|

[T | 1 | Substation i installed TWU |

0 | Substation i without TWU |

Multi-objective optimal configuration model I and II are equal. The more constraints they have, the easier the problem is solved.

- (1)
Because blind area is located at the terminal of the lines, such as [O

_{M}, O_{1}] and [O_{N−1}, O_{N}] in Fig. 3, it is necessary to installed extra TWU in substation M and N. It can use single-terminal fault location principle to locate the fault occurs at the blind area. - (2)
For local center substation, if the number of out and in feeders is more than 4, TWU shall be installed.

- (3)
The terminal substations must install TWU.

### 2.4 Multi-terminal traveling wave fault location method

#### 2.4.1 Determination of fault section

Due to the unknown fault position, it is necessary to judge the fault section based on the traveling wave-front signal recorded in the detection point.

_{i}. Taking the section (O

_{i–1}, O

_{i}) as a reference, it can divide all the substations with TWU installed into two Detection Arrays [I]

_{N}and [I]

_{M}. Thus, Initial traveling wave-front arrival times recorded by the substations from Detection Arrays [I]

_{N}and [I]

_{M}form Computation Time Arrays [t]

_{N}and [t]

_{M}. Because of the temporal correlation, the transmission times that initial traveling wave-front passes through the starting point M or N to any substation in the Detection Arrays can be calculated as follows:

_{NX}and L

_{MY}can be obtained from the topology structure, and v

_{NX}and v

_{MY}are the univariate functions of the distance that can be calculated online

^{[23]}.

_{N}and [t]

_{M}satisfy Eq. (9), it means that the fault point is within section (O

_{i–1},O

_{i}). Thus the shortest transmission path can be uniquely determined.

_{i}and t

_{j}are the initial traveling wave arrival times recorded by the substations from Detection Arrays [I]

_{N}and [I]

_{M}, respectively. Both T

_{iM}and T

_{iN}can be calculated using Eq. (8). Considering the errors caused by different influence factors, a margin

*δ*is taking into consideration in Eq. (9), and its nominal value is 0.5us.

#### 2.4.2 Multi-terminal fault location algorithm

_{i}, t

_{j}are from Computation Time Array [t]

_{N}and [t]

_{M}respectively, and L

^{min}

_{ij}is the shortest transmission line between substations i and j.

Converting the fault distance d_{fi} to one of the terminals M of the fault line, d_{fM} can be calculated by Eq. (11), where l_{Mi} is the distance between substation i with installed TWU and the reference terminal M.

_{N}and [I]

_{M}can calculate the fault location d

_{fi}and d

_{fM}, and then fuse all the calculated d

_{fM}using weightings as:

The principle for setting the weights is dependent on the fault line. The substations, which are joined by the fault line directly, has its weight set to 1, and the rest of the substations have their weights set to 1/(n + 1), where n is the substation sequence numbers passing the shortest path from the fault line.

## 3 Results and simulation

### 3.1 Simulation model

### 3.2 Realization for the optimal TWU configuration

#### 3.2.1 Step 1: searching section connecting points

Figure 4 shows the IEEE 30-bus testing system, which has 41 lines and 30 substations. Assuming each substation installs TWU, the section connecting points and their corresponding substations can be calculated based on Eqs. (3) and (4) using Dijkstra. The calculation results are shown in Table 5 in Appendix A.

From Table 5, it can be seen that the whole network is fully observable because the section connecting point both have O_{N} and O_{M}

#### 3.2.2 Step 2: multi-objective optimal configuration realization

Based on the section connecting points and their corresponding substations, a matrix [H_{L×2}](1 ≤ L ≤ 41) can be obtained. The first column is the minimum section connecting point O_{M}, while the second column is the maximum section connecting point O_{N}. The matrix [H_{L×2}] is shown in Table 6 in Appendix A.

_{M}]

_{L}/[O

_{N}]

_{L}is 1, the substation must install TWU, and matrix [A] is obtained. For the IEEE 30-bus testing system, matrix [A] is as follows:

_{M}and [A]

_{N}are formed as:

The minimum sharing sets between [A]_{M} and [A]_{N} are then searched, i.e. [5,7], [16,17], [1,2], [18,19] in this case. One substation in each of the matrix is chosen to install TWU.

For substations in the matrix [1,2], [5,7], [16,17], [18,19], it is desirable to install TWU in local center substations 2, 5, 17 and 18.

Finally, the optimal TWU configuration is in the following 13 substations: 2,3,5,8,11,13,14,17,18,21,26,29,30, as shown in Fig. 4(b).

### 3.3 Realization for the multi-terminal traveling wave fault location

#### 3.3.1 Step 3: fault section judgment

_{2},O

_{3}).

Initial traveling wave arrival times recorded in substations installed TWU

TWU | Initial traveling wave arrival time/us | TWU | Initial traveling wave arrival time/us |
---|---|---|---|

2 | 1071.92 | 17 | 1082.19 |

3 | 154.10 | 18 | 1267.12 |

5 | 1246.58 | 21 | 1821.92 |

8 | 1243.15 | 26 | 2845.89 |

11 | 1376.71 | 29 | 2452.05 |

13 | 277.40 | 30 | 1715.75 |

14 | 993.15 |

#### 3.3.2 Step 4: calculation of the fault position

First, it calculates the fault distance d_{fi}, and then converts the fault distance to the reference terminal 3 of the fault line: d_{f3}. Weights are applied for each substation installed with TWU, and the final fault location can be calculated using Eq. (12). Thus, the final fault point is located at 45.078 kM from substation 3, and the absolute error is 0.078 kM.

## 4 Conclusion

- (1)
A multi-objective optimal TWU configuration method is proposed based on network full observability and minimum number of TWU, which significantly decrease the one-off investment.

- (2)
A novel traveling wave fault location method is presented in the paper. The method can directly match the shortest transmission path without the need for simplifying complicated loops and matching steps, and is immune to fault position and topology structure. It can be easily realized and has strong feasibility.

- (3)
The proposed method can achieve precise fault location with only limited numbers of TWU and can effectively improve the economics and practice for the multi-terminal traveling wave fault location system.

## Declarations

### Acknowledgement

Project supported by the Key Project of Smart Grid Technology and Equipment of National Key Research and Development Plan of China (2016YFB0900600), Project supported by the National Natural Science Foundation Fund for Distinguished Young Scholars(51425701), the National Natural Science Foundation of China(51207013), the Hunan Province Natural Science Fund for Distinguished Young Scholars(2015JJ1001), the Education Department of Hunan Province Project(15C0032).

### Competing interests

No conflict of interest exits in the submission of this manuscript, and manuscript is approved by all authors for publication. I would like to declare on behalf of my co-authors that the work described was original research that has not been published previously, and not under consideration for publication elsewhere, in whole or in part. All the authors listed have approved the manuscript that is enclosed.

### Authors’ contributions

FD writing paper; propose the new method; simulation analysis. XJZ is the supervisor the first author; revise the whole paper. LLP revises the simulation analysis. All authors read and approved the final manuscript.

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## Authors’ Affiliations

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