# Dir-MUSIC Algorithm for DOA Estimation of Partial Discharge Based on Signal Strength Represented by Antenna Gain Array Manifold

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Dir-MUSIC Algorithm

#### 2.1. Derivation

#### 2.2. CRLB of the Direction Estimation

## 3. Simulation Research on Algorithm Performance

#### 3.1. Relation between Incoming Wave Direction Estimation and SNR

#### 3.2. Research on Direction-Finding Performance under the Condition of Array Manifold Error

#### 3.3. Relation between Incoming Wave Direction Estimation and Number of Array Element

#### 3.4. Comparison with the Method Based on Phase Information

## 4. Experimental System Construction and Positioning Test

#### 4.1. Experimental System Construction

#### 4.2. Positioning Experiment

## 5. Conclusions

## Author Contributions

## Funding

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

- Robles, G.; Fresno, J.M.; Sánchez-Fernández, M.; Martínez-Tarifa, J.M. Antenna Deployment for the Localization of Partial Discharges in Open-Air Substations. Sensors
**2016**, 16, 541. [Google Scholar] [CrossRef] - Li, J.; Zhang, X.; Han, X.; Yao, X. A Partial Discharge Detection Method for SF6 Insulated Inverted Current Transformers Adopting Inner Shield Case as UHF Sensor. IEEE Trans. Power Deliv.
**2018**, 33, 3237–3239. [Google Scholar] [CrossRef] - Moore, P.J.; Portugues, I.E.; Glover, I.A. Radiometric location of partial discharge sources on energized high-Voltage plant. IEEE Trans. Power Deliv.
**2005**, 20, 2264–2272. [Google Scholar] [CrossRef] - Zhang, F.; Wei, B.; Liang, B.; Wang, H.; Wang, B.; Feng, G. Simulation comparison of SSE and TDOA methods for UHF direction finding of partial discharge in substation area. Energy Rep.
**2020**, 6, 416–423. [Google Scholar] [CrossRef] - Li, J.; Han, X.; Liu, Z.; Yao, X. A Novel GIS Partial Discharge Detection Sensor with Integrated Optical and UHF Methods. IEEE Trans. Power Deliv.
**2018**, 33, 2047–2049. [Google Scholar] [CrossRef] - Markalous, S.M.; Tenbohlen, S.; Feser, K. Detection and location of partial discharges in power transformers using acoustic and electromagnetic signals. IEEE Trans. Dielectr. Electr. Insul.
**2008**, 15, 1576–1583. [Google Scholar] [CrossRef] - Ha, S.; Cho, J.; Lee, J. Numerical Study of Estimating the Arrival Time of UHF Signals for Partial Discharge Localization in a Power Transformer. J. Electromagn. Eng. Sci.
**2018**, 18, 94–100. [Google Scholar] [CrossRef] - Li, Z.; Luo, L.; Sheng, G.; Liu, Y.; Jiang, X. UHF partial discharge location method in substation based on dimension-reduced RSSI fingerprint. Iet Gener. Transm. Distrib.
**2018**, 12, 398–405. [Google Scholar] [CrossRef] - Desai, B.M.A.; Sarathi, R. Identification and localisation of incipient discharges in transformer insulation adopting UHF technique. IEEE Trans. Dielectr. Electr. Insul.
**2018**, 25, 1924–1931. [Google Scholar] [CrossRef] - Polak, F.; Sikorski, W.; Siodla, K. Location of partial discharges sources using sensor arrays. In Proceedings of the International Conference on High Voltage Engineering and Application, Poznan, Poland, 8–11 September 2014; pp. 1–4. [Google Scholar]
- Huang, J.; Wang, J.; Tan, Y.; Wu, D.; Cao, Y. An Automatic Analog Instrument Reading System Using Computer Vision and Inspection Robot. IEEE Trans. Instrum. Meas.
**2020**, 69, 6322–6335. [Google Scholar] [CrossRef] - Cho, K.H.; Kim, H.M.; Jin, Y.H.; Liu, F.; Moon, H.; Koo, J.C.; Choi, H.R. Inspection Robot for Hanger Cable of Suspension Bridge: Mechanism Design and Analysis. IEEE/ASME Trans. Mechatronics
**2013**, 18, 1665–1674. [Google Scholar] [CrossRef] - Katrasnik, J.; Pernus, F.; Likar, B. A Survey of Mobile Robots for Distribution Power Line Inspection. IEEE Trans. Power Deliv.
**2010**, 25, 485–493. [Google Scholar] [CrossRef] - Lorenz, R.G.; Boyd, S.P. Robust minimum variance beam forming. IEEE Trans. Signal Process.
**2005**, 53, 1684–1696. [Google Scholar] [CrossRef] [Green Version] - Richmond, C.D. Capon–Bartlett cross-spectrum and a perspective on robust adaptive filtering. Signal Process.
**2020**, 171, 107473. [Google Scholar] [CrossRef] - Roy, R.; Kailath, T. ESPRIT-estimation of signal parameters via rotational invariance techniques. IEEE Trans. Acoust. Speech Signal Process.
**1989**, 37, 984–995. [Google Scholar] [CrossRef] [Green Version] - Schmidt, R. Multiple emitter location and signal parameter estimation. IEEE Trans. Antennas Propag.
**1986**, 34, 276–280. [Google Scholar] [CrossRef] [Green Version] - Forster, P.; Ginolhac, G.; Boizard, M. Derivation of the theoretical performance of a Tensor MUSIC algorithm. Signal Process.
**2016**, 129, 97–105. [Google Scholar] [CrossRef] [Green Version] - Stoica, P.; Nehorai, A. MUSIC, maximum likelihood, and Cramer-Rao bound. IEEE Trans. Acoust. Speech Signal Process.
**1989**, 1176, 032001. [Google Scholar] [CrossRef] - Rao, B.D.; Hari, K.V.S. Performance analysis of Root-Music. IEEE Trans. Acoust. Speech Signal Process.
**1989**, 37, 720–741. [Google Scholar] [CrossRef] - Rangarao, K.V.; Venkatanarasimhan, S. gold-MUSIC: A Variation on MUSIC to Accurately Determine Peaks of the Spectrum. IEEE Trans. Antennas Propag.
**2013**, 61, 2263–2268. [Google Scholar] [CrossRef] - Wang, Y.; Chen, J.; Fang, W. Joint estimation of DOA and delay using TST-MUSIC in a wireless channel. IEEE Signal Process. Lett.
**2001**, 8, 58–60. [Google Scholar] [CrossRef] - Yan, F.; Jin, M.; Qiao, X. Low-Complexity DOA Estimation Based on Compressed MUSIC and Its Performance Analysis. IEEE Trans. Signal Process.
**2013**, 61, 1915–1930. [Google Scholar] [CrossRef] - Lin, J.D.; Fang, W.H.; Wang, Y.Y.; Chen, J.T. FSF MUSIC for Joint DOA and Frequency Estimation and Its Performance Analysis. IEEE Trans. Signal Process.
**2006**, 54, 4529–4542. [Google Scholar] [CrossRef] - Gunjal, M.M.; Raj, A.A.B. Improved Direction of Arrival Estimation Using Modified Music Algorithm. In Proceedings of the International Conference on Communication and Electronics Systems (ICCES), Coimbatore, India, 10–12 June 2020; pp. 249–254. [Google Scholar]
- Liu, Q.; Zhu, M.X.; Wang, Y.B.; Deng, J.B.; Li, Y.; Zhang, G.J.; Zhao, X.F. UHF antenna array arrangement optimization for partial discharge direction finding in air-insulted substation based on phased array theory. IEEE Trans. Dielectr. Electr. Insul.
**2017**, 24, 3657–3668. [Google Scholar] [CrossRef] - Pang, X.; Wu, H.; Li, X.; Qi, Y.; Jing, H.; Zhang, J.; Xie, Q. Partial discharge ultrasonic detection based on EULER-MUSIC algorithm and conformal array sensor. IET Gener. Transm. Distrib.
**2018**, 12, 3596–3605. [Google Scholar] [CrossRef] - Li, Q.; Wang, N.; Yi, D. Numerical Analysis; Tsinghua University Press: Beijing, China, 2001; pp. 52–58. [Google Scholar]

**Figure 4.**Direction-finding error in different directions (SNR = −10). (

**a**) Error scatter plot. (

**b**) Error box diagram.

**Figure 6.**Array diagram and AGAR with different number of elements. (

**a**) Array diagram. (

**b**) AGAR (N = 8). (

**c**) AGAR (N = 4).

SNR | 10 | 5 | 0 | −5 | −10 |
---|---|---|---|---|---|

Accuracy | 100% | 100% | 100% | 99.17% | 72.78% |

SNR | 10 | 5 | 0 | −5 | −10 |
---|---|---|---|---|---|

Accuracy | 100% | 100% | 98.17% | 85.62% | 47.67% |

SNR | 10 | 5 | 0 | −5 | −10 |
---|---|---|---|---|---|

Accuracy of the proposed method | 100% | 100% | 100% | 99.17% | 72.78% |

Accuracy of the phase method | 100% | 100% | 97.44% | 76.75% | 39.00% |

Sample Rate | 1 G | 500 M | 100 M |
---|---|---|---|

Accuracy of the proposed method | 100% | 91.64% | 79.97% |

Accuracy of the phase method | 97.22% | 72.33% | 56.25% |

Real PD Coordinates | Mean of Calculated Angle | Mean of Angle Error | Standard Deviation of Angle Error |
---|---|---|---|

$(7.5,-{96}^{\xb0})$ | $-95.{25}^{\xb0}$ | $0.{75}^{\xb0}$ | $1.{68}^{\xb0}$ |

$(7.5,-{66}^{\xb0})$ | $-73.{55}^{\xb0}$ | $-7.{55}^{\xb0}$ | $1.{43}^{\xb0}$ |

$(7.5,-{19}^{\xb0})$ | $16.{8}^{\xb0}$ | $2.{20}^{\xb0}$ | $0.{41}^{\xb0}$ |

$(7.5,-{10}^{\xb0})$ | $-17.{1}^{\xb0}$ | $-7.{10}^{\xb0}$ | $0.{31}^{\xb0}$ |

$(7.5,{10}^{\xb0})$ | $13.{85}^{\xb0}$ | $3.{85}^{\xb0}$ | $0.{58}^{\xb0}$ |

$(7.5,{17}^{\xb0})$ | $16.{2}^{\xb0}$ | $-0.{80}^{\xb0}$ | $0.{95}^{\xb0}$ |

$(7.5,{28}^{\xb0})$ | $23.{65}^{\xb0}$ | $-4.{35}^{\xb0}$ | $2.{48}^{\xb0}$ |

$(7.5,{93}^{\xb0})$ | $93.{70}^{\xb0}$ | $0.{70}^{\xb0}$ | $0.{57}^{\xb0}$ |

$(14,-{90}^{\xb0})$ | $-93.{15}^{\xb0}$ | $-3.{15}^{\xb0}$ | $2.{11}^{\xb0}$ |

$(18.9,17.{5}^{\xb0})$ | $22.{05}^{\xb0}$ | $3.{45}^{\xb0}$ | $7.{50}^{\xb0}$ |

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Xu, W.; Chen, B.; Li, Y.; Hu, Y.; Li, J.; Zeng, Z.
Dir-MUSIC Algorithm for DOA Estimation of Partial Discharge Based on Signal Strength Represented by Antenna Gain Array Manifold. *Sensors* **2022**, *22*, 5406.
https://doi.org/10.3390/s22145406

**AMA Style**

Xu W, Chen B, Li Y, Hu Y, Li J, Zeng Z.
Dir-MUSIC Algorithm for DOA Estimation of Partial Discharge Based on Signal Strength Represented by Antenna Gain Array Manifold. *Sensors*. 2022; 22(14):5406.
https://doi.org/10.3390/s22145406

**Chicago/Turabian Style**

Xu, Wencong, Bingshu Chen, Yandong Li, Yue Hu, Jianxun Li, and Zijing Zeng.
2022. "Dir-MUSIC Algorithm for DOA Estimation of Partial Discharge Based on Signal Strength Represented by Antenna Gain Array Manifold" *Sensors* 22, no. 14: 5406.
https://doi.org/10.3390/s22145406