# Application of Shannon Wavelet Entropy and Shannon Wavelet Packet Entropy in Analysis of Power System Transient Signals

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## Abstract

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## 1. Introduction

## 2. Application of SWE and SWPE in a Power System

#### 2.1. Application of SWE in a Power System

#### 2.2. Application of SWPE in a Power System

#### 2.3. Problems Existed in SWE and SWPE in a Power System

- When the measured signal is more complex and contains a lot of random signals, there is the severe energy leakage and frequency aliasing in the wavelet coefficients (or reconstructed signals) with increasing of the wavelet decomposition scale [32]. So, the complexity and feature of signal can not be accurately expressed when the adjacent wavelet coefficients (or reconstructed signals) are taken as basic data to participate in the calculation of SWE and SWPE.
- When most signal components concentrate in the high frequency band, due to the roughness of wavelet decomposition in the high frequency band, the high frequency components of similar frequency will be in the same scale and calculation accuracy of SWE is directly reduced.
- For feature extraction of different transient signals, the studies, about the relationship between different entropy statistical properties and the signal feature, are still in the initial stage, which needs theoretical basis to support the transient signal extraction.
- For the different transient signals, sampling frequency of signals and wavelet decomposition scale exert influence on the accuracy and speed of feature extraction, but there has been no relevant research lately.

## 3. Comparison of Feature Extraction Accuracy and Wavelet Aliasing Effect on SWE and SWPE

#### 3.1. Comparison in Accuracy of Feature Extraction for SWE and SWPE

#### 3.2. Wavelet Aliasing Effect on SWE and SWPE

## 4. Conclusions

- Basic theory about analysis and operation mechanism of transient signals based on wavelet and different entropy should be deeply studied and improved. For the negative influence of wavelet aliasing on SWE and SWPE, selecting different entropy of various statistical properties, optimizing the parameter of entropy, adjusting sampling frequency and selecting different orthogonal wavelet bases should be considered to reduce the effect of wavelet aliasing on accuracy of feature extraction.
- When SWE and SWPE are applied to relay protection, there are some difficulties such as high sampling rate, complex calculation, etc. So, engineering applications put forward higher requirements for the ability of real time application. The further researches should focus on the optimizing algorithm structure and the improving operation speed of SWE and SWPE.

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 3.**Partial discharge (PD) detection process. (

**a**) Working principle diagram of high frequency current transformer (HFCT); (

**b**) Schematic diagram of PD detection system.

**Figure 9.**Relation between Renyi entropy with different values of q and probability distribution. (

**a**) q = 0.1; (

**b**) q = 0.5; (

**c**) q = 0.99; (

**d**) q = 2.

Model | Cable Core | Cross-Sectional Area | Insulation Layer | Metal Sheath | The Voltage Rating |
---|---|---|---|---|---|

YJLW03 | Coppersplicing wire | 800 mm² | XLPE | Aluminum | 127 kV/220 kV |

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**MDPI and ACS Style**

Chen, J.; Dou, Y.; Li, Y.; Li, J.
Application of Shannon Wavelet Entropy and Shannon Wavelet Packet Entropy in Analysis of Power System Transient Signals. *Entropy* **2016**, *18*, 437.
https://doi.org/10.3390/e18120437

**AMA Style**

Chen J, Dou Y, Li Y, Li J.
Application of Shannon Wavelet Entropy and Shannon Wavelet Packet Entropy in Analysis of Power System Transient Signals. *Entropy*. 2016; 18(12):437.
https://doi.org/10.3390/e18120437

**Chicago/Turabian Style**

Chen, Jikai, Yanhui Dou, Yang Li, and Jiang Li.
2016. "Application of Shannon Wavelet Entropy and Shannon Wavelet Packet Entropy in Analysis of Power System Transient Signals" *Entropy* 18, no. 12: 437.
https://doi.org/10.3390/e18120437