# Fault Sensing Using Fractal Dimension and Wavelet
## 1 Introduction  
It is important for power systems to run without faults. However, different types of faults often occur [1; 2].  
In neutral grounded power systems, single-phase ground faults account for 70%-80%, two-phase faults and two-phase ground faults account for 10%, and three-phase faults account for 5% of all faults that occur. Ground faults account for 90% of cases and the single-phase ground faults account for 84% of cases [3; 4; 5].  
In most of the literature, the online cable recognition methods concentrate on fractal theory, wavelet transform, neural network, genetic algorithms, and chaos theory. However, the research results can only be achieved in laboratory conditions [6].  
Fractal methods have developed rapidly in recent years due to good adaptation and good cross properties [7; 8; 9]. Scientists often combine it with other methods for signal processing [10]. More and more scholars are studying the fault diagnosis methods for power systems by combining fractal theory with other theories. For example, one research group used fractal theory and spectral analysis to select the single-phase fault phase in a small current grounded system [11]. In addition, researchers have compared the fractal dimensions of the transient currents between the fault phase and the non-fault phase to recognize the single-phase fault [12; 13]. Other researchers studied the state features of the transient signals of the high frequencies; these signals were caused by power system faults. The researchers combined the chaos theory with the fractal theory to analyze and classify the operational state of the power system [14; 15; 16; 17].  
On the other hand, wavelet theory is one of the outstanding achievements of mathematics research. It has been applied extensively in non-linear field theory. Wavelet analysis possesses localizedcharacteristics in the time-frequency domain. It can highlight mutative components of the processed signals by flexibly changing the window of the time-frequency domain, and can then extract the power cable fault information effectively [18; 19; 20; 21]. After comparing the wavelet modulus difference of the target traveling wave from the two ends, the fault type can be recognized [22]. However, this method fails to select the faulty phases of two-phase grounded faults. However, the fault type could be recognized according to the relationship between the amplitudes of the current modules [23]. Another study proposed a fault location method based on the genetic algorithm using the transient components of three-phase currents [24]. These methods have made great contributions to fault detection in power systems. However, these methods are still in the theoretical stages and have not been used in practice.  
Based on the aforementioned methods, a new fusion sensing (FS) method was proposed by using the improved fractal dimension and a developed maximum wavelet modulus for short-circuit fault recognition of online power cables in this paper.  
The organization of this paper is as follows: Short-circuit fault components in online power cables are described in Section 2. The improved fractal box dimension (IFBD) recognition algorithm is proposed in Section 3. The developed maximum wavelet coefficient (DMWC) recognition algorithm is described in Section 4. The FS method is proposed by combining the IFBD algorithm and the DMWC algorithm in Section 5. The analysis of the experiment and the results are reported in Section 6, which includes three cases of different initial angles, different transient resistances, and different fault distances. The conclusions are drawn in Section 7.