## 10 Conclusions  
This paper introduced a method for the detection and classification of faults in a power network integrated with solar energy. The detection of various faults, including phase to ground, double-phase  
Figure 16: Transmission network of Bhadla region of Rajasthan state in India.  
Figure 17: Fault index with AG fault on 400 kV bus of 400 kV GSS Bhadla, Rajasthan, India.  
fault, double phases to ground and three-phase fault with and without the involvement of solar energy, were successfully achieved using the proposed fault index. This FI was obtained using the Wigner distribution function (WD-index) and the alienation coefficient (ALN-index)-based decomposition of the current signals. The classification of the faults was achieved using the number of faulty phases which were identified using the proposed FI. However, a ground fault index based on the Wigner distribution function supporting the decomposition of negative sequence current is used for the discrimination of a double-phase fault and double phase to ground fault. It can be concluded that the algorithm is fast and accurate for the detection of all types of faults in the presence of SE in the grid. This algorithm works effectively in the presence of a high level noise, different fault incidence angles, transformers with different types of windings, high fault impedance and different fault locations. The algorithm is also effective in the discrimination of switching transients due to the capacitor switching, load switching and feeder tripping/reclosing from the faulty transients. Its performance is not affected by the presence of hybrid lines consisting of OH line and UG cable sections. The algorithm was successfully validated in a real-time network of Rajasthan state in India. It is also established that the performance of the proposed algorithm is better compared to the DWT, WPT and Stockwell transform at providing protection to the grid with solar energy penetration. As a future enhancement, more complex hybrid systems can also be utilized to test the developed method.  
Conceptualization, S.R.O., O.P.M., A.S. and S.K.G.; methodology, S.R.O. and O.P.M.; software, S.R.O. and O.P.M.; validation, S.R.O. and O.P.M.; formal analysis, S.R.O., B.K. and O.P.M.; investigation, S.R.O. and O.P.M.; resources, A.S., S.K.G., S.K.J., H.H.A.; data curation, S.R.O., B.K. and O.P.M.; writing-original draft preparation, S.R.O., B.K. and O.P.M.; writing-review and editing, B.K. and H.H.A.; visualization, B.K., H.H.A. and P.S.; supervision, A.S., S.K.G., S.K.J., H.H.A., and P.S. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding  
The authors declare that they have no known conflicts of interest.  
Abbreviations used in this article are detailed below:  
Alienation  
ANN Artificial neural network  
CB Circuit breaker  
CNN Convolution neural network  
DG Distributed generation  
DWT Discrete Wavelet transform  
ES Expert system  
FI Fault index  
FRDFT Fast recursive discrete Fourier transform  
FT Fuzzy set theory  
GFI Ground fault index  
GSS Grid substation  
IEEE Institute of Electrical and Electronics Engineers  
OH Overhead  
LFS Load flow study  
MATLAB Matrix laboratory  
MPPT Maximum power point tracking  
PR Protection relay  
PV Photovoltaic  
SE Solar energy  
SNR Signal to noise ratio  
SPS Special protection scheme  
TGFI Threshold of the ground fault index  
UG UndergroundWD Wigner distribution WPT Wavelet packet transform