1. APPLICATION OF NEURAL NETWORKS AND WAVELET TRANSFORMS IN HIGH IMPEDANCE FAULT DETECTION IN ELECTRICAL SYSTEMS
A. M. Sharaf, SMIEEE
S. M. A. Saleem
Department of Electrical and Computer Engineering
University of New Brunswick

2. Introduction - High Impedance Fault (HIF)
Definition : A High impedance fault (HIF) or Arc type fault is usually caused when a current carrying-wire or conductor inadvertently makes a non-solid or temporary-contact with the ground or is temporarily short-circuited with another current carrying conductor through a high impedance medium.
Examples of HIF-Arc fault :
A cable lying and touching the ground.
A tree branch touching one or two power cables.

3. Research Objectives and Methods
1. Investigate the best selection of mother wavelet, which best depicts the pattern of the High Impedance arc type fault for the Wavelets based fault detection.
2. Investigate the level of Fault diagnostic signal decomposition, which would yield good characteristic patterns for arc type HIF using the Wavelets based relaying scheme.

4. Research Objectives and Methods - cont.
3. Optimize the Neural Network architecture vis-à-vis the number of hidden layers, activation functions and the number of neurons for the Wavelets based fault detection.
4. Investigate an effective training algorithm to be adopted for training the Neural Network for the Wavelets based fault detection.
5. Design and validate a Neural Network based relaying scheme structure in Matlab/ Simulink for the Wavelets based fault detection scheme.

5. Matlab / Simulink HIF Model
The current-dependant-resistance nonlinearity is incorporated by a simple current dependent nonlinear resistance ‘Rf’ developed by Dr. Sharaf and defined as,
Eq (1)
where Rf0 = 100 Ω, Rf1 = 50 to 150 Ω, if0 = 70 A, α = 0.3 to 0.7, β = 2, Rf is usually high.
Arc-current extinction and re-ignition nonlinearity is incorporated by using a dead zone nonlinear function.
Arc current asymmetry is incorporated by modifying the ‘start’ and ‘end’ of the dead zone function such that the HIF current’s positive half cycle is greater than the negative half cycle.

6. Radial Electric Utility Distribution System - Single Line Diagram
Vs = 25 kV (L-L), Ls = 7 mH, Rs = 0.7 Ω, Rline = 0.25 Ω / km, Lline = mH / km, Cline = μF / km, l = 25 km, x = 0 to 25 km, Rload = 72 to 144 Ω, Lload = to H.
Figure 1. Single Line Diagram of a Radial Transmission / Utilization System (25 kV) with fault location (x). PT, CT are located at feeder bus Va.

7. Radial Electric Utility Distribution System - Per phase Equivalent Diagram
Figure 2. Simple per phase equivalent HIF – Arc fault lumped parameter circuit for Radial Distribution System used in digital simulations (developed by Dr. Sharaf).

8. Radial Electric Utility Distribution System - Functional Block Diagram
Figure 3. Functional block model of HIF – Arc fault in a Radial Distribution System.

9. Radial Electric Utility Distribution System - Functional Block Diagram
Figure 4. Dialog box for High impedance – Arc fault model for Radial Distribution System.

10. Digital Simulation - Radial System
TABLE I
TRAINING AND VALIDATION DATA FOR RADIAL AC SYSTEM
(50 CASE STUDIES)
H = HIF, L = Linear fault, B = Bolted fault, N = Normal operation, TR =Training, TS = Testing, x = distance to fault, 1) Ref. Eq. (1), 2) Ref. Figure 1.

11. Wavelets Transform
FFT has its limitations. The biggest drawback of FFT is that it provides only the frequency spectra information of the input time domain signal.
Wavelets provide similar information as provided by the FFT plus additional time information.
In wavelets, small windows are used to capture the high frequency information and large windows are used to capture the low frequency information.

12. Wavelets Transform
Wavelets Transforms do not employ sinusoids to extract the frequency information from the input time signal. Instead of sinusoids, wavelets transforms utilize ‘mother wavelets’.
The Wavelet Transform measures the correlation between the input signal and scaled and translated version of the ‘Mother Wavelet’.
DWT is obtained by using a multistage filter with the mother wavelet as the lowpass filter l (n) and its dual as the highpass filter h (n). The output of the highpass filter gives the detailed version of the high-frequency component of the signal. The low-frequency component is split to get the other details of the input signal.

13. Wavelets Packet Analysis
Another method of Discrete Wavelets Transform, which is employed in this thesis, is the Wavelet Packet Analysis. In Wavelet Packet Analysis, the details as well as the approximations are split as opposed to Wavelet Analysis where a signal is split into an approximation and a detail and then only the approximation is split into next level approximation and detail.

14. Wavelets Packet Analysis
Figure 5. Decomposition of signal ‘S’ using Wavelet Packet Analysis. Note that
Approximation and Details are further decomposed as compared to Simple Wavelet
Analysis, Figure 2. 3 where only the Approximation is further decomposed. ‘A’ and
‘D’ stand for Approximation and Detail respectively.

15. Why use Wavelets Transform for HIF - Arc Fault Detection ?
The fault current has discontinuities due to fault current temporary extinction and re-ignition phenomena. This attribute is used in the Wavelet detection method.
However, in the case of occurrence of a HIF - Arc fault, the magnitude of feeder current at the substation is relatively much higher than the HIF - Arc fault current. As a result the feeder current would be nearly sinusoidal and the ANN might not be able to distinguish between a faulty feeder current and a healthy feeder current.

16. Why use Wavelets Transform for HIF - Arc Fault Detection ?
Figure 6. Original Signal I(t) and the Wavelet Transformed Signal as measured by CT at feeder bus Va for HIF – Arc fault

17. Wavelets and Artificial Neural Networks in HIF - Arc Fault Detection Relaying Scheme
The instantaneous value of the feeder current i (t ) at the feeder substation bus are obtained.
i (t ) is transformed into the Wavelet domain using Wavelet Packet Analysis.
The signal is reconstructed at each node and analyzed to select the ‘best reconstruction’ from the signal decomposition tree also called Wavelet Packet Tree (WPT).
After many iterations, node (10, 2) and Daubechies4 Mother Wavelet (db4) was found to provide the best ‘diagnostic vector’.

18. Wavelets and Artificial Neural Networks in HIF - Arc Fault Detection Relaying Scheme
TABLE II
FEATURE VECTORS FOR TRAINING, TESTING AND CROSS-VALIDATING THE ELMAN ANN FOR RADIAL ELECTRIC UTILITY FEEDER DISTRIBU- TION SYSTEM

19. Artificial Neural Network Design Using Recurrent Network- Architecture
Elman Recurrent Network.
One hidden layer.
10 neurons in the hidden layer.
2 neuron in the output layer.
The activation function was tan-sigmoid for the hidden layer and pure-linear for the output layer.

20. Artificial Neural Network Design - Training Algorithms
1) Variable Learning Rate Backpropagation (traingdx)*
2) Resilient Backpropagation (trainrp)
3) BFGS Quasi-Newton (trainbfg)
4) Scaled Conjugate Gradient (trainscg)
5) Polak-Ribiére Conjugate Gradient (traincgp)
6) Fletcher-Powell Conjugate Gradient (traincg)
Variable Learning Rate Backpropagation (traingdx) algorithm* (number 1 above) was the fastest algorithm in all cases.

21. High Impedance - Arc Fault Detection and Relaying Scheme
Module-1: Input Block
Module-2: Signal Processing Block
Module-3: ANN Block
Module-4: Output Logical Block
Figure 11. Relay 2. FFT Hyper-plane ANN Based HIF – Arc fault Detection Scheme (developed by Dr. Sharaf ).

22. Conclusion - Research Extensions and Recommendations
The thesis developed and validated two novel ANN-Based HIF - Arc fault relaying schemes based on Dr. Sharaf’s Feature Vector Transformations.
Develop a Multi-tier detection approach using a combination of High impedance arcing type fault detection methods.
Rule-based identification and activation procedure be incorporated into any effective and robust HIF - Arc fault relaying scheme, so that it could accurately initiate the Trip / Isolate signal to the Circuit Breaker / Contactor / Oil Circuit Breaker as well as initiate the required Alarm and Fault-Recorder Activation.

23. Conclusion - Research Extensions and Recommendations - cont.
Extend the concept of the full n-dimensional hyper-plane / fault-phase / phase portraits degeneration recently developed by Dr. Sharaf, where new synthesized / transformed multi-input signal hyper-vector called the Anomaly-Graphic Feature (AGF) vector is traced in the 2-dimensional, 3-dimensional trajectory or any hyper-plane. The trajectory’s degenerative shape and temporal phase portrait pattern can be used by a graphic Object-detection software as indicative of HIF – Arc Faults.
Design a Radio frequency (RF) HIF – Arc fault detection scheme using active successive estimation and abduction rules.

24. Thank you
Questions Please