README.md

Introduction

This repository presents a classification algorithm for Power Quality (PQ) events using Artificial Neural Networks (ANNs). It utilizes four spectrum analysis techniques: (i) Short-Time Fourier Transform (STFT), (ii) Continuous Wavelet Transform (CWT), (iii) Discrete Stockwell Transform (DST), and (iv) Hilbert-Huang Transform (HHT). These spectra are used as input to a Convolutional Neural Network (CNN) for event classification.

Methodology

Signal Generation Models

PQ events were simulated using a numerical model (refer to [1]). The simulated events include:

• Sag: Voltage dips between 0.1 and 0.9 pu
• Swell: Voltage rises between 1.1 and 1.8 pu
• Interruption: Voltage drops below 0.1 pu
• Transient: Sudden voltage deviations
• Notch: Rapid drops and recoveries in voltage, often due to switching
• Harmonics: Multiple frequency components causing signal distortions
• Flicker: Long-term voltage variations causing visible light fluctuations

Equations for these events are in src/data_gen.py and in the table below.

Name	Equation	Range of $\beta$
Normal	$V(t) = \sin(wt + \alpha) \left(1 - \beta \cdot u(t-t_1) \cdot (1 - e^{t - t_1})\right)$	$\beta \in [0.93, 1.07]$
Sag	$V(t) = \sin(wt + \alpha) \left(1 - \beta \cdot u(t-t_1) \cdot (1 - e^{t - t_1})\right)$	$\beta \in [0.1, 0.9]$
Swell	$V(t) = \sin(wt + \alpha) \left(1 + \beta \cdot u(t-t_1) \cdot (1 - e^{t - t_1})\right)$	$\beta \in [1.1, 1.8]$
Interruption	$V(t) = \sin(wt + \alpha) \left(1 - \beta \cdot u(t-t_1) \cdot (1 - e^{t - t_1})\right)$	$\beta \in [0, 0.09]$
Transient	$V(t) = \sin(wt + \alpha) + \beta_{1}\cdot u(t-t_1) \cdot e^{-\beta_{2} (t-t_1)} \cdot \sin(w_{os}(t - t_1) + \alpha_{os})$	$\beta_{1} \in [1.2, 2]$, $\beta_{2} \in [200, 600]$
Notch	$V(t) = \sin(wt + \alpha) + [n_d \cdot p_m(v_n, v_{osc})]$	$n_d \in [0.2, 0.5]$
Harmonics	$V(t) = \sin(wt + \alpha) + \sum_{n=1}^{N} a_n \sin(n \cdot (wt + \alpha))$	$Thd \in [0.1, 0.5]$

Spectrum Analysis Techniques

Short-Time Fourier Transform (STFT)

STFT provides time-frequency analysis using sliding windows. It’s computed using librosa in src/signal_processing/compute_stft:

$$ X[k, n] = \sum_{m=0}^{N-1} x[n+m] \cdot W[m] \cdot e^{-j\frac{2\pi mk}{N}} $$

Continuous Wavelet Transform (CWT)

CWT analyzes frequency evolution using wavelets, offering better resolution than STFT. It’s computed in src/signal_processing/compute_cwt:

$$ X[a, b] = \frac{1}{\sqrt{|a|}} \sum_{n=0}^{N-1} x[n] \cdot \psi^* \left(\frac{n - b}{a}\right) $$

Discrete Stockwell Transform (DST)

DST combines STFT and CWT advantages for efficient time-frequency analysis. It’s computed in src/signal_processing/compute_st:

$$ S[k, n] = \sum_{m=0}^{N-1} H[n+m] e^{\frac{-2\pi^2 m^2}{n^2}} e^{\frac{j2\pi m k}{N}} $$

Hilbert-Huang Transform (HHT)

HHT analyzes nonlinear or non-stationary signals using Empirical Mode Decomposition (EMD) and Hilbert Transform. It’s computed in src/signal_processing/compute_hht:

$$ x(t) = \sum_{i=1}^{N} c_i(t) + r(t) $$

$$ A_i(t) = \sqrt{c_i^2(t) + ( \mathcal{H} \left[ c_i(t) \right] )^2} $$ $$ \phi_i(t) = \arctan \left( \dfrac{\mathcal{H} \left[ c_i(t) \right]}{c_i(t)} \right); ; \omega_i(t) = \dfrac{1}{2\pi}\dfrac{d\phi_i(t)}{dt} $$

$$ H_i(\omega, t) = A_i(t);; \omega_i(t) $$

Convolutional Neural Network (CNN)

The CNN architecture used by the project for classification consists of:

Layer Type	Parameters	Activation
Input Layer	Input_Size	-
Convolution Layer	filters=20, kernel_size=3	ReLU
Max Pooling Layer	pool_size=2	-
Convolution Layer	filters=10, kernel_size=3	ReLU
Max Pooling Layer	pool_size=2	-
Flatten Layer	-	-
Dense Perceptron Layer	units=64	ReLU
Dense Perceptron Layer	units=num_classes=8	Softmax