Optimizing Fault Detection Algorithms in Synchronous Generator Using Wavelet Transform and Fuzzy Logic for Enhanced Fault Analysis ^†

Abstract

This paper proposes a robust fault detection and analysis model for 126 MVA synchronous generators connected to 16 kV and 230 kV transmission lines, developed in MATLAB Simulink R2025a. The model simulates various fault scenarios, including short-circuit conditions, to enhance the fault detection accuracy. The proposed approach combines wavelet transform for precise signal decomposition with fuzzy logic for reliable decision-making, enabling real-time fault detection and classification. The enhanced signal processing framework facilitates faster fault identification and localization, while the fuzzy logic system ensures accurate and consistent fault categorization. The simulation results demonstrate significant improvements in the protection and operational control of synchronous generators, achieving both high reliability and precision. These findings underscore the algorithm’s suitability for deployment in modern power systems, offering a scalable and effective solution for fault management.

1. Introduction

Synchronous generators are essential to the reliability and stability of power systems, particularly in high-demand applications such as power plants and renewable energy installations. These generators are critical components of the electrical grid, converting mechanical energy into electrical energy with high efficiency. However, their operational longevity and performance are often compromised by various faults, including inter-turn short circuits (ITSCs) and eccentricity faults. If left undetected, such faults can lead to severe operational failures, resulting in costly downtime, equipment damage, and potential safety hazards. Traditionally, fault detection in synchronous generators has relied on methods like harmonic analysis of the stator terminal voltage, air gap magnetic field monitoring, and vibration analysis. While effective in controlled environments, these techniques often require invasive procedures and may fail to detect early-stage faults, especially under varying load conditions. Recent advancements in non-invasive monitoring techniques, such as stray flux monitoring, have shown promise in improving the fault detection accuracy [1].

Fault detection in synchronous generators is crucial for ensuring the reliable operation of power systems, particularly within hydropower plants. The diagnostic approaches are broadly classified as model-based or model-free [2]. Model-based techniques employ detailed mathematical models of the generator to predict nominal behavior and identify deviations indicative of faults. However, these methods can be computationally demanding and susceptible to inaccuracies in the underlying models. As a more practical alternative, model-free approaches, such as Motor Current Signature Analysis (MCSA), leverage the principle that many generator faults manifest as characteristic frequency components within the stator current [3]. Signal processing techniques, including Fast Fourier Transforms (FFT) and Hilbert analysis, are commonly employed to extract these diagnostic features [4]. While efficacious for certain fault types, current-based methods alone exhibit limitations in detecting incipient faults or those characterized by subtle current signatures. Moreover, the complex operating conditions and dynamic interactions inherent in hydropower plants can complicate MCSA-based fault diagnosis further. Recent research has explored advanced signal processing techniques, such as wavelet analysis and machine learning, to improve the sensitivity and robustness of fault detection in synchronous generators [5,6]. These limitations, in conjunction with the persistent need for more reliable and sensitive diagnostic techniques, motivate the present research and development, the primary contributions of which are as follows.

(1)

The development of a novel, robust fault detection and protection framework for condition monitoring in synchronous generators. This framework integrates multiple diagnostic techniques and utilizes the short-circuit response via wavelet packet decomposition and fuzzy logic.

(2)

The system’s effectiveness is validated through extensive simulations and experimental setups, demonstrating its practical applicability in real-world synchronous generator hydropower plant systems.

2. Materials and Methods

2.1. Mathematical Model Simulation of the Synchronous Generator

A mathematical model of a synchronous generator is the basis for the analysis of a synchronous and stable generator system, which includes the voltage equations and the magnetic line of force equations that describe the electromagnetic characteristics and rotor motion equations that specify the rotor speed and torque changes, the linkage with the power system, and the control of the generator excitation signal [4].

The electrical equation is

$$\begin{array}{l}{V}_d=r_s\cdot i_d+{\displaystyle \frac{d{\lambda }_d}{dt}}-{\lambda }_q\cdot {\omega }_r\\ V_q=r_s\cdot i_q+{\displaystyle \frac{d{\lambda }_q}{dt}}-{\lambda }_d\cdot {\omega }_r\end{array}$$

(1)

V_d, V_q is the stator’s winding voltage.

The flux equation is

$$\begin{array}{l}{\lambda }_d=X_d\cdot i_d+X_{ad}\cdot i_f+X_{ad}\cdot i_D\\ {\lambda }_q=X_q\cdot i_q+X_{aq}\cdot i_f+X_{aq}\cdot i_q\end{array}$$

(2)

The rotation equation is

$$\begin{array}{l}{T}_j{\displaystyle \frac{d\omega }{dt}}=T_m-T_e-D\omega \\ {\displaystyle \frac{d\theta }{dt}}=\omega \end{array}$$

(3)

$$T_e={\lambda }_d{i}_q-{\lambda }_q{i}_d$$

(4)

where T_j represents the inertia constant of the generator, while ω denotes the angular velocity. T_m, T_e correspond to the mechanical and electrical torque, respectively. D is the oscillation coefficient. λ_d and λ_q are the flux linkages, while i_d and i_q indicate the current components. Xd and Xq represent the synchronous reactance and Xad and Xaq are the mutual inductance of the direct axis and the quadrature axis.

2.2. MATLAB Model Simulations

This MATLAB Simulink model, shown in Figure 1, simulates a synchronous generator’s behavior under various operating and fault conditions. It features a 50 Hz phasor model to represent the electrical characteristics and integrates control systems.

Figure 2 shows a synchronous generator from a hydropower plant, where (a) illustrates the external view, highlighting the branded housing (ABB) and the associated external components, and (b) shows the internal view of the rotor and stator arrangement, along with key components, including windings, brushes, and the magnetic excitation system.

Table 1. Parameter values of synchronous generator.

Detailed Information	Parameter Value
Power	126 MVA
Voltage	16 kV
Rated speed	333.3 rpm
Excitation supply	180 V, 1260 A

contains the parameters of the generator at the Nam Theun Hin Boun Power Plant, LPDR, used to simulate a fault, as well as conditions such as a short circuit in a single winding, phase-to-ground faults, and interphase short circuits. A wavelet analysis is used to detect the response of the current and voltage signals, allowing fuzzy logic systems to identify and compare normal operation with fault conditions.

2.3. The Wavelet Transform

The wavelet transform overcomes the shortcomings of the traditional Fourier transform by efficiently analyzing the localized characteristics of time-varying, high-frequency fault transients, which are generally non-periodic. The analysis using the continuous wavelet transform (CWT) for a continuous function f(t) is mathematically represented as [7,8]

$$CWT(y,z)={\displaystyle \underset{-\infty }{\overset{+\infty }{\int }}f(t){\phi }_{y,z}(t)dt\forall y>0}$$

(5)

where φ_y,z is regarded as the mother wavelet and shifted by the factor z, scaled by y

$${\phi }_{y,z}(t)={\displaystyle \frac{1}{\sqrt{y}}}\phi \left({\displaystyle \frac{t-y}{z}}\right)y>0$$

(6)

and −∞ < b < +∞; thus, a discrete wavelet transform (DFT) is defined as

$$\mathrm{D}\mathrm{W}\mathrm{T}(\mathrm{m},\mathrm{n})={\displaystyle \underset{-\infty }{\overset{+\infty }{\int }}f(t){\phi }_{m,n}^{*}(t)dt}$$

(7)

A decomposition tree depicting the representation of the low- and high-frequency bands using approximate and detailed components of the discrete wavelet coefficients, respectively, is shown in Figure 3.

3. Methods

This section describes the proposed simulation method and the application of a signal analysis using wavelet classification and fuzzy logic for protection decision-making, which consists of seven parts. The algorithmic procedure for detecting signal faults in a synchronous generator is illustrated in the flowchart shown in Figure 4.

This flowchart provides a systematic and automated approach to real-time fault detection in synchronous generators, ensuring reliability and operational safety.

• Input data parameter: The procedure begins with the input of the voltage and current signals, encompassing both normal and fault conditions.
• Simulation via the Simulink model: The input data is processed using a Simulink model in MATLAB, simulating the voltage and signal behavior to emulate the real-time operating conditions of the synchronous generator.
• Computation of voltage and signal faults: The simulation results are used to compute any deviations or anomalies in the voltage and signal data, highlighting potential fault signatures.
• Wavelet detection algorithm: The wavelet transform is employed to detect high-frequency transient signals and localized variations in the computed data.
• Fuzzy decision algorithm: The output from the wavelet detection algorithm is fed into a fuzzy decision-making system.
• Threshold evaluation: The fuzzy decision algorithm compares the fault current (I_fault) against a predefined threshold (T_h). If |I_fault| ≥ T_h, the system determines that a fault is present. Otherwise, the process loops back for a further analysis.
• Fault handling: If a fault is detected, the system initiates the appropriate responses: Force trip fault signals: The system disconnects or isolates the affected components to prevent further damage.

4. Results and Discussions

4.1. The Simulation Results

The simulation waveforms of the stator phase currents and voltages under a short-circuit condition in a synchronous generator, obtained using real parameters, are presented in Figure 2a,b.

The waveform in Figure 5a shows that the magnitude of the initial fault current changes significantly. From the maximum short-circuit current of the phases Isc = 8.173 p.u. at time t = 0.07 s, Isa = 6.410 p.u. at time t = 0.1 s, and Isb = 5.410 p.u. at time t = 0.1 s, fluctuation in the fault signal at times 0.1–0.2 s can clearly be observed, and from Figure 5b, it can be seen that a change in voltage occurs during the fault, causing V_d and V_q = 0.25 p.u. to decrease; at time t = 0.1–0.2 s, the reason for this is that the effect of the symmetrical short-circuit current is limited by the leakage reactance of the generator.

4.2. Simulation Wavelet Detection

This section presents the simulation results of wavelet-based detection applied to fault conditions and its effectiveness in analyzing the current and voltage signals during single line-to-ground faults (SLGFs).

Figure 6 shows a case study of a single line-to-ground fault (SLGF) using a detect signal composed of two harmonic components at 100 Hz and 45 Hz, sampled at 1000 Hz. The wavelet analysis performed using the Daubechies db4 mother wavelet decomposes the signal into approximated (A5) and detailed (D1–D5) levels. The 100 Hz harmonic, ideally expected only in D3 (frequency band: 125–62.5 Hz), appears incorrectly in D2 (frequency band: 250–125 Hz), indicating leakage due to the limitations of the db4 wavelet’s associated filter, which is not sufficiently ideal for precise harmonic isolation.

4.3. Fuzzy Decision

As shown in the simulation diagram in Figure 1, vibration or current mode functions for the system can be selected, and the SLGFs are compared using the estimated features for different states of fault warning levels (low, medium, and high); the simulation rule base and membership functions are shown in Figure 7.

4.4. Discussion

The simulation demonstrates effective fault detection in a generator using a wavelet-transform-based classification method combined with a fuzzy decision-making system. The fuzzy logic model evaluates the vibration and current inputs through defined membership functions and decision rules, classifying the conditions as “good” or “warning”. This integrated approach can accurately identify single-line-to-ground faults, highlighting its robustness for generator fault diagnosis and protection in real-time applications [9,10].

5. Conclusions

This study successfully developed a refined fault detection and analysis model for 126 MVA synchronous generators interfaced with 16 kV and 230 kV transmission lines, employing MATLAB Simulink as the simulation platform. By integrating the wavelet transform for signal decomposition and fuzzy logic for intelligent decision-making, the proposed framework enhances the accuracy and reliability of real-time fault detection. This work contributes to advancing non-invasive diagnostic techniques, bridging gaps in the current methodologies by offering a comprehensive, real-time solution for multi-fault scenarios [11,12].