System and methods to estimate sheath to ground faults using online contactless time domain reflectometry in an HVDC cable system

Abstract

The present invention relates to a real-time monitoring system for detecting sheath-to-ground (SG) faults in high-voltage direct current (HVDC) cable systems. It employs a non-intrusive inductive coupler for Time-Domain Reflectometry (TDR), enabling continuous monitoring without disrupting operations. Combining TDR with Decision Tree Regression (DTR), the system processes fault reflections using historical data for precise fault localization. Fast Fourier Transform (FFT) enhances signal clarity by extracting frequency features, while an automated fault location algorithm ensures accurate fault estimation across varying cable lengths. Challenges such as signal dispersion, overlapping reflections, and environmental variations are addressed through dynamic sheath impedance calculations and real-time updates. Optimized for reliability and adaptability, this system minimizes signal distortion and improves fault detection, offering a cost-effective and efficient solution for HVDC cable fault diagnosis.

Description

[0001] SYSTEM AND METHODS TO ESTIMATE SHEATH TO GROUND FAULTS USING ONLINE CONTACTLESS TIME DOMAIN REFLECTOMETRY IN AN HVDC CABLE SYSTEM

[0002] TECHNICAL FIELD

[0003] The present invention relates generally to the field of high-voltage direct current (HVDC) cable systems and, more particularly, to a system and method for detecting and localizing sheath-to-ground faults in real-time.

[0004] BACKGROUND OF THE INVENTION

[0005] The ever-growing demand for efficient long-distance power transmission and the interconnection of power grids have driven the widespread adoption of high-voltage direct current (HVDC) systems. The reliability of HVDC systems is heavily dependent on the performance and longevity of their components, emphasizing the need for robust maintenance strategies. HVDC cables, as the backbone of these systems, rely on their metallic sheath for protection against environmental factors like moisture and mechanical damage while providing electrical insulation to prevent leakage currents. Maintaining the integrity of the sheath is critical for ensuring cable performance and longevity, as it mitigates issues like moisture ingress and mechanical wear, thus extending the cable's lifespan.

[0006] Sheath-to-ground (SG) faults occur when the cable's outer jacket is punctured, exposing the metallic sheath to environmental conditions. This compromise can result from improper handling, extreme environmental stress, or subpar craftsmanship. The primary risk of SG faults is moisture ingress, which can penetrate the cable's insulation layer, forming water trees that lead to partial discharges and, eventually, catastrophic cable failure. Moisture ingress also accelerates cable aging, reducing its lifespan. Early detection and localization of SG faults are crucial to preventing premature breakdowns and enhancing system reliability.

[0007] Attempts to detect SG faults in HVDC systems have used sheath current measurements at link boxes, but these methods are unsuitable for HVDC cables due to the negligible inductive effects and low current levels caused by capacitive coupling. Online, non-intrusive reflectometry techniques such as Time-Domain Reflectometry (TDR) and other variants namely, Time-Frequency Domain Reflectometry( TFDR), Spread Spectrum Time Domain Reflectometry (SSTDR), and stepped-frequency waveform reflectometry (SFWR) have proven effective for fault detection and insulation monitoring. However, for SG faults, the unique characteristics of the sheath — its thinness and conductive properties — make TDR an effective and simpler choice. Recent studies have shown that Gaussian chirp signals provide better resolution for fault detection but require careful tuning. For practical applications, an impulse waveform offers straightforward implementation and reliable performance for SG fault localization.

[0008] The accuracy of TDR can be enhanced with signal processing and machine learning techniques. While deep learning shows potential, its high computational requirements make it less practical. This invention introduces a novel approach using an inductive coupler for online TDR on the sheath of HVDC cables, combined with signal processing and Decision Tree Regression (DTR). This integrated method ensures precise localization of SG faults, addressing existing gaps and advancing HVDC cable condition monitoring.

[0009] Patent Literature KR20230169613A discloses A live cable diagnosis device and method using an inductive coupler and a step-frequency reflected wave measurement method according to a preferred embodiment of the present invention is based on an inductive coupler (inductive) based on stepped-frequency waveform reflectometry (SFWR). By diagnosing defects in a live cable using a coupler, the cable can be diagnosed even if the cable in operation is not turned off.

[0010] Patent Literature US2010073014A1 relates to a time-domain reflectometer and to a method of time-domain reflectometry, for testing electrical cables that may be faulty or have faulty terminations. The present invention provides a time domain reflectometer for testing an electrical cable. The time domain reflectometer includes a test signal generator, at least one line feed resistor, connected between the test signal generator and a pair of terminals, for connection to the ends of the electrical cable under test, and a signal processor, connected to the terminals, to receive a line signal including a reflection of a test signal transmitted into the cable under test. The signal processor is programmed to filter the line signal to enhance a portion of the signal indicative of any fault on the cable by balancing the signal according to the electrical characteristics of a normal cable of the same type as the cable under test by applying a filterfunction, and acquiring at least one estimate of the input admittance of the transmission line from known or estimated electrical characteristics of the cable under test.

[0011] Patent Literature WO2021099495A1 discloses a method for determining the state of a cable insulation parameter of a cable (301) in an electrical system, the method comprising the steps of: providing, by an AC voltage source (309), a plurality of alternating current signals between a conductor of the cable (301) and an electrical ground (311), wherein the plurality of alternating current signals comprise a plurality of frequencies, in which each alternating current signal comprises a different frequency greater than zero; measuring a frequency response for each of the plurality of alternating current signals; determining a plurality of phase shifts, each of the plurality of phase shifts begin between each injected alternating current signal and the corresponding measured frequency response, extrapolating the phase shifts to provide a parameter of the cable insulation.

[0012] Nevertheless, there are potential drawbacks regarding the above cited prior arts. It has been observed that KR20230169613A and WO2021099495A1 focus on general cable diagnostics but lack specific optimization for sheath-to-ground faults in HVDC systems. US2010073014A1 rely on traditional techniques like admittance analysis and waveform comparisons, which may struggle with the signal attenuation and distortion common in HVDC environments. None of the references integrate advanced signal processing and machine learning like Decision Tree Regression, limiting their precision and adaptability for fault localization in challenging conditions.

[0013] Hence there is a requirement for a new and modified approach by tailoring fault diagnostics specifically for sheath-to-ground faults in HVDC cables. Unlike the cited references, the current invention integrates advanced signal processing techniques and machine learning models like Decision Tree Regression, ensuring superior accuracy, non-intrusiveness, and practicality in online diagnostics. This innovation represents a significant improvement in fault localization under the unique challenges of HVDC cable.OBJECTIVE OF THE INVENTION

[0014] The objective of the present invention is to provide a system and method for detecting and localizing sheath-to-ground (SG) faults in high-voltage direct current (HVDC) cables in realtime, designed to enhance operational reliability and prevent service disruptions.

[0015] It is yet another objective of the present invention to offer a real-time, monitoring solution utilizing an inductive coupler integrated with Time-Domain Reflectometry (TDR), enabling continuous and accurate fault detection without interrupting cable operations.

[0016] It is another objective of the present invention to improve fault localization accuracy in real-time by integrating signal processing techniques, such as Fast Fourier Transform (FFT), and machine learning algorithms, specifically Decision Tree Regression (DTR).

[0017] It is yet another objective of the present invention to ensure adaptability of the system by accounting for variations in cable dimensions, electrical properties, and environmental conditions, providing robust performance in diverse HVDC installations.

[0018] It is yet another objective of the present invention to develop a cost-effective solution in realtime with straightforward implementation, utilizing optimized impulse waveforms and simple signal processing techniques for reliable fault estimation.

[0019] It is yet another objective of the present invention to enhance the longevity and safety of HVDC cable systems by enabling early detection of SG faults in real-time, thereby reducing maintenance costs and the risk of premature cable failure.

[0020] Other objects of the present invention, as well as particular features, elements and advantages thereof, will be clarified in or be apparent from the following description and the accompanying figures.SUMMARY

[0021] The following summary is provided to facilitate a clear understanding of the new features in the disclosed embodiment and it is not intended to be a full, detailed description. A detailed description of all the aspects of the disclosed invention can be understood by reviewing the full specification, the drawing and the claims and the abstract, as a whole.

[0022] The present invention describes an integrated real-time monitoring system designed for detecting sheath-to-ground (SG) faults in high-voltage direct current (HVDC) cables, specifically in real time. The system includes an inductive coupler for non-intrusive Time- Domain Reflectometry (TDR) to transmit and receive test impulses along the cable sheath, allowing continuous monitoring without affecting cable operation. A hybrid approach combines TDR with Decision Tree Regression (DTR), where TDR captures reflected signals from faults and DTR processes these signals using historical data to accurately locate faults. The system employs Fast Fourier Transform (FFT) to enhance signal clarity by extracting critical frequency features, compensating for dispersion and attenuation.

[0023] The system also integrates an automated real-time fault location algorithm, which uses the extracted frequency features and impedance parameters to estimate fault locations accurately, even in cases of overlapping signals or short transmission lines. The inductive coupler operates non-intrusively within a frequency band centred at 500 kHz to maintain signal integrity, while the impulse waveform is optimized at 100 kHz with a magnitude of 50V, ensuring compatibility with the sheath material. The transmission line model calculates key electrical parameters like resistance, capacitance, and inductance based on the sheath’s dimensions and material properties.

[0024] Additional enhancements include dynamic calculation of sheath impedance based on cable dimensions and grounding resistance, providing real-time updates for accurate fault estimation. The DTR model is further refined by training it with FFT-derived features like peak frequency and magnitude, improving fault localization. The system accounts for variations in cable dimensions and noise conditions, ensuring robustness and adaptability.Time-domain analysis is used to isolate fault-specific signals, and overlapping incident and reflected signals near the source are analysed to improve fault detection accuracy, reducing signal distortion. Lastly, field measurement data is incorporated to enhance real-time adaptability and precision in fault detection.

[0025] BRIEF DESCRIPTION OF THE DRAWINGS

[0026] The detailed description is described with reference to the accompanying figures. Throughout the drawings, the same drawing reference numerals will be understood to refer to the same elements and features. The features and advantages of the present proposed system will become more apparent from the following detailed description a long with the accompanying figures, which forms a part of this application.

[0027] Fig. 1. depicts a schematic model to perform an online Time-Domain Reflectometry (TDR) in the metallic sheath to estimate SG fault location in real-time according to an embodiment of the present invention.

[0028] Fig 2 shows the double circuit transmission line model to represent sheath of a cable according to an embodiment of the present invention.

[0029] Fig 3(a) depicts simulation results of TDR response for faults at different locations in its complete time spectrum of a 220 KV long cable wherein the x-axis represents time measured in milliseconds and y-axis represents voltage measured in volts (V).

[0030] Fig 3(b) depicts Fast Fourier Transform (FFT) of the complete time spectrum of the simulated TDR response having fault at different location wherein the x-axis represents frequency measured in Hertz (Hz) and the y-axis represents voltage (V) measured in volts.

[0031] Fig 4. (a) depicts simulation results of TDR response for faults at different locations in its modified time spectrum for a 25,000m long cable, according to an embodiment of the present invention.

[0032] Fig 4.(b) depicts FFT of the modified time spectrum of simulated TDR response having fault at different locations, according to an embodiment of the present invention.Fig.5 depicts a flowchart outlining the process of detecting and analysing faults in a cable system, according to an embodiment of the present invention.

[0033] Fig. 6 depicts an illustration of a basic regression decision tree.

[0034] Fig 7. depicts an experimental result of TDR response for faults at different locations in its complete time spectrum of a Type 1 cable, wherein the x-axis represents time measured in milliseconds and the y-axis represents voltage measured in volts (V).

[0035] Fig. 8 depicts FFT of the modified time spectrum of a Type 1 practical cable having faults at (a) 5m, (b) 10m, (c) 15m, (d) 20m, (e) 22.5m (f) 25m. The x-axis represents frequency measured in Mega Hertz and the y-axis represents voltage measured in volts (V).

[0036] Fig. 9 depicts the magnitude of faults at different locations for Type 1 cable, obtained from FFT graph and Algorithm 1. The x-axis represents frequency measured in Mega Hertz. The y-axis represents voltage measured in Millivolts.

[0037] Fig. 10 shows the experimental results of TDR response for faults at different locations in its complete time spectrum of a Type 2 cable. The x-axis represents time measured in milliseconds. The y-axis represents voltage measured in volts.

[0038] Fig. 11 shows the FFT of the modified time spectrum of a Type 1 practical cable having fault at (a) 7m, (b) 12.5m, (c) 18m, (d) 28m, (e) 35m and (f) 38.5m. The x-axis represents frequency measured in Mega Hertz and the y-axis represents voltage measured in volts.

[0039] Fig.12 depicts the magnitude of faults at different locations for Type 2 cable, obtained from FFT graph and Algorithm 1. The x-axis represents frequency measured in Mega Hertz. The y-axis represents voltage measured in millivolts / / is to be noted, however, that the appended drawing illustrates only typical embodiments of this system and are therefore should not be considered limiting of its scope, for the system may admit to other equally effective embodiments.

[0040] LIST OF REFERENCE NUMERALS

[0041] 10 - incident signal

[0042] 20 - reflected signal

[0043] 30 - FFT on modified time domain signal40 - DTR to predict fault location

[0044] 50 - conductor

[0045] 60 - conductor-to-sheath interface

[0046] 70 - sheath-to-ground interface

[0047] 80 - cable

[0048] 90 - cable sheath

[0049] DETAILED DESCRIPTION

[0050] The following is a description of the present application depicted in the accompanying drawings. However, the apparatus or device in the present application may be understood by a person having ordinary skill in the art without these specific details. In other instances, other well-known components regarding the said apparatus or device have not been described in detail so as not to obscure the subject matter of the present application. The subject matter of the present application will be more clearly understood from the following description of the embodiments thereof, given by way of example only with reference to the accompanying drawings, which are not drawn to scale.

[0051] If the specification states that a component or a feature “may” or “can” be included, that particular component or feature is not required to be included or have the characteristic. The use of open-ended terms like “comprising” and variations herein is meant to encompass the steps listed thereafter and equivalents thereof as well as additional items. As used herein, the singular forms “a,” “an,” and “the” designate both the singular and the plural, unless expressly stated to designate the singular only.

[0052] The term “HVDC” refers to High-voltage direct current and is an electric power transmission system that uses direct current (DC) for electric power transmission. HVDC cables are commonly used for long-distance power transmission, since they require fewer conductors and incur less power loss than equivalent AC lines. “SG faults” refer to sheath-to-ground faults that occur when the insulating sheath of a high-voltage cable comes into contact with the ground, leading to unwanted current leakage and potential system inefficiencies or failures. “TDR” refers to Time Domain Reflectometry which is a diagnostic technique used to locate faults in cables ortransmission lines. It works by sending a signal, such as an electrical pulse or chirp, down the line and analysing the reflected signals to determine the location and nature of any discontinuities or faults.

[0053] A “real-time” condition in this context, refers to the state where the HVDC cable system is operational and actively transmitting power, rather than being shut down or taken offline for inspection or testing. It implies that the detection and localization of sheath-to-ground faults occur during an online condition or a regular operation, without the need to interrupt the system's functionality.. The terms “real-time” condition and “online” condition of the HVDC cable system has been used interchangeably.

[0054] An “inductive coupler” is a non-intrusive device used to transfer or detect electrical signals through electromagnetic induction without requiring a direct electrical connection. It typically consists of a coil or transformer that is placed around or near a conductor, allowing it to inject or pick up signals, such as for diagnostics, communication, or power transfer in cables and circuits. “DTR” refers to Decision Tree Regression which is a machine learning algorithm used for predictive modelling, particularly regression tasks. It works by splitting data into branches based on decision rules derived from feature values, creating a tree structure. Each leaf node represents a predicted value based on the input features. DTR is highly interpretable and capable of capturing complex, non-linear relationships in the data, making it useful for tasks like fault localization in engineering systems. “FFT” refers to Fast Fourier Transform which is an algorithm that efficiently computes the Discrete Fourier Transform (DFT) of a signal. It transforms a signal from the time domain into the frequency domain, revealing the signal's frequency components. FFT is widely used in signal processing, communications, and engineering applications to analyse, filter, or process signals with speed and precision

[0055] The present invention is an advanced real-time monitoring system for detecting sheath-to-ground (SG) faults in HVDC cables, specifically during a real-time / an online condition of the said cable. It integrates an inductive coupler, Time-Domain Reflectometry (TDR), and automated diagnostics for continuous, non-intrusive monitoring without interrupting operations. Using a 100 kHz, 50V impulse waveform and a double-circuit transmission line model, the systemcalculates key cable parameters like impedance and propagation constants based on sheath dimensions and material properties. The inductive coupler ensures accurate signal transmission within a 500 kHz frequency band, enabling reliable detection and localization of faults.

[0056] Figure 1 illustrates a proposed schematic model for performing online Time Domain Reflectometry (TDR) in the metallic sheath of high-voltage cables to estimate sheath-to-ground (SG) fault locations. The system combines Time Domain Reflectometry (TDR) with Decision Tree Regression (DTR) to process reflected signals and identify fault locations. The circuit set-up operates as follows. An incident signal (10) is generated by a signal generator and injected into the cable sheath (90). If a fault (SG fault) exists, part of the signal reflects back, creating a reflected signal (20). An inductive coupler detects the reflected signal non-intrusively. The reflected signal (20) is processed, and its modified time-domain data (30) is subjected to Fast Fourier Transform (FFT) to analyse frequency components. The FFT-processed data is fed into a Decision Tree Regression (DTR) model to predict the fault location (40) accurately.

[0057] Fast Fourier Transform (FFT) is applied to isolate key features like peak frequency fpeakand magnitude, overcoming challenges of overlapping signals and noise. These features train the DTR model for precise fault localization (40), adapting to various cable lengths and conditions. By integrating real-time data acquisition, frequency analysis, and machine learning, the system provides robust and scalable fault detection, enhancing the reliability of HVDC power transmission.

[0058] The inductive coupler is employed to transmit and receive impulse waveforms within the sheath (90) of an HVDC cable (80). The auxiliary circuit comprises an impulse voltage source for signal transmission, a Digital Storage Oscilloscope (DSO) to capture the traveling wave waveform, and the inductive coupler, which operates through magnetic induction. This setup facilitates nonintrusive signal transmission and reception without requiring a direct electrical connection, as depicted in Figure 1.

[0059] Each inductive coupler functions effectively within a specific frequency band, ensuring linear signal transmission and reception. In this circuit setup, the coupler is designed to operate at a frequency band centred at 500 kHz, providing a stable, distortion-minimized channel for signalpropagation. To perform online Time-Domain Reflectometry (TDR) in the sheath, an impulse waveform with a frequency of 100 kHz and a magnitude of 50V is used. This choice ensures compatibility with the coupler’s linear frequency range and enhances the accuracy of fault localization. The circuit setup, shown in Figure 1, is simulated to model signal propagation and estimate fault locations within the cable accurately. Decision Tree Regression (DTR) is then applied, leveraging key features extracted from the simulation results. The DTR model (40) accounts for minor noise and linear distortions, improving the reliability of fault localization even under variable field conditions by compensating for subtle irregularities.

[0060] Building on the analysis from Figure 1, the transmission of the TDR impulse through the sheath is modelled using a double-circuit transmission line (TL) to extra key parameters from the cable dimensions. This model allows accurate representation of signal propagation along the sheath, depicted in Figure 2.

[0061] Figure 2 illustrates a cross-sectional view of a power cable and its equivalent circuit model, combining the physical structure (left) and the electrical circuit representation (right) of a small cable segment of length AZ. The physical structure shows concentric layers: the central layer being the conductor (50), the next layer being the insulation over the conductor with having a sheath thickness (d). The circuit model depicts three main paths: the conductor (C) path, conductor-to-sheath (CS) interface (60), and sheath-to-ground (SG) interface (70), incorporating key components like resistances of conductor and sheath, namely, (Rc and Rs), inductances (Lc, and Ls), capacitances (Ccs, and CSG), and conductance (Ges and GSG). This "double-circuit" model captures both conductor-to-sheath (60) and sheath-to-ground (70) interactions, enabling detailed analysis of cable behaviour at high frequencies, power losses, voltage drops, electromagnetic interference, and grounding system design.

[0062] According to Fig.2, the input impedance of the cable sheath can be analytically derived as:

[0063] g _ — p -i* tanst., “

[0064]

[0065] s-ns Cash ( yZ'j where,

[0066] y = + FJ& LyXG

[0067]

[0068] G = GCS+ GGS, C = CSG+ CSG

[0069] where in equation (1), Z denotes the total cable length, and RG represents the grounding resistance. The parameters Rsand Lscorrespond to the resistance and inductance of the sheath, respectively. Gcs, and GGSare the conductances between the conductor and sheath interfaces, and GSGare the conductances between the sheath and ground interfaces, as illustrated in Figure 2. Similarly, y (gamma) is the propagation constant, with alpha (a) and beta (0) representing the attenuation and phase constants. (4)

[0070] The propagation constant y, which includes the attenuation (a) and phase constants (0), is derived based on per-unit-length electrical parameters. These parameters are analytically defined as:

[0071] (5)

[0072] Li;= H / m (6)

[0073] T4? I Os = ““Try — — 7“F / m(7)

[0074] (8)

[0075]

[0076] = 2® / X teaS X or C5,f) S / m (9)

[0077] Here, represents the permeability of free space,

[0078]

[0079] represents relative permeability of the conductor material,

[0080]

[0081] represents the conductivity of the conductor material,

[0082]

[0083] represents the permittivity of free space,

[0084]

[0085] represents the relative permittivity of the insulating material and ta represents the dissipation factor, d represents the thickness of the sheath, r1and r2are the outer and inner radius of the sheath and rsis the outer radius of the jacket.

[0086] From equations (1) to (9), it is evident that the input sheath impedance (ZinS) is dependent on the cable's dimensions, electrical properties, and the length of each section (LH) between two solid grounding points. This input sheath impedance, (ZinS) will serve as a key that will be utilized to train the system for fault detection and localization.Referring back to Figure 2, the HVDC cable sheath (90), grounded at both ends forms a long section that can extend for thousands of meters. A sheath-to-ground (SG) fault occurs when the metallic sheath (90) comes into direct contact with the ground, puncturing the outer insulation. When an impulse is sent along the HVDC cable sheath, it always exhibits a negative reflection coefficient. In a healthy cable, the impulse reflects back from the solid grounding points at both ends. However, if an SG fault is present, the impulse reflects from the fault location, enabling the fault's position to be determined based on the reflection timing.

[0087] Since the magnitude and center frequency of the incident signal are fixed, reflections from a short cable section or a fault close to the source can overlap with the original signal before it fully dissipates, making the actual reflection indistinguishable, as illustrated in Figure 3(a). To address this issue and accurately estimate the location of an SG fault, the modified reflected signal captured by the DSO is analyzed using Fast Fourier Transform (FFT). This approach enhances signal clarity, reduces noise, and enables precise fault localization. In this section, a novel method for extracting key features from the modified reflected signal and employing Decision Tree Regression (DTR) to estimate SG fault locations is described in detail.

[0088] FFT Analysis of Signals Captured on the DSO: Challenges and Solutions

[0089] Figure 3(a) depicts simulation results of TDR response for faults at different locations in its complete time spectrum of a 220 KV long cable. The X-axis represents time measured in milliseconds and Y-axis represents voltage measured in volts (V). Figure 3(b) depicts Fast Fourier Transform (FFT) of the complete time spectrum of simulated TDR response having fault at different location.

[0090] As shown in Figure 3(a), faults closer to the source cause impulse signal tails with more pronounced negative dips compared to faults farther away. This occurs because frequencydependent attenuation progressively reduces the amplitude of high-frequency components over distance. Consequently, shorter cable sections experience less attenuation (2 is smaller, as shown in Equation (10)) than longer sections. The relationship between the voltage at a point along the sheath ( (F)and the initial input voltage at the source 2 = 0 (Vg) at a specific frequency is given by:F

[0091]

[0092] (Z;t) = (10) The is actually a linear combination of incident and reflected signal ( can be given as:

[0093]

[0094] F(zft) = 0 (ii) In (11), is the high-energy initial impulse whereas

[0095]

[0096] is a weaker, delayed, and potentially attenuated version due to the fault reflection. Since Fourier Transform is a linear operation, therefore FFT of ^(7, t), can be written as:

[0097]

[0098] = vswx?s^ent(^» / ) SsrtsdC2'# / ) (12)

[0099] Since

[0100]

[0101] has a much higher magnitude thansfjgt,fBd(t), the overall spectrum (t) is largely determined by

[0102]

[0103] The weaker

[0104]

[0105] only makes a minor addition to the spectrum and does not significantly alter the main frequency peaks or pattern in the FFT. Therefore, the FFT spectrum of SG fault for different length of the cable will be same as shown in Fig. 3(b), making it nearly impossible to estimate the location of SG fault. The proposed method to apply Fast Fourier Transform (FFT) to overcome distinctive fault features is described hereunder. Figure 4(a) depicts simulation results of TDR response for faults at different locations in its modified time spectrum for a 25,000m long cable, according to an embodiment of the present invention. The X-axis represents Time measured in milliseconds and the Y-axis measures Voltage (V). Figure 4 (b) depicts the Fast Fourier Transform (FFT) spectrum of the modified time spectrum of simulated TDR response having fault at different locations, according to an embodiment of the present invention, wherein the X-axis represents Frequency (in Hz) and Y-axis represents Voltage (V).

[0106] To overcome the challenges, the time-domain signal?(Z,t)is analysed starting from the minimum point of the negative dip in the impulse response, as shown in Figure 4(a). This eliminates the dominant influence of the incident wave

[0107]

[0108] and isolates the faultspecific reflections.

[0109] The FFT of the modified time-domain signal reveals distinct peaks for different fault locations, as shown in Figure 4(b). In the frequency domain, the peak frequency (7^^) and itscorresponding magnitude (JF J, / ’] ) are unique for each fault location. This distinctiveness is not observable in the time-domain analysis, as overlapping reflections obscure the fault signals.

[0110] The algorithm to extract ( / fWSfe)and iV’fZ, / ] jfrom the modified time-domain signal is outlined below. The steps of Algorithm 1 for extracting key parameters from the time-domain data is depicted below.

[0111] Stepl: Perform FFT on the modified time-domain signal (V!(Z, t)to obtain the spectrum [r

[0112]

[0113] ,

[0114] Step 2: Compute the magnitude |z[ZfjT] |for each frequency.

[0115] Step 3: Identify the index where | ' [Z, / ] is maximum:

[0116] 4^ = arg”“J| [Z,f]l

[0117] Step 4: Record the magnitude of the highest peak as F ’ [Z;] |and the corresponding frequency as f peak

[0118] Next step involves utilizing the Decision Tree Regressor (DTR) method to estimate the location of the sheath-to-ground (SG) faults. Precise measurements of key parameters such as peak frequency ( eak) and magnitude of the highest peak (|V" [f / ] are crucial for accurately estimating the sheath-to-ground (SG) fault location. However, practical measurements may be affected by noise, engineering variances, and measurement inaccuracies. To mitigate these challenges, simulations are conducted on cables of varying lengths and dimensions, introducing SG faults at different locations. The resulting datasets are then used to train the Decision Tree Regressor (DTR) model.

[0119] The key parameters of / ecsk, I IL and the input impedance (Z^ ) form the feature set for the DTR model. Testing datasets are derived from practical measurements of these parameters. The trained DTR model predicts the fault location L using this pre-processed input. The flowchart for estimating SG fault locations using the DTR-based online TDR method is shown in Figure 5.The flowchart in Figure 5 describes a Practical Testing outlining a systematic approach for diagnosing cable faults by combining signal measurements and advanced modelling techniques. Referring to Fig.5, the process begins with the measurement of the cable's electrical properties and its sheath dimensions / length (LH) as the input parameters (2^) Subsequently, Time Domain Reflectometry (TDR) is performed on the sheath using predefined signal parameters to capture time-domain signals, which are then modified and processed through a Fast Fourier Transform (FFT). This analysis determines the peak frequency ( jjeak) and the frequency-dependent voltage profile (f[Z, f] |) using a specialized algorithm. These outputs, along with the input parameters, are used as test data for further stages.

[0120] In the next stage, a Pre-possessed Distributed Time-Reflectometry (DTR) model is developed, depicted in Figure 5. The input parameters

[0121]

[0122] (Z^, tare generated via simulations for diverse test cases which are used to train the DTR model. The trained model is then employed in the decision-making process. Here, the probable fault location (LF) is determined.

[0123] Once the probable location of fault LF is determined, it is compared with LH, the length of each section between two solid grounding points, depicted in Figure 5. If LF = LH, the system concludes that no fault is present. Otherwise, the location is identified as a specific sheath-to-ground fault (LF ). The process ends by marking the fault's location for further analysis or corrective action. This systematic approach ensures precise measurements with simulation-based modelling to enable efficient and accurate cable fault diagnosis.

[0124] Decision Tree Regression (DTR) was employed to predict location values, selected for its interpretability and its ability to capture nonlinear relationships in the dataset. DTR is particularly suited for this application, as it recursively partitions the feature space ( ”U

[0125]

[0126] and IA / ] i) to minimize variance in the target variable, making it effective when handling structured data with non-linear patterns without extensive feature engineering. Unlike neural networks, DTR provides a more straightforward model that requires less computational power, is less prone to overfitting on smaller datasets, and does not require intensive hyperparameter tuning to achieve consistent results.A Decision Tree could be structured as follows: consider a tree as shown in Figure 6 having input feature vectors Al, A2 and A3 to predict output classes Zl, Z2, Z3 and Z4 by comparing with threshold values Tl, T2, and T3 values The prediction is determined by applying an if-then rule to the feature vector. This process continues, with each node representing a decision rule, until a terminal node or leaf is reached.

[0127] Figure 6 illustrates a basic regression decision tree, a core concept in machine learning used for predicting continuous values. The tree consists of three levels of decision nodes, where each internal node (rectangles) applies a threshold-based condition, and the leaf nodes (ovals) represent the final predictions (Z1-Z4). At the root node, the model checks if feature Al exceeds a threshold Tl, branching into " Yes" or " No" paths. Subsequent levels refine the decision: the left branch evaluates A2> T2, and the right branch checks A3> T3. The oval outcomes are determined by these conditions, with Z1-Z4 representing specific predictions based on the path followed. The tree's binary splits, hierarchical structure, and ability to handle non-linear relationships make it a powerful tool for regression tasks, where feature interactions are automatically managed.

[0128] DTR-based methods employ several key steps: defining an accuracy criterion, selecting splits, establishing a stopping condition, and optimizing tree structure. Prediction accuracy can be assessed using metrics like re-substitution error, cross-validation error, or test sample error. Splits are determined by minimizing the least-squared deviation to reduce node impurity. Splitting stops when a minimum node size is reached, preventing overfitting. Tree optimization is achieved through pruning, which reduces the tree’s complexity by setting an optimal minimum leaf size to balance error minimization and model simplicity. The mathematical details of the above methods are thoroughly explained below.

[0129] Working Examples and Simulation on the Tested Cables to Locate SG Faults

[0130] In the simulation, distinct types of XLPE (cross-linked polyethylene) cables, each with a length of 765 km, considered in simulation were analysed in Table I.

[0131] Y1Table I:

[0132] Types Voltage (KV) Current (A)

[0133] n r2(^)

[0134] (mm)

[0135] (mm) (mm)

[0136] 1 1 50 5.33 6.28 7.35 0.20123

[0137] 2 5 75 6.21 7.23 8.26 0.20392

[0138] 3 22 150 7.35 9.32 14.32 1.5657

[0139] 4 66 200 15.61 19.83 24.24 2.2438

[0140] 5 110 350 22.37 26.61 33.66 2.6524

[0141] 6 150 500 36.62 41.41 48.64 2.6789

[0142] 7 220 550 48.76 53.28 61.72 2.7026

[0143] 8 250 575 52.31 58.57 66.73 2.7125

[0144] 9 350 600 56.48 63.33 74.56 2.8026

[0145] 10 550 650 60.29 68.36 78.58 2.8654

[0146]

[0147] The radius of each cable type, along with the supplied DC voltage and current, is detailed in Table I, which is based on standard industrial cable models. The relative permeability was set to 1.00058, while the permittivity values for the insulation and outer jacket were considered as 2.3 and 2.8, respectively. A tan 5 of 0.0005 was used for both insulation and the outer jacket at a frequency of 100 kHz. The electrical parameters of the cable sheath were determined using equations (5)-(8). Using these parameters, the input impedance (ZinS ) was calculated for each cable type, with the results presented in the last column of Table I.

[0148] The cable sheath was solidly grounded, rendering the value of RG negligible; however, for simulation and practical validation, it was set to 0.2 Q, based on reported values. In simulations, sheath-to-ground (SG) faults were introduced at 17 different locations for each cable type, specifically at 5 m, 10 m, 25 m, 100 m, 250 m, 500 m, 1 km, 2.5 km, 10 km, 25 km, 50 km, 100 km, 150 km, 200 km, 250 km, 500 km, and 750 km. It should be noted that only a single type of cable length was considered for the simulation, as under normal operating conditions, both endsof the cable sheath are solidly grounded. An SG fault occurs only when the sheath comes into direct contact with the ground, allowing the analysis of faults at various locations to effectively simulate different shorter cable segments under normal conditions.

[0149] Time-Domain Reflectometry (TDR) analysis was performed, and the peak frequency (fpeak) and magnitude (|V'[Z,f] I) were recorded for all ten cable types across the 17 fault locations. It is to be noted that Figures 3 and 4 illustrate the TDR graphs and their corresponding FFT responses for Type 7 cable.

[0150] To validate the proposed method, two practical case studies were conducted. The specifications, including dimensions, operating voltage, current, and sheath impedance (ZinS), for both cables are presented in Table II. Table II comprises the two types of cables considered for practical test.

[0151] Table II:

[0152] Types Voltage Current

[0153] ) n (Q)

[0154] (KV (A)

[0155] (mm)

[0156] (mm) (mm)

[0157] 1 11 5 6.58 7.88 p ’^5 0.20392

[0158] 2 1.1 5.33 6.28 7.35 0.20123

[0159]

[0160] Both Type I and Type II cables featured XLPE insulation with an outer polyethylene jacket. Type 1 cable had a length of 30 m, while Type 2 cable measured 40 m. The relative permittivity values for the insulation and outer jacket were 2.41 and 2.7, respectively, with a tan 8 of 0.00048 at 100 kHz. The inductance of the inductive coupler used was 15mH (milliHenry).

[0161] An experimental setup was established employing a Tektronix-based function generator (model no. AFG3052C) to generate the incident waveform, and a Keysight digital oscilloscope (DSOX4054A) utilized to capture the TDR waveforms. Faults were introduced using a grounding rod with an impedance of 2 mQ (milliOhms) at specified locations: 5 m, 10 m, 15 m, 20 m, 22.5 m, and 25 m for Type 1 cable, and 7 m, 12.5 m, 18 m, 28 m, 35 m, and 38.5 m for Type 2 cable.The captured TDR waveforms were transferred to a computer, where FFT analysis was performed to extract the values of practical fpeak and I V'[Z,f] I. These values, combined with the calculated ZinS, constituted the testing dataset for the Decision Tree Regressor (DTR) model. This dataset was utilized to accurately estimate the exact fault locations, demonstrating the efficacy of the proposed methodology in precise fault diagnostics.

[0162] The estimation process for locating sheath-to-ground (SG) faults in the Type 1 cable system is described below. The complete time-domain responses of SG faults at various locations, as recorded by the digital storage oscilloscope (DSO), are presented in Figure 7.

[0163] Figure 7 illustrates the Time Domain Reflectometry (TDR) voltage responses measured at various fault locations (5 m to 25 m) along a Type 1 cable. The graph covers a time range of 4.98ms to 5.03ms and a voltage range of -50 V to +50 V, corresponding to six tested fault locations: 5 m, 10 m, 15 m, 20 m, 22.5 m, and 25 m. Key features of the waveforms include an initial voltage spike around 5ms, representing the incident pulse, and a negative reflection near 5.01ms, indicating the reflected pulse.

[0164] It is noted that the curves depict how the signal reflects differently based on fault distances, with greater distances resulting in more attenuated and delayed reflections. This variation in the reflected signals highlights the influence of fault location on the TDR response. As previously discussed, detecting reflections from faults located at shorter distances poses challenges due to the overlap of reflected signals when relying solely on conventional Time-Domain Reflectometry (TDR). To overcome this limitation, each captured waveform was processed using the proposed method prior to applying the Fast Fourier Transform (FFT). This preprocessing step enhances fault detection accuracy, particularly for closely located faults, ensuring reliable estimation of their locations.

[0165] The Fast Fourier Transform (FFT) spectra of the processed waveforms for the practical cable of Type 1 having fault at (a) 5m, (b) 10m, (c) 15m, (d) 20m, (e) 22.5m (f) 25m are presented in Figures 8(a) to 8(f).

[0166] From the FFT analysis of the practical cable with faults at various locations, the peak frequency fpeakand corresponding magnitude |V′[Z,f]| were determined using Algorithm 1, as illustratedin Figure 9. These extracted features, combined with the input impedance

[0167]

[0168] were then fed into the DTR system to estimate the SG fault location, as outlined previously in the flowchart in Figure 5. The accuracy of the DTR system in estimating the SG fault locations is summarized below. Table III displays the accuracy of the proposed method of the present invention for Type 1 cables.

[0169] Table III:

[0170] SL. No Actual Fault Location Estimated Fault Accuracy %

[0171] (m) Location (m)

[0172] 1. 5 4.9898 99.796

[0173] 2. 10 10.0006 99.994

[0174] 3. 15 14.7989 98.659

[0175] 4. 20 19.8786 99.393

[0176] 5. 22.5 22.5687 99.694

[0177] 6. 25 25.0156 99.937

[0178]

[0179] It is observed here that the proposed method of the present invention achieves a minimum accuracy of 99.393% in the Type 1 cable system, demonstrating its effectiveness in practical applications for estimating SG fault locations in HVDC cables.

[0180] Additionally, the estimation process for locating sheath-to-ground (SG) faults in the Type 2 cable system is described below. Similar to Type 1, the complete time-domain responses for faults at different locations, as captured by a Digital Storage Oscilloscope (DSO) is shown in Figure 10. Figure 10 depicts the Time Domain Reflectometry (TDR) voltage responses for a Type 2 cable, capturing fault reflections at distances ranging from 7m to 38.5m. The graph spans a time range of 4.9ms to 5.0ms and a voltage range of -50 V to +50 V, with tests conducted at six fault locations: 7 m, 12.5 m, 18 m, 28 m, 35 m, and 38.5 m. The waveform features an incident pulse, observed as a positive spike around 4.95ms, followed by reflected pulses appearing as negative dips. These reflections vary based on fault distance, with longer distances exhibiting greater attenuation and time delays. Compared to Figure 7, which represents the Type 1 cable, the Type 2 cable displays similar reflection patterns while maintaining distinct characteristics due todifferences in cable properties and fault locations. The FFT spectra of the modified time-domain signals for faults at various locations are presented in Figures 11(a) to 11(f), wherein the FFT of the modified time spectrum of practical cable of Type 2 having fault at (a) 7m, (b) 12.5m, (c) 18m, (d) 28m, (e) 35m (f) 38.5m is depicted. Table IV demonstrates the accuracy of the proposed method according to the present invention for Type 2 cables.

[0181] Table IV:

[0182] SL. Actual Fault Estimated Fault Location Accuracy %

[0183] No Location (m) (m)

[0184] 1. 7 7.0015 99.97857

[0185] 2. 12.5 12.4667 99.7336

[0186] 3. 18 17.9856 99.92

[0187] 4. 28 28.0014 99.995

[0188] 5. 35 35.0004 99.99886

[0189] 6. 38.5 38.4963 99.99039

[0190]

[0191] It is observed here that the proposed method of the present invention achieves a minimum accuracy of 99.7336% in the Type 2 cable system, demonstrating its effectiveness in practical applications for estimating SG fault locations in HVDC cables.

[0192] When evaluating the practical results and its implications for real-world applications validating the proposed method for estimating the location of sheath-to-ground (SG) faults under online conditions, two cable types with different ratings, dimensions, lengths, and power supply configurations were tested. Despite the presence of noise in an uncontrolled practical environment, the method demonstrated a minimum accuracy of 99.39% in detecting SG fault locations, as detailed in Tables III and IV.

[0193] For faults near the ground, the fault location is identified with greater precision compared to faults at the far end, as depicted in Figures 9 and 12. This difference arises because reflected signals from near-source faults return much sooner due to the shorter propagation distance. Conversely, for faults located farther away, the reflected signal experiences greater attenuationand delay, leading to a decrease in signal magnitude with increasing fault length. This behaviour is clearly illustrated in Figures 9 and 12, underscoring the efficacy of the method in accurately diagnosing faults across varying conditions.

[0194] The present invention offers several significant advantages, particularly in the context of estimating the location of sheath-to-ground (SG) faults in HVDC cables. The invention integrates online Time Domain Reflectometry (TDR) with Decision Tree Regression (DTR) analysis, combining both time-domain and frequency-domain features to improve fault detection accuracy. This method is especially useful for faults near the source, where traditional TDR methods struggle due to reflection overlaps.

[0195] The invention utilizes Fast Fourier Transform (FFT) on the modified TDR signals, extracting key frequency features such as peak frequency and magnitude. These features provide a reliable indication of fault location by compensating for signal dispersion and attenuation, thus enhancing the precision of fault localization. Furthermore, the method assumes a consistent capacitance between the conductor and sheath, which simplifies the analysis and reduces computational complexity. This assumption is well-suited for maintaining consistent cable conditions and is validated through practical testing, achieving an accuracy rate of at least 99.393%.

[0196] By leveraging a well-defined algorithm (Algorithm 1) and a flowchart-based processing method (as illustrated in Figure 5), the invention can be easily integrated into automated systems, enabling real-time fault detection and localization in HVDC cables. This feature is essential for on-site applications, as it provides an efficient, reliable tool for identifying SG faults in real-time without the need for manual inspection.

[0197] Additionally, the invention’s robustness is evident in its adaptability to various cable configurations and its ability to compensate for environmental noise, ensuring that fault detection remains effective even in uncontrolled conditions. The integration of FFT and DTR techniques enables enhanced signal clarity, reducing interference from noise and reflections. This also provides improved fault identification, particularly in cases where faults are located at longer distances from the source.Moreover, the invention offers significant improvements over existing technologies by providing a cost-effective, straightforward solution that does not require complex feature engineering or hyperparameter tuning. This makes the system more accessible and affordable for widespread adoption in HVDC systems. It is also scalable for large infrastructures, where early fault detection is critical to preventing extensive damage or downtime.

[0198] In conclusion, the present invention overcomes the limitations of existing fault detection technologies by integrating a hybrid TDR-DTR approach, leveraging frequency-domain analysis for improved accuracy, and ensuring robustness in real-world conditions. This results in a highly reliable and accurate solution for SG fault localization in HVDC cables, even in the presence of noise or challenging environmental factors.

[0199] While the foregoing written description of the invention enables one of ordinary skill to make and use what is considered presently to be the best mode thereof those of ordinary skill will understand and appreciate the existence of variations, combinations, and equivalents of the specific embodiment, method, and examples herein. The invention should therefore not be limited by the above-described embodiment, method, and examples, but by all embodiments and methods within the scope of the invention as claimed.

Claims

WE CLAIM:

1. A system for detecting sheath-to-ground (SG) faults in high-voltage direct current (HVDC) cables, in real-time comprising:an inductive coupler configured to transmit an impulse waveform into a metallic sheath of an HVDC cable (80) in real-time and receive a reflected signal (20);a signal generator configured to generate the impulse waveform at a frequency of 100 kHz and magnitude of 50V;a digital storage oscilloscope (DSO) configured to capture the reflected signal (20); wherein the system is configured to:analyse the reflected signal (20) starting from a minimum point of a negative dip in the impulse response;perform Fast Fourier Transform (FFT) on the analysed reflected signal to obtain a frequency spectrum;extract a peak frequency (f peak) and corresponding magnitude (|V′[Z, f]|) from the frequency spectrum;calculate an input sheath impedance (ZinS) based on cable dimensions and electrical properties; andinput the peak frequency (f peak), corresponding magnitude (|V′[Z, f]|), and input sheath impedance (ZinS) into a trained Decision Tree Regression (DTR) model to determine a location of a sheath-to-ground fault.

2. The system as claimed in claim 1, wherein the inductive coupler is configured to operate within a frequency band centred at 500 kHz.

3. The system as claimed in claim 1, the system configured to:compare the determined fault location (LF) with a length of a cable section (LH) between two solid grounding points;indicate absence of a fault when the determined fault location equals the length of the cable section (LF = LH); andindicate presence of a sheath-to-ground fault at the determined location when the determined fault location differs from the length of the cable section.

4. The system as claimed in claim 1, wherein the input sheath impedance (ZinS) is calculated based on outer and inner radii of the sheath (rl, r2), outer radius of a jacket (r3), thickness of the sheath (d), permeability of free space (s«c), relative permeability of conductor material, conductivity of conductor material, permittivity of free space, relative permittivity of insulating material; and dissipation factor.

5. The system as claimed in claim 1, wherein the peak frequency (f peak) and corresponding magnitude (|V′[Z, f]|) is extracted by:performing FFT on a modified time-domain signal to obtain a spectrum; computing magnitude for each frequency;identifying an index where the magnitude is maximum; andrecording the magnitude of the highest peak and the corresponding frequency.

6. A method for detecting sheath-to-ground faults in high-voltage direct current (HVDC) cables in real-time, comprising:transmitting, via an inductive coupler, an impulse waveform into a metallic sheath of an HVDC cable;receiving, via the inductive coupler, a reflected signal (20);capturing the reflected signal (20) using a digital storage oscilloscope; analysing the reflected signal starting from a minimum point of a negative dip in the impulse response;performing Fast Fourier Transform (FFT) on the analysed reflected signal to obtain a frequency spectrum;extracting a peak frequency (f peak) and corresponding magnitude (|V′[Z, f]|) from the frequency spectrum;calculating an input sheath impedance (ZinS) based on cable dimensions and electrical properties; anddetermining a location of a sheath-to-ground fault (LF) using a trained Decision Tree Regression (DTR) model based on the peak frequency, corresponding magnitude, and input sheath impedance.

7. The method of claim 6, further comprising:comparing the determined fault location (LF) with a length of a cable section (LH) between two solid grounding points;indicating absence of a fault when the determined fault location equals the length of the cable section (LF = LH); andindicating presence of a sheath-to-ground fault at the determined location when the determined fault location differs from the length of the cable section.

8. The method as claimed in claim 6, wherein the input sheath impedance (ZinS) is calculated using a double-circuit transmission line model that accounts for:conductor-to-sheath interactions; andsheath-to-ground interactions.

9. The method as claimed in claim 6, wherein the DTR model is trained using:simulated data from cables of varying lengths and dimensions;simulated sheath-to-ground faults at different locations; andcorresponding peak frequencies, magnitudes, and input impedances.

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