Partial Discharge Localization in Power Transformers Using Invariant Extended Kalman Filter

Alignment is a critical pre-processing step before initiating inertial navigation operations. The extended Kalman filter (EKF), commonly employed for aligning strap-down inertial navigation systems (SINS), faces challenges due to linearization limitations. In response to some of these challenges, the invariant extended Kalman filter (IEKF) was developed. A key requirement for utilizing IEKF is that the system dynamics must exhibit a group affine property. However, considering inertial measurement unit (IMU) errors as state variables violates this condition. This paper introduces an improved version of IEKF, named the proportional-integral invariant Extended Kalman Filter (PI-IEKF). This approach initially ignores IMU bias and drift to preserve the group affine property. To compensate for these uncertainties, the Kalman filter's innovation term is reformulated into a proportional-integral (PI) structure. The PI gains are tuned based on Lyapunov stability criteria by solving a Linear Matrix Inequality (LMI). The PI-IEKF not only addresses the uncertainties but also enhances alignment accuracy. The proposed approach was evaluated through simulations and field tests. Simulations addressed the nonlinear alignment problem in marine environment with typical wave disturbances, while field tests used an open-source dataset from vehicle-mounted sensors. Comparative results with conventional IEKF demonstrated significant improvements in convergence speed and robustness.

Recent advances in the utilization of Lie Groups for robotic localization have led to dramatic increases in the accuracy of estimation and uncertainty characterization. One of the novel methods, the Invariant Extended Kalman Filter (InEKF) extends the Extended Kalman Filter (EKF) by leveraging the fact that some error dynamics defined on matrix Lie Groups satisfy a log-linear differential equation. Utilization of these observations result in linearization with minimal approximation error, no dependence on current state estimates, and excellent convergence and accuracy properties. In this letter we show that the primary sensors used for underwater localization, inertial measurement units (IMUs) and doppler velocity logs (DVLs) meet the requirements of the InEKF. Furthermore, we show that singleton measurements, such as depth, can also be used in the InEKF update with minor modifications, thus expanding the set of measurements usable in an InEKF. We compare convergence, accuracy and timing results of the InEKF to a quaternion-based EKF using a Monte Carlo simulation and show notable improvements in long-term localization and much faster convergence with negligible difference in computation time.

Underwater vehicles heavily depend on the integration of inertial navigation with Doppler Velocity Log (DVL) for fusion-based localization. Given the constraints imposed by sensor costs, ensuring the optimization ability and robustness of fusion algorithms is of paramount importance. While filtering-based techniques such as Extended Kalman Filter (EKF) offer mature solutions to nonlinear problems, their reliance on linearization approximation may compromise final accuracy. Recently, Invariant EKF (IEKF) methods based on the concept of smooth manifolds have emerged to address this limitation. However, the optimization by matrix Lie groups must satisfy the “group affine” property to ensure state independence, which constrains the applicability of IEKF to high-precision positioning of underwater multi-sensor fusion. In this study, an alternative state-independent underwater fusion invariant filtering approach based on a two-frame group utilizing DVL, Inertial Measurement Unit (IMU), and Earth-Centered Earth-Fixed (ECEF) configuration is proposed. This methodology circumvents the necessity for group affine in the presence of biases. We account for inertial biases and DVL pole-arm effects, achieving convergence in an imperfect IEKF by either fixed observation or body observation information. Through simulations and real datasets that are time-synchronized, we demonstrate the effectiveness and robustness of the proposed algorithm.

Radio frequency (RF) detection of partial discharges (PD) is a long-established principle, being described in the international standard for partial discharge measurement. The growing market for mobile communication devices in recent years has led to big reductions in the cost of electronic hardware operating in the VHF and UHF bands, making advanced measurements of PD in these bands increasingly affordable. Some 20 years ago, ultra-high frequency methods for PD detection were pioneered in gas-insulated substations (GIS) and have since become widely accepted. Locating PD in GIS is essentially a one-dimensional problem. More recent research into PD location in power transformers, also using the UHF method, has had to address the more challenging problem of PD location in three-dimensions. Both the GIS and transformer applications monitor enclosed volumes, where the PD is within a metalclad system that traps the signal and provides good screening of external RF interference. At the same time, other researchers have developed RF detection and location systems for open environments, such as complete air-insulated substations. When deployed in a fixed installation or a surveying vehicle equipped with GPS, this system is capable of monitoring insulation defects as they develop, and provides a location capability using sophisticated signal processing. This paper begins with an overview of some aspects of radiometric monitoring techniques and goes on to outline some research challenges which it is hoped will attract the attention of the many researchers who are continuing to advance the areas of radiometric PD detection, measurement and location technology.

ABSTRACTThis article deals with the methods of finding partial discharge (PD) location in power transformers using ultra high frequency (UHF) measurements. The UHF technique utilises two methods to find the PD location, that is, the shortest path method and hyperbolic method. The shortest path method works based on the comparison of the measured data and the ones in the database. In the hyperbolic method, a hyperbolic equation is obtained between each two element subset of sensors. The coordinate that best fits all equations is known as the PD location, and can be obtained in three different ways, that is, iterative algorithms, the Fang method and Chan method. The convergence of iterative algorithms is limited by poor initial estimate, overshoot, mitigation of non‐convergence etc. The Fang and Chan methods are two closed‐form solutions that are used in the communication system to find the radiation source location. This article explains how to use these two methods to obtain the PD coordinate inside the power transformer. These two methods can find exactly the coordinate that best fits all hyperbolic equations. At the end of this article, several tests are carried out through CST software and the PD locations is estimated by all presented methods. The simulation results show how the Fang and Chan methods can overcome the limitations of the iterative method.

This paper reports on construction and verification of a high space resolution partial discharge (PD) location system for the next generation power module. A novel PD location method (polarity reversion method) is proposed by calculating electromagnetic wave (EMW) propagation characteristics inside the power module using finite difference time domain (FDTD) analysis. In addition, EMW signal characteristics under AC voltage and impulse voltage application are compared. Based on these results, an automatic PD location system has been successfully constructed under the impulse voltage application.

We constructed an on-line partial discharge (PD) monitoring system (PDOM) with a CT sensor, an analogue-digital converter, and a tablet PC. A sampling frequency for data acquisition is 100 MHz, and we exchange on-site PD data through a cloud system. We successfully measured PDs in the early stage of insulation deterioration of a cross-linked polyethylene (XLPE) cable in a field site. Additionally, following PD detection by using a PDOM, we can locate a PD position by using a PD locator (PDL) system. By locating a PD, we can estimate the actual PD magnitude considering attenuation factor of a high frequency pulse. We show how the PDL system works on a XLPE cable network with time synchronization between two positions by using an injection current pulse. The locating accuracy of the PDL system is evaluated.

For a given device, the rapidity and accuracy of device error coefficient calibration and attitude alignment of the rotational inertial navigation system mainly depend on the convergence rate of the nonlinear filtering algorithm. The traditional extended Kalman filter method has no theoretical convergence guarantee for nonlinear systems and requires a long time in the actual calibration process. Since the attitude is subject to the 3-D rotation transformation group, the error transfer equation can be better linearized by defining the error on the lie group to use the new observation information fully. This article proposes a primary method of using the invariant extended Kalman filter to carry out an inertial navigation system. In the continuous rotation of the framework, the accelerometer, gyroscope, and framework angle are used to calibrate the error coefficient of the accelerometer and gyroscope and estimate the base alignment error angle. Simulation and experiment results show that the proposed method can accomplish alignment and calibration in 10 min under a large initial attitude error.

The conventional extended Kalman filter (EKF) is based on Taylor's series approximation of nonlinear motion and measurement models. The EKF cannot be directly generalized to multitarget situations since the multitarget state variable X = {x₁,...,x_n} exhibits discontinuous jumps in target number: X = 0, X = {x₁}, X = {x₁, x₂}, etc. However, it is possible to extend X to a continuous multitarget state X = {x₁,..., x_n} via the concept of a point target-cluster x = (a,x) where x is interpreted as multiple targets co-located at target-state x, the expected number of which is a. We generalize the EKF to multitarget problems. We illustrate the approach by deriving predictor and corrector equations for a single-sensor, single-target EKF that integrates the functions of detection and tracking in the presence of missed detections and false alarms.

We introduce a magnetometer-plus-GPS aided inertial navigation system for a helicopter UAV. A nonlinear observer is required to estimate the navigation states, typically an Extended Kalman Filter (EKF). A novel approach is the invariant observer, a constructive design method applicable to systems possessing symmetries. We review the theory and design an invariant observer for our example. Using an invariant observer guarantees a simplified form of the nonlinear estimation error dynamics. These are stabilized using an adaptation of the Invariant EKF, a systematic approach to compute the gains of an invariant observer. The resulting design is successfully implemented and validated in experiment and shows an improvement in performance over a conventional EKF.

The acoustic emission (AE) method could be used to detect and locate partial discharges (PD) in cast-resin dry-type transformers. However, due to the high sound attenuation in the filled epoxy, the signal is prone to interference from external noises and thus, in practice, there is little possibility of detecting PD. In this study, two techniques were developed to alleviate the shortcomings of the AE method. First, a waveguide is installed on the high-voltage (HV) windings, so that the acoustic signals of PD will propagate to the AE sensors that are installed on both terminals of the waveguide. The location of the winding that has PD can then be detected from the difference in arrival time of the acoustic signals. Test results indicate that the waveguide technique is able to enhance the safety of a measurement system and offers the advantages of easy installation and higher flexibility. Second, a specially designed AE sensor pair is used to distinguish whether acoustic signals are generated by PD inside the HV winding or by the corona outside the transformers. Using these two techniques of waveguide and AE sensor pair not only greatly improves sensitivity but also increases the reliability of the measurement system. Practical test results show that the new techniques can be used to locate precisely the PD in HV windings.

The objective of this work is to assess the efficacy and reliability of a certain technique of acoustic emission measurement for detection and location of partial discharges in power transformers. The possibility of locating a simulated partial discharge was studied in the laboratory. The experimental setup involved an arrangement of increasing complexity, starting with a simple tank filled with insulating oil, up to simulation of an unenergized transformer. It was concluded that, under careful control of experimental parameters, such location is effective. The study was complemented with observations on transformers in the field. In this case, results were less reliable. While the acoustic emission test was not sensitive to intense discharges within the internal winding of a transformer, problems in two tap-switches and one mechanical problem were detected. Considering that the literature reports doubts on the effectiveness of the technique, it was found that measurement of acoustic emission is useful for defects external to the transformer winding. Taking into account its success in locating some kinds of defects, partial discharge measurements by both acoustic and electromagnetic means supplement other usual tests to increase the reliability of the final diagnosis.

Location of a partial discharge (PD) fault inside a transformer can be determined using the Ultrahigh Frequency (UHF) PD measurement technique. Hereby, the electromagnetic (EM) waves that propagate due to the PD are captured using specially designed probes that are inserted into the transformer tank through its oil drain valves. The difference in the arrival time (AT) of these signals is the base of an equation system, where the PD location and the PD inception time are unknown. In this contribution, the influence of erroneous determined ATs on the localization error is investigated using a two-dimensional analogy model. Furthermore, a novel method based on detection of abrupt changes in a certain statistical property of the signal for the AT determination is proposed. A test setup is utilized to evaluate the localization algorithm. Finally, the results are presented and the precision of the proposed method for PD localization using the UHF measurement technique is discussed.

Medium voltage underground cables are widely used in urban area as distribution power lines due to their advantages over overhead cables. Underground cables may suffer from partial discharge because of insulation degradation after certain period of time. In this paper, an improved multi-end partial discharge location algorithm called segmented correlation trimmed mean algorithm is proposed. The algorithm uses segmented correlation technique and trimmed mean data filtering technique to enhance the accuracy of partial discharge location algorithm. The algorithm had been tested in MATLAB environment which consists white Gaussian noise. First, discrete wavelet transform is carried out to suppress noisy signals. Next, segmented correlation technique is applied to the de-noised segmented partial discharge signals. Segmented correlation technique has manipulates partial discharge signals by performing cross correlation process on segmented partial discharge signals in order to reduce memory usage and algorithm execution time. Lastly, trimmed mean data filtering technique is applied to the estimated partial discharge location values to estimate new partial discharge location value. Trimmed mean data filtering technique does statistical process control on estimated partial discharge location values in order to minimize the error of estimated partial discharge location. The segmented correlation trimmed mean algorithm had been compared with the existing multi-end correlation-based algorithm. The result shown that the segmented correlation trimmed mean algorithm has better accuracy than multi-end correlation-based algorithm.

Power breakdown in high voltage transformers are very critical problem which cause a serious loss to the related economy. Partial discharge is one of the causes that issue the power breakdown. To identify the partial discharge before the breakdown occur, there are different kind of method, such as UHF method, acoustic method and light phenomena. Since the various kind of material in transformer which made partial discharge localization become more difficult. To achieve high accuracy in partial discharge localization in power transformer the min-max technique and trilateration technique with time of arrival and received signal strength are introduce in this research paper. This paper focus on the partial discharge localization with UHF method which use the advantage of electromagnetic signal to find the partial discharge location. The set of microstrip patch antenna which operate in UHF bandwidth ranging from 1 GHz to 3 GHz are use as transmitter and receiver antenna. The measurement results are present by the cumulative distribution function of partial discharge localization distance error, to investigate the suitable technique and parameter for partial discharge localization in power transformer. From the result, the trilateration technique with time of arrival parameter is provide the most accuracy results than other technique and parameter.