A parameter estimation method for untransposed transmission lines considering parameter identifiability under different internal faults

This study presents a new power transformer protection scheme based on extraction of positive and negative sequence components of superimposed differential currents. Different types of internal faults, magnetising inrush, and over‐excitation conditions have been generated by modelling in service power transformer of power transmission system of India using PSCAD/EMTDC software package. The simulation results clearly indicate the efficacy of the proposed scheme in detecting different types of internal faults like turn‐to‐turn, inter‐winding, line‐to‐ground, line‐to‐line, and line‐to‐line‐to‐ground. Together, the proposed scheme is competent to achieve effective discrimination between various external events (over‐excitation condition and various magnetising inrushes) and internal faults. Moreover, it provides equally promising results during current transformer (CT) saturation condition as well as for different connection and rating of the power transformer. Further, it remains stable during errors in the CT and tap change condition. Additionally, authenticity of the proposed scheme has been evaluated using internal fault and magnetising inrush data recorded in the real field. At the end, comparative assessment of the proposed scheme with the existing and conventional techniques clearly indicate its superiority in terms of better sensitivity for internal faults and higher stability during external events.

The paper presents a method for estimating the parameters of an untransposed transmission line, which can be represented by an equivalent π-model, in real-time. The estimation of parameters is performed using the Weighted Least Squares (WLS) method, which utilizes three sets of synchronized phasor measurements of voltages and currents at both ends of the transmission line, with at least one measurement containing a sufficient zero-sequence voltage component. This method could be used in general case - for both transposed and untransposed lines, that have balanced or unbalanced load. By applying this method, it is possible to calculate the values of self-impedances and mutual impedances, as well as the values for susceptances. By transforming these values into the system of symmetrical components, the impedances and susceptances of positive, negative, and zero sequences, as well as mutual impedances between the positive, negative, and zero sequences, are also determined. The parameters of the untransposed line were determined in two different cases. Voltage and current measurements at both end of the transmission line were generated using MATLAB Simulink software, where phasors were determined and later used as data input for the calculations. In the first idealized case, measurement errors were not considered, while in the second case, measurement error was modelled in the input data. In both cases, two methods were applied: the first one which estimates the unknown parameters of the untransposed line using equations for an untransposed transmission line, and the second one which estimates the unknown parameters based on equations for a transposed line.

The frequency components of an induction machine due to different types of internal faults and their combinations are studied in this paper. Instead of taking a look at the current and control signals directly, this paper studies the impact caused by the basic inner structure on the inductances and their frequency components. Modified winding function and equivalent air-gap length are computed such that the combinations of internal faults can be accommodated. Static and dynamic eccentricity reshape the air-gap in a direct manner, while saturation brings third order harmonics, which instead can be equivalently considered as the effect caused by the fluctuation of air-gap length. Thus eccentricity faults and saturation have combined impacts on the equivalent air-gap length. Modified winding function accounting for all space harmonics simplifies the computation of inductances, and is also adequate for the case with rotor asymmetry. By extracting frequency components, different internal fault features are revealed. ANSYS/Maxwell is employed to simulate different cases to verify the theoretical analysis.

A new approach for transformer protection based on Wavelet Transformation is proposed in this paper. In the proposed approach, transient current signals at both sides of a transformer are firstly captured and then analyzed by wavelet transform, from which the modular maxima (MM) are derived and subsequently used to discriminate between magnetizing inrush current and fault currents. Various types of internal faults and magnetizing inrush are modelled using Real-time Digital Simulator (RTDS). Extensive RTDS simulations were carried out to cover various transformer operational conditions such as magnetizing inrush with various closing angles of circuit breaker, various fault types on either side of transformer, fault currents under CT's saturation during server fault conditions. The sampled current signals of both sides of a transformer are then analyzed by Wavelet transform. A series of obvious characteristics are observed by decomposing the transient current signals into scale 5 (j=5) using Daubechies4 wavelet function. The multiplication of the MM on either side of transformer is then utilized to distinguish between inrush current, internal fault current and external fault current. Extensive simulation results proved that the new algorithm is simple, reliable, accurate, immune to CT's saturation, and is able to perform correctly for the worst cases where an internal fault occurs when a transformer is energized without load.

A fault location method for DC transmission line based on the distributed parameter model considering line parameter uncertainty

Most identification algorithms do not consider the prescribed error bound on the parameter estimation error information, which may result in the poor transient performance of parameter estimation during the identification process. In this study, a novel identification scheme is presented for the extended Wiener–Hammerstein systems with backlash non‐linearity, which is implemented by using prescribed performance function and error transformation technique. To improve the transient performance of parameter estimation, the prescribed performance function is designed to prescribe estimation error bound. Then, the error transformation technique is applied to transform the prescribed estimation error problem into an equivalent generalised error problem, which can simplify the design of identification algorithm. By developing the parameter updating law, the convergence of generalised error problem can be guaranteed, and the parameter estimation of considered system can be achieved. The numerical example and experiment results validate that the proposed scheme can provide more accurate parameter estimation and better transient performance than the available identification approaches.

The discrimination of inrush currents and internal fault currents in transformers is an important feature of a transformer protection scheme. The harmonic current restrained feature is used in conventional differential relay protection of transformers. A literature survey shows that the discrimination between the inrush currents and internal fault currents is still an area that is open to research. In this paper, the classification of internal fault currents and magnetic inrush currents in the transformer is performed by using an extended Kalman filter (EKF) algorithm. When a transformer is energized under normal conditions, the EKF estimates the primary side winding current and, hence, the absolute residual signal (ARS) value is zero. The ARS value will not be equal to zero for internal fault and inrush phenomena conditions; hence, the EKF algorithm will be used for discriminating the internal faults and inrush faults by keeping the threshold level to the ARS value. The simulation results are compared with the theoretical analysis under various conditions. It is also observed that the detection time of internal faults decreases with the severity of the fault. The results of various test cases using the EKF algorithm are presented. This scheme provides fast protection of the transformer for severe faults.

In this article, an adaptive dynamic surface control approach is proposed for uncertain strict‐feedback systems (SFSs) to guarantee both the prescribed transient tracking performance and the asymptotic tracking while realizing the accurate parameter estimation. It is assumed that SFSs are subject to linearly parametric uncertainties in both the drift terms and the control coefficients. A new inequality on the arctangent function, which can be widely used in the robust or the adaptive control designs, is established. Owing to this inequality, nonlinear robust filters with arctangent functions are designed and embedded into the backstepping control algorithm to avoid the “differential explosion” problem. Moreover, an improved forgetting‐factor‐based parameter estimation error reconstruction mechanism is proposed. And the obtained parameter estimation errors are integrated into the adaptive laws to achieve the accurate parameter estimation. Furthermore, the projection operator is applied to avoid the singularity problem of the control law. Besides, an asymmetric error transformation is introduced to restrict the tracking error within the prescribed performance envelope. It is proved that the tracking error and the parameter estimation errors asymptotically converge to zero and the tracking error satisfies the prescribed transient performance. Finally, the effectiveness of the proposed control approach is validated in terms of the single‐link manipulator actuated by a brush DC motor.

A new internal fault detection and classification technique for synchronous generators is presented. First, the presence of an abnormal/fault condition is detected based on the Negative Sequence Component (NSC) of neutral end current. Thereafter, the internal fault and abnormal/external-fault conditions are discriminated by utilizing the instantaneous phase angle between the NSCs of the terminal voltage and current. Subsequently, the internal fault is classified based on phase angle between NSCs of terminal voltage and neutral end current along with the zero sequence component of the neutral end current. Efficacy of the proposed scheme has been verified on a Phase Domain Synchronous Machine model developed on the Real Time Digital Simulator (RTDS̅). The results derived from various fault data sets show that the proposed technique is able to effectively distinguish between internal and external faults including special cases such as current transformer saturation, overloading and unbalance condition. Further, it provides added capability of detecting and identifying inter-turn faults irrespective of the winding configuration of the generator. Comparative assessment of the proposed scheme in terms of detection time and incorporation of different types of faults with the existing techniques proves its superiority.

This paper is based on recent electrical system studies carried out on an Imperial Chemical Industries (ICI) plant located in Scotland, which derives its power supplies from both in-house generators and grid interconnection. The objective was to examine methods of improving the transient response of the industrial system under various external and internal fault conditions, with a view to improving the security of supplies to important drives and auxiliaries. High levels of plant security and enhanced synchronous-generator stabffity are normally associated with multiple-grid and in-house distribution feeders, with corresponding low values of impedance between the supply sources and motor drives. However, this paper examines all aspects of system behaviour during fault conditions and concludes that, in this instance, an improvement to overall transient performance is achieved by increasing grid feeder reactance immediately after fault inception. In the case of external faults developing on the interconnected grid, computer-aided studies show the advantage of rapidly switching out one of the grid transformer feeders. Similarly, in the event of selected internal faults occurring, study results show the improvement achieved by rapidly opening normally closed ring mains, thereby doubling the effective ring feeder reactance.

This paper presents an improved current differential protective principle. Marti model of the transmission line is applied in this principle, which place emphasis on solving frequency-dependent line parameters. The operating current expressions for an internal fault are also deduced in frequency domain. Finally, simulating comparison have been carried out between the proposed protective principle and Bergeron model based protection for Chinese 1000kV UHVAC test demonstration project. Simulation results show that this improved principle has high reliability for both internal and external faults. The 1000kV UHVAC transmission lines which are being constructed in China, in hybrid with HVDC links, will form the backbone of the future Chinese grid to cope with the requirement of increased power transmission over longer distances. It is important for relay protection to secure normal operation of UHV grid. The split-phase current differential protection is first applied owing to its rapidity and absolute selection. But due to the negative impact of large distributed capacitive currents, the reliability and sensitivity of traditional current differential relay decay seriously (1). Therefore, some scientists proposed the novel protective principles, which can not be affected by capacitive current (2), (3), (4). Reference (2) put forward a principle of pilot differential protection based on Bergeron model. It describes that currents at both sides of a line could be calculated by means of Bergeron model formula firstly, and then compared with the measured currents at the same side. This comparative result is just operating current in this protective scheme. Here the calculated currents and the measured currents at the same side are taken for comparison, by contrast in a traditional current differential relay a current value at one side is subtracted from that at the opposite side. The advantage lies in the Bergeron model-based principle is independent on the capacitive current, and it is unnecessary to calculate the compensating current. It must be noted that a transmission line is assumed to have constant parameters in the Bergeron model. However it has long been recognized that line parameters vary with frequency in actual electromagnetic transient process. Therefore if Bergeron model formulas are used, there exits calculating errors which would cause the accuracy and sensibility of relays reduce obviously. In order to solve this problem, an improved current differential protective principle is presented in this paper. The principle applied Marti model of the transmission line, which is based on traveling wave propagation. The frequency-dependent characteristics of line parameters are taken into account. By using of this approach, we will get a more accurate result. In addition, a new criterion adapting to this principle are presented. Finally, by making use of EMTPE and MATLAB software, the improved current differential protective principle, and the protection based on Bergeron model are both simulated on the first 1000kV UHVAC transmission line in China, also called as the 1000kV UHVAC test demonstration project. Simulating comparison shows that this improved principle is correct and reliable.

In this article, a new algorithm based on time-frequency analysis of differential current is presented for power transformer protection. Since the differential currents are non-stationary signals, the hyperbolic S-transform can be used as a powerful signal processing tool that yields the complete information in both time and frequency domains. A criterion function is proposed based on some extracted features from the obtained hyperbolic S-matrix and frequency contours. By selecting the proper threshold value, the internal fault can be detected correctly from other conditions. Various conditions of internal and external faults, transformer energization, over-excitation, and different levels of current transformer saturation are simulated using PSCAD/EMTDC software (Manitoba HVDC Research Center Inc., Manitoba, Canada), while the important parameters that have a direct effect on the differential current waveform are considered. Current transformers are simulated using accurate Jiels–Atherton model, and a real 230/63-kV power transformer is modeled based on a unified magnetic equivalent circuit. The obtained results show that the proposed algorithm remains stable during external faults and sends a trip signal in less than one cycle in the case of internal fault condition, even when the current transformers are saturated. Also, the effectiveness of the proposed algorithm is verified by using real data obtained from an event recorder of a three-phase power transformer.

Accurate parameters are crucial in modern energy systems to ensure the reliable operation of all components. Given the substantial volume of data in monitored systems, high-performance methods are necessary. This paper proposes a new Bayesian multi-output regressor for estimating the parameters of a three-phase transmission line. The presented approach achieves acceptable accuracy in parameter estimation using only one end of the line. The Bayesian regressor is developed using information derived from the data themselves, eliminating the need to explicitly model the system. This capability allows the method to estimate parameters while accommodating different noise models, even in the presence of systematic errors and non-Gaussian random noise. The methodology was validated on various systems, including a two-bus system, IEEE 14-bus, IEEE 39-bus, and IEEE 118-bus, under diverse conditions such as varying sample sizes, loads, and noise levels. These tests demonstrate the robustness of the proposed approach.

A fault protection method is proposed for flexible direct-current (DC) power systems based on the cosine similarity of currents in current-limiting reactors. The typical characteristics of external and internal faults in a flexible DC power system were analyzed. The principles of cosine similarity and the fault current characteristics of current-limiting reactors were used to distinguish between internal and external faults. The ratio of the average positive and negative voltages of the current-limiting reactor was then used to distinguish the fault types and fault line. Finally, a simulation model of a circular flexible DC power system was constructed using MATLAB/Simulink software (2018b). The simulation results show that the proposed protection scheme can quickly and accurately identify the location and type of faults, and has a strong ability to withstand fault resistance and is less affected by distributed capacitance, noise, and communication delay.

Aiming at the problem that single‐network hopping signals have not fully utilised its frequency domain sparse characteristic in the parameter estimation, this study proposes a parameter estimation of frequency hopping (FH) signal based on multi‐measurement vector sparse Bayesian learning (MSBL) in modulation wideband converter (MWC). Since the FH signal is sparse in the frequency domain, the authors apply the MSBL method to estimate its parameters. After the signal is sampled by the MWC, the MSBL algorithm is used to reconstruct its support set. Then the time–frequency ridge method is used to estimate the signal's hop duration, time‐hopping, and carrier frequency based on the time–frequency map. Simulation experiments show that under the condition of low signal‐to‐noise ratio, the parameter estimation performance in the case can be improved by up to 65% and anti‐noise performance can be improved up to 6 db compared with the existing method. The result is very close to the Nyquist full sampling and can greatly improve the accuracy of the FH signal parameter estimation in the MWC system and relieve the pressure of the hardware.