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Fundamentals of Control Systems Engineering
Published in Anna M. Doro-on, Handbook of Systems Engineering and Risk Management in Control Systems, Communication, Space Technology, Missile, Security and Defense Operations, 2023
Anti-aliasing filter is a function for reducing aliasing by restricting the bandwidth of the signal to be sampled—usually an analogue filter with a natural frequency set to less than half the sampling frequency (Pratt 2000). When an analog signal contains a component with a frequency higher than the Nyquist frequency (half the sampling frequency fS), the sampled signal component appears to have a frequency less than the Nyquist frequency. The theory of discrete-time systems indicates that the maximum frequency (fmax) of a signal sent to the analog to digital converter should satisfy fmax < fs/2, where fs/2 is called the Nyquist frequency (Landau et al. 1988). If the analog signal component frequency f lies between odd integers (2n − 1) and (2n + 1) times the Nyquist frequency: (n−0.5)fS≤f<(n−0.5)fS
Identification in practice
Published in P. P. J. van den Bosch, A. C. van der Klauw, Modeling, Identification and Simulation of Dynamical Systems, 2020
P. P. J. van den Bosch, A. C. van der Klauw
where ωB is the bandwidth of the process. The bandwidth ωB of the process is defined as the maximum frequency ω for which the magnitude of the frequency function reaches the level of 1/2 times its static value (–3dB), and can, for example, be determined from preliminary experiments. To avoid aliasing effects, an anti-aliasing filter has to be added to the system. An anti-aliasing filter is a low-pass filter, with cut-off frequency around the Nyquist frequency. Note that the filter can only be realized with continuous (analogue) components, before the sampling takes place!
Sampling theory
Published in Paul Grimshaw, Michael Cole, Adrian Burden, Neil Fowler, Instant Notes in Sport and Exercise Biomechanics, 2019
If the sampling condition is not satisfied, then frequencies will overlap and the nature of the recorded signal will be different from the input signal. This overlap is called aliasing. To prevent aliasing, you can either 1) increase the sampling frequency or 2) introduce an anti-aliasing filter (or make the anti-aliasing filter more stringent). The anti-aliasing filter is used to restrict the bandwidth of the signal to satisfy the sampling condition. This holds in theory, but cannot be satisfied in practice as there may be some elements of the real signal that fall outside of the sampled range, and thus the recorded signal will not include all of the real signal. However, in most situations, the amount of information lost may be small enough that the aliasing effects are negligible.
Adaptive phasor estimation technique during off-nominal frequency for numerical relays
Published in Journal of Information and Telecommunication, 2018
Omar Sami Thiab, Łukasz Nogal, Ryszard Kowalik
Converting analog signals to sequences of numerical values passes through below steps. Surge filter: The large inrush in the input analog signals will be suppressed using surge filter for the safety of the digital relay.Anti-aliasing filter: To avoid possible errors in the evaluation of input signal, anti-aliasing filter is used according to the Nyquist criterion.Analog/digital sample and hold: To convert the input signal from analog to digital. To scan the whole signal, a data window of limited length is applied to acquire information on part of the signal. Within the section of the signals that are scanned by the data window, a limited number of points of the waveform are sampled. While the window moving forward, more samples are obtained at different snapshots of time. The sampling window length, numbers of samples in the window, as well as the shape of the sampling window are dependent on the relay algorithm.
Fault Location Scheme for Cross-Country Faults in Dual-Circuit Line Using Optimized Regression Tree
Published in Electric Power Components and Systems, 2020
Valabhoju Ashok, Anamika Yadav, Mohammad Pazoki, Almoataz Y. Abdelaziz
A precise and reliable fault location scheme is a prerequisite of the contemporary interconnected transmission network in recent days. When a fault takes place, the fault current contains of several objectionable frequencies and the DC offset exists rendering to the evolution of time pertaining to the zero crossing of the voltage signal. To avoid an error in a subsequent signal processing due to signal aliasing (arising false frequencies in a signal) the voltage and current signals are passed over an anti-aliasing filter (2nd order Butterworth filter). By using this 2nd order Butterworth filter, any undesired high frequencies (noise) can be removed before application of DWT. At the zero-fault inception instant, high magnitude of the DC offset exists in the fault current signal, which may saturate the current transformer and thus it causes to mal-operation of the distance relay. In this proposed ERT- model, exclusive datasets are designed by simulating prevalent fault scenarios on a practical CSPS network in MATLAB/Simulink software. All the fault simulation studies have been performed at 20 kHz sampling frequency and further down sampled to 1 kHz to reduce the computational burden while preprocessing of fault signals. It is very essential to extract appropriate topographies from the measured signal to design exclusive datasets for training/testing of the BGRT modules because efficacy of the ERT- model depends on learning ability of regression trees. Herein this paper, Discrete Wavelet Transform (DWT) has been employed to extract relevant topographies/feature. In this proposed scheme, exclusive datasets have been designed to train and test the ERT-model for location of CCFs. The generation of Dataset-I by varying different fault parameters has been done as follows: fault location () ((1-197) km in steps of 1 km), fault inception angle () (0°, 90°, and 270°), fault resistance () (0 Ω, 50 Ω, and 100 Ω), and fault type (A1G-B1G, A1G-B1C1G, and A1B1G-C1G). Totally, number of fault cases is 3(Fault Type) 86436 (fault cases)=259308.