Furthermore, by understanding the theory behind the accurate frequency and ROCOF is much more problematic. The transfer function of attenuation i. ROCOF is calculated via an additional differentiation from Keywords— Frequency measurement, Frequency estimation, frequency, further exacerbating the problems.
White noise, Gaussian noise, Colored noise, Signal to noise ratio, Power system measurements, Finite impulse response filters, This paper focusses on the effects of front-end white noise, Fourier transforms, Phasor Measurement Units. These introduce I. They can result in an excessively noisy frequency Frequency has always been, and will continue to be, a key measurement, and a ROCOF measurement in which the actual parameter within AC power systems.
ROCOF Rate of Change of Frequency has The analysis was extended to include other windows in [4], but been historically important as a measurand for protective the effect of windowing was determined by time-domain full- algorithm Monte-Carlo simulation, rather than analytically.
This is not scaling, and filter design. It is best performance against white noise. But, this is not true. The two heterodyned phase-by-phase DFT, Discrete Fourier split signals can still be reconsidered to re-combine back into Transform analyses, and the filtered Clarke transform. The the form of 1 , interfering constructively since they are rules and equations governing the effect of white noise on entirely correlated.
Zero-crossing Between points B and C, a quadrature oscillator is applied, and phased-locked-loop techniques are also considered for which is tuned to a frequency fT. Therefore, at point C of Fig. An overview of the process is show in Fig. In Fig. This will be filtered out later by H f , paper, but it is discussed in [6]. Only their frequencies are shifted downwards by fT. Also, a key point of understanding is that the two signal parts of each pair become de-correlated, and cannot be recombined into the form 1.
Between point C and point D of Fig. Other values could be used, with no changes to the final results of this paper, since both carrier and noise will be affected equally.
This filter has complex positive and negative frequency components with halved amplitudes unity gain at 0 Hz, but is designed to reject the image at point B of Fig. However, FIR filters are particularly useful since deep notches can often conveniently be placed at the image frequency, and linear phase response can be Fig.
In particular, the use of a rectangular boxcar filter fT, at point C of Fig. However, much Fig. The wanted measurement result responses and latencies tailored to a particular application. In contains only the component at 0 Hz, which represents a this paper, FIR filters are created by cascading tunable boxcar steady-state phasor measurement of the carrier. The function of filters together to provide effective image and harmonic filtering is to remove the unwanted components, in particular rejection, even while frequency varies from nominal.
Some of the image at - fC - fT which has the same amplitude as the the concepts were laid down in [7], although the method we component at 0 Hz, and also, most relevantly for this paper, at use is unconditionally not marginally stable, allows the use of all frequencies other than 0 Hz, where noise components can windows that are non-integer numbers of samples, and allows and will fall.
The method used is described in [] and operates extremely quickly in real-time [11]. To include the adaptive III. The noise degrades the Signal to Noise Ratio Loop. Firstly, all analogue input circuitry introduces a level of The heterodyne process between points A and C of Fig.
Second, some applications apply can be explained visually using Fig. Third, the heterodyning process when there are two discrete signal signal is quantised as it is sampled by the ADC, and assigned a components present in the real-valued sampled signal: a carrier digital value. Its effect can be estimated by [13]: Fig. However, clock jitters at 30ns or above [15] may have a noticeable impact on system performance. The combined effect of all four mechanisms need to be considered, to estimate overall SNR for the sampling front end.
ADC imperfections. The effect of white noise between points A and C several of the mechanisms, at least in part. However, the Fig. Every individual noise frequency analogue sensors, cables, circuits or amplifiers in the signal component in Fig. However, in a wave 1 it can be regarded as being composed of two equal practical application this is often not the case. At the same time, the most by half 2. This is shown in Fig.
This example value is used for investigations in section XI. In a scenario with a known or estimated SNR, at a sampling frequency fS, the relative power spectral density of Fig. LdBc f can be used to derive L f , a linear noise so they cannot be considered to recombine by linear addition power density, relative to a carrier with power 1, with units of e.
The effect of aliasing Furthermore, the RMS noise amplitude density relative to also plays a part in the de-correlation.
The noise level at point D of Fig. After the heterodyning and filtering action of H f , the image component is rejected and the carrier emerges at points D and E of Fig. The magnitude of the resulting complex exponential, 90 degrees [5]. In this case, the AM of Fig. The above two paragraphs allow the following equation PM component does [5, 6]. Any error in measuring this phase contributes to In this paper, the expressions for errors contain integrations frequency and ROCOF error. The analysis proceeds with a across the Nyquist range of frequencies, as continuous integral similar argument as 23 - For example, the to the error.
There is no heterodyning frequency translation during the Additionally, should a Park transform be used instead of the Clarke transformation process. Therefore, there is no Clarke transform, then so long as a quasi-static frequency decorrelation of either fundamental signal or noise components estimate is used to define the rotating reference frame, the Park due to a frequency translation.
Hence, an analysis of wideband transform result sensitivities to noise will be identical to those noise contribution needs to consider only the positive-half of of the Clarke transform. While rotating frame. So, the addition of the noise contributions from the three phases needs to be A. Other times could be used with the same the waveform samples, including the samples with biggest amplitude and highest SNR, are not included in the analysis.
Also, the options for filtering are limited. The methods excluding calculations and communications is equal model is therefore lengthy to describe, even though it does not to half the filter window time length. Since the measurements account for all the correlation mechanisms in perfect detail.
By comparison, a zero-crossing frequency measurement obtained across a base window of N cycles is constrained, in B. This means that the latency varies with time in a saw- in for example power-quality analysers, by locking on to the tooth fashion. PLLs are also commonly used within the frequency requires differentiation using 2 samples obtained control loops of power converters.
Table II describes the options for latency. All these PLLs also contain a single- step responses in the time domain. Table I is estimated from the time-domain response in this Ramp-rate filters were disabled since these nonlinear devices paper as 5 cycles ms.
It is well known that in the presence of white noise spread evenly across the whole Nyquist band e. However, the frequency measurement requires differentiation of phase. The validity of this If this chain is linear, then the order of the filter components assumption depends upon whether the noise is composed of can be adjusted without affecting the final result. So, instead of genuine white noise e. However, a special case can occur if the noise is dominated by ADC quantisation including static INL and DNL performances , with negligible analogue noise contribution, and the sample rate is an exact multiple of the signal fundamental frequency, and the input signal waveform is entirely steady-state.
In this corner case the noise can Fig. If the digital filter places a zero near any of those frequencies, the noise can Logic would then dictate that the lowest noise output would be highly attenuated, and errors reduced. The predictions and integration. However, a bounded integration over finite time simulations for FE and RFE from zero-crossings, for the same can be implemented.
This suggests that how the noise is split between white and quantisation types, the while a single boxcar filter has the best ENBW for a normal fundamental frequency, and the precise time of the measurement, when the measurement result is differentiated, measurement. The simulations were carried out measurement, which requires 2 stages of differentiation, by s2.
However, the results shown are derived from desktop simulations, and presented in Table III. The performance of the three-phase Clark-transform algorithm is shown to be exactly equivalent to the three-phase heterodyned measurements, for equivalent filtering, as predicted. In general, there is little marked difference between results using white noise, and results using purely quantisation noise. This type of noise is classified into two categories:. Solar Noise : Solar noise is generated by the sun.
As Sun is a large body with extremely high temperature thus it emits or releases high electrical energy in noise form over a broad frequency range. However, the intensity of the produced noise signal changes timely. This is so because the temperature change of the sun follows 11 years of the life cycle. Hence large electrical disturbances occur after the period of every 11 years. While at other years the noise level is comparatively low.
Cosmic Noise : This noise originates from the stars present in the outer space. As distant stars are also very high-temperature bodies and are also termed as the sun. The noise generated from the star is similar to that generated from the sun. Cosmic noise is also known as black body noise. Not only the stars but the galaxies and other virtual point sources like quasars and pulsars in the outer space produces cosmic noise. This type of extrinsic noise is also known as industrial noise.
These are basically the electrical noise that gets produced by the wear and tear of the circuit being used. The source of man-made noise is electric motors, high current circuits, florescent lights switch gears etc.
When these machines operate, arc discharge takes place and this discharge generates noise signals in the communication system. The frequency spectrum of man-made noise lies between 1 MHz to MHz.
They are called so because these are nothing but an integral part of the system. Proper designing of the communication system can reduce or overcome noise due to internal sources. As we already know that an electrical signal is transmitted through a channel by the help of conductors. So, the electrons present in the conductors move randomly.
The random motion of the electrons is the reason for the thermal energy received by the conductor. However, these free electrons are non-uniformly distributed within the conductor. Due to this a possibility also exist that at one end the number of free electrons will be comparatively higher than at the other end.
This non-uniform distribution of electrons provides the average voltage to be zero, however, the average power is not zero in this case. So, this non zero power is nothing but the noise. And as it is the outcome of thermal action. Hence also known as thermal noise power. Thermal noise is sometimes referred as Johnson noise or white noise. Shot noise in a communication channel is the result of random variation in the appearance of electrons and holes at the output side of the device.
These random movements are the result of discontinuities in the device which is being used by the system.
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