Digital multirate processing, i.e., signal processing that involves more than one sample rate, permits computationally efficient estimation of several electrical quantities. The new multirate algorithms for active power, voltage and current do not require periodicity of the input signals or synchronous sampling and give excellent accuracy. They replace the integration or summation of conventional methods with digital low pass filtering, implemented very efficiently in a decimator. A multirate flickermeter algorithm is also introduced, completed with a novel method which allows the evaluation of individual flicker sources of the power system while other sources remain active.

Digital multirate algorithms for measurement of voltage, current, power and flicker

Consider an autoregressive-moving average (ARMA) discrete-time sequence {x_{k}} with covariance sequence {R_{k}} . Equations are given for the solution of the AR coefficients {a_{k}}\min{1}\max{n} in terms of the covariances {R_{k}}\min{0}\max{2n-1} , and subsequent solution for the MA coefficients {b_{k}}\min{1}\max{n} in terms of the AR coefficients and the covariances {R_{k}}\min{0}\max{n-1} . The results are derived and presented somewhat differently than usual to complement the results of [1] for the synthesis of covariance-invariant digital filters. In the context of spectrum analysis, the results provide a means of performing ARMA spectrum analysis on data that arise as sampled data from a rational continuous-time process [2]. An important result, originally derived in [2], shows that the ARMA spectrum can be obtained without actually solving the nonlinear factorization problem for the MA coefficients.

A note on covariance-invariant digital filter design and autoregressive moving average spectrum analysis

The IEC 61000-4-15 standard describes the analog implementation of a flickermeter up to the output of block 4. The digital implementation of a flickermeter is accepted provided that it satisfies the accuracy specifications both for instantaneous flicker sensation per unit and for the short-term flicker severity or Pst. Nowadays, most of the commercial flickermeters are partially or totally digital. It is noticed that even though they comply with the accuracy specifications of the standard, they could yield maximum measurement differences of 30% in field tests according to some authors. In this paper the influence of the main parameters involved in the digital implementation of the UIE flickermeter has been analysed, both for instantaneous flicker sensation and for the Pst. The flickermeter has been implemented using the MATLAB programming language. The testing voltage signals can be analytically generated or read from field test record files. Four parameters has been analysed in order to quantify their influence in instantaneous flicker sensation: signal sampling rate; number of resolution bits in quantization; processing sampling rate; and influence of the high pass filter for demodulation. In relation to the flicker severity measurement accuracy, besides aforementioned parameters, the influence of the number of classes and of the type of classification in block 5 has been analysed.

Analysis of sensitivity to the main parameters involved in the digital implementation of the UIE flickermeter

Exact likelihood for stationary vector autoregressive moving average process

A novel approach to improving the frequency resolution of parametric power spectrum estimation for signals with rational spectra is discussed. Specifically, the effect of errors in the calculated autocorrelation values is considered. Analysis and numerical simulation reveal that the error sensitivity becomes acute when the poles are closely spaced, demonstrating one of the difficulties encountered when high-resolution spectrum estimates are required. To remedy this problem, two modified spectrum-estimation procedures are proposed. The first applies to situations where discrete-time techniques are used to estimate the spectra of continuous-time processes. It involves selecting the autocorrelation function sampling period to separate the poles. The second procedure involves desampling an autocorrelation sequence to separate closely spaced poles artificially. Numerical examples verify improved resolution for both procedures. >

Spectrum manipulation for improved resolution

When discretizing continuous-time filters, one is often interested in preserving a property termed covariance-invariance. Techniques are outlined for synthesizing discrete-time filters which are covariance-invariant with corresponding continuous-time filters. The synthesis techniques involve straightforward matrix decompositions or polynomial root-finding algorithms that can easily be programmed on a digital computer. Applications of the technique to digital filter synthesis are outlined, with example designs presented for covariance-invariant Butterworth and Chebyshev digital filters. Based on the frequency response of these designs it is argued that the method of covariance-invariance is superior to the methods of impulse-invariance and bilinear-z as a response matching design technique for the synthesis of digital filters. This superiority is especially apparent at sampling rates that are marginal with respect to filter critical frequencies. Moreover, the covariance-invariant designs are stably invertible solutions to a so-called spectral factorization problem. This property may be important in inverse filtering applications.

Covariance-invariant digital filtering

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Covariance-invariant digital filtering