Frequency and fundamental signal measurement algorithms for distributed control and protection applications

Increasing penetration of distributed generation within electricity networks leads to the requirement for cheap, integrated, protection and control systems. To minimise cost, algorithms for the measurement of AC voltage and current waveforms can be implemented on a single microcontroller, which also carries out other protection and control tasks, including communication and data logging. This limits the frame rate of the major algorithms, although analogue to digital converters (ADCs) can be oversampled using peripheral control processors on suitable microcontrollers. Measurement algorithms also have to be tolerant of poor power quality, which may arise within grid-connected or islanded (e.g. emergency, battlefield or marine) power system scenarios. This study presents a 'Clarke-FLL hybrid' architecture, which combines a three-phase Clarke transformation measurement with a frequency-locked loop (FLL). This hybrid contains suitable algorithms for the measurement of frequency, amplitude and phase within dynamic three-phase AC power systems. The Clarke-FLL hybrid is shown to be robust and accurate, with harmonic content up to and above 28% total harmonic distortion (THD), and with the major algorithms executing at only 500 samples per second. This is achieved by careful optimisation and cascaded use of exact-time averaging techniques, which prove to be useful at all stages of the measurements: from DC bias removal through low-sample-rate Fourier analysis to sub-harmonic ripple removal. Platform-independent algorithms for three-phase nodal power flow analysis are benchmarked on three processors, including the Infineon TC1796 microcontroller, on which only 10% of the 2000 mus frame time is required, leaving the remainder free for other algorithms

All-Pole Recursive Digital Filters Design Based on Ultraspherical Polynomials

A simple method for approximation of all-pole recursive digital filters, directly in digital domain, is described. Transfer function of these filters, referred to as Ultraspherical filters, is controlled by order of the Ultraspherical polynomial, nu. Parameter nu, restricted to be a nonnegative real number (nu ≥ 0), controls ripple peaks in the passband of the magnitude response and enables a trade-off between the passband loss and the group delay response of the resulting filter. Chebyshev filters of the first and of the second kind, and also Legendre and Butterworth filters are shown to be special cases of these allpole recursive digital filters. Closed form equations for the computation of the filter coefficients are provided. The design technique is illustrated with examples

On the eigenfilter design method and its applications: a tutorial

The eigenfilter method for digital filter design involves the computation of filter coefficients as the eigenvector of an appropriate Hermitian matrix. Because of its low complexity as compared to other methods as well as its ability to incorporate various time and frequency-domain constraints easily, the eigenfilter method has been found to be very useful. In this paper, we present a review of the eigenfilter design method for a wide variety of filters, including linear-phase finite impulse response (FIR) filters, nonlinear-phase FIR filters, all-pass infinite impulse response (IIR) filters, arbitrary response IIR filters, and multidimensional filters. Also, we focus on applications of the eigenfilter method in multistage filter design, spectral/spacial beamforming, and in the design of channel-shortening equalizers for communications applications

Theory and design of uniform DFT, parallel, quadrature mirror filter banks

In this paper, the theory of uniform DFT, parallel, quadrature mirror filter (QMF) banks is developed. The QMF equations, i.e., equations that need to be satisfied for exact reconstruction of the input signal, are derived. The concept of decimated filters is introduced, and structures for both analysis and synthesis banks are derived using this concept. The QMF equations, as well as closed-form expressions for the synthesis filters needed for exact reconstruction of the input signalx(n), are also derived using this concept. In general, the reconstructed. signalhat{x}(n)suffers from three errors: aliasing, amplitude distortion, and phase distortion. Conditions for exact reconstruction (i.e., all three distortions are zero, andhat{x}(n)is equal to a delayed version ofx(n))of the input signal are derived in terms of the decimated filters. Aliasing distortion can always be completely canceled. Once aliasing is canceled, it is possible to completely eliminate amplitude distortion (if suitable IIR filters are employed) and completely eliminate phase distortion (if suitable FIR filters are employed). However, complete elimination of all three errors is possible only with some simple, pathalogical stable filter transfer functions. In general, once aliasing is canceled, the other distortions can be minimized rather than completely eliminated. Algorithms for this are presented. The properties of FIR filter banks are then investigated. Several aspects of IIR filter banks are also studied using the same framework

Filter distortion effects on telemetry signal-to-noise ratio

The effect of filtering on the Signal-to-Noise Ratio (SNR) of a coherently demodulated band-limited signal is determined in the presence of worse-case amplitude ripple. The problem is formulated mathematically as an optimization problem in the L2-Hilbert space. The form of the worst-cast amplitude ripple is specified, and the degradation in the SNR is derived in a closed form expression. It is shown that when the maximum passband amplitude ripple is 2 delta (peak to peak), the SNR is degraded by at most (1 - delta squared), even when the ripple is unknown or uncompensated. For example, an SNR loss of less than 0.01 dB due to amplitude ripple can be assured by keeping the amplitude ripple to under 0.42 dB

Optimal design of nonuniform FIR transmultiplexer using semi-infinite programming

This paper considers an optimum nonuniform FIR transmultiplexer design problem subject to specifications in the frequency domain. Our objective is to minimize the sum of the ripple energy for all the individual filters, subject to the specifications on amplitude and aliasing distortions, and to the passband and stopband specifications for the individual filters. This optimum nonuniform transmultiplexer design problem can be formulated as a quadratic semi-infinite programming problem. The dual parametrization algorithm is extended to this nonuniform transmultiplexer design problem. If the lengths of the filters are sufficiently long and the set of decimation integers is compatible, then a solution exists. Since the problem is formulated as a convex problem, if a solution exists, then the solution obtained is unique and the local solution is a global minimum

Interleavers

The chapter describes principles, analysis, design, properties, and implementations of optical frequency (or wavelength) interleavers. The emphasis is on finite impulse response devices based on cascaded Mach-Zehnder-type filter elements with carefully designed coupling ratios, the so-called resonant couplers. Another important class that is discussed is the infinite impulse response type, based on e.g. Fabry-Perot, Gires-Tournois, or ring resonators