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

A Fast and Accurate Algorithm for Spherical Harmonic Analysis on HEALPix Grids with Applications to the Cosmic Microwave Background Radiation

The Hierarchical Equal Area isoLatitude Pixelation (HEALPix) scheme is used extensively in astrophysics for data collection and analysis on the sphere. The scheme was originally designed for studying the Cosmic Microwave Background (CMB) radiation, which represents the first light to travel during the early stages of the universe's development and gives the strongest evidence for the Big Bang theory to date. Refined analysis of the CMB angular power spectrum can lead to revolutionary developments in understanding the nature of dark matter and dark energy. In this paper, we present a new method for performing spherical harmonic analysis for HEALPix data, which is a central component to computing and analyzing the angular power spectrum of the massive CMB data sets. The method uses a novel combination of a non-uniform fast Fourier transform, the double Fourier sphere method, and Slevinsky's fast spherical harmonic transform (Slevinsky, 2019). For a HEALPix grid with $N$ pixels (points), the computational complexity of the method is $\mathcal{O}(N\log^2 N)$, with an initial set-up cost of $\mathcal{O}(N^{3/2}\log N)$. This compares favorably with $\mathcal{O}(N^{3/2})$ runtime complexity of the current methods available in the HEALPix software when multiple maps need to be analyzed at the same time. Using numerical experiments, we demonstrate that the new method also appears to provide better accuracy over the entire angular power spectrum of synthetic data when compared to the current methods, with a convergence rate at least two times higher

Comparisons of the execution times and memory requirements for high-speed discrete fourier transforms and fast fourier transforms, for the measurement of AC power harmonics

Conventional wisdom dictates that a Fast Fourier Transform (FFT) will be a more computationally effective method for measuring multiple harmonics than a Discrete Fourier Transform (DFT) approach. However, in this paper it is shown that carefully coded discrete transforms which distribute their computational load over many frames can be made to produce results in shorter execution times than the FFT approach, even for large number of harmonic measurement frequencies. This is because the execution time of the presented DFT actually rises with N and not the classical N2 value, while the execution time of the FFT rises with Nlog2N

P and M class phasor measurement unit algorithms using adaptive cascaded filters

The new standard C37.118.1 lays down strict performance limits for phasor measurement units (PMUs) under steady-state and dynamic conditions. Reference algorithms are also presented for the P (performance) and M (measurement) class PMUs. In this paper, the performance of these algorithms is analysed during some key signal scenarios, particularly those of off-nominal frequency, frequency ramps, and harmonic contamination. While it is found that total vector error (TVE) accuracy is relatively easy to achieve, the reference algorithm is not able to achieve a useful ROCOF (rate of change of frequency) accuracy. Instead, this paper presents alternative algorithms for P and M class PMUs which use adaptive filtering techniques in real time at up to 10 kHz sample rates, allowing consistent accuracy to be maintained across a ±33% frequency range. ROCOF errors can be reduced by factors of >40 for P class and >100 for M class devices

Algorithm based comparison between the integral method and harmonic analysis of the timing jitter of diode-based and solid-state pulsed laser sources

AbstractA comparison between two methods of timing jitter calculation is presented. The integral method utilizes spectral area of the single side-band (SSB) phase noise spectrum to calculate root mean square (rms) timing jitter. In contrast the harmonic analysis exploits the uppermost noise power in high harmonics to retrieve timing fluctuation. The results obtained show that a consistent timing jitter of 1.2ps is found by the integral method and harmonic analysis in gain-switched laser diodes with an external cavity scheme. A comparison of the two approaches in noise measurement of a diode-pumped Yb:KY(WO4)2 passively mode-locked laser is also shown in which both techniques give 2ps rms timing jitter

Power meter for Highly-Distorted Three-Phase Systems

This paper describes a low-cost, three-phase power meter, which is based on a fast, specially designed acquisition board coupled to a PC via the PC parallel/printer port or by means of an AT card. The power associated with the fundamental and first harmonics is computed by software that operates in the time domain and employs a sample-weighting procedure that makes the uncertainty related to the asynchronous sampling negligible. The low-cost acquisition board features two 8-bit 1 MHz converters and a local RAM, which decouples the PC clock from the measurement requirements. Hall effect transducers are used for the current channels and fast differential amplifiers for the voltage channels. The fast sampling frequency allows simple antialiasing filters to be employed. Digital filtering is used to reduce the sample number while increasing the resolution. The power uncertainty provided by this arrangement is less then 0.1 % with 2.5 measurements per second when a low-cost 486DX33-based PC is use

ARKCoS: Artifact-Suppressed Accelerated Radial Kernel Convolution on the Sphere

We describe a hybrid Fourier/direct space convolution algorithm for compact radial (azimuthally symmetric) kernels on the sphere. For high resolution maps covering a large fraction of the sky, our implementation takes advantage of the inexpensive massive parallelism afforded by consumer graphics processing units (GPUs). Applications involve modeling of instrumental beam shapes in terms of compact kernels, computation of fine-scale wavelet transformations, and optimal filtering for the detection of point sources. Our algorithm works for any pixelization where pixels are grouped into isolatitude rings. Even for kernels that are not bandwidth limited, ringing features are completely absent on an ECP grid. We demonstrate that they can be highly suppressed on the popular HEALPix pixelization, for which we develop a freely available implementation of the algorithm. As an example application, we show that running on a high-end consumer graphics card our method speeds up beam convolution for simulations of a characteristic Planck high frequency instrument channel by two orders of magnitude compared to the commonly used HEALPix implementation on one CPU core while maintaining at typical a fractional RMS accuracy of about 1 part in 10^5.Comment: 10 pages, 6 figures. Submitted to Astronomy and Astrophysics. Replaced to match published version. Code can be downloaded at https://github.com/elsner/arkco

Efficient detection for multifrequency dynamic phasor analysis

Analysis of harmonic and interharmonic phasors is a promising smart grid measurement and diagnostic tool. This creates the need to deal with multiple phasor components having different amplitudes, including interharmonics with unknown frequency locations. The Compressive Sensing Taylor-Fourier Multifrequency (CSTFM) algorithm provides very accurate results under demanding test conditions, but is computationally demanding. In this paper we present a novel frequency search criterion with significantly improved effectiveness, resulting in a very efficient revised CSTFM algorithm

Wavemoth -- Fast spherical harmonic transforms by butterfly matrix compression

We present Wavemoth, an experimental open source code for computing scalar spherical harmonic transforms (SHTs). Such transforms are ubiquitous in astronomical data analysis. Our code performs substantially better than existing publicly available codes due to improvements on two fronts. First, the computational core is made more efficient by using small amounts of precomputed data, as well as paying attention to CPU instruction pipelining and cache usage. Second, Wavemoth makes use of a fast and numerically stable algorithm based on compressing a set of linear operators in a precomputation step. The resulting SHT scales as O(L^2 (log L)^2) for the resolution range of practical interest, where L denotes the spherical harmonic truncation degree. For low and medium-range resolutions, Wavemoth tends to be twice as fast as libpsht, which is the current state of the art implementation for the HEALPix grid. At the resolution of the Planck experiment, L ~ 4000, Wavemoth is between three and six times faster than libpsht, depending on the computer architecture and the required precision. Due to the experimental nature of the project, only spherical harmonic synthesis is currently supported, although adding support or spherical harmonic analysis should be trivial.Comment: 13 pages, 6 figures, accepted by ApJ