Power Grid Frequency Estimation Based on Zero Crossing Technique Using Least Squares Method to Approximate Sampled Voltage Signal Around Zero Level

Abstract

The article presents the application of the least squares method to the estimation of voltage transition points through the zero level in order to determine the frequency of the power grid system. A linear approximation of the quantized voltage signal samples near zero has been applied, which ensures effective noise suppression and reduces measurement errors. An even sampling of the sinusoidal voltage disturbed by noise was assumed, and on this basis the corresponding mathematical relations were derived. The presented algorithm for processing signal samples is computationally simple and can be easily implemented in a microprocessor system. The dependence of the accuracy of the signal frequency measurement on: SNR signal ratio, ADC converter resolution, signal sampling rate and the number of samples used for approximation were investigated. The simulation tests of the presented method were carried out and the results were presented, which enable proper design of the measurement system (ADC converter resolution, sampling rate, number of points to approximate) depending on the expected signal SNR ratio and the expected accuracy of measurements. In order to verify the presented method in practice, a measuring system was implemented using the National Instruments NI USB 6009 Data Acquisition Card and a personal computer. The measurement algorithm was implemented in the LabVIEW environment. The structure of the program was presented and the method of implementation of the most important parts of the algorithm was discussed, as well as examples of measurement results. The developed method can be used to build an independent measuring instrument or it can be an element of a larger measuring system.