This paper deals with the amplitude estimation in the frequency domain of low-level sine waves, i.e. sine waves spanning a small number of quantization steps of an analog-to-digital converter. This is a quite common condition for high-speed low-resolution converters. A digitized sine wave is transformed into the frequency domain through the discrete Fourier transform. The error in the amplitude estimate is treated as a random variable since the offset and the phase of the sine wave are usually unknown. Therefore, the estimate is characterized by its standard deviation. The proposed model evaluates properly such a standard deviation by treating the quantization with a Fourier series approach. On the other hand, it is shown that the conventional noise model of quantization would lead to a large underestimation of the error standard deviation. The effects of measurement parameters, such as the number of samples and a kind of the time window, are also investigated. Finally, a threshold for the additive noise is provided as the boundary for validity of the two quantization models
Power systems that are highly loaded, especially by a stochastic supply of renewables and the presence of storages, require dynamic measurements for their optimal control. Phasor measurement units (PMUs) can be used to capture electrical parameters of a power system. Standards on the PMU dynamic performance have been modified to incorporate their new dynamic mode of operation. This paper examines the PMU dynamic performance and proposes essential algorithms for measurement accuracy verification. Measurements of dynamic input signals, which vary in amplitude or frequency, were taken during automated tests of two PMUs. The test results are presented and expounded with further recommendation for the performance requirements. This paper also presents and examines applied testing procedures with relevance to the specifications of the IEEE Standard for Synchrophasor C37.118.1™-2011 and its amendment C37.118.1a™-2014.