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.
It is well known that the magnitudes of the coefficients of the discrete Fourier transform (DFT) are invariant under certain operations on the input data. In this paper, the effects of rearranging the elements of an input data on its DFT are studied. In the one-dimensional case, the effects of permuting the elements of a finite sequence of length N on its discrete Fourier transform (DFT) coefficients are investigated. The permutations that leave the unordered collection of Fourier coefficients and their magnitudes invariant are completely characterized. Conditions under which two different permutations give the same DFT coefficient magnitudes are given. The characterizations are based on the automorphism group of the additive group ZN of integers modulo N and the group of translations of ZN. As an application of the results presented, a generalization of the theorem characterizing all permutations that commute with the discrete Fourier transform is given. Numerical examples illustrate the obtained results. Possible generalizations and open problems are discussed. In higher dimensions, results on the effects of certain geometric transformations of an input data array on its DFT are given and illustrated with an example.