Characterizing Synchronized Lissajous Curves to Scrutinize Power Distribution Synchro-Waveform Measurements

Synchro-Phasors in Power System

The Phasor Measurement Unit (PMU) is considered to be one of the most important measuring devices in the future of power system. The difference comes from its unique ability to provide synchronized phasor measurements of voltages and currents from widely dispersed locations in an electric power grid called synchrophasor technology .In SCADA system, the measured quantities remain constant during...

Trivariate polynomial approximation on Lissajous curves ∗

We study Lissajous curves in the 3-cube that generate algebraic cubature formulas on a special family of rank-1 Chebyshev lattices. These formulas are used to construct trivariate hyperinterpolation polynomials via a single 1-d Fast Chebyshev Transform (by the Chebfun package), and to compute discrete extremal sets of Fekete and Leja type for trivariate polynomial interpolation. Applications co...

Improving Monitoring, Control and Protection of Power Grid Using Wide Area Synchro-Phasor Measurements

When disturbances occur in power grid, monitoring, control and protection systems are required to stop the grid degradation, restore it to a normal state, and hence minimize their effects. However, in wide area power grid resulting from large extension and interconnection with neighbor grids, classical systems based on local independent measurements and decisions are not able to consider the ov...

Lissajous curves and semiclassical theory: The two-dimensional harmonic oscillator

The semiclassical treatment of the two-dimensional harmonic oscillator provides an instructive example of the relation between classical motion and the quantum mechanical energy spectrum. We extend previous work on the anisotropic oscillator with incommensurate frequencies and the isotropic oscillator to the case with commensurate frequencies for which the Lissajous curves appear as classical p...

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