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Using a PMU, it is simple to detect abnormal waveform shapes. A waveform shape described mathematically is called a phasor.. A phasor measurement unit (PMU) is a device used to estimate the magnitude and phase angle of an electrical phasor quantity (such as voltage or current) in the electricity grid using a common time source for synchronization.
Instantaneous phase and frequency are important concepts in signal processing that occur in the context of the representation and analysis of time-varying functions. [1] The instantaneous phase (also known as local phase or simply phase ) of a complex-valued function s ( t ), is the real-valued function:
The complex constant, which depends on amplitude and phase, is known as a phasor, or complex amplitude, [4] [5] and (in older texts) sinor [6] or even complexor. [6] A common application is in the steady-state analysis of an electrical network powered by time varying current where all signals are assumed to be sinusoidal with a common frequency ...
The amplitude and the phase of the waveform is transformed into a vector where the phase is translated to the angle between the phasor vector and X-axis and the amplitude is translated to vector length or magnitude. In this concept the representation and the analysis becomes very simple and the addition of two wave forms is realized by their ...
The instantaneous amplitude, and the instantaneous phase and frequency are in some applications used to measure and detect local features of the signal. Another application of the analytic representation of a signal relates to demodulation of modulated signals .
Unless θ (t) is a constant, the point in time t s at which the phase is stationary will vary according to the instantaneous frequency ω s. Expressing the difference between ( ω s - ω 0 ).t and θ (t) as a Taylor series about the time t s , but discarding all but the first three terms (of which the second term is zero, here), the Fourier ...
Time-varying phasors are used in dynamic analysis of a large power system. [ 1 ] [ 5 ] The phasor representation of sinusoidal voltages and currents is generalized to arbitrary waveforms . [ 2 ] This mathematical transformation eliminates the 60 Hertz (Hz) carrier which is the only time-varying element in the stationary case. [ 3 ]
Most transmission lines are high-voltage three-phase alternating current (AC), although single phase AC is sometimes used in railway electrification systems. Electricity is transmitted at high voltages (115 kV or above) to reduce the energy loss which occurs in long-distance transmission.