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Mathematics and basic principles of three-phase electric power. One voltage cycle of a three-phase system, labeled 0 to 360° (2π radians) along the time axis. The plotted line represents the variation of instantaneous voltage (or current) with respect to time. This cycle repeats with a frequency that depends on the power system.
Symmetrical components are most commonly used for analysis of three-phase electrical power systems. The voltage or current of a three-phase system at some point can be indicated by three phasors, called the three components of the voltage or the current. This article discusses voltage; however, the same considerations also apply to current.
The phase angle difference between voltage and current of each phase is not necessarily 0 and depends on the type of load impedance, Z y. Inductive and capacitive loads will cause current to either lag or lead the voltage. However, the relative phase angle between each pair of lines (1 to 2, 2 to 3, and 3 to 1) will still be −120°.
The voltages between the three phases are the same in magnitude, however the voltage magnitudes between a particular phase and the neutral vary. The phase-to-neutral voltage of two of the phases will be half of the phase-to-phase voltage. The remaining phase-to-neutral voltage will be √ 3 /2 the phase-to-phase voltage. So if A–B, B–C and ...
A Lissajous curve / ˈlɪsəʒuː /, also known as Lissajous figure or Bowditch curve / ˈbaʊdɪtʃ /, is the graph of a system of parametric equations. sin t + {\displaystyle x=A\sin (at+\delta ),\quad y=B\sin (bt),} which describe the superposition of two perpendicular oscillations in x and y directions of different angular frequency (a ...
Per-unit system. In the power systems analysis field of electrical engineering, a per-unit system is the expression of system quantities as fractions of a defined base unit quantity. Calculations are simplified because quantities expressed as per-unit do not change when they are referred from one side of a transformer to the other.
In electrical engineering, the alpha-beta ( ) transformation (also known as the Clarke transformation) is a mathematical transformation employed to simplify the analysis of three-phase circuits. Conceptually it is similar to the dq0 transformation. One very useful application of the transformation is the generation of the reference signal used ...
Lyapunov exponent. In mathematics, the Lyapunov exponent or Lyapunov characteristic exponent of a dynamical system is a quantity that characterizes the rate of separation of infinitesimally close trajectories. Quantitatively, two trajectories in phase space with initial separation vector diverge (provided that the divergence can be treated ...