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Set of three unbalanced phasors, and the necessary symmetrical components that sum up to the resulting plot at the bottom. In 1918 Charles Legeyt Fortescue presented a paper [4] which demonstrated that any set of N unbalanced phasors (that is, any such polyphase signal) could be expressed as the sum of N symmetrical sets of balanced phasors, for values of N that are prime.
For example, balanced two-phase power can be obtained from a three-phase network by using two specially constructed transformers, with taps at 50% and 86.6% of the primary voltage. This Scott T connection produces a true two-phase system with 90° time difference between the phases.
In 1937 and 1938, Edith Clarke published papers with modified methods of calculations on unbalanced three-phase problems, that turned out to be particularly useful. [1]
A three-phase induction motor has a simple design, inherently high starting torque and high efficiency. Such motors are applied in industry for many applications. A three-phase motor is more compact and less costly than a single-phase motor of the same voltage class and rating, and single-phase AC motors above 10 hp (7.5 kW) are uncommon. Three ...
Simplified calculations can then be carried out on these DC quantities before performing the inverse transformation to recover the actual three-phase AC results. As an example, the Park transformation is often used in order to simplify the analysis of three-phase synchronous machines or to simplify calculations for the control of three-phase ...
Two-phase motors draw constant power, just as three-phase motors do, so a balanced two-phase load is converted to a balanced three-phase load. However if a two-phase load is not balanced (more power drawn from one phase than the other), no arrangement of transformers (including the Scott-T transformers) can restore balance: Unbalanced current ...
A major concern with three phase power is that each phase be at similar voltages. A discrepancy between phases is known as phase imbalance. As a general guideline, unbalanced three-phase power that exceeds 4% in voltage variation can damage the equipment that it is meant to operate.
Notable contributors to the theoretical basis of alternating current calculations include Charles Steinmetz, Oliver Heaviside, and many others. [38] [39] Calculations in unbalanced three-phase systems were simplified by the symmetrical components methods discussed by Charles LeGeyt Fortescue in 1918.