Fortescue’s Theorem

Fortescue’s Theorem

Fortescue’s Theorem mainly worked for the unbalanced System in Electrical Engineering. This theorem follows the zero phase sequence system.

This zero phase sequence indicates that in a 3-phase system all phasors are stated in identical angels & their magnitude are equal.

In a brief the Fortescue’s Theorem say’s that,

In a unbalanced set of unbalanced phasors the system may be resolved in (n-1) balanced system for different phase sequence & non zero phase sequence.

Fortescue’s give this theorem in 1918 & this system is mention as “Three component method”. This method is perfect for setting symmetrical components.

In this Fortescue’s Theorem, The direction of the rotation is always as anticlockwise .Whether it is “+” or “-”. The “+” indicates the original phase system .In other “-” signs oppose on the other hand. This system is voltage defined. The system can be defined by the help of arbitrary label  “A, B, C”.

When this is In “ABC ”indicates positive.

When this is In “ACB” indicates negative.

 The phasor can be defined by the α-operator. This operator is used for the phasors rotates in 120 degree.

The operator minus alpha does not produce rotation through -120 degree.

This theorem has some basic concept's .They are:

Positive Phase Sequence Components : When a set of phasors are equal in magnitude, displaced from each other by 120 degree in phase and they have the same phase sequence as the original unbalanced phasors.

Negative Phase Sequence Components : When a set of phasors are equal in magnitude, displaced from each other by 120 degree in phase and they have the opposite  phase sequence as the original phasors.

Identical Phase Sequence Components : When a set of three phasors are  equal in magnitude with zero displacement from each other then the components of this set are all identical.

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