Nikola Tesla’s original polyphase power system was based on simple to build 2-phase components. However, as transmission distances increased, the more transmission line efficient 3-phase system became more prominent. Both 2-φ and 3-φ components coexisted for a number of years. The Scott-T transformer connection allowed 2-φ and 3-φ components like motors and alternators to be interconnected. Yamamoto and Yamaguchi:

In 1896, General Electric built a 35.5 km (22 mi) three-phase transmission line operated at 11 kV to transmit power to Buffalo, New York, from the Niagara Falls Project. The two-phase generated power was changed to three-phase by the use of Scott-T transformations. [MYA]

[MYA]Mitsuyoshi Yamamoto, Mitsugi Yamaguchi, “Electric Power In Japan, Rapid Electrification a Century Ago”, EDN, (4/11/2002). http://www.ieee.org/organizations/pes/public/2005/mar/peshistory.html

The Scott-T transformer set, Figure above, consists of a center tapped transformer T1 and an 86.6% tapped transformer T2 on the 3-φ side of the circuit. The primaries of both transformers are connected to the 2-φ voltages. One end of the T2 86.6% secondary winding is a 3-φ output, the other end is connected to the T1 secondary center tap. Both ends of the T1 secondary are the other two 3-φ connections.

Application of 2-φ Niagara generator power produced a 3-φ output for the more efficient 3-φ transmission line. More common these days is the application of 3-φ power to produce a 2-φ output for driving an old 2-φ motor.

In Figure below, we use vectors in both polar and complex notation to prove that the Scott-T converts a pair of 2-φ voltages to 3-φ. First, one of the 3-φ voltages is identical to a 2-φ voltage due to the 1:1 transformer T1 ratio, V_{P12}= V_{2P1}. The T1 center tapped secondary produces opposite polarities of 0.5V_{2P1} on the secondary ends. This ∠0^{o} is vectorially subtracted from T2 secondary voltage due to the KVL equations V_{31}, V_{23}. The T2 secondary voltage is 0.866V_{2P2} due to the 86.6% tap. Keep in mind that this 2nd phase of the 2-φ is ∠90^{o}. This 0.866V_{2P2} is added at V_{31}, subtracted at V_{23} in the KVL equations.

We show “DC” polarities all over this AC only circuit, to keep track of the Kirchhoff voltage loop polarities. Subtracting ∠0^{o} is equivalent to adding ∠180^{o}. The bottom line is when we add 86.6% of ∠90^{o} to 50% of ∠180^{o} we get ∠120^{o}. Subtracting 86.6% of ∠90^{o} from 50% of ∠180^{o} yields ∠-120^{o} or ∠240^{o}.

In Figure above we graphically show the 2-φ vectors at (a). At (b) the vectors are scaled by transformers T1 and T2 to 0.5 and 0.866 respectively. At (c) 1∠120^{o} = -0.5∠0^{o} + 0.866∠90^{o}, and 1∠240^{o} = -0.5∠0^{o} – 0.866∠90^{o}. The three output phases are 1∠120^{o} and 1∠240^{o} from (c), along with input 1∠0^{o} (a).

** Article extracted from** Lesson in Electric Circuits AC Volume Tony R Kuphaldt under Design Science License