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Three Phase Transformer Connections Phasor Diagrams

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Three-phase transformers are used quite extensively in power systems to transform a balanced set of three-phase voltages at a particular voltage level into a balanced set of voltages at another level. Transformers used between generators and transmission system, between transmission and sub-transmission system, and between sub-transmission and distribution systems are all three-phase transformer. Most commercial and industrial loads require a three-phase transformer to transform the three-phase distribution voltage to the ultimate utilization level.

A three-phase transformer is built for a specific connection and voltage transformation and the unit will have a nameplate with the internal connections shown.

Three-phase transformers are formed in either of two ways. The first method is to connect three single-phase transformers to form a three-phase bank. The second method is to manufacture a three-phase transformer bank with all three-phases located on a common multiplexed core. As far as analysis is concerned; there is no difference between the two methods.

            The primary windings and secondary windings of the three-phase transformers may be independently connected in either way (Y) or delta (∆) connection. As a result. Four types of three-phase transformers are in common use:

  1. Wye-wye ( Y-Y)

  2. Wye-delta ( Y-∆)

  3.  Delta-Wye (∆-Y)

  4. Delta-delta (∆-∆)

Wye-Wye Three-Phase Transformer Connection

Fig.1 (a): Wye-Wye Three Phase Transformer Connection

Y (Star) - Y (Star) Three Phase Transformer Phasor Diagram

Fig. 1(a): Y (Star) – Y (Star) Three Phase Transformer Phasor Diagram

Advantages of Y-Y Connection

  • Two voltage levels available
  • Graded High voltage insulation
  • Balanced connection when supplying 1-φ and 3-φ loads

Disadvantages of Y-Y Connection

  • Presence of 3rd harmonic component in ungrounded Y-Y connection.
  • Thermal over-heating

Wye-Delta Three-Phase Transformer Connection

Fig.1 (b): Wye-Delta Three Phase Transformer Connection

Advantages of Y- Connection

  • Neutral is available on primary side which can be earthed in order to avoid distortion.
  • Two voltage levels (single and three phase) are available.
  • Traps 3rd harmonic currents

Disadvantages of Y- Connection

  • Since primary and secondary are not in phase so cannot operate in parallel with other Y-Y or ∆-∆ transformers
  • Full insulation is required on ∆ side

It should be noted that to form a wye connection, the un-doted ends of the three windings (three primaries or three secondary’s) are joined together and form the neutral point and the dotted ends become the three line terminals. In forming a delta connection, the three windings belonging to the same side are connected in series in such a way that the sum of the phase voltages in the closed delta is equal to zero; then the line terminals are taken off the junctions of the windings.  

      The Y-∆ connection is commonly used in stepping down from a high voltage to a medium or low voltage level, as in distribution transformers. Conversely, the ∆-Y connection is used for stepping up to a high voltage, as in generation station transformer.

Delta-Wye Three-Phase Transformer Connection

Fig.1 (c): Delta-Wye Three Phase Transformer Connection

Delta-Wye Three Phase Transformer Phasor Diagram

Fig.1 (c): Delta-Wye Three Phase Transformer Phasor Diagram

Advantages of Delta-Wye Connection

  • Balanced connection when supplying 1-φ and 3-φ loads
  • The neutral point is available on Y-side.
  • Traps 3rd harmonics

Disadvantages of Delta-Wye Connection

  • Full insulation is required on Delta winding of transformers

Delta-Delta Three-Phase Transformer Connection

Fig.1 (d): Delta-Delta Three Phase Transformer Connection

Delta-Delta Three Phase Transformer Phasor Diagram

Fig.1 (d): Delta-Delta Three Phase Transformer Phasor Diagram

Advantages of Delta-Delta Connection

  • Ideal for three wire motor loads
  • Can easily stand single line shorts without any interruption.
  • Traps 3rd harmonics (circulating currents)

Disadvantages of Delta-Delta Connection

  • Full insulation required on high voltage winding
  • Since no neutral is available so its unbalanced connection when supplying to 1-φ and 3- φ loads

      The Y-Y connection is seldom used because of possible voltage unbalances and problems with third harmonic voltages. The ∆-∆ connection is used because of its advantage that one of the three single-phase transformers can be removed for repair or maintenance. The remaining two transformers continue to function as a three-phase bank, although the kVA rating of the bank is reduced to 58% of the original three-phase bank rating. This mode of operation is known as an open-delta connection or V-V connection.

      The open-delta connection is also used when the load is presently small but is expected to grow in the future. Thus, instead of installing a three-phase bank of three single-phase transformers right away, only two single-phase transformers are used for three-phase voltage transformation. The third single-phase transformer serves as a spare and is connected at a later stage when the load has grown.

            In either Y –Y or ∆-∆ connections, corresponding phase voltages are in phase. Similarly, corresponding line-to-line voltages in the primary and secondary are in phase. In other words, VAN is in phase with Van, and VAB is in phase with Vab. On the other hand, for both Y- ∆ and ∆-Y connections, it is customary in the United States to have the primary phase or line-to-line voltage lead by 30o; thus, VAN leads Van by 30o, and VAB leads Vab by the same amount of phase shift.

            Circuit analysis involving three-phase transformer under balanced conditions can be performed on a per-phase basis. This follows from the relationship that the per-phase real power and reactive power are one-third of the total real power and reactive power, respectively, of the three-phase transformer bank. It is convenient to carry out computations on a per-phase wye line-to-neutral basis.

When ∆ -Y, or Y-∆ connections are present, the parameters are referred to the Y side. In dealing with ∆-∆ connections, the ∆-connected impedances are converted to equivalent Y-connected impedances. The ∆-Y impedance conversion formula is:

\[{{Z}_{Y}}~=\frac{1}{3}{{Z}_{\Delta }}\]

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About Ahmad Faizan

Mr. Ahmed Faizan Sheikh, M.Sc. (USA), Research Fellow (USA), a member of IEEE & CIGRE, is a Fulbright Alumnus and earned his Master’s Degree in Electrical and Power Engineering from Kansas State University, USA.