3 Winding Transformers

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Introduction

At the beginning of a project engineers have many options to choose from when developing the design for the electrical distribution system. For instance consider the case of a new power plant consisting of 2 generators. Three transformation approaches are typically considered to interconnect the generators to the power system. The simplest approach is to serve both generators from a single 2-winding transformer, fig. 1a. This design is typically characterized with the lowest transformation cost but highest available fault duties on the generator bus. The second approach is to supply a single transformer for each generator, fig.1b. This design solves the fault current problem however the transformation costs increase dramatically. Many times to balance cost and fault current issues, engineers select 3-winding transformers, fig. 1c.

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The term 3-winding transformer can be misleading since a 3-winding transformer may have three or more windings internal to the tank of the transformer. Actually the term 3-winding means a transformer with 3 sets of bushings labeled H for the primary, X for the secondary, and Y for the tertiary, see fig. 2.

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Impedances are then specified from the H-X, H-Y and X-Y terminals in percent on a chosen winding (typically the X winding) kVA base. The design engineer is responsible for determining the impedances required for the application. The ANSI impedance tolerance for 3-winding transformers is ± 10%, not ± 7½%, for 2-winding transformers.

Transformer Winding Configurations

Several winding configurations are used in the industry, each with inherent impedance characteristics that engineers must be aware of. The Loosely-Coupled Stacked Secondary (LCSS) design is shown in fig. 3. Notice with this design there are actually four windings around the core. Physically, the H winding is split in two to match the height of the X and Y windings. Electrically, the H1 and H2 windings are configured in parallel inside the tank. This design approach is taken to balance the fields in the H windings when the secondary fields are unbalanced due to an imbalance in load or a fault condition. This design is intended to serve load equally and continuously through the secondary windings. It is not a good design selection if the secondary windings will serve an unbalanced load for an extended period of time, e.g., one secondary breaker open.

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In this case, with equal capacities on both the X and Y windings and impedances expressed on the same base, the following relationships hold.

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Another winding configuration is the Tightly-Coupled Stacked Secondary (TCSS) design, see fig. 4. In this case the secondary and tertiary windings are alternately wound around the core. The H-X and H-Y impedances are as previously defined. The X-Y impedance has the following relationship.

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This is not a good design selection in applications where high secondary and tertiary winding fault currents are a concern. This design is more commonly used in traction power and rectifier applications.

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A third option is the Low-High-Low (LHL) Design shown in fig. 5. Again the H-X and H-Y impedances are as previously defined. The impedance range available from the X-Y windings would be slightly larger than the LCSS design.

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Example 1

Consider a new 480V distribution system that includes 3000kVA of motor load and 600kVA of miscellaneous non-motor load.

  • Single 2-winding transformer
  • Two 2-winding transformers
  • 3-winding transformer utilizing a LCSS design
  • 3-winding transformer utilizing a TCSS design
  • 3-winding transformer utilizing a LHL design

In this application a total transformer winding capacity of 4000kVA is appropriate. Based on a primary voltage rating of 13.8kV and a standard BIL of 110kV, a typical impedance of 6% is assumed for the application. Table 1 summarizes the transformer ratings selected for each configuration.

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The results are summarized in Table 2. The initial rationale for considering a 3-winding transformer is confirmed. The single 2-transformer case has the highest fault duties with the lowest transformation cost. The two 2-winding transformer case has the highest transformation cost. A single 3-winding transformer balances both fault current and cost concerns. However, to maintain low fault duties, transformers of the LCSS or LHL design should be utilized.

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The equivalent circuit shown in fig. 6 accurately represents the transformer from a leakage impedance, mutual effects between windings, and load loss standpoint [1]. Exciting currents and no load losses are ignored. Also, please note it is not uncommon for one of the impedances to be negative or zero!

Example 2

Calculate the winding impedances for Cases 3 and 5 listed in Table 1, and then illustrate the calculation of the available fault current on the tertiary bus, see fig. 7. To simplify the calculations assume all reactance.

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Solution

First, convert system impedances to a 2MVA, 480V base.

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Z s-t IMPEDANCE LIMITS

The TCSS design establishes the lower limit for the secondary-tertiary winding impedance, while the LHL design establishes the upper limit. A theoretical upper limit can be calculated by assuming an infinite bus at the primary of the transformer while shorting the secondary and tertiary terminals (12).

Z Thévenin = Z H + Z X II Z Y (12)

Again this assumes equal capacities on both the X and Y windings with all impedances expressed on the same base. Impedance limits are summarized in Table 3. The results indicate a maximum upper limit for Z X-Y around 4 times Z H-X. At this point, the Thévenin impedance at the shorted secondary and tertiary terminals approaches zero.

Note when Z X-Y > 4 Z H-X , the result is an overall negative Thévenin impedance seen outside of the tank of the transformer. This is not possible.

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Example 3

Apply the results listed in this guide to the 3-winding transformer case of example 1, but in this case assume Z H-Y = Z H-X = 6.50% with equal capacities on both the X and Y windings.

  • for Z X-Y = 0.65% (TCSS) corresponds to a SC kA on the LV terminals of 57.5kA
  • for Z X-Y = 13.0% (LCSS) corresponds to a SC kA on the LV terminals of 47.0kA
  • for Z X-Y = 16.25% (LHL) corresponds to a SC kA on the LV terminals of 47.3kA
  • for Z X-Y = 26.0% corresponds to a SC kA on the LV terminals of 56.2k

These results illustrate that there is no practical advantage to increasing the secondary-to-tertiary impedance beyond ~2 times the primary-to-secondary impedance. Since higher impedances will only result in higher fault duties and losses.

References

  • Electrical Transmission and Distribution Reference Book, ABB Power T&D Company, Raleigh, North Carolina, 1997.
  • Harlow, J.H., Electric Power Transformer Engineering, CRC Press, New York, 2004.