Intro to Three-Phase Transformers

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TOPICS:

  1. Intro to Three-Phase Transformers
  2. Closing a Delta
  3. Three-Phase Transformer Calculations
  4. Open-Delta Connection
  5. Single-Phase Loads
  6. Closed Delta with Center Tap
  7. Closed Delta without Center Tap
  8. Delta–Wye Connection with Neutral
  9. T-Connected Transformers
  10. Scott Connection
  11. Zig-Zag Connection
  12. Harmonics
  13. Summary/Quiz

TERMINOLOGY:

  • Closing a delta
  • Delta–wye
  • Dielectric oil
  • High leg
  • One-line diagram
  • Open-delta
  • Orange wire
  • Single-phase loads
  • Tagging
  • Three-phase bank
  • Wye–delta

BASICS:

Three-phase transformers are used throughout industry. Almost all power generated in the United States and Canada is three phase.

Transformers step up voltage for transmission and step it down again for use inside a plant or commercial building. This article …

  • presents the difference between a true three-phase transformer and a three-phase transformer bank.
  • determines different voltage and current values in a three-phase transformer.
  • defines phase values in calculating the values of a transformer.
  • explains how harmonics are identified and overcome.
  • describes different three-phase transformer connections such as delta-wye, wye-delta, open-delta, T -connected, and Scott connected.
  • discusses installation and testing.

Learning Goals:

  • discuss the operation of three-phase transformers.
  • connect three single-phase transformers to form a three-phase bank.
  • calculate voltage and current values for a three-phase transformer connection.
  • connect two single-phase transformers to form a three-phase open-delta connection.
  • discuss the characteristics of an open-delta connection.
  • discuss different types of three-phase transformer connections and how they are used to supply single-phase loads.
  • calculate values of voltage and current for a three-phase transformer used to supply both three-phase and single-phase loads.
  • describe what a harmonic is.
  • discuss the problems concerning harmonics.
  • identify the characteristics of different harmonics.
  • perform a test to determine if harmonic problems exist.
  • discuss methods of dealing with harmonic problems.

FUNDAMENTALS

Three-phase transformers are used throughout industry to change values of three-phase voltage and current. Because three-phase power is the most common way in which power is produced, transmitted, and used, an under standing of how three-phase transformer connections are made is essential.

This unit discusses different types of three-phase transformer connections and presents examples of how values of voltage and current for these connections are calculated.

+++++1 Basic construction of a three-phase transformer. Core Primary Secondary

+++++2 Three-phase transformer.

+++++3 Wye-delta connected three-phase transformer.

+++++4 Delta-wye connected three-phase transformer.

+++++5 Identifying the windings.

+++++6 Three single-phase transformers.

Three-Phase Transformers

A three-phase transformer is constructed by winding three single-phase transformers on a single core. A figure of a three-phase transformer is shown below. The transformer is shown before it is mounted in an enclosure, which will be filled with a dielectric oil. The dielectric oil performs several functions. Because it is a dielectric, it provides electric insulation between the windings and the case. It is also used to help provide cooling and to prevent the formation of moisture, which can deteriorate the winding insulation.

Three-Phase Transformer Connections:

Three-phase transformers are connected in delta or wye configurations.

A wye-delta transformer, for example, has its primary winding connected in a wye and its secondary winding connected in a delta. A delta- wye transformer would have its primary winding connected in delta and its secondary connected in wye.

Connecting Single-Phase Transformers into a Three-Phase Bank:

If three-phase transformation is needed and a three-phase transformer of the proper size and turns ratio is not available, three single-phase transformers can be connected to form a three-phase bank. When three single-phase transformers are used to make a three-phase bank, their primary and secondary windings are connected in a wye or delta connection. The three transformer windings are labeled A, B, and C. One end of each primary lead is labeled H1, and the other end is labeled H2. One end of each secondary lead is labeled X1, and the other end is labeled X2.

+++++ three single-phase transformers labeled A, B, and C. The primary leads of each transformer are labeled H1 and H2, and the secondary leads are labeled X1 and X2. The schematic diagram is used to connect the three single-phase transformers into a three-phase wye-delta connection.

The primary winding is first tied into a wye connection. The schematic shows that the H2 leads of all three primary windings are connected together and the H1 lead of each winding is open for connection to the incoming powerline. Notice that the H2 leads of the primary windings are connected together and the H1 lead of each winding has been connected to the incoming powerline.

+++++7 Connecting three single-phase transformers to form a wye-delta three-phase bank.

+++++5 shows that the X1 lead of Transformer A is connected to the X2 lead of Transformer C. Notice that this same connection has been made. The X1 lead of Transformer B is connected to the X2 lead of Transformer A, and the X1 lead of Transformer C is connected to the X2 lead of Transformer B. The load is connected to the points of the delta connection.

Although we illustrate the proper schematic symbology for a three-phase transformer connection, some electrical schematics and wiring diagrams don’t illustrate three-phase transformer connections in this manner.

One type of diagram, called the one-line diagram, would illustrate a delta- wye connection. These diagrams are generally used to show the main power distribution system of a large industrial plant. The one-line diagram shows the main power to the plant and the transformation of voltages to different subfeeders. Notice that each transformer shows whether the primary and secondary are connected as a wye or delta and the secondary voltage of the subfeeder.

+++++8 One-line diagram symbol used to represent a delta-wye three-phase transformer connection.

+++++9 One-line diagrams are generally used to show the main power distribution of a plant.

+++++10 Testing for proper transformer polarity before closing the delta.

+++++11 Example Circuit 1 three-phase transformer calculation.

=== EXAMPLE:

A three-phase transformer connection is shown. Three single phase transformers have been connected to form a wye-delta bank. The primary is connected to a three-phase line of 13,800 V, and the secondary voltage is 480 V. A three-phase resistive load with an impedance of 2.77 V per phase is connected to the secondary of the transformer. Calculate the following values for this circuit:

E_P(PRIMARY) -phase voltage of the primary E_P(SECONDARY) -phase voltage of the secondary

Ratio-turns ratio of the transformer E_P(LOAD) -phase voltage of the load bank I_P(LOAD) -phase current of the load bank I_L(SECONDARY) -secondary line current I_P(SECONDARY) -phase current of the secondary

I_P(PRIMARY) -phase current of the primary

I_L(PRIMARY) -line current of the primary

Solution:

The primary windings of the three single-phase transformers have been connected to form a wye connection. In a wye connection, the phase voltage is less than the line voltage by a factor of 1.732 (the square root of 3). Therefore, the phase value of the primary voltage can be calculated using the formula ...

The secondary windings are connected as a delta. In a delta connection, the phase voltage and line voltage are the same:

E_P(SECONDARY) = E_L(SECONDARY)

E = 480 V

The turns ratio can be calculated by comparing the phase voltage of the primary with the phase voltage of the secondary:

The load bank is connected in a wye connection. The voltage across the phase of the load bank will be less than the line voltage by a factor of 1.732:

Now that the voltage across each of the load resistors is known, the current flow through the phase of the load can be calculated using Ohm's law:

Because the load is connected as a wye connection, the line current is the same as the phase current:

I_L(SECONDARY) = 100.049A

The secondary of the transformer bank is connected as a delta. The phase current of the delta is less than the line current by a factor of 1.732:

The amount of current flow through the primary can be calculated using the turns ratio. Because the primary has a higher voltage than the secondary, it will have a lower current. (Volts times amperes input must equal volts times amperes output.)

Because all transformed values of voltage and current take place across the phases, the primary has a phase current of 3.48 A. In a wye connection, the phase current is the same as the line current:

I_L(PRIMARY) = 3.48A

The transformer connection with all calculated values is shown.

===

+++++12 Example Circuit 1 with all missing values. ===

=== EXAMPLE 2

+++++13 Example Circuit 2 three-phase transformer calculation.

A three-phase transformer is connected in a delta-delta configuration. The load is connected as a wye, and each phase has an impedance of 7 V. The primary is connected to a line voltage of 4160 V, and the secondary line voltage is 440 V. Find the following values:

E_P(PRIMARY) -phase voltage of the primary E_P(SECONDARY) -phase voltage of the secondary Ratio-turns ratio of the transformer

E_L(LOAD) -line voltage of the load

E_P(LOAD) -phase voltage of the load bank

I_P(LOAD) -phase current of the load bank

I_L(LOAD) -line current of the load I_L(SECONDARY)

-secondary line current I_P(SECONDARY)

-phase current of the secondary I_P(PRIMARY)

-phase current of the primary I_L(PRIMARY)

-line current of the primary

Solution:

The primary is connected as a delta. The phase voltage will be the same as the applied line voltage:

E_P(PRIMARY) = E_L(PRIMARY)

E_P(PRIMARY) = 4160V

The secondary of the transformer is connected as a delta also. Therefore, the phase voltage of the secondary will be the same as the line voltage of the secondary:

E_P(SECONDARY) = 440 V

All transformer values must be calculated using phase values of voltage and current. The turns ratio can be found by dividing the phase voltage of the primary by the phase voltage of the secondary:

Ratio = 9.45:1

The load is connected directly to the output of the secondary. The line voltage applied to the load must therefore be the same as the line voltage of the secondary:

E_L(LOAD) = 440 V

The load is connected in a wye. The voltage applied across each phase will be less than the line voltage by a factor of 1.732:

The phase current of the load can be calculated using Ohm's law:

The amount of line current supplying a wye-connected load will be the same as the phase current of the load:

I_L(LOAD) = 36.292A

Because the secondary of the transformer is supplying current to only one load, the line current of the secondary will be the same as the line current of the load:

I_L(SECONDARY) = 36.292A

The phase current in a delta connection is less than the line current by a factor of 1.732:

The phase current of the transformer primary can now be calculated using the phase current of the secondary and the turns ratio:

In this example, the primary of the transformer is connected as a delta. The line current supplying the transformer will be higher than the phase current by a factor of 1.732:

I_L(PRIMARY) = I_P(PRIMARY) x 1.732

I_L(PRIMARY) = 2.217 A 3 1.732

I_L(PRIMARY) = 3.84 A

+++++14 Example Circuit 2 with all missing values.

===

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