3-phase Transformers Part 1.pptx

Three-phase transformers contain three separate primary and secondary windings on a common core. Using a common core provides better magnetic coupling and improves the efficiency of the transformer.

The windings are connected in either wye or delta. Most three-phase transformers will have at least one of the windings connected in delta. This is done to stabilize the voltage when load is added to the transformer. Recall that the line voltage and phase voltage are the same in a delta connection.

A wye-wye connection can be used if the load is a balanced three-phase load. The phase and line voltage will remain stable provided the current on each line is the same

A wye-wye connection can be used to provide both three-phase and single-phase loads provided the electric utility company supplies a fourth wire neutral to the primary of the transformer. Four wire wye connected secondary windings are very common in commercial locations. Common voltages for this connections are 208/120 and 480/277 volts.

Large threephase pad mounted transformers are often used by utility companies, industries, and commercial customers.

Single-phase transformers are often connected to form a threephase transformer bank. Transformer banks have a disadvantage is that they are not as efficient as a true three-phase transformer, but they do have a advantage in that if one transformer should fail only that one transformer has to be replaced.

In this example, the primary winding of three transformers have been connected in delta and the secondary windings have been connected in wye. The primary and secondary windings can be connected in any combination such as delta-wye, delta-delta, wye-delta, or wyewye.

In this example, a three-phase transformer has a its primary winding connected in wye and its secondary winding connected in delta. The line voltage connected to the primary is 4,170 volts and the line voltage of the secondary is 240 volts. The load is constructed of three resistors connected in wye. Each resistor has an impedance of 2.77 ohms.

Since the load is connected directly to the output of the transformer secondary, the line voltage of the load will be the same as the line voltage of the secondary.

The next step is to determine the phase voltage of the load. In a wye connection, the phase voltage is less than the line voltage by a factor of the square root of 3 or 1.732.

EL EP  3

240 EP  1.732

EP 138.6 Volts

The phase voltage is the voltage dropped each of the resistors that form the wye connected load. The phase current can now be determined using Ohm’s Law.

EP IP  Z

138.6 IP  2.77

I P  50 A

In a wye connection, the line current and phase current are the same. Therefore, 50 amperes of line current is necessary to supply the 50 amperes of phase current in the load. Since only one load is connected to the transformer secondary, the line current of the secondary will be 50 amperes also.

In a delta connection the phase current is less than the line current by a factor the square root of 3 or 1.732. The phase current of the transformer secondary is 28.9 amperes.

IL IP  3

50 IP  1.732

I P  28.9 A

In a delta connection the phase voltage and line voltage are the same. The phase voltage of the transformer secondary is 240 volts. At this point, all values of the connected load and secondary winding have been determined. The next step is to determine the values that apply to the primary winding.

In a wye connection the phase voltage is less than the line voltage by a factor of the square root of 3 or 1.732. The phase voltage of the wye connected primary is 2407.6 volts.

EL EP  3

4170 EP  1.732

EP  2407.6V

When determining values of current, voltage, and turns ratio for the transformer, only phase values can be used. In the illustration shown, three separate transformers have been designated as A, B, and C. The wye-delta transformer windings have also been labeled A, B, and C. Note that the B phase of the wye connected primary is actually the primary winding of transformer B, and that the B phase of the delta connected secondary is actually the secondary winding of transformer B. All transformation occurs between the primary and secondary windings of the transformer. The primary and secondary windings of the three transformers form the phase windings of the three-phase transformer connection.

The turns ratio of the transformer can now be determined using the phase values of the primary and secondary voltages. Since the primary voltage is higher than the secondary voltage, it has more turns of wire. The turns ratio is, therefore, 10:1. This indicates that there are 10 turns of wire in the primary for every 1 turn in the secondary. Turns Ratio 

Higher Voltage Lower Voltage

Turns Ratio 

2407.6 240

Turns Ratio 10

A basic rule of transformers is that power in must equal power out. The volt-amperes of the primary must equal the volt-amperes of the secondary. Since the primary has a higher voltage, it will have less current. The current will be less by a factor equal to the turns ratio. I P(Pr imary) 

I P( Seco ndary)

Turns Ratio

I P(Pr imary)

28.9  10

I P(Pr imary)  2.89 A

In a wye connection the line current is equal to the phase current. Therefore, the line current supplying the primary of the transformer is 2.89 amperes.

I Line  I Phase

The calculation can be checked by determining if the input power is equal to the output power. Use the formula for determining the apparent power in a threephase connection to determine if the primary and secondary values are approximately equal. There may be some difference due to rounding off of values. VA(Primary)  EL(Pr imary)  I L(Pr imary)  3 VA( Secondary)  EL( Secondary)  I L( Secondary)  3

VA(Primary)  4170  2.89 1.732 VA( Secondary)  240  50 1.732

VA(Primary)  20,873 VA( Secondary)  20,784

In this example a three-phase transformer contains a delta connected primary and wye connected secondary. The line voltage supplying the primary is 13,800 volts and the secondary line voltage is 480. Two loads are connected to the transformer. The first load contains three 4 ohm resistors connected in wye. The second load contains three 6 ohms resistors

Since both loads are connected to the secondary of the three-phase transformer, both have the same line voltage as the secondary.

In a wye connection the phase voltage is less than the line voltage by a factor of the square root of 3 or 1.732. The phase voltage of the wye connected load is 277.1 volts.

EL EP  3

480 EP  1.732

EP  277.1V

A voltage of 277.1 volts is applied across each of the 4 ohm resistors. The phase current of the wye connected load can be determined using Ohm’s Law.

EP IP  Z

277.1 IP  4

I P  69.3 A

In a wye connection the line current and phase current are the same. Therefore, the line current necessary to operate the wye connected load is 69.3 amperes.

In a delta connection, the line voltage and phase voltage are the same. Therefore, the phase voltage of the delta connected load is 480 volts.

A voltage of 480 volts is applied across each of the 6 ohm resistors. The phase current can be determined using Ohm’s Law. The phase current of the delta load is 80 amperes.

EP IP  Z

480 IP  6

I P  80 A

In a delta connection, the line current is greater than the phase current by a factor of the square root of 3 or 1.732. The amount of line current necessary to supply the delta load is 138.6 amperes.

IL  IP  3

I L  80 1.732

I L 138.6 A

The secondary of the transformer must supply the line current for all connected loads. Therefore, the line current supplied by the secondary is the sum of all connected load. The secondary has a line current of 207.9 amperes. I L(Total)  I L(Wye Load)  I L( Delta Load)

I L(Total)  69.3 138.6

I L(Total)  207.9 A

In a wye connection, the phase current and the line current are equal. Therefore, the phase current of the transformer secondary is 207.9 amperes.

In a wye connection, the phase voltage is less than the line voltage by a factor of the square root of 3 or 1.732. The phase voltage of the secondary is 277.1 volts.

EL EP  3

480 EP  1.732

EP  277.1V

In a delta connection, the line voltage and phase voltage are equal. The phase voltage of the primary is 13,800 volts.

Now that the primary and secondary phase voltages are known, the turns ratio can be determined by dividing the larger voltage by the smaller. The turns ratio is 49.8:1. This indicates that there are 49.8 turns of wire in the primary winding for every 1 turn in the secondary. Higher Voltage Turns Ratio  Lower Voltage

13,800 Turns Ratio  277.1

Turns Ratio  49.8

The phase current of the primary can be determined with the turns ratio. Since the primary voltage is greater than the secondary voltage, the primary current will be less. Divide the secondary phase current by the turns ratio to determine the primary phase current. I P(Pr imary) 

I P( Seco ndary) Turns Ratio

I P(Pr imary)

207.9  49.8

I P(Pr imary)  4.2 A

In a delta connection the line current is greater than the phase current by a factor of the square root of 3 or 1.732. The line current necessary to supply the primary is 7.3 amperes.

IL  IP  3

I L  4.2 1.732

I L  7.3 A

The calculation can be checked by determining if the input power is equal to the output power. Use the formula for determining the apparent power in a three-phase connection to determine if the primary and secondary values are approximately equal. There may be some difference due to rounding off of values. In this calculation there is a difference of 1643. Although this may appear to be a large difference, the two values are within 1% of each other. VA(Primary)  EL(Pr imary)  I L(Pr imary)  3 VA( Secondary)  EL( Seco ndary)  I L( Seco ndary)  3

VA(Primary) 13,800  7.31.732

VA(Primary) 174,482

VA( Secondary)  480  207.9 1.732

VA( Secondary) 172,839