# Three-Phase Transformers -- part 2

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### Closing a Delta

When closing a delta, connections should be checked for proper polarity before making the final connection and applying power. If the phase winding of one transformer is reversed, an extremely high current will flow when power is applied. Proper phasing can be checked with a voltmeter. If power is applied to the transformer bank before the delta connection is closed, the voltmeter should indicate 0 volt. If one phase winding has been reversed, however, the voltmeter will indicate double the amount of voltage.

For example, assume that the output voltage of a delta secondary is 240 volts. If the voltage is checked before the delta is closed, the voltmeter should indicate a voltage of 0 V if all windings have been phased properly. If one winding has been reversed, however, the voltmeter will indicate a voltage of 480 volts (240 V 1 240 V). This test will confirm whether a phase winding has been reversed, but it will not indicate whether the reversed winding is located in the primary or secondary. If either primary or secondary windings have been reversed, the voltmeter will indicate double the output voltage.

Note, however, that a voltmeter is a high-impedance device. It is not unusual for a voltmeter to indicate some amount of voltage before the delta is closed, especially if the primary has been connected as a wye and the secondary as a delta. When this is the case, however, the voltmeter will generally indicate close to the normal output voltage if the connection is correct and double the output voltage if the connection is incorrect.

### Three-Phase Transformer Calculations

To calculate the values of voltage and current for three-phase transformers, the formulas used for making transformer calculations and three-phase calculations must be followed. Another very important rule is that only phase values of voltage and current can be used when calculating transformer values.

Refer to Transformer A. All transformation of voltage and current takes place between the primary and secondary windings. Because these windings form the phase values of the three-phase connection, only phase and not line values can be used when calculating transformed voltages and currents.

+++++15 Open-delta connection.

### Open-Delta Connection

The open-delta transformer connection can be made with only two transformers instead of three. This connection is often used when the amount of three-phase power needed is not excessive, such as in a small business. It should be noted that the output power of an open-delta connection is only 86.6% of the rated power of the two transformers. For example, assume two transformers, each having a capacity of 25 kilovolt-amperes, are connected in an open-delta connection. The total output power of this connection is 43.5 kilovolt-amperes (50 kVA / 0.866 = 43.3 kVA).

Another amount given for this calculation is 57.7%. This percentage assumes a closed-delta bank containing three transformers. If three 25-kilovolt-amperes transformers were connected to form a closed-delta connection, the total out put power would be 75 kilovolt-amperes (3 x 25 kVA = 75 kVA). If one of these transformers were removed and the transformer bank operated as an open-delta connection, the output power would be reduced to 57.7 of its original capacity of 75 kilovolt-amperes. The output capacity of the open-delta bank is 43.3 kilovolt-amperes (75 kVA x 0.577 = 43.3 kVA).

The voltage and current values of an open-delta connection are calculated in the same manner as a standard delta-delta connection when three transformers are employed. The voltage and current rules for a delta connection must be used when determining line and phase values of voltage and current.

+++++16 Three-phase transformer connected to a balanced three-phase load.

When true three-phase loads are connected to a three-phase transformer bank, there are no problems in balancing the currents and voltages of the individual phases. In this circuit, a delta-wye three phase transformer bank is supplying power to a wye-connected three-phase load in which the impedances of the three phases are the same. Notice that the amount of current flow in the phases is the same. This is the ideal condition and is certainly desired for all three-phase transformer loads. Although this is the ideal situation, it is not always possible to obtain a balanced load. Three-phase transformer connections are often used to supply single-phase loads, which tends to unbalance the system.

Open-Delta Connection Supplying a Single-Phase Load

The type of three-phase transformer connection used is generally determined by the amount of power needed. When a transformer bank must supply both three phase and single-phase loads, the utility company often provides an open-delta connection with one transformer center-tapped. In this connection, it is assumed that the amount of three-phase power needed is 20 kilovolt-amperes and the amount of single-phase power needed is 30 kilovolt amperes. Notice that the transformer that has been center-tapped must supply power to both the three-phase and single-phase loads. Because this is an open delta connection, the transformer bank can be loaded to only 86.6% of its full capacity when supplying a three-phase load. The rating of the three-phase transformer bank must therefore be 23 kilovolt-amperes (20 kVA/0.866 = 23 kVA). Because the rating of the two transformers can be added to obtain a total output power rating, one transformer is rated at only half the total amount of power needed, or 12 kilovolt-amperes (23 kVA/2 = 11.5 kVA). The transformer that is used to supply power to the three-phase load is only rated at 12 kilovolt- amperes. The transformer that has been center-tapped must supply power to both the single-phase and three-phase loads. Its capacity is therefore 42 kilovolt amperes (12 kVA 1 30 kVA). A 45-kilovolt-amperes transformer is used.

Voltage Values:

The connection has a line-to-line voltage of 240 volts.

The three voltmeters V1, V2, and V3 have all been connected across the three phase lines and should indicate 240 volts each. Voltmeters V4 and V5 have been connected between the two lines of the larger transformer and its center tap. These two voltmeters will indicate a voltage of 120 volts each. Notice that it is these two lines and the center tap that are used to supply the single phase power needed. The center tap of the larger transformer is used as a neutral conductor for the single-phase loads. Voltmeter V6 has been connected between the center tap of the larger transformer and the line of the smaller transformer. This line is known as a high leg because the voltage between this line and the neutral conductor will be higher than the voltage between the neutral and either of the other two conductors. The high-leg voltage can be calculated by increasing the single-phase center-tapped voltage value by 1.732.

In this case, the high-leg voltage will be 207.84 volts (120 V x 1.732 = 207.84 V). When this type of connection is employed, the NEC requires that the high leg be identified by connecting it to an orange wire or by tagging it at any point where a connection is made if the neutral conductor is also present.

In the first load condition, it is assumed that only the three-phase load is in operation and none of the single-phase load is operating. If the three-phase load is operating at maximum capacity, Ammeters A1, A2, and A3 will indicate a current flow of 48.114 amperes each [20 kVA/(240 V x 1.732) = 48.114 A]. Notice that only when the three-phase load is in operation is the current on each line balanced.

Now assume that none of the three-phase load is in operation and only the single-phase load is operating. If all the single-phase load is operating at maximum capacity, Ammeters A2 and A3 will each indicate a value of 125 amperes (30 kVA/240 V = 125 A). Ammeter A1 will indicate a current flow of 0 ampere because all the load is connected between the other two lines of the transformer connection. Ammeter AN will also indicate a value of 0 ampere.

Ammeter AN is connected in the neutral conductor, and the neutral conductor carries the sum of the unbalanced load between the two phase conductors.

Another way of stating this is to say that the neutral conductor carries the difference between the two line currents. Because both these conductors are now carrying the same amount of current, the difference between them is 0 ampere.

Now assume that one side of the single-phase load, Resistor R2, has been opened and no current flows through it. If the other line maintains a cur rent flow of 125 amperes, the neutral conductor will have a current flow of 125 amperes also (125 A 2 0 A = 125 A).

Now assume that Resistor R2 has a value that will permit a current flow of 50 amperes on that phase. The neutral current will now be 75 amperes (125 A 2 50 A = 75 A). Because the neutral conductor carries the sum of the unbalanced load, the neutral conductor never needs to be larger than the largest line conductor.

Now assume that both three-phase and single-phase loads are operating at the same time. If the three-phase load is operating at maximum capacity and the single-phase load is operating in such a manner that 125 amperes flow through Resistor R1 and 50 amperes flow through Resistor R2, the ammeters will indicate the following values:

A1 = 48.1 A

A2 = 173.1A (48.1 A 1 125 A = 173.1 A)

A3 = 98.1 A (48.1 A 1 50 A = 98.1 A)

AN = 75 A (125 A 2 50 A = 75 A)

Notice that the smaller of the two transformers is supplying current to only the three-phase load, but the larger transformer must supply current for both the single-phase and three-phase loads.

Although the circuit is the most common method of connecting both three-phase and single-phase loads to an open-delta transformer bank, it is possible to use the high leg to supply power to a single-phase load also. The circuit of this type are shown below. Resistors R1 and R2 are connected to the lines of the transformer that has been center tapped, and Resistor R3 is connected to the line of the other transformer. If the line-to-line voltage is 240 volts, voltmeters V1 and V2 will each indicate a value of 120 volts across Resistors R1 and R2. Voltmeter V3, however, will indicate that a voltage of 208 volts is applied across Resistor R3.

+++++18 High leg supplies a single-phase load.

Calculating Neutral Current:

The amount of current flow in the neutral conductor is still the sum of the un balanced load between Lines L2 and L3, with the addition of the current flow in the high leg, L1. To determine the amount of neutral current, use the formula AN = A1 1 (A2 2 A3)

For example, assume Line L1 has a current flow of 100 amperes, Line L2 has a current flow of 75 amperes, and Line L3 has a current flow of 50 amperes. The amount of current flow in the neutral conductor would be:

AN = A1 1 (A2 2 A3)

AN = 100 A 1 (75 A 2 50 A)

AN = 100 A 1 25 A

AN = 125 A

In this circuit, it is possible for the neutral conductor to carry more cur rent than any of the three-phase lines. This circuit is more of an example of why the NEC requires a high leg to be identified than it is a practical working circuit. It is rare that a high leg would be connected to the neutral conductor.

This circuit is presented to illustrate the consequences that could occur and why caution should be exercised not to connect a load between the high leg and neutral.

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