Monday, January 12, 2015

Transformer Connections for Three-Phase Circuits: Three-phase transformers .

THREE-PHASE TRANSFORMERS

Electrical energy may be transferred from one three-phase circuit to another three-phase circuit. A three-phase transformer is used to accomplish this transfer, resulting in a change in the voltage. The core structure of this transformer consists of three legs. For each phase, the low-voltage and high-voltage windings are wound on one of the three legs.

Figure 14–17 shows the assembled core of a three-phase transformer, including the low-voltage coil windings. The flux in each coil leg is 120° out of phase with the flux values. This means that each flux will reach its maximum value at a different instant. At any point in time, at least one of the core legs will act as the return path for the fluxes in each of the other phases.

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The core structure and the coil windings of the three-phase transformer are placed in a single case, or tank. They are then covered with transformer oil or a nonflammable liquid such as Pyranol.

The connections between the coil windings are made inside the transformer case. Delta–delta, wye–wye, delta–wye, or wye–delta connections can be made.

Delta–delta-connected, three-phase transformers have three high-voltage leads and three low-voltage leads that are brought out through insulated bushings on the transformer case.

Four leads are brought out when the individual coil windings are connected in wye. The fourth lead is necessary for the neutral wire connection.

Figure 14–18 shows a three-phase transformer with both the high-voltage windings and the low-voltage windings connected in wye. The three-phase line voltage on the input side is 4160 V. The voltage across each high-voltage winding is 4160 -:- M3 = 2400 V.

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The voltage induced in each low-voltage secondary winding is 277 V. Because the three secondary windings are connected in wye, the line voltage on the output side is M3 X 277 = 480 V. The rating for this three-phase transformer is 2400/4160 V to 277/480 V.

Advantages of Three-Phase Transformers

Three-phase transformers are commonly used for both stepdown and stepup applications for the following reasons:

• The operating efficiency of a three-phase transformer is slightly higher than the overall efficiency of three separate single-phase transformers.

• The three-phase transformer weighs less and requires less space than do three separate

single-phase transformers.

• One three-phase transformer supplying the same kVA output costs less than three single-phase transformers.

• The necessary bus bar structure, switchgear, and wiring is installed in either an outdoor or an indoor substation. For a three-phase transformer, this equipment is easier to install and is less complex than that required by a transformer bank consisting of three single- phase transformers.

Disadvantage of the Three-Phase Transformer

The three-phase transformer has one disadvantage. If one of the phase windings becomes defective, then the entire three-phase unit must be taken out of service. A defective single-phase transformer in a three-phase bank can be disconnected. Partial service can be restored using the remaining transformers until a replacement unit is obtained. However, because transformers have a high reliability, most applications requiring large transformers use three-phase transformers.

The three problems that follow show how single-phase transformers are used in three- phase transformer banks.

PROBLEM 2

Statement of the Problem

A three-phase transformer bank is used to step down a 2400-V, three-phase, three-wire primary service to a 240-V, three-phase, three-wire secondary service. The transformer bank consists of three 20-kVA transformers. Each transformer has additive polarity. The high-voltage side of each transformer is rated at 2400 V. The low-voltage side of each transformer has two 120-V windings.

1. Draw a schematic diagram of the connections for this circuit. The leads of each trans- former are to be marked for additive polarity.

2. At the rated load and a lagging power factor of 0.80, determine

a. the rating of the transformer bank, in kVA.

b. the output at the rated load and lagging power factor of 0.80, in kW.

c. the secondary line current.

d. the secondary coil current and the coil voltage.

e. the primary coil current.

f. the primary line current.

Solution

1. In a delta connection, the coil and line voltages are equal. The primary line voltage is 2400 V. The high-voltage winding of each transformer is also rated at 2400 V. The line voltage on the secondary is to be 240 V. The two 120-V windings on the low side of each transformer can be connected in series to give 240 V. As shown in Figure 14–19, the transformer bank is connected in delta–delta.

2. a. The kVA capacity of the transformer bank is

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d. The coil voltage and the line voltage are the same in a delta connection. Thus, if the secondary line voltage is 240 V, the secondary coil voltage is also 240 V. The line current is equal to M3 times the coil winding current. The line current was found to be 144.5 A. The secondary coil current is

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This ratio is also the ratio between the turns on the high-voltage and low-volt- age sides. Unit 13 states that the turns on the windings are inversely proportional to the current. This means that

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PROBLEM 3

Statement of the Problem

For the delta–delta transformer bank described in problem 2, one transformer is dam- aged. The remaining two transformers are reconnected in open delta:

1. What is the capacity of the open-delta bank in kVA?

2. Assuming that the transformer bank is loaded to the rated kVA capacity with a balanced load having a lagging power factor of 0.80, determine

a. the kW output.

b. the line current on the secondary side.

Solution

1. The kVA capacity of the open-delta bank is 58% of the capacity of the original closed-delta bank:

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PROBLEM 4

Statement of the Problem

A 4800-V, three-phase, three-wire primary voltage is stepped down to a 120/208- V, three-phase, four-wire, secondary service. The transformer bank used consists of three single-phase transformers. Each transformer is rated at 15 kVA, 4800/120 V. The load is a noninductive heater unit consisting of three 1-!1 sections connected in wye to the three- phase, four-wire, secondary system.

1. Draw a schematic diagram of the connections for the transformer bank. Assume each transformer has additive polarity.

2. Determine

a. the kVA capacity of the transformer bank.

b. the kVA load on the transformer bank.

c. the secondary line current.

d. the primary line current.

Solution

1. The primary line voltage is 4800 V. The high-voltage windings are also rated at 4800 V. Thus, the primary windings are connected in delta. The low-voltage windings of the transformer are rated at 120 V. These windings are connected in wye to give a three-phase, four-wire, 120/208-V service. For wye connections, the line voltage is M3 times the coil voltage. In this case, the line voltage is M3 X 120 = 208 V. See Figure 14–20.

2. a. The capacity of the transformer bank is 15 + 15 + 15 = 45 k VA

b. The current taken by each heater element is

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The line current in each of the three line wires of the wye system is 120 A. The total kVA load is

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