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BUS DUCTS AND PANEL PROBLEMS

Triplen harmonic currents can also cause problems with neutral bus ducts and connecting lugs. A neutral bus is sized to carry the rated phase current. Because triplen harmonics can cause the neutral current to be higher than the phase current, it is possible for the neutral bus to become overloaded.

Electrical panels and bus ducts are designed to carry currents that operate at 60 Hz. Harmonic currents produce magnetic fields that operate at higher frequencies. If these fields should become mechanically resonant with the panel or bus duct enclosures, the panels and bus ducts can vibrate and produce buzzing sounds at the harmonic frequency.

Telecommunications equipment is often affected by harmonic currents. Tele- communication cable is often run close to power lines. To minimize interference, communication cables are run as far from phase conductors as possible and as close to the neutral conductor as possible. Harmonic currents in the neutral conductor induce high- frequency currents into the communication cable. These high-frequency currents can be heard as a high-pitched buzzing sound on telephone lines.

Determining Harmonic Problems on Single-Phase Systems

There are several steps that can be followed in determining whether there is a problem with harmonics. One step is to do a survey of the equipment. This is especially important in determining whether there is a problem with harmonics in a single-phase system.

1. Make an equipment check. Equipment such as personal computers, printers, and fluorescent lights with electronic ballast are known to produce harmonics. Any piece of equipment that draws current in pulses can produce harmonics.

2. Review maintenance records to see whether there have been problems with circuit breakers tripping for no apparent reason.

3. Check transformers for overheating. If the cooling vents are unobstructed and the transformer is operating excessively hot, harmonics could be the problem. Check transformer currents with an ammeter capable of indicating a true RMS current value. Make sure that the voltage and current ratings of the transformer have not been exceeded.

It is necessary to use an ammeter that responds to true RMS current when making this check. Some ammeters respond to the average value, not the RMS value. Meters that respond to the true RMS value generally state this on the meter. Meters that respond to the average value are generally less expensive and do not state that they are RMS meters.

Meters that respond to the average value use a rectifier to convert the alternating current into direct current. This value must be increased by a factor of 1.111 to change the average reading into the RMS value for a sine-wave current. True RMS responding meters calculate the heating effect of the current. The chart in Figure 14–34 shows some of the differences between average indicating meters and true RMS meters. In a distorted waveform, the true RMS value of current will no longer be average × 1.111 (Figure 14–35). The distorted wave- form generally causes the average value to be as much as 50% less than the RMS value.

value of 36.8 A, and the average ammeter indicates a value of 24.8 A. Determine the ratio of the two measurements by dividing the average value by the true RMS value:

A ratio of 1 would indicate no harmonic distortion. A ratio of 0.5 would indicate extreme harmonic distortion. This method does not reveal the name or sequence of the harmonic distortion, but it does indicate whether there is a problem with harmonics.

The most accurate method for determining whether there is a harmonics problem is to use a harmonic analyzer. The harmonic analyzer will determine the name, sequence, and amount of harmonic distortion present in the system.

Determining Harmonic Problems on Three-Phase Systems

Determining whether a problem with harmonics exists in a three-phase system is similar to determining the problem in a single-phase system. Because harmonic problems in a three-phase system generally occur in a wye-connected, four-wire system, this example will assume a delta-connected primary and wye-connected secondary with a center-tapped neutral as shown in Figure 14–32. To test for harmonic distortion in a three- phase, four-wire system, measure all phase currents and the neutral current with both a true RMS indicating ammeter and an average indicating ammeter. It will be assumed that the three-phase system being tested is supplied by a 200-kVA transformer, and the current values shown in Figure 14–37 were recorded. The current values indicate that a problem with harmonics does exist in the system. Note the higher current measurements made with the true RMS indicating ammeter, and also the fact that the neutral current is higher than any phase current.

Dealing with Harmonic Problems

After it has been determined that harmonic problems exist, something must be done to deal with them. It is generally not practical to remove the equipment causing the harmonic distortion, so other methods must be employed. It is a good idea to consult a power quality expert to determine the exact nature and amount of harmonic distortion present. Some general procedures for dealing with harmonics follow:

1. In a three-phase, four-wire system, the 60-Hz part of the neutral current can be reduced by balancing the current on the phase conductors. If all phases have equal current flow, the neutral current would be zero.

2. If triplen harmonics are present on the neutral conductor, harmonic filters can be added at the load. These filters can help reduce the amount of harmonics on the line.

3. Pull extra neutral conductors. The ideal situation would be to use a separate neutral for each phase, instead of using a shared neutral.

4. Install a larger neutral conductor. If it is impractical to supply a separate neutral conductor for each phase, increase the size of the common neutral.

5. Derate or reduce the amount of load on the transformer. Harmonic problems generally involve overheating of the transformer. In many instances it is necessary to derate the transformer to a point that it can handle the extra current caused by the harmonic distortion. When this is done, it is generally necessary to add a second transformer and divide the load between the two.

Determining Transformer Harmonic Derating Factor

Probably the most practical and straightforward method for determining the derating factor for a transformer is recommended by the Computer & Business Equipment Manufacturers Association. To use this method, two ampere measurements must be made. One is the true RMS current of the phases and the second is the instantaneous peak phase current. The instantaneous peak current can be determined with an oscilloscope connected to a cur- rent probe or with an ammeter capable of measuring the peak value. Many of the digital clamp-on ammeters are capable of measuring the average, true RMS, and peak values of current. For this example, it will be assumed that peak current values are measured for the 200-kVA transformer discussed previously. These values are added to the previous data obtained with the true RMS and average indicating ammeters (Figure 14–38). The formula for determining the transformer harmonic derating factor (THDF) is

This formula will produce a derating factor somewhere between 0 and 1.0. Because the instantaneous peak value of current is equal to the RMS value × 1.414, if the current wave- forms are sinusoidal (no harmonic distortion), the formula will produce a derating factor of 1.0. Once the derating factor is determined, multiply the derating factor by the kVA capacity of the transformer. The product will be the maximum load that should be placed on the transformer.

SUMMARY

• Most electrical energy is generated by three-phase alternating-current generators.

1. Three-phase systems are used to transmit and distribute this electrical energy.

2. For economy, the generated three-phase voltage is stepped up to an extremely high voltage by three-phase transformers for long-distance transmission over the three-phase system.

3. Three-phase transformers are used at distribution points to step down the high voltage to a safe and usable level.

• A large three-phase transformer is completely enclosed in one container. Three single- phase transformers, connected in a bank, can be used to transform the voltages of three- phase systems at distribution points.

1. These transformers may be connected in any one of four standard ways:

a. Delta–delta

b. Wye–wye

c. Delta–wye

d. Wye–delta

2. Another method is the open-delta (or V) connection. This connection uses only two single-phase transformers to transform the voltages on a three-phase system.

• The delta–delta connection:

1. The delta–delta connection is used to supply an industrial load by stepping down a 2400-V, three-phase, three-wire service to a 240-V, three-phase, three-wire service.

2. For most applications, the load is balanced and the three single-phase transformers have the same kilovolt-ampere rating.

3. The primary and the secondary windings are connected in delta.

4. To determine the total capacity in kilovolt-amperes of a delta–delta-connected transformer bank, the three kVA ratings are added.

• For any delta-connected circuits and systems:

1. Each transformer winding is connected across the two line leads; thus, the line voltage and the transformer coil winding voltage are the same.

2. The line current is equal to M3 or 1.73 times the coil winding current.

3. In a closed-delta transformer connection, each line wire is fed by two trans- former coil currents that are out of phase. These coil currents do not add directly, but must be added vectorially to obtain the line current.

• Feeding a dual load using a delta–delta connection—some power companies use a delta–delta-connected transformer bank to feed two types of loads:

1. A 240-V, three-phase industrial load.

2. A 120/240-V, single-phase, three-wire lighting load.

a. The transformer supplying the lighting load is larger than the other two trans- formers of the three-phase system.

b. The neutral wire is tied to the midpoint of the 240-V, low-voltage secondary winding.

c. Many transformers have two 120-V windings. These windings are connected in series and the neutral is brought out at the midpoint to give a 120/240-V service.

3. Both lines A and C have 120 V to the grounded neutral. Line B has approximately 208 V to ground. This connection can be a serious hazard and cannot be used for lighting service.

• Procedure for making a closed-delta connection:

1. Two primary winding leads are brought out of the transformer and are marked H1 and H2. It is assumed that H1 is the beginning and H2 is the ending of each high-voltage winding. The H2 end of each primary winding is connected to the beginning (H1) of the next primary winding to form a series arrangement.

2. One three-phase primary source line is connected to each junction of two windings. With a 2400-V source, each of the primary windings has a line voltage of 2400 V impressed across it.

3. Once the high-voltage primary connections are made, the three-phase, 2400-V input may be energized and tested for the correct phase rotation. If the phase rotation is incorrect, the circuit is deenergized and any two line wires are interchanged.

4. To determine whether a transformer has additive or subtractive polarity, the terminal markings or the nameplate data can be checked.

5. The secondary closed-delta connection is the same as the primary connection, with X1 substituted for H1 and X2 substituted for H2. The primary side of the delta-connected transformer may be connected so as to cause a polarity reversal in one of its legs. A phase inversion on the primary side must be corrected on the secondary side.

a. Determine whether the voltage output of each of the three transformers is the same as the voltage rating on the nameplate.

b. Connect the end of one secondary winding to the beginning of another secondary winding. If the connection is correct, the voltage across the open ends of the two transformers should be the same as the output of each transformer. If the connections are not correct, the resultant voltage is M3 times the secondary rated voltage. The phase reversal is corrected by interchanging the connections to one of the coils.

c. With the correct voltage on the two coils, add the end of the third secondary winding coil to the beginning of the second coil. The resultant voltage is opposite to each secondary voltage and has a magnitude equal to the secondary voltage. If the voltage is zero across the last pair of open leads, they can be connected together. A line wire is attached at each of the connection points. These three line wires form the three-phase output. If the voltage reading is not zero, reverse the connections of the last transformer coil before the delta connection is closed and the output lines are added.

• The percentage load on a transformer bank connected in closed delta, in terms of its rated capacity, is

• The total output of a closed-delta connection is

• The wye–wye connection:

1. This connection can be used when the load on the secondary side is balanced. If the secondary load consists of three-phase motors only and the load currents are balanced, the wye–wye connection can be used.

2. This connection cannot be used if the secondary load becomes unbalanced. An unbalanced load causes a serious imbalance in the three voltages of the trans- former bank.

3. A fourth wire, known as the neutral wire, is added to eliminate unbalanced volt- ages. It is connected between the source and the common point on the primary side of the transformer bank.

a. Each high-voltage winding is connected between the neutral and one of the three line leads. If the source is 2400/4160 V, the voltage across each high-voltage winding is 2400 V. The voltage across the three line leads is M3 X 2400, or 4160 V.

b. The neutral wire maintains a constant voltage across each of the high-volt- age windings, even when the load is unbalanced.

c. The neutral wire is grounded and helps protect the three high-voltage windings from lightning surges.

4. With the secondary connected in wye, each low-voltage winding is connected between the secondary neutral and one of the three line leads.

a. For a four-wire, three-phase system rated at 2400/4160 V and 120/280 V, the voltage output of each secondary winding is 120 V. There are 120 V between the neutral wire and any one of the three secondary line leads.

b. The voltage across the line wires is M3 X 120, or 208 V.

(1) 208-V, three-phase service is available for industrial power loads such as three-phase motors.

(2) 120 V is available for lighting loads.

5. Nearly all wye–wye-connected transformers use three single-phase transformers having the same kVA capacity:

6. In a wye–wye connection, a defective transformer must be replaced before the bank can be reenergized.

• The delta–wye connection:

1. This connection is also used for transformation to step up or step down a voltage.

2. The primary windings are connected in delta and the secondary windings are connected in wye.

3. This connection is used at a generator station to step up the voltage. The input voltage is stepped up by the transformer ratio. This voltage is further increased by M3, or 1.73 times the secondary coil voltage. The high voltage is then connected directly to three-phase transmission lines.

4. The insulation requirements are reduced for the secondary windings because the coil voltage is only 58% of the line voltage. (This fact is very important when the secondary side has a very high voltage.)

5. This connection can also be used at the distribution point to step down the voltage.

6. The delta–wye connection can be used for a three-phase, four-wire system for power and lighting.

a. In a 208/120-V system, 208 V supplies the three-phase power load and 120 V supplies the lighting load.

b. In a 480/277-V system, 480 V supplies the three-phase power load and 277 V supplies the lighting load.

(1) Standard 120-V fluorescent lighting fixtures are used with special ballasts for operation on 277-V circuits.

(2) A 277/480-V, three-phase, four-wire system has the following advantages:

(a) The I2 R drop is reduced in feeders and branch circuits, resulting in an increase in the operating efficiency.

(b) Smaller sizes of copper conductors, conduits, and equipment can be used to save up to 25% of the installation cost.

(c) The load demands on the 277/480-V system can be increased with a minimum of changes and expense.

c. In a building using a 277/480-V, three-phase system, the additional require- ment of a 120-V service uses little power. A transformer is added to step down the voltage from 480 V to 120/240 V. A small air-cooled transformer can be used to supply the 120-V service and is centrally located.

• The wye–delta connection:

1. This connection is used to step down relatively high transmission line voltages at the load center. A transformer bank of this type is commonly used to step down voltages of 60,000 V or more.

2. Advantages of the delta–wye connection are

a. the three-phase voltage is reduced by the transformer ratio times 1.73.

b. the insulation requirements are reduced for the high-voltage windings because the wye primary coil voltage is only 58% of the primary line voltage.

• For the delta–wye and wye–delta connections, the three single-phase transformers generally have the same kVA capacity, and the total capacity of the transformer bank, in kVA, is obtained by adding the kVA ratings of the three transformers.

• The open-delta connection (V connection):

1. This connection uses two transformers only.

2. It can be used in emergency situations when one of three transformers is damaged in a three-phase service. The damaged transformer is cut out of the system, and the configuration of the open-delta connection is used.

3. With two transformers supplying the service, the total capacity is only 58% of the capacity of the closed-delta connection.

4. On the secondary side, the line voltage and the line current are the same as the secondary coil current and voltage.

5. The original transformer installation may consist of an open-delta bank. As the industrial power load requirements increase, a third transformer may be added. When the third transformer is added, a delta–delta bank (closed-delta bank) is formed.

6. The total kVA capacity for an open-delta bank is Total kVA = kVA1 + kVA2 X 0.866

• Advantages of an enclosed three-phase transformer:

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

2. The three-phase transformer weighs less and requires less space than do three separate single-phase transformers.

3. The three-phase transformer supplies the same kVA output and costs less than three single-phase transformers.

4. The installation equipment required (such as bus bars, switchgear, and wiring) is easier to install and is less complex than that required by a transformer bank consisting of three single-phase transformers.

• If the three-phase transformer develops a problem, such as a defective phase winding, then the entire three-phase unit must be taken out of service.

• T-connected transformers are similar to an open-delta connection in that only two trans- formers are required to make the connection.

1. Before two transformers can be connected T, one transformer must have a 50% tap on both the primary and secondary windings. It is preferable for the second transformer to have an 86.6% tap.

2. T-connected transformers are generally wound specially for the purpose and are contained in the same case.

3. The phase balance of the T-connected transformer is better than that of an open- delta bank.

4. The T-connected transformer can be connected to supply three-phase, four-wire service in a manner similar to that for a four-wire wye connection.

• Scott-connected transformers are similar to T-connected ones in that the main trans- former must have a 50% tap on both the primary and secondary, and the teaser trans- former must have an 86.6% tap.

1. The Scott connection is used to produce two-phase power from a three-phase connection.

2. A two-phase system has voltages 90° out of phase with each other.

• The zigzag connection is generally used for grounding purposes.

• Harmonics can cause heating problems in ac circuits.

• Harmonics are generally caused by devices that cause pulsations on the line such as switching power supplies and variable-frequency drives.

• The third harmonic generally causes overload conditions on neutral conductors.

• It is sometimes necessary to derate transformers because of harmonic problems.

Achievement Review

1. An industrial plant has a 2400-V, three-phase, three-wire service. It uses three 100-kVA, single-phase transformers. Each transformer is rated at 2400/240 V. The transformers supply a 240-V, three-phase, three-wire system. Each trans- former has additive polarity.

a. Draw a connection diagram showing how the transformer bank is connected.

Mark the polarity of all transformer leads.

b. A balanced load of 200 kW at a lagging power factor of 0.70 is supplied by the transformer bank. Determine

1. the secondary line current.

2. the secondary coil current.

3. the primary coil current.

4. the primary line current.

2. What is the percentage of load in kVA on the transformer bank described in question 1?

3. Explain a procedure that may be used to connect the secondary windings of single-phase transformers in closed delta.

4. a. Assume that one of the transformers in the delta–delta transformer bank in question 1 is cut out of service because it is damaged by lightning. Assuming that plant operations are cut to a minimum so that the peak load does not exceed the capacity of the two remaining transformers, show how they could be connected during this emergency.

b. What is the maximum balanced load, in kilowatts, at a lagging power factor of 0.70, that may be connected to the transformer bank during the emergency described in part a of this question?

5. Explain a procedure that may be used to connect the secondary windings of three single-phase transformers in wye.

6. Three single-phase, 20-kVA, 2400/120-V transformers are connected in a three- phase transformer bank. The transformers have additive polarity. The bank steps down the 2400/4160-V, three-phase, four-wire primary service to a 120/208-V, three-phase, four-wire secondary service. This service supplies both a 120-V, single-phase lighting load and a 208-V, three-phase motor load. Draw a schematic diagram of the connections for this transformer bank.

7. a. What is the maximum balanced three-phase load, in kVA, that can be connected to the transformer bank in question 6?

b. If the load has a lagging power factor of 0.80, what is the maximum output in kW that can be obtained from the transformer bank?

8. Give two practical applications for a delta–wye transformer bank. Give one practical application for a wye–delta transformer bank.

9. A three-phase, four-wire, wye-connected transmission system has a voltage of approximately 60,550 V across the three line wires. In addition, there is 35,000 V from each line wire to the neutral. This voltage is to be stepped down at a substation to supply energy to a 5000-V, three-phase, three-wire distribution sys- tem. Each transformer is rated at 35,000/5000 V, 2000 kVA. Each transformer has subtractive polarity. Draw a schematic wiring diagram for this circuit and determine

a. the full-load capacity of the bank, in kVA.

b. the line current on the secondary side when the transformer bank is loaded to its rated capacity.

c. the line current on the primary side when the transformer bank is loaded to its rated capacity, neglecting any losses.

10. What are typical applications of a 277/480-V, three-phase, four-wire, wye- connected system? What are the advantages of such a system?

11. a. List several advantages of a three-phase transformer, as compared with a three-phase bank consisting of three single-phase transformers.

b. Give one disadvantage of the use of a three-phase transformer.

12. The high-voltage windings of a three-phase transformer are connected in wye. The low-voltage windings are connected in delta. The actual ratio between the high- voltage windings and their respective low-voltage windings is 10:1. The primary side of the transformer is supplied from a three-phase, four-wire, 2400/4160-V circuit. The secondary output is a three-phase, three-wire service for a three-phase industrial motor load. Determine

a. the secondary voltage.

b. the kVA output of the bank, when the current supplied to the motor load on the secondary is 60 A in each line wire.

c. the line current in each line wire on the high-voltage primary side of the trans- former, neglecting any losses.

13. What is the frequency of the second harmonic?

14. Of the following, identify those that are considered triplen harmonics: third, sixth, ninth, twelfth, fifteenth, and eighteenth.

15. Would a positive rotating harmonic or a negative rotating harmonic be more harmful to an induction motor? Explain your answer.

16. What instrument should be used to determine what harmonics are present in a power system?

17. A 22.5-kVA single-phase transformer is tested with a true RMS ammeter and an ammeter that indicates the peak value. The true RMS reading is 94 A. The peak reading is 204 A. Should this transformer be derated, and if so, by how much?

PRACTICE PROBLEMS FOR UNIT 14

In the following problems, three single-phase control transformers have been con- nected to operate with a primary voltage of 240 V and a secondary voltage of 120 V. This gives each transformer a turns ratio of 2:1. It will be assumed that a line-to-line voltage of 208 V is connected to the primary winding, and that the load connected to the secondary has an impedance of 4 !1 in each phase. Find the unknown values in each of the following problems. It will be necessary to use the formulas in the Transformers and Three-Phase Connections sections of Appendix 15.

[Note: When computing values of voltage and current between the primary and secondary windings, use phase values and not line values.] In the following problems:

HARMONICS

Harmonics are voltages or currents that operate at a frequency that is a multiple of the fundamental power frequency. If the fundamental power frequency is 60 Hz, for example, the second harmonic would be 120 Hz, the third harmonic would be 180 Hz, and so on. Harmonics are produced by nonlinear loads that draw current in pulses rather than in a continuous manner. Harmonics on single-phase power lines are generally caused by devices such as computer power supplies, electronic ballasts in fluorescent lights, triac light dimmers, and so on. Three-phase harmonics are generally produced by variable-frequency drives for ac motors and electronic drives for dc motors. A good example of a pulsating load is one that converts ac cur- rent into dc and then regulates the dc voltage by pulsewidth modulation (Figure 14–29). Many regulated power supplies operate in this manner. The bridge rectifier in Figure 14–29 changes the alternating current into pulsating direct current. A filter capacitor is used to smooth the pulsations. The transistor turns on and off to supply power to the load. The amount of time the transistor is turned on compared with the time it is turned off determines the output dc voltage. Each time the transistor turns on, it causes the capacitor to begin discharging. When the transistor turns off, the capacitor will begin to charge again. Current is drawn from the ac line each time the capacitor charges. These pulsations of current produced by the charging capacitor can cause the ac sine wave to become distorted. These distorted current and voltage waveforms flow back into the other parts of the power system (Figure 14–30).

Harmonic Effects

Harmonics can have very detrimental effects on electrical equipment. Some common symptoms of harmonics are overheated conductors and transformers and circuit breakers that seem to trip when they should not. Harmonics are classified by name, frequency, and sequence. The name refers to whether the harmonic is the second, third, fourth, and so on of the fundamental frequency. The frequency refers to the operating frequency of the harmonic. The second harmonic operates at 120 Hz, the third at 180 Hz, the fourth at 240 Hz, and so on. The sequence refers to the phasor rotation with respect to the fundamental waveform. In an induction motor, a positive sequence harmonic would rotate in the same direction as the fundamental frequency. A negative sequence harmonic would rotate in the opposite direction of the fundamental frequency. A particular set of harmonics called “triplens” has a zero sequence. Triplens are the odd multiples of the third harmonic (third, ninth, fifteenth, twenty-first, and so on). A chart showing the sequence of the first nine harmonics is shown in Figure 14–31.

Harmonics with a positive sequence generally cause overheating of conductors and transformers, and circuit breakers. Negative-sequence harmonics can cause the same heating problems as positive harmonics plus additional problems with motors. Because the phasor rotation of a negative harmonic is opposite that of the fundamental frequency, it will tend to weaken the rotating magnetic field of an induction motor, causing it to produce less torque. The reduction of torque causes the motor to operate below normal speed. The reduction in speed results in excessive motor current and overheating.

Although triplens do not have a phasor rotation, they can cause a great deal of trouble in a three-phase, four-wire system, such as a 208/120-V or 480/277-V system. In a common 208/120-V, wye-connected system, the primary is generally connected in delta and the secondary is connected in wye (Figure 14–32).

Single-phase loads that operate on 120 V are connected between any phase conduc- tor and the neutral conductor. The neutral current will be the vector sum of the phase currents. In a balanced three-phase circuit (where all phases have equal current), the neutral current will be zero. Although single-phase loads tend to cause an unbalanced condition, the vector sum of the currents will generally cause the neutral conductor to carry less current than any of the phase conductors. This is true for loads that are linear and draw a continuous sine-wave current. When pulsating (nonlinear) currents are connected to a three-phase, four-wire system, triplens harmonic frequencies disrupt the normal phasor relationship of the phase currents and can cause the phase currents to add in the neutral conductor instead of cancel. Because the neutral conductor is not protected by a fuse or circuit breaker, there is real danger of excessive heating in the neutral conductor.

Harmonic currents are also reflected in the delta primary winding, where they circulate and cause overheating. Other heating problems are caused by eddy current and hysteresis losses. Transformers are typically designed for 60-Hz operation. Higher harmonic frequencies produce greater core losses than the transformer is designed to handle. Transformers that are connected to circuits that produce harmonics must sometimes be derated or replaced with transformers that are specially designed to operate with harmonic frequencies.

Transformers are not the only electrical component to be affected by harmonic cur- rents. Emergency and standby generators can be affected in the same way as transformers. This is especially true for standby generators used to power data-processing equipment in the event of a power failure. Some harmonic frequencies can even distort the zero crossing of the waveform produced by the generator.

CIRCUIT BREAKER PROBLEMS

Thermomagnetic circuit breakers use a bimetallic trip mechanism that is sensitive to the heat produced by the circuit current. These circuit breakers are designed to respond to the heating effect of the true RMS current value. If the current becomes too great, the bimetallic mechanism trips the breaker open. Harmonic currents cause a distortion of the RMS value, which can cause the breaker to trip when it should not, or not to trip when it should. Thermomagnetic circuit breakers, however, are generally better protection against harmonic currents than electronic circuit breakers. Electronic breakers sense the peak value of current. The peaks of harmonic currents are generally higher than the fundamental sine wave (Figure 14–33). Although the peaks of harmonic currents are generally higher than the fundamental frequency, they can be lower. In some cases, electronic breakers may trip at low currents and in other cases they may not trip at all.

HARMONICS

Harmonics are voltages or currents that operate at a frequency that is a multiple of the fundamental power frequency. If the fundamental power frequency is 60 Hz, for example, the second harmonic would be 120 Hz, the third harmonic would be 180 Hz, and so on. Harmonics are produced by nonlinear loads that draw current in pulses rather than in a continuous manner. Harmonics on single-phase power lines are generally caused by devices such as computer power supplies, electronic ballasts in fluorescent lights, triac light dimmers, and so on. Three-phase harmonics are generally produced by variable-frequency drives for ac motors and electronic drives for dc motors. A good example of a pulsating load is one that converts ac cur- rent into dc and then regulates the dc voltage by pulsewidth modulation (Figure 14–29). Many regulated power supplies operate in this manner. The bridge rectifier in Figure 14–29 changes the alternating current into pulsating direct current. A filter capacitor is used to smooth the pulsations. The transistor turns on and off to supply power to the load. The amount of time the transistor is turned on compared with the time it is turned off determines the output dc voltage. Each time the transistor turns on, it causes the capacitor to begin discharging. When the transistor turns off, the capacitor will begin to charge again. Current is drawn from the ac line each time the capacitor charges. These pulsations of current produced by the charging capacitor can cause the ac sine wave to become distorted. These distorted current and voltage waveforms flow back into the other parts of the power system (Figure 14–30).

Harmonic Effects

Harmonics can have very detrimental effects on electrical equipment. Some common symptoms of harmonics are overheated conductors and transformers and circuit breakers that seem to trip when they should not. Harmonics are classified by name, frequency, and sequence. The name refers to whether the harmonic is the second, third, fourth, and so on of the fundamental frequency. The frequency refers to the operating frequency of the harmonic. The second harmonic operates at 120 Hz, the third at 180 Hz, the fourth at 240 Hz, and so on. The sequence refers to the phasor rotation with respect to the fundamental waveform. In an induction motor, a positive sequence harmonic would rotate in the same direction as the fundamental frequency. A negative sequence harmonic would rotate in the opposite direction of the fundamental frequency. A particular set of harmonics called “triplens” has a zero sequence. Triplens are the odd multiples of the third harmonic (third, ninth, fifteenth, twenty-first, and so on). A chart showing the sequence of the first nine harmonics is shown in Figure 14–31.

Harmonics with a positive sequence generally cause overheating of conductors and transformers, and circuit breakers. Negative-sequence harmonics can cause the same heating problems as positive harmonics plus additional problems with motors. Because the phasor rotation of a negative harmonic is opposite that of the fundamental frequency, it will tend to weaken the rotating magnetic field of an induction motor, causing it to produce less torque. The reduction of torque causes the motor to operate below normal speed. The reduction in speed results in excessive motor current and overheating.

Although triplens do not have a phasor rotation, they can cause a great deal of trouble in a three-phase, four-wire system, such as a 208/120-V or 480/277-V system. In a common 208/120-V, wye-connected system, the primary is generally connected in delta and the secondary is connected in wye (Figure 14–32).

Single-phase loads that operate on 120 V are connected between any phase conduc- tor and the neutral conductor. The neutral current will be the vector sum of the phase currents. In a balanced three-phase circuit (where all phases have equal current), the neutral current will be zero. Although single-phase loads tend to cause an unbalanced condition, the vector sum of the currents will generally cause the neutral conductor to carry less current than any of the phase conductors. This is true for loads that are linear and draw a continuous sine-wave current. When pulsating (nonlinear) currents are connected to a three-phase, four-wire system, triplens harmonic frequencies disrupt the normal phasor relationship of the phase currents and can cause the phase currents to add in the neutral conductor instead of cancel. Because the neutral conductor is not protected by a fuse or circuit breaker, there is real danger of excessive heating in the neutral conductor.

Harmonic currents are also reflected in the delta primary winding, where they circulate and cause overheating. Other heating problems are caused by eddy current and hysteresis losses. Transformers are typically designed for 60-Hz operation. Higher harmonic frequencies produce greater core losses than the transformer is designed to handle. Transformers that are connected to circuits that produce harmonics must sometimes be derated or replaced with transformers that are specially designed to operate with harmonic frequencies.

Transformers are not the only electrical component to be affected by harmonic cur- rents. Emergency and standby generators can be affected in the same way as transformers. This is especially true for standby generators used to power data-processing equipment in the event of a power failure. Some harmonic frequencies can even distort the zero crossing of the waveform produced by the generator.

CIRCUIT BREAKER PROBLEMS

Thermomagnetic circuit breakers use a bimetallic trip mechanism that is sensitive to the heat produced by the circuit current. These circuit breakers are designed to respond to the heating effect of the true RMS current value. If the current becomes too great, the bimetallic mechanism trips the breaker open. Harmonic currents cause a distortion of the RMS value, which can cause the breaker to trip when it should not, or not to trip when it should. Thermomagnetic circuit breakers, however, are generally better protection against harmonic currents than electronic circuit breakers. Electronic breakers sense the peak value of current. The peaks of harmonic currents are generally higher than the fundamental sine wave (Figure 14–33). Although the peaks of harmonic currents are generally higher than the fundamental frequency, they can be lower. In some cases, electronic breakers may trip at low currents and in other cases they may not trip at all.

T-CONNECTED TRANSFORMERS

Another connection involving the use of two transformers to supply three-phase power is the T connection (Figure 14–21). In this connection, one transformer is generally referred to as the main transformer and the other is called the teaser transformer. The main transformer must contain a center or 50% tap for both the primary and secondary winding, and it is preferred that the teaser transformer contain an 86.6% voltage tap for both the primary and secondary winding. Although the 86.6% tap is preferred, the connection can be made with a teaser transformer that has the same voltage rating as the main transformer. In this instance, the teaser transformer is operated at reduced flux (Figure 14–22). This connection permits two transformers to be connected T instead of open delta in the event that one transformer of a delta–delta bank should fail.

Transformers intended for use as T-connected transformers are often specially wound for the purpose, and both transformers are often contained in the same case. When making the T connection, the main transformer is connected directly across the power line. One primary lead of the teaser transformer is connected to the center tap of the main transformer, and the 86.6% tap is connected to the power line. The same basic connection is made for the secondary. A vector diagram illustrating the voltage relationships of the T connection is shown in Figure 14–23. The greatest advantage of the T connection over the open-delta connection is that it maintains a better phase balance, and the T-connected transformer can be connected to provide a three-phase, four-wire output similar to that of a four-wire wye connection. T-connected transformers used to provide three-phase, four-wire power generally have voltages of 480/277 or 208/120 V. The greatest disadvantage of the T connection is that one transformer must contain a center tap of both its primary and secondary windings.

SCOTT CONNECTION

The Scott connection is used to convert three-phase power into two-phase power using two single-phase transformers. The Scott connection is very similar to the T connection in that one transformer, called the main transformer, must have a center or 50% tap, and the second or teaser transformer must have an 86.6% tap on the primary side. The difference between the Scott and T connections lies in the connection of the secondary windings (Figure 14–24). In the Scott connection, the secondary windings of each transformer pro- vide the phases of a two-phase system. The voltages of the secondary windings are 90° out of phase with each other. The Scott connection is generally used to provide two-phase power for the operation of two-phase motors.

ZIGZAG CONNECTION

The zigzag or interconnected wye transformer is primarily used for grounding pur- poses. It is used mainly to establish a neutral point for the grounding of fault currents. The zigzag connection is basically a three-phase autotransformer whose windings are divided into six equal parts (Figure 14–25). In the event of a fault current, the zigzag connection forces the current to flow equally in the three legs of the autotransformer, offering minimum impedance to the flow of fault current. A schematic diagram of the zig- zag connection is shown in Figure 14–26.

THREE-PHASE–TO–SIX-PHASE CONNECTIONS

There are some instances when it is desirable to have a power system with more than three phases. A good example of this is when it is necessary to convert or rectify alternating current into direct current with a minimum amount of ripple (pulsations of voltage). Power supplies that produce a low amount of ripple require less filtering. One of the most common three-phase-to-six-phase connections is the diametrical connection (Figure 14–27). The diametrical connection is preferred because it requires only one low-voltage winding on each transformer. If these windings are center-tapped, a neutral conductor can be provided for the six-phase output, permitting half-wave rectification to be used. The high-voltage windings can be connected in wye or delta, but the delta is preferred because it helps reduce harmonics in the secondary winding. A schematic diagram of a diametrical connection with a delta-connected primary and three-phase half-wave rectifier is shown in Figure 14–28.

T-CONNECTED TRANSFORMERS

Another connection involving the use of two transformers to supply three-phase power is the T connection (Figure 14–21). In this connection, one transformer is generally referred to as the main transformer and the other is called the teaser transformer. The main transformer must contain a center or 50% tap for both the primary and secondary winding, and it is preferred that the teaser transformer contain an 86.6% voltage tap for both the primary and secondary winding. Although the 86.6% tap is preferred, the connection can be made with a teaser transformer that has the same voltage rating as the main transformer. In this instance, the teaser transformer is operated at reduced flux (Figure 14–22). This connection permits two transformers to be connected T instead of open delta in the event that one transformer of a delta–delta bank should fail.

Transformers intended for use as T-connected transformers are often specially wound for the purpose, and both transformers are often contained in the same case. When making the T connection, the main transformer is connected directly across the power line. One primary lead of the teaser transformer is connected to the center tap of the main transformer, and the 86.6% tap is connected to the power line. The same basic connection is made for the secondary. A vector diagram illustrating the voltage relationships of the T connection is shown in Figure 14–23. The greatest advantage of the T connection over the open-delta connection is that it maintains a better phase balance, and the T-connected transformer can be connected to provide a three-phase, four-wire output similar to that of a four-wire wye connection. T-connected transformers used to provide three-phase, four-wire power generally have voltages of 480/277 or 208/120 V. The greatest disadvantage of the T connection is that one transformer must contain a center tap of both its primary and secondary windings.

SCOTT CONNECTION

The Scott connection is used to convert three-phase power into two-phase power using two single-phase transformers. The Scott connection is very similar to the T connection in that one transformer, called the main transformer, must have a center or 50% tap, and the second or teaser transformer must have an 86.6% tap on the primary side. The difference between the Scott and T connections lies in the connection of the secondary windings (Figure 14–24). In the Scott connection, the secondary windings of each transformer pro- vide the phases of a two-phase system. The voltages of the secondary windings are 90° out of phase with each other. The Scott connection is generally used to provide two-phase power for the operation of two-phase motors.

ZIGZAG CONNECTION

The zigzag or interconnected wye transformer is primarily used for grounding pur- poses. It is used mainly to establish a neutral point for the grounding of fault currents. The zigzag connection is basically a three-phase autotransformer whose windings are divided into six equal parts (Figure 14–25). In the event of a fault current, the zigzag connection forces the current to flow equally in the three legs of the autotransformer, offering minimum impedance to the flow of fault current. A schematic diagram of the zig- zag connection is shown in Figure 14–26.

THREE-PHASE–TO–SIX-PHASE CONNECTIONS

There are some instances when it is desirable to have a power system with more than three phases. A good example of this is when it is necessary to convert or rectify alternating current into direct current with a minimum amount of ripple (pulsations of voltage). Power supplies that produce a low amount of ripple require less filtering. One of the most common three-phase-to-six-phase connections is the diametrical connection (Figure 14–27). The diametrical connection is preferred because it requires only one low-voltage winding on each transformer. If these windings are center-tapped, a neutral conductor can be provided for the six-phase output, permitting half-wave rectification to be used. The high-voltage windings can be connected in wye or delta, but the delta is preferred because it helps reduce harmonics in the secondary winding. A schematic diagram of a diametrical connection with a delta-connected primary and three-phase half-wave rectifier is shown in Figure 14–28.

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.

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.

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

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

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

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:

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

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

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.

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.

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

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

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

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:

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

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

DELTA–WYE CONNECTION

Delta–wye transformer connections may also be used for voltage transformation. The delta–wye connection is used both to step up and step down voltage. As shown in Figure 14–11, the primary windings are connected in delta and the secondary windings are connected in wye.

Delta–Wye Transformer Bank

The delta–wye transformer bank shown in Figure 14–11 is used to step up the volt- age at a generating station. The input voltage is stepped up by the transformer ratio. This voltage is further increased by the factor of 1.73. The high-voltage output is then connected directly to three-phase transmission lines. These transmission lines deliver the energy to users who may be miles away from the generating station. The use of the delta–wye connection means that the insulation requirements are reduced for the secondary windings. This fact is very important when the secondary side has a very high voltage. (Recall that the coil voltage is only 58% of the line voltage, where 1 -:- M3 = 1 -:- 1.73 = 0.58 = 58%.)

In Figure 14–11, the ac generators deliver energy to the generating station bus bars at a three-phase potential of 13,800 V. For the three single-phase transformers, the primary windings are each rated at 13,800 V. The windings are connected in delta to the bus bars of the generating station. The coil and line voltages are the same in a delta connection. Therefore, each primary winding has 13,800 V applied to it. The stepup ratio of the transformers shown is 1:5. This means that the voltage output of the secondary of each single-phase transformer is 5 X 13,800 = 69,000 V. The three secondary windings are connected in wye. Each high-voltage secondary winding is connected between the secondary neutral and one of the three line wires. The voltage between the neutral and any one of the three line wires is the same as the secondary coil voltage, or 69,000 V. The voltage across the three line wires is M3 X 69,000 = 119,370 V, or 120,000 V.

Three-phase output voltages can be balanced because of the neutral wire on the high- voltage secondary. This is true even when the load current is unbalanced. The neutral wire is grounded at the transformer bank. It is also grounded at intervals on the transmission line. The neutral wire helps protect the high-voltage secondary windings of the three single-phase transformers from damage due to lightning surges.

Stepping Down Voltages Using the Delta–Wye Connection

The delta–wye connection can also be used for applications where the voltage is stepped down. For example, assume that energy is to be transferred from a 13,800-V, three-phase, three-wire distribution system to a 277/480-V, three-phase, four-wire sys- tem. This voltage is then used to supply the power and lighting needs of a large office building.

Figure 14–12 shows the delta–wye-connected transformer bank used in this case. The primary side of the transformer bank is connected in delta to a three-phase, three- wire, 13,800-V distribution circuit. The line voltage and the voltage across each primary coil winding are all equal to 13,800 V. The transformer ratio is 50:1. As a result, the secondary coil winding voltage of each transformer is 13,800 -:- 50 = 276 V.

The secondary side of the transformer bank is connected in wye. The voltage from the grounded neutral to each of the three line wires is 277 V. The voltage across the line wires is M3 X 277, or 480 V.

Three-Phase, Four-Wire System of Power and Lighting

The standard voltage for lighting circuits is 120 V. Industrial power applications normally use either 208 or 240 V. However, power and lighting applications also can be served by a 277/480-V, three-phase, four-wire system.

Modern lighting applications generally require a high level of light intensity. Fluorescent lighting units furnish light having the required intensity. Standard 120-V fluorescent lighting fixtures are used with special ballasts for operation on 277-V circuits. Motors wound for 480 V, rather than 208 or 220 V, can be used for air- conditioning units, fans, pumps, and elevators. In office buildings, the lighting demand can be as much as 7 to 10 volt-amperes per square foot (VA/ft2). The motor load may aver- age as much as 4 VA/ft2. A 277/480-V, three-phase, four-wire system has the following advantages:

• The voltage drop is reduced in feeders and branch circuits, resulting in an increase in the operating efficiency.

• Smaller sizes of copper conductors, conduits, and equipment can be used to save up to 25% of the installation costs.

• The load demands on the 277/480-V system can be increased with a minimum of changes and expense.

All office buildings have miscellaneous loads requiring 120 V. These loads include desk lamps, office machines, and communications equipment. Under normal conditions, such loads are only a fraction of the total load and can be supplied from small air-cooled transformers. These transformers are located on each floor of the building. They are connected to the 277/480-V system and step down the voltage from 480 V to 120 V.

WYE–DELTA CONNECTIONS

The wye–delta transformer bank is used to step down relatively high transmission line voltages at the load center. A transformer bank of this type is commonly used to step down three-phase voltages of 60,000 V or more. There are two advantages in using the wye–delta connection. The first is that the three-phase voltage is reduced by the transformer ratio times 1.73. The second advantage is that there is a reduction in the insulation requirements for the high-voltage windings. Less insulation is required because the actual primary coil voltage is only 58% of the primary line voltage.

The diagram of a wye–delta transformer bank is shown in Figure 14–13. This bank is located at the end of a three-phase, four-wire transmission line. The primary three-phase voltage of 60,900 V is stepped down to 4400 V, three phase. Three single-phase trans- formers are used. The high-voltage side of each transformer is rated at 1000 kVA, 35,200

V. Each low-voltage side is rated at 4400 V. The voltage ratio of each transformer is 8:1. Assume that the three-phase primary line voltage is 60,900 V. As shown in Figure 14–13, the three single-phase transformers are connected in wye on the high-voltage side. The primary line voltage is 60,900 V. Therefore, the voltage impressed across the primary winding of each transformer is

Balanced three-phase voltages are obtained even when there are unbalanced load cur- rents because of the neutral wire on the high-voltage primary input. The neutral wire is grounded and gives lightning surge protection.

For both delta–wye and wye–delta connections, the three single-phase transform- ers generally have the same kVA capacity. The total capacity of the transformer bank in kVA is obtained by adding the kVA ratings of the three transformers. In Figure 14–13, for example, each single-phase transformer is rated at 1000 kVA and the total capacity of the transformer bank is 3000 kVA.

OPEN-DELTA CONNECTION

It is possible to achieve three-phase transformation of energy by using two trans- formers only. One connection that will do this is called the open-delta connection (V connection). On occasion, one of the three transformers in a delta–delta bank will become defective. To restore three-phase service to consumers as soon as possible, the defective transformer is cut out of the system and the configuration of the open-delta connection is used.

The following example describes a typical use of the open-delta connection. A delta– delta connection is made using three 50-kVA transformers. Each one is rated at 2400 V on the high-voltage side and 240 V on the low-voltage side. This closed-delta transformer bank steps down 2400 V, three phase to 240 V, three phase to supply an industrial consumer. One of the transformers is damaged by lightning, resulting in a power failure. The three-phase service must be restored at once.

By disconnecting all of the leads of the damaged transformer, the closed-delta bank becomes an open-delta bank, as shown in Figure 14–14.

The student may expect that the total kVA capacity of the open-delta bank will be two- thirds of the capacity of the closed-delta bank. Actually, the capacity of an open-delta bank is only 58% that of a closed-delta bank. For this example, the total capacity of the delta– delta bank is equal to the sum of the kVA capacities of the three transformers: 50 + 50 + 50 = 150 kVA. When one transformer is disconnected, an open-delta connection is formed. The total kVA capacity is now only 58% of the capacity of the closed-delta connection: 150 X 0.58 = 87 kVA (or 86.6% of the total capacity of the two remaining transformers).

Capacity of the Open-Delta Connection

In Figure 14–15, three 1-kVA transformers are connected to form a closed-delta connection. The secondary voltage of each transformer is 100 V. The maximum current for each winding is 10 A (1000 kVA/100 V = 10 A). The total power for this connection can be found by using the formula

DELTA–WYE CONNECTION

Delta–wye transformer connections may also be used for voltage transformation. The delta–wye connection is used both to step up and step down voltage. As shown in Figure 14–11, the primary windings are connected in delta and the secondary windings are connected in wye.

Delta–Wye Transformer Bank

The delta–wye transformer bank shown in Figure 14–11 is used to step up the volt- age at a generating station. The input voltage is stepped up by the transformer ratio. This voltage is further increased by the factor of 1.73. The high-voltage output is then connected directly to three-phase transmission lines. These transmission lines deliver the energy to users who may be miles away from the generating station. The use of the delta–wye connection means that the insulation requirements are reduced for the secondary windings. This fact is very important when the secondary side has a very high voltage. (Recall that the coil voltage is only 58% of the line voltage, where 1 -:- M3 = 1 -:- 1.73 = 0.58 = 58%.)

In Figure 14–11, the ac generators deliver energy to the generating station bus bars at a three-phase potential of 13,800 V. For the three single-phase transformers, the primary windings are each rated at 13,800 V. The windings are connected in delta to the bus bars of the generating station. The coil and line voltages are the same in a delta connection. Therefore, each primary winding has 13,800 V applied to it. The stepup ratio of the transformers shown is 1:5. This means that the voltage output of the secondary of each single-phase transformer is 5 X 13,800 = 69,000 V. The three secondary windings are connected in wye. Each high-voltage secondary winding is connected between the secondary neutral and one of the three line wires. The voltage between the neutral and any one of the three line wires is the same as the secondary coil voltage, or 69,000 V. The voltage across the three line wires is M3 X 69,000 = 119,370 V, or 120,000 V.

Three-phase output voltages can be balanced because of the neutral wire on the high- voltage secondary. This is true even when the load current is unbalanced. The neutral wire is grounded at the transformer bank. It is also grounded at intervals on the transmission line. The neutral wire helps protect the high-voltage secondary windings of the three single-phase transformers from damage due to lightning surges.

Stepping Down Voltages Using the Delta–Wye Connection

The delta–wye connection can also be used for applications where the voltage is stepped down. For example, assume that energy is to be transferred from a 13,800-V, three-phase, three-wire distribution system to a 277/480-V, three-phase, four-wire sys- tem. This voltage is then used to supply the power and lighting needs of a large office building.

Figure 14–12 shows the delta–wye-connected transformer bank used in this case. The primary side of the transformer bank is connected in delta to a three-phase, three- wire, 13,800-V distribution circuit. The line voltage and the voltage across each primary coil winding are all equal to 13,800 V. The transformer ratio is 50:1. As a result, the secondary coil winding voltage of each transformer is 13,800 -:- 50 = 276 V.

The secondary side of the transformer bank is connected in wye. The voltage from the grounded neutral to each of the three line wires is 277 V. The voltage across the line wires is M3 X 277, or 480 V.

Three-Phase, Four-Wire System of Power and Lighting

The standard voltage for lighting circuits is 120 V. Industrial power applications normally use either 208 or 240 V. However, power and lighting applications also can be served by a 277/480-V, three-phase, four-wire system.

Modern lighting applications generally require a high level of light intensity. Fluorescent lighting units furnish light having the required intensity. Standard 120-V fluorescent lighting fixtures are used with special ballasts for operation on 277-V circuits. Motors wound for 480 V, rather than 208 or 220 V, can be used for air- conditioning units, fans, pumps, and elevators. In office buildings, the lighting demand can be as much as 7 to 10 volt-amperes per square foot (VA/ft2). The motor load may aver- age as much as 4 VA/ft2. A 277/480-V, three-phase, four-wire system has the following advantages:

• The voltage drop is reduced in feeders and branch circuits, resulting in an increase in the operating efficiency.

• Smaller sizes of copper conductors, conduits, and equipment can be used to save up to 25% of the installation costs.

• The load demands on the 277/480-V system can be increased with a minimum of changes and expense.

All office buildings have miscellaneous loads requiring 120 V. These loads include desk lamps, office machines, and communications equipment. Under normal conditions, such loads are only a fraction of the total load and can be supplied from small air-cooled transformers. These transformers are located on each floor of the building. They are connected to the 277/480-V system and step down the voltage from 480 V to 120 V.

WYE–DELTA CONNECTIONS

The wye–delta transformer bank is used to step down relatively high transmission line voltages at the load center. A transformer bank of this type is commonly used to step down three-phase voltages of 60,000 V or more. There are two advantages in using the wye–delta connection. The first is that the three-phase voltage is reduced by the transformer ratio times 1.73. The second advantage is that there is a reduction in the insulation requirements for the high-voltage windings. Less insulation is required because the actual primary coil voltage is only 58% of the primary line voltage.

The diagram of a wye–delta transformer bank is shown in Figure 14–13. This bank is located at the end of a three-phase, four-wire transmission line. The primary three-phase voltage of 60,900 V is stepped down to 4400 V, three phase. Three single-phase trans- formers are used. The high-voltage side of each transformer is rated at 1000 kVA, 35,200

V. Each low-voltage side is rated at 4400 V. The voltage ratio of each transformer is 8:1. Assume that the three-phase primary line voltage is 60,900 V. As shown in Figure 14–13, the three single-phase transformers are connected in wye on the high-voltage side. The primary line voltage is 60,900 V. Therefore, the voltage impressed across the primary winding of each transformer is

Balanced three-phase voltages are obtained even when there are unbalanced load cur- rents because of the neutral wire on the high-voltage primary input. The neutral wire is grounded and gives lightning surge protection.

For both delta–wye and wye–delta connections, the three single-phase transform- ers generally have the same kVA capacity. The total capacity of the transformer bank in kVA is obtained by adding the kVA ratings of the three transformers. In Figure 14–13, for example, each single-phase transformer is rated at 1000 kVA and the total capacity of the transformer bank is 3000 kVA.

OPEN-DELTA CONNECTION

It is possible to achieve three-phase transformation of energy by using two trans- formers only. One connection that will do this is called the open-delta connection (V connection). On occasion, one of the three transformers in a delta–delta bank will become defective. To restore three-phase service to consumers as soon as possible, the defective transformer is cut out of the system and the configuration of the open-delta connection is used.

The following example describes a typical use of the open-delta connection. A delta– delta connection is made using three 50-kVA transformers. Each one is rated at 2400 V on the high-voltage side and 240 V on the low-voltage side. This closed-delta transformer bank steps down 2400 V, three phase to 240 V, three phase to supply an industrial consumer. One of the transformers is damaged by lightning, resulting in a power failure. The three-phase service must be restored at once.

By disconnecting all of the leads of the damaged transformer, the closed-delta bank becomes an open-delta bank, as shown in Figure 14–14.

The student may expect that the total kVA capacity of the open-delta bank will be two- thirds of the capacity of the closed-delta bank. Actually, the capacity of an open-delta bank is only 58% that of a closed-delta bank. For this example, the total capacity of the delta– delta bank is equal to the sum of the kVA capacities of the three transformers: 50 + 50 + 50 = 150 kVA. When one transformer is disconnected, an open-delta connection is formed. The total kVA capacity is now only 58% of the capacity of the closed-delta connection: 150 X 0.58 = 87 kVA (or 86.6% of the total capacity of the two remaining transformers).

Capacity of the Open-Delta Connection

In Figure 14–15, three 1-kVA transformers are connected to form a closed-delta connection. The secondary voltage of each transformer is 100 V. The maximum current for each winding is 10 A (1000 kVA/100 V = 10 A). The total power for this connection can be found by using the formula

FEEDING A DUAL LOAD

Some power companies use a delta–delta-connected transformer bank to feed two types of loads. These loads consist of a 240-V, three-phase industrial load and a 120/240-V, single-phase, three-wire lighting load.

One single-phase transformer supplies the single-phase, three-wire lighting load. This transformer usually is larger than the other two transformers. The 120/240-V, single-phase, three-wire service is obtained from this transformer by bringing out a tap from the mid- point of the 240-V, low-voltage secondary winding. Many transformers have two 120-V windings. As explained in Unit 13, these windings can be connected in series, with a tap brought out at the midpoint to give 120/240-V service.

Three single-phase transformers are connected as a delta–delta bank in Figure 14–5. Each transformer has two 120-V windings. When these windings are connected in series, each transformer has a total output of 240 V. The high-voltage primary windings are con- nected in closed delta. The low-voltage output windings or secondary windings are also connected in closed delta to give three-phase, 240-V service to the industrial power load. Because the middle transformer also feeds the single-phase, three-wire, 120/240-V light- ing load, a tap is made at the midpoint on the secondary output side of the transformer to give 120/240-V service. This tap feeds to the neutral wire of the single-phase, three-wire system and is grounded.

A check of the connections in Figure 14–5 shows that there is 120 V to ground on both lines A and C of the three-phase, 240-V secondary system. However, line B will have 208 V to ground. The condition can be a serious hazard and cannot be used for lighting service.

THE WYE CONNECTION

The wye connection is another standard method of connecting single-phase trans- formers to obtain three-phase voltage transformation. The wye connections must be made systematically to avoid errors. The student must be familiar with and able to use the basic voltage and current relationships for this type of connection. In Unit 10, the following information was given for the three-phase wye connection:

• The line current and the coil winding current are equal.

• The line voltage is equal to M3 times the coil winding voltage.

Figure 14–6 shows three single-phase transformers connected in wye–wye. The H2 leads of the high-voltage windings are considered to be the ends of each of the high-volt- age windings and are connected together. The H1 (beginning) lead of each transformer is

connected to one of the three line leads. When this connection is shown in a schematic diagram, it looks like the letter Y (which is written as wye). The connection may also be called a star connection.

In general, the low-voltage winding leads are marked and the polarity is shown on the transformer nameplate. However, the following procedure should be used to make the low- voltage secondary connections:

1. Energize the three-phase, wye-connected, high-voltage side of the transformer bank.

The voltage output of each of the three transformers must be the same as the name- plate rating.

2. Deenergize the primary. Connect the X2 ends of two low-voltage secondary windings, as shown in Figure 14–7A. With all three X1s open and clear, energize the primary. If the connections are made correctly, the voltage across the open ends is M3 times the secondary winding voltage. In this case, the voltage across the open ends is 208 V, as indicated in the vector diagram.

Secondaries Incorrectly Connected

The secondaries of the two transformers are shown connected incorrectly in Figure 14–7B. In this case, the voltage across the open ends is the same as the secondary voltage of each transformer. According to the vector diagram, the resultant voltage is only 120 V. The connections can be corrected by reversing the leads of transformer 2. As a result, the voltage across the open ends will be 208 V.

Secondaries Properly Connected

The correct wye connections are shown in Figure 14–8A for the secondary windings of the three transformers. The voltage across each pair of line leads is equal to M3 times the secondary coil voltage or 208 V. The vector diagram in Figure 14–8B shows the relationship between the coil voltages and the line voltages in a three-phase, wye-connected system.

The wye–wye connection can be used in those applications where the load on the secondary side is balanced. If the load consists of three-phase motor loads only, and the load currents are balanced, then the wye–wye connection can be used. This connection cannot be used if the secondary load becomes unbalanced. An unbalanced load causes a serious imbalance in the three voltages of the transformer bank.

The Neutral Wire

A fourth wire known as the neutral wire is added to eliminate unbalanced voltages. The neutral wire is connected between the source and the common point on the primary side of the transformer bank.

The diagram in Figure 14–9 shows a wye–wye-connected transformer bank having a three-phase, four-wire, 2400/4160-V input and a three-phase, four-wire, 120/208-V output. On the high-voltage input side, the neutral wire is connected to the common point. This is the point where all three high-voltage primary winding (H2 ) leads terminate. The voltage from the neutral to any one of the three line leads is 2400 V. Each high-voltage winding is connected between the neutral and one of the three line leads. This means that each high- voltage winding is connected across 2400 V. The voltage across the three line leads is M3 X 2400 V, or 4160 V. The neutral wire maintains a nearly constant voltage across each of the high-voltage windings, even when the load is unbalanced. The neutral conducts any unbalance of current between the source and the neutral point on the input side of the transformer bank. The neutral wire is grounded and helps protect the three high-voltage windings from lightning surges.

For the transformer bank shown in Figure 14–9, the three-phase, four-wire sys- tem feeds from the low-voltage side of the bank to the load. Each low-voltage wind- ing is connected between the secondary neutral and one of the three line leads. The voltage output of each secondary winding is 120 V. Thus, there is 120 V between the neutral and any one of the three secondary line leads. The voltage across the line wires is M3 X 120, or 208 V. The use of a three-phase, four-wire secondary provides two voltages that can be used for different load types:

1. A 208-V, three-phase service is available for industrial power loads such as three- phase motors.

2. The use of a neutral wire means that 120 V is available for lighting loads.

Neutral Wire Used on Primary and Secondary

Figure 14–10 shows the connections for a wye–wye-connected transformer bank. Note that both the primary and secondary sides contain a neutral wire. Each transformer has two 120-V, low-voltage windings connected in parallel. The voltage output for each single-phase transformer is 120 V. Because this is a three-phase, four-wire system, the

following voltages are available: (1) a three-phase, 208-V service for motor loads and (2) a 120-V, single-phase service for the lighting loads. The lighting load should be distributed evenly between the three transformers. Thus, an attempt is always made to balance the lighting circuits from the line wire to the neutral.

Nearly all wye–wye-connected transformer banks use three single-phase transformers having the same kilovolt-ampere capacity. The individual kVA ratings are added to find the capacity of the transformer bank. For example, if a bank consists of three transformers, each rated at 25 kVA, the total rating is 25 + 25 + 25 = 75 kVA.

In a wye–wye connection, a defective transformer must be replaced before the wye– wye transformer bank can be reenergized. Unlike a delta–delta bank, a wye–wye trans- former bank cannot be temporarily reconnected in an emergency using two single-phase transformers only.