Transformer Calculations: Word Problems © Ted “Smitty” Smith E Light Electric Services, Inc.

The first several slides of this presentation are a review of calculations. Read them over and take some notes as they will help you on your journeyman’s exam as well as while doing this drill. Click the slide to advance to the next slide as you are ready. You will reach a slide which says “START”. This is the beginning of the timed portion of the drill. Click that slide and the questions slides will start running. Each slide will remain in place for 3-5 minutes depending on the difficulty of the calculation. A sound will go off letting you that it has moved to the next slide. Attempt to answer the question. If you finish before the timer goes off, click the slide and it will go to the next question. If you do not finish, simply stop working that problem and start on the next. When you reach the end of the timed portion you will see a slide that says “STOP”. Click on that slide and each of the questions will reappear and this time you can click them to move to the next slide, which will have the answer. Please call me if you have any issues or questions and I will be happy to arrange a time for us to review. Directions

Line and Phase The Wires All three phase system are made of 3 coils of wire. Each coil has 2 wires In a three phase system there will be a total of 6 wires The three phase system will have 3 line wires We have to wire the six wires together to form 3 wires Wired in series: Delta Wired in parallel: Wye The Values All three phase systems have two values for each of the properties of Electricity Line and Phase Line is the value experienced between any two line wires Phase is the value experienced on any one coil

The three coils of a three phase system are 120 degrees out of phase with each other. This means that each coil is producing a different voltage and amperage at any given instant. If the values of two coils are being added together then the value is not simply twice the value of one coil. It is the value of the coil times the square root of 3 which is 1.732 The Multiplier

Line Phase Relationships Wye Connected System Line Voltage is 1.732 times greater than Phase Voltage Line Current is equal to Phase Current Delta Connected System Line Voltage is equal to Phase Voltage Line Current is 1.732 time greater than Phase Current

Overcurrent Protection Transformer Overcurrent Protection Use Table 450.3(A) for over 1000 Volts Use Table 450.3(B) for less than 1000 Volts These are the MAXIMUM sized OCPD for the transformer ONLY. Overcurrent Protection Conductors Conductors are sized for the minimum size to handle the line current Different sizes for both sides OCPD is sized based on 240.4, 240.21 if tap rules are used This means that the OCPD will most likely be much smaller than what is allowed for the Transformer OCPD.

Steps Using the Line/Phase relationship rules determine the Line Current for Primary and Secondary Size the conductor for both sides based on 310.15(b)(16) and don’t forget to take 110.14(C) into account Size the Overcurrent protection based on the conductor ampacity using the OCPD rules in Article 240 Double check that the OCPD sized is less than what is allowed in 450.3 VERIFY

Watch Out: Know What They Are Asking They use transformer calculations in three different categories on the license examination General Knowledge Transformers Calculations This means they can use them for ohms law, knowledge of electrical theory and code requirements. Read the question carefully and know what they are asking. If they are asking for OCPD sizes for the conductor and transformer use 240.4 If they are just asking for OCPD for the transformer only use max. size in 450.3

Open Delta and Closed Delta ( See Next Slide) A three phase Open Delta system uses only two coils to make a three line system. This used to be common but is more rare today. A closed delta uses three coils and is more common. In both systems one coil can be center tapped to make a neutral. The voltage between either of the lines connected to the center tapped coil and the center tap conductor will be half of the voltage between the two line conductors. The voltage between the line that is connected to the non-center tapped coil and the center tapped conductor will be 1.732 times greater than the voltage between the center tapped conductor and the conductors of connected to the centered tapped coil.

Open and Closed Delta Closed Delta with Center Tap Open Delta with Center Tap Article 110.15 of the NEC requires that the line conductor which is 208V to the grounded conductor be colored Orange. Only the lines connected to the center tapped coil can be used for 120 V loads.

Open and Closed Delta Transformers Theory (SEE NEXT SLIDE) If a second voltage is needed such as 240 and 120 volts, then one coil is center tapped and that conductor is grounded. All of the 120 volt loads will be on one coil between two lines and the grounded conductor. This one coil will have to be larger than the other two because it will carry the current of all the 240 volt loads and all the 120 volts loads. The other two coils will only carry the current for the 240 volt loads.

Pole Mounted Transformers Open Delta with a Grounded Conductor Comparison of High Leg Closed Delta Secondary and Wye Secondary

Click here to start the timed portion of the Drill

1. What is the minimum sized copper THW conductor which can be used to feed the primary of a three phase, Delta:Delta, 4160 Volt primary to 460 Volt secondary transformer? The secondary line current is 362 amperes. The transformer terminations are rated for 75 degrees C.

1. 8 AWG Primary line current is 40.22 A. In the 75C column of 310.15(B)(16) this requires a 8 AWG conductor.

2. What is the maximum sized inverse time circuit breaker which can be used to provide primary only protection for the conductors and transformer of a three phase, Delta:Wye, 480V to 208 V transformer? Assume the secondary conductors will be less than 10 feet in length. Assume the terminations are rated for 75 degrees C. The secondary phase current of the transformer is 52 amperes. Assume the smallest sized conductor allowed will be used for the primary feed. RHW Aluminum wire will be used.

2. 50 A The primary line current is 38.9 A. The 75C column of 310.15(B)(16) requires a 6 AWG conductor. The maximum sized breaker is 50 A based on 240.4 This is smaller than what is allowed for transformer max. OCPD in 450.3(B)

3. What is the primary line current experienced on a three phase, Wye:Wye transformer if the transformer has a turns ratio of 33.3:1 and a secondary line current of 600 amperes?

3. 18 amperes Secondary line current is 600 A so secondary phase current is 600 amperes. Voltage increases 33.3 times form secondary to primary, so current decreases 33.3 times. Primary phase current is 18 amperes so primary line current is 18 amperes.

Copyright 2005 Ted "Smitty" Smith 4. What is the amount of current flowing between A line and B line on the secondary of a three phase, Delta: Wye transformer if the primary line voltage is 13,800 V and the secondary phase voltage is 277 V? The current on one coil of the primary is 32.13 amperes. Assume all three phases have balanced loads. Copyright 2005 Ted "Smitty" Smith

4. 1600 Amperes This is just a fancy way of asking what is the secondary line current. If the primary line voltage is 13,800 volts the primary phase voltage is 13,800 volts. If the secondary phase voltage is 277 V the transformer has a turns ratio of 49.8: 1. If the primary phase current is 32.13 amperes then the voltage goes down 49.8 times from primary to secondary, so the current will go up 49.8 times. 32.13 x 49.8=1600. If the secondary phase current is 1600 amperes the secondary line current will be 1600 amperes.

Copyright 2005 Ted "Smitty" Smith 5. What is the maximum size inverse time circuit breaker which can be used to provide primary overcurrent protection for the transformer for a three phase, Delta:Wye, 480V to 208V transformer if the transformer is feeding a load which is rated at 200 amperes? Assume separate secondary overcurrent protection will be provided. Copyright 2005 Ted "Smitty" Smith

5. 200 A They are only asking for the transformer overcurrent protection, not the conductors. Therefore we will only use 450.3. If the primary line voltage is 480 the primary phase voltage is 480. If the secondary line voltage is 208 the secondary phase voltage is 120. The turns ratio is 4:1. If the secondary line current is 200 amperes the secondary phase current is 200 amperes. The voltage goes up 4 times from secondary to primary, so the current will go down 4 times. 200/4= 50. If the primary phase current is 50 amperes the primary line current will be 1.732 times greater. 50 x 1.732= 86.6. T450.3(B) allows the maximum sized OCPD to be 250% of the primary line current. 86.6 x 2.5= 216.5. No note allowing us to go up to the next standard size so we go down to a 200 A according to 240.6

6. What is the minimum sized TW aluminum conductor which can be used to feed a Wye:Delta, three phase transformer which has a 4:1 turns ratio? The primary line voltage is 480 V and the secondary phase current is 346.4 amperes. The transformer’s terminations are rated for 75 degrees C.

6. 1/0 Aluminum If the secondary phase current is 346.4 and the transformer has a 4:1 turns ratio then the voltage will go up 4 times from the secondary to the primary, so the current will go down 4 times. 346.4/4=86.6 amperes. If the primary phase current is 86.6 amperes then the primary line current is 86.6 amperes. Using the 60c column of 310.15(B)(16) a 1/0 Aluminum would be required.

7. What is the voltage experienced between the neutral and the high leg conductor of an open delta three phase system if the line voltage is 460 volts?

7. 398.36 volts If the line voltage is 460 volts then the phase voltage will be 460 volts. The neutral will be center tapped on one coil, so the voltage between either line connected to that coil will be 230 volts. 230 x 1.732= 398.36

Copyright 2008 Ted "Smitty" Smith 8. What is the minimum amount of single phase, pole mounted transformers required to feed a three-phase service for a building which will need both 230 volts and 115 volts? Copyright 2008 Ted "Smitty" Smith

8. Two A three phase open delta connection with a center tapped grounded conductor could be used.

CLICK HERE TO PROCEED WITHOUT THE TIMER AND REVIEW THE QUESTIONS AND ANSWERS

1. What is the minimum sized copper THW conductor which can be used to feed the primary of a three phase, Delta:Delta, 4160 Volt primary to 460 Volt secondary transformer? The secondary line current is 362 amperes. The transformer terminations are rated for 75 degrees C.

1. 8 AWG Primary line current is 40.22 A. In the 75C column of 310.15(B)(16) this requires a 8 AWG conductor.

2. What is the maximum sized inverse time circuit breaker which can be used to provide primary only protection for the conductors and transformer of a three phase, Delta:Wye, 480V to 208 V transformer? Assume the secondary conductors will be less than 10 feet in length. Assume the terminations are rated for 75 degrees C. The secondary phase current of the transformer is 52 amperes. Assume the smallest sized conductor allowed will be used for the primary feed. RHW Aluminum wire will be used.

2. 50 A The primary line current is 38.9 A. The 75C column of 310.15(B)(16) requires a 6 AWG conductor. The maximum sized breaker is 50 A based on 240.4 This is smaller than what is allowed for transformer max. OCPD in 450.3(B)

3. What is the primary line current experienced on a three phase, Wye:Wye transformer if the transformer has a turns ratio of 33.3:1 and a secondary line current of 600 amperes?

3. 18 amperes Secondary line current is 600 A so secondary phase current is 600 amperes. Voltage increases 33.3 times form secondary to primary, so current decreases 33.3 times. Primary phase current is 18 amperes so primary line current is 18 amperes.

Copyright 2005 Ted "Smitty" Smith 4. What is the amount of current flowing between A line and B line on the secondary of a three phase, Delta: Wye transformer if the primary line voltage is 13,800 V and the secondary phase voltage is 277 V? The current on one coil of the primary is 32.13 amperes. Assume all three phases have balanced loads. Copyright 2005 Ted "Smitty" Smith

4. 1600 Amperes This is just a fancy way of asking what is the secondary line current. If the primary line voltage is 13,800 volts the primary phase voltage is 13,800 volts. If the secondary phase voltage is 277 V the transformer has a turns ratio of 49.8: 1. If the primary phase current is 32.13 amperes then the voltage goes down 49.8 times from primary to secondary, so the current will go up 49.8 times. 32.13 x 49.8=1600. If the secondary phase current is 1600 amperes the secondary line current will be 1600 amperes.

Copyright 2005 Ted "Smitty" Smith 5. What is the maximum size inverse time circuit breaker which can be used to provide primary overcurrent protection for the transformer for a three phase, Delta:Wye, 480V to 208V transformer if the transformer is feeding a load which is rated at 200 amperes? Assume separate secondary overcurrent protection will be provided. Copyright 2005 Ted "Smitty" Smith

5. 200 A They are only asking for the transformer overcurrent protection, not the conductors. Therefore we will only use 450.3. If the primary line voltage is 480 the primary phase voltage is 480. If the secondary line voltage is 208 the secondary phase voltage is 120. The turns ratio is 4:1. If the secondary line current is 200 amperes the secondary phase current is 200 amperes. The voltage goes up 4 times from secondary to primary, so the current will go down 4 times. 200/4= 50. If the primary phase current is 50 amperes the primary line current will be 1.732 times greater. 50 x 1.732= 86.6. T450.3(B) allows the maximum sized OCPD to be 250% of the primary line current. 86.6 x 2.5= 216.5. No note allowing us to go up to the next standard size so we go down to a 200 A according to 240.6

6. What is the minimum sized TW aluminum conductor which can be used to feed a Wye:Delta, three phase transformer which has a 4:1 turns ratio? The primary line voltage is 480 V and the secondary phase current is 346.4 amperes. The transformer’s terminations are rated for 75 degrees C.

6. 1/0 Aluminum If the secondary phase current is 346.4 and the transformer has a 4:1 turns ratio then the voltage will go up 4 times from the secondary to the primary, so the current will go down 4 times. 346.4/4=86.6 amperes. If the primary phase current is 86.6 amperes then the primary line current is 86.6 amperes. Using the 60c column of 310.15(B)(16) a 1/0 Aluminum would be required.

7. What is the voltage experienced between the neutral and the high leg conductor of an open delta three phase system if the line voltage is 460 volts?

7. 398.36 volts If the line voltage is 460 volts then the phase voltage will be 460 volts. The neutral will be center tapped on one coil, so the voltage between either line connected to that coil will be 230 volts. 230 x 1.732= 398.36

Copyright 2008 Ted "Smitty" Smith 8. What is the minimum amount of single phase, pole mounted transformers required to feed a three-phase service for a building which will need both 230 volts and 115 volts? Copyright 2008 Ted "Smitty" Smith

8. Two A three phase open delta connection with a center tapped grounded conductor could be used.