POST-GRADUATE STUDENT COURSE
EMANUEL EDUARDO PIRES VAZ
DEDICATORY
In name of Sofia
My first book on transformers was dedicated to my granddaughter; books and papers have followed with dedications to relatives and others. Today the cycle closes up by the seven years old of Sofia with a new number dedicated to
my granddaughter
INTRODUCTION
In the chapter "0" we remember certain laws of electromagnetism and the electromagnetic induction: Classical physics is applied. The chapter corresponds to two lessons of the post-graduate course of our university. These lessons are taught as I learned them from my engineering professor who has taught in several universities in the world.
PREFACE
This book accompanies a life of teaching at various universities in Portugal and abroad at the chair of electric machines and long practice in one of the biggest factories of electric transformers. It is the know-how of the author of this book and the accompanying at the eminent professor who gave the lessons essentially contained in Chapters 3 to 6 - the theory of electric transformers - which are reformulated and properly applied to the needs of the present time. They worked and investigated at the University of Porto.
In the estimated more than 100 000–year history of modern humans, few accomplishment have had as great an impact on the human culture as the development and utilization of electric power. Every aspect of life in modern industrialized nations now depends on electrical power, with more applications being developed daily. Electricity can be generated at a remote location and transmitted to users by power lines, which sets the stage for increasing human contact with electrical energy.
The electric and magnetic theories and laws which accomplish coils and electric transformers are treated and sufficiently well explained in this book; skills in their design and practical electrician calculation are a constant for the practical technician or the engineering student, and for all engineers who need have continuing education.
This author began as nuclear physicist by the Institute of High Culture; in 1974 joined General Tyre as maintenance engineer for seven years and with 105 engineering collaborators a treatise on Preventive Maintenance was written. His experience about transformers for the last 35 years and his teaching activity have become this book in a precious pearl which I do not stop to applaud.
12th August 2012
João Pedro Barbosa Vaz
INDEX
Dedicatory
Preface
Acknowledgments
Introduction
0.1. Magnetic fields
0.2. Definition
0.3. B and H
0.4. Force due to a magnetic field
0.4.1.Force on a charged particle
0.4.2. Force on a current –carrying wire
0.4.3. Direction of force
0.5. Faraday`s law of induction.
0.5.1. Maxwell`s equation version of Faraday`s law.
0.5.2. Relation between two versions
0.6. Magnetic flow meter
0.7. History
0.8. Electrical generators
0.9. Transformer
0.10. Lorentz force
0.10.1. History and significance
0.10.2. Lorentz force in special relativity
0.10.3. Covariant form of the Lorentz force
CHAPTER 1
1.1. A brief history of inductance
1.1.1. Self-inductance and reactive reactance
1.1.1.1. Solenoid Field from Ampere`s law
1.1.2. Faraday`s lew
1.1.2.1. Inductive reactance
1.1.3. Lenz`s law
Bibliography.
44. CHAPTER II
2. Optimal shape design of a single or a multiple coil device for several coils.
2.1.Mutual inductance.
2.2. Inductance calculations.
2.2.1. SI electricity / electromagnetism units, table 2.1.
2.3. State the type of moving field used to generate an emf in a conductor.
2.3.1. Electromotive force.
2.3.2. Mutual inductance study.
2.3.3. Self inductance.
2.3.4. Energy in an inductor.
2.3.5. R-L series circuit
2.4. The following examples show how to find the inductance of the following shapes.
2.4.1. Inductance of a coaxial cable.
2.4.2. Taking the internal inductances into account (low frequencies), where f is the outer radius of the outer conductor.
2.4.3. Inductance of round parallel wires.
2.44. Inductance of a round wire over a ground plane.
2.4.5. Self inductance of a straight round wire.
2.4.5.1. Calculations for the next example are.
2.4.5.2. Inductance of a single-layered air core coil.
2.4.5.2.1. Some calculations for the next example.
2.4.5.3. Inductance of a multi-layered air core coil.
2.4.5.4. Inductance of a toroid with a square cross section.
2.4.5.4.1. Calculations for the next examples are.
2.4.6. Some calculations of coils.
2.4.6.1. Choke coils of a 
Table 2.2 Copper wire standardized diameter.
Table 2.3. Coil core sizes.
2.5. Efficiency of a filter.
2.5.1. Filters for speakers
2.6. Transformers for a vibrator.
2.7. Output transformers.
2.7.1. Cross section of the core.
2.7.1.1. Number of turns of the primary from the cross section of the core.
2.7.1.2. Transformer turns ratio.
2.7.1.3. Cross sections of wires.
2.7.1.4. Cross section of the core.
2.7.1.5. Number of turns of the primary.
2.7.1.6. Number of turns of the secondary.
2.7.1.7. Cross section of the wire of the primary.
2.7.1.8. Cross section of the secondary.
2.8. Grounding and shielding.
2.9. Winding arrangement of output transformers.
2.9.1. Faraday shield.
2.9.1.1. Primary cold ends facing secondary winding.
2.9.1.2. Five section structure for increased bandwidth.
2.9.2. Mixed feedback drive circuits for audio output transformers.
2.10. Transformer design philosophies
2.10.1. Winding technique.
2.10.2. Dual coil structure.
2.10.3. Choice of core shape and core materials.
2.10.4. Long lifetime and high insulation requirements.
2.10.5. Price and performance considerations.
2.11. Where quality and transformers meet.
2.12. Modulation transformers.
2.13. Coils for radio frequency.
2.13.1. Solenoid coils (only one layer).
2.13.1.1. Single layer coil inductance.
2.13.2. Bee nest coils.
2.14. Determining the inductance of a coil.
2.15. A new and accurate method to measure self inductance and mutual inductance of coils.
2.15.1. Relative methods.
2.15.2. Circuit analyse.
2.15.3. Accuracy of results.
2.1.6. Auto transformers.
2.16.1. Practical example.
Table 2.3. Current densities which are admissible for transformer windings.
2.17. Project for a winding semi- automatic machine.
2.18. Optimal shape design of a multiple –coil device for induction heating.
Table 2.4. Sample points for temperature test.
Table 2.5. Design variables initial values and ranges
2.18.1. Coupled electromagnetic- thermal simulation.
2.18.2. Thermal problem.
2.18.3. Coupled problems
2.19. Optimisation and evolutionary strategy.
2.19.1. Optimisation methods and benefits of using the evolutionary strategy.
2.19.2. OptiNet: An optimisation tool.
2.19.3.1. Sensitivity of the variables.
2.19.3. Results.
Table 2.6. Sample points for temperature check.
Table 2.7. Design variables sensitivity.
2.20. Solenoids.
2.20.1. self-inductance of solenoids.
2.20.2. The current-sheet solenoid.
2.20.3. Effective current-sheet diameter (LF).
2.20.4. Effective current-sheet diameter (HF).
2.20.5. Internal inductance.
2.20.6. LF-HF transition frequency.
2.20.7. Internal inductance factor.
2.20.8. Magnetic field non-uniformity (Nagaoka`s coefficient).
2.20.9. Lundin`s Handbook Formula.
2.20.10. Asymptotically-correct approximations for KL.
2.20.11. Rayleigh-Niven formula (for short coils).
2.20.11.1. Coffin`s Fprmula (for short coils).
2.20.12. Weloster-Hevelock Formula (for long coils).
2.20.13. Wheeler`s Formulae.
2.20.14. Wheeler`s continuous formula (optimised).
2.20.15. Defective formula.
2.20.16. Rosa`s round-wire corrections.
2.21. Self-inductance correction.
2. 22. Mutual-inductance correction.
Table 2.8. Rosa`s correction for the mutual inductance of round wires.
2.23. Formula for Rosa`s mutual inductance correction parameter.
2.24. Apparent inductance.
2.25. Solenoid inductance calculations: St.Anthony`s formula.
2.26. Additional sources of deviation.
2.27. Conductor length.
136. References.
CHAPTER 3.
3. Transformers
3.1. What a transformer is.
3.2. How a transformer works.
3.2.1. Principle of magnetic induction applied to coils.
3.3. Equilibrium between magnetic flux, induced voltage and exciting current.
3.4. The transformer with d.c. voltage applied.
3.5. Equilibrium with alternating voltage applied.
3.6. Equilibrium when the transformer is loaded.
3.7. Performance characteristics.
3.8. Single phase transformers.
3.8.1Electrical circuits: windings.
3.8.2. Functioning principle.
3.83. Ideal transformer.
3.8.3.1. Functioning equations.
3.8.3.2. Vector diagram.
3.8.3.3. Efficiency .
3.8.3.4. Symbolic equations
3.8.4. Real transformer.
3.8.4.1. Hysteretic and Foucault currents.
3.8.4.2. Equations for the real transformer.
3.8.4.3. Vector diagram for the real transformer.
3.85. Transformation ratio.
3.9. Analyse of the functioning of a transformer under energetic point of view.
3.9.1. Distributing of the absorbed power.
3.10. Efficiency.
3.11. An equivalent circuit for the real transformer.
3.12. Simplified equivalent circuit. 3.13. Some definitions about transformer characteristics.
3.13.1. Nominal Power.
3.13.2. Frequency.
3.14. Some definitions about voltage drops.
3.14.1. Vector voltage drops.
3.14.2. Absolute voltage drops.
3.14.3. Relative voltage drop.
3.14.4. Resistive voltage drop.
3.14.5. Relative resistive voltage drop.
3.14.6. Relative resistive voltage drops in percent.
3.15. Problems on voltage drops.
3.15.1 Determination of the absolute voltage drop or of the regulation.
3.16. External characteristics.
3.16.1. Voltage drop variation at the two plugs of transformer secondary and delivering an electric current and with power factor.
3.16.2. Analytic expressions for external characteristics of a transformer.
3.16.3. External characteristics in a Kapp approximation.
3.17. Efficiency of a transformer.
3.18. Relation between core losses and copper losses.
3.19. Economic tests for a transformer.
3.19.1. Open circuit test.
3.19.2. Be careful with this test.
3.19.3. Short- circuit test.
3.20. Transformer in shunt.
3.20.1. Connecting condition.
3.20.2. Load distribution.
3.21. Graphic method calculated load distribution for two transformers in shunt.
3.22. Study of two transformers in shunt with two different voltages at the secondary in open circuit.
3.23. Characteristics alteration with frequency for a transformer.
3.24. Three- phase transformers.
3.25. Three-phase bank and a three-phase unity.
3.26. Some advantages for a three- phase unity.
3.26. Some advantages for a three-phase bank.
3.28. Some differences between transformer bank and three-phase unity.
3.28.1. Three-phase transformer core.
3.29. Three-phase transformer functioning in charge balanced regimen.
3.29.1. Transformation ratio in a three-phase system.
3.30. Different types of transformers according to winding connection.
3.30.1. DY transformer.
3.30.2. DY transformer.
3.31. Transformer ratio for each transformer.
3.32. Capacity.
3.33. Equations for voltages and for currents.
3.33.1. Kapp`s equation for voltages.
3.34. Current equation.
3. 35. Economic analyse of a transformer copper weight waste in each connection types.
3.36. Study the three-phase transformer under the point of view of third order harmonic and the unbalanced regimen.
3.36.1. Introduction.
3.36.2. Angular deviation
3.37. Analyse of the different connection types.
3.38. Triple frequency harmonics.
3.39. Some important considerations about insulated neutral point and neutral point connected to ground.
3. 39. 1. Insulated neutral point.
3.39.2. Neutral point on secondary connected to ground.
Bibliography.
CHAPTER 4.
4. Transformer connections.
4.1. Single-phase connections.
4.2. The autotransformer.
4.3. Impedance of an autotransformer.
4.4. Limitation of an autotransformer.
4.5. Short circuit of the lines on one side of an autotransformer.
4.6. Impulse voltage distribution in an autotransformer
4.7. Multiwinding transformers.
4.7.1. Equivalent circuit of a three-winding transformer.
4.7.2. Stray and Eddy current losses and equivalent resistance of transformers.
4.7.3. Short-circuits in a transformer with three windings
CHAPTER 5.
5. Transformer temperature.
5.1. Introduction.
5.2. Heat flow from oil to air with forced air or forced-oil cooler.
5.2.1. Temperature transients following load changes.
5.22. Dissipation of heat into the cooling medium.
5.23. Heating of cooling liquid.
5. 24. Appendix.
5.25. Concluding comments.
5.2.6. Oil flow by separate pumps.
Literature.
CHAPTER 6.
Classroom Problems (1 to 15).
CHAPTER 7.
7. Maintenance, protection and detection of faults.
7.1. Paint.
7.2. Auxiliary equipment.
7.3. Oil preservation.
7.4. Sealed cases for oil protection.
7.5. Conservator tank.
7.6 Gas-oil seal.
7.7. Oil conditioning.
7.8. Detection of deterioration of oil.
7.9. Effect of moisture on insulation.
7.10. Segregation of moist oil.
7.10.1. Accumulation of moisture in transformers in service.
7.10.2. Drying transformers in the field.
7.11. Protection of transformers.
7.11.1. Protection against overloads.
7.11.2. Hot-oil thermometers.
7.11.3. Hot-spot thermometer.
7.11.3.1. Fuse protection.
7.11.3.2. Internal circuit breakers for distribution transformers.
7.12. Protection of secondary banks.
7.13. Coordination of thermal device with relays and fuses.
7.14. The thermal lead device in a transformer with forced –oil flow.
7.14.1. Thermal load device in multiwinding or multiphase transformers.
- Protection against lightning and switching surge voltages.
7.16. Limitation of lightning voltages.
7.17. Insulation of electrical components under vacuum.
7.17.1. Casting of electric components with resin.
7.17.2.Preparation of cost constituents.
7.17.3. Vacuum casting equipment.
7.18. Drying of power transformers.
7.18.1- Preparation.
7.18.2. Pressure reduction.
7.18.3. Fine vacuum.
7.18.4. Design of a plant.
7.18.4.1. Vacuum oven.
7.18.4.2. Kerosene evaporator.
7.18.4.3. Leakage –air –vacuum pump.
7.18.4.4. Conclusions.
7.19. Experimental study of DC dielectric breakdown strength in magnetic fluids.
7.20. Applications in transformer technology of polymer concrete composites.
7.21. Corona resistant dielectric material.
7.21.1. Surge voltage builds up during switching of traction transformer under no load conditions.
7.22. Skin and proximity effects in inductive components.
Table 7.1.
7.23. Proximity effect.
7.24. Conclusion.
References.
Appendices
Appendix 1. The table–integrals.
Appendix 2. Laplace transforms.
Appendix- 3. Upgrading an induction wattmeter.
Appendix- 4. A new phase- sequence indicator.
Appendix. 5. A new electromagnetic phase meter.
References.
Appendix -6.
6.A.1. Preventive maintenance
6.A.1.1. Major types of maintenance.
6.A.2. Improvement maintenance.
6.A.2.1 Corrective maintenance.
6.A.2.2. Preventive maintenance.
6.A.2.2.1. On –condition.
6.A.2.2.2. Condition monitor.
6.A.2.2.2.1. Scheduled.
6.A.2.2.2.2. Management control.
6.A.2.2.2.1. Overtime.
6.A.2.2.2.2.2. Work loads.
6.A.2.2.2.3. Disadvantages.
6.A.3. Designing a PM program for transformers.
6.A.4. Failures that can be prevented.
6.A.5. Maintenance to prevent failures
6.A.6. Personnel.
6.A.7. Service teams.
6.A.8. When and how to start.
6.A.9. Economics of PM.
Appendix-7.
7.A.1. Economics of transformers design and application.
7.A.2. Transformer costs.
7.A.3. Optimum design.
7.A.4. Variation of load losses with the transformer at no-load and those with other loads..
7.A.5. Optimum design based fixed flux density and conductor area.
7.A.6. Evaluation of cost of power.
7.A.6.1. Cost of operation of the transformer.
7.A.7. Determination of kilowatts and kilovolt-amperes lost in the transformer.
Appendix-8
8.A.1. The universal maintenance catalogue.
8.A.1.1. Appraising maintenance performance.
8.A.1.2. Administrative costs of measurement system.
8.A.1.3. Average percentage of time spent by maintenance supervisors in an eight hour day per study conducted of 149 companies.
8.A.1.4. Number of employees on maintenance payroll per a study of 100 companies.
8.A.1.5. Sales necessary to carry excess inventories.
8.A.1.6. Estimate annual costs to carry one euro of excessive inventory before taxes.
8.A.2. General statistics.
8.A.2.1. Man power required.
8.A.2.2. Ratio figures for number of items of equipment to be maintained per man
8.A.2.3. Cost of maintenance hour
8.A.2.4. Breakdown cost component.
8.A.2.5. Progress in cost reduction efforts.
8.A.2.5.1. Incentive coverage.
8.A.2.5.2. Cost per productive hour.
8.A.3. Productive hour realization.
8.A.3.1. Labour cost to apply one euro worth of material.
8.A.4. Evaluation of preventive maintenance.
8.A.4.1. Maintenance costs.
8.A.4.1.1. Maintenance costs as percent of plant investment–book.
8.A.4.1.2. Decrease in maintenance costs unit of production- first year.
8.A.4.1.3. Increase units produced per maintenance euro spent.
8.A.5. Inventory turnover rate per year.
8.A.5.1. Breakdown repair hours.
8.A.5.2. Importance of breakdown repairs.
8.A.5.3. Equipment availability.
8.A.5.4. Breakdowns caused by low quality maintenance.
8.A.5.5. Importance of low quality maintenance breakdowns.
8.A.5.6. Poor production quality caused by low quality maintenance.
8.A.6. Direct supervision, foremen.
8.A.6.1. Maintenance effectiveness.
8.A.6.1.1. Emergency man hours.
8.A.6.2. Emergency and all other unscheduled man-hours.
8.A.6.3. Equivalent down time caused by breakdown.
8.A.7. Preventive maintenance coverage.
8.A.7.1. Man–hours of work entered in log books.
8.A.7.2. Material delivered to work site by warehouse.
8.A.7.3. Stock requisitions fitted from stock.
8.A.7.4. Productive time craftsmen.
8.A.7.5. Coverage with estimates.
8.A.7.6. Crafts man activity level.
8.A.7.7. Overdue work orders.
8.A.7.8. Work under turnover.
8.A.7.8.1. Current backlog in crew weeks.
8.A.7.9. Total back log in crew weeks.
8.A.7.10. Maintenance work orders planned and scheduled daily.
8.A.7.11. Scheduled hours versus hours worked as scheduled.
8.A.7.12. Scheduled hours versus total hours worked.
8.A. 7.13. Work orders executed as scheduled.
8.A.8. Compliance with estimated man-hours.
8.A.9. Ratio of maintenance coordinators to hourly personnel.
8.A.10. Factors, goals and indices.
8.A.10.1. Maintenance administration.
8.A.10.2. Factor.
8.A.10.2.1. Manpower efficiency (use of skill and effort) 100%= normal.
8.A.10.2.2. Overtime hours per month.
Appendix- 9.
9.A.1. Numerical integration: two level formula.
9.A.2. Differential equations.
Appendix-10.
10.A.1. Appraising maintenance performance.
10.A.2. General maintenance objectives.
10.A.2.1. Post-PM.
10.A.3. Shutdown planning.
10.A.4. Critical path.
Optical illusion.
Books published by the same author.
Books ready to publish of the same author.
Post face.
Nota do autor: Ainda vendo os direitos desta publicação; interessa-me o dinheiro todo junto. This e-manuscript can be sold yet because I am interested in receiving the whole money imediately after it has been published. Emanuel Eduardo Pires Vaz.
Target Audience: Engineering students of the second and third cycle of university, professional engineers. the book was written using a language easily understood for technicians. It contains an appendix about the economy and maintenance of a transformer factory
Resume: Magnetic fields. Definition. B and H. Force due to a magnetic field. Force on a charged particle. Force on a current –carrying wire. Direction of force. Faraday`s law of induction. Maxwell`s equation version of Faraday`s law. Relation between two versions. Magnetic flow meter. History. Electrical generators. Transformer. Lorentz force. History and significance. Lorentz force in special relativity. Covariant form of the Lorentz force. A brief history of inductance. Self-inductance and reactive reactance. Solenoid Field from Ampere`s law. Faraday`s law. Inductive reactance. Lenz`s law. Bibliography. Optimal shape design of a single or a multiple coil device for several coils. Mutual inductance. Inductance calculations. SI electricity / electromagnetism units, table 2.1. State the type of moving field used to generate an emf in a conductor. Electromotive force. Mutual inductance study. Self inductance. Energy in an inductor. R-L series circuit. Inductance of a coaxial cable. Taking the internal inductances into account (low frequencies), where f is the outer radius of the outer conductor. Inductance of round parallel wires. Inductance of a round wire over a ground plane. Self inductance of a straight round wire. Calculations for the next example are. Inductance of a single-layered air core coil. Some calculations for the next example. . Inductance of a multi-layered air core coil. Inductance of a toroid with a square cross section. Calculations for the next examples are. Some calculations of coils. Choke coils of a Table 2.2. Copper wire standardized diameter. Table 2.3. Coil core sizes. Efficiency of a filter. Filters for speakers. Transformers for a vibrator. Output transformers. Cross section of the core. Number of turns of the primary from the cross section of the core. Transformer turns ratio. Cross sections of wires. Cross section of the core. Number of turns of the primary. Number of turns of the secondary. Cross section of the wire of the primary. Cross section of the secondary. Grounding and shielding. Winding arrangement of output transformers.
2.9.1. Faraday shield. Primary cold ends facing secondary winding. Five section structure for increased bandwidth. Mixed feedback drive circuits for audio output transformers. Transformer design philosophies. Winding technique. Dual coil structure. Choice of core shape and core materials. Long lifetime and high insulation requirements. Price and performance considerations. Where quality and transformers meet. Modulation transformers. Coils for radio frequency. Solenoid coils (only one layer). Single layer coil inductance. Bee nest coils. Determining the inductance of a coil. A new and accurate method to measure self inductance and mutual inductance of coils. Relative methods. Circuit analyse. Accuracy of results. Auto transformers. Practical example. Current densities which are admissible for transformer windings. Project for a winding semi- automatic machine. Optimal shape design of a multiple –coil device for induction heating. Sample points for temperature test. Design variables initial values and ranges. Coupled electromagnetic- thermal simulation. Thermal problem. Coupled problems. Optimisation and evolutionary strategy. Optimisation methods and benefits of using the evolutionary strategy. OptiNet: An optimisation tool. Sensitivity of the variables. Results. Sample points for temperature check. Design variables sensitivity. Solenoids. Self-inductance of solenoids. The current-sheet solenoid. Effective current-sheet diameter (LF). Effective current-sheet diameter (HF). Internal inductance. LF-HF transition frequency. Internal inductance factor. Magnetic field non-uniformity (Nagaoka`s coefficient). Lundin`s Handbook Formula. Asymptotically-correct approximations for KL. Rayleigh-Niven formula (for short coils). Coffin`s Formula (for short coils). Weloster-Hevelock Formula (for long coils). Wheeler`s Formulae. Wheeler`s continuous formula (optimised). Defective formula. Rosa`s round-wire corrections. Self-inductance correction. Mutual-inductance correction. Rosa`s correction for the mutual inductance of round wires. Formula for Rosa`s mutual inductance correction parameter. Apparent inductance. Solenoid inductance calculations: St.Anthony`s formula. Additional sources of deviation. Conductor length. References. Transformers. What a transformer is. How a transformer works. Principle of magnetic induction applied to coils. Equilibrium between magnetic flux, induced voltage and exciting current. The transformer with d.c. voltage applied. Equilibrium with alternating voltage applied. Equilibrium when the transformer is loaded. Performance characteristics. Single phase transformers. Electrical circuits: windings. Functioning principle. Ideal transformer. Functioning equations. Vector diagram. Efficiency. Symbolic equations. Real transformer. Hysteretic and Foucault currents. Equations for the real transformer. Vector diagram for the real transformer. Transformation ratio. Analyse of the functioning of a transformer under energetic point of view. Distributing of the absorbed power. Efficiency. An equivalent circuit for the real transformer. Simplified equivalent circuit. Some definitions about transformer characteristics. Nominal Power. Frequency. Some definitions about voltage drops. Vector voltage drops. Absolute voltage drops. Relative voltage drop. Resistive voltage drop. Relative resistive voltage drop. Relative resistive voltage drops in percent. Problems on voltage drops. Determination of the absolute voltage drop or of the regulation. External characteristics. Voltage drop variation at the two plugs of transformer secondary and delivering an electric current and with power factor. Analytic expressions for external characteristics of a transformer. External characteristics in a Kapp approximation. Efficiency of a transformer. Relation between core losses and copper losses. Economic tests for a transformer. Open circuit test. Be careful with this test. Short- circuit test. Transformer in shunt. Connecting condition. Load distribution. Graphic method calculated load distribution for two transformers in shunt. Study of two transformers in shunt with two different voltages at the secondary in open circuit. Characteristics alteration with frequency for a transformer. Three- phase transformers. Three-phase bank and a three-phase unity. Some advantages for a three- phase unity. Some advantages for a three-phase bank. Some differences between transformer bank and three-phase unity. Three-phase transformer core. Three-phase transformer functioning in charge balanced regimen. Transformation ratio in a three-phase system. Different types of transformers according to winding connection. DY transformer. DY transformer. Transformer ratio for each transformer. Capacity. Equations for voltages and for currents. Kapp`s equation for voltages. Current equation. Economic analyse of a transformer copper weight waste in each connection types. Study the three-phase transformer under the point of view of third order harmonic and the unbalanced regimen. Introduction. Angular deviation. Analyse of the different connection types. Triple frequency harmonics. Some important considerations about insulated neutral point and neutral point connected to ground. Insulated neutral point. Neutral point on secondary connected to ground. Bibliography. Transformer connections. Single-phase connections. The autotransformer. Impedance of an autotransformer. Limitation of an autotransformer. Short circuit of the lines on one side of an autotransformer. Impulse voltage distribution in an autotransformer. Multiwinding transformers. Equivalent circuit of a three-winding transformer. Stray and Eddy current losses and equivalent resistance of transformers. Short-circuits in a transformer with three windings. Transformer temperature. Introduction. How flow from oil to air with forced air or forced-oil cooler. Temperature transients following load changes. Dissipation of heat into the cooling medium. Heating of cooling liquid. Appendix. Concluding comments. Oil flow by separate pumps. Literature. Classroom Problems (1 to 15). Maintenance, protection and detection of faults. Paint. Auxiliary equipment. Oil preservation. Sealed cases for oil protection. Conservator tank. Gas-oil seal. Oil conditioning. Detection of deterioration of oil. Effect of moisture on insulation. Segregation of moist oil. Accumulation of moisture in transformers in service. Drying transformers in the field. Protection of transformers. Protection against overloads. Hot-oil thermometers. Hot-spot thermometer. Fuse protection. Internal circuit breakers for distribution transformers. Protection of secondary banks. Coordination of thermal device with relays and fuses. The thermal lead device in a transformer with forced –oil flow. Thermal load device in multiwinding or multiphase transformers. Protection against lightning and switching surge voltages. Limitation of lightning voltages. Insulation of electrical components under vacuum. Casting of electric components with resin. Preparation of cost constituents. Vacuum casting equipment. Drying of power transformers. Preparation. Pressure reduction. Fine vacuum. Design of a plant. Vacuum oven. Kerosene evaporator. Leakage –air –vacuum pump. Conclusions. Experimental study of DC dielectric breakdown strength in magnetic fluids. Applications in transformer technology of polymer concrete composites. Corona resistant dielectric material. Surge voltage builds up during switching of traction transformer under no load conditions. Skin and proximity effects in inductive components. Table 7.1. Proximity effect. Conclusion. References. Appendixes. Appendix 1. The table–integrals. Appendix 2. Laplace transforms.Appendix- 3. Upgrading an induction wattmeter. Appendix- 4. A new phase- sequence indicator. Appendix. 5. A new electromagnetic phase meter. References. Appendix -6. Preventive maintenance. Major types of maintenance. Improvement maintenance. Corrective maintenance. Preventive maintenance. On –condition. Condition monitor. Scheduled. Management control. Overtime. Work loads. Disadvantages. Designing a PM program for transformers. . Failures that can be prevented. Maintenance to prevent failures. Personnel. Service teams. When and how to start. Economics of PM. Appendix-7. Economics of transformers design and application. Transformer costs. Optimum design. Variation of load losses with the transformer at no-load and those with other loads. Optimum design based fixed flux density and conductor area. Evaluation of cost of power. Cost of operation of the transformer. Determination of kilowatts and kilovolt-amperes lost in the transformer.
Appendix-8. The universal maintenance catalogue. Appraising maintenance performance. Administrative costs of measurement system. Average percentage of time spent by maintenance supervisors in an eight hour day per study conducted of 149 companies. Number of employees on maintenance payroll per a study of 100 companies. Sales necessary to carry excess inventories. Estimate annual costs to carry one euro of excessive inventory before taxes. General statistics. Man power required. Ratio figures for number of items of equipment to be maintained per man Cost of maintenance hour. Breakdown cost component. Progress in cost reduction efforts. Incentive coverage. Cost per productive hour. Productive hour realization. Labour cost to apply one euro worth of material. Evaluation of preventive maintenance. Maintenance costs. Maintenance costs as percent of plant investment–book. Decrease in maintenance costs unit of production- first year. Increase units produced per maintenance euro spent.
8.A.5. Inventory turnover rate per year. Breakdown repair hours. Importance of breakdown repairs. Equipment availability. Breakdowns caused by low quality maintenance. Importance of low quality maintenance breakdowns. Poor production quality caused by low quality maintenance. Direct supervision, foremen. Maintenance effectiveness. Emergency man hours. Emergency and all other unscheduled man-hours. Equivalent down time caused by breakdown. Preventive maintenance coverage. Man–hours of work entered in log books. Material delivered to work site by warehouse. Stock requisitions fitted from stock. Productive time craftsmen. Coverage with estimates. Crafts man activity level. Overdue work orders. Work under turnover. Current backlog in crew weeks. Total back log in crew weeks. Maintenance work orders planned and scheduled daily. Scheduled hours versus hours worked as scheduled. Scheduled hours versus total hours worked. Work orders executed as scheduled. Compliance with estimated man-hours. Ratio of maintenance coordinators to hourly personnel. Factors, goals and indices. Maintenance administration. Factor. Manpower efficiency (use of skill and effort) 100%= normal. Overtime hours per month. Appendix- 9. Numerical integration: two level formula. Differential equations. Appendix-10. Appraising maintenance performance. General maintenance objectives. Post-PM. Shutdown planning. Critical path. Optical illusion.
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