Transformers Book
We have already finished our book of transformers called "Transformers Book" is a product of 40 years of experience in the field and the achievement of many projects with a lot of different good results. Transformers book is not a theoretical work but a theoretic - practical work of Years of labor, despite it´s strong mathematical and physical background.
We know that a big part of this book is not found in any similar work, because We had been looking for those subjects by many years without any success. We gathered many papers of the IRE, IEE, IEEE and other societies of same importance in combination with our own work through many years to make possible its construction.
We could had written it in our own language but We tried to write it in English, with the intention to reach more people like possible, around the world.
The content:
Transformers Book
Chapter 1 - What is a transformer
1.1 A Brief History.
Chapter 2 - The transformer: A magnetic Component
2.1 Structure of the Matter
2.2 A brief view over atomic physics
2.3 Ferromagnetic Materials
2.4 The ferromagnetic domains.
2.5 The domains walls
2.6 The initial Magnetization Curve ( Virgin curve).
2.7 The initial permeability.
2.8 The loss Angle δ
2.9 The hysteresis loop
2.10 The Hysteresis loop surveying of a particular material Through:
Operational amplifier integrator approach
Microcontroled integrator approach
Digital oscilloscope Approach
2.11 Magnetic Flux
2.12 Flux Density.
2.13 Absolute and relative permeability
2.14 Complex permeability
2.15 Apparent permeability
2.16 Incremental permeability
2.17 Remanence ratio
2.18 Spin relaxation.
2.19 Magnetization M
2.20 Limiting frequency
2.21 Magnetostriction
2.22 Magnetic Losses
2.23 The losses measurements through.
Special operational amplifiers
Digital Oscilloscope
2.24 Core Flux density, diffusion and the skin depth
2.25 The Foucault and Eddy currents in the core.
2.26 Separation of losses
2.27 Pulverization and lamination needs for Eddy currents reduction and skin depth partial solution.
2.28 The core losses at different configurations, voltages and current waveforms.
2.29 The core dimensions and the effects of their forms
2.30 Power losses in the core.
2.31 The different natures of losses
2.32 The steinmetz approach.
2.33 Calculation and the measurement of losses at different flux waveforms.
2.34 The problem of the stray capacitance
2.35 A surveying of different magnetic materials and cores.
2.36 E I Cores for small Transformers
2.37 C Cores and C Composed cores for medium Power transformers.
2.38 The problems of composition.
2.39 Composed lamination for high power transformers
2.40 Cruciform cored transformers, optimization and the minimum degree.
2.41 Simulations essays using FEA to see the behavior of the compositions.
2.42 The importance in the definition of lamination standards.
Chapter 3 - The diffusion of the current over the conductors.
3.1 Ampere´s Law
3.2 Exercises with unit turn and hypothetical infinite conductors.
3.3 Exercises with hypothetical infinite solenoid and its local fields.
3.4 The concept of Layer
3.5 Exercises with hypothetical various layers, infinite solenoid and its local fields.
3.6 The a coil faced by a counter current turn.
3.7 The windings and their currents.
3.8 The second field of the transformer
3.9 Various configurations.
3.10 Visualization of the second field by FEA (Finite Elements Analysis)
3.11 The profile of the second field
3.12 The Definition of “Portion”.
3.13 “Portion” Visualization by FEA.
3.14 The winding faced to a reluctance
3.15 Solenoidal winding and core
3.16 Field Profile in a solenoidal topology
3.17 Planar winding and core
3.18 Field Profile in a planar topology
Chapter 4 - The leakage inductance
4.1 What is inductance
4.2 The general inductance equation.
4.3 Inductance of a Toroid using the general inductance equation.
4.4 The dispersion field and leakage inductance
4.5 The profile of the field
4.6 The field profile seen through software simulation FEA (Finite Elements Analysis)
4.7 The Volume of the coil
4.8 Volumetric Integration of the energy to obtain the leakage inductance.
4.9 The usage of the inductance equation for determination of the leakage inductance
4.10 Minimization or Maximization of the leakage Inductance
4.11 Effects of the Dispersion field.
4.12 The calculation of the field in the core window through FEA simulation and determination of the leakage inductance by this mean.
4.13 The magnetic losses of one inductor.
4.14 The equivalent circuit of a transformer at low, medium and high frequencies.
4.15 The mathematical modeling, Matlab and Simulink models of transformers
Chapter 5 - The current capacity of the core window.
5.1 The utilization factor of the various window forms.
5.2 The problem of the conductor form.
5.3 The current density of the conductor directly related to temperature.
5.4 The total current of a one equivalent turn of the window.
Chapter 6 - The magnetic cross sectional area.
6.1 The definition of the formula of flux from Faraday´s law.
6.2 The voltage induced in one turn depending of flux density, frequency and magnetic cross surface area.
6.3 The flux density dependence of temperature, external surface and power loss density of the core.
6.4 Curves of power losses of different materials.
Chapter 7 - The power of a transformer
7.1 The core window multiplied by magnetic cross sectional area The “ Area product” of a transformer.
7.2 A study of optimization “By cost Constraint” of a three phase power transformer. The definition of an algorithm.
Chapter 8 - Exciting current of a transformer.
8.1 The magnetizing current (inductive part)
8.2 The real part.
Chapter 9 - The problem of the inrush current
9.1 The effect of magnetic memory of the core.
9.2 The problem of the initial value
9.3 The value of the saturation and the slope of the curve.
9.4 The profile of the inrush current
9.5 The sympathetic inrush current
9.6 The magnetic pulse outside the transformer due to the inrush (Dangerous Consequences).
Chapter 10 - Transient magnetic effects over current diffusion of conductors.
10.1 Exercises with unit turn and hypothetical infinite conductors, faced to a suddenly applied field.
10.2 The gradual penetration of the field and the growing of the current diffusion.
10.3 The exponential of diffusion.
10.4 The exponential diffusion and the alternating current field.
10.5 The integration of the exponential, the unity and the skin depth.
10.6 The skin depth explained and totally clear.
10.7 The skin depth simulated and visualized by FEA
10.8 The proximity of two conductors.
10.9 The interaction of two conductors carrying currents and its diffusion.
10.10 The proximity effect and Visualization by FEA.
10.11 The combination of proximity effect and skin depth.
10.12 The Skin depth proximity effect – Visualization by FEA
10.13 The current at different Layers and the Eddy currents.
10.14 The AC resistance of a conductor
10.15 The difficulty and complexity due to distortion of the diffusion shapes over the cross sectional area of the conductors, giving the “Quarter moon effect” over round conductors.
10.16 The Dowell Work.
10.17 The simplifications of Dowell and a consistent approach.
10.18 The AC resistance of a conductor at one layer
10.19 The AC total resistance of the winding.
10.20 Calculation of the additional losses of a transformer due to the skin depth proximity effect.
10.21 The limits of frequency in a solenoidal technology and usage of planar topologies for Mhz transformers.
10.22 Optimization of the conductor height in a coil.
10.24 A survey through various measurements to define de various origins of losses in a conductor.
10.25 The DC component.
10.26 The AC component at various frequencies.
10.27 Simulations of additional losses through Matlab and Simulink.
10.28 Complete model of additional losses combined with modified steinmetz model for approximated analysis of temperature.
Chapter 11 - The effect of frequency and consequently of waveforms in skin proximity effect.
11.1 The influence of waveform over the losses
11.2 A convenient approach
11.3 The original work of P.S.Venkatraman
11.4 The simplification of the problem.
11.5 The AC resistance for complex waveforms
11.6 The optimization of the height of the coil due to number of layers, frequency waveforms and configuration of the coils.
11.7 The simplification of the approach and degeneration of elements.
11.8 Coil with metal sheets
11.9 The optimization of windings; metal sheets or wires ?
11.10 The litz wires.
1 1.11 The co-lateral effects with litz wires, At “Strand level” or at a “Package level”.
11.12 Optimization of transformers for a particular waveform and frequency.
Chapter 12 - The inductors and chokes faced to skin proximity effect.
12.1 The problem of absence of counter current turn in a inductor or choke.
12.2 The effect of the counter reluctance.
12.3 The consequent standard profile of an inductor.
12.4 The effect of the gap.
12.5 The magnetostatic fields.
12.6 The model for calculation of losses of a cylinder immersed in a homogeneous field.
12.7 The myopia effect of the gap and the effect of the distance on the current diffusion, seen By FEA (Finite Element Analysis)
12.8 The modeling and simulations by FEA (Finite Elements Analysis).
12.9 The improvement of the diffusion by multiple gaps seen by FEA
12.10 The optimization of distance in multiple gaps
12.11A search for a general rule.
12.12 The effect of the relative position of the conductor in relation to the gap seen by FEA.
12.12 The effect of slots.
12.14 The definition of size departing from the area of the window and the magnetic cross sectional area.
12.14 The magnetic losses of one inductor
12.15 The feasibility to design planar inductors for high powers (High Vars chokes)
Chapter 13 - Transformers like a Voltage or Current power supply.
13.1 Transformer as a voltage source
13.2 The problem of the voltage regulation. Factors Involved
13.3 The voltage accuracy as a potential measurement transformer
13.4 The transformer as a current source
13.5 The problem of the current regulation. Factors involved
13.6 The current accuracy as a current measurement transformer.
Chapter 14 - The problem of Temperature.
14.1 The external area approach (Average temperature)
14.2 The weigh and loss approach (Average Temperature)
14.3 Calculation of temperature drop between layers
14.4 Temperature measurement of power transformers
14.5 Temperature measurement at light load and nominal voltage
14.6 Temperature measurement at nominal load and low voltage.
14.7 The size and weight versus temperature time constant and the transient thermal impedance.
14.8 The hot spots ant its measurements.
14.9 The forced cooling of transformers.
Chapter 15 - Power Transformer optimization
15.1 The point of maximum efficiency
15.2 The curve of maximum points efficiency: maximum copper weight side or maximum core weight side.
Chapter 16 – Optimization constraints.
16.1 By temperature
16.2 By Voltage Regulation
16. 3 By special dimensions
16.4 By Cost
16.5 By efficiency.
Chapter 17 - The problem of skin proximity effect in high power transformers
17.1 The orthogonality between proximity and skin effect
17.2The exact calculation of proximity effect
17.3 The exact calculation of skin effect
Chapter 18 – Polyphase Transformers
18.1 Three Phase Transformers
18.2 Delta open and scott Transformers
18.3 Zig-Zag Topologies
18.4 Multiple Zig-Zag Topologies
18.5 Extended delta topologies
18.6 The transformers for high power industrial rectifiers and multiple topologies.
18.7 The problem of multiple waveforms in the windings for polyphase topologies.
18.8 The calculations of additional losses due to proximity skin effect in multiple windings at different waveforms.
Chapter 19 - the end Effect
19.1 Demonstration of the end effect by FEA (Finite Elements Analysis)
19.2 Causes
19.3 A thermographic photo showing the end effect
19.4 The difficulty to find a solution.
19.5 A difficulty far partial solution
Chapter 20 - The strange effect
20.1 Who is the strange ?
20.2 Definitions
20.3 Solutions
Chapter 21 - Designing K factor transformers
21.1 Definition of the K factor
21.1 The ambiguity of the K factor due to a non definition of a waveform and limit for the harmonic order
21.3 The danger of usual practices of over dimensioning of power transformers.
21.4 The definition of the Value of K due to reference load of the IEC 62040-1-1 exposed to the self impedance of the transformer. In this case K =20.
21.5 The skin proximity effect due to K=20 waveform spectra.
21.6 The calculation of power losses
21.7 The complete Matlab and Simulink models for the calculation of K transformers.
21.8 A definition of a standard design procedure in Matcad and calculations tools of Matlab.
Chapter 22 – Designing Planar Transformers and inductors
22.1 The planar approach
22.2 The windings problems and solutions
22.3 The printed circuit winding
22.4 Multiple printed circuit winding and flexible printed circuit
22.5 Interleaving coil and its effects over the H profile and the improvement of losses.
22.6 Calculations of Additional losses due to skin proximity effect.
22.7 Copper or aluminum Foil for higher solutions
22.8 The planar inductor, limitation by the fixed H profile.
22.9 Planar solutions
Chapter 23 - Designing mains medium power Transformer (500KVA) using the (Cost Constraint algorithm) of the chapter 7
23.1 The problems involved – (Normally no one mind such problems.)
23.2 Concluding; the usage of copper or aluminum. (Ditto)
23.3 Optimizing the height of the coil. (Ditto).
23.4 One simple mathematical, Matlab and Simulink Model for power transformers calculations
Chapter 24 - Designing a power choke of various tenths of KVAR using planar topology to solve gaps problems.
24.1 The geometric problem
24.2 Construction problems
24.3 Calculation of losses
24.4 Demonstrating the results by FEA
Chapter 25 - Designing a selective 100Khz power supply inductor with 2 different conductors.
25.1 Designing the inductor with Wire
25.2 Designing the inductor with foils
25.3 Calculating the inductor and concluding the impossibility to go ahead.
25.4 Installing a very thin conductor in parallel that solves the problem.
25.5 Calculations to see the solution.
Appendix A
Appendix B
Appendix C
Appendix D