Electric Power Transformer Engineering

James H. Harlow, James H. Harlow

• Publisher: CRC Press
• Year: 2017
• ISBN:
  9781351833103
• Edition: 3
• Topic: Tecnología e ingeniería
• Subtopic: Ingeniería eléctrica y telecomunicaciones

Electric Power Transformer Engineering, Third Edition expounds the latest information and developments to engineers who are familiar with basic principles and applications, perhaps including a hands-on working knowledge of power transformers. Targeting all from the merely curious to seasoned professionals and acknowledged experts, its content is structured to enable readers to easily access essential material in order to appreciate the many facets of an electric power transformer.

Topically structured in three parts, the book:

• Illustrates for electrical engineers the relevant theories and principles (concepts and mathematics) of power transformers
• Devotes complete chapters to each of 10 particular embodiments of power transformers, including power, distribution, phase-shifting, rectifier, dry-type, and instrument transformers, as well as step-voltage regulators, constant-voltage transformers, transformers for wind turbine generators and photovoltaic applications, and reactors
• Addresses 14 ancillary topics including insulation, bushings, load tap changers, thermal performance, testing, protection, audible sound, failure analysis, installation and maintenance and more

As with the other books in the series, this one supplies a high level of detail and, more importantly, a tutorial style of writing and use of photographs and graphics to help the reader understand the material. Important chapters have been retained from the second edition; most have been significantly expanded and updated for this third installment. Each chapter is replete with photographs, equations, and tabular data, and this edition includes a new chapter on transformers for use with wind turbine generators and distributed photovoltaic arrays. Jim Harlow and his esteemed group of contributors offer a glimpse into the enthusiastic community of power transformer engineers responsible for this outstanding and best-selling work.

A volume in the Electric Power Engineering Handbook, Third Edition.

Other volumes in the set:

• K12642 Electric Power Generation, Transmission, and Distribution, Third Edition (ISBN: 9781439856284)
• K12648 Power Systems, Third Edition (ISBN: 9781439856338)
• K13917 Power System Stability and Control, Third Edition (9781439883204)
• K12650 Electric Power Substations Engineering, Third Edition (9781439856383)

Watch James H. Harlow's talk about his book:

Part One: http://youtu.be/fZNe9L4cux0

Part Two: http://youtu.be/y9ULZ9IM0jE

Part Three: http://youtu.be/nqWMjK7Z_dg

1 Theory and Principles

Dennis J. Allan and Harold Moore

Merlin Design

H. Moore and Associates

1.1 Air Core Transformer

1.2 Iron or Steel Core Transformer

1.3 Equivalent Circuit of an Iron-Core Transformer

1.4 The Practical Transformer

• Magnetic Circuit
• Leakage Reactance
• Load Losses
• Short-Circuit Forces
• Thermal Considerations
• Voltage Considerations

Bibliography

Transformers are devices that transfer energy from one circuit to another by means of a common magnetic field. In all cases except autotransformers, there is no direct electrical connection from one circuit to the other.

When an alternating current flows in a conductor, a magnetic field exists around the conductor, as illustrated in Figure 1.1. If another conductor is placed in the field created by the first conductor such that the flux lines link the second conductor, as shown in Figure 1.2, then a voltage is induced into the second conductor. The use of a magnetic field from one coil to induce a voltage into a second coil is the principle on which transformer theory and application is based.

1.1 Air Core Transformer

Some small transformers for low-power applications are constructed with air between the two coils. Such transformers are inefficient because the percentage of the flux from the first coil that links the second coil is small. The voltage induced in the second coil is determined as follows.

E=Ndϕdt108⁢(1.1)

where

N is the number of turns in the coil

dϕ/dt is the time rate of change of flux linking the coil

ϕ is the flux in lines

At a time when the applied voltage to the coil is E and the flux linking the coils is ϕ lines, the instantaneous voltage of the supply is:

e=√2Ecosωt=Ndϕdt108⁢(1.2)

Figure 1.1 Magnetic field around conductor.

Figure 1.2 Magnetic field around conductor induces voltage in second conductor.

dϕdt=(√2cosωt108)N⁢(1.3)

The maximum value of ϕ is given by:

ϕ=(√2Ε108)(2πfΝ)⁢(1.4)

Using the MKS (metric) system, where ϕ is the flux in webers,

E=Ndϕdt⁢(1.5)

and

ϕ=(√2E)(2πfN)⁢(1.6)

Since the amount of flux ϕ linking the second coil is a small percentage of the flux from the first coil, the voltage induced into the second coil is small. The number of turns can be increased to increase the voltage output, but this will increase costs. The need then is to increase the amount of flux from the first coil that links the second coil.

1.2 Iron or Steel Core Transformer

The ability of iron or steel to carry magnetic flux is much greater than air. This ability to carry flux is called permeability. Modern electrical steels have permeabilities in the order of 1500 compared with 1.0 for air. This means that the ability of a steel core to carry magnetic flux is 1500 times that of air. Steel cores were used in power transformers when alternating current circuits for distribution of electrical energy were first introduced. When two coils are applied on a steel core, as illustrated in Figure 1.3, almost 100% of the flux from coil 1 circulates in the iron core so that the voltage induced into coil 2 is equal to the coil 1 voltage if the number of turns in the two coils are equal.

Continuing in the MKS system, the fundamental relationship between magnetic flux density (B) and magnetic field intensity (H) is:

B=μ0H⁢(1.7)

where μ₀ is the permeability of free space = 4π × 10⁻⁷ Wb A⁻¹ m⁻¹.

Replacing B by ϕ/AandH by (IN)/d

where

ϕ is the core flux in lines

N˙

is the number of turns in the coil

I is the maximum current in amperes

A is the core cross-section area

the relationship can be rewritten as:

ϕ=(μNAI)d⁢(1.8)

where

d is the mean length of the coil in meters

A is the area of the core in square meters

Figure 1.3 Two coils applied on a steel core.

Then, the equation for the flux in the steel core is:

ϕ=(μ0μrNAI)d⁢(1.9)

where, μ_r is the relative permeability of steel ≈1500.

Since the permeability of the steel is very high compared with air, all of the flux can be considered as flowing in the steel and is essentially of equal magnitude in all parts of the core. The equation for the flux in the core can be written as follows:

ϕ=0.225EfN⁢(1.10)

where

E is the applied alternating voltage

F is the frequency in hertz

N is the number of turns in the winding

In transformer design, it is useful to use flux density, and Equation 1.10 can be rewritten as:

B=ϕA=0.225E(fAN)⁢(1.11)

where, B is the flux density in tesla (webers/square meter).

1.3 Equivalent Circuit of an Iron-Core Transformer

When voltage is applied to the exciting or primary winding of the transformer, a magnetizing current flows in the primary winding...