Page 130 - Maxwell House

110 Chapter 2

core electrons interact with steel atomic lattice and part of their kinetic energy converts into
heat (Ohmic loss) increasing the whole transformer temperature. In the case of excessive
heating, the transformer can be damaged or even destroyed. That is why large power
transformers are contained inside the protecting tank equipped with cooling fans, oil pumps, or
water-cooled heat exchangers for active cooling.

In Chapter 3 it will be demonstrated that Ohmic power loss = ∫ ∘ (see (3.11)).

Combining this equity with = σ we should come to conclusion that the power loss is
proportional to the ratio | | /σ. It turns out that n times drop in current density can cut the
2

power loss in times. Therefore, any reduction in eddy current density increases the
2
transformer efficiency. Eddy current cannot be eliminated, but it can be significantly reduced
by manufacturing the core from thin sheets of steel, as shown in 2.10.6c, with a very thin surface
coating of insulating varnish or a low conductive oxide layer. As shown, each layer of the core
consists of E- and I-shaped sections of metal. These sections are pressed together to form the
laminated core. Subsequently, the total magnetic flux is split up into many n-times less strong
partial fluxes, as shown in Figure 2.10.6b, that reduces the eddy current density in each sheet
and total core power loss at the same rate.

The eddy current analysis in power transformers with lamination and without it as any of real
3D magnetic field problems is challenging and far from being a routine task. For illustration,
38
Figure 2.10.7a demonstrates the magnetic flux distribution in solid core transformer with
currents (blue and black arrows) in the two layer winding. The red areas correspond to the flux
of the highest intensity while the blue ones at its lowest. In fact, the modern transformers are
quite sophisticated devices, hard in design and can be as gigantic as shown in Figure 2.10.7b .
39
Laminated steel sheets stacked together are widely used to reduce eddy current loss not only in
the transformer but as a steel portion of the starter and rotor in electric motors and generators.
40
The example of such laminated starter with the coil is shown in Figure 2.10.7c . The reader
can find more information about the transformer, motors, and electrical generators in
specialized literature [11].

a) b) c)

Figure 2.10.7 a) Magnetic flux distribution, b) High voltage transformer, c) Starter from
laminated steel sheets

38 Public Domain Image, source: https://www.comsol.com/model/e-core-transformer-14123
39 Public Domain Image, source: http://www.lubrita.com/news/68/683/Sparking-the-Transformer-Oil-
Market/
40 Public Domain Image, source: https://grabcad.com/requests/stator-winding-of-ac-motor--1