transformer engineering design and practice 1_phần 4 pdf

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2

Magnetic Characteristics

The magnetic circuit is one of the most important active parts of a transformer. It

consists of laminated iron core and carries flux linked to windings. Energy is

transferred from one electrical circuit to another through the magnetic field

carried by the core. The iron core provides a low reluctance path to the magnetic

flux thereby reducing magnetizing current. Most of the flux is contained in the

core reducing stray losses in structural parts. Due to on-going research and

development efforts [1] by steel and transformer manufacturers, core materials

with improved characteristics are getting developed and applied with better core

building technologies. In the early days of transformer manufacturing, inferior

grades of laminated steel (as per today’s standards) were used with inherent

high losses and magnetizing volt-amperes. Later on it was found that the

addition of silicon content of about 4 to 5% improves the performance

characteristics significantly, due to a marked reduction in eddy losses (on

account of the increase in material resistivity) and increase in permeability.

Hysteresis loss is also lower due to a narrower hysteresis loop. The addition of

silicon also helps to reduce the aging effects. Although silicon makes the

material brittle, it is well within limits and does not pose problems during the

process of core building. Subsequently, the cold rolled manufacturing

technology in which the grains are oriented in the direction of rolling gave a new

direction to material development for many decades, and even today newer

materials are centered around the basic grain orientation process. Important

stages of core material development are: non-oriented, hot rolled grain oriented

(HRGO), cold rolled grain oriented (CRGO), high permeability cold rolled

grain oriented (Hi-B), laser scribed and mechanically scribed. Laminations with

lower thickness are manufactured and used to take advantage of lower eddy

losses. Currently the lowest thickness available is 0.23 mm, and the popular

thickness range is 0.23 mm to 0.35 mm for power transformers. Maximum

Copyright © 2004 by Marcel Dekker, Inc.

36 Chapter 2

thickness of lamination used in small transformers can be as high as 0.50 mm.

The lower the thickness of laminations, the higher core building time is required

since the number of laminations for a given core area increases. Inorganic

coating (generally glass film and phosphate layer) having thickness of 0.002 to

0.003 mm is provided on both the surfaces of laminations, which is sufficient to

withstand eddy voltages (of the order of a few volts).

Since the core is in the vicinity of high voltage windings, it is grounded to drain

out the statically induced voltages. If the core is sectionalized by ducts (of about 5

mm) for the cooling purpose, individual sections have to be grounded. Some users

prefer to ground the core outside tank through a separate bushing. All the internal

structural parts of a transformer (e.g., frames) are grounded. While designing the

grounding system, due care must be taken to avoid multiple grounding, which

otherwise results into circulating currents and subsequent failure of transformers.

The tank is grounded externally by a suitable arrangement. Frames, used for

clamping yokes and supporting windings, are generally grounded by connecting

them to the tank by means of a copper or aluminum strip. If the frame-to-tank

connection is done at two places, a closed loop formed may link appreciable stray

leakage flux. A large circulating current may get induced which can eventually

burn the connecting strips.

2.1 Construction

2.1.1 Types of core

A part of a core, which is surrounded by windings, is called a limb or leg.

Remaining part of the core, which is not surrounded by windings, but is essential

for completing the path of flux, is called as yoke. This type of construction

(termed as core type) is more common and has the following distinct advantages:

viz. construction is simpler, cooling is better and repair is easy. Shell-type

construction, in which a cross section of windings in the plane of core is

surrounded by limbs and yokes, is also used. It has the advantage that one can use

sandwich construction of LV and HV windings to get very low impedance, if

desired, which is not easily possible in the core-type construction. In this book,

most of the discussion is related to the core-type construction, and where required

reference to shell-type construction has been made.

The core construction mainly depends on technical specifications,

manufacturing limitations, and transport considerations. It is economical to have

all the windings of three phases in one core frame. A three-phase transformer is

cheaper (by about 20 to 25%) than three single-phase transformers connected in a

bank. But from the spare unit consideration, users find it more economical to buy

four single-phase transformers as compared to two three-phase transformers.

Also, if the three-phase rating is too large to be manufactured in transformer

works (weights and dimensions exceeding the manufacturing capability) and

Copyright © 2004 by Marcel Dekker, Inc.

Magnetic Characteristics 37

transported, there is no option but to manufacture and supply single-phase units.

In figure 2.1, various types of core construction are shown.

In a single-phase three-limb core (figure 2.1 (a)), windings are placed around

the central limb, called as main limb. Flux in the main limb gets equally divided

between two yokes and it returns via end limbs. The yoke and end limb area

should be only 50% of the main limb area for the same operating flux density. This

type of construction can be alternately called as single-phase shell-type

transformer. Zero-sequence impedance is equal to positive-sequence impedance

for this construction (in a bank of single-phase transformers).

Sometimes in a single-phase transformer windings are split into two parts and

placed around two limbs as shown in figure 2.1 (b). This construction is

sometimes adopted for very large ratings. Magnitude of short-circuit forces are

lower because of the fact that ampere-turns/height are reduced. The area of limbs

and yokes is the same. Similar to the single-phase three-limb transformer, one can

have additional two end limbs and two end yokes as shown in figure 2.1 (c) to get

a single-phase four-limb transformer to reduce the height for the transport

purpose.

Figure 2.1 Various types of cores

Copyright © 2004 by Marcel Dekker, Inc.

38 Chapter 2

The most commonly used construction, for small and medium rating

transformers, is three-phase three-limb construction as shown in figure 2.1 (d).

For each phase, the limb flux returns through yokes and other two limbs (the same

amount of peak flux flows in limbs and yokes). In this construction, limbs and

yokes usually have the same area. Sometimes the yokes are provided with a 5%

additional area as compared to the limbs for reducing no-load losses. It is to be

noted that the increase in yoke area of 5% reduces flux density in the yoke by

5%, reduces watts/kg by more than 5% (due to non-linear characteristics) but

the yoke weight increases by 5%. Also, there may be additional loss due to

cross-fluxing since there may not be perfect matching between lamination steps

of limb and yoke at the joint. Hence, the reduction in losses may not be very

significant. The provision of extra yoke area may improve the performance

under over-excitation conditions. Eddy losses in structural parts, due to flux

leaking out of core due to its saturation under over-excitation condition, are

reduced to some extent [2,3]. The three-phase three-limb construction has

inherent three-phase asymmetry resulting in unequal no-load currents and

losses in three phases; the phenomenon is discussed in section 2.5.1. One can

get symmetrical core by connecting it in star or delta so that the windings of three

phases are electrically as well as physically displaced by 120 degrees. This

construction results into minimum core weight and tank size, but it is seldom used

because of complexities in manufacturing.

In large power transformers, in order to reduce the height for transportability,

three-phase five-limb construction depicted in figure 2.1 (e) is used. The magnetic

length represented by the end yoke and end limb has a higher reluctance as

compared to that represented by the main yoke. Hence, as the flux starts rising, it

first takes the path of low reluctance of the main yoke. Since the main yoke is not

large enough to carry all the flux from the limb, it saturates and forces the

remaining flux into the end limb. Since the spilling over of flux to the end limb

occurs near the flux peak and also due to the fact that the ratio of reluctances of

these two paths varies due to non-linear properties of the core, fluxes in both main

yoke and end yoke/end limb paths are non-sinusoidal even though the main limb

flux is varying sinusoidally [2,4]. Extra losses occur in the yokes and end limbs

due to the flux harmonics. In order to compensate these extra losses, it is a normal

practice to keep the main yoke area 60% and end yoke/end limb area 50% of the

main limb area. The zero-sequence impedance is much higher for the three-phase

five-limb core than the three-limb core due to low reluctance path (of yokes and

end limbs) available to the in-phase zero-sequence fluxes, and its value is close to

but less than the positive-sequence impedance value. This is true if the applied

voltage during the zero-sequence test is small enough so that the yokes and end

limbs are not saturated. The aspects related to zero-sequence impedances for

various types of core construction are elaborated in Chapter 3. Figure 2.1 (f)

shows a typical 3-phase shell-type construction.

Copyright © 2004 by Marcel Dekker, Inc.