TRANSFORMERS

TRANSFORMERS

A transformer is a device that changes ac electric power at one voltage level to ac

electric power at another volt age level through the action of a magnetic field. It

consists of two or more coils of wire wrapped around a common ferromagnetic

core. These coils are (usually) not directly connected. The only connection between the coils is the common magnetic flux present within the core.

One of the transformer windings is connected to a source of ac electric

power, and the second (and perhaps third) transformer winding supplies electric

power to loads. the transformer winding connected to the power source is called

the primary winding or input winding, and the winding connected to the loads is

called the secondary winding or output winding. I f there is a third winding on the

transformer, it is called the tertiary winding.

WHY TRANSFORMERS ARE

IMPORTANT TO MODERN LIFE

The first power distribution system in the United States was a 120-V dc system invented by Thomas A. Edison to supply power for incandescent light bulbs. Edison's first central power station went into operation in New York City in September 1882. Unfortunately, his power system generated and transmitted power at such low voltages that very large currents were necessary to supply significant

amounts of power. These high currents caused huge voltage drops and power

losses in the transmission lines, severely restricting the service area of a generating

station. In the 1880s, central power stations were located every few city blocks

to overcome this problem. The fact that power could not be transmitted far with

low-voltage dc power systems meant that generating stations had to be small and

localized and so were relatively inefficient.

The invention of the transformer and the concurrent development of ac

power sources eliminated forever these restrictions on the range and power level

of power systems. A transformer ideally changes one ac voltage level to another

voltage level without affecting the actual power supplied. If a transformer steps up

the voltage level of a circuit, it must decrease the current to keep the power into

the device equal to the power out of it. therefore, ac electric power can be generated

at one central location, its voltage stepped up for transmission over long distances

at very low losses, and its voltage stepped down again for final use. Since

the transmission losses in the lines of a power system are proportional to the

square of the current in the lines, raising the transmission voltage and reducing the

resulting transmission currents by a factor of 10 with transformers reduces power

transmission losses by a factor of 100.Without the transformer, it would simply

not be possible to use electric power in many of the ways it is used today.

In a modern power system, electric power is generated at voltages of 12 to

25 kV. Transformers step up the voltage to between 110 kV and nearly 1000 kV for

transmission over long distances at very low losses. Transformers then step down

the voltage to the 12- to 34.5-kV range for local distribution and finally permit the

power to be used safely in homes, offices, and factories at voltages as low as 120 V.

TYPES AND CONSTRUCTION

OF TRANSFORMERS

The principal purpose of a transformer is to convert ac power at one voltage level

to ac power of the same frequency at another voltage level. Transformers are also used for a variety of other purposes (e.g., voltage sampling, current sampling, and

impedance transformation), but this subject  is primarily devoted to the power

transformer.

Power transformers are constructed on one of two types of cores. One type

of construction consists of a simple rectangular laminated piece of steel with the

transformer windings wrapped around two sides of the rectangle. This type of

construction is known as core form and is illustrated in Figure 2. The other type

consists of a three-legged laminated core with the windings wrapped around the

center leg. this type of construction is known as shell form and is illustrated in

Figure 3. In either case, the core is constructed of thin laminations electrically

isolated from each other in order to minimize eddy currents.

The primary and secondary windings in a physical transformer are wrapped

one on top of the other with the low-voltage winding innermost. Such an arrangement serves two purposes:

1 . It simplifies the problem of insulating the high-voltage winding from the core.

2. It results in much less leakage flux than would be the case if the two windings were separated by a distance on the core. Power transformers are given a variety of different names, depending on their use in power systems. A transformer connected to the output of a generator and used to step its voltage up to transmission levels ( 110+ kV) is sometimes called a unit transformer. The transformer at the other end of the transmission line, which steps the voltage down from transmission levels to distribution levels (from 2.3 to 34.5 kV), is called a substation transformer. Finally, the transformer that takes the distribution voltage and steps it down to the final voltage at which the power is actually used (110, 208, 220 V, etc.) is called a distribution transformer. All these devices are essentially the same- the only difference among them is their intended use.

In addition to the various power transformers, two special-purpose transformers

are used with electric machinery and power systems. The first of these

special transformers is a device specially designed to sample a high voltage and

produce a low secondary voltage directly proportional to it. Such a transformer is

called a potential transformer. A power transformer also produces a secondary

voltage directly proportional to its primary voltage; the difference between a potential transformer and a power transformer is that the potential transformer is designed to handle only a very small current. The second type of special transformer

is a device designed to provide a secondary current much smaller than but directly

proportional to its primary current. This device is called a current transformer.

Both special-purpose transformers are discussed in a later section of this subject.

THE IDEAL TRANSFORMER

An ideal transformer is a lossless device with an input winding and an output

winding. The relationships between the input voltage and the output voltage, and

betwccn the input current and the output current , are give n by two simple equations.

Figure 4 shows an ideal transformer.

The transformer shown in Figure 4 has Np turns of wire on its primary

side and Ns turns of wire on its secondary side. the relationship between the voltage vp(t) applied to the primary side of the transformer and the voltage vs(t) produced

on the secondary side is

 

where a is defined to be the turns ratio of the transformer:

the relationship between the current i_p(t) flowing into the primary side of the transformer and the current is(t) flowing out of the secondary side of the transformer is

Notice that the phase angle of Vp is the same as the angle of Vs and the phase angle

of  I_p is the same as the phase angle of I_s. The turns ratio of the ideal transformer

affects the magnitudes of the voltages and currents, but not their angles.

Five above equations describe the relationships between the magnitudes

and angles of the voltages and currents on the primary and secondary sides of the

transformer, but they leave one question unanswered: Given that the primary circuit

's voltage is positive at a specific end of the coil, what would the polarity of

the secondary circuit's voltage be? In real transformers, it would be possible to tell

the secondary 's polarity only if the transformer were opened and its windings examined.

To avoid this necessity, transformers utilize the dot convention. The dots

appearing at one end of each winding in Figure 4 tell the polarity of the voltage

and current on the secondary side of the transformer. The relationship is as

follows:

1. If the primary voltage is positive at the dotted end of the winding with respect

to the undotted end, then the secondary voltage will be positive at the dotted

end also. Voltage polarities are the same with respect to the dots on each side

of the core.

2. If the primary current of the transformer flows into the dotted end of the primary

winding, the secondary current will flow out of the dotted end of the secondary winding.

Power in an Ideal Transformer

The power supplied to the transformer by the primary circuit is given by the

equation

 where Ɵp is the angle between the primary voltage and the primary current. The

power supplied by the transformer secondary circuit to its loads is given by the

equation 

 where Ɵ_s is the angle between the secondary voltage and the secondary current.

Since voltage and current angles are unaffected by an ideal transformer,Ɵp - Ɵs =Ɵ.

The primary and secondary windings of an ideal transformer have the same power

factor.

How does the power going into the primary circuit of the ideal transformer

compare to the power coming out of the other side? it is possible to find out

through a simple application of the voltage and current equations.

 the power out of a transformer is

 Applying the turns-ratio equations gives Vs = Vp /a and Is = aIp, so

 Thus, the output power of an ideal transformer is equal to its input power.

The same relationship applies to reactive power Q and apparent power S:

 and

What assumptions are required to convert a real transformer into the ideal

transformer described previously? they are as follows:

I. the core must have no hysteresis or eddy current s.

3. The leakage flux in the core must be zero, implying that all the flux in the

core couples both windings.

4. the resistance of the transformer windings must be zero.

While these conditions are never exactly met, well-designed power transformers

can come quite close.

THE AUTOTRANSFORMER

On some occasions it is desirable to change voltage levels by only a small amount.

for example, it may be necessary to increase a voltage from 110 to 120 V or from

13.2 to 13.8 kV these small rises may be made necessary by voltage drops that

occur in power systems a long way from the generators. In such circumstances, it

is wasteful and excessively expensive to wind a transformer with two full windings,

each rated at about the same voltage. A special-purpose transformer, called

an autotransformer. Is used instead A diagram of a step-up autotransformer is shown in Figure 32. In Figure 32a, the two coils of the transformer are shown in the conventional manner. In Figure 32b, the first winding is shown connected in an additive manner to the second winding. Now, the relationship between the voltage on the first winding and the voltage on the second winding is given by the turns ratio of the transformer.

However, the voltage at the output of the whole transformer is the sum of

the voltage on the first winding and the voltage on the second winding. The first

winding here is called the common winding, because its voltage appears on both

sides of the transformer. The smaller winding is called the series winding, because

it is connected in series with the common winding.

A diagram of a step-down autotransformer is shown in Figure 33. Here

the voltage at the input is the sum of the voltages on the series winding and the

common winding, while the voltage at the output is just the voltage on the common

winding.

Because the transformer coils are physically connected, a different terminology

is used for the autotransformer than for other types of transformers. The

voltage on the common coil is called the common voltage Vc , and the current in

that coil is called the common current [c]. The voltage on the series coil is called

the series voltage VSE, and the current in that coil is called the series current IsE.

The voltage and current on the low-voltage side of the transformer are called VL

and IL , respectively, while the corresponding quantities on the high-voltage side

of the transformer are called VH and IH . The primary side of the autotransformer

(the side with power into it) can be either the high-voltage side or the low-voltage

side, depending on whether the autotransformer is acting as a step-down or a stepup

transformer. From Figure 32b the voltages and currents in the coils are related

by the equations

 

 

THREE-PHASE TRANSFORMERS

Almost all the major power generation and distribution systems in the world today

are three-phase ac systems. Since three-phase systems play such an important role

in modern life, it is necessary to understand how transformers are used in them.

Transformers for three-phase circuits can be constructed in one of two

ways. One approach is simply to take three single-phase transformers and connect

them in a three-phase bank. An alternative approach is to make a three-phase

transformer consisting of three sets of windings wrapped on a common core.

These two possible types of transformer construction are shown in Figures 36

and 37. The construction of a sing le three-phase transformer is the preferred

practice today, since it is lighter, smaller, cheaper, and slightly more efficient. The

older construction approach was to use three separate transformers. That approach

had the advantage that each unit in the bank could be replaced individually in the

event of trouble, but that does not outweigh the ad vantages of a combined threephase unit for most applications . However, there are still a great many installations consisting of three single-phase units in service.

A discussion of three-phase circuits is included in Appendix A. Some readers

may wish to refer to it before studying the following material.

Three-Phase Transformer Connections

A three-phase transformer consists of three transformers, either separate or combined on one core. The primaries and secondaries of any three-phase transformer can be independently connected in either a wye (Y) or a delta (d ). This gives a total of four possible connections for a three-phase transformer bank:

1. Wye-wye (Y-Y)

2. Wye-delta (Y -∆)

3. delta-wye (∆-Y)

4. delta-delta (∆-∆)

these connections are shown in Figure 38.

the key to analyzing any three-phase transformer bank is to look at a single

transformer in the bank. Any single transformer in the bank behaves exactly like

the single-phase transformers already studied. the impedance, voltage regulation,

efficiency, and similar calculations for three-phase transformers are done on

a per-phase basis, using exactly the same techniques already developed for

single-phase transformers.

the advantages and disadvantages of each type of three-phase transformer

connection are discussed below.