ALL-DAY EFFICIENCY

-> is defined as the ratio of the energy (kilowatt-hours) delivered by the transformer in a 24-hour period to the energy input in the same period of time.-> to determine the all-day efficiency, it is necessary to know how the load varies from hour to hour during the day.

Example:

The transformer of example 18 operates with the following loads during a 24-hr period: 1 ½ times rated kva, power factor = 0.8, 1hr; 1 ¼ times rated kva, power factor = 0.8, 2hr; rated kva, power factor = 0.9, 3hr; ½ rated kva, power factor = 1.0, 6hr; ¼ rated kva, power factor = 0.8; no-load, 4hr. Calculate the all-day efficiency.

Solution:

Energy output, kw-hr Energy losses, kw-hrW1 = 1.5 x 5 x 0.8 x = 6.0 (1 ½)2 x 0.112 x 1

= 0.252W2 = 1.25 x 0.8 x 2 = 10.0 (1 ½)2 x 0.112 x 2

= 0.350W3 = 1 x 5 x 0.9 x 3 = 13.5 1 x 0.112 x 3 = 0.336W6 = 0.5 x 5 x 1.0 x 6 = 15.0 (1/2)2 x 0.112 x 6

= 0.168W8 = 0.25 x 5 x 1.0 x 8 = 10.0 (1/4)2 x 0.112 x 8

= 0.056 ____

Total. . . . . . . . 54.5 Iron = 0.04 x 24 = 0.960 _____ Total. . . . . . . . .. . . . 2.122

All-day Efficiency = (1 – 2.122/54.5 + 2.122) x 100 = 96.25%

AUTOTRANSFORMERSIn principle and in general construction, the

autotransformer does not differ from the conventional two-winding transformer, but it differ from the way in which the primary and the secondary are interrelated. In conventional transformer, the primary and secondary windings are completely insulated from each other but are magnetically linked by a common core. In autotransformer, the two windings, primary and secondary, are both electrically and magnetically interconnected: a part of the single continuous winding is common to both primary and secondary.

Two ways in constructing Autotransformer:

1.] in one arrangement, there is a single continuous winding with taps brought out at a convenient points determined by the desired secondary voltages.2.] in other arrangement, there are two or more distinct coils which are electrically connected to form a continuous winding.

Autotransformers are cheaper than conventional two-winding transformers of similar rating. They also have a better regulation, and operate at a higher efficiencies. However, they are considered unsafe for use on ordinary distribution circuits because the high-voltage primary circuit is directly connected to the low-voltage secondary circuit.

They are frequently used in connection with the starting of certain types of ca motors, so that lower than line voltage is applied during the starting period.

INSTRUMENT TRANSFORMERInstrument transformers are used to measure

comparatively high values of current or voltage.

Two kinds of Instrument Transformers:1.] Current Transformer-> is used with an ammeter to measure the current in an ac circuit. -> in practice, it is connected to ordinary 5-amp ammeters

-> it has a primary coil of one or more turns of heavy wire, which is always connected in series in the circuit in which the current is to be measured.-> the secondary has many turns of comparatively fine wire, which must always be connected across the ammeter terminals.2.] Potential Transformers-> is used with a voltmeter to measure the potential difference, or voltage in an ac circuit.-> are generally employed with standard 150-volt voltmeters.

Clamp-on or Clip-on Ammeter-> a practical design of current transformer.-> has a laminated core so arranged that it may be opened out at a hinged section by pressing a trigger.-> when the core is opened, it permits the admission of the current-carrying conductor, whereupon the trigger is released and the core is closed tight by a spring. The current-carrying conductor acts as a single-turn primary, while the accurately wound secondary is permanently connected to the ammeter conveniently mounted in the handle.

Important Aspects of Current Transformer-> is that its secondary must never be permitted to be open-circuited because, unlike distribution and power transformers which are connected to constant-potential sources, the voltage across the primary winding varies over a wide range as the load changes.

Important Aspects of Potential Transformer-> Potential Transformer are carefully designed, extremely accurate-ratio step-down transformers. They are used with standard low-range voltmeters, the deflection of which , when multiplied by the ratio of transformation, gives the true voltage on the high side. They differ very little from the ordinary two-winding transformers, except that they handle a very small amount of power.

TRANSFORMER POLARITY Transformers are often connected in parallel to supply a common load, in much the same way as are alternators and dc generators for the same purpose. Two or three transformers are connected together so that they may be used in polyphase systems. It is necessary that the polarity of the transformers be known before the connections are made.

Polarity of a Transformers-> refers to the relative directions of the induced voltages in the primary and secondary windings with respect to the manner in which the terminal leads are brought out and marked. Standard notations are additive polarity and subtractive polarity.

PARALLEL OPERATION OF TRANSFORMERSSeveral important conditions must be fulfilled if two or more transformer are to operate successfully in parallel to deliver a common load.

These important conditions are:1.] the voltage ratings of both primaries and secondaries must be identical. This implies that the transformation ratios are the same.2.] the transformers must be properly connected with regard to polarity.3.] the equivalent impedances should be inversely proportional to the respective kilovolt-ampere ratings.4.] the ratio of the equivalent resistance to the equivalent reactance (Re:Xe) of all transformers should be the same.

*The parallel operation of two or more transformers requires that the primaries be joined to the same source and that the secondaries be connected to the same load.

No-load Operation

When the secondary load is removed, with switch S open, the primaries will still be energized and secondaries will still remain connected in parallel. Since the latter are in phase opposition with respect to each other, no current can circulate in these windings if the induced voltages are exactly equal; this condition can exist only if the ratio of transformation of the two transformers are exactly equal. If the transformer 1 has a ratio of transformation a1 which is different that of transformer 2, which has a ratio of transformation a2, the circulating current in the secondary Ic will be

Ic = (a1-a2)Vs / a1Ze1+a2Ze2

Where: Ze1 = equivalent impedance of transformer 1 in secondary terms

Ze2 = equivalent impedance of transformer 2 in secondary terms

Example 27: The following information is given in connection with two transformers that are connected in parallel:

Transformer 1 Transformer 2 rating = 25 kva rating = 35 kva2,360/230 volts 2,300/230 voltsZe = 0.08, in secondary terms Ze = 0.06, in secondary terms

Calculate the secondary circulating current at no load.

Solution:

a1 = 2,360/230 = 10.26 a2 = 2,300/230 = 10

Ic = (10.26 – 10) 230/ [(10.26 x 0.08) + (10 x 0.06)] = 59.8 / (0.821 + 0.6) = 42.1 A

Load Operation—Equal Ratios of Transformation

When two transformers having equal ratios of transformation are connected in parallel, the total load current will divide between them in inversely as their equivalent impedances.

Example:The following information is given for two transformers connected in parallel and delivering a total load of 300 kva:

Transformer 1 Transformer 2

Rating = 150 kva Rating = 250 kva6,900/230 volts 6,900/230 voltsZe = 9.4, in primary terms Ze = 5.8, in primary term

Calculate the load current and kilovolt-amperes delivered by each transformer.

Solution:

Total current IT = 300,00 / 6,900 = 43.5 amp

I1 / I2 = 5.8 / 9.4 I1 = (5.8 / 9.4) x I2

Also,IT = I1 + I243.5 = [(5.8 / 9.4) x I2] + I2 = 1.617 I2

I2 = 26.9 amp I1 = 43.5 – 26.9 = 16.6 amp

Therefore :kva1 = 6.9 x 16.6 = 114.4kva2 = 6.9 x 26.9 = 185.6

total = 300 kva

Load Operation—Unequal Ratios of TransformationWhen two transformers having unequal ratios of

transformation are connected in parallel, the total load current will drive in accordance with the following equations:

I1 = [(a2 – a1)Vs + (a2Ze2It)] / [(a1Ze1) + (a2Ze2)]

I2 = [(a1 – a2)Vs + (a1Ze1It)] / [(a1Ze1) + (a2Ze2)]

Example:The transformer of example 27 deliver a total load of 46 kva.

Calculate the secondary currents and the kilovolt-ampere load of each one.

Solution:a1 = 10.26 a2 = 10 Ze1 = 0.08 Ze2 = 0.06

It = 46,00 / 230 = 200 ampI1 = [(10-10.26)230 + (10 x 0.06 x 200)] / [(10.26 x 0.08) + (10 x 0.06)] = (-59.8 + 120) / 1.421 = 60.2 / 1.421 = 42.4I2 = [(10.26 – 10)230 + (10.26 x 0.08 x 200)] / [(10.26 x 0.08) + (10 x 0.06)] = (59.8 + 164) / 1.421 = 223.8 / 1.421 = 157.6

Kva1 = 42.4 x 0.23 = 9.75Kva2 = 157.6 x x0.23 = 36.25

Three- phase Transformer ConnectionsTransformers that must handle a considerable amount of

power are generally grouped together in banks for polyphase service. In three-phase systems, two or three identical transformers may be used in a bank for this purpose.

Four standard ways of connecting 3-phase transformer banks:1.] wye-wye2.] delta-delta3.] delta-wye4.] wye-delta

1.] WYE-WYE CONNECTIONS

If the ratio of transformation is a, the same ratio will exist between the line voltages on the primary and secondary sides. This connection will give satisfactory service only if the three-phase load is balanced. When the load is unbalanced, the electrical neutral will shift from its exact centre to a point that will make the three lone-to-neutral voltages unequal. The advantage of this system of connections is that the insulation is stressed only to the extent of the line-to-neutral voltage, which is 58% of the line-to-line voltage.

2.]DELTA-DELTA CONNECTION

This arrangement is generally used in systems in which the voltages are high and especially when continuity of service must be maintained even though one of the transformers should fail. When one of the transformers is removed from a delta-delta bank, operation continues on what is known as open delta. The ratio of transformation existing between primary and secondary line voltage will be exactly the same as that of each transformer.

3.] WYE-DELTA CONNECTION

This scheme of connection, is generally employed where it is necessary to step-up the voltage, for example, at the beginning of a high-tension transmission system. On the high sides of transformer, insulation is stressed only to the extent of 58% of the line-line voltage.

4.] WYE -DELTA CONNECTION

This connection is the reverse of the delta-wye connection. It is used principally where the voltage is to be stepped down. It is also employed in moderately low-voltage distribution circuits for stepping down from transmission voltages of 4,000 – 8,000 volts to 230 and 115 volts. The points made concerning delta-wye connections supply equally well here.

THE V-V CONNECTION

If one of the transformers of a delta-delta bank is removed and a three-phase source is connected to the primaries, three equal 3-phase voltages will be measured at the secondary terminals at no load. This method of transforming 3-phase power , using 2 transformers, is called open delta or V-V connection.

THE T-T CONNECTION

Another 2-transformer method that can be used to transform 3-phase power from one voltage to another is the T-T connection. It was first proposed by Charles F. Scott and is frequently called the Scott connection.

MAIN TRANSFORMER-must have at least

two primary and two secondary coils so that

a center tap may be brought out from each

other.

TEASER TRANSFORMER-must have primary and secondary windings the numbers of turns of w/c

are 86.6% of the respective turns of the

main transformer.

FIG. 212The kilovolt-ampere ratings of the

MAIN and TEASER TRANSFORMER will be exactly the same, even thought the voltage across the latter is only 886.6% of that across the former.

The reason for this is that kVA loads carried by the TWO HALVES of the MAIN TRANSFORMER are out of phase by 6O electrical degrees; the result is that when these are vectorially added, their sum equals the kVA load on the teasier transforrmer.

THREE-PHASE TRANSFORMER-more economical to use a three phase

transformer than, as previously discussed, a bank of three single

phase transformer.

Proper flux densities are maintained because the three phase currents are displaced 120 electrical

degrees w/ respect to each other.

TWO GENERAL ARRANGEMENT OF THE WINDINGS AND THE CORECORE TYPE, the three primary & secondary

windings surround a considerably part of the magnetic core. FIG. 214a

SHELL TYPE, the magnetic circuits surround a considerable portion of the 3 phase primary & secondary windings.

Advantage:The former transformer can be operated

in open DELTA should one of the windings be damaged;