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2-0

PowerPoint Slides to accompany

Electr ic Machinery Sixth Edition

A.E. Fitzgerald

Char les Kingsley, Jr.Stephen D. Umans

Chapter 2

Transformers

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2-1

Transformer with open secondary.

Figure 2.4

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2-2

No-load phasor diagram.

Figure 2.5

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2-3

Ideal transformer and load.

Figure 2.6

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2-4

Three circuits which are identical atterminals ab when the transformeris ideal.

Figure 2.7

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2-5

Equivalent circuits for Example 2.2 (a) Impedancein series with the secondary. (b) Impedance referredto the primary.

Figure 2.8

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2-6

Schematic view of mutualand leakage fluxes in atransformer.

Figure 2.9

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2-7

Steps in thedevelopmentof the

transformerequivalentcircuit.

Figure 2.10

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2-8

Equivalent circuits for transformer of Example 2.3referred to (a) the high-voltage side and (b) thelow-voltage side.

Figure 2.11

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2-9

Approximate transformer equivalent circuits.

Figure 2.12

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2-10

Cantilever equivalent circuit for Example 2.4.

Figure 2.13

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2-11

No-Load Test (or Open-Circuit Test)

Short-Circuit Test

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2-12

Example:

Test are performed on a 1Ø, 10kVA, 2200/220V, 60Hz transformer and the following resultsare obtained for Open-Circuit:

Open-Circuit Test(high-voltage side open)

Short-Circuit Test(low-voltage side shorted)

Voltmeter 220 V 150V

Ammeter 2.5A 4.55A

Wattmeter 100W 215W

The ratings of the windings are as follows:

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2-13

a) Derive the parameters for the approximate equivalent circuits referred to the low-voltageside and the high-voltage side.

Open-Circuit Test (high-voltage side open)

Voltmeter Ammeter Wattmeter 220 V 2.5A 100W

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2-14

Short-Circuit Test (low-voltage shorted)

Voltmeter Ammeter Wattmeter

150 V 4.55A 215W

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2-15

b) Express the excitation current as a percentage of the rated current

This is (2.5/45.5) x 100% = 5.5% of the rated current of the winding

c) Determine the power factor for the no-load and short-circuit tests.

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2-16

Voltage Regulation


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2-17

Voltage Regulation – Example

Determine the voltage regulation in percent for the following load conditions.

a) 75% full load, 0.6 power factor lagging

1Ø, 10kVA, 2200/220V, 60Hz


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2-18

b) 75% full load, 0.6 power factor leading


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2-19

Autotransformer.

Example:

A 1Ø, 100kVA, 2000/200V two-winding transformer is connectedas an autotransformer as shown in Figure, such that more than2000V is obtained at the secondary. The portion ab is the 200Vwinding, and the portion bc is the 2000V winding. Compute thekVA rating as an autotransformer.

A 1Ø, 100kVA, connected as an autotransformer can deliver 1100 kVA. Also note that the 200V winding must havesufficient insulation to withstand a voltage of 2200V toground.


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2-20

Three-Phase Transformers

A set of three similar single-phase transformers may be connected to form a three-phasetransformer. The primary and secondary windings may be connected in either wye (Y) ordelta ( Δ). There are therefore four possible connections:

Y- Δ: This connection is commonly used to step down a high voltage to a lower voltage.

Δ-Y: This connection is commonly used to step up voltage.

Δ- Δ: This connection has the advantage that one transformer can be removed for repairand the ramaining two can continue to deliver three-phase power at a reduced rating of58% of that of he original bank. This is known as the open-delta or V connection.

Y-Y: This connection is rarely used because of problems with the exciting current andinduced voltages.


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py g p , q p p y

2-21

Common three-phase transformer connections; thetransformer windings are indicated by the heavy lines.

Figure 2.19


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py g p , q p p y

2-22

Three-Phase Transformers – Phase Shift

Consider the phasor voltages, shown in Fig. 2.18, for the Y- Δ connections. The phasoresV

AN

and Va

are aligned, but the line voltage V AB

of the primary leads the line voltage Vab

of the secondary by 30°. It can be shown that Δ-Y connection also provides a 30° phase shiftbetween line-to-line voltages, whereas Δ- Δ and Y-Y connections have no phase shift in their line-to-line voltages.


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Three-Phase Transformers – Single Phase Equivalent Circuit

The voltages and currents in one phase are the same as those in other phases (for balanced load), except that there is a phase displacement of 120°. Therefore, analysis of one phase is sufficient to determine the variables on the two sides of the transformer.

A single phase equivalent circuit can be conveniently obtained if all sources, transformer windings, and loas impedances are considered to be Y-connected.


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2-24


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2-25

Three-Phase Transformers – Single Phase Equivalent Circuit

Example:

Three 1Ø, 50kVA, 2300/230V, 60Hz transformers are connected to form a 3Ø, 4000/230Vtransformer bank. The equivalent impedance of each transformer referred to low voltage is0.012+j0.016Ω. The 3Ø transformer supplies a 3Ø, 120kVA, 230V, 0.85 PF (lag) load.

a) Draw a schematic diagram sowing the transformer connection

b) Determine the transformer windwing currents.

c) Determine the primary voltage (line-to-line) required.

d) Determine the voltage regulation.

a) Schematic diagram sowing the transformer connection


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2-26

b)

c)

d)


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2-27

PER-UNIT (PU) System

Example:

The exciting current of a Ø, 10kVA, 2100/210V, 60Hz transformers is 0.25A when measuredon the high-voltage side. Its equivalent impedance is 10.4+j31.3Ω when referred to thehigh-voltage side. Taking the transformer rating as base,

a) Determine the base values of voltages, currents, and impedances for both high-voltageand low-voltage sides.

b) Express the exciting current in per-unit form for both sides.

c) Obtain the equivalent circuit in per-unit form.


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a)

b)

c)

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