electric machines i - philadelphia university...polarity of a transformer consider a 220/110v...

Electric Machines I Three Phase Transformers

1

Dr. Firas Obeidat

2

Table of contents

1 • Introduction

2 • Wye-Wye Connection

3 • Wye-Delta Connection

4 • Delta-Wye Connection

5 • Delta-Delta Connection

6 • Polarity of a Transformer

7

• Parallel Operation of Transformers

8 • Transformer Vector Group

Dr. Firas Obeidat Faculty of Engineering Philadelphia University

3 Dr. Firas Obeidat Faculty of Engineering Philadelphia University

Introduction

A three-phase power transformer is used at the

power generating station to step-up the voltage.

Whereas in the power distribution substation,

the three-phase voltage is again stepped down

through a three-phase distribution transformer.

A three-phase transformer can be made either

by three windings wound on a common core or

by three single-phase transformer connected

together in a three-phase bank.

The first approach is a cheaper one that results

in a transformer with smaller size and less

weight. The main disadvantage of the first

approach is that if one phase becomes defective,

then the whole transformer needs to be

replaced. Whereas in the second approach, if

one of the transformers becomes defective then

the system can be given power by an open delta

at a reduced capacity. In this case, the defective

transformer is normally replaced by a new one.


Introduction

The primary and secondary windings of the transformer may be connected

in either by wye (Y) or delta (Δ).

Three-phase transformer connections

Y-Y

(Wye-Wye)

Y-Δ

(Wye-Delta)

Δ-Y

(Delta-Wye)

Δ-Δ

(Delta-Delta)


Wye-Wye Connection

At the primary side, the phase voltage can be written as,

At the secondary side, the phase voltage can be written as,

The ratio of the primary

line voltage to the

secondary line voltage of

this connection is,


Wye-Wye Connection

The Y- Y connection has two very serious problems

1) If loads on the transformer circuit are unbalanced, then the voltages on

the phases of the transformer can become severely unbalanced.

2) Third-harmonic voltages can be large.

If a three-phase set of voltages is applied to a Y- Y transformer, the voltages

in any phase will be 120o apart from the voltages in any other phase.

However, the third-harmonic components of each of the three phases will be

in phase with each other. There are always some third-harmonic components

in a transformer because of the nonlinearity of the core, and these

components add up. The result is a very large third-harmonic component of

voltage on top of the 50-ar 60-Hz fundamental voltage. This third-harmonic

voltage can be larger than the fundamental voltage itself.

This type of connection of a three-phase transformer is rarely used for large

amount of power transmission.


Wye-Wye Connection

Unbalance problem and the third-harmonic problem can be solved by:

• Solidly ground the neutrals of the transformers, especially the primary winding's neutral. This connection permits the additive third-harmonic components to cause a current flow in the neutral instead of building up large voltages. The neutral also provides a return path for any current imbalances in the load.

• Add a third (tertiary) winding connected in Δ to the transformer bank. If a third Δ-connected winding is added to the transformer. then the third-harmonic components of voltage in the Δ will add up, causing a circulating current flow within the winding. This suppresses the third-harmonic components of voltage in the same manner as grounding the transformer neutrals. The Δ-connected tertiary windings need not even be brought out of the transformer case, but they often are used to supply lights and auxiliary power within the substation where it is located. The tertiary windings must be large enough to handle the circulating currents, so they are usually made about one-third the power rating of the two main windings.


Wye-Wye Connection

Advantages Disadvantages

Magnetizing current of transformer has 3rd harmonic component

The third harmonic present in the alternator voltage may appear on the secondary side. This causes distortion in the secondary phase voltages

If the load on the secondary side unbalanced then the shifting of neutral point is possible

Less dielectric strength in insulating materials

phase voltage is less

Cross section of winding is large i.e. stronger to bear stress during short circuit

Line current is equal to phase current

Requires less turns per winding ie cheaper

Phase voltage is 1/√3 times of line voltage


Wye-Delta Connection

The expression of the primary line voltage is

At the secondary side, the line voltage is

The ratio of primary phase voltage to secondary phase voltage is

The ratio of primary line voltage to secondary line voltage is

The primary phase current is

The turns ratio is



The expression of the secondary phase current is

The secondary line current is

This connection does have one problem; Because of the connection, the

secondary voltage is shifted 30° relative to the primary voltage of the

transformer. The fact that a phase shift has occurred can cause problems in

paralleling the secondaries of two transformer banks together. The phase

angles of transformer secondaries must be equal if they are to be paralleled,

which means that attention must be paid to the direction of the 30o phase

shift occurring in each transformer bank to be paralleled together.

The connection will cause the secondary voltage to be lagging if the system

phase sequence is abc. If the system phase sequence is acb, then the

connection will cause the secondary voltage to be leading the primary voltage

by 30o.


Delta-Wye Connection


The line voltage at the secondary side is


The phase current at the primary side is

For this connection, the turns ratio is

In this case, the secondary phase

current is



Delta-Wye Connection



Delta-Delta Connection


The line voltage at the secondary side is



The output capacity in delta-delta

connection can be expressed as

and

𝑆 = 3𝑉𝐿𝐼𝐿 = 3𝑉𝑝𝐼𝑝

𝑝 = 3𝑉𝐿𝐼𝐿𝑐𝑜𝑠θ = 3𝑉𝑝𝐼𝑝𝑐𝑜𝑠θ


Delta-Delta Connection



Three Phase Transformers

Primary winding Secondary winding




√3V

I

V

aI

V/a√3V/a

I

V√3V

√3aI

V/aaI

√3I

IV

aI

V/a√3V/a

√3I

IV

√3aI

V/aaI

The relations between three phase current/voltage and single phase current/voltage



Example: A three-phase transformer is connected to an 11 kV supply and

draws 6 A current. Determine

(i) line voltage at the secondary side,

(ii) the line current in the secondary coil.

Consider the turns ratio of the transformer is 11.

Also, consider delta-wye and wye-delta connections.

1- For delta-wye connection

𝐼𝑝1 =𝐼𝐿1

3=

6

3= 3.46 𝐴



2- For wye-delta connection

𝐼𝐿2 = 𝐼𝑝2 = 𝑎𝐼𝑝1 = 11 × 3.46 = 38 𝐴


Polarity of a Transformer

Polarity of a transformer is defined as the relative directions of induced

voltages between the high voltage and low voltage terminals.

The polarity of a transformer is very

important to construct three-phase

transformer bank, parallel connection of

transformer, connection of current

transformer (CT) and potential transformer

(PT) power with metering device.

Two polarities namely additive and

subtractive are used in the transformer.

A polarity of a transformer is said to be an

additive if the measured voltage between the

high voltage and the low voltage terminals is

greater than the supply voltage at the high

voltage terminals.

A polarity is said to be a subtractive if the

measured voltage between the high voltage

and the low voltage terminals is lower than the

supply voltage at the high voltage terminals. Subtractive polarity

Additive polarity


Polarity of a Transformer

Consider a 220/110V single-phase

transformer with the high voltage

and the low voltage terminals for

testing polarities. The high voltage

terminal H1 is connected to the low

voltage terminal X1 by a cable. The

voltmeter is connected between H2

and X2. In this case, the turns ratio

of the transformer is,

V1/V2=220/110=2.

A voltage of 110 V is applied to the

primary side. In this case, a voltage

of 55 V (110/2) will appear at the

secondary terminals. If the meter

read out the voltage of 165 V (110 +

55) then the transformer is said to

be in additive polarity.

If the voltmeter reads the voltage of

55V (110−55) then the transformer

is said to be in subtractive polarity.

Testing for additive polarity

Testing for subtractive polarity


Parallel Operation of Transformers

For supplying a load in excess of the rating

of an existing transformer, two or more

transformers may be connected in parallel

with the existing transformer.

The transformers are connected in

parallel when load on one of the

transformers is more than its capacity.

The reliability is increased with parallel

operation than to have single larger unit.

The cost associated with maintaining the

spares is less when two transformers are

connected in parallel.

It is usually economical to install another transformer in parallel instead of

replacing the existing transformer by a single larger unit. The cost of a spare

unit in the case of two parallel transformers (of equal rating) is also lower

than that of a single large transformer. In addition, it is preferable to have a

parallel transformer for the reason of reliability. With this at least half the

load can be supplied with one transformer out of service.




the parallel transformers may have very low impedance, which creates

the high short circuit currents

The bus ratings could be too high

The risk of circulating currents running from one transformer to

another Transformer

Increasing short-circuit currents that increase necessary breaker

capacity

Maximize electrical system flexibility

Maximize power system reliability

Maximize electrical system availability

Maximize electrical system efficiency



Condition for Parallel Operation of Transformer:

1- The voltage rating of both primaries and secondaries should be identical,

i.e. the transformers should have the same turn ratio.

If the transformers connected in parallel have slightly different voltage ratios, then due to the inequality of induced emfs in the secondary windings, a circulating current will flow in the loop formed by the secondary windings under the no-load condition, which may be much greater than the normal no-load current.

The current will be quite high as the leakage impedance is low. When the secondary windings are loaded, this circulating current will tend to produce unequal loading on the two transformers, and it may not be possible to take the full load from this group of two parallel transformers (one of the transformers may get overloaded).

A small voltage difference may cause sufficiently high circulating current causing unnecessary extra I2R loss.




2- The percentage impedances should be equal in magnitude and have same

X/R ratio in order to avoid circulating currents and operation in different

power factor.

If this condition is not satisfied then the impedance triangles are not

identical in shape and size, parallel operation will still be possible, but the

power factor at which the two transformers operate will be different (one

transformer will operate with higher power factor and the other with

lower power factor) from the power factor of the common load. In this

case the two transformers will not share the load in proportion to their

KVA ratings.




3- The polarity of the two transformers should be the same.

Polarity of transformer means the instantaneous direction of induced emf

in secondary. If the instantaneous directions of induced secondary emf in

two transformers are opposite to each other when same input power is fed

to the both of the transformers, the transformers are said to be in opposite

polarity.

The transformers should be properly connected with regard to their

polarity. If they are connected with incorrect polarities then the two emfs,

induced in the secondary windings which are in parallel, will act together

in the local secondary circuit and produce a short circuit.

Polarity of all transformers run in parallel should be same otherwise huge

circulating current flows in the transformer but no load will be fed from

these transformers.

If the instantaneous directions of induced secondary emf in two

transformers are same when same input power is fed to the both of the

transformers, the transformers are said to be in same polarity. Inside the

loop formed by the two secondaries the resulting voltage must be zero.




3- The polarity of the two transformers should be the same.

4- Phase sequences and phase angle shifts must be the same (for three-phase

transformer).

The transformer windings cab be connected in variety of ways which

produce different magnitudes and phase displacement of secondary voltages



Overall summary of different connection types of parallel transformers

Transformer

Parallel

Connection Types

Equal

Loading

Unequal

Loading

Overloading

Concerns

Circulating

Currents

Recommended

Connection

Equal impedances—

Equal ratios— Same kVA Yes No No No Yes

Equal impedances—

Equal ratios— Different

kVA

No Yes No No Yes

Unequal impedances—

Equal ratios— Same kVA No Yes Yes No No


Equal ratios— Different

kVA

No Yes Yes No No


Unequal ratios— Same

kVA

Yes No Yes Yes No


Unequal ratios—

Different kVA

No Yes Yes Yes No



Case I: Equal Impedances-Equal Ratios-Same kVA

𝐼 = 𝐼𝐴 + 𝐼𝐵

𝐼𝐴 =𝑍𝐵

𝑍𝐴 + 𝑍𝐵𝐼

𝐼𝐵 =𝑍𝐴

𝑍𝐴 + 𝑍𝐵𝐼

𝑉2 = 𝐸 − 𝐼𝐴 𝑍𝐴 = 𝐸 − 𝐼𝐵𝑍𝐵 = 𝐸 − 𝐼𝑍𝐴𝐵

𝐼𝐴 𝑍𝐴 = 𝐼𝐵𝑍𝐵

𝐼𝐴

𝐼𝐵=

𝑍𝐵

𝑍𝐴

Case II: Equal Impedances-Equal Ratios-Different kVA



Case I: Equal Impedances-Equal Ratios-Same kVA

𝐼𝐴 =𝐾𝑉𝐴𝐴/%𝑍𝐴

𝐾𝑉𝐴𝐴/%𝑍𝐴 +𝐾𝑉𝐴𝐵/%𝑍𝐵𝐼

𝐼𝐵 =𝐾𝑉𝐴𝐵/%𝑍𝐵

𝐾𝑉𝐴𝐴/%𝑍𝐴 +𝐾𝑉𝐴𝐵/%𝑍𝐵𝐼

𝐾𝑉𝐴𝐴 =𝐾𝑉𝐴𝐴/%𝑍𝐴

𝐾𝑉𝐴𝐴/%𝑍𝐴 +𝐾𝑉𝐴𝐵/%𝑍𝐵𝐾𝑉𝐴𝐿𝑜𝑎𝑑

𝐾𝑉𝐴𝐵 =𝐾𝑉𝐴𝐵/%𝑍𝐵


%𝑍𝑇 =𝑍𝑇𝐼𝑇

𝑉𝑇× 100 =

𝑍𝑇

𝑉𝑇2 𝑆𝑇 × 100

Where:

IA = load current from transformer A

IB = load current from transformer B

% ZA = % impedance of transformer A

% ZB = % impedance of transformer B

kVAA = kVA rating of transformer A

kVAB = kVA rating of transformer B

% ZT = % impedance of any transformer

IT = rated current of any transformer

VT = rated voltage of any transformer

ST = KVA rating of any transformer

Case II: Equal Impedances-Equal Ratios-Different kVA



Case III: Unequal Impedances-Equal Ratios-Same kVA

Case IV: Unequal Impedances-Equal Ratios-Different kVA

The equations for case III

and Case IV are the same

equations for case I and

case II.



Example: Connecting two 2000 kVA, 5.75% impedance transformers in

parallel, each with the same turn ratios to a 4000 kVA load. What is the

loading on the transformers?

𝐾𝑉𝐴𝐴 = 𝐾𝑉𝐴𝐵 =𝐾𝑉𝐴𝐴/%𝑍𝐴


𝐾𝑉𝐴𝐴 = 𝐾𝑉𝐴𝐵 =2000/5.75

2000/5.75+2000/5.75× 4000 =

348

348+348× 4000 = 2000 𝐾𝑉𝐴

Example: Connecting 3000 kVA and 1000 kVA transformers in parallel, each

with 5.75% impedance, each with the same turn ratios, connected to a

common 4000 kVA load. What is the loading on each transformer?



=3000/5.75

3000/5.75+1000/5.75× 4000 = 3000 𝐾𝑉𝐴





=1000/5.75

3000/5.75+1000/5.75× 4000 = 1000 𝐾𝑉𝐴

Example: Connecting two 2000 kVA transformers in parallel, one with 5.75%

impedance and the other with 4% impedance, each with the same turn ratios,

connected to a common 3500 kVA load. What is the loading on each

transformer?



=2000/5.75

2000/5.75+2000/4× 3500 = 1436 𝐾𝑉𝐴



=2000/4

2000/5.75+2000/4× 3500 = 2064 𝐾𝑉𝐴

The 4% impedance

transformer is overloaded

by 3.2%, while the 5.75%

impedance transformer is

loaded by 72%.



Example: Connecting two transformers in parallel with one 3000 kVA with

5.75% impedance, and the other a 1000 kVA with 4% impedance, each with

the same turn ratios, connected to a common 3500 kVA load. What is the

loading on each transformer?



=3000/5.75

2000/5.75+2000/4× 3500 = 2366 𝐾𝑉𝐴



=1000/4

2000/5.75+2000/4× 3500 = 1134 𝐾𝑉𝐴

The 4% impedance transformer is overloaded

by 13.4%, while the 5.75% impedance

transformer is loaded by 78.8%.


Transformer Vector Group

The primary and secondary windings of a three-phase transformer are

connected either in the same (delta-delta or star-star), or different (delta-

star or star-delta) configuration-pair.

The secondary voltage waveforms of a three-phase transformer are in

phase with the primary waveforms when the primary and secondary

windings are connected in the same configuration. This condition is known

as ‘no phase shift’ condition.

If the primary and secondary windings are connected in different

configuration pair then the secondary voltage waveforms will differ from

the corresponding primary voltage waveforms by 30 electrical degrees.

This condition is called a ‘30° phase shift’ condition.

The windings and their position to each other are usually marked by

vector group. The vector group is used to identify the phase shift between

the primary and secondary windings. In the vector group, the secondary

voltage may have the phase shift of 30° lagging or leading, 0° i.e., no phase

shift or 180° reversal with respect to the primary voltage.



The transformer vector group is

labeled by capital and small letters

plus numbers from 1 to 12 in a

typical clock-like diagram.

The capital letter indicates primary

winding and small letter represents

secondary winding.

In the clock diagram, the minute

hand represents the primary line to

neutral line voltage, and its place is

always in the 12. The hour hand

represents the secondary line to

neutral voltage and its position in

the clock changes based on the

phase shift


Vector Groups Used in the Three Phase Transformer Connection

Group I

0 o’clock, zero phase displacement

Yy0

Dd0

Dz0

Group II

6 o’clock, 180° phase displacement

Yy6

Dd6

Dz6

Group III

1 o’clock, -30° lag phase displacement

Dy1

Yd1

Yz1

Group IV

11 o’clock, 30° lead phase displacement

Dy11

Yd11

Yz11


electric machines i - philadelphia university...polarity of a transformer consider a 220/110v...

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