EPMN301 Lect5 fall2019 - scholar.cu.edu.eg 3. They are used to adjust the transformer output voltage...

Transformer Introduction Construction Theory of Operation Ideal Transformer Transformer Rating Equivalent Circuit Per-Unit System Voltage Regulation Efficiency Tests No-Load Current and In-rush Current Special Transformers Three Phase Transformers Parallel Operation Practical Aspects for transformers

1

Transformer: Special Transformers

1. Auto-transformers2. Three-windings Transformers3. Instrumental Transformers


1. Auto-transformers

The primary and secondary windings are electrically connected, so a part of the winding is common to both.



1 2

2

. V Vtrans ratioV+

=

1 1 2 1 1 2

1 2 1 2

( / ).( / )

V V N N N Ntrans ratioV N N N+ +

= =

1 2

1 2 1 2

I NI I N N

=+ +



2 1 2( )LS V I I= +

12 1 1

2

( ( ))LNS V I IN

= +

11 2 2

2

( ( ))LNS I V VN

= +1 1 2( )L inS I V V S= + =

1 1 2 1AutoS V I V I= + 2 1 2 2AutoS V I V I= +

1(1 )Auto convS Sn

= +1 1 1 1 2 1( / )AutoS V I V I N N= +1

2

NnN

=


1. Auto-transformersAdvantages of Auto Transformer:1. Same losses , but higher KVA output, so higher

efficiency. 2. Uses single winding so its lesser in size and weight.3. Lower exciting current.4. Better voltage regulation. (lower Zeq)Disadvantages of Auto Transformer:1. Higher short circuit current. (lower Zeq)2. No isolation exists between the primary and secondary

windings


1. Auto-transformersApplications of Auto transformers1. They are generally used to connect transmission lines of slightly

different voltages ( e.g., 115 kV and 138 kV or 138 kV and 161 kV)2. They are employed to compensate for voltage drops on long feeder

circuits where it is important that each load device receives the same voltage ( e.g., on airfield lighting circuits to ensure uniform lamp intensity)

3. They are used to adjust the transformer output voltage in order to keep the system voltage constant with varying load. (variable auto-transformer)

4. They offer variable voltage control in the laboratory setup: as we move the sliding contact, virtually all of the coil can become the series coil. Therefore, the entire coil must be sized for maximum current.




2. Three-Winding transformers

Sometimes in high rating transformer, a third winding is constructed in addition to the primary and the secondary windings. The third winding is called the tertiary winding, and because of the three windings, the transformer is called a three winding transformer.The voltage of the tertiary winding differs than the primary and secondary winding.





Equivalent Circuit


2. Three-Winding transformersApplications:1. It is used for supplying the power to the auxiliary

appliances like the fan, tube light, etc. of the substations and auxiliary systems in power stations.

2. Can be used for interconnecting transmission lines which are working at different voltage and power levels .

3. Static or synchronous condensers may be connected to tertiary windings for reactivate power injection into the system for voltage control.


3. Instrumental Transformers

a. Potential (Voltage) Transformers: (PT/VT)It’s a step-down transformer used with measuring equipment. The secondary rated voltage level istypically 120 V.


3. Instrumental Transformers

b. Current Transformers: (CT)The current transformer is a step-up transformer, with the current carrying conductor acting as primary and the secondary winding wound around it. The secondary rated current level is typically 5 A.

Transformer: Three-phase Transformers


Most power transformers are three-phase transformers. Three-phase transformers can be constructed either as a

single three limbs three-phase transformer or a three-phase bank of three identical single-phase transformers.

Three-phase transformer banks has the advantage that each unit can be replaced independently in case of damage, but they are more expensive and bigger in size.

Three phase single unit transformers are cheaper (by about 15%), lighter and smaller in size.

Core type construction is more common in single-unit three-phase transformers.




Construction

Core Type


Construction

Core Type


Construction

Shell Type


Connections 1

2

NnN

=


General Rules for three-phase transformers 1. All given voltages and currents are line values.2. Powers (S,P or Q) given are 3-phase values.

3. All given impedance values are per-phase values.4. The equivalent circuit are the per-phase line-to-neutral

equivalent circuit. (i.e. in order to use it you have to convert delta to star)

5. Number of turns or turns ratios are phase values.

3 3FL L LS V I V If f= =

11

2 2

VNnN V

f

f

= =


General Rules for three-phase transformers 5. Transformation ratio =6. When referring line values from one side to another use

the transformation ratio, for phase values use the turns ratio.

7. Per-unit values are independent of the connections. (since we are working with per-phase line to neutral eq. ct.)

1

2

L

L

VV

2L

bb

VZS

=

(3 )b FLS S f-= 1 1b LV V= 2 2b LV V=

1 113

bb FL

b

SI IV

= = 2 223

bb FL

b

SI IV

= =


General Rules for three-phase transformers

8. The shunt branch in the equivalent circuit is usually neglected since most 3-phase transformer ratings are above 100 kVA.

Per-phase line-to-neutral Eq. Ct. ref. to the primary side


Voltage Regulation & Efficiency

Using the per-unit formulas are more convenient .

2cos( ) 100eq pu sckZe q f= ´

2

22

cos1cos eqpuc pu

k

k k RR

fh

f=

+ +


Example: Three single-phase, 50-kVA 2400/240-V transformers, are connected Y-∆ in a three-phase 150-kVA bank to step down the voltage at the load end of a feeder whose impedance is 0.15 + j 1.00 Ω/phase. The voltage at the sending end of the feeder is 4160 V line-to-line. On their secondary sides, the transformers supply a balanced three-phase load through a feeder whose impedance is 0.0005 + j0.0020 Ω/phase. The transformer impedance referred to the high voltage side is 1.42+j1.82 Ω/phase.Find the line-to-line voltage at the load when the load draws rated current from the transformers at a power factor of 0.80 lagging.


Example:

3*1-phase-transformersEach 50 kVA, 2400/240

ZeqHV = 1.42+j1.82(per-phase values)

Y/∆Three-phase bank

150 kVA, 2400*√3/240(line-to-line values)

0.15+j1.0 0.0005+j0.002

Load

Supply 4160 V

(line-to-line)

ZfSZfR

IFL (transformer)at 0.8 lag

(3 )1

1

20.8A3FL

FLLL

SI

Vf-= = (3 )

22

360.843FL

FLLL

SI A

Vf-= =


Solution: Referred to HV side (star connected)2

1_

2

LLfR HV fR

LL

VZ ZV

æ ö÷ç ÷= ç ÷ç ÷çè ø1 20.8AFLI =

4160 24003sLnV V= =

Per-phase line-to-neutral Eq. Ct.

Trans. ratio

_ 0.15 0.6fR HVZ j= +

'_( )Load s L fS T fR HVV V I Z Z Z= - + + ' 2329LoadV = 233LoadLLV V=


Solution: Referred to LV side (delta connected)2

2_L

1

LLfS V fS

LL

VZ ZV

æ ö÷ç ÷= ç ÷ç ÷çè ø' 240 138.6

3sLnV V= = Trans. ratio

'_( )

LVLoad s L fS LV T star fRV V I Z Z Z= - + + 134LoadV V= 233LoadLLV V=

2 360.84FLI A=

2

2

1LV HVT T

VZ Z

Vf

f

æ ö÷ç ÷ç= ÷ç ÷÷çè ø

Turns ratio 3

LV

LV

T DeltaT Star

ZZ =


Solution: in p.u.2 2

3(3 )

4160 115.4150 10

HVLLbHV

b

VZS f-

æ ö÷ç ÷ç= = = W÷ç ÷÷ç ´è ø

1 .sV p u= 1 .I p u=

2 2

3(3 )

240 0.384150 10

LVLLbLV

b

VZS xf-

æ ö÷ç ÷ç= = = W÷ç ÷÷çè ø

_ .0.0005 0.002 0.0013 .0052

0.384fR p ujZ j+

= = +

_ .0.15 1 0.0013 0.0087

115.4fS p ujZ j+

= = +

.1.42 1.82 0.012 0.016

115.4THV

Tp ubHV

ZZ j jZ

= = ++

=

./ 3 0.0047 0.006 0.012 0.016

0.384TLV

Tp ubLV

Z jZ jZ

+= = = +OR


Solution: in p.u.

( )Load s L fS T fRV V I Z Z Z= - + +

0.97 . .LoadV p u=

233LoadLLV V=

240bLVV V=

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EPMN301 Lect5 fall2019 - scholar.cu.edu.eg 3. They are used to adjust the transformer output voltage...

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