epmn301 lect5 fall2019 - scholar.cu.edu.eg 3. they are used to adjust the transformer output voltage...
TRANSCRIPT
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
Transformer: Special Transformers
1. Auto-transformers
The primary and secondary windings are electrically connected, so a part of the winding is common to both.
Transformer: Special Transformers
1. Auto-transformers
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
=+ +
Transformer: Special Transformers
1. Auto-transformers
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
=
Transformer: Special Transformers
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
Transformer: Special Transformers
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.
Transformer: Special Transformers
1. Auto-transformers
Transformer: Special Transformers
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.
Transformer: Special Transformers
2. Three-Winding transformers
Transformer: Special Transformers
2. Three-Winding transformers
Equivalent Circuit
Transformer: Special Transformers
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.
Transformer: Special Transformers
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.
Transformer: Special Transformers
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
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.
Transformer: Three-phase Transformers
Transformer: Three-phase Transformers
Transformer: Three-phase Transformers
Construction
Core Type
Transformer: Three-phase Transformers
Construction
Core Type
Transformer: Three-phase Transformers
Construction
Shell Type
Transformer: Three-phase Transformers
Connections 1
2
NnN
=
Transformer: Three-phase Transformers
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
= =
Transformer: Three-phase Transformers
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
= =
Transformer: Three-phase Transformers
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
Transformer: Three-phase Transformers
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=
+ +
Transformer: Three-phase Transformers
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.
Transformer: Three-phase Transformers
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-= =
Transformer: Three-phase Transformers
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=
Transformer: Three-phase Transformers
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 =
Transformer: Three-phase Transformers
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
Transformer: Three-phase Transformers
Solution: in p.u.
( )Load s L fS T fRV V I Z Z Z= - + +
0.97 . .LoadV p u=
233LoadLLV V=
240bLVV V=