Chapter 2
TransformersPart I
1
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproducBon or display.
Small Step up/down Transformers
hEp://www.mohawkelectro.com/images/transformer_family.jpg
2
A Simplified Power System
hEp://en.wikibooks.org/wiki/Electronics/Transformers
3
112MVA, 220/36kV Power
Transformer
hEp://www.meppi.com/Products/Transformers/Power/Pages/CoreformTransformers.aspx
4
Pole Mounted Transformers
•
•
•
•
Liquid filled, 1 or 3 phase
Small (eg 25kVA)
Different levels of protecBon, as
required (e.g., fuse cutout, surge
arrester, circuit breakers)
Typically the protecBon is
aEached to the outside of the
transformer
Source: http://www.freefoto.com/preview/13-20-72/Electricity-Transformer-mounted-on-a-Utility-Pole
5
Pad Mounted Transformers
•
•
•
Used for underground
distribution
Liquid filled or dry-type, 1
or 3 phase
Medium sized (eg 225kVA)
Source: http://www.zeppaenterprises.com/electric/2000amptrans.jpg
6
Network Transformers
•
•
•
Located in vaults,
supplies power to
secondary networks or
spot networks
Liquid filled, 3 phase
Large (300-2500kVA)
Source: hEp://www.howard-ind.com/howardtransformers/ Images/Network%20Transformer%20%28Vault%20Type%20Crop%.jpg
7
Cutaway view of liquid-immersed
construcBon transformer
•
The conservator (reservoir) at
top provides liquid-toatmosphere isolation as coolant
level and temperature changes.
•
The walls and fins provide
required heat dissipation
balance.
8
Core and shell types
9
LaminaBng the core greatly reduces
eddy-current losses
10
Single Phase MagneBc Model
11
Ideal Transformer
• The relative permeability of the core is very high
• No Leakage Flux, hence Leakage Flux of the two
windings are neglected.
• Ideal windings has no resistances.
• Ideal core has no reluctance.
• Core losses are neglected.
12
• From Farady’s Law
• Since there is no magneBc potenBal drop in
the ideal core,
NsI p (t )= NsIs (t )
I p (t ) Ns 1
=
=
Is (t ) N p a
13
14
Dot Convention
• The “dots” help to determine the polarity of the voltage
and direction of the current in the secondary winding.
• If the primary voltage is positive at the dotted end of the
winding with respect to the undotted end, then the
secondary voltage will be positive at the dotted end also.
• If the primary current of the transformer flows into the
dotted end of the primary winding, the secondary current
will flow out of the dotted end of the secondary winding.
15
Impedance Transformation Through an Ideal Transformer
• The load impedance ZL is given by
Vs
ZL =
Is
• The apparent impedance of the primary circuit is
• Z’L is the load impedance “referred” or “reflected” to the
primary side.
16
Theory of Operation of Non-Ideal Single-Phase
Transformers
In a real transformer, the following non-ideal facts must be
considered:
•Copper Losses in primary and secondary windings: these
are modeled as series resistors Rp and Rs for the primary
and secondary windings, respectively.
•Small portion of the core flux leaks outside the core and
passes through one winding only. This flux will be
presented by a leakage inductance. Both primary and
secondary coils generate leakage flux which are modeled
as series inductances Xp and Xs in the primary and
secondary windings, respectively.
17
• Core Losses which are due to heating losses produced
by Eddy Current and Hysteresis Losses in the core.
These losses are presented by a shunt resistor RC in the
primary winding.
• Magnetizing Current which flows in the primary current to
establish the flux in the core. This is modeled as a shunt
inductance Xm in the primary winding.
The equivalent circuit for a single-phase non-ideal
transformer is shown below:
18
• The equivalent circuit may be simplified by reflecting
impedances, voltages, and currents from the secondary
to the primary as shown below:
• Below is the transformer model referred to Secondary
Side.
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
19
• Simplified equivalent circuit referred to primary side:
• Simplified equivalent circuit referred to secondary side:
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
20