Transcript Introduction to Technical Mathematics

07 - Transformers
07 - Transformers
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The intent of this presentation is to present enough information to provide the reader with a
fundamental knowledge of transformers used within Michelin and to better understand basic
system and equipment operations.
07 - Transformers
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07 - Transformers
Single Phase Transformers
Ideal Transformer Characteristics
The basic transformer consists of two coils electrically insulated from each other and wound upon a
common core. Magnetic coupling is used to transfer electric energy from one coil to another. The coil,
which receives energy from the AC source, is called the primary. The coil, which delivers energy to the
AC load, is called the secondary. The core of transformers used at low frequencies is generally made
of magnetic material, usually sheet steel. Cores of transformers used at higher frequencies are made of
powdered iron and ceramics, or nonmagnetic materials. Some coils are simply wound on nonmagnetic
hollow forms such as cardboard or plastic so that the core material is actually air.
RL
07 - Transformers
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07 - Transformers
Single Phase Transformers
If a transformer is assumed to be operating under an ideal or perfect condition, the transfer of energy
from one voltage to another is accompanied by no losses.
Voltage Relationship
The voltage (V) on the coils of a transformer is directly proportional to the number (N) of turns on the
coils. This voltage relationship is expressed by the formula:
Where:
Vpri = voltage on primary coil, V
Vsec = voltage on secondary coil, V
Npri = number of turns on primary coil
Nsec = number of turns on secondary coil
RL
Vpri / Vsec = Npri / Nsec
07 - Transformers
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07 - Transformers
Single Phase Transformers
Step-up and Step-down transformers
A voltage ratio of 1:4 (read as 1 to 4) means that for each volt on the transformer primary, there is 4 volts
on the secondary. When the secondary voltage is greater than the primary voltage, the transformer is a
step-up transformer. A voltage ratio of 4:1 means that for every 4 volts on the primary, there is only 1
volt on the secondary. When the secondary voltage is less than the primary voltage, the transformer is
called a step-down transformer. The voltage relationship discussed previously will apply to both step-up
and step-down transformers.
Current Relationship
The current (I) in the coils of a transformer is inversely proportional to the voltage (V) on the coils. This
current relationship is expressed by the formula:
Where:
Vpri = voltage on primary coil, V
Vsec = voltage on secondary coil, V
Ipri = current in the primary coil, A
Isec = current in the secondary coil, A
07 - Transformers
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V pri
I
= sec
V sec
I pri
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07 - Transformers
Single Phase Transformers
Efficiency
The efficiency of a transformer is equal to the ratio of the power output of the secondary winding to
power input of the primary winding. An ideal transformer is 100% efficient because it delivers all the
energy it receives. Because of core and copper losses, the efficiency of even the best practical
transformer is less than 100%. Efficiency expressed as an equation is:
Where:
Eff = efficiency
Psec = power output from the secondary coil, W
Ppri = power input to the primary coil, W
Eff =
07 - Transformers
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output power
P
= sec
input power
P pri
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07 - Transformers
Single Phase Transformers
Transformer Power Ratings
Transformer capacity is rated in kilo-volt-amperes (KVA). This transformer rating is sometimes
represented by the letter S. Since power in an AC circuit depends on the power factor of the load and
the current in the load, an output rating in kilowatts must specify the power factor.
For an ideal transformer we would assume efficiency to be 100%. Since our calculations will deal with
ideal transformers, we can state the following relationships:
Where:
VApri = power input to the primary coil, VA
VAsec = power output from the secondary coil, VA
Vpri = primary voltage
Ipri = primary current
Vsec = secondary voltage
Isec = secondary current
07 - Transformers
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VA pri = V pri  I pri
VAsec = V sec  I sec
VA pri = VAsec
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07 - Transformers
Single Phase Transformers
Dual Voltage Primary Wiring Diagram
Low Voltage Connection
240v
240v
240v
H1
X1
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H3
60v
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H2
H4
60v
X2
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07 - Transformers
Single Phase Transformers
High Voltage Connection
480v
240v
240v
H1
X1
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H3
H2
60v
H4
60v
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X2
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07 - Transformers
Single Phase Transformers
Single Phase Transformer Calculations
I
I sec
pri
Vpri
Vsec
Npri
Given:
Npri = 1500 turns
Nsec = 1000 turns
Vpri = 100 V
Find:
Vsec =
07 - Transformers
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Solution:
Nsec
Npri / Nsec = Vpri / Vsec
1500 / 1000 = 100 / x
X = 66.67 Volts
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07 - Transformers
Single Phase Transformers
Single Phase Transformer Calculations
I
I sec
pri
Vpri
Vsec
Npri
Given:
Find:
Npri = 4000 turns
Nsec = 400 turns
Isec = 6 A
Ipri =
What is the turn’s ratio?
07 - Transformers
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Nsec
Solution:
Npri / Nsec = turns ratio
4000 / 40 = 10
Np / Ns = Is / Ip
4000 / 400 = 6 / x
x = 0.6 A
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07 - Transformers
Single Phase Transformer Calculations
I
I sec
pri
Vpri
Vsec
Npri
Given:
Find:
Vpri = 300 V
Vsec = 24 V
Isec = 1 A
Npri = 1000 turns
Nsec =
Given:
VApri = 100
Vpri = 460 V
Vsec = 110 V
Find:
Ipri =
Isec =
Ipri =
Solution: Nsec = 80; Ipri = 0.08 A
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Nsec
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Solution: Ipri = 0.217 A; Isec = 0.909 A
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07 - Transformers
Single Phase Transformers
Single Phase Transformer Calculations
IPri
ISec
VPri
NPri
Given:
Find:
Npri = 1000 turns
Nsec= 500 turns
Vpri = 200 volts
Vsec
Solution: Vsec = 100 V
07 - Transformers
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RL
VSec
NSec
Given:
Npri = 5000 turns
Nsec= 500 turns
Isec = 5 amps
Find:
Ipri
Solution: Ipri = 0.5 A
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07 - Transformers
Single Phase Transformers
Single Phase Transformer Calculations
IPri
ISec
VPri
VSec
NPri
Given:
Find:
Npri = 1000 turns
Vpri = 200 volts
Vsec= 24 volts
Isec = 2 amps
Nsec
Ipri
07 - Transformers
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RL
NSec
Given:
Find:
Vsec = 110 volts
Ssec =1100 VA
Nsec = 55 turns
Vpri = 200 volts
Isec; Ipri; Npri; Spri
Ratio of the transformer
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07 - Transformers
Single Phase Transformers
Single Phase Transformer Calculations
IPri
ISec
VPri
VSec
NPri
Given:
Find:
RL
NSec
Vpri = 200 volts
Ipri = 5 amps
Npri= 1000 turns
Nsec = 200 turns
Vsec
Isec
07 - Transformers
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07 - Transformers
Transformer Nameplate Data
Introduction
The data found on a typical transformer nameplate is shown below. Note that the transformer capacity is
rated in KVA and not KW. The load connected to the secondary windings will determine the power
factor, and thus, the apparent power for the output circuit of the transformer. Further, the KVA rating
represents the full load output of the transformer and not the input. The other data on the nameplate
usually includes the voltage rating of the high and low voltage windings, the frequency, number of
phases, percent impedance, polarity, maximum temperature rise and the gallons of transformer oil
required, if oil filled.
Control Transformer
Below is an example of a control transformer utilizing a dual voltage primary windings and a single
voltage secondary winding. The primary voltage should be either 240 volts or 480 volts. The primary
windings must be connected in parallel for 240 volts and connected in series for 480 volts. The
secondary should always produce 24 volts.
07 - Transformers
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07 - Transformers
Transformer Nameplate Data
The power rating is 0.1 kVA or 100VA.
Below is an example of a control transformer utilizing a multi-tap primary winding and a single voltage
secondary winding. The primary voltage could be a variety of voltages ranging from 208 volts up to 480
volts. The primary windings must be connected according to the correct voltage applied to the primary
winding. The secondary should always produce 24 volts.
07 - Transformers
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07 - Transformers
Troubleshooting Single Phase Transformers
The transformer below is a single phase control transformer connected for high voltage on the primary
(480volts) and 120 volts on the secondary. To troubleshoot the transformer with an ohm-meter you
should check the ohmic value for the primary and then the ohmic value for the secondary. You must
make sure that the wires connecting the primary and secondary windings are not connected to any other
device that would cause a reading through them. The ohmic valve will depend on the size of the
transformer. The reading will usually be a low ohmic value which should show continuity through the
windings.
H1
H3
H2
H4
480v/120v
X1
07 - Transformers
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X2
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07 - Transformers
Troubleshooting Single Phase Transformers
The transformer below is a single phase power transformer connected for high voltage on the primary
(480volts) and 240 volts on the secondary. To troubleshoot the transformer with an ohm-meter you
should check the ohmic value for the primary and then the ohmic value for the secondary. You must
make sure that the wires connecting the primary and secondary windings are not connected to any other
device that would cause a reading through them. The ohmic value will depend on the size of the
transformer. The reading will usually be a low ohmic value which should show continuity through the
windings.
H1
H2
480v/240v
X1
07 - Transformers
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X2
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