Transformer Efficiency and Applications - Learn

Transformer Efficiency and Applications – Learn

The Ideal transformer model makes two assumptions:

Flux linkage or flux transfer is perfect. This means that all of the flux in the primary coil also passes through the secondary coil.
The transformer is 100% efficient and no energy is lost.

In reality this is not the case, the secondary voltage and current will be less than predicted by the Ideal transformer equations and this also results in some power loss. This occurs due to three main reasons:

Incomplete flux linkage (or flux leakage): Some of the magnetic field generated by the primary coil is lost and does not entirely pass through the secondary coil.
Resistive heat production: The primary and secondary coils of transformers are made from copper wires. As a current passes through the wires they heat up, this results in energy (and power) being lost in both the primary and secondary coils.
Eddy currents in the iron core: The changing magnetic field passing through the iron core creates eddy currents.

Eddy Currents

Induced currents not only occur in coils and wires. They can also occur on larger conductors, like solid pieces or sheets of metal. When there is relative motion between a magnetic field and a larger conductor, the resulting induced current is a circular loop of current. These circular loops of current are called Eddy currents.

Eddy currents are also an application of Lenz’s Law. The magnetic fields set up by the eddy currents oppose the changes in flux that created it. The direction of the eddy current is determined using the right hand grip rule and applying Lenz’s Law:

Determine in which direction the original magnetic field is changing
The thumb points in the direction of the opposing field
Fingers wrap in the direction of the eddy current

In the example below a metal plate is moving from left to right through a magnetic field directed into the page. As it moves into the field from the left, the magnetic field is increasing into the page. This will induce an eddy current with a resulting field which opposes this, i.e. out of the page. Using the right hand grip rule with the thumb pointing out of the page, the fingers indicate the eddy current that forms will be anticlockwise in direction. The same process is used as the plate moves out of the field on the right – the field is increasing out of the page, induced field points into the page, right hand grip rule indicates the eddy current will be clockwise:

Reducing the Effects of Eddy Currents in Transformers

Eddy currents that are produced in the iron core of a transformer result in a significant amount of heat and energy loss. To reduce the effect of eddy currents, the iron core consists of a series of laminations which are insulated from each other and placed so that the laminations interfere with the eddy currents. This results in smaller eddy currents and less energy/heat loss.

Distribution of Energy Using High-Voltage Transmission Lines

Cities and towns require huge amounts of energy and power stations are often large distances away from the cities and regional centres that they provide electricity too. This creates a problem with power loss along the transmission lines. Transmission lines are very long conductors and even good conductors have a small resistance. Over such large distances the total resistance of these transmission lines can be significant and this results in large energy losses from station to consumer.

The efficient transmission of energy across the vast array of networks is a huge challenge for engineers, especially considering the large distances that transmission lines transport energy in this country. The power lost in a circuit is given by: $P=IV$ . Given that $V=IR$ , the power equation can also be written as: $P={ I }^{ 2 }R$ .

From this equation, it can be seen that transmitting power with a large current will result in larger energy losses. The challenge for engineers is to now transmit electricity at a low current for as far as is practically possible. This is mostly achieved using transformers. Recall that the power in the primary coil is equal to the power in the secondary coil. Also, recalling that: $P=IV$ , it can be seen that transmitting at a large voltage will result in a smaller current.

Power stations use a step-up transformer to increase the voltage near the source, and importantly, this results in a smaller current. As the transmission lines get closer to cities and towns, the voltage is decreased using a step-down transformer before eventually stepping down to 415V for industrial sites and 240V for residential areas. Importantly, given the equation: $P={ I }^{ 2 }R$ , decreasing the current by a factor of 2, results in a 4-fold decrease in energy loss!

Example:

A power station needs to transport 400MW of power to a nearby city along a transmission line with a total resistance of 2.0Ω. What would be the total power loss if the initial voltage was 250kV?

Answer:

using: $P=IV$ and making $I$ the subject: $I=\cfrac { P }{ V }$

$I=\cfrac { 400\times { 10 }^{ 6 } }{ 250\times { 10 }^{ 3 } }$

$I=1600\:A$

using: power loss, $P={ I }^{ 2 }R$ ,

$P={ 1600 }^{ 2 }\times 2$

$P={ 5.12\times 10 }^{ 6 }\:W$