What is an ideal transformer?Know about it's application,advantages and disadvantages of it

Introduction

Transformers play a vital role in electrical engineering by enabling efficient transmission and distribution of electrical power. The ideal transformer serves as a fundamental concept for understanding the principles of energy transfer. This post explores the ideal transformer’s characteristics, operation, applications, benefits, and the theoretical perfection it represents within electrical systems.

Diagram of an ideal transformer showing a core with primary and secondary coils. Blue arrows indicate magnetic flux. Labels detail currents and voltages.

Understanding the Ideal Transformer

The ideal transformer is a theoretical concept in electrical engineering that simplifies the analysis of transformer behavior. Real transformers have losses from factors like resistance, hysteresis, and eddy currents, but the ideal transformer is a mathematical abstraction with perfect efficiency and performance. Although ideal, it is a useful tool for understanding the basic principles of electrical energy transformation.

Working Principles of an ideal transformer

1.Faraday's Law

Faraday’s law states that changing the magnetic flux through a coil generates an electromotive force (EMF). In a transformer, alternating current (AC) flowing through the primary coil creates a varying magnetic flux, which induces a voltage in the secondary coil.

2.Conservation of Energy

The perfect transformer preserves energy without losses, with power in primary winding matching power in secondary winding, disregarding resistance and magnetic core losses.We will consider two cases,

when such a transformer is on no-load
when it is loaded

1.Transformer on No-load

The primary input current under no-load condition has to supplyiron-loss in the core i.e., hysteresis loss and eddy current loss
A very small amount of copper-loss in primary.

Hence the no-load primary input current `I_0` is not at 90° behind `V_1` but lags it by an angle `theta_0` which is less than 90°. No-load primary input power `W_0` = `V_1` `I_0` cos `theta_0`. Figure 1 shows the vector diagram of an actual transformer under no-load condition.

As seen from Fig. 1, primary current `I_0` has two components.1.One in phase with `V_1`. This is known as active or working or iron-loss component `I_w`, because it supplies the iron-loss plus a small quantity of primary Cu-loss.

`I_w` = `I_0` cos `theta_0`

The other component is in quadrature with `V_1` and is known as magnetizing component because its function is to sustain the alternating flux in the core. It is wattless.

`I_mu=I_0sinleft(theta_0right)`

Obviously `I_0` is the vector sum of `I_w` and `I_mu`, hence `I_0=sqrt{I_mu^2+I_w^2}`

The no-load primary current `I_0` is very small as compared to full load primary current. As `I_0` is very small, hence no-load primary copper-loss is negligibly small which means that no-load primary input is practically equal to the iron-loss in a transformer.

Diagram showing a right triangle in a coordinate system, with hypotenuse labeled I0, vertical leg labeled Iw, horizontal leg labeled Iμ, and angle θ.

Figure 1

2.Transformer on-load

When the secondary is loaded, secondary current `I_2` is set up. The magnitude of `I_2` is determined by the characteristic of the load. The secondary current sets up its own mmf (= `N_2` `I_2`) and hence its own flux `phi_2` which is in opposition to the main primary f, which is due to `I_0`. The opposing secondary flux `phi_2` weakens the primary flux momentarily and primary back emf `E_1` tends to reduce. For a moment `V_1` gains the upper hand over `E_1` and hence causes more current (`I'_2`) to flow in primary.

The current `I'_2` is known as load component of primary current.This current is in phase opposition to current `I_2`. The additional primary mmf `N_2``I'_2` sets up a flux `phi'_2` which opposes `phi_2` (but is in the same direction as f) and is equal to it in magnitude. Thus, the magnetic effects of secondary current `I_2` get neutralized immediately by additional primary current `I'_2`. The whole process is illustrated in Fig. 2. Hence, whatever may be the load conditions, the net flux passing through the core is approximately the same as at no-load.Due to this reason the core-loss is also practically the same under all load conditions.

Diagram of electrical circuits with transformers showing different current paths and loads. Each of the three diagrams features coils, cores, and labeled currents, illustrating various circuit configurations and electromagnetic principles.

Figure 2

As `phi_2`=`phi'_2`

∴`N_2I_2=N_1I'_2`

∴`I'_2=frac{N_2}{N_1}times I_2=KI_2`

Hence, when transformer is on load, the primary winding has two currents `I_0` and `I'_2` (which is antiphase with `I_2` and K times its magnitude). The total primary current is the vector sum of `I_0` and `I'_2`. Figure 3 shows the vector diagrams for a loaded transformer.In Fig. 3, current `I'_2` is in phase with `E_2` (for non-inductive loads).In Fig. 3, it is lagging behind `E_2` (for inductive loads).

$Diagram of three phasor plots illustrating voltage and current relationships. Each plot shows vectors labeled as $I_1$, $I_2'$, $I_0$, with angles $θ_0$, $θ_1$, $θ_2$. The graphs are meant to show variations in phasor angles and lengths.$

Figure 3

If we neglect `I_0` as compared to `I'_2` as shown in Fig. 2.5(c), then `phi_1` = `phi_2` and thus `N_1I'_2=N_1I_1=N_2I_2`

`frac{I_1}{I_2}=frac{N_2}{N_1}=K`

It shows that under load conditions, the ratio of primary and secondary currents is constant.

Applications of Ideal Transformers

Even if real transformers are as perfect as ideal ones, they are essential in how one highlights and designs practical electric systems.

Voltage Transformation

The exacting transformers are popular as a stepping up and stepping down device in power transmission and distribution systems worldwide. This actually gives more opportunity to transfer energy over large distances with the same efficiency.

Current Transformation

The power transformer provides a range of current levels to match the requirements of various electrical devices and systems.

Isolation

Transformers achieve electrical insolation between the primary and secondary windings bia isolated electrical connections and improved security in a variety of applications.

Impedance Matching

Transformers play the role of impedance matching in electronic circuits, enabling optimal power transfer.

Advantages of Ideal Transformers

Efficiency

An ideal unit operates at 100% efficiency, meaning it does not waste any energy flowing in or out. This makes it a very useful theoretical model for understanding transformers since, in theory, it eliminates concerns about energy losses.

Simplicity

Ideal transformers bring simplicity in calculations and analysis by the means of scattering resistances, core losses, and leakage inductance, and revolve around the main principle of energy conversion to and from.

Conservation of Energy

The ideal transformer therefore respects the principle of the conservation of energy, which is an important concept in the understanding of how energy flow occurs in electric systems.

Conclusion

Though purely theoretical, the perfect transformer plays a crucial role in shaping our understanding of energy conversion principles in electrical systems. It serves as a foundational reference for analyzing and designing practical transformers. While the perfect transformer exists only as an abstract mathematical model, its influence permeates electrical engineering, guiding engineers to develop efficient and reliable power systems that sustain modern society.

What is an ideal transformer?Know about it’s application,advantages and disadvantages of it