Title: Raising & Lowering Transformer Voltages (Including Testing)
Course: WGF 107 DEVELOPMENT > Section: Content

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The assumptions to characterize the ideal transformer are:

- The windings of the transformer have no resistance. Thus, there is no copper loss in the winding, and hence no voltage drop.
- Flux is confined within the magnetic core. Therefore, it is the same flux that links the input and output windings.
- Permeability of the core is infinitely high which implies that net mmf (amp-turns) must be zero (otherwise there would be infinite flux) hence I_P N_P - I_S N_S = 0.
- The transformer core does not suffer magnetic hysteresis or eddy currents, which cause inductive loss.

If the secondary winding of an ideal transformer has no load, no current flows in the primary winding.

The circuit diagram (below) shows the conventions used for an ideal, i.e. lossless and perfectly coupled transformer having primary and secondary windings with N_P and N_S turns, respectively.

Operation of a transformer at its designed voltage but at a higher frequency than intended will lead to reduced magnetizing current. At a lower frequency, the magnetizing current will increase. Operation of a transformer at other than its design frequency may require assessment of voltages, losses, and cooling to establish if safe operation is practical. For example, transformers may need to be equipped with 'volts per hertz' over-excitation relays to protect the transformer from overvoltage at higher than rated frequency.

One example of state-of-the-art design is traction transformers used for electric multiple unit and high-speed train service operating across the country border and using different electrical standards, such transformers' being restricted to be positioned below the passenger compartment. The power supply to, and converter equipment being supply by, such traction transformers have to accommodate different input frequencies and voltage (ranging from as high as 50 Hz down to 16.7 Hz and rated up to 25 kV) while being suitable for multiple AC asynchronous motor and DC converters & motors with varying harmonics mitigation filtering requirements.

Large power transformers are vulnerable to insulation failure due to transient voltages with high-frequency components, such as caused in switching or by lightning.^[31]
Image | Ideal transformer with a source and a load. N_P and N_S are the number of turns in the primary and secondary windings respectively.
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Energy losses[edit]

A theoretical (ideal) transformer does not experience energy losses, i.e. it is 100% efficient. The power dissipated by its load would be equal to the power supplied by its primary source. In contrast, a real transformer is typically 95 to 99% efficient, due to several loss mechanisms, including winding resistance, winding capacitance, leakage flux, core losses, and hysteresis loss. Larger transformers are generally more efficient than small units, and those rated for electricity distribution usually perform better than 98%.^[32]

Experimental transformers using superconducting windings achieve efficiencies of 99.85%.^[33] The increase in efficiency can save considerable energy in a large heavily loaded transformer; the trade-off is in the additional initial and running cost of the superconducting design.

As transformer losses vary with load, it is often useful to express these losses in terms of no-load loss, full-load loss, half-load loss, and so on. Hysteresis and Eddy current losses are constant at all load levels and dominate overwhelmingly without load, while variable winding joule losses dominating increasingly as load increases. The no-load loss can be significant, so that even an idle transformer constitutes a drain on the electrical supply. Designing energy efficient transformers for lower loss requires a larger core, good-quality silicon steel, or even amorphous steel for the core and thicker wire, increasing initial cost. The choice of construction represents a trade-off between initial cost and operating cost.^[34]

Transformer losses arise from:

Winding joule losses

Current flowing through winding conductors causes joule heating. As frequency increases, skin effect and proximity effect causes winding resistance and, hence, losses to increase.

Core losses

Hysteresis losses

Each time the magnetic field is reversed, a small amount of energy is lost due to hysteresis within the core. According to Steinmetz's formula, the heat energy due to hysteresis is given by

, and,

hysteresis loss is thus given by

where, f is the frequency, η is the hysteresis coefficient and β_max is the maximum flux density, the empirical exponent of which varies from about 1.4 to 1 .8 but is often given as 1.6 for iron.^[34]^[35]^[36]

Eddy current losses

Ferromagnetic materials are also good conductors and a core made from such a material also constitutes a single short-circuited turn throughout its entire length. Eddy currents therefore circulate within the core in a plane normal to the flux, and are responsible for resistive heating of the core material. The eddy current loss is a complex function of the square of supply frequency and inverse square of the material thickness.^[34] Eddy current losses can be reduced by making the core of a stack of plates electrically insulated from each other, rather than a solid block; all transformers operating at low frequencies use laminated or similar cores.

Magnetostriction related transformer hum

Magnetic flux in a ferromagnetic material, such as the core, causes it to physically expand and contract slightly with each cycle of the magnetic field, an effect known as magnetostriction, the frictional energy of which produces an audible noise known as mains hum or transformer hum.^[4]^[37] This transformer hum is especially objectionable in transformers supplied at power frequencies^[h] and in high-frequency flyback transformers associated with PAL system CRTs.

Stray losses

Leakage inductance is by itself largely lossless, since energy supplied to its magnetic fields is returned to the supply with the next half-cycle. However, any leakage flux that intercepts nearby conductive materials such as the transformer's support structure will give rise to eddy currents and be converted to heat.^[38] There are also radiative losses due to the oscillating magnetic field but these are usually small.

Mechanical vibration and audible noise transmission

In addition to magnetostriction, the alternating magnetic field causes fluctuating forces between the primary and secondary windings. This energy incites vibration transmission in interconnected metalwork, thus amplifying audible transformer hum.^[39]
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