**Non-linear loads cause additional load losses in power transformers which must be compensated through the use of copper (with its higher conductivity), appropriate winding configurations and oversizing.**

Power transformers are frequently used to supply non-linear loads such as static rectifiers, variable speed drives and electronic power supplies. While the supply voltage is sinusoidal, the resulting currents are not and contain higher order harmonics in addition to the fundamental component. These harmonic currents cause additional load losses and thus additional heating with consequences for transformer design and construction.

**Main and additional load losses – theoretical background**

Resistive I2R losses, the main component of load losses, are easy to determine as these are dependent on the amplitude rather than the frequency of currents, and can therefore be arithmetically added together for all harmonics, to give the total main load losses.

However, the determination of additional load losses can be quite complex. The current distribution across the conductor cross-section is non-uniform, being more concentrated where the physical proximity to the other winding is greater, and is influenced by factors such as conductivity, frequency, geometry, distances between windings and reels, dimensions of spacers, etc. In essence, the effective conductor cross-section is reduced and its effective resistance is increased.

Other similar phenomena include losses due to current circulation among parallel sections, imperfect compensation of ampere turns, proximity and skin effects, radial and leakage fluxes etc. All of these make a theoretical determination of additional losses extremely challenging.

**Additional losses – experimental results**

Experiments have been conducted<ref> on pairs of transformers with different designs, geometries, winding configurations, insulations and conductor materials in order to determine and compare the respective additional load loss components with both sinusoidal and non-sinusoidal currents. There are three key takeaways from these experiments:

- Additional load losses are a substantial proportion (up to 20%) of total load losses and can therefore not be neglected.
- Additional load losses vary widely (up to 3 times) with design and construction between similarly sized transformers.
- Additional load losses increase disproportionately (up to 2.5 times) with non-sinusoidal currents.

**Consequences for design and construction**

Since additional load losses are influenced greatly by the transformer geometry, winding configurations, insulation and conductor materials, great attention needs to be paid to these during design, especially when the transformer is to feed non-linear loads. In particular, the current distribution is more uniform with copper conductors due to the higher conductivity. Finally, the transformer must be suitably over-dimensioned to cater for the additional heating caused by non-linear loads.

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**Reference**

*Losses due to poor PQ in Power Transformers, Angelo Baggini, University of Bergamo, Italy*

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