Transformer Losses

Zack Swafford
November 26, 2016

Submitted as coursework for PH240, Stanford University, Fall 2016


Fig. 1: A simple diagram of a transformer. (Source: Wikimedia Commons)

Transformers are electrical devices that transfer energy, typically between two AC circuits of different voltages. This is useful and important in many applications, but particularly in the context of large-scale power grids it is relevant because it is most efficient to transmit energy long distances from the source at a high voltage, but typical applications (such as household consumption) require a much more modest one. [1]

At its heart, the operation of a transformer is quite simple. Two coils (typically labelled primary and secondary) are wound around a conductor. As variable current passes through the central conductor, magnetic fields appear and change. The varying magnetic field in the conductor creates something of the opposite effect in the secondary coil, inducing an electromotive force in that coil. In this manner, a different voltage is in the second coil, and the voltage has been transformed. [1,2] This entire process is illustrated in Fig. 1.


In an ideal world, a transformer could be used to change voltages perfectly without diminishing overall power. The energy of the primary coil would be completely transferred to the secondary one. In this case, we could simply apply Faraday's law of induction twice to see that the ratio of the primary and secondary voltages VP and VS is proportional to the ratio of the numbers NP and and NS of coils in the primary and secondary windings. If Φ is the magnetic flux through the circuit, then

VP = - NP (
) VS = - NS (
) VP
= - NP
- NS
= NP

Further, because the power would be perfectly conserved, the ratio of the voltages would be inversely proportional to the ratio of the currents.

In reality, ideal operation is impossible because there are some losses which are inevitable. These losses are roughly divided into two categories: load losses and core (or no-load) losses. Load losses are so-called because they vary with respect to the load on the transformer; no-load losses do not.

1. Load Losses

The simplest loss is the generic Joule (or heat) loss due to resistance in the wires that all electrics are susceptible to. With a higher current and higher resistance in the wires, the loss increases, as it does with any electric circuit. [3] Specifically, this loss is proportional to the current squared times the resistance. [1]

2. Core Losses

The primary kinds of core losses, which do not vary with respect to the load, are hysteresis and eddy current losses. Hysteresis losses are due to the varying magnetic field through the core. As the magnetization of the core changes, the magnetic domains change their orientation (specifically, they reverse every half cycle and return to their original orientation every full cycle). As the magnetic domains shift, they occasionally encounter some resistance, creating heat and diminishing the overall energy. This loss is linear with respect to the frequency of the current because it is based on how often these magnetic domains must shift. [1]

Eddy currents appear in any nontrivial electromagnetic application and are essentially small magnetic fields which are artifacts of imperfections of the circuit and run perpendicular to the axis of the primary magnetic field. [3] The energy of such currents is, in this case, dissipated as heat in the core's material. Because they grow with respect to the magnetic field, they are based on the square of the applied voltage to the transformer. [3,4]

Some other core losses are sometimes enumerated, but they are an almost irrelevant fraction of the overall loss.

3. Leakage Flux

Magnetic flux which only passes through one of the two coils, and "leaks" is another artifact of an imperfect transformer. Ideally, such an effect is nonexistent, but with imperfections in the windings sometimes the flux is not maintained within the coils. In this case, power is not actually lost, as it is commonly perceived - instead, the leakage flux is simply stored and discharged in a more erratic way as the voltage of the transformer varies, resulting in a less regular output voltage. [4]

This unideal voltage regulation is usually not preferred and steps are taken to minimize it. However, in applications where the load voltage is very irregular (and particularly if the load is prone to short-circuit) this leakage flux can be used to mitigate and dampen the effect of the circuit.


Because transformers are so critical to energy infrastructure it is potentially beneficial to know more about them and their losses, and how such losses can be minimized. Because they are so ubiquitous, small improvements to transformers can make a large difference in energy consumption. [5,6] They are usually regulated by national governments, in fact, to ensure minimal losses.

With some small adaptations, transformers can also be used for applications other than voltage changing. For instance, wireless chargers usually function in much the same way as transformers. They do not have a central core, which is less optimal but by the same principle the charging coil creates a magnetic field which induces a current in the receiving coil. In this way, power can be transferred without physical contact, or at least without more complex wiring and connections. [7]

© Zack Swafford. The author grants permission to copy, distribute and display this work in unaltered form, with attribution to the author, for noncommercial purposes only. All other rights, including commercial rights, are reserved to the author.


[1] W. T. McLyman, Transformer and Inductor Design Handbook, 4th Ed. (CRC press, 2016).

[2] R. Petkov, "Optimum Design of a High-Power, High-Frequency Transformer," IEEE Trans. Power Electr. 11, 33 (1996).

[3] P. L. Dowell, "Effects of Eddy Currents in Transformer Windings," Pr. Inst. Electr. Elect. 113, 1387 (2010).

[4] W. G. Hurley, W. H. Wolfle, and J. G. Breslin, "Optimized Transformer Design: Inclusive of High-Frequency Effects," IEEE Trans. Power Electr. 13, 651 (1998).

[5] H. De Keulenaer, D. Chapman, and S. Fassbinder, "The Scope For Energy Saving in the EU Rhrough the Use of Energy-Efficient Electricity Distribution Transformers," IEEE 943006, 18 Jun 01.

[6] A. E. Farrell, H. Zerriffi, and H. Dowlatabadi, "Energy Infrastructure and Security," Annu. Rev. Environ. Resour. 29, 421 (2004).

[7] S.-Y. Hui, "Inductive Battery Charger System With Primary Transformer Windings Formed in a Multi-Layer Structure," U.S. Patent No. 7,164,255, 16 Jan 07.