Even though the methods for calculating electrical machines develop constantly and have actually reached quite far, there is still one topic where we electrical engineers really continue to struggle: the fundamental frequency stator iron losses. Perhaps one reason why these losses have been overlooked during the times is that they can be easily and accurately measured, or at least so everyone thinks, and so the standards say. In reality, measuring these losses can be surprisingly difficult, especially with high-speed machines. Another reason may be that in general purpose induction motors the iron losses are rather small. However, in some other machine types, especially when the frequency increases, they become significant.

The first problem with iron losses is the lack of understanding on the phenomena. Perhaps the best explanation is according to Bertotti [1] that there are three loss components: hysteresis loss, eddy current loss, and excess loss. In more details, the academic world describes them as: the losses caused by magnetising the iron, the losses caused by the currents that circle the flux path, and something else that seems to be observable. Everyone can agree with the first two, but regarding the last component the academic world continues to argue. A typical way to define the excess losses is to take the measured total losses and to subtract the calculated hysteresis and eddy current losses. In theory this would work, but unfortunately now all the measurement and calculation errors together with manufacturing non-linearities all go into the excess losses. And further, elements in hysteresis and eddy current losses that the traditional equations do not cover, such as minor hysteresis loops, also fall into the excess loss category. Hence, it is no wonder that this loss component is difficult to explain. Many text books on electrical machines, for example [2 and 3], do not even recognise the excess loss term.

Traditionally the iron losses are calculated as specific losses of the steel [W/kg], multiplied by the weight of the iron stack and by empirical coefficient that takes the manufacturing effects into account. The specific loss is usually given in the steel datasheet for 1.5 T and 50 Hz. This value is then adjusted to the real flux density and frequency. The traditional approach is probably the most accurate, but it also has some pitfalls.

One issue is the definition on how the stator is magnetised. For the stator yoke region, the specific loss is adjusted for the maximum flux density in the yoke, but the weight is given for the entire yoke. At a certain time instant perhaps one third of the stator yoke is magnetised with the given flux density and the rest with less or none, but still the entire yoke is considered for the weight. The principle is the same for the stator teeth as well. Depending on the tooth geometry, the valid flux density may not always be the very highest, but it is anyway defined for the tooth having the highest flux, while the weight is defined as all teeth put together. If only the hysteresis losses are considered, this is probably correct, since the behaviour is sinusoidal and the loss calculation is based on the peak value. But is it correct with the eddy currents? On the other hand, when the losses are calculated with FEM, only the actual flux densities at the given time instant are used. So, the sinusoidal effect of hysteresis losses is not considered. This seems conflicting.

Another problem is the frequency adjustment for the specific loss. Hysteresis losses depend directly on frequency, but eddy current losses depend on the square of frequency. They are both included in the specific loss, so how to adjust the frequency? Calculation by vt-tek uses an adjustment (*f* / 50 Hz)^{1.5}. For example, Boldea [2] recommends an exponent of 1.3. Based on more accurate data on electrical steels, we can say that these both can be valid. It only depends on the flux density, on the steel grade, and on the discussed frequency range. However, for instance in a high-speed induction machine this difference easily covers 20% of the total iron losses. In a big picture, this could mean some tenths of a percent in the machine efficiency, and perhaps 10 – 20 degrees Celsius in the machine outer surface temperature. So, the difference is significant.

The empirical coefficients in the iron loss equation refer to defects, non-linearities and so on caused by the manufacturing. The empirical coefficients in literature are normally between 1.5 – 2.0 and they vary depending on the machine type and location (teeth or yoke). So, their effect is huge. The stator manufacturing raises many questions. The academic world has lately woken up to this issue, and some answers can be already found in publications. However, the following general questions remain still valid.

Let us begin from the first step in making the stator stack: what is the difference between the sheet cutting method: stamping vs. laser-cutting? They probably cause different kind of deformation to the edges of the steel and insulation layer on the sheet. Then, what is the effect of the fixing method at the back of the stack: old-school arc welding vs. modern laser-welding? And what is the effect when the sheets are joined with other means, such as by glueing the back of the stack? Presumably, the iron losses will reduce, because with glue, there should not be any short-circuits at the back. Another puzzle is related to the thickness of lamination. Obviously, it has an influence on the specific loss, but does it also affect the empirical coefficient? Basically, it should, since smaller sheet thickness means larger number of sheets, and hence more cutting edges and more possible short-circuits in the stack.

After the stator is finished, it is often shrink-fitted into the machine frame. The question is: does the hard shrink short-circuit the laminates? Further, in high-voltage machines the very first component of the insulation system that goes into the stator slots is called “conductive layer”. Its purpose is to reduce partial discharges by levelling the potential difference between the laminates. In other words, to short-circuit them. Even though called “conductive” the material is actually much more resistive than metals. But does it still affect to the iron losses? And finally, if something goes wrong in the winding and the stator is re-wound, the first procedure is to burn the old coils out. How much does this affect to the iron losses? Some motor manufacturers say it affects significantly when done in some coil-winding workshop, and hence such a procedure should be banned. But then they claim that it has virtually no effect when performed in their own workshop.

The analytical calculation on the iron losses considers the no-load case. The flux densities are defined based on ideal magnetic circuit and the losses are calculated for fundamental frequency. However, the measurements consider the “iron losses” as all the measured losses except stator no-load copper losses and mechanical losses. So, the winding harmonics and slotting harmonics are included, together with measurement errors and all additional losses that appear in no-load. On the other hand, if the iron losses are based on FEM calculation, it is usually carried out at full-load conditions. At full load the main flux enters the airgap with diagonal path causing the tooth tips in stator and rotor to see very high flux densities, and also to experience much higher losses. Since this is a fundamental frequency effect, the FEM collects these losses, and therefore produces losses that do not correlate with the no-load case.

So, if the iron losses obtained from analytical calculation, FEM calculation, and measurements all match, something must have gone wrong. In principle, the FEM calculation alone will never be able to deliver the correct iron losses. The manufacturing effect will always remain empirical, and the FEM cannot tackle it. The user has to correct the results by some empirical factor.

As seen above, there are many conflicts and open questions regarding the iron loss calculation. In any case, empirical information is vital in getting them correct. If the frequency greatly differs from 50 Hz, it is recommended to try to get the specific loss data of the given steel at the given frequency. At the test stand as much information as possible should be collected, instead of just having someone to run some routine tests. Regarding the iron losses, every machine is different. The machine type, size, geometry, frequency, and even manufacturer all have influence. Finally, the correct iron losses are not found in books or academic publications. It is very much up to the engineers themselves to get them right.

**References:**

1 Bertotti, G., “General Properties of Power Losses in Soft Ferromagnetic Materials”, *IEEE Transactions on Magnetics*, Vol. 24, No. 1, January 1988.

2 Boldea, I., *Synchronous Generators*, CRC Press, Boca Raton, FL, USA, 2006.

3 Pyrhönen, J., Jokinen, T., Hrabovcová, V., *Design of Rotating Electrical Machines*, 2^{nd} ed., Joh Wiley \& Sons, Ltd, 2014.