It is very difficult to briefly answer the question of choosing the switching frequency. In General, the situation is as follows: any component of the power supply has parasitic characteristics. With increasing frequency, their influence on the operation of the circuit increases. The higher the frequency, the more critical the choice of components and the more attention you need to pay to the layout of the Converter. Increasing the switching frequency allows to reduce the size of the Converter, but requires a higher qualification from the designer.

Dear Andrii,

Thanks for replying.

Yes this is true in practice. However, is there a mathematical trade-off can be done for selecting the frequency of the power supply in an optimum range?

A few decades ago, such a question simply did not arise.

The conversion frequency was selected as high as possible

according to the capabilities of the power switching components.

Since in any case it was tens of hertz - tens of kilohertz.

And the criterion was very simple: "take the most modern transistor

and use it as much as possible" (Very simplified !!!).

Today we can use switching elements at frequencies in megahertz.

And here the inductances of the transformer leads may already be decisive.

How to express it purely mathematically? In my opinion,

a pure model is impossible or extremely complex.

Too many factors to consider when analyzing.

How can this be done? Narrow down the decision area.

Obviously, the criteria for the power converter of the processor

and the welding machine will be different.

Perfect.

Dear Hamzeh,

i think one criteria not mentionend is also EMI requirements (or did you mean this with power quality?), at least in industrial practice. E.g. some standards require the measurement of conducted emissions starting at 150kHz. Therefore the switching frequency is often limited to below this value or to below half of this value. In this case the fundamental of the switiching waveform has not to be measured to comply with the standard. There are several ICs for PWM controllers operating at typ. 60 - 70 kHz for this reason.

Dear Burkhard,

Thank for your reply.

Yes, EMI filter is also a part of design and its duty is different from power quality. So, EMI probably imposes limitations on the switching frequency.

My understanding from your comment is that upper bound of switching frequency is limited by EMI regulations. While, EMI filter is a low-pass filter and can strongly washout higher frequencies. In addition, measurement of high frequency pollution may be done at the output ports of the EMI filter where high frequency harmonics have been removed. So, I'm not sure how EMI can limit upper bound of switching frequency. I think we need more discussion in this case.

One example paper where optimal frequency is discussed is [1]. However, this paper deals with optimal frequency of MFT and there is no discussion about power electronic aspects. So, how we can extend such a study to find optimum frequency of an specific converter?

[1] Leibl, M., et al. (2016). "Design and Experimental Analysis of a Medium Frequency Transformer for Solid-State Transformer Applications." IEEE Journal of Emerging and Selected Topics in Power Electronics PP(99): 1-1.

This article does not consider a general theory, but a specific case. In my practice there was a project in which I had to choose a low frequency converter due to the cooling requirements of the transformer. The fact is that the converter worked in specific conditions and the transformer could be cooled only with the help of a special adapter. And a large contact area was required. I had to use a larger core than required. To reduce losses in the core material, it was necessary to reduce the frequency of the converter. But I do not think that this particular case can somehow affect the general principles of frequency selection. Use the maximum frequency that the components you select allow. Electromagnetic compatibility issues are also important. With EMI, not everything is clear. But an EMC filter at 200KHz is definitely more compact and easier to implement than a filter at 20KHz.

Dear Hamzeh and Andrii,

yes clearly an EMC Filter is a lowpass and therefore easier to design, if the required corner frequency is higher. But what I wanted to say was the in industrial practice sometimes you set the frequency below the lowest frequency which has to measured. Therefore the fundamental, which has the highest amplitude does not have to be considered, in filter design.

Regarding the initial question, I think it is very difficult to find a single optimum switching frequency, as the question is, what is optimal in a sense that there are different objective to achieve:

- volume/weight

. cost

- price

etc.

Therefore I would be surprised, if there is a single optimal frequency.

This is exactly what I wanted to say. It is impossible to answer this question exclusively mathematically.

Dear Burkhard and Andrii

Thanks for participation in the discussion.

We got two main points up to now from our discussion:

1- Finding the best compromise for switching frequency is difficult and complicated. Switching frequency is usually selected based on experience and device capabilities and there is no clear way for this purpose.

2 - Maximizing switching frequency can be a separate objective function in addition to other objectives such as weight/volume/cost/efficiency/EMI-EMC/Power quality. So, switching frequency can be an optimization parameter (x) and also an optimization objective f(x) in the same time.

For the next step we can discuss on how to find a simplified mathematical model.

As you know, the most exact mathematical models are finite-element model with exact geometrical considerations. However we can approximate converter behavior with analytical formulas from mentioned objectives point of view with a degree of exactness. So, at least we can divide frequency spectra two intervals and find out the effective objective in each one.

The choice of frequency is a balancing act between:

- The turn on and off times of the semiconductors, which set an upper limit,

- The size of the transformer core, which sets a lower limit,

- Hysteresis loss in the core which sets and upper limit,

- Wire diameter and type (e.g. circular, strip or litz) which sets a upper limit,

- Allowable size or mass of the unit which sets a lower limit.

Note that it is the harmonic content of the switching transients which pose an EMI hazard, not the switching frequency by itself.

Dear Tony

Thanks for the proposed trade-off for switching frequency selection in medium frequency transformers (MFTs) and related converters.

Collector current vs frequency and temperature curves which are rarely given by semiconductor manufacturers can be use to impose an upper and lower bound for switching frequency in the design. For instance, IGBT module IKW25N120T2 of Infineon switching frequency must be lower than 100 kHz to prevent overheating at Ic=20A (Curves are attached). For higher currents maximum frequency reduces.

Yes, in the IKW25N120T2 device you mention, the important factor is the turn off. No IGBT can turn off very fast because of the charge build up in the base which has to decay. As it turns off it passes a high current but at an appreciable voltage and this causes dissipation in the collector region. So you don't want it to turn off too often, which is why this implies an upper limit to the switching frequency.

Dear Tony,

I agree with you. Current rating is 25 A where maximum switching frequency is 50 kHz. For an efficiency oriented design 50 kHz is too high. for a three phase converter implemented with this switch, a rough estimation of losses (neglecting conduction losses) is 50*4.5*6 = 1350 W. While the power rating is 25*3*220=16500 W. Final efficiency is lower than 91% which is not acceptable. So, practical maximum value of switching frequency is lower than 50 kHz.

Hi Hamzeh Beiranvand,

Check out the following article. It seemed related to your question.

https://masteringelectronics.blogspot.com/2020/02/switching-frequency-how-do-you-choose.html

Thanks,

Subrahmanyam.