“Steinmetz's equation”的意思、由来-开放百科全书

where

is the time average power loss per unit volume in mW per cubic centimeter,

is frequency in kilohertz, and

is the peak magnetic flux density;

, and

, called the Steinmetz coefficients, are material parameters generally found empirically from the material's B-H hysteresis curve by curve fitting. In typical magnetic materials, the Steinmetz coefficients all vary with temperature.

The energy loss, called core loss, is due mainly to two effects: magnetic hysteresis and, in conductive materials eddy currents, which consume energy from the source of the magnetic field, dissipating it as waste heat in the magnetic material. The equation is used mainly to calculate core losses in ferromagnetic magnetic cores used in electric motors, generators, transformers and inductors excited by sinusoidal current. Core losses are an economically important source of inefficiency in alternating current (AC) electric power grids and appliances.

If only hysteresis is taken into account (à la Steinmetz), the coefficient

will be close to 1 and

will be 2 for nearly all modern magnetic materials. However, due to other nonlinearities,

is usually between 1 and 2, and

is between 2 and 3. The equation is a simplified form that only applies when the magnetic field

has a sinusoidal waveform and does not take into account factors such as DC offset. However, because most electronics expose materials to non-sinusoidal flux waveforms, various improvements to the equation have been made. An improved

generalized Steinmetz equation, often referred to as iGSE, can be expressed as^[2]^[3]

where

and

are the same parameters used in the original equation. This equation can calculate losses with any flux waveform using only the parameters needed for the original equation, but it ignores the fact that the parameters, and therefore the losses, can vary under DC bias conditions.^[4] DC bias cannot be neglected without severely affecting results, but there is still not a practical physically-based model that takes both dynamic and nonlinear effects into account.^[6] However, this equation is still widely used because most other models require parameters that are not usually given by manufacturers and that engineers are not likely to take the time and resources to measure.^[1]

The Steinmetz coefficients for magnetic materials may be available from the manufacturers. However, manufacturers of magnetic materials intended for high-power applications usually provide graphs that plot specific core loss (watts per volume or watts per weight) at a given temperature against peak flux density

, with frequency as a parameter. Families of curves for different temperatures may also be given. These graphs apply to the case where the flux density excursion is ±

. In cases where the magnetizing field has a DC offset or is unidirectional (i.e. ranges between zero and a peak value), core losses can be much lower but are rarely covered by published data.

See also

References

1. ^¹{{cite web| title=Accurate Prediction of Ferrite Core Loss with Nonsinusoidal Waveforms Using Only Steinmetz Parameters| author=Venkatachalam| year=2012| accessdate=2013-07-31| publisher=Dartmouth College| url=http://engineering2.dartmouth.edu/inductor/papers/IGSE.pdf|display-authors=etal}}
2. ^¹²{{cite book | last1 = Sudhoff | first1 = Scott D. | title = Power Magnetic Devices: A Multi-Objective Design Approach | publisher = John Wiley and Sons | date = 2014 | location = | pages = 168–169 | language = | url = https://books.google.com/books?id=ANfFAgAAQBAJ&pg=PT168#v=onepage&q&f=false | doi = | id = | isbn = 978-1118824634 }}
3. ^¹²{{cite book | last1 = Rashid | first1 = Muhammad H. | title = Power Electronics Handbook, 4th Ed. | publisher = Butterworth-Heinemann | date = 2017 | location = | pages = 573 | language = | url = https://books.google.com/books?id=HxdHDgAAQBAJ&pg=PA573&dq=%22steinmetz+equation%22 | doi = | id = | isbn = 978-0128114087 }}
4. ^¹{{cite journal| title=Core Losses Under the DC Bias Condition Based on Steinmetz Parameters| journal=IEEE Transactions on Power Electronics| volume=27| issue=2| page=953| date= February 2012| authors=Mühlethaler| url=http://www.hpe.ee.ethz.ch/uploads/tx_ethpublications/05936124_01.pdf|display-authors=etal| doi=10.1109/TPEL.2011.2160971}}
5. ^{{cite journal | last1 = Steinmetz| first1 = Charles P.| title = On the law of hysteresis| journal = Trans. AIEE| volume = 9| issue = 2| pages = 3–62| date = 1892| url = http://ieeexplore.ieee.org/document/1457110/| issn = | doi = 10.1109/PROC.1984.12842| id = | accessdate = November 28, 2017}}
6. ^{{cite journal| last1=Reinert| first1=J.| last2=Brockmeyer| first2=A.| last3=De Doncker| first3=R.W.| title=Calculation of losses in ferro- and ferrimagnetic materials based on the modified Steinmetz equation| journal=Proceedings of 34th Annual Meeting of the IEEE Industry Applications Society| year=1999| pages=2087–92| volume=3| doi=10.1109/IAS.1999.806023| isbn=978-0-7803-5589-7}}

See also

References

External links