Method Of Inductance Parameter Extraction For Multi-Conductor Segments

Inductance is a macroscopic equivalent parameter for reflecting magnetic field generated by conductor loop with conductive current.In many pratical situations,current distribution need to be analysed in a part of conductor loop,whereas the whole conductor loop is unknow.For example,the high voltage high power press-pack IGBT module is wisely applied in the voltage source control high voltage direct current transmission system.Tens of IGBT chips are parallel connected in an IGBT module.When the IGBT module is switching-on or switching off,the current distribution is affected by the parameters of chips and the indutance due to different locations,whereas the whole conductor loop containing IGBT is un-certained.This kind of problem is called multi-conductor segment problem in this paper.Recently many scholars made effort in this problem,and mainly proposed three theories,including magnetic flux method based on vitual conductor loop,energy method based on magnetic field energy in space and partial element equivalent circuit method.Thereinto,inductance calculated by the magnetic flux method and the partial element equivalent circuit method are consistent,and could be computed faster than energy method.However for multi-conductor problem,results obtained by the former two methods are different with the result by energy method.Therefore,this paper presents an inductance parameter extraction method for multi-conductor segment,based on the analysis of magnetci field energy and vector potential.The proposed method could accruately represent the ralationship between current and magnetic field energy.This paper progressively does research in following three steps,and applies in some practical situations.Firstly,multi-condutor segment model is difined,and formula of corresponding magnetic field energy in space is derived.Charge will accumulate on the end sections of conductor as time-varying,and generate displament current in space.The continuity of current is satisfied by displacement current.Analysis shows that the root reason of difference between the flux method and the energy method is that displacement current is not completely considered in the flux method.Based on the formulas of vector potential under different divergence gauge,the simplified formula of magnetic field energy for multi-conductor segment model is derived,which lays a analytical foundation for inductance extraction.Then,inductance of multi-conductor segment model is defined based on magnetic field energy in space.Analysis shows the proposed method could accurately represent the relationship between current and magnetic field energy in space.In addition,the computation could be accelerated under Coulomb gauge.Therefore,approximate formulas of multi-conductor segment models in different situation is derived and verified.Afterwards,modifed partial element equivalent circuit method is proposed based on the relationship equation between magnetic field energy,electric field energy and complex power.Every part of the equation could be represented by a macroscopic circuit element,including resistor,inductor,capacitor and source.Analysis shows that the formula of inductance parameter extraction is similar with existing method but could reflect the relationship equation of energy after modifying.In addition,vector potential formula with retard is derived for inductance extraction in high frequency.The proposed method is valified by application of antenna analysis.Finally,the proposed method is used in some practical applications,including indutance analysis of the whole conductor loop,current distribution in conductor under eddy effect and current distribution in press-pack IGBT module.Simulation are varified by comparison with analytical results or experiment.