Pasquale Arpaia (1) , Alessandro Masi (2) , Giovanni Spiezia (2) , Antonio Zanesco (1)

IMMW 14 - 14IMMW 14 - 14thth International Magnetic Measurement International Magnetic Measurement WorkshopWorkshop26-29 September 2005, Geneva, Switzerland26-29 September 2005, Geneva, Switzerland

Dynamic Characterization of NonlinearDynamic Characterization of Nonlinear

Magnets by Modeling and Measuring Magnets by Modeling and Measuring

Magnetic Field Phase SpectrumMagnetic Field Phase Spectrum

Pasquale Arpaia(1), Alessandro Masi(2), Giovanni Spiezia(2), Antonio Zanesco(1)

(1) Università del Sannio, Dipartimento di Ingegneria, Italy(2) CERN, AT-MTM Group, Switzerland


State of the artState of the art

investigation of magnet macroscopic

behavior in industrial applications

• New digital measurement systems to determine magnetic characteristics

• Development of adequate nonlinear models for transfer functions when imposing a flux for generating currents


Measurement method: basic ideasMeasurement method: basic ideas

Analytic relationship between dynamic hysteresis and Analytic relationship between dynamic hysteresis and current phase spectrumcurrent phase spectrum

Decomposition of nonlinear material behavior in a Decomposition of nonlinear material behavior in a hysteretic component and a non-hysteretic componenthysteretic component and a non-hysteretic component


Relationship between hysteresis Relationship between hysteresis

and current phase spectrumand current phase spectrum

k

ii tiNItENIttNI

210 )sin()sin()cos()(

hn

ii tiNINItNI

10 )cos()(

Non-hysteretic behavior Symmetrical hysteretic behavior

Asymmetrical hysteretic behavior

hii ni ...1,2

,2

)()()cos()(1

0 i

n

ii tioscNINItNItt

h

ii = i=1…nk


Material non linearity Material non linearity

decompositiondecomposition

Asymmetrical hymmetrical hysteretic characteristic

2

)()()(

NINI

NI c

Common-mode component

2

)()()(

NINI

NI d

Differential component


Dynamic model of hysteretic Dynamic model of hysteretic

materialmaterial

tNItNItNI oe


Characterization of the measurement Characterization of the measurement

methodmethod

NI(t)

nh

Measurement uncertainty

Noise

)(ˆ),(ˆ dc ININ

Model estimate

MEASUREMENT METHOD

rms[NI-NI]^


Simulation resultsSimulation results

rms of the model error in estimating NI for an added white noise

Sigma=0.0010Sigma=0.0008Sigma=0.0005

Sigma=0.0003

Sigma=0.0001



Sigma=0.001

Sigma=0.0008Sigma=0.0005

Sigma=0.0003

Sigma=0.0001

rms of the model error in estimating NI for an added LF noise



Sigma=0.001

Sigma=0.0008Sigma=0.0005

Sigma=0.0003

Sigma=0.0001

rms of the model error in estimating NI for an added HF noise


Comparison with classical algorithmComparison with classical algorithm

Comparison between polynomial interpolation and proposed method in case of white noise

Classical method

Proposed method

nh= 15

n = 30

Noise Standard Deviation

Classical method

Proposed method


Comparison with classical Comparison with classical

algorithmalgorithmComparison between polynomial interpolation and proposed

method in case of LF noise


Classical method

Proposed methodClassical method

Proposed method

nh= 15

n = 30


Comparison with classical algorithmComparison with classical algorithm

Comparison between polynomial interpolation and proposed method in case of HF noise

Classical method

Proposed method

nh= 15

n = 30

Classical method

Proposed method



Experimental resultsExperimental results

Lab measurement station


Method application to an actual Method application to an actual

casecase

Ferrite (Mn-Zn)Ferrite (Mn-Zn)

FrequencyFrequency 200 Hz 200 Hz

Maximum flux densityMaximum flux density

nnhh= 15= 15

ffcc = 25.6 kHz = 25.6 kHz

f=25 Hzf=25 Hz

nncc= 1024= 1024

Measurement conditions

Bmax= 0.08 T

Bmax= 0.17 T

Bmax= 0.28 T


ResultsResults

Proposed method performance for Bmax= 0.08T

Induzione magnetica B (T)

Cam

po

mag

net

ico

H

(A/m

)

Experimental points

Proposed method

Magnetic flux density - B(T)

Mag

net

ic F

ield

- H

Mag

net

ic F

ield

– H

(A

/m)


ResultsResults

Proposed method performances for Bmax= 0.17T

Induzione magnetica B(T)

Cam

po

mag

net

ico

H

(A/m

)

Experimental points

Proposed method


Mag

net

ic F

ield

– H

(A

/m)


ResultsResults

Proposed method performances for Bmax= 0.28TC

amp

o m

agn

etic

o H

(A

/m)

Experimental points

Proposed method

Mag

net

ic F

ield

– H

(A

/m)



ConclusionsConclusions

o Method to characterize magnet Method to characterize magnet dynamic behavior by modeling and dynamic behavior by modeling and measuring current phase spectrum measuring current phase spectrum

o Preliminary validation on digital Preliminary validation on digital signals affected by different noisessignals affected by different noises

o Comparison in simulation with results Comparison in simulation with results obtained by a classical estimation obtained by a classical estimation methodmethod

o Experimental verification by a lab Experimental verification by a lab measurement station measurement station

o Satisfactory results Satisfactory results Good alternative at Good alternative at classical methods suitable for DSP implementationclassical methods suitable for DSP implementation

Pasquale Arpaia (1) , Alessandro Masi (2) , Giovanni Spiezia (2) , Antonio Zanesco (1)

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