Paper ID SGD5451 EMD-Prony for phasor estimation in harmonic and - PowerPoint PPT Presentation

Paper ID SGD5451 EMD-Prony for phasor estimation in harmonic and noisy conditions Jalal Khodaparast Ghadikolaei Olav Bjarte Fosso Marta Molinas Postdoctoral researcher Professor Professor Marta.molinas@ntnu.no Jalal.khodaparast@ntnu.no Olav.fosso@ntnu.no Signal Analysis Research Lab

Phasor Estimation Empirical Prony Mode Algorithm Decomposition (EMD) EMD-Prony Denoising Order of signal Prony 2

First-Order Prony algorithm   1      j 2 f t * j 2 f t Main signal s ( t ) p e p e 1 1 2  p  phasor j ae     1 1 s [ 0 ]     . . .     . . First step of .          n n Prony   Z Z p .  1 1       . . . *     p .       . . s [ n ]     . . .            N 1 ( N 1 )  s [ N 1 ]   Z Z 1 1 Second step of          2 F z ( z Z ).( z Z ) z a z a Prony 1 1 1 2     s [ 2 ] s [ 0 ] s [ 1 ]     s [ 3 ] s [ 1 ] y [ 2 ]      s [ 4 ]   s [ 2 ] s [ 3 ]    a      . . . 1   .       a Third step of Prony 2 . . .         . . .            s [ N 1 ] s [ N 2 ] s [ N 3 ] 3

Frequency analysis of Prony 10    jk t s ( t ) e 0  k 1 Empirical Mode Decomposition (EMD) A time domain algorithm for separating a non-linear and non-stationary signal into its individual components. Sifting process Intrinsic Mode Function (IMF) stopping index L    s ( t ) R IMF k  k 1 4 Determination of Prony ’ s order Hurst Index

Mode mixing in EMD   s ( t ) s ( t ) s ( t ) 1 2   s ( t ) cos( 2 t ) 1     s ( t ) a cos( 2 t ) 2 Decomposition procedure is done with different noisy data and Ensemble EMD (EEMD) finally mean (ensemble) of the corresponding IMFs provides the final result. Detection of Mode mixing      s ( t ) cos( 2 50 t ) 0 . 2 cos( 2 300 t ) t 0 . 15      s ( t ) cos( 2 50 t ) 0 . 2 cos( 2 90 t ) t 0 . 15 5

Simulation Results Denoising using EMD     s ( t ) cos( 2 f t 0 . 5 ) w ( t ) 0     2 3 f 50 10 0 Hurst Index HI_1=0.3576 HI_2=0.2743 HI_3=0.2022 HI_4=0.3010 HI_5=0.7347 Method Amplitude Error Phase Error Prony 0.2851 0.2601 6 EMD-Prony 0.0171 0.0157

Simulation Results Prony's model order EMD performance         s ( t ) cos( 2 f t 0 . 5 ) 0 . 3 cos( 2 ( 5 f ) t ) 0 . 15 cos( 2 ( 8 f ) t ) 0 0 0 Method Amplitude Error Phase Error Prony 0.4636 1.4553 EMD-Prony 5 ˣ 10 -8 4.8 ˣ 10 -7 7

Simulation Results Prony's model order EEMD performance         s ( t ) cos( 2 f t 0 . 5 ) 0 . 3 cos( 2 ( 5 f ) t ) 0 . 15 cos( 2 ( 5 . 6 f ) t ) 0 0 0 Method Amplitude Error Phase Error Hurst Index Prony 0.5845 1.2230 IMF1=0.1739 IMF2=0.2993 EMD-Prony 3.4 ˣ 10 -7 3.02 ˣ 10 -6 IMF3=0.2022 IMF4=0.5721 IMF5=0.6468 IMF6=0.7927 8

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