comparison of voltage harmonic identification methods for single-phase and three-phase systems

Comparison of Voltage Harmonic Identification Methods for Single-Phase and Three-Phase Systems

R. Alcaraz, E.J. Bueno, S. Cóbreces, F.J. Rodríguez, C.Girón, F. Huerta

Department of Electronics. University of Alcalá (Spain)

[email protected]@depeca.uah.es

IECON 2006

University of Alcalá Department of Electronics

Researching group in Electronic Engineering applied to the Renewable Energies

M. LiserreDepartment of Electrical and

Electronics Engineering Polytechnic of Bari (Italy)

[email protected]

mailto:[email protected]

Contents

1. Introduction

2. Objectives

3. Single-Phase algorithms

4. Three-Phase algorithms

5. Experimental setup

6. Experimental results

7. Conclusions

Department of Electronics

IECON 2006Researching group in Electronic Engineering applied to the Renewable Energies

University of Alcalá

Introduction


Nonlinear loads

Problem

Harmonic

Voltage distorsion

Increased losses and heating

Missoperation of protective equipment

Solutions

Passive filters Active filters (AF)

Isolated harmonic voltage

Specific frequency

Operation not limited to a certain load

Resonances

Inject the undesired harmonic with 180º phase shift

More difficult implementation

More expensive

IECON 2006Researching group in Electronic Engineering applied to the Renewable Energies


Introduction


Active Filter• Harmonic identification (voltage or current)

• Synchronization

Voltage

Current

Identification methods

Based on frequency-domain:• Discrete Fourier Transform (DFT)• Fast Fourier Transform (FFT)

Based on system model:• Kalman Filter

Based on transformations of frames

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Single-phase systems

Three-phase systems

Contents

1. Introduction

2. Objectives





7. Conclusions


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Objectives


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pulses

11 hgggPCC eee

)(kig

kek g 11 ),(

)(kid

)(tu

)(kuDC

)(kiq

PWMgenerator

uDC controller Current

Controller

Grid voltage meas.

ADC & SPLL

L

Harmonic identification

Grid current meas.

n

keg

PCC

Harmoniccompensation

uDC

CDC

uDC meas.

)(kig

• To obtain the exact information of the amplitude and phase of each harmonic.

• To rebuilt exactly each harmonic.

• Application: Active filters, feedforward of current controller for power converters.

Contents1. Introduction2. Objectives3. Single-Phase algorithms

– Detection based on DFT– Detection based on Wavelet– Detection based on Kalman Filter– Detection based on correlators in quadrature

4. Three-Phase algorithms5. Experimental setup6. Experimental results7. Conclusions


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Detection method based on DFT


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22log N

• c = 1 for positive seq. and -1 for negative seq. • θ(k) =ω1k-π/2 is the sPLLoutput.• γ is the sPLL delay

• The DFT of N1 points is carried out for each sample that arrives from the grid voltage signal.

• The actual sample and N1 -1 previous samples are used, and for this reason the buffer N1 samples is necessary.

• As the phase changes from one sample to the following sample, it is necessary the use of a Phase Loocked Loop (PLL), which recovers the instantaneous phase of the grid signal.

DFT: Experimental setup


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• Perfect identification.

• In the worst cases, the response time is 2T1=40ms.

• Correct operation under unbalanced grid voltages.

• Run time depends on the identified harmonics, aprox. 120s.

Wavelet


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Multiresolution algorithms 5 levels

Identification system (with family

Daubechies40)

The Wavelet algorithm transforms the signal under investigation into another one that includes frequency and time domain informations.

Wavelet: Simulation results


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Non-correct identification. Only it is possible to recover correctly the harmonics 1 and 5.

Kalman Filter


• Characteristics– Optimal and robust estimation of magnitudes of sinusoids– Ability to track time-varying parameters– Synchronization of the two control blocks in the AF

State equation

Measumerent equation

Covarianze for w(k) and v(k)

1st Kalman filter gain

2nd Update estimate with harmonic measumerent z(t)

3rd Compute error covariance

4th Project ahead

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Kalman Filter: Continuous model

)()(0

0)(

1

1 twtxtx

)()(01)( tvtxtz


State equation


State equation Measumerent equation

)()(

...0

.........

0...1

twtx

N

N

x

n

)()(01...01)( tvtxtz

Tn txtxtxtx )(...)()()( 221

Constant B(k)

0

0

1

1

i

iN i

)())()·cos(()(

)())()·sin(()(

11112

21111

txtttEdt

tdx

txtttEdt

tdx

x1(t) and x2(t) complementary

x2(t) leads x1(t) 180º

Constant A(k)

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Kalman Filter: Discrete model with variable reference

)()(10

01)1( kkxkx

Tkxkxkx )()()( 21

)()()sin()cos()( 11 kvkxkkkz


s(k)= E(k)cos(ω1k+Φ(k)) = E(k)·cos(Φ(k))·cos(ω 1k) - E(k)·sin(Φ(k))·sin(ω1k)

x1(k)= E(k)·cos(Φ(k))

x2(k)= E(k)·sin(Φ(k))

In-phase component

Quadrature-phase component

State equation

ω(k) time variation


v(k) high frequency noise

Noise-free voltage signal s(k) (n harmonics)

n

iiks

11i (k))k(k)cos(iE)(

•Ei(k) and Φi(k) amplitude of the phasor and phase of the ith harmonic

•n harmonic order

State equation


)()(

...0

.........

0...

)1( kwkx

I

I

kx

)()(

)sin(

)cos(

...

)sin(

)cos(

)(

1

1

1

1

kvkx

kn

kn

k

k

kz

T

Tn kxkxkxkx )(...)()()( 221

B(k) time-varying vector

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Kalman Filter: Discrete model with stationary reference

)()()cos()sin(

)sin()cos()1(

11

11 kwkxkx

Tkxkxkx )()()( 21

)()(01)( kvkxkz


s(k)= E(k)cos(ω 1k+Φ(k))

x1(k)= E(k)·cos(ω1k + Φ(k))

x2(k)= E(k)·sin(ω 1k + Φ(k))

State equation

ω(k) time variation


v(k) high frequency noise

State equation Measumerent equation

)()(

...0

.........

0...

)1(1

kwkx

M

M

kx

n

)()(01...01)( kvkxkz

Tn kxkxkxkx )(...)()()( 221

Constant B(k)

At k+1 s(k+1)=E(k+1)·cos(ω1k+ ω1+Φ(k+1))=

x1(k+1)= x1(k)cos(ω1) – x2(k)sin(ω1)

x2(k+1)= E(k+1)·sin(ω1k+ ω1+Φ(k+1))=

x2(k+1)= x1(k)sin(ω1) + x1(k)cos(ω1)

)cos()sin(

)sin()cos(

11

11

ii

iiM i

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

....

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

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

212

224223

112111

kkEkxkkEkx

kkEkxkkEkx

kkEkxkkEkx

nnnnn

Constant A(k)

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Kalman Filter: Identification Systems


)()(

.....

)()(

)()(

12

32

11

nxne

nxne

nxne

ii

Identification block

Stationary reference Variable reference and SPLL

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2)( 1

kwk

)(

)(tan)(

)()(

)(tan)(

)()()(

1

211

112

21

22

212

kx

kxk

knkx

kxk

kxkxkE

n

nn

nnn


Variable reference and SPLL

B(k) depends on w1k!

Solution: SPLL

)])()2

)(([(cos(·)()( kknckEke nnn

High peak voltages during transitory by the grid disturbances!

Variable reference and Time shift

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21)( kkM


Variable reference and Time shift

k = k1 + k2

k2 delay between grid starts up and identification system is connected to the grid

s(k)= E(k)cos(ω1k+ω1k2+Φ(k))

x1(k)= E(k)·cos(ΦM(k))

x2(k)= E(k)·sin(ΦM(k))

)()()sin()cos()( 1111 kvkxkkkz

Φ1(k)=ΦM(k)

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Kalman Filter: Experimental Results


CONTINUOUS DISCRETE MODEL STATIONARY REFERENCE

DISCRETE MODEL VARIABLE REFERENCE

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Selection of Kalman filter parameters

2

2

V 05.0

covariance state and varianceNoise

)V (10matrix Diagonal

matrix covarianceInitial)0(

periodtionInitializacyclehalfFirst

0vectorprocessInitial)0(ˆ

QyR

P

x

Correlators in quadrature


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To make the system faster and simpler, the correlators in quadrature will be implemented by means of adapted filters,which are characterized to have an impulsive response h(k) =s(N1-k), being s(k) the signal that the corresponding correlator uses in the detection. Therefore, the impulsive responses of the used filters to identify the harmonic n are:

Contents


1. Introduction2. Objectives3. Single-Phase algorithms4. Three-Phase algorithms

• Synchronous Reference Methods (SRF)• Instantaneous Reactive Power Theory (IRPT)

5. Experimental setup6. Experimental results7. Conclusions

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Synchronous Reference Method (SRF)


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HPF

Instantaneous Reactive Power Theory (IRPT)


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• When the grid voltage signal is unbalanced, a non-correct harmonic identification is produced.

• Due to the dq-components rotating in opposite directions, the voltage and current fundamental harmonic produce a dc-component plus ac-component in the instantaneous power therefore, harmonic distortion can not be recovered with a HPFand the inverse Park Transform

Contents


1. Introduction

2. Objectives





7. Conclusions

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Experimental Setup


DSP TMS320C6713 with ADCs MAX1309 of 12 bits

DIGILAB 2E

Link Board

Interface Board

TMS320C6713 DSK

Optical transmitters

Optical receivers

ADCsRelays

Digital Signal Processing

Acquisition card

Glue logic

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Contents


1. Introduction

2. Objectives





7. Conclusions

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Experimental results: Comparison Criterions


100(%)

before

afterbefore

THD

THDTHDIF

Improvement Factor (IF)

2

2

1

1100(%)

nnVV

THD

• balanced grid

• unbalanced grid

• frequency deviations < 0.1%

Transient Response Quality

Related with the maximum peak level identified during a transitory due to disturbance in the grid

PF=Vpident/Vpgrid <15

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Run Time

Time that algorithms takes in its execution

Transient Response Time TRT

Delay between a disturbance in the grid voltage and the system harmonic identification<100 ms

Experimental results: Kalman Filter


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Experimental results: Single-Phase Systems


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Balanced grid voltages Unbalanced grid voltages Drift frequency 0.1Hz

Transient Response Time Transient Response Quality

Experimental results: Three-Phase Systems


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Balanced grid voltages Unbalanced grid voltages Drift frequency 0.1Hz

Transient Response Time Transient Response Quality Run Time

Contents


1. Introduction

2. Objectives





7. Conclusions

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Conclusions• In the present work, an overview and comparison of different techniques for harmonics

identification in single-phase and three-phase systems has been achieved.

• As contribution, some modifications have been made on existing methods. Also, for the case of single-phase, the method based on correlators in quadrature have been proposed for the first time.

• The identification technique more suitable for each situation depends the characteristics of the environment where this is used.

• For single-phase the identification technique, that better results obtains, is the based on FFT and sPLL, since it obtains the best factors IF, TRT and PF.

• On the other hand, for the three-phase systems, experimental results and simulation show that the synchronous harmonic dq-frame method (with the utilization of transformations realized in sPLL) is the best solution. This technique permits a selective filtering, obtains a correct operation with balanced, unbalanced grid signals, has an excellent dynamic response (as transient time and transient quality) and very reduced algorithm execution time.

• The analysis have been validated by simulations and experimental results carried out with the digital signal processor TMS320C6713.


IECON 2006



Comparison of Voltage Harmonic Identification Methods for Single-Phase and Three-Phase Systems

R. Alcaraz, E.J. Bueno, S. Cóbreces, F.J. Rodríguez, C.Girón, F. Huerta

Department of Electronics. University of Alcalá (Spain)

[email protected]@depeca.uah.es

IECON 2006

University of Alcalá Department of Electronics


M. LiserreDepartment of Electrical and

Electronics Engineering Polytechnic of Bari (Italy)

[email protected]

ACKNOWLEDGMENTS

This work has been financied by the Spanish administration (ENE2005-08721-C04-01)

mailto:[email protected]

comparison of voltage harmonic identification methods for single-phase and three-phase systems

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renewable energiesto

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undesired harmonic

grid voltage signal