using kalman filter to voltage harmonic identification in single-phase systems
DESCRIPTION
Alcalá University. Department of Electronics. Using Kalman filter to voltage harmonic identification in single-phase systems. Raúl Alcaraz, Emilio J. Bueno, Santiago Cóbreces, Francisco J. Rodríguez, Marta Alonso , David Díaz, Santiago Muyulema Department of Electronics. Alcalá University - PowerPoint PPT PresentationTRANSCRIPT
Using Kalman filter to voltage harmonic identification in
single-phase systems
Raúl Alcaraz, Emilio J. Bueno, Santiago Cóbreces, Francisco J. Rodríguez, Marta Alonso,
David Díaz, Santiago MuyulemaDepartment of Electronics. Alcalá University
[email protected] [email protected]
SAAEI 2006
Alcalá University Department of Electronics
Researching group in Control and Power Electronics Systems
Contents
• Introduction• Kalman filter• Grid voltage models in state variable
– Discrete model with variable reference– Discrete model with stationary reference– Continuous model
• Identification systems• Experimental results• Conclusions
SAAEI 2006
Alcalá University Department of Electronics
Researching group in Control and Power Electronics Systems
Contents
• Introduction• Kalman filter• Grid voltage models in state variable
– Discrete model with variable reference– Discrete model with stationary reference– Continuous model
• Identification systems• Experimental results• Conclusions
SAAEI 2006
Alcalá University Department of Electronics
Researching group in Control and Power Electronics Systems
Introduction
SAAEI 2006
Alcalá University Department of Electronics
Researching group in Control and Power Electronics Systems
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
Introduction
SAAEI 2006
Alcalá University Department of Electronics
Researching group in Control and Power Electronics Systems
Active Filter• Harmonic identification (voltage or current)
• Synchronization
Voltage
Current
Identification methods
Discrete Fourier Transform (DFT), spectral observer, Hartley transform, Fast Fourier Transform (FFT)
DFT and FFT problems:
•Aliasing
•Leakage
•Picket-fence effect
Non-accurate identification
KALMAN FILTER
Contents
• Introduction• Kalman filter• Grid voltage models in state variable
– Discrete model with variable reference– Discrete model with stationary reference– Continuous model
• Identification systems• Experimental results• Conclusions
SAAEI 2006
Alcalá University Department of Electronics
Researching group in Control and Power Electronics Systems
Kalman Filter
SAAEI 2006
Alcalá University Department of Electronics
Researching group in Control and Power Electronics Systems
• 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
Contents
• Introduction• Kalman filter• Grid voltage models in state variable
– Discrete model with variable reference– Discrete model with stationary reference– Continuous model
• Identification systems• Experimental results• Conclusions
SAAEI 2006
Alcalá University Department of Electronics
Researching group in Control and Power Electronics Systems
Discrete model with variable reference
)()(10
01)1( kkxkx
Tkxkxkx )()()( 21
)()()sin()cos()( 11 kvkxkkkz
SAAEI 2006
Alcalá University Department of Electronics
Researching group in Control and Power Electronics Systems
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
Measumerent equation
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 Measumerent 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
Contents
• Introduction• Kalman filter• Grid voltage models in state variable
– Discrete model with variable reference– Discrete model with stationary reference– Continuous model
• Identification systems• Experimental results• Conclusions
SAAEI 2006
Alcalá University Department of Electronics
Researching group in Control and Power Electronics Systems
Discrete model with stationary reference
)()()cos()sin(
)sin()cos()1(
11
11 kwkxkx
Tkxkxkx )()()( 21
)()(01)( kvkxkz
SAAEI 2006
Alcalá University Department of Electronics
Researching group in Control and Power Electronics Systems
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
Measumerent equation
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)
Contents
• Introduction• Kalman filter• Grid voltage models in state variable
– Discrete model with variable reference– Discrete model with stationary reference– Continuous model
• Identification systems• Experimental results• Conclusions
SAAEI 2006
Alcalá University Department of Electronics
Researching group in Control and Power Electronics Systems
Continuous model
)()(0
0)(
1
1 twtxtx
)()(01)( tvtxtz
SAAEI 2006
Alcalá University Department of Electronics
Researching group in Control and Power Electronics Systems
Grid continuousDiscrete models error
State equation
Measumerent 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)
Contents
• Introduction• Kalman filter• Grid voltage models in state variable
– Discrete model with variable reference– Discrete model with stationary reference– Continuous model
• Identification systems• Experimental results• Conclusions
SAAEI 2006
Alcalá University Department of Electronics
Researching group in Control and Power Electronics Systems
Identification Systems
SAAEI 2006
Alcalá University Department of Electronics
Researching group in Control and Power Electronics Systems
)()(
.....
)()(
)()(
12
32
11
nxne
nxne
nxne
ii
Identification block
Stationary reference Variable reference and SPLL
Identification Systems
2)( 1
kwk
)(
)(tan)(
)()(
)(tan)(
)()()(
1
211
112
21
22
212
kx
kxk
knkx
kxk
kxkxkE
n
nn
nnn
SAAEI 2006
Alcalá University Department of Electronics
Researching group in Control and Power Electronics Systems
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
Identification Systems
21)( kkM
SAAEI 2006
Alcalá University Department of Electronics
Researching group in Control and Power Electronics Systems
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)
Contents
• Introduction• Kalman filter• Grid voltage models in state variable
– Discrete model with variable reference– Discrete model with stationary reference– Continuous model
• Identification systems• Experimental results• Conclusions
SAAEI 2006
Alcalá University Department of Electronics
Researching group in Control and Power Electronics Systems
Experimental results
100(%)
before
afterbefore
THD
THDTHDIF
SAAEI 2006
Alcalá University Department of Electronics
Researching group in Control and Power Electronics Systems
Selection of Kalman filter parameters
Improvement Factor (IF)
2
2
1
1100(%)
nnVV
THD
•balanced grid
•unbalanced grid
•frequency desviations < 0.1%
2
2
V 05.0
covariance state and varianceNoise
)V (10matrix Diagonal
matrix covarianceInitial)0(
periodtionInitializacyclehalfFirst
0vectorprocessInitial)0(ˆ
QyR
P
x
Transient Response Time TRT
Delay between a disturbance in the grid voltage and the system harmonic identification<100 ms
Transient Response Quality
Related with the maximum peak level indentified during a transitory
PF=Vpident/Vpgrid <15
Comparison Criterions
Experimental Results
SAAEI 2006
Alcalá University Department of Electronics
Researching group in Control and Power Electronics Systems
SIMULATION MATLAB
PRACTICAL DSP TMS320C6713 with ADCs MAX1309 of 12 bits
DIGILAB 2E
Link Board
Interface Board
TMS320C6713 DSK
Optical transmitters
Optical receivers
ADCsRelays
Signal processing
Acquisition card
Glue logic
Experimental Results
SAAEI 2006
Alcalá University Department of Electronics
Researching group in Control and Power Electronics Systems
•1 Grid voltage balanced
•2 Grid voltage unbalanced
•3 Grid voltage with frequency deflection
•4 Results from [Round and Ingram. EPE Conf 1992]
CONTINUOUS DISCRETE MODEL STATIONARY REFERENCE
DISCRETE MODEL VARIABLE REFERENCE
Contents
• Introduction• Kalman filter• Grid voltage models in state variable
– Discrete model with variable reference– Discrete model with stationary reference– Continuous model
• Identification systems• Experimental results• Conclusions
SAAEI 2006
Alcalá University Department of Electronics
Researching group in Control and Power Electronics Systems
Conclusions• Necessity of the harmonic identification in active
filters to improve the grid power quality• FFT is widely usedproblems in some situation• Kalman filter
– Accurate– Not sensitive to a certain sampling frequency
• Three grid models show the flexibility of the Kalman filtering scheme
• Continuous model without disturbances• Discrete model with stationary referencewithout
dips• Discrete model with variable reference equal or
better than the FFT• Computationally not-complex linear Kalman filter
implementationSAAEI 2006
Alcalá University Department of Electronics
Researching group in Control and Power Electronics Systems
ACKNOWLEDGMENT
This work has been financied by the Spanish administration (ENE2005-08721-C04-01)
Using Kalman filter to voltage harmonic identification in
single-phase systems
Raúl Alcaraz, Emilio J. Bueno, Santiago Cóbreces, Francisco J. Rodríguez, Marta Alonso,
David Díaz, Santiago MuyulemaDepartment of Electronics. Alcalá University
[email protected] EMAIL RAUL
SAAEI 2006
Alcalá University Department of Electronics
Researching group in Control and Power Electronics Systems