Using Kalman filter to voltage harmonic identification in single-phase systems

1. Alcalá University Department of Electronics Using Kalman filter to voltage harmonic identification in single-phase systems Raúl Alcaraz, Emilio J. Bueno, SantiagoCóbreces, Francisco J. Rodríguez, Marta Alonso, David Díaz, Santiago Muyulema Department of Electronics. Alcalá University marta.alonso@depeca.uah.es raul.alcaraz@uclm.es Researching group in Control and Power Electronics Systems SAAEI 2006

2. Alcalá University Department of Electronics 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 Researching group in Control and Power Electronics Systems SAAEI 2006

3. Alcalá University Department of Electronics 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 Researching group in Control and Power Electronics Systems SAAEI 2006

4. Alcalá University Department of Electronics Introduction Voltage distorsion Increased losses and heating Missoperation of protective equipment Problem Nonlinear loads Harmonic Solutions Passive filters Active filters (AF) Isolated harmonic voltage Specific frequency Operation not limited to a certain load Resonances More difficult implementation More expensive Inject the undesired harmonic with 180º phase shift Researching group in Control and Power Electronics Systems SAAEI 2006

5. Alcalá University Department of Electronics Introduction • Harmonic identification (voltage or current) Active Filter • Synchronization Identification methods Discrete Fourier Transform (DFT), spectral observer, Hartley transform, Fast Fourier Transform (FFT) Voltage • DFT and FFT problems: • Aliasing • Leakage • Picket-fence effect Non-accurate identification Current KALMAN FILTER Researching group in Control and Power Electronics Systems SAAEI 2006

6. Alcalá University Department of Electronics 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 Researching group in Control and Power Electronics Systems SAAEI 2006

7. Alcalá University Department of Electronics 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 Covarianze for w(k) and v(k) State equation Measumerent equation 1st Kalman filter gain 4th Project ahead 2nd Update estimate with harmonic measumerent z(t) 3rd Compute error covariance Researching group in Control and Power Electronics Systems SAAEI 2006

8. Alcalá University Department of Electronics 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 Researching group in Control and Power Electronics Systems SAAEI 2006

9. Alcalá University Department of Electronics Discrete model with variable reference s(k)= E(k)cos(ω1k+Φ(k)) = E(k)·cos(Φ(k))·cos(ω1k) - 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 Noise-free voltage signal s(k) (n harmonics) • Ei(k) and Φi(k) amplitude of the phasor and phase of the ith harmonic • n harmonic order ω(k) time variation State equation Measumerent equation Measumerent equation v(k) high frequency noise B(k) time-varying vector Researching group in Control and Power Electronics Systems SAAEI 2006

10. Alcalá University Department of Electronics 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 Researching group in Control and Power Electronics Systems SAAEI 2006

11. Alcalá University Department of Electronics Discrete model with stationary reference s(k)= E(k)cos(ω1k+Φ(k)) x1(k)= E(k)·cos(ω1k + Φ(k)) x2(k)= E(k)·sin(ω1k + Φ(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) State equation State equation Measumerent equation ω(k) time variation Constant B(k) Constant A(k) Measumerent equation v(k) high frequency noise Researching group in Control and Power Electronics Systems SAAEI 2006

12. Alcalá University Department of Electronics 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 Researching group in Control and Power Electronics Systems SAAEI 2006

13. Alcalá University Department of Electronics Continuous model Grid continuousDiscrete models error State equation State equation Measumerent equation Constant A(k) Measumerent equation Constant B(k) x1(t) and x2(t) complementary x2(t) leads x1(t) 180º Researching group in Control and Power Electronics Systems SAAEI 2006

14. Alcalá University Department of Electronics 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 Researching group in Control and Power Electronics Systems SAAEI 2006

15. Alcalá University Department of Electronics Identification Systems • Stationary reference • Variable reference and SPLL Identification block Researching group in Control and Power Electronics Systems SAAEI 2006

16. Alcalá University Department of Electronics Identification Systems • Variable reference and Time shift • Variable reference and SPLL B(k) depends on w1k! Solution: SPLL High peak voltages during transitory by the grid disturbances! Researching group in Control and Power Electronics Systems SAAEI 2006

17. Alcalá University Department of Electronics Identification 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)) Φ1(k)=ΦM(k) Researching group in Control and Power Electronics Systems SAAEI 2006

18. Alcalá University Department of Electronics 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 Researching group in Control and Power Electronics Systems SAAEI 2006

19. Alcalá University Department of Electronics Experimental results Selection of Kalman filter parameters Comparison Criterions 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 Improvement Factor (IF) • balanced grid • unbalanced grid • frequency desviations < 0.1% Researching group in Control and Power Electronics Systems SAAEI 2006

20. Optical transmitters ADCs Interface Board Relays Optical receivers Link Board DIGILAB 2E TMS320C6713 DSK Alcalá University Department of Electronics Experimental Results SIMULATIONMATLAB PRACTICALDSP TMS320C6713 with ADCs MAX1309 of 12 bits Acquisition card Signal processing Glue logic Researching group in Control and Power Electronics Systems SAAEI 2006

21. Alcalá University Department of Electronics Experimental Results • 1Grid 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 Researching group in Control and Power Electronics Systems SAAEI 2006

22. Alcalá University Department of Electronics 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 Researching group in Control and Power Electronics Systems SAAEI 2006

23. Alcalá University Department of Electronics Conclusions • Necessity of the harmonic identification in active filters to improve the grid power quality • FFT is widely usedproblems 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 referencewithout dips • Discrete model with variable reference  equal or better than the FFT • Computationally not-complex linear Kalman filter implementation ACKNOWLEDGMENT This work has been financied by the Spanish administration (ENE2005-08721-C04-01) Researching group in Control and Power Electronics Systems SAAEI 2006

24. Alcalá University Department of Electronics Using Kalman filter to voltage harmonic identification in single-phase systems Raúl Alcaraz, Emilio J. Bueno, SantiagoCóbreces, Francisco J. Rodríguez, Marta Alonso, David Díaz, Santiago Muyulema Department of Electronics. Alcalá University marta.alonso@depeca.uah.es EMAIL RAUL Researching group in Control and Power Electronics Systems SAAEI 2006