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 SAAEI 2006 Alcalá UniversityDepartment 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 UniversityDepartment 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 UniversityDepartment of Electronics Researching group in Control and Power Electronics Systems

Introduction SAAEI 2006 Alcalá UniversityDepartment 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 filtersActive 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 UniversityDepartment 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 UniversityDepartment of Electronics Researching group in Control and Power Electronics Systems

Kalman Filter SAAEI 2006 Alcalá UniversityDepartment 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) 1 st Kalman filter gain 2 nd Update estimate with harmonic measumerent z(t) 3 rd Compute error covariance 4 th 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 UniversityDepartment of Electronics Researching group in Control and Power Electronics Systems

Discrete model with variable reference SAAEI 2006 Alcalá UniversityDepartment of Electronics Researching group in Control and Power Electronics Systems s(k)= E(k)cos(ω 1 k+Φ(k)) = E(k)·cos(Φ(k))·cos(ω 1 k) - E(k)·sin(Φ(k))·sin(ω 1 k) x 1 (k)= E(k)·cos(Φ(k)) x 2 (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) E i (k) and Φ i (k) amplitude of the phasor and phase of the i th harmonic n harmonic order State equationMeasumerent equation 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 UniversityDepartment of Electronics Researching group in Control and Power Electronics Systems

Discrete model with stationary reference SAAEI 2006 Alcalá UniversityDepartment of Electronics Researching group in Control and Power Electronics Systems s(k)= E(k)cos(ω 1 k+Φ(k)) x 1 (k)= E(k)·cos(ω 1 k + Φ(k)) x 2 (k)= E(k)·sin(ω 1 k + Φ(k)) State equation ω(k) time variation Measumerent equation v(k) high frequency noise State equationMeasumerent equation Constant B(k) At k+1 s(k+1)=E(k+1)·cos(ω 1 k+ ω 1 +Φ(k+1))= x 1 (k+1)= x 1 (k)cos(ω 1 ) – x 2 (k)sin(ω 1 ) x 2 (k+1)= E(k+1)·sin(ω 1 k+ ω 1 +Φ(k+1))= x 2 (k+1)= x 1 (k)sin(ω1) + x 1 (k)cos(ω1) 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 UniversityDepartment of Electronics Researching group in Control and Power Electronics Systems

Continuous model SAAEI 2006 Alcalá UniversityDepartment of Electronics Researching group in Control and Power Electronics Systems Grid continuous  Discrete models  error State equation Measumerent equation State equationMeasumerent equation Constant B(k) x 1 (t) and x 2 (t) complementary x 2 (t) leads x 1 (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 UniversityDepartment of Electronics Researching group in Control and Power Electronics Systems

Identification Systems SAAEI 2006 Alcalá UniversityDepartment of Electronics Researching group in Control and Power Electronics Systems Identification block Stationary referenceVariable reference and SPLL

Identification Systems SAAEI 2006 Alcalá UniversityDepartment of Electronics Researching group in Control and Power Electronics Systems Variable reference and SPLL B(k) depends on w 1 k! Solution: SPLL High peak voltages during transitory by the grid disturbances! Variable reference and Time shift

Identification Systems SAAEI 2006 Alcalá UniversityDepartment of Electronics Researching group in Control and Power Electronics Systems Variable reference and Time shift k = k 1 + k 2 k 2  delay between grid starts up and identification system is connected to the grid s(k)= E(k)cos(ω 1 k+ω 1 k 2 +Φ(k)) x 1 (k)= E(k)·cos(Φ M (k)) x 2 (k)= E(k)·sin(Φ M (k)) Φ 1 (k)=Φ M (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 UniversityDepartment of Electronics Researching group in Control and Power Electronics Systems

Experimental results SAAEI 2006 Alcalá UniversityDepartment of Electronics Researching group in Control and Power Electronics Systems Selection of Kalman filter parameters Improvement Factor (IF) balanced grid unbalanced grid frequency desviations < 0.1% 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=V pident /V pgrid  <15 Comparison Criterions

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

Experimental Results SAAEI 2006 Alcalá UniversityDepartment 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] CONTINUOUSDISCRETE 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 UniversityDepartment 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 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 SAAEI 2006 Alcalá UniversityDepartment of Electronics Researching group in Control and Power Electronics Systems ACKNOWLEDGMENT This work has been financied by the Spanish administration (ENE 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 Muyulema Department of Electronics. Alcalá University RAUL SAAEI 2006 Alcalá UniversityDepartment of Electronics Researching group in Control and Power Electronics Systems