Extended Complex Kalman Filter Research Articles

Modified Extended Complex Kalman Filter for DC Offset and Distortion Rejection in Grid-Tie Transformerless Converters

Proper operation of the grid-tie transformerless converters under unbalanced and distorted conditions entails a precise detection of the frequency and fundamental component of the grid voltage. One of the main problems that could arise during the estimation of grid parameters is the existence of a DC offset generated from measurement and A/D conversion. This undesirable induced DC offset could appear as a part of the reference sinusoidal current of grid-tie converters. Although literature has proposed the use of an extended complex Kalman filter (ECKF) for the estimation of positive and negative sequence voltage components as a promising competitor to phase locked loops, mitigating the effect of possible DC offsets when a Kalman filter is employed remains scarce. This paper proposes a new extended complex Kalman filter to improve the filter stability for estimating the frequency and the fundamental positive and negative symmetrical components of the grid voltages, where DC offset, scaling error, and noise can successfully be rejected. The theoretical findings are experimentally validated.

Space vector-based model predictive current controller for grid-connected converter under unbalanced and distorted grid without a phase-locked loop

This paper presents an improved current control strategy for a three-phase voltage source converter connected to distorted grid. The proposed controller can successfully compensate the induced harmonic currents, while suppressing possible active power ripple. To manage various objectives and deal with tough restrictions, model predictive control can offer a promising solution. However, a modified extended complex Kalman filter is introduced to estimate the positive and negative fundamental components of the grid voltages which are used with the real and reactive power references to generate pure sinusoidal reference currents without the need for a phase-locked loop (PLL), avoiding its challenges under abnormal grid conditions. An improved space vector-based model predictive control (SVM-MPC) is proposed to regulate the real and reactive power components. The main target of this controller is to maintain harmonic free grid currents, even in unbalanced and distorted grid conditions, with enhanced performance in terms of fast dynamic response and good steady-state behavior. The proposed SVM MPC uses Pythagoras theorem to determine duty factors, avoiding trigonometric functions, which improves the computational burden and implementation complexity. In addition, fixed switching frequency can be ensured. Simulation and experimental results are carried out to validate the effectiveness and the practical feasibility of the proposed controller under distorted grid conditions.

Model Predictive Controlled IM Drive based on IT2FNN Controller

Abstract In this paper, the predictive torque control (PTC) based induction motor (IM) drive using an interval type-2 fuzzy neural network (IT2FNN) controller in the speed control loop is designed and tested in simulations. The states required for the proposed motor drive are estimated by extended complex Kalman filter (ECKF). The ECKF performs online estimations of stator currents, rotor fluxes, rotor mechanical speed, and rotor resistance. Compared to conventional extended Kalman filter (EKF), which estimates the same states/parameters, the designed ECKF has less computational burden because it does not contain matrix inverse and the matrix dimensions have been reduced. In addition, the rotor resistance estimated by ECKF is updated online to the PTC system. Thus, the performance of the PTC-based IM drive is improved against variations in the rotor resistance, whose value changes with operating conditions such as frequency and temperature. In order to force both the ECKF observer and the proposed IM drive, a challenging scenario containing the wide speed range operation of the IM is designed. Simulation results confirm the performance of the proposed speed-sensorless PTC-based drive that uses an IT2FNN controller in the speed control loop and the estimation performance of the ECKF observer.

Phase demodulation from a spatial carrier fringe pattern using extended complex Kalman filter

A spatial carrier fringe pattern analysis technique is proposed for the phase demodulation using the extended complex Kalman filter. A state space model is defined based on the spatial evolution model of the fringe signal in a given row or column of the fringe pattern depending on the direction of carrier fringes. Since the state space model incorporates one of the state associated with the carrier fringe frequency, its value need not be known apriori for the phase demodulation. Furthermore, the proposed method is capable of removing carrier phase contribution from the estimated phase using the carrier fringe frequency estimate. Simulation and experimental results substantiates the applicability of the proposed method.

Sensorless control of wind power generator with flywheel energy storage system

For the purpose of sensorless low-speed control of direct-drive permanent magnet synchronous generator–based wind power systems, a technique based on the rotating high-frequency voltage-signal injection is discussed in this article, which improves the efficiency of the method and eliminates the phase shift introduced by traditional filters; band pass and low-pass filters are replaced by an extended complex Kalman filter algorithm. In addition, a flywheel energy storage system based on a squirrel cage induction machine is connected with the wind power generator by a DC bus through two power converters. For sensorless control of the induction machine, a rotor speed estimation method based on the extended complex Kalman filter is established. Finally, network connection interface of the complete system is presented and the efficiency of the proposed sensorless control of the whole chain of wind power generation is shown by numerical simulations using MATLAB/Simulink environment.

Fuzzy-Controller-Designed-PV-Based Custom Power Device for Power Quality Enhancement

In this paper, a three-phase series hybrid active filter (SEHAF) interconnected with photovoltaic (PV) system and dc–dc boost converter is proposed to minimize sag, swell, and harmonics caused due to nonlinear power electronic loads. The SEHAF consists of a voltage source inverter (VSI) with a capacitor connected across it to provide consistency in managing and compensating the reactive power. This minimizes the sag, swell, and harmonics present in the source and load voltages. With the integration of PV, the voltage across the dc-link capacitor of VSI is controlled effectively, which helps in better compensation. Reference current generation is done using the proposed robust extended complex Kalman filter (RECKF) technique. The performance of the PV-integrated-HAF is analyzed using a synchronous reference frame with proportional-integral (PI) as well as fuzzy logic controller (FLC) and is compared with the proposed RECKF technique. The PV-integrated hybrid power system is developed using MATLAB/SIMULINK. Further, real-time digital simulation using OPAL-RT OP5142 is also carried out to support the simulation results. It is observed that the proposed control scheme provides better harmonic compensation compared to conventional PI and FLC.

Square‐root‐extended complex Kalman filter for estimation of symmetrical components in power system

The paper presents a square-root-extended complex Kalman filter (SRECKF) by decomposing covariance matrix with its square-root forms to improve stability of the filter for estimating complex number. αβ transformation is used to map three-phase instantaneous voltages in the abc phases into instantaneous voltages on the αβ axes, and a non-linear state equation and observation equation of the three-phase voltages are built by introducing a complex vector and defining state variables. Positive symmetrical component, negative symmetrical components, and frequency of the three-phase voltages are estimated using traditional extended complex Kalman filter (ECKF), the estimation results show that the method proposed here are superior to traditional extended complex Kalman filter on estimation accuracy and convergence rate.

Kalman Filtering Technique for Rooftop-PV System Under Abnormal Grid Conditions

This paper presents a robust extended complex Kalman filter based control for multifunctional double stage grid-connected solar photovoltaic array (SPVA) system. The main contributions this paper, include the following: first, real power generation from SPVA fulfills the requirement of the connected loads and it provides the surplus power to the distribution network, second, it behaves as a distribution static compensator, which performs various functionalities, such as grid currents balancing, harmonics mitigation, unity power factor operation, finally, it is capable to operate under polluted grid scenarios, such as undervoltage, overvoltage, and imbalanced grid voltages. The SPVA feed-forward term is incorporated in the control technique to enhance the dynamic response of the system. The real coded particle swarm optimization based metaheuristic approach is used for optimal tuning of the dc link voltage proportional integral controller. Simulation results illustrate the effectiveness of the presented control algorithm under variations in point of common coupling voltage. Test results illustrate the behavior of the grid-connected SPVA system subjected to various perturbations, such as undervoltages, overvoltages, distorted and imbalanced grid voltages, etc. The total harmonic distortions of grid currents are achieved well within recommended limits.

Experimental design of a new fast sensorless control of DFIG in complex domain

In this study, a new robust sensorless control of doubly-fed induction generator (DFIG) in the complex domain has been investigated. The proposed sensorless control is based on the extended complex Kalman filter (ECKF) and proportional–integral complex controller. The design of this sensorless control in the complex domain allowed a threefold objective: a decrease in the system's dimension by half, an optimisation in the implementation of the control strategy and a decrease of the CPU computational time. In fact, to obtain the latter, the dimension of the DFIG model involved in this control has been halved, which leads to a reduction in the control's schema. Moreover, all the matrices involved in the ECKF have smaller dimensions than those of the real extended Kalman filter and no matrix inversion is needed because the output of the system is a scalar variable. The proposed sensorless control has been tested experimentally for several operating points, namely: nominal operation, operation under asymmetrical voltage dip and parameter variations. Moreover, the observability of the complex state model has been analysed and the required conditions for the local weak observability have been defined. The experimental results confirm the theoretical study and show a good reliability and a high rotor speed estimation accuracy.

Adaptive complex‐EKF‐based DOA estimation for GPS spoofing detection

In this study, a simple but effective spoofing detection method using a global positioning system (GPS) directional antenna is proposed which exploits the difference between the estimated direction-of-arrival (DOA) and the measured DOA from a GPS almanac and ephemeris data. The receiving signal's DOA is estimated by using a single antenna power measurement-based complex extended Kalman filter (EKF) which is a complex valued state space based estimation technique. Furthermore, an adaptive logic is applied to the complex EKF to reduce the effect of the measurement disturbance. To maintain the validity of the proposed algorithm, it is assumed that the spoofer is aware of the target's location, but that its DOA is not perfectly the same as that of the authentic GPS signal. In addition, the orientation of the directional antenna is known by using an attitude and heading reference system that is attached to the antenna, and its antenna radiation pattern is also known. The proposed detection method is evaluated using a theoretical analysis and simulations. It is finally confirmed that the proposed algorithm can detect a spoofing signal according to the different direction angles of the spoofing signal, and especially those with low DOAs.

Tracking Electromechanical Oscillations: An Enhanced Maximum-Likelihood Based Approach

Lightly damped electromechanical oscillations are major operating concerns if failed to be detected at an early stage. This paper improved the existing extended complex Kalman filter (ECKF) technique of tracking electromechanical oscillations using synchrophasor measurements. The proposed algorithm adopted a distributed architecture for estimating oscillatory parameters from local substations. The novelty lies in handling maximum likelihood (ML) to enhance the convergence property in tracking multiple modes using an expectation maximization (EM) approach. This was achieved by encapsulating the augmented Lagrangian (AL) in the maximization step of the EM algorithm, which utilized a novel ECKF-based smoother (ECKS). Performance evaluations were conducted using IEEE 68-bus system and recorded synchrophasor measurements collected from the New Zealand grid. Random noise variance test cases were generated to examine the performance of the proposed algorithm. To ensure the robustness to random noisy conditions, the algorithm was tested based on exhaustive Monte Carlo simulations. Comparisons were made with the existing Prony analysis (PA), Kalman filter (KF), and distributed EM-based FB-KLPF.

Using disturbance records to automate the diagnosis of faults and operational procedures in power generators

Nowadays, it is a common practice in power generation utilities to monitor the generation units using digital fault recorders. As the disturbance records are generally analysed and stored at a central office or control centre, it has become difficult for engineers to analyse all this data. Some of the main steps in developing automated diagnosis tools to help in this task are the segmentation and feature extraction of the recorded signals and decision making. This study presents a methodology to extract meaningful information from each segment of a disturbance signal. In the approach described in this study, the segmentation is performed by an extended complex Kalman filter. The main features extracted from each segment are symmetrical components at fundamental frequency of voltage and current signals. Feature extraction uses root-mean-square values to obtain the symmetrical components of the three phase quantities. This methodology focuses on offline analysis of fault recorder data of power generators and it is developed not only to fault analysis, but also to verify normal operational procedures, from which result most of the disturbance records. This study also describes an expert system that can be used to automatically classify each record into known categories, focusing the engineer's attention to the most relevant occurrences.

Model predictive‐based shunt active power filter with a new reference current estimation strategy

This study presents a new reference current estimation method using proposed robust extended complex Kalman filter (RECKF) together with model predictive current (MPC) control strategy in the development of a three-phase shunt active power filter (SAPF). A new exponential function embedded into the RECKF algorithm helps in the estimation of in phase fundamental component of voltage ( v h ) at the point of common coupling considering grid perturbations such as distorted voltage, measurement noise and phase angle jump and also for the estimation of fundamental amplitude of the load current ( i h ). The estimation of these two variables ( v h , i h ) is used to generate reference signals for MPC. The proposed RECKF-MPC needs less number of voltage sensors and resolves the difficulty of gain tuning of proportional-integral (PI) controller. The proposed RECKF-MPC approach is implemented using MATLAB/SIMULINK and also Opal-RT was used to obtain the real-time results. The results obtained using the proposed RECKF together with different variants of Kalman filters (Kalman filter (KF), extended KF (EKF) and extended complex KF (ECKF)) and PI controller are analysed both in the steady state as well as transient state conditions. From the above experimentation, it was observed that the proposed RECKF-MPC control strategy outperforms over PI controller and other variants of Kalman filtering approaches in terms of reference tracking error, power factor distortion and percentage total harmonic distortion in the SAPF system.

Research on Stator Flux and Rotor Speed Estimation for Induction Motor Based on Extended Complex Kalman Filter

This paper proposes a stator flux and rotor speed estimation method for induction motor (IM) based on extended complex Kalman filter (ECKF). A complex-valued model is adopted that allows a simpler and more effective state estimation of IM. And a third order ECKF has been designed for IM model by neglecting the mechanical equation, which is a valid hypothesis when the motor is operated at a constant rotor speed. The stator flux and rotor speed estimation obtained from ECKF are applied for direct torque control (DTC) of induction motor. This method for state estimation is more effective and easier than the one performed on the corresponding real-valued model, as it obtains observability conditions directly in terms of stator current and flux complex-valued vectors. The proposed ECKF achieves a good performance in DTC of IM. Simulation experiment results in Matlab/Simulink environment validate the proposed method.

Extended complex Kalman filter for sensorless control of an induction motor

This paper deals with the design of an extended complex Kalman filter (ECKF) for estimating the state of an induction motor (IM) model, and for sensorless control of systems employing this type of motor as an actuator. A complex-valued model is adopted that simultaneously allows a simpler observability analysis of the system and a more effective state estimation. The observability analysis of this model is first performed by assuming that a third order ECKF has to be designed, by neglecting the mechanical equation of the IM model, which is a valid hypothesis when the motor is operated at constant rotor speed. It is shown that this analysis is more effective and easier than the one performed on the corresponding real-valued model, as it allows the observability conditions to be directly obtained in terms of stator current and rotor flux complex-valued vectors. Necessary observability conditions are also obtained along with the well-known sufficient ones. It is also shown that the complex-valued implementation allows a reduction of 35% in the computation time w.r.t. the standard real-valued one, which is obtained thanks to the lower dimensions of the matrices of the ECKF w.r.t. the ones of the real-valued implementation and the fact that no matrix inversion is required. The effectiveness of the proposed ECKF is shown by means of simulation in Matlab/Simulink environment and through experiments on a real low-power drive.

A Robust Extended Complex Kalman Filter and Sliding-mode Control Based Shunt Active Power Filter

—This article presents the design of a new shunt active power filter that employs a modified robust extended complex Kalman filter approach with an exponential robust term embedded for reference current estimation together with a current controller based on the sliding-mode control concept. The robust extended complex Kalman filter exploits a new weighted exponential function to handle these grid perturbations to estimate the reference signal in shunt active power filter system. The current controller in the proposed shunt active power filter has been designed using a sliding-mode control strategy because of its ability to handle parameter uncertainties and ease in implementation. To test the effectiveness of the proposed shunt active power filter, extensive simulations were performed using MATLAB/Simulink (The MathWorks, Natick, Massachusetts, USA), and real-time studies were made using OPAL-RT (Montreal, Quebec, Canada). Results obtained from the above studies using the proposed shunt active power filter together with the different variants of Kalman filter (Kalman filter, extended Kalman filter, extended complex Kalman filter) are analyzed, and it is observed that the proposed robust extended complex Kalman filter-sliding-mode control based shunt active power filter provides accurate and improved harmonics mitigation and reactive power compensation.

Sparse ACEKF for phase reconstruction

We propose a novel low-complexity recursive filter to efficiently recover quantitative phase from a series of noisy intensity images taken through focus. We first transform the wave propagation equation and nonlinear observation model (intensity measurement) into a complex augmented state space model. From the state space model, we derive a sparse augmented complex extended Kalman filter (ACEKF) to infer the complex optical field (amplitude and phase), and find that it converges under mild conditions. Our proposed method has a computational complexity of N(z)N logN and storage requirement of O(N), compared with the original ACEKF method, which has a computational complexity of O(NzN(3)) and storage requirement of O(N(2)), where Nz is the number of images and N is the number of pixels in each image. Thus, it is efficient, robust and recursive, and may be feasible for real-time phase recovery applications with high resolution images.

Enhancing Kalman Filter for Tracking Ringdown Electromechanical Oscillations

Ringdown detection methods like Kalman filter and Prony analysis have been developed to aid transmission operators to track lightly-damped inter-area oscillations. Kalman filter detection is dependent on a priori system knowledge and is designed to monitor the dominant mode. The objective of this paper is to extend Kalman filter to track multiple modes. Thus, extended complex Kalman filter (ECKF) based procedure is formulated and assessed. While retaining the recursive Kalman filter engine, the proposed method redefines the state variable representation to directly estimate the modal parameters instead of using the existing polynomial rooting approach. It also integrates Hankel singular value decomposition (HSVD) to provide better estimates of the initial conditions.

A New Phase Detection Method by Using Kalman Filter

This paper proposes a phase detection method for harmonics and unbalanced voltage conditions. The proposed method uses harmonics and unbalanced voltage compensation circuit in addition to basic PLL (Phase Locked Loop) circuit. In the harmonic compensation circuit, the harmonic voltage component are eliminated from the input voltages using specific harmonic detection method. Besides, frequency information of power system used in the specific harmonic detection method is estimated by an extended complex Kalman filter. In the unbalanced voltage compensation circuit, the input voltage is normalized after the calculated positive sequence component. By means of the proposed method, excellent phase detection performance can be achieved under harmonics and unbalanced voltage conditions. Moreover, detection of positive sequence voltage component becomes possible under voltage drop conditions due to faults in power systems. The effectiveness of the proposed method is verified by simulation results.

Nonlinear system modeling and identification using Volterra‐PARAFAC models

SUMMARYDiscrete‐time Volterra models are widely used in various application areas. Their usefulness is mainly because of their ability to approximate to an arbitrary precision any fading memory nonlinear system and to their property of linearity with respect to parameters, the kernels coefficients. The main drawback of these models is their parametric complexity implying the need to estimate a huge number of parameters. Considering Volterra kernels of order higher than two as symmetric tensors, we use a parallel factor (PARAFAC) decomposition of the kernels to derive Volterra‐PARAFAC models that induce a substantial parametric complexity reduction. We show that these models are equivalent to a set of Wiener models in parallel. We also show that Volterra kernel expansions onto orthonormal basis functions (OBF) can be viewed as Tucker models that we shall call Volterra‐OBF‐Tucker models. Finally, we propose three adaptive algorithms for identifying Volterra‐PARAFAC models when input–output signals are complex‐valued: the extended complex Kalman filter, the complex least mean square (CLMS) algorithm and the normalized CLMS algorithm. Some simulation results illustrate the effectiveness of the proposed identification methods. Copyright © 2011 John Wiley & Sons, Ltd.