An extended Kalman filter approach for accurate instantaneous dynamic phasor estimation

This paper proposes the application of a non-linear Extended Kalman Filter (EKF) for accurate instantaneous dynamic phasor estimation. An EKF-based algorithm is proposed to better adapt to the dynamic measurement requirements and to provide real-time tracking of the fundamental harmonic components and power system frequencies. This method is evaluated using dynamic compliance tests defined in the IEEE C37.118.1-2011 synchrophasor measurement standard, providing promising results in phasor and frequency estimation, compliant with the accuracy required in the case of off-nominal frequency, amplitude and phase angle modulations, frequency ramps, and step changes in magnitude and phase angle. An important additional feature of the method is its capability for real-time detection of transient disturbances in voltage or current waveforms using the residual of the filter, which enables flagging of the estimation for suitable processing

Kalman Filters for Parameter Estimation of Nonstationary Signals

An adaptive Taylor-Kalman filter with PSO tuning for tracking nonstationary signal parameters in a noisy environment with primary focus on time-varying power signals has been presented in this piece of work. In order to deal with the dynamic envelope of the power signal, second-order Taylor expansion has been used such that the Taylor coefficients are updated with the PSO-tuned Taylor-Kalman Filter algorithm. In addition to this, for fast convergence, a self-adaptive particle swarm optimization technique has been used for obtaining the optimal values of model and measurement error covariances of the Kalman filter. The proposed algorithm is linear and therefore has less computational burden, which is easier to be implemented on a hardware platform like DSP processor or FPGA. The proposed PSO-tuned Taylor-Kalman filter exhibits robust tracking capabilities even under changing signal dynamics, immune to critical noise conditions, harmonic contaminations, and also reveals excellent convergence properties

Technique for Measurement of Weld Resistance for AC Resistance Spot Welding via Instantaneous Phasor Measurement

The resistance measurement in the resistance spot welding (RSW), is an ongoing research topic. The high current flow during the welding process induces an electromagnetic field in the wires which are attached to the electrodes to measure tip voltage. This results an additional voltage drop which is proportional to the derivative of current. Also the presence of silicon controlled rectifier (SCR) in the welding power supply generates harmonics in both supply voltage and current. These issues together complicate the methods for resistance estimation. A set of simultaneous linear equations is derived for the on-line measurement of dynamic resistance and induced voltage constant by using the dynamic circuit analysis of weld setup. This can be solved to determine the weld resistance using instantaneous phasors measurements for the 1st, 3rd and 5th harmonics of current and measured voltage signals. The instantaneous phasor measurements for these desired harmonics are obtained by employing the following proposed method. In this thesis, a new method for the measurement of instantaneous phasor is proposed for the narrow band signals. The proposed algorithm is based on the internal model principle (IMP) defined for the cancellation of a sinusoidal disturbance signal. The IMP has two states, exhibiting the properties of being sinusoidal and orthogonal. The instantaneous values of IMP states are defined as real and imaginary components of a complex signal at each time instant. The instantaneous measurements of envelope and phase of a sinusoidal signal are determined from instantaneous values of complex signal by using arithmetic properties of complex numbers. In case of signal comprising of sum of sinusoids of different frequencies, the approach for obtaining instantaneous phasor for each sinusoidal component is presented by connecting multiple internal models in the parallel and open-loop configuration. The instantaneous phasor measurement of fundamental frequency signal is not only advantageous in detecting faults like short circuiting, harmonic distortion and frequency variations but it can also be applied to protect power system from these faults. In this work, the applicability of the proposed instantaneous phasor measurement algorithm is analyzed for scenarios of power disturbances due to the the harmonic distortion and decaying DC offset. The results are discussed and compared with few existing methods

Three-Phase Synchrophasor Estimation Through Taylor Extended Kalman Filter

Synchronized phasor and frequency measurements are key tools for the monitoring and management of modern power systems. In a dynamic scenario, it is fundamental to define algorithms that allow accurately measuring time-varying signals, with short latencies and high reporting rates. A dynamic phasor model can help the design of these algorithms and, in particular, of those based on Kalman filtering approach. In this paper, an Extended Kalman filter formulation that considers the Taylor expansions of amplitudes and phase angles in three-phase signals is introduced. The proposed dynamic model takes into account the inherent relationship among the phases and includes harmonics in a effective way. The performance of the method permitting both synchrophasor and frequency measurements are assessed by simulations, considering also the combined effect of dynamics and disturbances. The algorithm shows tracking capabilities and the flexibility which is mandatory to deal with different conditions

Dynamic synchrophasor estimation by extended Kalman filter

Fast synchronized measurements of the phasor, frequency, and rate of change of frequency are expected to be very important for the automated control actions in the smart grid context. In this regard, measurement latency must be kept as short as possible for an effective control implementation when networks characterized by extremely fast dynamics are concerned. Kalman filter (KF)-based estimation algorithms appear to be attractive in this context; however, the conventional implementations suffer from significant limitations in their ability to deal with different types of dynamic conditions due to approximations in the model and in the associated uncertainty. This article proposes an innovative solution, based on an extended KF algorithm using a Taylor model, which is shown to provide improved tracking ability in a vast range of dynamic conditions. A novel element in the proposed technique is the representation of model uncertainty, which takes into account the intrinsic correlation among errors that appear in the state–space description under dynamic conditions. A compatibility check between the forecast and measurement result is also introduced as an effective and metrologically sound approach to detect large unexpected changes in the tracked parameters in order to achieve a fast response of the algorithm also under those conditions. The performance of the algorithm is thoroughly investigated by means of simulation to demonstrate the significant improvement compared to other KF solutions in some conditions of practical relevance

Adaptive filtering algorithms for quaternion-valued signals

Advances in sensor technology have made possible the recoding of three and four-dimensional signals which afford a better representation of our actual three-dimensional world than the ``flat view'' one and two-dimensional approaches. Although it is straightforward to model such signals as real-valued vectors, many applications require unambiguous modeling of orientation and rotation, where the division algebra of quaternions provides crucial advantages over real-valued vector approaches. The focus of this thesis is on the use of recent advances in quaternion-valued signal processing, such as the quaternion augmented statistics, widely-linear modeling, and the HR-calculus, in order to develop practical adaptive signal processing algorithms in the quaternion domain which deal with the notion of phase and frequency in a compact and physically meaningful way. To this end, first a real-time tracker of quaternion impropriety is developed, which allows for choosing between strictly linear and widely-linear quaternion-valued signal processing algorithms in real-time, in order to reduce computational complexity where appropriate. This is followed by the strictly linear and widely-linear quaternion least mean phase algorithms that are developed for phase-only estimation in the quaternion domain, which is accompanied by both quantitative performance assessment and physical interpretation of operations. Next, the practical application of state space modeling of three-phase power signals in smart grid management and control systems is considered, and a robust complex-valued state space model for frequency estimation in three-phase systems is presented. Its advantages over other available estimators are demonstrated both in an analytical sense and through simulations. The concept is then expanded to the quaternion setting in order to make possible the simultaneous estimation of the system frequency and its voltage phasors. Furthermore, a distributed quaternion Kalman filtering algorithm is developed for frequency estimation over power distribution networks and collaborative target tracking. Finally, statistics of stable quaternion-valued random variables, that include quaternion-valued Gaussian random variables as a special case, is investigated in order to develop a framework for the modeling and processing of heavy-tailed quaternion-valued signals.Open Acces

Performance Improvement of Wide-Area-Monitoring-System (WAMS) and Applications Development

Wide area monitoring system (WAMS), as an application of situation awareness, provides essential information for power system monitoring, planning, operation, and control. To fully utilize WAMS in smart grid, it is important to investigate and improve its performance, and develop advanced applications based on the data from WAMS. In this dissertation, the work on improving the WAMS performance and developing advanced applications are introduced.To improve the performance of WAMS, the work includes investigation of the impacts of measurement error and the requirements of system based on WAMS, and the solutions. PMU is one of the main sensors for WAMS. The phasor and frequency estimation algorithms implemented highly influence the performance of PMUs, and therefore the WAMS. The algorithms of PMUs are reviewed in Chapter 2. To understand how the errors impact WAMS application, different applications are investigated in Chapter 3, and their requirements of accuracy are given. In chapter 4, the error model of PMUs are developed, regarding different parameters of input signals and PMU operation conditions. The factors influence of accuracy of PMUs are analyzed in Chapter 5, including both internal and external error sources. Specifically, the impacts of increase renewables are analyzed. Based on the analysis above, a novel PMU is developed in Chapter 6, including algorithm and realization. This PMU is able to provide high accurate and fast responding measurements during both steady and dynamic state. It is potential to improve the performance of WAMS. To improve the interoperability, the C37.118.2 based data communication protocol is curtailed and realized for single-phase distribution-level PMUs, which are presented in Chapter 7.WAMS-based applications are developed and introduced in Chapter 8-10. The first application is to use the spatial and temporal characterization of power system frequency for data authentication, location estimation and the detection of cyber-attack. The second application is to detect the GPS attack on the synchronized time interval. The third application is to detect the geomagnetically induced currents (GIC) resulted from GMD and EMP-E3. These applications, benefited from the novel PMU proposed in Chapter 6, can be used to enhance the security and robust of power system