Combination of Kalman filter and least error square techniques in power system

An algorithm based on the concept of combining Kalman filter and Least Error Square (LES) techniques is proposed in this paper. The algorithm is intended to estimate signal attributes like amplitude, frequency and phase angle in the online mode. This technique can be used in protection relays, digital AVRs, DGs, DSTATCOMs, FACTS and other power electronics applications. The Kalman filter is modified to operate on a fictitious input signal and provides precise estimation results insensitive to noise and other disturbances. At the same time, the LES system has been arranged to operate in critical transient cases to compensate the delay and inaccuracy identified because of the response of the standard Kalman filter. Practical considerations such as the effect of noise, higher order harmonics, and computational issues of the algorithm are considered and tested in the paper. Several computer simulations and a laboratory test are presented to highlight the usefulness of the proposed method. Simulation results show that the proposed technique can simultaneously estimate the signal attributes, even if it is highly distorted due to the presence of non-linear loads and noise.

Decentralized peak power control based on short-term forecast using modified Kalman filter

This paper proposes a method of short term load forecasting with limited data, applicable even at 11 kV substation levels where total power demand is relatively low and somewhat random and weather data are usually not available as in most developing countries. Kalman filtering technique has been modified and used to forecast daily and hourly load. Planning generation and interstate energy exchange schedule at load dispatch centre and decentralized Demand Side Management at substation level are intended to be carried out with the help of this short term load forecasting technique especially to achieve peak power control without enforcing load-shedding.

Plant-wide predictive control for a thermal power plant based on a physical plant model

A constrained non-linear, physical model-based, predictive control (NPMPC) strategy is developed for improved plant-wide control of a thermal power plant. The strategy makes use of successive linearisation and recursive state estimation using extended Kalman filtering to obtain a linear state-space model. The linear model and a quadratic programming routine are used to design a constrained long-range predictive controller One special feature is the careful selection of a specific set of plant model parameters for online estimation, to account for time-varying system characteristics resulting from major system disturbances and ageing. These parameters act as nonstationary stochastic states and help to provide sufficient degrees-of-freedom to obtain unbiased estimates of controlled outputs. A 14th order non-linear plant model, simulating the dominant characteristics of a 200 MW oil-fired pou er plant has been used to test the NPMPC algorithm. The control strategy gives impressive simulation results, during large system disturbances and extremely high rate of load changes, right across the operating range. These results compare favourably to those obtained with the state-space GPC method designed under similar conditions.

Kalman tracking linear predictor for vowel intelligibility enhancement on european portuguese HMM based speech synthesis

The recent developments on Hidden Markov Models (HMM) based speech synthesis showed that this is a promising technology fully capable of competing with other established techniques. However some issues still lack a solution. Several authors report an over-smoothing phenomenon on both time and frequencies which decreases naturalness and sometimes intelligibility. In this work we present a new vowel intelligibility enhancement algorithm that uses a discrete Kalman filter (DKF) for tracking frame based parameters. The inter-frame correlations are modelled by an autoregressive structure which provides an underlying time frame dependency and can improve time-frequency resolution. The system’s performance has been evaluated using objective and subjective tests and the proposed methodology has led to improved results.

Adaptive filtering for high quality HMM based speech synthesis

In this work an adaptive filtering scheme based on a dual Discrete Kalman Filtering (DKF) is proposed for Hidden Markov Model (HMM) based speech synthesis quality enhancement. The objective is to improve signal smoothness across HMMs and their related states and to reduce artifacts due to acoustic model's limitations. Both speech and artifacts are modelled by an autoregressive structure which provides an underlying time frame dependency and improves time-frequency resolution. Themodel parameters are arranged to obtain a combined state-space model and are also used to calculate instantaneous power spectral density estimates. The quality enhancement is performed by a dual discrete Kalman filter that simultaneously gives estimates for the models and the signals. The system's performance has been evaluated using mean opinion score tests and the proposed technique has led to improved results.

Advances in sequential data assimilation and numerical weather forecasting: an Ensemble Transform Kalman-Bucy Filter, a study on clustering in deterministic Ensemble Square Root Filters, and a test of a new time stepping scheme in an atmospheric model

This dissertation deals with aspects of sequential data assimilation (in particular ensemble Kalman filtering) and numerical weather forecasting. In the first part, the recently formulated Ensemble Kalman-Bucy (EnKBF) filter is revisited. It is shown that the previously used numerical integration scheme fails when the magnitude of the background error covariance grows beyond that of the observational error covariance in the forecast window. Therefore, we present a suitable integration scheme that handles the stiffening of the differential equations involved and doesn’t represent further computational expense. Moreover, a transform-based alternative to the EnKBF is developed: under this scheme, the operations are performed in the ensemble space instead of in the state space. Advantages of this formulation are explained. For the first time, the EnKBF is implemented in an atmospheric model. The second part of this work deals with ensemble clustering, a phenomenon that arises when performing data assimilation using of deterministic ensemble square root filters in highly nonlinear forecast models. Namely, an M-member ensemble detaches into an outlier and a cluster of M-1 members. Previous works may suggest that this issue represents a failure of EnSRFs; this work dispels that notion. It is shown that ensemble clustering can be reverted also due to nonlinear processes, in particular the alternation between nonlinear expansion and compression of the ensemble for different regions of the attractor. Some EnSRFs that use random rotations have been developed to overcome this issue; these formulations are analyzed and their advantages and disadvantages with respect to common EnSRFs are discussed. The third and last part contains the implementation of the Robert-Asselin-Williams (RAW) filter in an atmospheric model. The RAW filter is an improvement to the widely popular Robert-Asselin filter that successfully suppresses spurious computational waves while avoiding any distortion in the mean value of the function. Using statistical significance tests both at the local and field level, it is shown that the climatology of the SPEEDY model is not modified by the changed time stepping scheme; hence, no retuning of the parameterizations is required. It is found the accuracy of the medium-term forecasts is increased by using the RAW filter.

Automatic absolute orientation of scanned aerial photographs

Image orientation is a basic problem in Digital Photogrammetry. While interior and relative orientations were succesfully automated, the same can not be said about absolute orientation. This process can be automated by using an approach based on relational matching and a heuristic that uses the analytical relation between straight features in the object space and its homologous in the image space. A build-in self-diagnosis is also used in this method, that is based on the implementation of data snooping statistic test in the process of spatial resection, using the Iterated Extended Kalman Filtering (IEKF). The aim of this paper is to present the basic principles of the proposed approach and results based on real data.

Line based camera calibration in machine vision dynamic applications

The problem of dynamic camera calibration considering moving objects in close range environments using straight lines as references is addressed. A mathematical model for the correspondence of a straight line in the object and image spaces is discussed. This model is based on the equivalence between the vector normal to the interpretation plane in the image space and the vector normal to the rotated interpretation plane in the object space. In order to solve the dynamic camera calibration, Kalman Filtering is applied; an iterative process based on the recursive property of the Kalman Filter is defined, using the sequentially estimated camera orientation parameters to feedback the feature extraction process in the image. For the dynamic case, e.g. an image sequence of a moving object, a state prediction and a covariance matrix for the next instant is obtained using the available estimates and the system model. Filtered state estimates can be computed from these predicted estimates using the Kalman Filtering approach and based on the system model parameters with good quality, for each instant of an image sequence. The proposed approach was tested with simulated and real data. Experiments with real data were carried out in a controlled environment, considering a sequence of images of a moving cube in a linear trajectory over a flat surface.

Localización y seguimiento de aeronaves mediante sistemas de multilateración de área extensa

El continuo crecimiento de la demanda del transporte aéreo, junto con los nuevos escenarios de intervención militar, están obligando a una optimización en el uso del espacio aéreo. De este modo, la UE y los EEUU (a través de SESAR y NextGen respectivamente) han asentado las bases para una nueva gestión del tráfico aéreo (ATM). Con ello, se pretende aumentar la capacidad de aeropuertos y rutas aéreas, otorgando mayor flexibilidad al uso del espacio aéreo sin comprometer la seguridad de los usuarios. Desde un punto de vista puramente técnico, la clave de este cambio de modelo está en el conocimiento de la posición de cada aeronave en cada instante. En este sentido, la tendencia en ATM es el uso de ADS-B como fuente principal de posicionamiento. Sin embargo, debido a que este sistema está basado en la difusión de la posición obtenida a través de GPS, es necesario un sistema de seguimiento independiente. Actualmente, la intención es migrar del radar secundario de vigilancia (SSR) a la multilateración de área extensa (WAM), con el fin de mejorar la integridad de la posición para aplicaciones en ruta. Aprovechando el rápido despliegue de ADS-B, se pretende reutilizar sus estaciones base para WAM. Cada estación base que recibe el mensaje ADS-B de la aeronave envía conjuntamente la medida del tiempo de llegada (TOA) de dicho mensaje al centro de tráfico aéreo. La posición de la aeronave se obtiene mediante multilateración, cuya técnica consiste en utilizar las medidas de TOA de un mismo mensaje ADS-B obtenidas en las distintas estaciones base. El objetivo es estimar la posición de cada aeronave con la mayor precisión posible. Para poder diseñar el sistema que permite alcanzar este objetivo, son dos los aspectos básicos a estudiar. Por una parte, la identificación y posterior caracterización de los errores (tanto sistemáticos como aleatorios) que afectan a la medida de TOA. Por otra parte, es necesario el estudio de los sistemas de seguimiento, basados en versiones sofisticadas del filtro de Kalman (IMM, UKF). Una vez establecidos estos dos pilares, la presente tesis doctoral propone un sistema que permite efectuar el seguimiento de las aeronaves, corrigiendo los efectos de las principales distorsiones que afectan a la medida de TOA: la refracción troposférica y el error de sincronismo. La mejora en la precisión de la localización ha sido evaluada mediante simulación de escenarios hipotéticos. ABSTRACT The ever-growing demand in the air transportation and the new military intervention scenarios, are generating a need to optimize the use of the airspace. This way, the EU and the USA (through SESAR and NextGen respectively) have set the ground to overhaul the current air traffic management. The intention is to enhance the capacity of airports and air routes, providing greater flexibility in the use of airspace without jeopardizing the security of the end-users. From a technical perspective, the key for this change lies in the knowledge of the aircraft position. The trend in Air Traffic Management (ATM) is to rely on ADS-B as the main source for aircraft positioning. However, this system is based on the aircraft’s self-declaration of its own (often GPS-based) navigation solution. It is therefore necessary to have an independent surveillance system. Nowadays, the intention is to gradually migrate from Secondary Surveillance Radar (SSR) towards Wide Area Multilateration (WAM) in order to enhance surveillance integrity for en-route applications. Given the fast deployment of ADS-B, the aim is to use its base stations for WAM. Each station sends the Time of Arrival (TOA) of the received ADS-B messages to the air traffic center (ATC). The aircraft position is obtained through multilateration, using the TOA of the same message measured by each station. The aim is to accurately estimate the position of each aircraft. Knowledge from two key areas has to be gathered prior to designing such a system. It is necessary to identify and then characterize the errors (both systematic and random) affecting the TOA measurements. The second element is the study of tracking systems based on sophisticated versions of the Kalman filtering (e.g. IMM, UKF). Based on this knowledge, the main contribution of this Ph.D. is an aircraft tracking system that corrects the effects of the main errors involved in the TOA measurement: tropospheric refraction and synchronization issues. Performance gains in positioning accuracy have been assessed by simulating hypothetical WAM scenarios.

Online estimation of distorted power system signal parameters

An algorithm based on the concept of Kalman filtering is proposed in this paper for the estimation of power system signal attributes, like amplitude, frequency and phase angle. This technique can be used in protection relays, digital AVRs, DSTATCOMs, FACTS and other power electronics applications. Furthermore this algorithm is particularly suitable for the integration of distributed generation sources to power grids when fast and accurate detection of small variations of signal attributes are needed. Practical considerations such as the effect of noise, higher order harmonics, and computational issues of the algorithm are considered and tested in the paper. Several computer simulations are presented to highlight the usefulness of the proposed approach. Simulation results show that the proposed technique can simultaneously estimate the signal attributes, even if it is highly distorted due to the presence of non-linear loads and noise.

Analysis of distrubances in large interconnected power systems

World economies increasingly demand reliable and economical power supply and distribution. To achieve this aim the majority of power systems are becoming interconnected, with several power utilities supplying the one large network. One problem that occurs in a large interconnected power system is the regular occurrence of system disturbances which can result in the creation of intra-area oscillating modes. These modes can be regarded as the transient responses of the power system to excitation, which are generally characterised as decaying sinusoids. For a power system operating ideally these transient responses would ideally would have a “ring-down” time of 10-15 seconds. Sometimes equipment failures disturb the ideal operation of power systems and oscillating modes with ring-down times greater than 15 seconds arise. The larger settling times associated with such “poorly damped” modes cause substantial power flows between generation nodes, resulting in significant physical stresses on the power distribution system. If these modes are not just poorly damped but “negatively damped”, catastrophic failures of the system can occur. To ensure system stability and security of large power systems, the potentially dangerous oscillating modes generated from disturbances (such as equipment failure) must be quickly identified. The power utility must then apply appropriate damping control strategies. In power system monitoring there exist two facets of critical interest. The first is the estimation of modal parameters for a power system in normal, stable, operation. The second is the rapid detection of any substantial changes to this normal, stable operation (because of equipment breakdown for example). Most work to date has concentrated on the first of these two facets, i.e. on modal parameter estimation. Numerous modal parameter estimation techniques have been proposed and implemented, but all have limitations [1-13]. One of the key limitations of all existing parameter estimation methods is the fact that they require very long data records to provide accurate parameter estimates. This is a particularly significant problem after a sudden detrimental change in damping. One simply cannot afford to wait long enough to collect the large amounts of data required for existing parameter estimators. Motivated by this gap in the current body of knowledge and practice, the research reported in this thesis focuses heavily on rapid detection of changes (i.e. on the second facet mentioned above). This thesis reports on a number of new algorithms which can rapidly flag whether or not there has been a detrimental change to a stable operating system. It will be seen that the new algorithms enable sudden modal changes to be detected within quite short time frames (typically about 1 minute), using data from power systems in normal operation. The new methods reported in this thesis are summarised below. The Energy Based Detector (EBD): The rationale for this method is that the modal disturbance energy is greater for lightly damped modes than it is for heavily damped modes (because the latter decay more rapidly). Sudden changes in modal energy, then, imply sudden changes in modal damping. Because the method relies on data from power systems in normal operation, the modal disturbances are random. Accordingly, the disturbance energy is modelled as a random process (with the parameters of the model being determined from the power system under consideration). A threshold is then set based on the statistical model. The energy method is very simple to implement and is computationally efficient. It is, however, only able to determine whether or not a sudden modal deterioration has occurred; it cannot identify which mode has deteriorated. For this reason the method is particularly well suited to smaller interconnected power systems that involve only a single mode. Optimal Individual Mode Detector (OIMD): As discussed in the previous paragraph, the energy detector can only determine whether or not a change has occurred; it cannot flag which mode is responsible for the deterioration. The OIMD seeks to address this shortcoming. It uses optimal detection theory to test for sudden changes in individual modes. In practice, one can have an OIMD operating for all modes within a system, so that changes in any of the modes can be detected. Like the energy detector, the OIMD is based on a statistical model and a subsequently derived threshold test. The Kalman Innovation Detector (KID): This detector is an alternative to the OIMD. Unlike the OIMD, however, it does not explicitly monitor individual modes. Rather it relies on a key property of a Kalman filter, namely that the Kalman innovation (the difference between the estimated and observed outputs) is white as long as the Kalman filter model is valid. A Kalman filter model is set to represent a particular power system. If some event in the power system (such as equipment failure) causes a sudden change to the power system, the Kalman model will no longer be valid and the innovation will no longer be white. Furthermore, if there is a detrimental system change, the innovation spectrum will display strong peaks in the spectrum at frequency locations associated with changes. Hence the innovation spectrum can be monitored to both set-off an “alarm” when a change occurs and to identify which modal frequency has given rise to the change. The threshold for alarming is based on the simple Chi-Squared PDF for a normalised white noise spectrum [14, 15]. While the method can identify the mode which has deteriorated, it does not necessarily indicate whether there has been a frequency or damping change. The PPM discussed next can monitor frequency changes and so can provide some discrimination in this regard. The Polynomial Phase Method (PPM): In [16] the cubic phase (CP) function was introduced as a tool for revealing frequency related spectral changes. This thesis extends the cubic phase function to a generalised class of polynomial phase functions which can reveal frequency related spectral changes in power systems. A statistical analysis of the technique is performed. When applied to power system analysis, the PPM can provide knowledge of sudden shifts in frequency through both the new frequency estimate and the polynomial phase coefficient information. This knowledge can be then cross-referenced with other detection methods to provide improved detection benchmarks.

Urban dynamic origin-destination matrices estimation

The aim of this paper is to explore a new approach to obtain better traffic demand (Origin-Destination, OD matrices) for dense urban networks. From reviewing existing methods, from static to dynamic OD matrix evaluation, possible deficiencies in the approach could be identified: traffic assignment details for complex urban network and lacks in dynamic approach. To improve the global process of traffic demand estimation, this paper is focussing on a new methodology to determine dynamic OD matrices for urban areas characterized by complex route choice situation and high level of traffic controls. An iterative bi-level approach will be used, the Lower level (traffic assignment) problem will determine, dynamically, the utilisation of the network by vehicles using heuristic data from mesoscopic traffic simulator and the Upper level (matrix adjustment) problem will proceed to an OD estimation using optimization Kalman filtering technique. In this way, a full dynamic and continuous estimation of the final OD matrix could be obtained. First results of the proposed approach and remarks are presented.

Performance control of distributed generation using digital estimation of signal parameters

The Queensland University of Technology (QUT) allows the presentation of a thesis for the Degree of Doctor of Philosophy in the format of published or submitted papers, where such papers have been published, accepted or submitted during the period of candidature. This thesis is composed of seven published/submitted papers, of which one has been published, three accepted for publication and the other three are under review. This project is financially supported by an Australian Research Council (ARC) Discovery Grant with the aim of proposing strategies for the performance control of Distributed Generation (DG) system with digital estimation of power system signal parameters. Distributed Generation (DG) has been recently introduced as a new concept for the generation of power and the enhancement of conventionally produced electricity. Global warming issue calls for renewable energy resources in electricity production. Distributed generation based on solar energy (photovoltaic and solar thermal), wind, biomass, mini-hydro along with use of fuel cell and micro turbine will gain substantial momentum in the near future. Technically, DG can be a viable solution for the issue of the integration of renewable or non-conventional energy resources. Basically, DG sources can be connected to local power system through power electronic devices, i.e. inverters or ac-ac converters. The interconnection of DG systems to power system as a compensator or a power source with high quality performance is the main aim of this study. Source and load unbalance, load non-linearity, interharmonic distortion, supply voltage distortion, distortion at the point of common coupling in weak source cases, source current power factor, and synchronism of generated currents or voltages are the issues of concern. The interconnection of DG sources shall be carried out by using power electronics switching devices that inject high frequency components rather than the desired current. Also, noise and harmonic distortions can impact the performance of the control strategies. To be able to mitigate the negative effect of high frequency and harmonic as well as noise distortion to achieve satisfactory performance of DG systems, new methods of signal parameter estimation have been proposed in this thesis. These methods are based on processing the digital samples of power system signals. Thus, proposing advanced techniques for the digital estimation of signal parameters and methods for the generation of DG reference currents using the estimates provided is the targeted scope of this thesis. An introduction to this research – including a description of the research problem, the literature review and an account of the research progress linking the research papers – is presented in Chapter 1. One of the main parameters of a power system signal is its frequency. Phasor Measurement (PM) technique is one of the renowned and advanced techniques used for the estimation of power system frequency. Chapter 2 focuses on an in-depth analysis conducted on the PM technique to reveal its strengths and drawbacks. The analysis will be followed by a new technique proposed to enhance the speed of the PM technique while the input signal is free of even-order harmonics. The other techniques proposed in this thesis as the novel ones will be compared with the PM technique comprehensively studied in Chapter 2. An algorithm based on the concept of Kalman filtering is proposed in Chapter 3. The algorithm is intended to estimate signal parameters like amplitude, frequency and phase angle in the online mode. The Kalman filter is modified to operate on the output signal of a Finite Impulse Response (FIR) filter designed by a plain summation. The frequency estimation unit is independent from the Kalman filter and uses the samples refined by the FIR filter. The frequency estimated is given to the Kalman filter to be used in building the transition matrices. The initial settings for the modified Kalman filter are obtained through a trial and error exercise. Another algorithm again based on the concept of Kalman filtering is proposed in Chapter 4 for the estimation of signal parameters. The Kalman filter is also modified to operate on the output signal of the same FIR filter explained above. Nevertheless, the frequency estimation unit, unlike the one proposed in Chapter 3, is not segregated and it interacts with the Kalman filter. The frequency estimated is given to the Kalman filter and other parameters such as the amplitudes and phase angles estimated by the Kalman filter is taken to the frequency estimation unit. Chapter 5 proposes another algorithm based on the concept of Kalman filtering. This time, the state parameters are obtained through matrix arrangements where the noise level is reduced on the sample vector. The purified state vector is used to obtain a new measurement vector for a basic Kalman filter applied. The Kalman filter used has similar structure to a basic Kalman filter except the initial settings are computed through an extensive math-work with regards to the matrix arrangement utilized. Chapter 6 proposes another algorithm based on the concept of Kalman filtering similar to that of Chapter 3. However, this time the initial settings required for the better performance of the modified Kalman filter are calculated instead of being guessed by trial and error exercises. The simulations results for the parameters of signal estimated are enhanced due to the correct settings applied. Moreover, an enhanced Least Error Square (LES) technique is proposed to take on the estimation when a critical transient is detected in the input signal. In fact, some large, sudden changes in the parameters of the signal at these critical transients are not very well tracked by Kalman filtering. However, the proposed LES technique is found to be much faster in tracking these changes. Therefore, an appropriate combination of the LES and modified Kalman filtering is proposed in Chapter 6. Also, this time the ability of the proposed algorithm is verified on the real data obtained from a prototype test object. Chapter 7 proposes the other algorithm based on the concept of Kalman filtering similar to those of Chapter 3 and 6. However, this time an optimal digital filter is designed instead of the simple summation FIR filter. New initial settings for the modified Kalman filter are calculated based on the coefficients of the digital filter applied. Also, the ability of the proposed algorithm is verified on the real data obtained from a prototype test object. Chapter 8 uses the estimation algorithm proposed in Chapter 7 for the interconnection scheme of a DG to power network. Robust estimates of the signal amplitudes and phase angles obtained by the estimation approach are used in the reference generation of the compensation scheme. Several simulation tests provided in this chapter show that the proposed scheme can very well handle the source and load unbalance, load non-linearity, interharmonic distortion, supply voltage distortion, and synchronism of generated currents or voltages. The purposed compensation scheme also prevents distortion in voltage at the point of common coupling in weak source cases, balances the source currents, and makes the supply side power factor a desired value.

Dynamic equivalent state estimation for multi-area power systems with synchronized phasor measurement units

This paper proposes a new approach for state estimation of angles and frequencies of equivalent areas in large power systems with synchronized phasor measurement units. Defining coherent generators and their correspondent areas, generators are aggregated and system reduction is performed in each area of inter-connected power systems. The structure of the reduced system is obtained based on the characteristics of the reduced linear model and measurement data to form the non-linear model of the reduced system. Then a Kalman estimator is designed for the reduced system to provide an equivalent dynamic system state estimation using the synchronized phasor measurement data. The method is simulated on two test systems to evaluate the feasibility of the proposed method.