In this book, Andrew Harvey sets out to provide a unified and comprehensive theory of structural time series models. Unlike the traditional ARIMA models, structural time series models consist explicitly of unobserved components, such as trends and seasonals, which have a direct interpretation. As a result the model selection methodology associated with structural models is much closer to econometric methodology. The link with econometrics is made even closer by the natural way in which the models can be extended to include explanatory variables and to cope with multivariate time series. From the technical point of view, state space models and the Kalman filter play a key role in the statistical treatment of structural time series models. The book includes a detailed treatment of the Kalman filter. This technique was originally developed in control engineering, but is becoming increasingly important in fields such as economics and operations research. This book is concerned primarily with modelling economic and social time series, and with addressing the special problems which the treatment of such series poses. The properties of the models and the methodological techniques used to select them are illustrated with various applications. These range from the modellling of trends and cycles in US macroeconomic time series to to an evaluation of the effects of seat belt legislation in the UK.

Forecasting, Structural Time Series Models and the Kalman Filter

The enabling of ac microgrids in distribution networks allows delivering distributed power and providing grid support services during regular operation of the grid, as well as powering isolated islands in case of faults and contingencies, thus increasing the performance and reliability of the electrical system. The high penetration of distributed generators, linked to the grid through highly controllable power processors based on power electronics, together with the incorporation of electrical energy storage systems, communication technologies, and controllable loads, opens new horizons to the effective expansion of microgrid applications integrated into electrical power systems. This paper carries out an overview about microgrid structures and control techniques at different hierarchical levels. At the power converter level, a detailed analysis of the main operation modes and control structures for power converters belonging to microgrids is carried out, focusing mainly on grid-forming, grid-feeding, and grid-supporting configurations. This analysis is extended as well toward the hierarchical control scheme of microgrids, which, based on the primary, secondary, and tertiary control layer division, is devoted to minimize the operation cost, coordinating support services, meanwhile maximizing the reliability and the controllability of microgrids. Finally, the main grid services that microgrids can offer to the main network, as well as the future trends in the development of their operation and control for the next future, are presented and discussed.

Control of Power Converters in AC Microgrids

This paper presents a new multiresonant frequency-adaptive synchronization method for grid-connected power converters that allows estimating not only the positive- and negative-sequence components of the power signal at the fundamental frequency but also other sequence components at other harmonic frequencies. The proposed system is called MSOGI-FLL since it is based on both a harmonic decoupling network consisting of multiple second-order generalized integrators (MSOGIs) and a frequency-locked loop (FLL), which makes the system frequency adaptive. In this paper, the MSOGI-FLL is analyzed for single- and three-phase applications, deducing some key expressions regarding its stability and tuning. Moreover, the performance of the MSOGI-FLL is evaluated by both simulations and experiments to show its capability for detecting different harmonic components in a highly polluted grid scenario.

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Multiresonant Frequency-Locked Loop for Grid Synchronization of Power Converters Under Distorted Grid Conditions

The Kalman filter is the minimum-variance state estimator for linear dynamic systems with Gaussian noise. Even if the noise is non-Gaussian, the Kalman filter is the best linear estimator. For nonlinear systems it is not possible, in general, to derive the optimal state estimator in closed form, but various modifications of the Kalman filter can be used to estimate the state. These modifications include the extended Kalman filter, the unscented Kalman filter, and the particle filter. Although the Kalman filter and its modifications are powerful tools for state estimation, we might have information about a system that the Kalman filter does not incorporate. For example, we may know that the states satisfy equality or inequality constraints. In this case we can modify the Kalman filter to exploit this additional information and get better filtering performance than the Kalman filter provides. This paper provides an overview of various ways to incorporate state constraints in the Kalman filter and its nonlinear modifications. If both the system and state constraints are linear, then all of these different approaches result in the same state estimate, which is the optimal constrained linear state estimate. If either the system or constraints are nonlinear, then constrained filtering is, in general, not optimal, and different approaches give different results.

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Kalman filtering with state constraints: a survey of linear and nonlinear algorithms

Synchronization and power sharing for droop-controlled inverters in islanded microgrids

In this paper, the performance assessment of three software single-phase phase-locked loop (PLL) algorithms is carried out by means of dynamic analysis and experimental results. Several line disturbances such as phase-angle jump, voltage sag, frequency step, and harmonics are generated by a DSP together with a D/A converter and applied to each PLL. The actual minus the estimated phase-angle values are displayed, providing a refined method for performance evaluation and comparison. Guidelines for parameters adjustments are also presented. In addition, practical implementation issues such as computational delay effects, ride-through, and computational load are addressed. The developed models proved to accurately represent the PLLs under real test conditions.

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Comparison of Three Single-Phase PLL Algorithms for UPS Applications

This article addresses the state-estimation problem for linear and non-linear systems for the case in which prior knowledge is available in the form of an equality constraint. The equality-constrained Kalman filter (KF) is derived as the maximum-a-posteriori solution to the equality-constrained state-estimation problem for linear and Gaussian systems and is compared to alternative algorithms. Then, four novel algorithms for non-linear equality-constrained state estimation based on the unscented KF are presented, namely, the equality-constrained unscented KF, the projected unscented KF, the measurement-augmentation unscented KF, and the constrained unscented KF. Finally, these methods are compared on linear and non-linear examples.

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State estimation for linear and non-linear equality-constrained systems

The famous chaotic oscillator known as Chua's circuit, despite the robustness of the chaotic behaviour to parametric mismatches, requires the construction of noncommercial valued inductors. A low cost inductorless version of Chua's circuit is presented. It is argued that the new circuit is better suited for control and synchronisation purposes.

Inductorless Chua's circuit

On unscented Kalman filtering with state interval constraints

This paper considers the state-estimation problem with a constraint on the data-injection gain. Special cases of this problem include the enforcing of a linear equality constraint in the state vector, the enforcing of unbiased estimation for systems with unknown inputs, and simplification of the estimator structure for large-scale systems. Both the one-step gain-constrained Kalman predictor and the two-step gain-constrained Kalman filter are presented. The latter is extended to the nonlinear case, yielding the gain-constrained unscented Kalman filter. Two illustrative examples are presented.

Leonardo A. B. Tôrres

Papers

Comparison of Three Single-Phase PLL Algorithms for UPS Applications

State estimation for linear and non-linear equality-constrained systems

Inductorless Chua's circuit

On unscented Kalman filtering with state interval constraints

Gain-Constrained Kalman Filtering for Linear and Nonlinear Systems