The purpose of this paper is to provide a comprehensive presentation and interpretation of the Ensemble Kalman Filter (EnKF) and its numerical implementation. The EnKF has a large user group, and numerous publications have discussed applications and theoretical aspects of it. This paper reviews the important results from these studies and also presents new ideas and alternative interpretations which further explain the success of the EnKF. In addition to providing the theoretical framework needed for using the EnKF, there is also a focus on the algorithmic formulation and optimal numerical implementation. A program listing is given for some of the key subroutines. The paper also touches upon specific issues such as the use of nonlinear measurements, in situ profiles of temperature and salinity, and data which are available with high frequency in time. An ensemble based optimal interpolation (EnOI) scheme is presented as a cost-effective approach which may serve as an alternative to the EnKF in some applications. A fairly extensive discussion is devoted to the use of time correlated model errors and the estimation of model bias.

The Ensemble Kalman Filter: Theoretical formulation and practical implementation

Series Preface * Preface to the Third Edition * 1 Linear Systems * 2 Nonlinear Systems: Local Theory * 3 Nonlinear Systems: Global Theory * 4 Nonlinear Systems: Bifurcation Theory * References * Index

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Differential Equations and Dynamical Systems

This paper presents a review of advanced control techniques for microgrids. This paper covers decentralized, distributed, and hierarchical control of grid-connected and islanded microgrids. At first, decentralized control techniques for microgrids are reviewed. Then, the recent developments in the stability analysis of decentralized controlled microgrids are discussed. Finally, hierarchical control for microgrids that mimic the behavior of the mains grid is reviewed.

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Advanced Control Architectures for Intelligent Microgrids—Part I: Decentralized and Hierarchical Control

Unit commitment, one of the most critical tasks in electric power system operations, faces new challenges as the supply and demand uncertainty increases dramatically due to the integration of variable generation resources such as wind power and price responsive demand. To meet these challenges, we propose a two-stage adaptive robust unit commitment model for the security constrained unit commitment problem in the presence of nodal net injection uncertainty. Compared to the conventional stochastic programming approach, the proposed model is more practical in that it only requires a deterministic uncertainty set, rather than a hard-to-obtain probability distribution on the uncertain data. The unit commitment solutions of the proposed model are robust against all possible realizations of the modeled uncertainty. We develop a practical solution methodology based on a combination of Benders decomposition type algorithm and the outer approximation technique. We present an extensive numerical study on the real-world large scale power system operated by the ISO New England. Computational results demonstrate the economic and operational advantages of our model over the traditional reserve adjustment approach.

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Adaptive Robust Optimization for the Security Constrained Unit Commitment Problem

1. Introduction. 2. The Nature of Power System Oscillations. 3. Modal Analysis of Power Systems. 4. Modal Analysis for Control. 5. Power System Structure and Oscillations. 6. Generator Controls. 7. Power System Stabilizers. 8. Power System Stabilizers - Problems and Solutions. 9. Robust Control. 10. Damping by Electronic Power System Devices. A1. Model Data Formats and Block Diagrams. A2. Equal Eigenvalues. Index.

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Power System Oscillations

1 Introduction 2 Electromagnetic Transients 3 Synchronous Machine Modeling 4 Synchronous Machine Control Models 5 Single-Machine Dynamic Models 6 Multimachine Dynamic Models 7 Multimachine Simulation 8 Small-Signal Stability 9 Energy Function Methods Appendix A: Integral Manifolds for Model Bibliography Index

Power System Dynamics and Stability

Uncertainty in power systems operations has been traditionally managed by multistage decision making and operating reserve requirements. A familiar example of multistage decisions is day-ahead unit commitment and real-time economic dispatch. An alternate approach for managing uncertainty is a stochastic formulation, which allows the explicit modeling of the sources of uncertainty. This paper compares stochastic and reserve methods and evaluates the benefits of a combined approach for the efficient management of uncertainty in the unit commitment problem. Numerical studies show that unit commitment solutions obtained for the combined approach are robust and superior with respect to the traditional approach in terms of both economics and reliability metrics.

Uncertainty Management in the Unit Commitment Problem

The relationship is presented between a detailed power system dynamic model and a standard load-flow model. The linearized dynamic model is examined to show how the load-flow Jacobian appears in the system dynamic-state Jacobian for evaluating steady-state stability. Two special cases are given for the situation when singularity of the load-flow Jacobian implies singularity of the system dynamic-state Jacobian. The standard load-flow Jacobian can provide information about the existence of a steady-state equilibrium point for a specified level of loading or interchange. There are two very special cases when the determinant of the standard load-flow Jacobian implies something about the steady-state stability of a dynamic model. Both of these cases involve very drastic assumptions about the synchronous machines and their control systems. The load level which produces a singular load-flow Jacobian should be considered an optimistic upper bound on maximum loadability. >

Power system steady-state stability and the load-flow Jacobian

Day-ahead uncertainty management in power systems has traditionally been approached by means of multistage decision making and operating reserve requirements An alternate approach for managing uncertainty is a stochastic formulation, which allows the explicit modeling of the sources of uncertainty The large investments in wind power has increased the importance of operations uncertainty management due to the considerable operational uncertainty wind plants have This paper evaluates the benefits of a combined approach that uses stochastic and reserve methods for the efficient management of uncertainty in the unit commitment problem for systems with significant amount of wind power Numerical studies on a model of the PSCo system show that the unit commitment solutions obtained for the combined approach are robust and superior with respect to the traditional approach in terms of economic metrics and curtailed wind power

Wind power day-ahead uncertainty management through stochastic unit commitment policies

We suggest a new mechanism for interarea electric power system oscillations in which two oscillatory modes interact near a strong resonance to cause one of the modes to subsequently become unstable. The possibility of this mechanism for oscillations is shown by theory and computational examples. Theory suggests that passing near strong resonance can be expected in general power system models. The mechanism for oscillations is illustrated in 3- and 9-bus examples with detailed generator models.

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Peter W. Sauer

Papers

Power System Dynamics and Stability

Uncertainty Management in the Unit Commitment Problem

Power system steady-state stability and the load-flow Jacobian

Wind power day-ahead uncertainty management through stochastic unit commitment policies

Is strong modal resonance a precursor to power system oscillations