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

System Identification I

Applied Numerical Analysis. By C.F. Gerald. Pp. xii, 340. £3·60. 1970. (Addison-Wesley.)

During the last decade, a big progress has been achieved in the analysis and numerical treatment of Initial Value Problems (IVPs) in Differential Algebraic Equations (DAEs) and Ordinary Differential Equations (ODEs). In spite of the rich variety of results available in the literature, there are still many specific problems that require special attention. Two of such, which are considered in this work, are the optimization of order of accuracy and reduction of cost of functional evaluations of Explicit Runge - Kutta (ERK) methods.

Traditionally, the maximum attainable order p of an s-stage ERK method for advancing the solution of an IVP is such that
p(s)
 4
 
In 1999, Goeken presented an s-stage ERK Method of order p(s)=s +1,s>2.
However, this work focuses on the design of a new approximation algorithm that reduces the cost of functional evaluations and yet increases the attainable order higher 
U n and Jonhson [94]; and the classical ERK methods. The order p of 
the new scheme called Multiderivative Explicit Runge-Kutta (MERK) Methods is such that p(s) 2. The stability, convergence and implementation for the optimization of IVPs in DAEs and ODEs systems are also considered.

Numerical solution of initial value problems in differential - algebraic equations

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Stochastic Processes And Filtering Theory

In this paper, we extend a previous study on a totally enclosed thermal model of a synchronous generator, with temperature state estimation using experimental data. The extension includes a new formulation of the system model, with four different model variations with and without temperature dependence in the metal, air, and water heat capacities and the copper resistances, where temperature variation in water and/or air requires a non-standard heat exchanger model. In the former study, the Unscented Kalman Filter (UKF) was used for state estimation. Here, we include both the UKF as well as the Ensemble Kalman Filter (EnKF) in the comparison. UKF and EnKF are compared based on estimation accuracy and computational speed. Results show that EnKF exhibits lower RMSE for the innovation process and thus is more accurate than the UKF even with a “minimum” of 50 particles, but the UKF with 6 sigma points (3 states) is faster. It is too early to conclude which of 4 models is more accurate, as they need to be tuned individually wrt. parameter fitting.

/pdf/state-estimation-of-a-thermal-model-of-air-cooled-3ov4w9rf6p.pdf

State Estimation of a Thermal Model of Air-cooled Synchronous Generator

Droop Control of Hydro Power System in OpenHPL

/pdf/formulation-of-stochastic-mpc-to-balance-intermittent-solar-2hmr7n5z.pdf

Formulation of Stochastic MPC to Balance Intermittent Solar Power with Hydro Power in Microgrid

This paper is concerned with power system modeling using the Modelica language in comparison to a traditional simulation tool. Though most common power system simulation tools are computationally efficient and reasonably user-friendly, they have a closed architecture. Thus, there is motivation to use an open-source modeling language to describe electric networks, such as Modelica. A well-established benchmark for power system studies was analyzed. Regarding the voltage as a function of time, a reasonable agreement was found between the simulation results of the used simulation tools for long-term voltage stability. However, a comparison of faster electromechanical mechanisms, such as rotor angle stability, demands more detailed models in the Modelica tool.

https://www.ep.liu.se/ecp/108/010/ecp14108010.pdf

Power system stability study using modelica

Optimal design and operation of a planned full-scale UASB reactor at a dairy 8 farm are determined using optimization algorithms based on steady state sim- 9 ulations of a dynamic AD process model combined with models of the reac- 10 tor temperature and heat exchanger temperatures based on energy balances. 11 Available feedstock is 6 m 3 /d dairy manure produced by the herd. Three alter- 12 native optimization problems are solved: Maximization of produced methane 13 gas ow, minimization of reactor volume, and maximization of power surplus. 14

Bernt Lie

Papers

State Estimation of a Thermal Model of Air-cooled Synchronous Generator

Droop Control of Hydro Power System in OpenHPL

Formulation of Stochastic MPC to Balance Intermittent Solar Power with Hydro Power in Microgrid

Power system stability study using modelica

Optimal Design and Operation of a UASB Reactor for 1