Chalmers Univ. of Technology and Göteborg Univ., Diss.--Göteborg, 2006.

Thesis (Ph. D.)--University of Texas at Austin, 2003. / Vita. Includes bibliographical references. Available also from UMI Company.

Thesis (Ph. D.)--University of Washington, 2003. / Vita. Includes bibliographical references (p. 152-162).

published_or_final_version / Statistics and Actuarial Science / Master / Master of Philosophy

Not available / text

published_or_final_version / Statistics / Doctoral / Doctor of Philosophy

Parameter tting will facilitate model validation of the generic dynamic model for type-3 WTGs. In this thesis, a test system including a single 1.5 MW DFIG has been built and tested in the PSCAD/EMTDC environment for dynamic responses. The data generated during these tests have been used as measurements for the parameter tting which is carried out using the unscented Kalman lter. Two variations of the generic type-3 WTG model (the detailed model and the simpli ed model) have been compared and used for parameter estimation. The detailed model is able to capture the dynamics caused by the converter and thus has been used for parameter tting when inputs are from a fault scenario. On the other hand, the simpli ed model works well for parameter tting when a wind speed disturbance is of interest. Given measurements from PSCAD, the estimated parameters using both models are indeed improvements compared to the original belief of the parameters in terms of prediction error.

The use of characteristic functions to represent well-known sets in graph theory such as dominating, irredundant, independent, covering and packing sets - leads naturally to fractional versions of these sets and corresponding fractional parameters. Let S be a dominating set of a graph G and f : V(G)~{0,1} the characteristic function of that set. By first translating the restrictions which define a dominating set from a set-based to a function-based form, and then allowing the function f to map the vertex set to the unit closed interval, we obtain the fractional generalisation of the dominating set S. In chapter 1, known domination-related parameters and their fractional generalisations are introduced, relations between them are investigated, and Gallai type results are derived. Particular attention is given to graphs with symmetry and to products of graphs. If instead of replacing the function f : V(G)~{0,1} with a function which maps the vertex set to the unit closed interval we introduce a function f' which maps the vertex set to {0, 1, ... ,k} (where k is some fixed, non-negative integer) and a corresponding change in the restrictions on the dominating set, we obtain a k-dominating function. In chapter 2 corresponding k-parameters are considered and are related to the classical and fractional parameters. The calculations of some well known fractional parameters are expressed as optimization problems involving the k- parameters. An e = 1 function is a function f : V(G)~[0,1] which obeys the restrictions that (i) every non-isolated vertex u is adjacent to some vertex v such that f(u)+f(v) = 1, and every isolated vertex w has f(w) = 1. In chapter 3 a theory of e = 1 functions and parameters is developed. Relationships are traced between e = 1 parameters and those previously introduced, some Gallai type results are derived for the e = 1 parameters, and e = 1 parameters are determined for several classes of graphs. The e = 1 theory is applied to derive new results about classical and fractional domination parameters. / Thesis (M.Sc.)-University of Natal, 1995.

Parameter tting will facilitate model validation of the generic dynamic model for type-3 WTGs. In this thesis, a test system including a single 1.5 MW DFIG has been built and tested in the PSCAD/EMTDC environment for dynamic responses. The data generated during these tests have been used as measurements for the parameter tting which is carried out using the unscented Kalman lter. Two variations of the generic type-3 WTG model (the detailed model and the simpli ed model) have been compared and used for parameter estimation. The detailed model is able to capture the dynamics caused by the converter and thus has been used for parameter tting when inputs are from a fault scenario. On the other hand, the simpli ed model works well for parameter tting when a wind speed disturbance is of interest. Given measurements from PSCAD, the estimated parameters using both models are indeed improvements compared to the original belief of the parameters in terms of prediction error.

Modeling of chemical engineering systems often necessitates using non-linear models. These models can range in complexity, from a simple analytical equation to a system of differential equations. Regardless of what type of model is being utilized, determining parameter estimates is essential in everyday chemical engineering practice. One promising approach to non-linear regression is a technique called Markov Chain Monte Carlo (MCMC).This method produces reliable parameter estimates and generates joint confidence regions (JCRs) with correct shape and correct probability content. Despite these advantages, its application in chemical engineering literature has been limited. Therefore, in this project, MCMC methods were applied to a variety of chemical engineering models. The objectives of this research is to (1) illustrate how to implement MCMC methods in complex non-linear models (2) show the advantages of using MCMC techniques over classical regression approaches and (3) provide practical guidelines on how to reduce the computational time. MCMC methods were first applied to the biological oxygen demand (BOD) problem. In this case study, an implementation procedure was outlined using specific examples from the BOD problem. The results from the study illustrated the importance of estimating the pure error variance as a parameter rather than fixing its value based on the mean square error. In addition, a comparison was carried out between the MCMC results and the results obtained from using classical regression approaches. The findings show that although similar point estimates are obtained, JCRs generated from approximation methods cannot model the parameter uncertainty adequately. Markov Chain Monte Carlo techniques were then applied in estimating reactivity ratios in the Mayo-Lewis model, Meyer-Lowry model, the direct numerical integration model and the triad fraction multiresponse model. The implementation steps for each of these models were discussed in detail and the results from this research were once again compared to previously used approximation methods. Once again, the conclusion drawn from this work showed that MCMC methods must be employed in order to obtain JCRs with the correct shape and correct probability content. MCMC methods were also applied in estimating kinetic parameter used in the solid oxide fuel cell study. More specifically, the kinetics of the water-gas shift reaction, which is used in generating hydrogen for the fuel cell, was studied. The results from this case study showed how the MCMC output can be analyzed in order to diagnose parameter observability and correlation. A significant portion of the model needed to be reduced due to these issues of observability and correlation. Point estimates and JCRs were then generated using the reduced model and diagnostic checks were carried out in order to ensure the model was able to capture the data adequately. A few select parameters in the Waterloo Polymer Simulator were estimated using the MCMC algorithm. Previous studies have shown that accurate parameter estimates and JCRs could not be obtained using classical regression approaches. However, when MCMC techniques were applied to the same problem, reliable parameter estimates and correct shape and correct probability content confidence regions were observed. This case study offers a strong argument as to why classical regression approaches should be replaced by MCMC techniques. Finally, a very brief overview of the computational times for each non-linear model used in this research was provided. In addition, a serial farming approach was proposed and a significant decrease in computational time was observed when this procedure was implemented.