STATIONARY AND NON-STATIONARY STATE SPACE MODELS

Abstract. The concepts of time invariance, stationarity, non-stationarity and immemorial time are considered for state space models (SSMs). Necessary and sufficient conditions for stationarity are given and connected with standard conditions. Expressions are given for the unconditional mean and covariance matrix of the state of a time-immemorial SSM. Application of the results is made to a variety of theoretical and empirical models and the initialization of the Kalman filter in the non-stationary case and for the ARIMA ( p, d, q ) model.     

Complete transformer model for electromagnetic transients

A complete, three phase transformer model for the calculation of electromagnetic transients is presented. The model consists of a set of state equations solved with the trapezoidal rule of integration in order to obtain an equivalent Norton circuit at the transformer terminals. Thus the transformer model can be easily interfaced with an electromagnetic transients program. Its main features are: (a) the basic elements for the winding model are the turns; (b) the complete model includes the losses due to eddy currents in the windings and in the iron core; and (c) the solution of the state equations is obtained in decoupled iterations. For validation, the frequency response of the model is compared with tests on several transformers. Applications to the calculation of transients are given for illustration     

Modal Kalman filtering based impedance relaying

An algorithm is presented for computer distance relaying. It is based on modal Kalman filtering (MKF) to estimate fundamental phasors, MKF exploits all the measurement information available from a three-phase line and is founded on enhanced models of the electromagnetic transients noise. To support the modeling of noise for different faults, a study of nontrivial electrical networks with accurate electromagnetic transients modeling is made for 400 kV transmission lines. MKF fits the behavior of the different modal noise for the Clarke phasors, but it is invariant for each type of fault, assuring robustness and minimum error variance. To computer distance, Clarke αB phasors are transformed to +/- symmetrical components, and then a well-known expression is used to computer the positive impedance. Statistical analysis if presented to assess observation time versus estimation accuracy for the different types of line faults     

Total and acid-soluble fluoride content of infant cereals, beverages and biscuits from Brazil

Total fluoride (TF) and HCl 0.01 M ('gastric juice')-soluble fluoride (SF) were analysed in infant foods, beverages and calcium-rich biscuits. Samples were divided into seven categories: children cereals (A), chocolate-flavoured milk (B), soy beverages (C), filled biscuits (D), non-filled biscuits (E), wafer biscuits (F) and corn starch biscuits (G). Mean TF concentrations ± SD (amplitude, unit µg F ml^-1 or µg F g^-1) were: (A) 4.25 ± 3.04 (0.20 - 7.84, n = 6); (B) 0.34 ± 0.47 (0.05-1.27, n = 6); (C) 0.15 ± 0.07 (0.09-0.29, n = 8); (D) 8.44 ± 1.76 (7.65-10.47, n = 4); (E) 12.41 ± 1.15 (10.69-13.68, n = 4); (F) 0.35 ± 0 (0.34-0.36, n = 4) and (G) 7.77 ± 1.12 (6.86-8.68, n = 2). Five samples of cereals, one sample of chocolate-flavoured milk and 10 samples of biscuits were analysed for SF. In cereals analysed for SF, all fluoride was soluble, while for the chocolate-flavoured milk, approximately 50% of TF was soluble. Regarding the biscuits analysed for SF approximately 20% of TF was soluble. It was observed that some of the cereals and beverages, and most of the biscuits analysed, might be important contributors to total daily fluoride intake. When consumed just once per day, cereals and beverages might supply up to 25% of the maximum recommended daily fluoride intake (0.07 mg F kg^-1 body weight) for a 2-year-old child (12 kg). For the filled, non-filled and corn starch biscuits, when 3, 32 or 20 units of them, respectively, are consumed just once per day, they may supply up to 16% of the maximum recommended daily fluoride intake. However, only approximately 25% of fluoride absorption occurs from the stomach and 75% from the small intestine. Therefore, a higher fluoride bioavailability is possible.     

Quantifying technological aspects of process sustainability: a thermodynamic approach

Thermodynamic analysis has greatly helped to compare and to improve the energy efficiency of all kinds of technological processes, and recently we have also attempted to analyse some important biochemical processes under intracellular conditions. This work has pointed to some key strategies on sustainable process operation, such as the exceptionally high thermodynamic efficiencies of chemical and solar energy conversion in living cells.From this it was expected that the sustainability strategies of specific biochemical processes and those of the ecosphere as a whole could be of guidance to current technological processes, especially now that there is a growing demand from government and industry to effectively deal with sustainability aspects in process analysis. Our focus on this issue has led to methodologies to quantify technological aspects of sustainability by making use of thermodynamic principles. Three indicators were constructed to express three technological aspects of process sustainability. First, an indicator for the sustainability of resource utilization considers the thermodynamic input and the availability the resources used in the process. Secondly, an efficiency indicator focuses on the conversion and loss of thermodynamic quantities in the process itself. Thirdly, an indicator for environmental compatibility takes into account the thermodynamic input required to prevent possible negative side effects of the process, such as global warming or water pollution. The three indicators are used to reflect on (un)sustainable characteristics of current technological processes compared to biochemical processes. Finally, we address the drawbacks of combining indicator values to express overall sustainability.