Original scientific paper In this paper identification and parameter estimation of a hydro generator thermal system using collected input and output data is presented. Third order state space model is constituted on the basis of a set of independent output variable (temperature) measurements derived from the system response to three thermal sources. Data were collected during a heat run and site acceptance test of a refurbished machine. Least squares (LS or RLS) methodology is used in parameter estimation procedure. Minimisation is performed on weighted measurement and model output distance squares. During the procedure system and input matrices were obtained. Thereafter, spectral properties of system matrix are analysed using calculated eigenvalues and eigenvectors. Eigenvalues assignment to the physical system objects is performed via L2 norm calculation and ranked to output variable sensitivities with respect to their time constants (negative reciprocal eigenvalues). Finally, simplified analogous lumped parameter scheme of the machine thermal system has been outlined.
Keywords: hydro generator; L2 norm; least squares method; parameter estimation; thermal system
Identifikacija i estimacija parametara toplinskog sustava hidrogeneratoraIzvorni znanstveni članak U ovom radu predstavljena je identifikacija i estimacija parametara toplinskog sustava hidrogeneratora pri čemu se koriste prikupljeni podaci o ulazima i izlazima sustava. Na temelju odziva sustava na pobudu tri izvora topline mjeren je skup nezavisnih izlaznih varijabli (temperatura) te je načinjen model toplinskog sustava trećeg reda. Podaci su prikupljani prilikom zagrijavanja i terenskog testiranja obnovljenog stroja. Za estimaciju parametara korištena je metoda najmanjih kvadrata. Minimizacija se provodi za otežana mjerenja i izlaze sustava. Ovim se postupkom dobivaju matrica sustava i ulazna matrica. Nakon toga se pomoću svojstvenih vektora i svojstvenih vrijednosti analiziraju spektralna svojstva matrice sustava. Dodjeljivanje svojstvenih vrijednosti objektima fizikalnog sustava provodi se izračunom L2 norme i rangira se prema osjetljivostima izlaznih varijabli u odnosu na njihove vremenske konstante (koje su negativne i recipročne u odnosu na svojstvene vrijednosti). Na kraju rada dana je pojednostavljena analogna shema s koncentriranim parametrima.
The work presents a comparison of results of the calculation of eddy current losses in the induction motor teeth by virtue of the analytical method and the finite element method. Under the assumption that sheet permeability and conductivity are constant, total eddy current losses can be calculated as the aggregate of pulsation and surface losses. Instructions are given regarding the manner of calculation of total losses in the teeth for all teeth forms, taking into consideration the suppression of flows in the sheets, flow attenuation in the teeth and the sheet and sheet package processing factors. Valuation of the analytical model of loss calculation was also made by virtue of comparison with the measurements.
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