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Recent Developments of Electrical Drives - Part 46

Recent Developments of Electrical Drives - Part 46. The book stating the recent developments of electrical drives, can be useful for engineers and researchers investigating and designing electrical and electronic devices as well as for students and young researchers dealing with electrical and electronic engineering, computer sciences (advanced computer modelling, sophisticated control systems with artificial intelligence tools applied, optimal design bye use of classical and genetic algorithms employed), applied mathematics and all the topics where electromagnetic, thermal, mechanical phenomena occur | III-3.5. Improved Modeling of Three-Phase Transformer Analysis 453 Figure 2. Calculated Fourier series curve and measured curve. The calculated Fourier series curve and the measured curve are illustrated in Fig. 2. The Fourier coefficients ak are computed once then stored for the determination of B f H or U f I for all possible values of H or I. The measured curve considered in this study corresponds to the line-to-line voltage in the primary and to the current of the phase A of the primary winding. Numerical approach Two methods have been developed for this approach. For both methods the leakage inductances Lai La2 of the primary and secondary windings as well as the zero-sequence inductances L 01 L 02 are considered as constants. The first one considers the total magnetic flux as state variables. The corresponding set of six differential equations is given by d W B 7 dt B uABC - RABC iABC u abc Rabc iabc 8 where RABC is the resistances of the primary windings and Rabc is the resistances of the secondary windings. The total magnetic flux of different windings including zero-sequence flux are given by W L i 9 The self and mutual inductances are expressed in function of the magnetic reluctances R1T R2T R3T of the equivalent magnetic circuit-diagrams with N1 N2 the turns of the primary respectively secondary windings. For example the magnetizing inductance of the primary winding A respectively the mutual inductance between the primary winding A and 454 Kawkabani and Simond the secondary one b are given by L N2 Lh1A d d rT R3T R1T -------- R2T R3T N2 R2T R3T R1T R2T R1T R3T R2T R3T 10 L Ab -n n2 r3T R1T R2T R1T R3T R2T R3T 11 Similar expressions are determined for all the inductances. The determination of the magnetic flux at each integration step permits to evaluate and adapt by the B-H curve the different magnetic reluctances as well as different inductances. Some numerical software package like SIMSEN 2 http simsen.epfl.ch use essentially the currents as state .