Research On Characteristics Of Transformer Under DC-Biased Magnetization By Harmonic Balance Finite Element Method

The power transformer is susceptible to DC bias in the operation of high voltage direct current (HVDC) transmission system. In-depth analysis of mechanism of DC bias phenomenon contributes to manufacture and maintenance of transformer. The harmonic balance finite element method (HBFEM) is effective to solve the nonlinear time-periodic electromagnetic field. It is very important in aspects of both theory and application to study the HBFEM basic theory, computation method, and DC bias problem of power transformer in frequency.Sponsored by the National Natural Science Foundation of China under grant 50677016 and Nutural Science Foundation of Hebei Province under grant E2006000772, this paper combines DC-biasing experiment with numerical analysis to invesigate the magnetizing and loss characteristics of laminated core model (LCM) under DC bias condition. Main achievements are presented as follows:1. DC-biasing experiments in accordance with different ways of DC-biased magnetization are carried out on Epstein frame and LCM respectively. Magnetizing current in exciting coil and magnetic field in magnetic core are calculated by the HBFEM. Comparing the calculated results with the experimental data shows consistency. Harmonic analysis of magnetizing current is performed to observe the effect of DC bias and alternating voltage on each harmonic component.2. The decomposed harmonic-balanced method applicable to DC-biasing case is proposed. The block Gauss-Seidal algorithm and relaxation iterative method are employed to solve harmonic solutions of magnetizing current and magnetic vetor potential sequntially. Memory requirement is reduced greatly by the decomposed method, which is suitble for lagre-scale computation. Variations of DC flux and AC flux are analyzed under different DC bias and AC excitations.3. A modified iterative method (MIM) to predict DC flux in LCM and a new method to simulate the DC-biasing hysteresis loops are presented. To obtain accurate DC flux, hysteresis model based on consuming function is adopted in MIM to simulate DC-biasing hysteresis effects and the DC-biasing magnetizing curve is revised. The asymmetric DC-biasing magnetizing curves and hysteresis loops are analyzed to explore the effect of DC bias on magnetizing charateristic of LCM.4. The fixed-point harmonic-balanced finite element method (FPHBFEM) is presented. Different ways to determine the fixed-point reluctivity lead to different convergent performance of harmonic solutions, therefore globlly convergent algorithm (GCA) and locally convergent algorithm (LCA) in FPHBFEM are derived respectively. Significantly decreased memory requirement in GCA give rise to short computational time. Compared with HBFEM, harmonic solutions in LCA converge faster with the same memory cost.5. The magnetizing curve under normal condition and DC-biasing magnetizing curve are used in finite element method respecitvely to calculte the magnetic field in LCM under DC-biased magnetization. Analysis of calculated magnetizing current and flux density demonstrates that the calculated results stem from DC-biasing magnetizing curve are more accurate. Hysteresis effects of LCM under normal and DC bias condition are considered in FPHBFEM and the calculated magnetizing currents agree well with the measurd one. The hysteretic charateristics in different places in LCM are analyzed through the harmonic solution of DC-biasing magnetic field.