Finite Element Analysis of Three-Phase Three-Limb Power Transformers Under DC Bias

Steady-state time-periodic finite element analysis of a brushless DC motor drive considering motion

“…The observed very slow convergence relates to the continuous operation of diode elements. For the remaining starting points the model has converged within the given iteration limit and these results show how important it is to use close estimates of the starting point in this type of model as long as it has to be practical [14]. However, if the permanent-magnet brushless machines are considered, the rotational speed at a given point can be estimated well using even the basic equations of a DC machine and the lumped parameters obtained from simple magnetostatic computations.…”

“…Once the waveform of angular speed is obtained from (8), the rotation angle required for detection of the commutation zone can be calculated from: (14) assuming for k = 1 initial value " 0 which corresponds to initial rotor position.…”

“…This one, in addition to the known features of the Newton-Raphson method when applied to the time-periodic models regarding a problematic convergence [13], makes the iterative process unstable. For that reason, in the solution of the current problem the Newton-Raphson method will be replaced by the fixed-point technique [13,14]. The discretized physical equation of mechanical balance (12) will be substituted by the artificial equation of the form:…”

“…and D Fp is the fixed-point coefficient being constant during the iterative process [13,14]. By proper selection of D Fp the rise of T r from one iteration to another may be slowed down to the extent which provides the convergence at the price of reducing its rate.…”

“…The basic TPFEM gathers equations for all time-steps in a particular nonsymmetric system of equations, and consequently, it requires extensive computations and suitable solvers. There are a few implementations of this method, which make it more cost-effective, namely: the explicit error correction methods [11] or parallelization [12,14]. Currently, there are the system-level simulators available whose functionality includes the ability to predict the steady-state waveforms in switched circuits using this method [15], yet this is not the case in the state-of-the-art finite element analysis systems.…”