The one well-known one-dimensional method for calculating the AC resistance of multilayer transformer windings contains a built-in orthogonality which has not been reported previously. Orthogonality between skin effect and proximity effect makes a more generalized approach for the analytical solution of AC resistance in windings possible. This includes a method to calculate the AC resistance of round conductor windings which is not only convenient to use, but gives more accurate answers than the basic one-dimensional method because the exact analytical equations for round conductors can be used. >

Improved analytical modeling of conductive losses in magnetic components

This paper reviews some of the major approaches to modeling and simulation in power electronics, and provides references that can serve as a starting point for the extensive literature on the subject. The major focus of the paper is on averaged models of various kinds, but sampled-data models are also introduced. The importance of hierarchical modeling and simulation is emphasized.

Modeling and simulation of power electronic converters

A computer-oriented method for the time-domain analysis of networks with internally controlled ideal switches is presented No assumptions are made about the continuity of the circuit response at the switching instants; even Dirac impulses are permitted In fact, it is shown that Dirac impulses must be considered for the analysis of some switched networks, even though they may only be present for intermediate steps of the analysis Several topological changes may be needed at each switching instant to ensure that the topology after switching is valid The theories have been implemented in a computer program, SWANN The network equations are generated with a two-graph modified nodal analysis technique, rather than the state equation formulation Various internally controlled switches are permitted, such as the ideal diode, thyristor, and voltage- and current-controlled switches Numerical results show the generality and accuracy of the method on three switched networks >

Time-domain analysis of networks with internally controlled switches

This paper presents a users' perspective of simulation in power electronic and motion control systems. The rationale for simulation in research, education and in the design process, and the details of how simulation is carried out are discussed. Characteristics of a reliable simulation program are outlined and the hierarchical approach to simulation is stressed. Numerical solution issues in the simulation of "stiff" systems such as power electronics and motion control are discussed in general terms. A brief overview of the widely used simulation programs is provided along with the challenges in modeling the semiconductor devices. In conclusion, observations are made with respect to the future role and nature of computer simulations. >

Simulation of power electronic and motion control systems-an overview

A method for fast time-domain simulation of piecewise-linear networks with switches is described in this paper. The method is based on a discrete-time switch model that consists of a constant conductance in parallel with a current source. In each simulation step, the value of the current source is updated as a function of known network signals. The function takes one of two forms, depending on the state (on or off) of the switch. Since the system matrix is constant, regardless of the states of the switches, simulation time is essentially the same as for a linear, time-invariant network of the same complexity. The paper discusses selection of the model and simulation parameters. The simulation algorithm is described and an example is included. It is shown that the method is not only efficient but also quite general and void of convergence problems. Its primary application is for long-term transient simulation of power electronic systems such as switching power converters. >

A method for fast time-domain simulation of networks with switches

By considering the set of short-circuit tests which can be performed on a multiwinding transformer, analytical expressions are derived for the leakage inductances between all pairs of transformer windings, expressions which depend only on the winding geometry and the frequency of excitation. For each short-circuit test, a simplified field analysis gives the complete solution for the frequency-independent magnetic field intensity between winding layers, and the frequency-dependent distribution of magnetic field intensity within each layer. Then, for any frequency of interest, the magnetic energy stored in each winding layer and interlayer space is calculated, and the results are summed to give the total energy stored in the entire winding space of the transformer. Finally, the leakage inductance between excited and short-circuited windings is derived from the total stored energy. Experimental data are provided that illustrate the accuracy and the limitations of such leakage-inductance calculations as well as the accuracy of AC-winding-resistance calculations carried out using a similar, previously published method. >

Calculating the short-circuit impedances of a multiwinding transformer from its geometry

An algorithm is presented for the efficient and accurate simulation of switched-mode piecewise-linear systems, a subclass of which includes regulated energy-storage dc-to-dc converters. Three key features of the new algorithm that lead to significant improvements in computational efficiency and accuracy are 1) a state-transition-matrix table-lookup scheme to solve differential equations describing the system, 2) a modified binary-search strategy to obtain an initial estimate of the instant at which the system topology switches, and 3) a quadratic extrapolation for the accurate final determination of the switching instant. The computational efficiency of a program using the new algorithm is demonstrated by comparing its execution time with that of a program employing a standard fixed-step-size integration algorithm. The accuracy of the new algorithm is verified by comparing results obtained from the simulations with results obtained analytically, and by comparing data from the simulation of two different regulated converters with data measured experimentally.

An Efficient Algorithm for the Time-Domain Simulation of Regulated Energy-Storage DC-to-DC Converters

Accelerated convergence to the steady-state solution of closed-loop regulated switching-mode systems is achieved by more accurately computing the sensitivity matrices involved through a new matrix-based algorithm. By taking into consideration the variation of the timing of the intracycle intervals of a switching-mode system with respect to changes in the state vector, the new algorithm is able to predict system sensitivity with considerably greater accuracy but only slight penalty in computation time over existing algorithms. Newton-Raphson iteration is then applied to compute the steady state, substantially speeding up convergence to the solution as compared to brute-force simulation methods.

Accelerated convergence to the steady-state solution of closed-loop regulated switching-mode systems as obtained through simulation

An algorithm is presented for the efficient and accurate simulation of switched-mode piecewise-li near systems, a subclass of which includes regulated energy-storage dc-to-dc converters. Three key features of the new algorithm that lead to significant improvements in computational efficiency and accuracy are: (1) a state-transition-matrix table-lookup scheme to solve differential equations describing the system, (2) a modified binary-search strategy to obtain an initial estimate of the instant at which the system topology switches, and (3) a quadratic extrapolation for the accurate final determination of the switching instant. The computational efficiency of a program using the new algorithm is demonstrated by comparing its execution time with that of a program employing a standard fixed-step-size integration algorithm. The accuracy of the new algorithm is verified by comparing results obtained from the simulations with results obtained analytically, and by comparing data from the simulation of two different regulated converters with data measured experimentally.

A fast algorithm for the time-domain simulation of switched-mode piecewise-linear systems

One single-layer and two four-layer example winding structures are used to illustrate the impact of excitation frequency on the magnetic field intensity and current density distributions in transformer windings. By plotting the distributions as phasors in three-dimensional isometric plots, greater insight is gained into the origin and behavior of eddy currents. This insight enhances the design engineer's ability to understand and evaluate the available design options. >

Ronald C. Wong

Papers

Calculating the short-circuit impedances of a multiwinding transformer from its geometry

An Efficient Algorithm for the Time-Domain Simulation of Regulated Energy-Storage DC-to-DC Converters

Accelerated convergence to the steady-state solution of closed-loop regulated switching-mode systems as obtained through simulation

A fast algorithm for the time-domain simulation of switched-mode piecewise-linear systems

Magnetic-field-intensity and current-density distributions in transformer windings