Equivalent circuits of electromagnetic devices are an efficient alternative to full transient EM analysis especially when phenomenon such as inrush currents are investigated. The time-constants in such cases generally, for a 50 Hz transformer, are in the order of several minutes hence rendering full transient EM simulation time consuming. On the circuit level, the simulation time involved is a fraction of the EM transient case. Furthermore, parametric analysis may take place in the circuit simulation allowing what-if scenarios to be tested e.g. effect of system impedance on inrush behavior.
This article shows the application of CST EM STUDIO® (CST EMS) magnetostatic solvers within the System and Assembly Modeling (SAM) framework to the emulation of two standard transformer tests for the extraction of T-equivalent circuit parameters at 50 Hz. An important requirement is the facility to account for the non-linear magnetization inductance in such a equivalent circuit. The circuit is then tested in CST DESIGN STUDIO™ the results of which are then compared to the CST EMS transient solver....
SAM allows the user to create a workflow for specific applications. The user may wish to use a particular equivalent circuit topology that allows for the modeling of certain effects. There are several equivalent circuit topologies that may be applied. Once a topology has been chosen, the SAM framework allows the user to define the necessary tasks.
Figure 1 shows a typical textbook equivalent circuit definition consisting of leakage and magnetizing inductances. These inductances can be derived by the application of the CST EMS magnetostatic solver. Two simulations are required: a so-called Buck Test and a standard open circuit test. The two simulations are based on a single CST STUDIO SUITE® master project on which all simulation tasks are based. Any changes to the master project will be inherited by the simulation tasks meaning that parametric or optimization can be easily carried out in the SAM framework.
The simulation task models will, however, deviate from each other in simulation settings depending on their function. Figure 2 shows the first simulation in the workflow being a standard open circuit test. In this case, the secondary current in the simulation is set to zero and the primary current is swept from zero to a maximum level define by the user. The maximum value will be influenced by the use of the equivalent circuit. For inrush current simulations, the maximum current may be up to 10 times the rated current.
The results of the open circuit test, in the form of a non-linear magnetization characteristic, are then transferred to the CST DS schematic as a SPICE model block. The flux linkage is shown which reflects the non-linear nature of the core which has been defined as a non-linear steel. The flux linkage is converted to an inductance in the spice model extraction. CST EMS does, however, offer other post-processing data such as the inductance matrices and energy/co-energy. Furthermore, the equivalent model may be tested with the CST EMS low frequency transient solver which can also simulate the open circuit and short circuit conditions.
The next simulation task, shown in figure 3, is a buck test which is a recognised simulation technique which delivers accurate leakage inductance values as opposed to those obtained via the emulation of a short circuit test. In the buck test, the number of Ampere Turns in coils are equal and opposite. If the current is modified to ensure this criterion, it it possible to extract the correct proportions of primary and leakage inductances - which is not possible in the measured short circuit test. The buck test is more accurate, from a simulation point of view, since it ensures that the magnetization current is exactly zero as opposed to the approximately zero value obtained via short circuit tests. A buck test is not easy to apply in measurement and is therefore an advantage that simulation offers .
Once the magnetostatic tasks have been performed and the extracted parameters transfered to the schematic, the circuit simulation is then started. On both magnetic field and circuit levels, parameterization may be applied. Effects of gaps in gapped cores, and geometrical and material changes may be investigated.
In Figure 4, an example is given of a sympathetic inrush calculation where two identical transformers based on the same equivalent circuit have been used. A transient circuit task has been set up with a simusoidal excitation at 50 Hz. A system network impedance has been defined consisting of an inductance and resistance. The equivalent circuit has been reduced for this example to account for just the magnetization current. The transformers are switched on after 20 and 40 ms respectively. The effect of the switching on the inrush current are also shown in Figure 4. It is apparent from the current waveform that the time constants involved are very long rendering a full EM transient simulation an extremely long process. An equivalent circuit approach is therefore much more efficient. Furthermore, changes to the circuit toplogy require no further EM simulations.
The System Assembly and Modeling (SAM) framework can be applied to the derivation of workflows for particular appplications such as transformer modeling and the efficient calculation of inrush currents. Such an approach may be taken even further. For example, other types of simulation such as electrostatic, may be applied to include parasitic capacitive effects at higher frequencies. Due to to the arbitrary nature of equivalent circuit topolgies, customization of the workflow is necessary and is supported by the SAM framework.
 D.A. Lowther, P.P. Silvester, "Computer-Aided Design in Magnetics", Springer-Verlag Berlin and Heidelberg GmbH & Co. KG, 1985, ISBN-13: 978-3642706738