Alexander Sauseng

This contribution presents a practical approach for determining the parameters of a topological lumped‐element (LE) three‐phase transformer model in a shell‐type configuration from a two‐dimensional finite‐element (FE) simulation. Based on the observations of the magnetic flux density from the FE simulation around the coils, we propose a manual fitting of the LE primary current signals to those from the FE simulation by adjusting the leakage parameters of the LE model. This straightforward fitting is possible because the LE leakage parameters influence specific time sections of the primary current signal shape almost independently of each other. The no‐load and short‐circuit cases are considered for the practical fitting procedure, implying that load cases are also captured, in contrast to merely using a no‐load fitting technique. The applicability and the limitations are discussed, and the results are finally concluded.

The paper is devoted to the modeling of a three-phase, three-legged transformer under no-load and inrush current conditions. To simplify the study, transformer simulations are carried out in the ATPDraw environment, which now incorporates a dynamic hysteresis model (DHM). The main distinction of the DHM-based transformer models proposed from existing analogues lies in their ability to replicate transformer behavior over an extended range of excitation voltages. In addition to the use of the DHM, this improvement is achieved by reproducing a variable nature of equivalent air gaps at core joints. Two model versions with variable core gaps differ in whether they account for or disregard magnetic anisotropy of the core steel. Both these experiment-oriented models were fitted accurately to the same measured data by using individual flux–current characteristics of their gaps. In such a way, we have demonstrated the difficulties in distinguishing between effects caused by the core gaps and magnetic anisotropy in practical transformer modeling. By extending the method of variable core gaps to inrush currents modeling, residual fluxes in the core and current peaks were replicated accurately. The results simulated with the topological models presented are in a good agreement with measurements performed on a 300 kVA Yyn 11.350/0.235 kV transformer.

This paper introduces a new anhysteresis curve for electromagnetic simulations such as transformers, rotating machines, or magnetic devices. Unlike existing anhysteresis curves, the introduced curve has several advantages, including continuous differentiability, smoothness for numerical solvers, and characterization using four parameters, each responsible for a specific magnetization region. The new anhysteresis curve is validated by fitting various magnetic materials, and its accuracy is compared to well-known curves such as the (double) Langevin function, the inverse tangent function, and the hyperbolic tangent function. Inverting the constitutive law in magnetics, containing the proposed anhysteresis curve, is also in the scope of this paper because b-based finite element formulations, such as the magneto(quasi)static vector potential formulation, require the inverse material relation.

Incorporating the magnetic core material in a lumped‐element transformer model generally results in a nonlinear network with hysteresis. Such a network can be solved subsequently in the time domain using time‐stepping methods. The transient response reveals the inrush, whose decay time is generally enormous compared to the time constant of the excitation period (e.g., 20 ms for a voltage source with a frequency of 50 Hz). To directly obtain the steady‐state solution of the lumped‐element transformer model, the harmonic balance method is superior to such an analysis, because it is a frequency domain approach inherently yielding the steady‐state solution. The great advantage of harmonic balance is that it can handle nonlinearities by evaluating them in the time domain and using their spectral components in the frequency domain. This paper theoretically derives the harmonic balance algorithm and further solves a lumped‐element single‐phase transformer model based on a mutual and leakage flux approach utilizing Hopkinson 's law. The nonlinear network element is represented by an energy‐based dry friction‐like hysteresis model depicting the core material of the transformer. The hysteresis parameters are fitted to no‐load current measurements, and the no‐load case, the short‐circuit case, and a chosen load case are simulated and compared to measurements. The algorithm's efficiency in terms of iterations and computational time is demonstrated by simulating with several excitation frequencies and for several load cases and comparing it to a transient analysis revealing the transformer's inrush.

This contribution is about network-based transformer models. Two models (single- and three-phase) are derived, whereas Hopkinson’s analogy is used to depict the magnetic domain. Therein, an energy-based hysteresis model is incorporated to represent the magnetic core. The solution strategy is a second-order variable step size backward differentiation formula (BDF2) in time domain, yielding the transient response of the two transformers. Finally, the simulation results are compared to measurements.

Purpose: A precise numerical simulation environment for transformer models can be challenging due to the hysteretic core behavior. Assuming linear material laws ensures efficient and straightforward solution schemes in the time domain, which, in contrast, do not incorporate saturation effects, inrush phenomena or hysteresis losses. The purpose of this paper is a time-stepping algorithm for a topologically correct lumped-element three-phase transformer model, including nonlinearities and hysteresis in the transformer’s core. Design/methodology/approach: The general methodology is to set up a quasi-linear differential algebraic equation system of the transformer model based on modified nodal analysis, which is subsequently solvable using a variable step size backward differentiation formula of second order. The core sections are represented by an energy-based dry friction-like hysteresis model. The connection between the magnetic and electric domain is enabled by Hopkinson’s analogy. The presented time-stepping algorithm can be implemented straightforwardly in a numerical environment. Findings: The time-stepping algorithm converges to high accuracy in a few iterations and yields the transient response of the three-phase transformer model. A comparison to inrush measurements demonstrates the algorithm’s practicability and additionally validates the transformer model. Originality/value: The differential algebraic equation system of the lumped-element transformer model incorporates an energy-based dry friction-like hysteresis model. The solution scheme is a second-order backward differentiation formula to solve the hysteretic system in the time domain.

Incorporating the magnetic core material in a lumped-element transformer model generally results in a nonlinear network with hysteresis. This network can be solved subsequently in time domain, yielding the transient response of the transformer. To directly obtain the steady-state solution, the method of harmonic balance is superior to such a transient analysis since it is a frequency domain approach capable of handling nonlinearities. For this reason, harmonic balance is derived theoretically and further applied to a dedicated single-phase transformer network based on a mutual and leakage flux approach. The nonlinear network element is represented by an energy-based dry-friction-like hysteresis model depicting the core material of the transformer. Finally, the results of harmonic balance are compared to measurements and the algorithm's efficiency is discussed.