A time-stepping algorithm for hysteretic lumped-element transformer models

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.