Correctly modelling the nonlinear saturation characteristics of the transformer iron core is of great importance in steady-state calculations (harmonics and power quality) and calculations of the electromagnetic transients (inrush current, ferroresonance, temporary overvoltages). Thus, this paper presents an original estimation algorithm for determining the transformer nonlinear saturation characteristic from the measured inrush and steady-state current waveforms in entire windows of occurrences. The proposed algorithm is based on the minimization of a specifically defined cost function by applying the Nelder–Mead method, which was used to create a balance between the transformer steady-state current and the inrush current at zero residual flux. The algorithm uses the BDF numerical method in the background to solve the stiff differential equation system. By applying the appropriate indexes of quality estimation, it was demonstrated that, out of a total of twelve proposed analytical functions, the best optimization results were achieved with three proposed functions (the Frolich extended, three-term polynomial and special hyperbolic function). Detailed performances and accuracy suggested that the estimation algorithm has been verified by a very close agreement between the simulation results and measured transformer current waveforms in the steady-state and different inrush current scenarios.

中文翻译：

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用Nelder-Mead优化法确定单相变压器饱和特性

正确模拟变压器铁芯的非线性饱和特性对于稳态计算（谐波和电能质量）和电磁瞬态计算（涌入电流、铁磁谐振、暂时过电压）非常重要。因此，本文提出了一种原始的估计算法，用于根据整个事件窗口中测量的涌流和稳态电流波形来确定变压器非线性饱和特性。所提出的算法基于通过应用 Nelder-Mead 方法来最小化特定定义的成本函数，该方法用于在零剩余通量时在变压器稳态电流和涌流之间建立平衡。该算法在后台使用BDF数值方法求解刚性微分方程组。通过应用适当的质量估计指标，证明了在总共十二个建议的分析函数中，三个建议的函数（Frolich 扩展、三项多项式和特殊双曲线函数）实现了最佳优化结果。详细的性能和准确性表明，在稳态和不同浪涌电流情况下，仿真结果与测量的变压器电流波形非常接近，验证了估计算法。使用三个建议函数（Frolich 扩展、三项多项式和特殊双曲函数）实现了最佳优化结果。详细的性能和准确性表明，在稳态和不同浪涌电流情况下，仿真结果与测量的变压器电流波形非常接近，验证了估计算法。使用三个建议函数（Frolich 扩展、三项多项式和特殊双曲函数）实现了最佳优化结果。详细的性能和准确性表明，在稳态和不同浪涌电流情况下，仿真结果与测量的变压器电流波形非常接近，验证了估计算法。