This paper proposes a novel multi-scale cable model in phase-coordinates exploiting the fully-coupled structure of the nodal admittance matrix instead of using the conventional approach based on the Method of Characteristics (MoC). The usage of the admittance modeling allows a straightforward representation of cables regardless of their lengths as it does not require a minimum time-step below the transient time associated with the fastest mode. In addition, some accuracy issues regarding the rational modeling of the nodal admittance matrix are overcome resorting to the Folded Line Equivalent (FLE) transformation.

Following the so-called frequency-adaptive simulation of transients (FAST) concept, the trapezoidal rule and recursive convolution expressions are rewritten to perform computations using analytic signals or complex variables. This will allow the possibility to combine electromagnetic and electromechanical trasients phenomena in the same simulation environment with a unique mathematical model.

A novel variable time-step algorithm is presented and its flexibility is so general that can be incorporated in Electromagnetic Transient (EMT) software such as EMTP-RV, PSCAD or Hypersim in straightforward way.

Besides keeping the accuracy of the classic EMT-modeling, the proposed formulation provides a sensible gain in the overall computation time without significant loss of accuracy and also smooth transitions regardless of the time-step length.

本文提出了一种新型的多尺度电缆相位坐标模型，该模型利用节点导纳矩阵的完全耦合结构，而不是使用基于特征方法（MoC）的常规方法。导纳建模的使用可以直接表示电缆，而不必考虑电缆的长度，因为它不需要比与最快模式相关的瞬态时间短的最小时间步长。另外，借助于折线等效（FLE）变换可以克服关于节点导纳矩阵的合理建模的一些精度问题。

在所谓的瞬态频率自适应仿真（FAST）概念之后，梯形规则和递归卷积表达式被重写以使用解析信号或复变量执行计算。这将使在相同的模拟环境中将电磁和机电瞬态现象与独特的数学模型结合在一起的可能性成为可能。

提出了一种新颖的可变时步算法，其灵活性如此广泛，可以直接将其集成到诸如EMTP-RV，PSCAD或Hypersim之类的电磁瞬态（EMT）软件中。

除了保持经典EMT建模的准确性外，所提出的公式还提供了总体计算时间的显着收益，而没有明显的准确性损失，并且无论时间步长如何，过渡过程都非常平稳。