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Numerical Instability in EMTP-ATP Due to Negative Inductance

A negative leakage inductance may appear in the representation of the three winding saturable transformer (Saturable Transformer Component - STC) because of the star equivalent used for the STC. The consequence of the negative inductance is the existence of one large positive system matrix eigenvalue, when state space form is applied. The appearance of the positive eigenvalue is the primary reason for numerical instability of the trapezoidal rule when it is applied in EMTP. On the other hand, without the adjustment of the transformer model, the BDF numerical rule stays stable for large positive eigenvalues because of its particular characteristics in the area of numerical stability. The problem of numerical instability is illustrated on the test case for circuits with negative leakage inductance. Such circuits represent physically stable systems for which the BDF numerical rule may give a stable numerical response, contrary to the trapezoidal rule.

transformer model; unstable response; numerical instability; trapezoidal rule; backward differentiation formulas BDF rule; stability domain

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