We propose a hybrid method for computing transient stability power flow limits of a longitudinal system, alternative to the conventional pure time-domain approach. This method, called SIME (single machine infinite bus equivalent), results from time-domain methods coupled with a particular direct method so as to combine advantages of both. Time-domain methods are especially interesting for their ability to embed any power system modelling. The particular direct method, on the other hand, provides two types of assets. One concerns computational efficiency, owing to the derivation of a direct stopping criterion which reduces significantly the required time-domain simulations. The other concerns the possibility of assessing margins and identifying the critical system machines. This paper benefits from the stopping criterion together with margin calculation to efficiently assess transient stability transfer limits on major transmission lines of a longitudinal power system. Moreover, it proposes a convenient way of handling multi-swing instability phenomena-and this is an additional asset over the SIME version developed so far. This "augmented" version is illustrated on the Hydro-Quebec system, modelled in its normal way; the simulations use typical stability scenarios and operating conditions. The performances of the obtained results are assessed in terms of accuracy and computing gains.
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