Stability analysis of a non-Park-transformable electrical machine model

The stability properties of a linear or linearized, periodically-varying model of an electrical machine can be studied as a function of speed via direct computation of the monodromy matrix, from which the characteristic exponents can be determined. The machine used as an example in this paper is the nonsalient-pole damped alternator described in [1], and also used as an example in [2]. The characteristic exponents are obtained in [1] by a completely different method. Although round-off error interferes with the computation of the fast (and hence rather unimportant) exponents at very low speeds, the monodromy computation provides a straightforward method for determining the characteristic exponents of the periodically-varying system. A conjecture in [2] on the asymptotes of the exponents in the low-speed limit is proved and extended here, and results in [2] on the high-speed limit are reformulated in the setting of classical averaging theory.