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Single-phase self-excited reluctance generators provide a good alternative to single-phase induction generators used in standalone generator applications. This is because of their simplicity, ruggedness, and higher efficiency. The determination of the conditions for the generator to self-excite, typically the critical speed and/or capacitance(s), plays an important role in the design of the system. So far, such analysis has only considered the behavior of the generator under constant speed and loading conditions. However, with most standalone generators driven by sustainable sources, and thus most applications of single-phase self-excited synchronous generators, the speed is by far not constant, but permanently changes over time-the wind being the classical example. This paper discusses the effects of such fluctuating speed on the minimum capacitance required to self-excite single-phase self-excited reluctance generators. It presents a new method to determine these capacitances by analyzing the overall system damping and amplifying components of the eigenvalues with lower and upper natural frequencies. The analysis is expanded to different generator parameters and loading conditions.