There are two important considerations in the development of an electrical model for RF cavities to be used for system analysis or LLRF loop design, being: transient response and cavity impedance mismatch. In the literature, however, either one or both of these issues are often neglected depending whether the RF cavity is being looked at from high-power or low-level RF perspectives. In this work, a transient model for storage ring RF cavities under beam loading is developed so that it represents the important RF aspects of the cavity such as impedance mismatch and reflected voltage as well as its transient response, for example at start-up or upon beam arrival. As a special case, the model is applied to the RF cavity of the ALBA storage ring to study the effects arising from beam loading, system start-up and delays on the performance of the LLRF regulation loops. For the simulation of the regulation loops in time domain a mathematical technique is introduced to map the RF frequency to baseband, leading to the baseband-equivalent model of the cavity with almost the same results as the conventional cavity model but with significantly higher simulation speed.