The operation of a solar-driven H2O-LiBr Absorption Chiller (AbC) is subjected to various limitations regarding its ability to satisfy efficiently the required cooling demand while avoiding certain internal conditions, such as H2O-LiBr solution crystallization and water freezing. These circumstances would lead to problematic situations and jeopardize the continuous operation of the system. Thus, the development of accurate control strategies is an issue of interest. A new operational control strategy approach is introduced and tested through simulation studies, by employing a transient model of the entire solar cooling application. A prototype under development is used for the parametrization of the direct air-cooled AbC model used in the simulations. The developed control strategy aims to minimize the electrical consumption of the auxiliary components of the AbC (i.e., fan, pumps) during the partial load operation period, by using a fuzzy logic interference rule for determining the cooling capacity demand and then applying an optimization algorithm for determining the velocity of the auxiliary components. Within the proposed control strategy, a fast-calculation model is embedded, which predicts the chiller’s capacity under variable external conditions and partial load operation. The electrical COP is increased up to 2.2 times with respect to a baseline case, based on a basic two-step control strategy, while allowing the chiller to operate smoother, minimizing the crystallization and freezing risk.