Weak power distribution systems are those that are highly sensitive to fluctuations in voltage magnitude and/or frequency. Due to the intrinsic intermittency and inertia-less nature of photovoltaic systems, the connection of a utility-scale photovoltaic plant to a weak distribution system can lead to grid instability or even collapse. This paper presents a structured framework for performing grid connection studies to evaluate the integration of photovoltaic plants into weak distribution systems. The two main characteristics of weak distribution systems (i.e., low-inertia and high-impedance connection points) are handled separately since each factor has distinct issues, risks and mitigation methods. Also, some systems may only exhibit weakness in one of these aspects, but not the other. Recommendations are provided in the paper for the appropriate studies to be performed and the features to be investigated for the development of utility-scale photovoltaic plants connected to weak distribution systems.