With the large-scale integration of distributed generation (DG) sources, the uncertain characteristics of their output have posed unprecedented challenges to the safe operation of distribution networks (DNs). In this paper, probabilistic models for the output of DG, including wind turbine generators (WTGs) and photovoltaic (PV) systems are established. Risk-averse utility functions are then introduced to calculate risk indicators for bus voltage violation and branch flow violation, with probabilistic load flow (PLF) used to calculate the operational risks of the DNs. Finally, the modified IEEE 33-bus system is used as a case study to validate the rationality of the proposed indicators and to analyze the impact of DG integration at different locations and capacities on the network's risk indicators. Simulation results show that the integration of DG is likely to cause power flow violations on branches at the head of the DN. As the penetration rate of DG increases, the system risk value initially remains basically stable and then sharply increases. Moreover, decentralized integration of DG leads to a lower system total risk compared to centralized integration.