To comprehensively assess the risk of multiple faults that are due to transmission line and hidden faults in secondary systems during severe weather, a risk assessment method for power systems considering primary and secondary coupled multiple faults is proposed. First, the characteristics of transmission line faults caused by meteorological disasters are analyzed, and the characteristics of primary and secondary coupled multiple faults are summarized. Second, a primary and secondary coupled multiple fault model is established by considering the fault probability of transmission lines and protection devices. Then, a Latin hypercube sampling method is applied to quickly generate the initial fault set and evaluate the loss of load, node voltage out-of-limit, branch power flow out-of-limit, and other risk indeices. Finally, the proposed method is tested using the IEEE39-node system. The results reveal that the power system faces more serious risks when considering primary and secondary coupled multiple faults; the use of Latin hypercube sampling allows taking into account fault probability distribution differences of transmission lines within different meteorological subareas and improve computational efficiency; multidimensional risk ranking can effectively screen critical lines and buses that affect power grid risk within severe weather subareas, and provide a decision basis for power grid risk prevention and weak link management.