Searching for the Extreme Operating Conditions (EOCs) is one of the core problems of power system relay protection setting calculation. The current methods based on brute-force search, heuristic algorithms, and mathematical programming can hardly meet the requirements of today's power systems in terms of computation speed due to the drastic changes in operating conditions induced by renewables and power electronics. This paper proposes an EOC fast search method, named Graph Dueling Double Deep Q Network (Graph D3QN), which combines graph neural network and deep reinforcement learning to address this challenge. First, the EOC search problem is modeled as a Markov decision process, where the information of the underlying power system is extracted using graph neural networks, so that the EOC of the system can be found via deep reinforcement learning. Then, a two-stage Guided Learning and Free Exploration (GLFE) training framework is constructed to accelerate the convergence speed of reinforcement learning. Finally, the proposed Graph D3QN method is validated through case studies of searching maximum fault current for relay protection setting calculation on the IEEE 39-bus and 118-bus systems. The experimental results demonstrate that Graph D3QN can reduce the computation time by 10 to 1000 times while guaranteeing the accuracy of the selected EOCs.