The Extreme Operating Conditions Search (EOCS) problem is one of the key problems in relay setting calculation, which is used to ensure that the setting values of protection relays can adapt to the changing operating conditions of power systems over a period of time after deployment. The high penetration of renewable energy and the wide application of inverter-based resources make the operating conditions of renewable power systems more volatile, which urges the adoption of the online relay setting calculation strategy. However, the computation speed of existing EOCS methods based on local enumeration, heuristic algorithms, and mathematical programming cannot meet the efficiency requirement of online relay setting calculation. To reduce the time overhead, this paper, for the first time, proposes an efficient deep learning-based EOCS method suitable for online relay setting calculation. First, the power system information is formulated as four layers, i.e., a component parameter layer, a topological connection layer, an electrical distance layer, and a graph distance layer, which are fed into a parallel graph neural network (PGNN) model for feature extraction. Then, the four feature layers corresponding to each node are spliced and stretched, and then fed into the decision network to predict the extreme operating condition of the system. Finally, the proposed PGNN method is validated on the modified IEEE 39-bus and 118-bus test systems, where some of the synchronous generators are replaced by renewable generation units. The nonlinear fault characteristics of renewables are fully considered when computing fault currents. The experiment results show that the proposed PGNN method achieves higher accuracy than the existing methods in solving the EOCS problem. Meanwhile, it also provides greater improvements in online computation time.