In this paper, we use a nonlinear model of a grid-connected Archimedes wave swing (AWS) to explore the actual generation potential of this wave energy conversion system. Our model has never been used before for a grid-connected AWS. The control system employs six proportional-integral (PI) controllers to maximize the energy harvest from waves, to minimize the generator power losses, and to maintain both the grid and DC link voltages at their reference values. The PI controller parameters were selected using a hybrid augmented grey wolf optimizer and cuckoo search (AGWO-CS) algorithm. The results obtained from MATLAB Simulink for different types of grid fault, with successful and unsuccessful reclosing of the circuit breakers, were compared with results from the particle swarm optimization (PSO) and COOT algorithms. To verify the accuracy of our control system, a grid-connected AWS was tested experimentally using a real-time RT-LAB simulator combined with OP4510. The results validated the efficiency and superiority of the control system using AGWO-CS and the results from simulation and experiment were similar.