A maiden attempt has been made to propose the detailed modelling of fast charging electrical vehicle (EV)stations connected to a hybrid grid-renewable energy source (RES like solar, mini-hydro, and wind) system considering EV demand characteristics and arrival time, departure time, state of charge and battery capacity. This helps achieve the maximum profit and reduce energy demand from the grid. Simulations are performed with a novel meta-heuristic algorithm named by hybrid genetic with pattern search (hGPS) algorithm for the first time. They are used for optimizing the charging station's system parameters, which maximize the net present value (NPV). The investigations are performed by the probabilistic distribution of the EV demand based on EV behaviours and is simulated with the sequential Monte-Carlo method by considering hourly intervals. The obtained economic considerations using hybrid genetic with pattern search (hGPS) algorithm are compared with Genetic Algorithm (GA), Pattern Search (PS) algorithm and are observed that hybrid genetic with pattern search (hGPS) maximizes the profit over others. It is also evident that with the proposed method, the power transferred capacity limit among system network and grid reduces the impact of the grid on the system network.