This work introduces a current control strategy for Voltage Source Inverters (VSI) using data-driven control systems, particularly employing a framework based on Deep Reinforcement Learning agents. Unlike the other techniques in the literature, we have avoided using a modulator by including a Deep Q-Network agent. In addition, an analysis of the impact of different Deep Neural Network (DNN) architectures on control system performance, specifically considering the number of layers and neurons, is presented. To this end, different DQN agents were designed, trained, and tested. Also, a two-level voltage source power inverter is simulated to validate the proposed data-driven control based on DQN agents. The performance of the control strategy is analyzed in terms of computational cost, Root Mean Square Error (RMSE), and Total Harmonic Distortion (THD). Simulated results reveal that the proposed control strategy performs strongly in the current control, with a maximum RMSE of 0.83 A and a THD of 5.29 % at a 10 kHz sampling frequency when a DNN with one layer and five neurons is used.