To enhance the move towards a sustainable society, the solar Photovoltaic (PV) industry and its applications are progressing at a rapid rate. However, the associated issues need to be addressed when connecting PV to the grid. Advanced and efficient controllers are required for the DC link to control the second harmonic ripple and current controllers to inject quality active and reactive power to the grid in the grid-connected PV system. In this paper, DC-link voltage, active power, and reactive power are successfully controlled in stationary reference using Adaptive-PI (A-PI) and Adaptive-Sliding Mode Controller (A-SMC) for a 3 kW single-phase two-stage transformerless grid-connected inverter. A Resonant Harmonic Compensator (RHC)-based Proportional Resonant (PR) controller is employed in the current-controlled loop. The magnitude, phase, and frequency information of the grid voltage are provided by Second-Order General Integral (SOGI)-based PLL that has harmonic immunity, fast-tracking accuracy, and a rapid-dynamic response. MATLAB®/Simulink®/Simscape R2017b were used for the test bench implementation. Two scenarios were considered: in the first case, the input PV power feedforward loop was avoided, while in second case, it was included. The feedforward loop of input PV power improved the overall system dynamics. The results show that the designed controller improves both the steady-state and dynamic performance as compared with a proper-regulated PI-controller. The proposed controllers are insensitive to active and reactive power variations, and are robust, stable, faster, and fault tolerant, as compared to controllers from prior studies.