The power inverter topologies are indispensable devices to incorporate distributed generation schemes, like photovoltaic energy sources into the AC main. The nonlinear behavior of the power inverter draws a challenge when it comes to their control policy, rendering linear control methods often inadequate for the application. The control complexity can be further increased by the LCL filters, which are the preferred way to mitigate the current ripple caused by the inverter switching. This paper presents a robust variable structure control for a three-phase grid-tied inverter with an LCL filter. As well to the benefits of the sliding mode control (SMC), which is one of the control methods applied by power converters founded in literature, the proposed control scheme features a novel partial state observer based on the immersion and invariance technique, which thanks to its inherent robustness and speed of convergence is adequate for this application. This observer eliminates the need for physical current sensors, decreasing the overall cost and size, as well as probable sources of noise. The proposed controller is meant for a three-phase grid-tied inverter to inject active power to the grid while harmonics generated by nonlinear loads are compensated. The simulation results prove the effectiveness of the proposed method by compensating for current harmonics produced by the nonlinear loads and maintaining a low total harmonic distortion as recommended by the STD-IEEE519-2014, regardless of whether the system provides active power or not.