This article presents the control of a three-phase three-wire (3P-3W) dual-stage grid-tied PV-battery storage system using a multi-objective grass-hopper optimization (MOGHO) algorithm. The voltage source converter (VSC) control of the presented system is implemented with adaptive kernel width sixth-order maximum correntropy criteria (AKWSOMCC) and maximum power point tracking (MPPT) control is accomplished using the variable step-size incremental conductance (VSS-InC) technique. The proposed VSC control offers lower mean square error and better accuracy, convergence rate and speed as compared to peer adaptive algorithms, i.e., least mean square (LMS), least mean fourth (LMF), maximum correntropy criteria (MCC), etc. The adaptive Gaussian kernel width is a function of the error signal, which changes to accommodate and filter Gaussian and non-Gaussian noise signals in each iteration. The VSS-InC based MPPT is provided with a MOGHO based modulation factor for better and faster tracking of the maximum power point during changing solar irradiation. Similarly, an optimized gain conventional PI controller regulates the DC bus to improve the power quality, and DC link stability during dynamic conditions. The optimized DC-link generates an accurate loss component of current, which further improves the VSC capability of fundamental load current component extraction. The VSC is designed to perform multi-functional operations, i.e., harmonics elimination, reactive power compensation, load balancing and power balancing at point of common coupling during diverse dynamic conditions. The MOSHO based VSS-InC, and DC bus performance is compared to particle swarm optimization (PSO) and genetic algorithm (GA). The proposed system operates satisfactorily as per IEEE519 standards in the MATLAB simulation environment.