The presented work employs the multiple random feature kernel mean p-power algorithm (MRFKMP) for the voltage source converter (VSC) control of a three-phase four-wire grid-tied dual-stage photovoltaic-hybrid energy storage system (HESS) to achieve multiple objectives during various induced dynamic conditions. The proposed control enables the VSC to accomplish manifold goals, i.e., reactive power compensation, power quality enhancement, load, power balancing at common coupling point and grid voltage balancing during unity power factor mode of operation. The proposed system is scrutinized under steady-state and numerous dynamic states such as irradiation variation, specified power mode, abnormal grid voltage, load, and grid voltage unbalancing. The seamless control facilitates the swift resynchronization of the grid as well as maintaining stability during islanding and re-synchronization operations while satisfying the necessary load requirements. The associated HESS consisting of battery and ultra-capacitor is competent enough in managing the interruptions occurring on the grid, load and photovoltaic side. The DC bus voltage is controlled by the PI controller, which is tuned by the generalized normal distribution algorithm and kept at the desired level during diverse operating conditions. The optimized DC bus generates an accurate loss component of current and further enhances the VSC performance. The proposed system is investigated by simulation and found acceptable as per IEEE 519 standards.