This paper presents Nyström minimum kernel risk-sensitive loss (NysMKRSL) based control of a three-phase four-wire grid-tied dual-stage PV-hybrid energy storage system, under varying conditions such as irradiation variation, unbalanced load, and abnormal grid voltage. The Voltage Source Converter (VSC) control enables the system to perform multifunctional operations such as reactive power compensation, load balancing, power balancing, and harmonics elimination while maintaining Unity Power Factor (UPF). The proposed VSC control delivers more accurate weights with fewer oscillations, hence reducing overall losses and providing better stability to the system. The seamless control with the Hybrid Energy Storage System (HESS) facilitates the system’s grid-tied and isolated operation. The HESS includes the battery, fuel cell, and ultra-capacitor to accomplish the peak shaving, managing the disturbances of sudden and prolonged nature occurring due to load unbalancing and abnormal grid voltage. The DC link voltage is regulated by tuning the PI controller gains utilizing the Salp Swarm Optimization (SSO) algorithm to stabilize the system with minimum deviation from the reference voltage, during various simulated dynamic conditions. The optimized DC bus control generates the accurate loss component of current, which further enhances the performance of the proposed VSC control. The presented system was simulated in the MATLAB 2016a environment and performed satisfactorily as per IEEE 519 standards.