Here, an implementation of three-phase grid-tied single-stage solar photovoltaic (PV) system is done at adverse grid situations of voltage unbalances. The proposed convex combination of least mean square (CCLMS) control approach is adaptive in nature, which extracts the fundamental component of load current (FCI) with fast convergence and provides good performance than conventional controls. The CCLMS algorithm overcomes the compromise of LMS filters between precision and tracking capability due to fixed stepping by providing a combination of two filters for precision and fast tracking. The perturb and observe (P&O)-based maximum power point tracking (MPPT) is employed for peak power extraction from a PV array. The system is tested in the laboratory on a developed prototype at several adverse conditions like voltages unbalance, load currents unbalances, and irradiation changes. The system performance is acceptable and harmonics distortion is in the limits according to the IEEE-519 standard while supplying energy to the utility and to the loads. Nomenclature i sa , i sb , i sc grid currents v sab , v sbc PCI line voltages i La , i Lb , i Lc three phase load currents i vsc PV-VSC currents i sa *, i sb *, i sc * grid reference currents V dc * , V dc reference and sensed DC link voltages P pv , V pv , I pv PV array-power, voltage and current u pa , u pb , u pc unit templates (in-phase) w pa , w pb , w pc fundamental active load current weight component w qa , w qb , w qc fundamental reactive load current weight component w sp net active fundamental component weight w sq net reactive fundamental component weight w lpa average weight of fundamental active load components R f , C f ripple filter components (resistance and capacitance) u qa , u qb , u qc unit templates (quadrature) CCLMS convex combination of least mean square