Power fluctuations happens due to highly stochastic solar irradiance nature and this could cause unwanted power quality issues in photovoltaic (PV) system. First predicting the PV output then mitigating the fluctuation by using energy storage system is one of the most effective power fluctuation mitigation method. Incremental learning algorithm such as incremental self-organizing map can be used to actively learn and predict power output. Although significant improvement in terms of mitigated events can be achieved in this kind of system, it still suffers from prediction accuracy due to the highly fluctuating PV profile. In this paper, a time-series unsupervised learning algorithm namely the Time-Series Self-Organizing Incremental Neural Network (TS-SOINN) is proposed to better predict the highly stochastic PV output. It incorporates a novel weighted memory layer to give higher emphasis to recent observation and improves data overlap issues in the conventional self-organizing map algorithm. In the simulation results, the TS-SOINN achieves prediction rate of 93.81% which outperforms the latest unsupervised incremental learning algorithm, M-SOINN by 33.44% and the TS-SOINN mitigated 89.13% power fluctuation events whereas M-SOINN only mitigated 79.62% events. In addition, the TS-SOINN is implemented in Altera Stratix V GS Field Programmable Gate Array (FPGA) board to run real-time prediction. This hardware architecture is able to increase new node and remove inactive nodes throughout the real-time prediction. The hardware TS-SOINN is integrated with mitigation engine to smoothen out power fluctuation events in PV grid-tied system, the experimental results show that the proposed system mitigated 83.33% of power fluctuation events at the grid and the battery state-of-charge maintains within 30%-100%.