Imbalance costs caused by forecasting errors are considerable for grid-connected wind farms. In order to reduce such costs, two onsite storage technologies, i.e., power-to-hydrogen-to-power and lithium battery, are investigated considering 14 uncertain technological and economic parameters. Probability density distributions of wind forecasting errors and power level are first considered to quantify the imbalance and excess wind power. Then, robust optimal sizing of the onsite storage is performed under uncertainty to maximize wind-farm profit (the net present value). Global sensitivity analysis is further carried out for parameters prioritization to highlight the key influential parameters. The results show that the profit of power-to-hydrogen-to-power case is sensitive to the hydrogen price, wind forecasting accuracy and hydrogen storage price. When hydrogen price ranges in (2, 6) (sic)/kg, installing only electrolyzer can earn profits over 100 k(sic)/MWWP in 9% scenarios with capacity below 250 kW/MWWP, under high hydrogen price (over 4 (sic)/kg); while installing only fuel cell can achieve such high profits only in 1.3% scenarios with capacity below 180 kW/MWWP. Installing both electrolyzer and fuel cell (only suggested in 22% scenarios) results in profits below 160 k(sic)/MWWP, and particularly 20% scenarios allow for a profit below 50 k(sic)/MWWP due to the contradictory effects of wind forecasting error, hydrogen and electricity price. For lithium battery, investment cost is the single highly influential factor, which should be reduced to 760 (sic)/kWh. The battery capacity is limited to 88 kW h/MWWP. For profits over 100 k(sic)/MWWP (in 3% scenarios), the battery should be with an investment cost below 510 (sic)/kWh and a depth of discharge over 63%. The power-tohydrogen-to-power case is more advantageous in terms of profitability, reliability and utilization factor (full-load operating hours), while lithium battery is more helpful to reduce the lost wind and has less environmental impact considering current hydrogen market.