The structure of the day-ahead electricity market obliges wind farm owners (WFOs) to make commitments hours before delivery. Due to the uncertainty of wind generation, WFOs bid in the electricity market with the prediction of its generation that, more often than not, is different from the actual generation. Therefore, WFOs experience deviations between their commitment to the electricity market and the actual generation, namely overproduction and underproduction, which are subject to penalties. This paper investigates solutions to decrease such deviation and increase the profit of the WFO. To this end, the joint planning and operation of electrical energy storage (EES) and power-to-gas (P2G) units to be paired with wind farms are evaluated while considering both the electricity and gas markets. Two case studies, with only EES and with both the EES and P2G units, are conducted to reveal the potential of the proposed approach considered, while risk analyses are performed to study the impact of different risk criteria on the decisions of WFO. This problem is formulated as an MINLP and then recast into MILP to obtain global solutions. Results offer the best strategies for WFOs to enhance their profit under the existing uncertain conditions.