Power-to-gas (P2G) technology opens up another perspective for effective, long-term, large-scale energy storage, so that it can promote large-scale wind power integration. Under this background, this study introduces P2G technology into the economic dispatch model of wind power integrated systems. First, an uncertainty interval model of wind power is built based on the probability distribution of wind power prediction error. Then, considering P2G's function of absorbing surplus wind power and undertaking downward spinning reserve, the factors that influence P2G's ability in enhancing the accommodation of wind power are analysed through theoretical derivation. Consequently, the relationship between the maximum wind power integration and the power delivered to the P2G facilities under a given capacity of P2G can be further understood. Moreover, an economic dispatch model incorporating wind power, P2G facilities and battery energy storage systems is established and a feasible region relaxation algorithm is proposed to deal with the non-smooth functions in the proposed model. Case studies are conducted on a modified IEEE 39-bus system. The results verify the correctness of theoretic analysis and show that the proposed model can help to reduce wind power curtailment and enhance the security and economy of the power system.