The operation of energy systems considering a multi-carrier scheme takes several advantages of economical, environmental, and technical aspects by utilizing alternative options is supplying different kinds of loads such as heat, gas, and power. This study aims to evaluate the influence of power to hydrogen conversion capability and hydrogen storage technology in energy systems with gas, power, and heat carriers concerning risk analysis. Accordingly, conditional value at risk (CVaR)-based stochastic method is adopted for investigating the uncertainty associated with wind power production. Hydrogen storage system, which can convert power to hydrogen in off-peak hours and to feed generators to produce power at on-peak time intervals, is studied as an effective solution to mitigate the wind power curtailment because of high penetration of wind turbines in electricity networks. Besides, the effect constraints associated with gas and district heating network on the operation of the multi-carrier energy systems has been investigated. A gas-fired combined heat and power (CHP) plant and hydrogen storage are considered as the interconnections among power, gas and heat systems. The proposed framework is implemented on a system to verify the effectiveness of the model. The obtained results show the effectiveness of the model in terms of handling the risks associated with multi-carrier system parameters as well as dealing with the penetration of renewable resources.