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The complexity and the cost of maintaining power system security using only supply-side mechanisms is likely to increase in the future, especially due to the increasing generation from the renewable energy sources. Advances in control and information technology offer a possibility for the demand to participate in the system reserve market. By providing reserve, consumers could maximize their benefits derived from electricity markets. We present a new approach to the stochastic modeling of the demand-side reserve provision in co-optimized electricity and reserve markets in the case of growing wind power production. The proposed stochastic market model was formulated as a linear two-stage mixed-integer stochastic program and accounts for the costs and benefits that consumers derive from participating in the reserve market. It is shown that the contribution of the consumers to the system reserve may be necessary for the in the high wind power production case. The proposed method was tested on IEEE Reliability Test System.