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This paper represents a calculation method of stochastic generation cost (SGC) taking into consideration the wind power generation expressed as random variables, and shows its necessity. As wind power generation is stochastically predictable, a system demand should be expressed to a random variable with its own probability density function (PDF) instead of a constant value in unit commitment (UC) and economic dispatch (ED) problems, etc. Assuming that the produced wind power generation is fully consumed in power systems, total generation distributed to thermal generators, which becomes a modified system load, is equal to the difference between total system demand and total wind power generation. Given that the total wind generation is based on normal distribution, the modified system load should be also based on normal distribution. The proposed method is applied to illustrative examples and simple UC problems.