Convex Optimization
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In this paper, we study supply and demand management in the presence of conventional and renewable energy sources, where the latter is represented by a single wind turbine. Total social welfare, defined in terms of consumer utility and cost of power production (both scheduled and renewable), is maximized while the probability of power shortfall due to the uncertainty in the wind power production is limited by an upper bound. We find the outage-limiting optimal production and consumption schedules, and demonstrate superiority over a competing policy which ensures that total power production meets the demand on the average.