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This paper proposes a methodology to model and solve the problem of stochastic economic dispatch incorporating renewable energies. In this context, demand and generation randomness (wind speed, solar radiation and rates of failure) are considered. Demand, wind speed, solar radiation and unavailability are modeled through Normal, Weibull, Beta and Uniform distributions respectively. The problem is therefore recognized as a stochastic process. Consequently, the cost of load shedding is considered. In order to define the optimal power allocation for each generator, the proposed methodology uses Group SO (3) orthogonal matrices (Lie's algebra), the marginal costs of the generators, the customer damage cost and MonteCarlo trials. The result contains generation, marginal cost and load shedding statistics, among others.

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