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A Comprehensive Stochastic Mathe Matical Model Essay

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rates, minimum-up/minimum-down times, and start-up/shut-down times torespond quickly in order to mitigate any transient issue. Furthermore, the proposed framework enhances system flexibility bycoordinating operations of DERs and thus makes the system furthercapable of handling dynamic matters with the least operation cost, as illustrated in the steady-state study.

5. Conclusions
The significant increase in penetration of renewable energygeneration is expected to affect the operational aspects of powersystems and more specifically isolated micro grids that mainly relyon renewable energy sources. Indeed, the issue of UC schedulesand real-time dispatch of a micro grid with controllable DGs is morecomplicated in the presence of high wind and solar generation pen-etration. To address these operational challenges, it is necessaryto manage the variability and uncertainty associated with theseenergy sources. It has become clearer than ever that a flexiblemicro grid is vital. In this paper, a comprehensive stochastic mathe-matical model has been developed to enable operation interactionof DERs under uncertainty in islanded micro grids. Hence prob-abilistic coordination of DERs on micro grid operations has beenexamined with respect to their independent presence and withconsideration of the hourly interruption cost for residential, com-mercial, and industrial customers in order to determine the optimalprobabilistic interruptible load, if required. The simulation resultsshow that

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