Non-convexity in the Design Space of Wind-Battery Systems
Wind-battery system design problems typically embody a non-linear generator characteristic. If the co-relation between the load and generation profiles is poor, the solution set is likely to be non-convex. That is, for a certain rotor blade diameter and generator rating combinations within the feasible design region, no solution exists. Reasons for such non-convexities are identified and parameterized with an illustrative example. It is found that the likelihood of a non-convex solution set is profound when the power supply reliability is high and the ratio of standard deviation to mean wind speed at the site is within a certain range (0.3–0.6 in this case). Design space methodology helps to predict the occurrence of a non-convex solution set and can aid the planner/decision-maker in selecting a global optimal solution in the light of non-convexity. When the design space is non-convex, arbitrary oversizing of design variables may lead to non-compliance with overall reliability requirement.
KeywordsNon-convexity Design space Wind-battery system Wind speed uncertainty Chance constraint programming
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