Non-convexity in the Design Space of Wind-Battery Systems

  • Anindita Roy
  • Santanu Bandyopadhyay


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.


Non-convexity Design space Wind-battery system Wind speed uncertainty Chance constraint programming 


  1. Roy, A., Kedare, S. B., & Bandyopadhyay, S. (2011). Design and optimization of isolated wind-battery systems incorporating multiple wind generators. Wind Engineering, 35(2), 223–245.Google Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Anindita Roy
    • 1
  • Santanu Bandyopadhyay
    • 2
  1. 1.Department of Mechanical EngineeringPimpri Chinchwad College of EngineeringPuneIndia
  2. 2.Department of Energy Science & EngineeringIndian Institute of Technology BombayMumbaiIndia

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