On the Existence of Non-convexities in the Design Space of Isolated Wind-battery Systems

A set of all feasible design options depicted graphically on a diagram with system design variables is known as the design space. For an isolated wind-battery system, the design space is depicted on a rotor diameter vs. generator rating diagram with battery bank size as a parameter. Design space representation enables the distinction between the feasible and infeasible combinations of design variables. It forms a basis to understand the inter-relation between different design variables outlining the tradeoffs in design. In certain cases, it is observed that the feasible solution set may lead to a non-convex design space. Non-convexities in the design space imply that intuitive selection or arbitrary over sizing of design parameter(s) may lead to non-compliance with respect to overall reliability requirement. Through an illustrative example, it is shown that the primary reasons leading to design space non-convexity are the uneven distribution of wind speed standard deviation in the time horizon, high overall system reliability requirement and the wind regime of the site under consideration. From a graph of system reliability vs. coefficient of variation of wind speed (COV), it is observed that non-convexity in design space is most likely to occur for particular combinations of system reliability requirement and COV of wind speed. This representation facilitates predicting the occurrence of non-convexity in the design envelope prior to detailed system design and optimization; thus providing valuable insight to the system designer and preventing a possible failure of performance and loss of investment.