  This letter proposes an enhanced sufficient battery model (ESBM) as well as a
binary search algorithm for a sharp inner-approximation of the aggregate
flexibility of thermostatically controlled load (TCL) arrays. Compared with the
previous work on generalized battery models, this ESBM preserves the merits of
being sufficient and mitigates the conservativity. Moreover, unlike the work
ignoring the coupling constraints that may also restrict TCLs' aggregate
flexibility, our ESBM can readily handle these constraints. Numerical tests
validate the merits of using the ESBM and its significance for power system
operations.
