This paper establishes an optimal power flow based framework for quantifying the amount and assessing the ability of DSO to enable the provision of flexibility service to the TSO. Within this framework, a comparison of three different formulations is conducted on several real life distribution networks and IEEE test cases considering computational effort and quality of solution as metrics. By reformulating the branch flow variant of the original problem, a convex approximation approach is established and assessed with regards to exactness and suboptimality of the solution. Based on the results of smaller test cases we develop a method that is able to efficiently solve the problem for large test case instances. The results indicate significant advantages of reformulations over the classical approach on smaller test cases as well as its usefulness when solving more demanding test cases.