The partially averaged Navier-Stokes (PANS) model, proposed in Girimaji (2006), allows to simulate turbulent flows either in RANS, LES or DNS mode. The PANS model includes f k which denotes the ratio of modeled to total kinetic energy. In RANS, f k = 1 while in DNS it tends to zero. In the present study we propose an improved formulation for f k based on the H-equivalence introduced by Friess et al. (2015). In this formulation the expression of f k is derived to mimic Improved Delayed Detached Eddy Simulation (IDDES). This new formulation behaves in a very similar way as IDDES, even though the two formulations use different mechanisms to separate modeled and resolved scales. They show very similar performance in separated flows as well as in attached boundary layers. In particular, the novel formulation is able to (i) treat attached boundary layers as properly as IDDES, and (ii) "detect" laminar initial/boundary conditions, in which case it enforces RANS mode. Furthermore, it is found that the new formulation is numerically more stable than IDDES.