Storage is widely considered in economic dispatch (ED) problems. To prevent simultaneous charging and discharging of a storage device

a storage-concerned ED problem should involve complementarity constraints for every storage device to make the problem strongly non-convex. In this case

the conventional Karush-Kuhn-Tucker optimality conditions are unsuitable

and the methods that are normally effective are also invalid. In our recent paper

we proposed a new exact relaxation method that directly removes the complementarity constraints from a storage-concerned ED model to make it convex and easy to solve. This paper extends the previous study by presenting and analyzing two new groups of sufficient conditions that guarantee exact relaxation. Different application conditions of these groups of sufficient conditions are discussed. Numerical tests are performed to show the benefit of using the exact relaxation method and the different suitable application conditions of these groups of sufficient conditions. This paper contributes to a wide application of exact relaxation in storage-concerned ED problems.