This paper addresses the problem of estimating lower bounds on the power consumption in scheduled data flow graphs with a fixed number of allocated resources before binding. The estimated bound takes into account the effects of resource sharing. It is shown that by introducing Lagrangian multipliers and relaxing the low power binding problem to the Assignment Problem, which can be solved in, a tight and fast computable bound is achievable. Experimental results show the good quality of the bound. In most cases, deviations smaller than 5% from the optimal binding were observed. The proposed technique can for example be applied in branch and bound high-level synthesis algorithms for efficient pruning of the design space. The estimated lower bound can also be used as a starting point for low power binding heuristics to find optimal or near optimal binding solutions.