Planning with global state constraints is an extension of classical planning in which some properties of each state are derived via a set of equations, rules or constraints. This extension enables more elegant modelling of networked physical systems such as power grids. So far, research in this setting focused on domains where action costs are constant, rather than a function of a state in which the action is applied. This limitation prevents us from accurately specifying the objective in some real-world domains, leading to generation of suboptimal plans. For example, when reconfiguring a power network, we often need to temporarily leave some users without electricity for a certain amount of time, and in such circumstances it is desirable to reduce the unsupplied load over the total time span. This preference can be expressed using statedependent action costs. We extend planning with global state constraints to include state-dependent action costs, adapt abstraction heuristics to this setting, and show improved performance on a set of problems.