Many critical infrastructures such as the power transmission grid are heterogeneous both in their basic structure and in some of their underlying characteristics, This heterogeneity can be good for system robustness if it reduces the spread of failures or bad if it adds risk or vulnerability to the system. In this paper we investigate the effect of heterogeneity in the strength of the links between parts of the system network structures, as well as the balance of local generation and demand, on the robustness of the power transmission grid using the OPA complex system model of the power transmission system. It is found that increasing or decreasing the reliability of the links between parts of the grid changes the likelihood of different size failures with neither being optimal for all sizes. Furthermore, imbalances between load and generation in the local regions further degrades the system reliability.