In early design phases and during software evolution, design-time energy efficiency analyses enable software architects to reason on the effect of design decisions on energy efficiency. Energy efficiency analyses rely on accurate power models to estimate power consumption. Deriving power models that are both accurate and usable for design time predictions requires extensive measurements and manual analysis. Existing approaches that aim to automate the extraction of power models focus on the construction of models for runtime estimation of power consumption. Power models constructed by these approaches do not allow users to identify the central set of system metrics that impact energy efficiency prediction accuracy. The identification of these central metrics is important for design time analyses, as an accurate prediction of each metric incurs modeling effort. We propose a methodology for the automated construction of multi-metric power models using systematic experimentation. Our approach enables the automated training and selection of power models for the design time prediction of power consumption. We validate our approach by evaluating the prediction accuracy of derived power models for a set of enterprise and data-intensive application benchmarks.