This research will develop an overall framework and specific tools for multi-criterial analysis of polyphase energy processing systems with non-linear loads. Specifically, the PIs will develop an adaptive procedure for dealing with parametric uncertainties, and extend the analysis to transient operation. These developments will provide a quantitative basis for assessment of achievable performance in large classes of energy processing systems, which in turn will serve as inputs to model-based engineering design. Intellectual merit: A unified Hilbert space-based framework for separating the active and reactive components of power provides a theoretical foundation for applications in ac power systems equipped with power electronics-based compensators - commercial buildings, high-performance industrial and distribution systems serving sensitive loads, modern more electric ships and aircraft. This will impact analysis and design of networks incorporating distributed generation, and may prove relevant in other applications, from future hybrid road vehicles to energy-constrained portable electronics and power MEMS. Broader impact: This research project will contribute to unification of knowledge in the areas of system and energy engineering, adaptive signal processing and applied mathematics. The PIs are developing teaching materials in the form of modules that can be included into graduate and undergraduate courses in energy engineering and signal processing. The proposal includes plans to involve high school teachers interested in energy efficiency through a Research Experience for Teachers (RET) supplement.