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Dynamically adaptive systems (DAS) such as smart grids, cloud computing applications, sensor networks and P2P networks tend to change their structure at runtime. Therefore, design-time modeling for such systems are sometimes not enough to incorporate self-* properties. To this end, we have developed a dynamic mathematical modeling framework for runtime optimizations for DAS. In this paper, we describe how our system engineers a linear programming model by using a smart-grid application for power distribution as a case-study. At runtime whenever an optimization is desired this modeling framework captures the state of the system, converts it into an appropriate linear programming model, plan the changes using mathematical manipulations and apply the changes to the actual system. Our results show that this framework is able to capture accurate runtime models of large power systems and is able to adapt itself with the change in the size or structure of the system.