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Optimal Adaptive Linearizations of the AC Power Flow Equations

The power flow equations are an integral part of models used in many aspects of planning and operations in power systems, including day-ahead and intra-day generation dispatch, security assessment, and expansion planning. The AC Power Flow equations, widely accepted to be the most accurate steady-state model of the system, are non-linear and pose significant computational challenges when used in the above applications. To address this issue, several simplified power flow models are commonly used instead of the AC equations, the most popular among which are the linear DC approximation in transmission systems and the LinDistFlow in distribution systems. These approximations are derived using simplifying physical/engineering assumptions such as ignoring the resistance of transmission lines in the DC approximation. However, the quality of these approximations depends on both the specifics of the operating condition and the application of interest, where one type of approximation error might be of more significance than others. This paper provides a framework for deriving computationally tractable approximations to the AC power flow equations that are both "adaptive" - tailored to be accurate around a given range of operating conditions for a specific system, and "optimal" - designed to minimize the error metric of interest to the application. By restricting our search to tractable models (e.g., linear), the approximations can then be used within large optimization problems such as Optimal Power Flow (OPF).


Krishnamurthy Dvijotham    
Pacific Northwest National Laboratory
United States

Sidhant Misra    
Los Alamos National Laboratory
United States

Daniel K. Molzahn    
Argonne National Laboratory
United States


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