FERC Optimal Power Flow and Formulation Papers
The AC Optimal Power Flow (ACOPF) is at the heart of Independent System Operator (ISO) power markets and vertically integrated utility dispatch. ACOPF simultaneously optimizes real and reactive power. An approximated form of the ACOPF is solved in some form annually for system planning, daily for day-ahead commitment markets, and even every 5 minutes for real-time market balancing. The ACOPF was first formulated in 1962 by Carpentier. With advances in computing power and solution algorithms, we can model more constraints and remove unnecessary limits and approximations that were previously required to find a good solution in reasonable time. Today, 50 years after the problem was formulated, we still do not have a fast, robust solution technique for the ACOPF. Finding a good solution technique for the ACOPF could potentially save tens of billions of dollars annually. The ACOPF formulation co-optimizes real and reactive power, internalizes losses (not estimated as in the ‘DC’ model) and has explicated voltage bounds, but requires more time to solve and better data. The current-voltage formulation (IV-ACOPF) has linear network flow equations. Its non-convexities occur at injection and withdrawal busses when current and voltage are converted to real and reactive power and its thermal constraints expressed in term of current magnitude. It better models thermal constraints by limiting the line current instead of power flow. The iterative linear approximation (ILIV-ACOPF) solves faster and is more robust than most other approaches examined. Parameter tuning can improve performance. With binary variables, for example, as in the unit commitment and optimal transmission switching problems, linear approximations can be solved faster than nonlinear models. In this series of papers, we seek to present the ACOPF problem through clear formulations of the problem, its constraints and its parameters. We survey historical approaches to solving the problem. We also formulate and test several approaches and algorithms to solving the ACOPF. We find that rectangular formulation solves faster than the polar formulation for the larger problems. We also present an iterative approximation and test it against a set of standard nonlinear solvers.
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