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Despite strong connections through shared application areas, research effortson power market optimization (e.g., unit commitment) and power networkoptimization (e.g., optimal power flow) remain largely independent. A notableillustration of this is the treatment of power generation cost functions, wherenonlinear network optimization has largely used polynomial representations andmarket optimization has adopted piecewise linear encodings. This work combinesstate-of-the-art results from both lines of research to understand the bestmathematical formulations of the nonlinear AC optimal power flow problem withpiecewise linear generation cost functions. An extensive numerical analysis ofnon-convex models, linear approximations, and convex relaxations acrossfifty-four realistic test cases illustrates that nonlinear optimization methodsare surprisingly sensitive to the mathematical formulation of piecewise linearfunctions. The results indicate that a poor formulation choice can slow downalgorithm performance by a factor of ten, increasing the runtime from secondsto minutes. These results provide valuable insights into the best formulationsof nonlinear optimal power flow problems with piecewise linear cost functions,a important step towards building a new generation of energy markets thatincorporate the nonlinear AC power flow model.

The Impacts of Convex Piecewise Linear Cost Formulations on AC Optimal Power Flow