The impacts of convex piecewise linear cost formulations on AC optimal power flow

Despite strong connections through shared application areas, research efforts on power market optimization (e.g., unit commitment) and network optimal flow) remain largely independent. A notable illustration of this is the treatment generation cost functions, where nonlinear has used polynomial representations adopted piecewise linear encodings. This work combines state-of-the-art results from both lines to understand best mathematical formulations AC flow problem with functions. An extensive numerical analysis non-convex models, approximations, convex relaxations across fifty-four realistic test cases illustrates that methods are surprisingly sensitive formulation The indicate a poor choice can slow down algorithm performance by factor ten, increasing runtime seconds minutes. These provide valuable insights into problems an important step towards building new energy markets incorporate model.