Extending complementarity-based approach for handling voltage band regulation in power flow

In power flow analysis, the Newton-Raphson method is typically combined with heuristics for enforcing voltage regulation constraints. However, these heuristics can cause jumps and cycles in the numerical process that further degrade this method's limited robustness. In a previous work, mathematical optimization techniques were explored for developing a robust power flow method, but the voltage regulation considered was limited to that provided by generators. In this work, these techniques are extended to model controllers that provide voltage band regulation. In particular, complementarity constraints are used to model automatic tap-changing transformers and switched shunt devices. The proposed method has been compared with the typical heuristics-based method on power flow cases of about 2.5k buses. The results obtained suggest that the proposed method makes smoother and more monotonic progress towards solutions, is more effective in reducing voltage band violations, and inherits robustness from the previously-explored techniques on which it is based.