Mapping between transmission constraint penalty factor and OPF solution in electricity markets: analysis and fast calculation

Abstract -- In electricity markets, transmission constraint relaxation is frequently used to ensure the feasibility of the optimal power flow (OPF) problem and avoid the expensive yet ineffective congestion adjustment. However, transmission constraint penalty factors have a considerable impact on the market scheduling and prices. There is still no consensus on how to properly set the penalty factors. In this paper, the impact of transmission constraint penalty factors on the market solution is quantitatively investigated via the sensitivity analysis of the DC OPF model. Parametric programming is performed to determine the change of the market scheduling and prices with respect to the change of penalty factors. In particular, we prove for the very first time that when the objective function of the market model is quadratic, the parametric programming can be conveniently performed without the need of re-optimizing the DC OPF model in most cases. On this basis, an efficient method is proposed for exactly characterizing the mapping between the penalty factors and the market solution. Case studies show that the proposed method could be up to 100 times quicker than re-optimizing the DC OPF model as in the traditional parametric programming process.