Linearized Model for Active and Reactive LMP Considering Bus Voltage Constraints

With the increasing integration of large scale renewable energy into power system and the variation of bus voltage, the pricing of reactive power is more necessary than ever before. This paper proposes a novel model to calculate active and reactive Locational Marginal Price (LMP) simultaneously based on a linear optimal power flow (LOPF). First, an augmented Generation Shift Distribution Factors (GSDF) is introduced based on the linear power flow model with considerations of bus voltage and reactive power. Second, the linear optimal power flow model is constructed using GSDF to jointly calculate active LMP and reactive LMP. Third, the components of LMP such as the energy component, line congestion component, and voltage constraint component are derived from LOPF model. Finally, the case study on IEEE 30-bus case illustrates that the model outperforms the DCOPF on the active LMP, and presents acceptable results on reactive LMP compared with ACOPF.