Title: A Linear LMP Model for Active and Reactive Power with Power Loss

Abstract: Pricing the reactive power is more necessary than ever before because of the increasing challenge of renewable energy integration on reactive power balance and voltage control. However, reactive power price is hard to be efficiently calculated because of the non-linear nature of optimal AC power flow equation. This paper proposes a linear model to calculate active and reactive power LMP simultaneously considering power loss. Firstly, a linearized AC power flow equation is proposed based on an augmented Generation Shift Distribution Factors (GSDF) matrix. Secondly, a linearized LMP model is derived using GSDF and loss factors. The formulation of LMP is further decomposed into four components: energy, congestion, voltage limitation and power loss. Finally, an iterate algorithm is proposed for calculating LMP with the proposed model. The performance of the proposed model is validated by the IEEE-118 bus system.