  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.
