IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 22, NO. 4, NOVEMBER 2007 1475 DCOPF-Based LMP Simulation: Algorithm, Comparison With ACOPF, and Sensitivity Fangxing Li, Senior Member, IEEE, and Rui Bo, Student Member, IEEE Abstract—The locational marginal pricing (LMP) methodology has become the dominant approach in power markets. Moreover, the dc optimal power flow (DCOPF) model has been applied in the power industry to calculate locational marginal prices (LMPs), es- pecially in market simulation and planning owing to its robustness and speed. In this paper, first, an iterative DCOPF-based algorithm is presented with the fictitious nodal demand (FND) model to calcu- late LMP. The algorithm has three features: the iterative approach is employed to address the nonlinear marginal loss; FND is pro- posed to eliminate the large mismatch at the reference bus if FND is not applied; and an offset of system loss in the energy balance equation is proved to be necessary because the net injection mul- tiplied by marginal delivery factors creates doubled system loss. Second, the algorithm is compared with ACOPF algorithm for ac- curacy of LMP results at various load levels using the PJM 5-bus system. It is clearly shown that the FND algorithm is a good esti- mate of the LMP calculated from the ACOPF algorithm and out- performs the lossless DCOPF algorithm. Third, the DCOPF-based algorithm is employed to analyze the sensitivity of LMP with re- spect to the system load. The infinite sensitivity or step change in LMP is also discussed. Index Terms—DCOPF, energy markets, fictitious nodal demand (FND), locational marginal pricing (LMP), marginal loss pricing, optimal power flow (OPF), power markets, power system planning, sensitivity analysis. I. INTRODUCTION T HE locational marginal pricing (LMP) methodology has been the dominant approach in power markets to calculate electricity prices and to manage transmission congestion. LMP has been implemented or is under consideration at a number of ISOs such as PJM, New York ISO, ISO-New England, Cali- fornia ISO, and Midwest ISO [1]–[3]. Locational marginal prices (LMPs) may be decomposed into three components: marginal energy price, marginal congestion price, and marginal loss price [5], [6]. Several earlier works [7]–[11] have reported the modeling of LMPs, especially in marginal loss model and related issues. Reference [7] points out the significance of marginal loss price, which may differ up to 20% among different zones in New York Control Area based on actual data. Reference [8] presents a slack-bus-inde- pendent approach to calculate LMPs and congestion compo- nents. Reference [9] presents a real-time solution without re- Manuscript received October 18, 2006; revised August 6, 2007. Paper no. TPWRS-00743-2006. The authors are with the Department of Electrical and Computer Engineering, The University of Tennessee, Knoxville, TN 37996 USA (e-mail: fli6@utk.edu). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TPWRS.2007.907924 peating a traditional power flow analysis to calculate loss sen- sitivity for any market-based slack bus from traditional Energy Management System (EMS) products based on multiple gen- erator slack buses. Reference [10] demonstrates the usefulness of dc power flow in calculating loss penalty factors, which has a significant impact on generation scheduling. The authors of [10] also point out that it is not advisable to apply predetermined loss penalty factors from a typical scenario to all cases. Reference [11] presents LMP simulation algorithms to address marginal loss pricing based on the dc model. From the viewpoint of generation and transmission planning, it is always crucial to simulate or forecast LMPs, which may be obtained using the traditional production (generation) cost optimization model, given the data on generation, transmission, and load [4], [5]. Typically, dc optimal power flow (DCOPF) is utilized for LMP simulation or forecasting based on production cost model via linear programming (LP) owing to LP’s robust- ness and speed. The popularity of DCOPF lies in its natural fit into the LP model. Moreover, various third-party LP solvers are readily available to plug into DCOPF model to reduce the de- velopment effort for the vendors of LMP simulators. In indus- trial practice, DCOPF has been employed by several software tools for chronological LMP simulation and forecasting, such as ABB’s GriveView™, Siemens’ Promod ® , GE’s MAPS™, and PowerWorld [12], [13]. In addition, other literature shows the acceptability of dc model in power flow studies if the line flow is not very high, the voltage profile is sufficiently flat, and the ratio is less than 0.25 [14]. It should be noted that in this paper the production cost is assumed to have a linear model. A quadratic cost curve can be represented with piecewise-linear curves to allow the applica- tion of LP. In this paper, first, an iterative DCOPF-based algorithm is pre- sented with the fictitious nodal demand (FND) model to calcu- late LMPs. The algorithm has three features: the iterative ap- proach is employed to address the nonlinear marginal loss; FND is proposed to eliminate the large mismatch at the reference bus if FND is not applied; and an offset of system loss in the en- ergy balance equation is proved to be necessary because the net injection multiplied by marginal delivery factors creates dou- bled system loss. Section II reviews the LMP calculation with delivery factors. Section III discusses the observation of a large nodal mismatch at the reference bus. Section IV presents a new algorithm for LMP simulation based on FND model to elimi- nate the nodal mismatch. Second, the proposed DCOPF-FND-based algorithm is com- pared with ACOPF algorithm for accuracy of LMP results at various load levels using the PJM 5-bus system. It is shown that 0885-8950/$25.00 © 2007 IEEE