650 IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 26, NO. 2, APRIL 2011 Hourly Scheduling of DC Transmission Lines in SCUC With Voltage Source Converters Azim Lotfjou, Mohammad Shahidehpour, Fellow, IEEE, and Yong Fu, Member, IEEE Abstract—This paper presents the modeling of high-voltage direct current (dc) transmission systems with voltage-source con- verters (VSCs) in security-constrained unit commitment (SCUC). The impact of VSC-DC transmission system on the economics and the security of integrated ac/dc transmission systems is discussed. The nonlinear ac/dc equations are linearized and the Newton–Raphson method is utilized to solve the linearized net- work in the base case and contingencies. The SCUC solution will determine the optimal hourly schedule of controllable VSC-DC transmission systems in electricity markets. Numerical examples show the efficiency of the proposed model. Index Terms—High-voltage direct current transmission lines, se- curity-constrained unit commitment, voltage-source converters. NOMENCLATURE Index of ac buses. Superscript for contingency. Number of ac buses. AC-side voltage of the converter . Index of dc converters. Index of units. Index of hour. Superscript for an injection. DC current of converter . On/off state of generating unit at time . , State and generation dispatch solution of unit at time . Index of lines. Index of ac bus terminals connected with converters. , Subscript for maximum and minimum values. Modulation index of converter . Generation dispatch of unit at time . Manuscript received June 17, 2009; revised September 13, 2010; accepted October 25, 2010. Date of publication December 17, 2010; date of current ver- sion March 25, 2011. This work was supported by the U.S. Department of Energy under Grants # DE-EE 0001380.000 and DE-EE 0002979. Paper no. TPWRD-00454-2009. A. Lotfjou and M. Shahidehpour are with the Electrical and Computer Engi- neering Department, Illinois Institute of Technology, Chicago, IL 60616 USA (e-mail: ms@iit.edu). Y. Fu is with the Electrical and Computer Engineering Department, Missis- sippi State University, Mississippi State, MS 39762 USA. Digital Object Identifier 10.1109/TPWRD.2010.2090908 DC active power through converter . Withdrawal real power at ac bus . Active power injected into the converter . DC reactive power through the converter . Withdrawal reactive power at the ac bus . Reactive power injected into converter . Resistance of the dc line. , Slack variables for real power mismatch at bus . , Slack variables for reactive power mismatch at bus . Objective of SCUC subproblem. Leakage reactance of coupling transformer connected to converter . AC voltage at bus . DC voltage of converter . Power factor lagging/leading angle of converter ( for rectifier for inverter). , Active and reactive power mismatch at ac bus . , Mismatches of dc power flow equations related to converter . Permissible real power adjustment for unit . Bus-unit incidence matrix. Admittance matrix of dc network for converter . Generating unit state vector (0 or 1 values). , Generating unit state and economic dispatch solutions. , Vector of dc current and its increment vector. , , , , , Jacobian matrices. , Modulation index vector and its increment vector. Initial modulation index vector. , , , Mismatch vectors. 0885-8977/$26.00 © 2010 IEEE