934 IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 19, NO. 2, MAY 2004 A Common Modeling Framework of Voltage-Sourced Converters for Load Flow, Sensitivity, and Dispatch Analysis Xuan Wei, Joe H. Chow, Behruz Fardanesh, and Abdel-Aty Edris, Senior Member, IEEE Abstract—This paper discusses the use of injected shunt and series voltage sources to model voltage-sourced converter (VSC)-based flexible ac transmission systems (FACTS) controllers such as the unified power-flow controller (UPFC) and the interline power-flow controller (IPFC). Compared to traditional power network models including only shunt voltage injections, the inclusion of series voltage injections provides a new capability of power system models and offers a common modeling framework in which a Newton–Raphson load-flow solution and a network sensitivity analysis can be readily developed. The sensitivities can be used for optimal dispatch of FACTS controllers. Index Terms—Flexible ac transmission system controllers, interline power flow controller, Newton–Raphson algorithm, op- timal dispatch, sensitivity analysis, unified power-flow controllers, voltage-sourced converters. I. INTRODUCTION T HIS paper concerns the modeling and analysis of flexible ac transmission system (FACTS) controllers using the self- commutated voltage-sourced converters (VSCs) [1]. These con- trollers include static synchronous compensators (STATCOMs) [2], static synchronous series compensators (SSSCs), unified power-flow controllers (UPFCs) [3]–[8], and interline power flow controllers (IPFCs) [9], [10]. Furthermore, the flexibility of VSC-based FACTS controllers can be increased when two VSCs are used either to provide shunt or series compensation. This is the case of the convertible static compensator (CSC) in- stalled at the Marcy Substation of the New York Power Au- thority (NYPA) [9]. The Marcy CSC configuration is similar to the one in Fig. 1, except that the Marcy unit has only one series transformer in each transmission line. By closing the ap- propriate switches, the Marcy CSC can operate in 11 different compensation modes. For systems with three or more coupled VSCs, it is possible to connect and operate them as a unit to form a generalized unified power-flow controller (GUPFC) [11]. The VSCs can also be coupled to energy systems such as supercon- ducting magnetic energy storage system (SMES) or a battery storage device [12]. Manuscript received November 14, 2003. This research was supported in part by EPRI and NYPA. X. Wei and J. H. Chow are with the Electrical, Computer, and System En- gineering Department, Rensselaer Polytechnic Institute, Troy, NY 12180-3590 USA (e-mail: chowj@rpi.edu). B. Fardanesh is with the Manhattan College, Riverdale, NY 10471 USA, and also with NewYork Power Authority, White Plains, NY 10601 USA. A.-A. Edris is with the Electric Power Research Institute, Palo Alto, CA 94303-0813 USA. Digital Object Identifier 10.1109/TPWRS.2004.826753 Fig. 1. Multiple configurations of a convertible static compensator (CSC). In contrast to thyristor-controlled FACTS controllers such as the static var compensator (SVC) and the thyristor-controlled series compensator (TCSC), which can be modeled simply as variable shunt and series susceptances, respectively, the studies of VSC-based controllers such as unified power-flow controller (UPFC) and IPFC are more complex. Ideally, a VSC injects a voltage component into a power system and should be mod- eled as a voltage source. A traditional power network consists of only shunt injections and shunt voltage sources. Thus, to ac- commodate a series VSC on a transmission line, bus injections are added to the from-bus and the to-bus [12], [13]. This has the disadvantage that the line flow on the series VSC equiva- lent transformer reactance not be identical to the flow on the actual equipment, in addition to the need of adjusting the bus injections such that the proper line flow and bus voltage specifi- cations are met. The power injection model in [14] uses directly a series voltage source power injection, by requiring additional equations as constraints, which need to be solved in an optimal power-flow setting. Another approach is to model shunt and series VSCs directly as shunt and series voltage injections, respectively [16]–[21]. This approach represents a common modeling framework, where the VSC variables from the load-flow solution can be used to directly initialize electromagnetic transient programs and dynamic simulation programs. In particular, as shown in this paper, the sensitivity analysis of the VSC control variables using the network equations consisting of shunt and series voltage injections can be readily obtained in such a framework. The FACTS controller sensitivities, similar to generation shift factors [25] affecting network flows, are useful for the 0885-8950/04$20.00 © 2004 IEEE