ACCEPTED TO IEEE TRANSACTIONS ON POWER SYSTEMS, JUNE 2016 1 Hybrid Power Flow Controller Steady-state Modeling, Control, and Practical Application Behnam Tamimi, Student Member, IEEE, Claudio Ca˜ nizares, Fellow, IEEE, and Claudia Battistelli, Member, IEEE Abstract—Steady-state models of the Hybrid Power Flow Controller (HPFC) for power flow and optimal power flow (OPF) studies are presented in this paper, considering the multiple control modes of the device. A strategy for control mode switching and limit handling in power flow calculations is proposed. The OPF model of the HPFC represents all the device control and physical limits as constraints in the mathematical formulation, so that the HPFC can be optimally dispatched as a part of the transmission system control assets. The power flow model is demonstrated and validated through loadability studies on a two-area benchmark test system, where the OPF model is used to determine the optimal ratings of the device based on a cost-benefit analysis. A study is also presented of the HPFC application to Ontario-Canada’s grid, to address particular congestion problems in this network; an HPFC cost analysis is also shown for this system. The presented studies demonstrate the application of the proposed models for planning and operation studies, illustrating the performance, effectiveness, and feasibility of the controller to solve congestion issues in a real grid. Index Terms—Congestion relief, FACTS, HPFC, modeling, OPF, power flow. I. I NTRODUCTION F LEXIBLE AC Transmission System (FACTS) controllers offer new opportunities to better control power systems, as well as enhance power transfer capabilities [1]. Several Voltage-Source Converter (VSC) FACTS have been proposed in the literature, particularly the Static Synchronous Compen- sator (STATCOM), the Series Static Synchronous Compen- sator (SSSC), and the Unified Power Flow Controller (UPFC) [2]. Among these controllers, the UPFC is a versatile device that can control various system variables independently [3] (e.g. bus voltage magnitudes and transmission line active and reactive power flows), and its application to solve congestion problems in an actual grid is demonstrated in [4]. However, the capital cost of this controller is a major obstacle for the wide application of this technology in power systems. Thus, a cost effective VSC-based FACTS controller is introduced in [5], which yields operating characteristics similar to those of the UPFC while requiring a lower capital investment. This controller may consist of converters as well as passive compo- nents (e.g. capacitor banks), and is referred to as the Hybrid Power Flow Controller (HPFC). Compared to the UPFC, the savings stem from a few structural differences between the two This work has been supported by NSERC and Hydro One Inc. through a Collaborative Research and Development (CRD) grant. B. Tamimi, C. Ca˜ nizares are with the Department of Electrical and Computer Engineering, University of Waterloo, Waterloo, ON, Canada (e- mail: ccanizares@uwaterloo.ca). C. Battistelli is currently with the Department of Electrical and Electronic Engineering, Imperial College, London, UK (e-mail: c.battistelli@imperial.ac.uk). devices, including the use of half-sized converters and passive elements for supplying the bulk of the required reactive power, as discussed in [5]. The benefits of an HPFC are defined by its limits and operating constraints. Therefore, the impact of the controller limits on its performance must be considered during planning and operation stages. However, previously published works on the HPFC do not discuss the device operating limits and their implications in congestion studies adequately [5]–[7]. Thus, in [5], the device is introduced, and an interesting geometrical representation of the devices operating region is presented. An Electromagnetic Transients Program (EMTP) model of the HPFC is briefly studied in [6]. The performance of the HPFC with regard to improving the power transfer capability of a system is compared with that of the UPFC in [7], based on time domain simulations. In the current paper, a novel model of the HPFC appropriate for congestion studies, which are for the most part based on power-flow analyses, and its various possible control modes are presented and applied to address congestion issues. The controller is modeled from the system point of view, and thus its terminals are considered in the model, which is consistent with its operation requirements. The controller’s internal variables are also properly represented in the proposed model, which allows handling the device limits accurately and thus modeling the multiple control modes defined in this paper. The proposed model is integrated into a widely popular power flow production program using a sequential approach to allow its integration into commercial power system analysis software packages. An HPFC model for OPF applications is also introduced, proposing a concise mathematical model of the HPFC for OPF applications that considers the device ratings and its control variables and limits directly. These proposed models are then used to demonstrate their applications in planning and operation studies, evaluating the performance and the effectiveness of the device using realistic test systems and practical assumptions and scenarios. The rest of the paper is organized as follows: After re- viewing the basics of the HPFC in Section II, its steady-state circuit model and associated operating modes are introduced in Section III, together with an effective strategy to handle the operating limits in power flow studies. The device model for OPF applications is presented in Section IV. In Section V, the device is applied to address congestion issues in two test systems, namely, a two-area system and a detailed model of Ontario-Canada’s grid; several studies based on the proposed model and realistic scenarios are carried out to evaluate the performance and show the benefits of the HPFC, demonstrat- ing the feasibility of the device to solve actual congestion