IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 27, NO. 1, JANUARY 2012 131 Steady-State Model and Power-Flow Analysis of Single-Phase Electronically Coupled Distributed Energy Resources Mohamed Zakaria Kamh, Member, IEEE, and Reza Iravani, Fellow, IEEE Abstract—This paper develops and presents the steady-state, fundamental-frequency model of the single-phase distributed energy resource (DER) unit which utilizes a single-phase voltage-sourced converter (VSC) as the interface medium. The model represents: 1) different operating and control modes and 2) the operational constraints and limits of the VSC and the host grid. The model is included in a sequential power-flow analysis method using: 1) a backward-forward sweep algorithm for single-phase laterals and 2) a sequence-components frame solver for three-phase networks. The interface-VSC operating limits are accommodated in the power-flow algorithm as an inter- leaved step to increase computational efficiency of the power-flow analysis tool. Case studies are conducted to evaluate and verify 1) the accuracy of the proposed model and 2) the computational efficiency of the power-flow algorithm. Index Terms—Distributed energy resources, electric vehicles, single-phase voltage-sourced converter (VSC), power-flow analysis. I. INTRODUCTION T HE increasing demand for the clean and renewable energy resources and the governmental policies (e.g., the feed-in tariff (FIT) and microFIT programs [1], [2]) are the main driving forces to the wide-spread penetration of the distributed genera- tion (DG) units into the medium- and low-voltage distribution grids. The expected presence of the plug-in hybrid electric ve- hicle (PHEV) [3] and the electric vehicle (EV) [4] will also im- pact the distribution grids due to the additional load of charging the vehicle batteries. Moreover, EVs with the vehicle-to-grid (V2 G) power-transfer capability can inject power into the dis- tribution network, thus also act as DG units [5]–[8]. The single-phase ac–dc voltage-sourced converter (VSC) is the most widely-adopted interface medium for small scale DER units [9]–[12]. The single-phase VSC is efficient, compact, expandable, bidirectional, and can be connected to single- and three-phase distribution networks [13], [14]. As such, an array of dynamic and steady-state models of single-phase VSC-coupled DER units, incorporated in the power system software tools, is essential to analyze, plan, and control the active distribution systems. Among these software tools, the Manuscript received January 02, 2011; revised May 27, 2011; accepted September 25, 2011. Date of publication November 29, 2011; date of current version December 23, 2011. Paper no. TPWRD-00003-2011. The authors are with the Department of Electrical and Computer En- gineering, University of Toronto, Toronto, ON M5S 3G4 Canada (e-mail: mohamed.kamh@ieee.org; iravani@ecf.utoronto.ca). Digital Object Identifier 10.1109/TPWRD.2011.2172640 steady-state power-flow analysis tool is the focus of this paper. Accurate power-flow analysis is not only to determine the system steady-state operating point, but also to accurately and efficiently initialize dynamic analysis tools (e.g., the electro- magnetic transients analysis tools [15]). The steady-state models of the three-phase VSC have been extensively reported and incorporated in different three-phase power-flow analysis algorithms for the three-phase distribu- tion grid [16]–[20]. However, the steady-state model of the single-phase VSC-based DER units, including the operating constraints of the VSC and the host grid, has not been reported. This paper: 1) develops a steady-state, fundamental frequency model of the single-phase VSC-coupled DER unit and 2) incor- porate the model into a power-flow algorithm. The developed VSC-coupled DER model presents: • the VSC operational and control modes (e.g., bidirectional power exchange, constant power-factor, reactive power support [13]); • the VSC operational limits and constraints (e.g., max- imum current, maximum modulation index, and maximum voltage) at the point of common coupling (PCC). The sequential power-flow method, presented in [17]–[20] is deployed to incorporate the single-phase VSC-coupled DER model in a three-phase power-flow algorithm. Based on the se- quential approach, the VSC terminal conditions are evaluated. Then, if any of the interface-VSC or host DER unit constraints are violated, the real and reactive reference setpoints of the VSC controllers are updated to guarantee compliance with the operational constraints of the DER unit and its interface-VSC [17]. Finally, the VSC terminal voltage is specified prior to pro- ceeding to the following power-flow iteration. The sequential power-flow algorithm is easy to implement and readily permits integration of various control functions and operating limits of the interface VSC [21]. The proposed VSC model is incorporated into two different algorithms within the sequential power-flow method, namely: 1) the single-phase backward-forward sweep algorithm (BFSA) [22], [23] for power-flow analysis of single-phase laterals, and 2) the three-phase sequence-components frame power-flow solver (SFPS) [17] for the analysis of three-phase networks. The details of the BFSA, the SFPS, and models of power lines, loads, transformers, and other apparatus have been reported in the technical literature [16]–[18], [22]–[25] and are not reiter- ated in this paper. Several case studies are conducted to validate the proposed VSC model and demonstrate the computational efficiency of the sequential power-flow technique. 0885-8977/$26.00 © 2011 IEEE