0885-8950 (c) 2018 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TPWRS.2019.2902468, IEEE Transactions on Power Systems IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. X, NO. X, XXX 20XX 1 Continuation Load Flow Considering Discontinuous Behaviors of Distribution Grids Luan F. S. Colombari, Roman Kuiava, Member, IEEE, Vedran Peric, Member, IEEE, and Rodrigo A. Ramos, Senior Member, IEEE Abstract—The reduction in bus voltage magnitudes as the load demand grows may lead to sudden disconnection of loads and/or distributed generation units, in distribution grids, caused by undervoltage protection schemes. As proposed in this paper, this discontinuous behaviour of distribution grids can be modeled as a sudden load variation in traditional static Voltage Stabil- ity Assessment methods, such as the continuation power flow (CPFLOW). A discussion on the impacts of these discontinuities on the equilibrium diagram of the system is presented in this paper, as well as a set of numerical simulations showing that the traditional CPFLOW algorithm presents convergence problems caused by the discontinuities under analysis. From this perspective, this paper proposes an algorithm based on novel predictor/corrector and identification schemes, which are capable of successively calculating the discontinuities that exist in the equilibrium loci of the system under analysis, as well as the Maximum Loadability Point and the type of bifurcation. A simplified modeling approach that eliminates the need for a complex (and computationally expensive), detailed description of distribution grids is also elaborated and incorporated into the proposed algorithm. The simulated examples show that the proposed algorithm adequately handles the problem, yelding more accurate results than the traditional CPFLOW algorithm. Index Terms—Voltage stability, load modeling, continuation power flow, predictor/corrector method. I. I NTRODUCTION P OWER systems are nowadays operated closer to their lim- its in an overall sense, which makes them more prone to voltage stability problems. One example of voltage instability was seen in Brazil in 2009, when the three transmission lines that deliver power from the Itaipu power plant to the bulk power grid were disconnected. This disturbance caused voltage sags in the state of Sao Paulo, which resulted in disconnection of the HVDC link between Brazil and Paraguay [1]. Problems like this motivated this research, with the aim of developing more robust and accurate voltage stability assessment algo- rithms, that can upgrade or even replace the traditional voltage stability assessment tools [2]. Traditional Voltage Stability Assessment (VSA) methods typically rely on algorithms that assume a continuous be- haviour of the load [3], which is an assumption that may Luan F. S. Colombari is with the Brazilian Navy, Rio de Janeiro, Brazil, e-mail: colombari@marinha.mil.br. Roman Kuiava is with the Department of Electrical Engineering, Federal University of Parana (UFPR), Curitiba, Brazil, e-mail: kuiava@eletrica.ufpr.br. Vedran Peric is with the General Electric (GE) Energy Consulting, Munich, Germany, e-mail: vedran.peric@ge.com. Rodrigo A. Ramos is with the Department of Electrical Engineer- ing, University of Sao Paulo (USP), Sao Carlos, Brazil, e-mail: ro- drigo.ramos@ieee.org. Manuscript received —–; revised ——. not hold in practice, taking into account several particular characteristics of current power systems operation, such as the presence of undervoltage load shedding (ULS), distributed generation (DG) undervoltage protection, and modern demand side management schemes [4]. In the case of DG, these small generators may exhibit discontinuous behaviours (due to protection actuation) during disturbed operational regimes, in order to comply with the grid codes. Also, typical load shedding and demand side management schemes clearly pro- duce discontinuous behaviours of the loads in distribution grids. Several authors have tried to address this issue as reported in [5] and [6] where the mandatory disconnection of DG was considered during dynamic simulations. In [5], it was demonstrated that inadvertent undervoltage trip of a DG unit may cause instability in bulk power systems. In [6], a transmission system Maximum Loadability Point (MLP) was estimated from small successive increments in its load. This study concluded that mandatory disconnection of DGs units may cause a signicant reduction in the Voltage Stability Margin (VSM) of the system. Both studies are based on dynamic voltage stability analyses, which provide accurate results but are often too computationally expensive for control center applications. A practical alternative to dynamic analysis comprises static techniques employing the power flow problem formulation and the estimation of equilibrium diagrams or PV curves of the system [7]–[9]. A reliable technique to trace equilibrium diagrams of power systems and to estimate their MLPs is the Continuation Power Flow (CPFLOW) method [2], [7]. However, traditional algorithms based on CPFLOW suffer from several convergence issues in cases where the system exhibits discontinuous behaviours. Examples of equipments with discontinuous behaviour are switchable shunt capacitors and excitation limiters of generators [10]. These devices are responsible for sudden structural (parametric) changes in the power system model which, in turn, causes discontinuities in its equilibrium diagram. There have been several attempts to analyze voltage stability in the presence of discontinuities. For example, in [10]–[12], generator reactive limits (Q-limits) as well as switching capacitors were considered. However, none of these contributions treat other types of system discontinu- ities such as ULS schemes or mandatory DG disconnections. This paper attempts to fill this gap in static VSA methods by taking into account these discontinuous behaviours of distribution grids. First, the paper proposes a simple but effi- cient method to model discontinuities in the distribution grids, which eliminates the need for a detailed representation of these