Reliability Constrained Distribution Feeder Reconfiguration for Power Loss Minimization Joel Jose and Anupama Kowli Department of Electrical Engineering Indian Institute of Technology Bombay Mumbai, India {joeljose, anu.kowli}@iitb.ac.in Abstract—This paper presents a path-based mixed integer quadratic programming (MIQP) formulation of distribution feeder reconfiguration (DFR) for loss minimization and reliabil- ity enhancement. Analytical expressions for standard reliability indices like SAIFI and EDNS are obtained by adopting stan- dard assumptions regarding component failures. A path-based modeling framework is adopted to allow for easy evaluation of the reliability indices. The proposed path-to-branch incidence matrix results in linear expressions for the reliability indices and power flow equations. These linear models are suitably deployed in a flexible DFR optimization framework wherein reliability can feature in either via objectives or constraints. The proposed MIQP formulations are applied to different test systems to optimize network losses or reliability or both. Numerical results showcase the wide range of capabilities of the proposed formulations. I. I NTRODUCTION Distribution feeder reconfiguration (DFR) is an important tool in distribution management systems. It allows for chang- ing the network topology by appropriately switching the statuses of the normally closed sectionalizing switches and normally open tie switches. The flexibility offered by such switching actions has been traditionally used for minimizing network losses, load balancing and service restoration [1], [2], [3]. DFR has been shown to improve system reliability as well [4]. While reduction in active power losses is attractive to the utilities as it directly translates to profits, they are also required to adhere to reliability standards set by regulatory councils. Furthermore, the move towards smarter systems and the opportunity for customers to choose between service providers also necessitate that the utilities endeavor to improve service reliability: DFR offers one way to achieve this goal [5]. Finally, smart grid technologies are expected to herald an era where line switching in real time will be feasible. To fully realize the potential of line switching for improving system performance, a rigorous decision making framework is needed. This paper proposes an MIQP approach to determine optimal system configuration with respect to loss minimization and reliability enhancement. The DFR problem has been traditionally studied in the context of power loss minimization [1], [6], [7]. The al- gorithms in these references can be generally classified as branch-exchange algorithms, wherein an appropriate pair of sectionalizing switch and tie switch are opened and closed simultaneously to attain a new radial network topology that lowers network losses. Reference [1] lays down the foundation for identifying the optimal choice of tie-sectionalizer pair for switching. A greedy search algorithm for achieving this is proposed in [2]. Such methods have the disadvantage that the resultant topology is dependent on initial configuration. Combinatorial methods using non-linear power flow equations and integer variables representing switch statuses render DFR as a mixed integer non-linear programming problem. Using DistFlow equations [2], Taylor and Hover [8] present mixed- integer quadratic, quadratic constrained and second-order cone programming formulations for the DFR problem. A linear power flow based MIQP formulation presented in [9] is able to find optimal configurations in a short time even though it uses a ZI load model for the distribution system. Inherent complexity of mixed integer programming has paved the way for heuristic approaches to be applied to the DFR problem [10]. Fuzzy logic [11], genetic algorithms [12], [13] and evolutionary programming [14] are some of the common choices. The application of heuristics is even more common when multiple objectives such as loss min- imization and reliability enhancement come into play [15], [16], [17]. Attempting multi-objective DFR optimization as a mixed integer program is a very hard problem and to the best of authors’ knowledge has not been attempted. This paper outlines preliminary steps towards such optimization. Appending reliability oriented objectives in the DFR prob- lem is complicated by the modeling considerations that come into play. Rigorous modeling of reliability indices in the DFR problem requires probabilistic methods and state sampling. Due to the difficulty in optimizing reliability indices directly, some papers propose load balancing as the method to improve reliability by relieving component stress [3], [18]. Heuristic methods have been applied for solving the DFR problem where reliability is included as an objective or constraint [6], [19]. Heuristic methods have the disadvantage that the solutions obtained may not be globally optimal. It is also difficult to ascertain the nature of the optimum to which the algorithm converges. In this paper, suitable yet reasonable assumptions are adopted to derive analytical expressions for standard reliability indices which are then incorporated as constraints or objectives in the DFR optimization problem. The 978-1-4799-5141-3/14/$31.00 c  2016 IEEE