T S S Senarathna Department of Electrical Engineering University of Moratuwa Sri Lanka sisitha@outlook.com M A K S. Boralessa Department of Electrical Engineering University of Moratuwa Sri Lanka kalhansandaru@gmail.com K T M Udayanga Hemapala Department of Electrical Engineering University of Moratuwa Sri Lanka udayanga@uom.lk Abstract—Modern distribution networks are more inclined to integrate distributed energy generation (DEG) into their systems. Protection problems occur when using conventional protection solutions on these DEG integrated networks. Optimal coordination of overcurrent relays while minimizing the operating time is one of the popular research interests. Optimization algorithms are used to solve this multi-objective constrained optimization problem. In this paper, various methods of problem formulation in literature are compared to observe their effect on final relay operating times. Keywords—Distributed Generation, Objective function, Genetic algorithm, Near-end faults, Far-end faults, Protection coordination I. INTRODUCTION Sustainable power systems are more focused on integrating renewable distributed generation in order to cope with the ever-increasing demand. This creates a novel problem set that needs to be addressed to harvest the full potential of these DG equipped distribution networks. Directional Overcurrent relay (DOCR) coordination problem becomes a critical issue when it comes to the meshed networks with distributed generation. Since 1988 [1], this problem has been tackled in order to find the perfect method of obtaining DOCR settings. With the growth of interest towards microgrids, which are multi-sourced and multi-loop in nature, the interest in the protection solutions has also increased. Coordination techniques for DOCRs have been identified in the literature as Conventional methods, Optimization techniques, and Computational Intelligence. Conventional methods include trial and error and topological analysis. The Trial and error methods require manual calculations, and they are slow and require a large number of iterations to reach the solution. Topological analysis is based on graph theory and functional dependencies [2]. They are mainly dependent on the selection of proper “Break Points,” which is similar to an initial value. They also fail to obtain the most optimal solution. The optimization techniques are a more mature solution for the coordination problem. They have two main problem formulation methods as Linear and Non-linear. In Linear formulation, a linear function of relay Time Dial Setting (TDS) is formulated while selecting the pickup current setting (Plug Setting (PS)) values by previous experience [3]. Simplex, dual simplex, and two-phase simplex are some of the methods that are being used to solve linearly formulated problems. In non-linear formulation, both TDS and PS are considered as variables while only the TDS was continuous, and PS was treated as a discrete-valued variable. Mixed- integer non-linear programming (MINLP) was a popular method of solving non-linear formulated problems. Computational Intelligence methods have become the present interest in solving the Relay coordination problem. Out of these methods, Nature-inspired algorithms (NIA) are specialized in optimization problems, and they are the most popular option [4]. There are over hundreds of NIA developed and they are categorized in literature as Bio-inspired, Swarm intelligence-based, Physics and chemistry-based and Other. Some of these algorithms are Particle swarm optimization (PSO), Genetic algorithm (GA) which are classical algorithms and more novel algorithms such as Firefly algorithm (FA), Teaching Learning-Based Optimization (TLBO) and Grey wolf optimization (GWO). The NIAs are widely being used mainly due to their superiority over other methods. Some of the advantages can be listed as Simplicity, flexibility, Derivative-free mechanism, Local optimum avoidance, and Robustness. In this paper, the problem of calculating the optimal DOCR settings is formulated as a non-linear constrained optimization problem. Problem formulation is done in three methods used by the majority of the literature. The second section introduces the problem formulation and the third phase includes the detail on test systems. Section four presents the results obtained from different problem formulations and compares them for their impact on final relay operating times. II. PROBLEM FORMULATION A. Optimization Optimization is the search of the best set of values for variables of one or more objective functions while fulfilling necessary constraints. The Objective function (OF) establishes the final aim of the optimization problem, and the decision variables control the value of OF. These decision variables are usually bound to a pre-defined decision space and can be either continuous or discrete. Constraints on the decision variable values make way to an optimal solution within the feasible space. B. Objective Function Formulation Formulation of the Objective Function is the primary step of optimization. In DOCR protection, TDS and PS are considered the main decision variables. Equation (1) gives the operating time of the DOCR written in terms of TDS and PS, according to IEC 60255 standards. = ௄ భ ×஽ௌ ൫ூ ೑ (௉ௌ×஼ ೝ ) ⁄ ൯  మ ଵ (1) Here, T is the operating time, TDS and PS have conventional meanings, If is the fault current, CTr is the Current transformer ratio and K1, K2 depends on the type of the curve, which the relay is using. When TDS and PS being 2019 IEEE Region 10 Humanitarian Technology Conference Depok, Indonesia | November 12-14, 2019 Effect of the Different Objective Function Formulations on DOCR Setting Optimization 80 978-1-7281-0834-6/19/$31.00 ©2019 IEEE