A new optimization formulation for determining the optimum reach setting of distance relay zones by probabilistic modeling

In this paper, by probabilistic modeling of uncertainties, the problem of determining the reach setting of distance relay zones is presented as a new optimization problem. For this purpose, uncertainties are modeled based on their probability density functions. Then, by using the Monte-Carlo process, the impedance seen by the distance relay is obtained. In this paper, probabilistic sensitivity and selectivity indices are defined for each zone of the distance relay. Therefore, the problem of determining the optimum reach setting of distance relay for each zone is converted to an optimization problem with the objective of maximizing of the probabilities indices of sensitivity and selectivity. The objective function and the constraints of the optimization problem are defined based on the protection philosophy of each of the three different zones of the distance relay. Considering the fact that the optimization problem is nonlinear and non-convex, the particle swarm optimization (PSO) is used to solve this problem. The proposed optimization problem is applied on a 9-bus network, and the reach settings of distance relays are calculated and compared with those of the conventional approach. Also, uncertainties are prioritized based on the amount of their impact on the probabilistic indices of sensitivity and selectivity.