Parameter uncertainty in the optimal coordination of overcurrent relays

Generally, the relay coordination problem is solved without considering parameter uncertainties, while uncertainties in the line parameters and current transformer ratios make the fault current passing through the overcurrent relay inaccurate and could cause the miscoordination. To overcome this drawback, in this paper, a novel method based on interval analysis is introduced to model parameter uncertainties in the coordination problem. Considering parameter uncertainties, the coordination constraints are formulated as a set of inequalities with interval coefficients. Monte Carlo simulation technique is used to determine the boundary values of these interval coefficients. In this case, the optimal coordination problem is formulated as an interval linear programming problem. Using mathematical theorems, the optimal value of interval linear programming problem can be obtained by solving a standard linear programming problem. The proposed method is applied to the 8-bus and Institute of Electrical and Electronics Engineers 30-bus test systems, and the results show the ability of interval method to model the parametric uncertainties.