تجزیه و تحلیل Presolve و راه حل نقطه داخلی از مشکل هماهنگی برنامه ریزی خطی از رله های جاری جهت دار

A linear programming interior point algorithm is proposed for the solution of the problem of coordinating directional overcurrent relays in interconnected power systems considering definite time backup relaying. The proposed algorithm is a variation of the primal–dual approach that uses multiple correctors of centrality. Pre-solution problem filtering simplification techniques are used prior to the application of the linear programming algorithm. Results are presented for the application of the methodology on a realistic test case, a 115–69 kV power system with 108 buses, 86 lines, 61 transformers, and 97 directional overcurrent relays. Optimal solutions are found in an automatic fashion, using the algorithm for the settings of the ground relays as well as for the phase relays. The application of the pre-solution problem simplification techniques is highly recommended, resulting in a significant reduction of the size and complexity of the linear programming problem to be solved. The interior point approach reaches a feasible point in the close vicinity of the final optimal result in only one or two iterations. This fact represents an advantage for on-line applications. The proposed methodology and in particular the use of the presolve problem simplification techniques is shown as a new valuable tool for the setting of directional overcurrent relays in interconnected power systems.

The determination of the time dial settings of directional overcurrent relays in meshed power systems in order to comply with the requirements of sensibility, selectivity, reliability and speed was stated as an optimization problem in 1987 [1]. The application of the simplex method for linear programming to the solution of this problem has been successful [1], [2], [3], [4] and [8]. The problem of re-calculating the settings of the relays after a network expansion, reducing the number of relays to be reset, was solved by means of an iterative application of the optimization methodology proposed in [1], [2], [3], [4], [5], [6], [7] and [8]. In this case, the problem is augmented in each iteration and different solutions are found successively using the linear programming technique. Multiobjective optimization concepts were applied to find a tradeoff between the number of relays to be reset and the sum of the operation times. The consideration of the transient changes of the system configuration that take place during the fault clearing process was also recently addressed in Ref. [4]. The consideration of definite time relaying, i.e. instantaneous units, distance relays and breaker failure relays for the formulation and solution of the optimization problem is presented in Ref. [5] and a comparison of the application of the feasibility of the relay time coordination under different criteria is studied in Ref. [9]. However, up to date, the optimal relay coordination problem has been solved only using the traditional simplex method for linear programming. The purpose of this work is to evaluate the goodness of the proposed pre-solution techniques when applied to this particular problem, as well as the application of a different optimization technique, a primal–dual interior point predictor–corrector approach with multiple correctors of centrality.

The optimal operation time coordination problem of directional overcurrent relays considering definite time back-up units (second zone of distance relays and breaker failure relays) can be solved using interior point linear programming techniques. The resultant time dial settings assure a coordinated operation of the relays and guarantee the minimum possible operation times. The application of the proposed presolve analysis results in a significant reduction of the size and complexity of the linear programming problem to be solved accelerating the overall solution time. The impact of the presolve analysis is such that the selection of the algorithm to be applied for the solution of the linear programming problem turns out to be a point of little relevance given the small size of the optimization problem to be solved. The proposed primal–dual interior point algorithm with multiple correctors represents a reliable tool for the solution of the problem providing a solution for the relay settings, which is relatively close to the optimal solution even after the first iteration only. This fact represents an advantage for on-line applications.