International Journal of Electrical Power & Energy Systems
Presolve analysis and interior point solutions of the linear programming coordination problem of directional overcurrent relays
Introduction
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], [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], [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.
Section snippets
Statement of the problem
The coordination of the operation of directional overcurrent relays in interconnected power systems can be stated as an optimization problem in the following fashion [1], [8]:
Minimize: weighted sum of operation times
Subject to:
relay time–current characteristics,
relay operation time coordination constraints that assure the selectivity of the solution:
associated to directional overcurrent relays
associated to definite time backup relaying:
instantaneous units
distance relays
breaker failure relays
Solution methodology
In order to solve the linear programming problem stated in , , an interior point primal–dual algorithm developed by Gondzio [10] was used. This method, called higher-order primal dual method (HOPDM), is a variant of the original primal–dual algorithm first introduced by Kojima et al. [11], based on the work by Megiddo [12]. A detailed study about primal–dual interior point methods can be found in Wright [13]. These methods have been shown to be very successful computationally. Indeed, they are
Results
The performance of the proposed methodology was evaluated by its application to the following test cases.
Conclusions
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
References (18)
- et al.
Optimal coordination of directional overcurrent relays in interconnected power systems
IEEE Trans Power Delivery
(1988) - et al.
Coordination of directional overcurrent relay timing using linear programming
IEEE Trans Power Delivery
(1996) - et al.
An on-line coordination algorithm for adaptive protection using linear programming technique
IEEE Trans Power Delivery
(1996) - et al.
Optimal coordination of directional overcurrent relays in interconnected power systems
IEEE Trans Power Delivery
(1997) Protective relaying. Principles and applications
(1987)Review of recent practices and trends in protective relaying
IEEE Trans Power Apparatus Syst
(1981)- et al.
Mathematical models representing time–current characteristics of overcurrent relays for computer applications
IEEE Trans Power Apparatus Syst
(1978) - et al.
Optimal coordination of directional overcurrent relays considering definite time backup relaying
IEEE Trans Power Delivery
(1998) - Pérez L, Urdaneta A, Sorrentino E, Garayar F, Urizar A, Ledezma J, Alcalá G, Canache C, Sanz O, Carrión N, Fernández J,...
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