Presolve analysis and interior point solutions of the linear programming coordination problem of directional overcurrent relays

doi:10.1016/S0142-0615(00)00097-1

International Journal of Electrical Power & Energy Systems

Volume 23, Issue 8, November 2001, Pages 819-825

https://doi.org/10.1016/S0142-0615(00)00097-1 Get rights and content

Abstract

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.

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

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The optimization of protection coordination problems has received a great deal of attention [12]. This optimization problem (OP) has been formulated as linear programming (LP) [13,14], non-linear programming (NLP) which considers that the Ip tap settings are continuous [15,16], and mixed-integer non-linear programming (MINLP) considering the discrete Ip settings [17,18]. In some studies, the LP has been utilized to optimize the TDS of relays, while pick-up currents were considered to be pre-defined.
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View full text

Presolve analysis and interior point solutions of the linear programming coordination problem of directional overcurrent relays

Abstract

Introduction

Section snippets

Statement of the problem

Solution methodology

Results

Conclusions

Optimal coordination of directional overcurrent relays in interconnected power systems

IEEE Trans Power Delivery

Coordination of directional overcurrent relay timing using linear programming

IEEE Trans Power Delivery

An on-line coordination algorithm for adaptive protection using linear programming technique

IEEE Trans Power Delivery

Optimal coordination of directional overcurrent relays in interconnected power systems

IEEE Trans Power Delivery

Protective relaying. Principles and applications

Review of recent practices and trends in protective relaying

IEEE Trans Power Apparatus Syst

Mathematical models representing time–current characteristics of overcurrent relays for computer applications

IEEE Trans Power Apparatus Syst

Optimal coordination of directional overcurrent relays considering definite time backup relaying

IEEE Trans Power Delivery