MILP approach for optimal coordination of directional overcurrent relays in interconnected power systems

Highlights

• A MILP is proposed for nonlinear DOCRs coordination problem formulation.

• The proposed formulation is easier to be solved by branch and bound.

• Pickup current and time multiplier settings of DOCRs are as optimization variables.

• Proposed method is compared with some previous heuristics and NLP approaches.

• Proposed method is guaranteed to converge to global optimal settings.

Abstract

The coordination problem of directional overcurrent relays (DOCRs) is a non-linear and non-convex optimization one. Until now, several methods based on the heuristics and non-linear programming (NLP) approaches have been proposed for solving the problem. Drawback of these methods is that they are likely to be trapped in local minima. In order to overcome the drawback, in this paper, the problem is formulated as a mixed integer linear programming (MILP) while pickup current setting (I_set) and time multiplier setting (TMS) of relays are considered as optimization variables. This formulation is easier to be solved by branch and bound (B&B) approach, because at each branch there is a linear and convex sub-problem. Furthermore, for the first time, the proposed method is guaranteed to converge to global optimal settings. The proposed method is evaluated using a 3-bus, an 8-bus, the IEEE 14-bus and the modified IEEE 30-bus test systems. The results are compared with some previous heuristics and NLP approaches. Based on the obtained results, it can be seen that, better optimal settings for DOCRs are obtained by using the proposed method in comparison with previous methods.

Introduction

Directional overcurrent relays can commonly be used as the primary protection in distribution and sub-transmission systems or as the backup protection in transmission system. In order to have fast and selective protection system, DOCRs should be coordinated. Generally, two sets of parameters, including I_set and TMS are determined in DOCRs coordination. DOCRs coordination problem is a non-linear and non-convex optimization problem. So far, numerous approaches have been proposed for solving the DOCRs coordination problem. Generally, these approaches can be categorized based on the heuristics and mathematical approaches.

In Refs. [1], [2], [3], a linear programming (LP) method is used to determine optimal TMS of overcurrent relays while pickup currents are assumed to be known. DOCRs coordination problem is solved by evolutionary algorithms such as particle swarm optimization (PSO) [4], genetic algorithm (GA) [5], [6], differential evolution (DE) algorithms [7] and using teaching learning based optimization (TLBO) algorithm [8]. A hybrid genetic algorithm (GA) and LP (HGA-LP) method is employed to solve the coordination problem in Ref. [9]. In Ref. [10], the DOCRs coordination problem is solved by using hybrid GA and NLP (HGA-NLP) method. A hybrid PSO and LP method is proposed for solving the problem [11], [12]. Seeker algorithm is applied to solve DOCRs coordination problem whereas the problem is formulated as a mixed integer nonlinear programming (MINLP) [13]. In Ref. [14], a biogeography based optimization (BBO) and hybrid BBO with LP (BBO-LP) are proposed to determine the optimal TMS and I_set of DOCRs. In Ref. [15], a MILP approach is proposed optimal coordination of non-directional overcurrent relays in radial systems by considering TMS of relays as optimization variable while pickup currents are previously determined. In Ref. [16], a modified real coded GA is proposed for DOCRs coordination that incorporates bounded exponential crossover and power mutation in the algorithm. In Ref. [17], DOCRs coordination problem is formulated as a quadratically constrained quadratic programming model. Optimal settings of DOCRs are obtained using symbiotic organism search optimization technique [18]. A hybrid gravitational search algorithm and sequential quadratic programming (GSA-SQP) is proposed to solve the coordination problem [19]. In Ref. [20], the DOCR coordination problem is solved by enhanced differential evolution algorithm. In Ref. [21], the DOCR coordination problem is formulated as a MINLP and also the problem is solved by using hybrid GA and another heuristic algorithm. It is worth noting that, heuristics and mathematical approaches such as GA [22], modified adaptive PSO [23], HGA-LP [24] and hybrid interval GA and interval linear programming [25] are used to solve distance and overcurrent relays coordination problem.

In LP method, it is assumed that pickup currents of DOCRs are predetermined. Therefore, there is no guarantee for converging to global optimal settings for relays. In the other words, heuristics and NLP approaches are likely to be trapped in local minima due to non-linearity and non-convexity of the coordination problem. Therefore, in this paper, in order to overcome these drawbacks, a new formulation based on the mixed integer linear programming is proposed DOCRs coordination, and branch and bound method is applied to solve the problem. Therefore, Non-linear and non-convex coordination problem is converted to linear and convex ones at each branch according to proposed formulation. This matter makes the problem easier to be solved and guarantees converging to global optimal settings as well. The proposed method is tested on four test systems. Presented results show that the proposed method is efficient and successful in determination of DOCRs settings.

The rest of this paper is organized as follows: In Section 2, the MILP formulation is described. In Section 3, at first, the DOCRs coordination problem is generally presented and then is formulated as a MILP problem. The proposed method is used to determine the optimal settings in the 3-bus, the 8-bus, the IEEE 14-bus and the modified IEEE 30-bus test systems in Section 4. Finally, the conclusion is presented in Section 5.