Complexity

Volume 2018, Article ID 4605769, 11 pages

https://doi.org/10.1155/2018/4605769

## Hybridized Symbiotic Organism Search Algorithm for the Optimal Operation of Directional Overcurrent Relays

Department of Mathematics, Abdul Wali Khan University Mardan, Mardan, Pakistan

Correspondence should be addressed to Muhammad Sulaiman; ku.oc.oohay@315namialus

Received 3 September 2017; Revised 5 December 2017; Accepted 21 December 2017; Published 23 January 2018

Academic Editor: Danilo Comminiello

Copyright © 2018 Muhammad Sulaiman et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

This paper presents the solution of directional overcurrent relay (DOCR) problems using Simulated Annealing based Symbiotic Organism Search (SASOS). The objective function of the problem is to minimize the sum of the operating times of all primary relays. The DOCR problem is nonlinear and highly constrained with two types of decision variables, namely, the time dial settings (TDS) and plug setting (PS). In this paper, three models of the problem are considered, the IEEE 3-bus, 4-bus, and 6-bus, respectively. We have applied SASOS to solve the problem and the obtained results are compared with other algorithms available in the literature.

#### 1. Introduction

Due to rapidly growing power systems, the stability and security issues are highly important for the power system researchers [1–3]. The protection systems are mainly used to detect and clear faults as fast and selective as possible [4–6]. The protection relays are used for detecting the faults in the system and to detach the faulty parts from the system in real time. Proper coordination of relays is essential to maintain the appropriate operation of the overall protection system. There are various types of relays with different operating principles. An example of these relays, which are used as a good technical tool for the protection of power systems, is directional overcurrent relay [7–9]. Such a relay is divided into two units, that is, the instantaneous unit and the time overcurrent unit. The parameters to be defined in the overcurrent unit are the time dial settings (TDS) and the plug settings (PS). Computers have made the huge calculations in DOCR problems in power systems easy [10, 11]. Different optimization algorithms are used to solve the relays coordination problems in which the objective function is to minimize activity time of all main relays. The constraints of this optimization problem are considered in the second layer of relay, which should respond, if the main layer of relay fails to operate on nearby fault. This depends on the variables, TDS, PS, and the minimized working time of relay. There is a nonlinear relationship between the operating time of overcurrent relays, TDS, and PS.

In electrical engineering, the power system engineering has the longest history among all other areas. Ever since, different numerical optimization techniques have been applied to power systems engineering and played an important role [12]. Optimization problems are usually nonlinear, which have nonlinear objective functions and constraints [13, 14].

Nowadays, researchers use different optimization algorithms to find the optimal solutions for the problems of relays settings and coordination. Examples of these optimization algorithms are Evolutionary Algorithm (EA) [15], Differential Evolution (DE) [16], Modified Differential Evolution (MDE) [17], Self-Adaptive Differential Evolutionary (SADE) [18], Particle Swarm Optimization (PSO) [19], Modified Particle Swarm Optimizer [20, 21], Evolutionary Particle Swarm Optimization (EPSO) [22], Box-Muller Harmony Search (BMHS) [23], Zero-One Integer Programming (ZOIP) approach [24, 25], Covariance Matrix Adaptation Evolution Strategy (CMA-ES) [26], Seeker Algorithm [27], Chaotic Differential Evolution Algorithm (CDEA) [28], Adaptive Differential Evolution [29], Artificial Bee Colony (ABC) [30], Firefly Optimization Algorithm (FOA) [31], Modified Swarm Firefly Algorithm (MSFA) [32], and Biogeography Based Optimization (BBO) [33]. BFOA has been applied to obtain the optimal location and size of multiple distributed generators (DG) [34], optimal placement and sizing of DG [35], power system harmonics estimation [36], distribution systems reconfiguration for loss minimization [37], minimum load balancing index for distribution system [38], power system stabilizer for the suppression of oscillations [39], and optimum economic load dispatch [40].

During the last few years, PSO algorithm has been applied for Optimal Power Flow (OPF) control in power systems [41], OPF problem with FACTS devices [42], economic dispatch problems [43], optimal sizing and placement of DG [44], optimal location and sizing of static synchronous series compensator [45], and optimized controller design of energy storage devices [45, 46].

This paper proposes the use of a hybrid optimization technique—namely, Simulated Annealing based Symbiotic Organism Search (SASOS) [1, 47]—to find the optimal solutions for the relays settings. This algorithm is applied to different models of the DOCR problems such as the IEEE 3-bus, 4-bus, and 6-bus models. To check the efficiency of the proposed algorithm for the three cases, we have minimized the total activity time for each relay.

#### 2. Problem Formulation

There are two important settings in each overcurrent relay for its satisfactory operations. The time dial settings (TDS) represent the activation time of each relay and the relay operation is decided by the plug settings (PS). The plug settings (PS) depend on the maximum load current and fault current due to short circuit. The main factors which control the total operating time of the relay are TDS and PS, and the fault current is represented by [15, 22], wherewhere denotes the fault current at the current transformer (CT) initial terminal and is the primary rating of CT. Constants , , and are assigned values 0.14, 0.02, and 1.0, respectively, and that is according to IEEE standards [26].

The current, seen by the relay, denoted by , is equal to the ratio between and , which is a nonlinear equation:

##### 2.1. Objective Function

In coordination studies [22], the main objective is to minimize the total time taken in operation of primary relays for clearing a fault. The objective function takes the following form:wherewhere is the relay operation time to clear a near-end fault while is its operation time in case of a far end fault. and represent the relays fixed at the ends of the front line.

##### 2.2. Constraints

The objective function is bound to the three constraints related to , , and .

Equation (5) represents the bound constraints on TDS: and are the lower and upper bounds for TDS, whose values are given by 0.05 and 1.1, respectively, while varies from 1 to .

The second constraint is PS of the relay that takes the following form: and are the lower and upper bounds of PS, whose values are given by 1.25 and 1.50, respectively, while varies from 1 to .

The third constraint is related to the fault current and pickup current. The operating time of relay depends on the type of relay. According to [24, 33], the operating time of relay is defined by and are the lower and upper bounds for relay functioning time, whose values are adopted as 0.05 and 1, respectively.

During the optimization procedure, the time taken by primary relays to coordinate with the backup relays is constrained as inwhere CTI represents the specified coordination time.

and represent the working time of primary and backup relays, which can be obtained using the following equations:

##### 2.3. The Standard IEEE System of 3-Bus

There are six overcurrent relays in this model. According to the number of relays, the value assigned to each of and is 6 and the number of decision variables is 12, and this means to and the variables to . Figure 1 shows the 3-bus model.