The Plant Propagation Algorithm for the Optimal Operation of Directional Over-Current Relays in Electrical Engineering

In modern and large scale power distribution topologies, directional relays play an important role in the operation of an electrical system. These relays must be coordinated optimally so that their overall operating time is reduced to a minimum. They are sensor protection devices for the power systems and must be coordinated properly. The present work uses a metaheuristic optimization technique known as the Plant Propagation Algorithm (PPA) in order to suggest improved solutions for the optimization problem of coordination of directional overcurrent relays (DOCRs). We have obtained comparatively better solutions for the overall operating times taken by relays fitted on important positions in the system. Our findings are useful in isolating the faulty lines efficiently and in keeping the continuity of power supply. The difference in response times taken in coordination between primary relays and corresponding backup relays is minimized. The output of our experiments is compared with various algorithms and classical optimization techniques, which are found in the literature. Moreover, graphical analyses are presented for each problem to further clarify the results.


INTRODUCTION
ower systems consist of different transmission systems [1], which are interconnected to other sub-transmission systems. Ideal protection for such transmission systems can be achieved by placing sensing devices like DOCRs in appropriate positions. Furthermore, these devices must be good in terms of cost and technicality. The function of DOCRs is to separate the faulty lines in the event of any fault in the system. They serve as logical units and they trip the line if a fault occurs in the neighborhood of relays suitable values for these variables, one can guarantee the efficient and proper coordination of the DOCRs to maintain power supply through healthy lines and avoid disruption.
The classical approach to solve the optimal coordination of DOCRs is the hit and trails approach [2]. The main drawback of classical approaches was slow convergence and hence an increased number of iterations to reach the best solution. In the beginning, Urdeneta et al. [3] implemented the optimization theory to solve this problem. They modeled the situation as a non-linear, non-convex objective function subject to several design constraints. They suggested a technique to consider the dynamic variations in the network's structure for the coordination of DOCRs using linear programming. 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 [2, 3].
Yazdaninejadi et al. [4] presented a non-linear programming approach that is tackled based on genetic algorithm (GA) to solve the problem of minimizing the overall operating time of primary and backup relays. Moreover, many researchers have suggested optimization techniques to get a better solution of DOCRs problem, like, real coded genetic algorithm [5], Teaching Learning-Based Optimization (TLBO) algorithm [6], a multiple embedded crossover PSO (Particle Swarm Optimization) [7], opposition based chaotic differential evolution algorithm [8], interior point method [9], PSO-TVAC (Time Variant Acceleration Coefficients) based on Series Compensation [10], modified electromagnetic field optimization algorithm [11], Hybridised SA-SOS (Simulated Annealing based Symbiotic Organism Search) algorithm [12] and improved firefly algorithm [13].
In this paper, we have successfully implemented PPA [14][15][16][17][18][19][20][21][22][23][24], for the solution of standard IEEE (3, 4, and 6 bus) test systems. The two types of decision variables were PS and TDS and the sum of operating times taken by all main relays which were needed to operate for clarity of fault(s) in their respective sections. They were estimated along with the minimization objective function bounded by several constraints. These constraints were further classified as selectivity constraints and bounds on each term of the objectives.
The rest of this paper is organized such that, Section 2 contains the problem complexity and our suggested optimization technique, Section 3 presents the problem formulation and a detailed description of three case studies (IEEE 3, 4 and 6 bus models) of DOCRs problem. Section 4 reviews the basic Plant Propagation Algorithm. In Section 5, results and discussion are given. Subsequently, Section 6 concludes this paper by summarizing the achievements and future challenges of this study.

SUGGESTED ALGORITHM
The coordination of relays is a highly non-linear and complex optimization problem subject to various constraints, with the objective to minimize the overall operating time of each primary relay. The optimal relay coordination of DOCRs leads to a multimodal/ non-convex constrained optimization problem with complex search space. The problem gets more difficult to solve, due to nonlinearity, as the number of relays increases [12,13,25,26].
PPA is chosen to solve the above-mentioned problem of DOCRs. PPA was earlier implemented to design engineering problems such as gearshift problem, spring design problem and welded beam problem [14][15][16][17][18][19][20][21][22][23][24]. These problems are related to design engineering and the results obtained by PPA were good as compared to other state-of-the-art. So efforts were made to check further efficiency of PPA in solving the problem of DOCRs.

PROBLEM FORMULATION
The time taken by a relay, denoted by T, is a non-linear function of the variables PS and TDS. The mathematical formulation of operating time is given in equation (1)

The Plant Propagation Algorithm for the Optimal Operation of Directional Over-Current Relays in Electrical Engineering
In this equation, PS and TDS are unknown decision variables. a, b and c are based on the experiments and are predefined values for the behavior of the system. These values are fixed as 0.14, 0.02 and 1 respectively. The current transformer CT and the number of turns it has, defines the value of CTpri_rating. To bear the current, CT performs the role of reducing the level of the current for relays involved. Each relay is associated with each CT and thus CTpri_rating is a known value in the problem. The fault current I is continuously read by the measuring tools and it is a system-dependent value and is pre-assigned to it.
The number of constraints on the system is according to the number of lines involved in the system. These details are given in Table 4 for the problems considered in this paper. Real power systems may be made up of bigger sizes involving several types of DOCRs [2-13].

Objective Function
The objective involved in the problem of coordination of DOCRs, by implementing a suitable optimization technique, involves the minimization of total operating times subject to constraints on the decision variables. Those relays which are first to be operated are called primary relays. The fault, which is closed to a relay, is called pri_close fault while a fault away from the relay on the other side of the line is called pri_far fault. Thus, the objective function is a sum of operating times taken by all primary relays involved whether the time is taken to clear a pri_close fault or pri_far fault. Mathematically, the objective function is presented in equation (2). (7) T primary is operating time of primary relay and T backup is operating time of backup relay and CTI is coordinating time interval.

Problem-1: The IEEE 3 Bus Model
For the coordination problem of the IEEE 3-bus model, the value of each of N1 and N2 is six (equal to the number of relays or twice the lines). Accordingly, there are 12 decision variables (two for each relay) in this problem i.e. TDS 1 to TDS 6 and PS 1 to PS 6 . The value of CTI for Problem-1 is 0.3. Figure 1 shows the 3-bus model. Mathematical form of the objective function for a 3bus model is as follows:

Problem-2: The IEEE 4 Bus Model:
In the optimal coordination of 4-bus model, values of both type of variables N1 and N2 is taken as 8, which is double of total lines involved or same as the number of relays installed in the system. This model is illustrated in Fig.2. Furthermore, this problem is of 16 dimensions and thus involves 16 design variables. As discussed earlier, these two types of variables are named as TDS 1 -TDS 8 and PS 1 -PS 8 . CTI=0.3 for Problem-2. The mathematical form for a 4-bus model is as follows.

Problem-3: The IEEE 6 Bus Model:
In the optimal coordination of 6-bus model, values of both type of variables N1 and N2 is taken as 14, which is double of total lines involved or same as the number of relays installed in the system. This model is illustrated in Fig.3. Furthermore, this problem is of 28 dimensions and thus involves 28 design variables. As discussed earlier, these two types of variables are named as TDS 1 -TDS 14

PLANT PROPAGATION ALGORITHM (PPA)
PPA is a Nature-inspired metaheuristic which simulates the way strawberry plants propagate to occupy the space in which they happen to grow. It is a population/ multi-solutions based technique. Unlike the single solution-based techniques like Simulated

The Plant Propagation Algorithm for the Optimal Operation of Directional Over-Current Relays in Electrical Engineering
Annealing (SA), it is initialized from a randomly generated population of solutions generated from a normal distribution. Two aspects of a metaheuristic, exploration, and exploitation [14][15][16][17][18][19][20][21][22][23][24], are very important to be balanced. Exploitation means to visit the neighborhood of a current solution very well. On the other hand, exploration is to introduce diversity in the population with solutions generated from approximately all over the domain space. A mother plant Pk is in position Xk in n dimensional space i.e. X G = [x G , x NG ⋯ , x _G ]. Let Npop denotes the number of candidate plants in the initial population. PPA is furnished in detail as in Algorithm1. Plants in a position with enough food will send out many short runners. ii) Those plants, which are situated in a position with poor conditions, will send few long runners.
It is obvious, that exploitation is implemented by using the idea of short runners while exploration of search space is done by sending a few long runners within the search space.
The  (11). The length of a runner based on the normalized function is calculated as in equation (12). After all parent plants in the population have generated their allocated runners, new child plants are evaluated and the population is sorted in ascending/ descending according to their fitness value. In this way, the poor plants with lower growth are truncated from the population. The number of runners allocated to a given parent solution is proportional to its fitness as in equation (11), Every solution Xi generates at least one runner and the length/perturbation added to each such runner is inversely proportional to its growth as in equation (12), dx i j= 2(1 -Ni) (α -0.5), for j = 1,…., n, where n is the problem dimension. Having calculated dxi, the extent to which the runner will reach, the search equation (13) that finds the next neighborhood to explore is yi,j = xi,j + ( bj -aj ) dx i j, for j = 1,…., n.

RESULTS AND DISCUSSION
The 3-bus model has one generator 3 transmission lines and six DOCRs on these lines. A diagram showing this The Plant Propagation Algorithm for the Optimal Operation of Directional Over-Current Relays in Electrical Engineering whole model of 3-bus and a complete setup of 12 design variables (TDS 1 -TDS 6 and PS 1 -PS 6 ) is depicted in Fig. 1 Fig. 2. The 6-bus model has three generators, seven lines, and fourteen DOCRs fixed on these lines. A diagram showing this whole model of 6bus and a complete setup of 28 design variables (TDS 1 -TDS 14 and PS 1 -PS 14 ) is depicted in Fig. 3. The best solutions found in literature, as in Tables (1-3 Figures 4-9. It is interesting to note that with increasing the complexity, PPA produced better results as compared to the 3-bus and 4-bus cases.

CONFLICT OF INTEREST
The authors declare that none of them have any competing interests in the manuscript.