*3.2. Optimization Methods for Solving the OCR Coordination Problem*

In Section 3.2, the OCR coordination problem in a network connected to DGs is presented as an optimization task. This section presents two optimization algorithms, namely GA and GSA–SQP, as common and new powerful optimization algorithms for solving OCR coordination problems [8,37].

## 3.2.1. Genetic Algorithm Optimization (GA)

For solving complicated optimization problems, the genetic algorithm (GA) has been vastly used as an iterative optimization technique [46,47]. The GA technique considers various applicable solutions to obtain the best solution; it proves its worth in the power system protection coordination problem. Using GA in [37,47] was solely for power grids, without considering nonstandard OCR curves and renewable energy sources. In this study, the GA methodology is utilized as an innovative iterative optimization model to transact with the overcurrent coordination problem for a distribution system with DGs. Generally, the simulation of the GA is used with a specific population size, where the possible solutions for the proposed optimization problem are described by the population. Chromosome populations or individuals are the possible solutions in the population [37,39]. In the next step, an OF evaluates all solutions for the current generation; this step is called the fitness function (Equation (6)). The result of the fitness value is mainly associated with the proposed optimization problem for each solution. Creating a new population uses fitness evaluation by utilizing selecting, crossing, and mutating techniques.

In this paper, the general GA flowchart for the proposed ORC coordination problem is presented in Table 2. The process of the GA model launches for a profile group of first-generation OCR OTs. Therefore, for each OCR OT profile, Equation (6) of the objective function is used to evaluate fitness. Thus, an appropriate selection technique picks the parent OCR operating time profiles. For the next generation, the selection of the best performance (better fitness value or fittest solution) will be selected. These profiles are chosen for crossover as well as for creating a new generation (population); this step known as reproduction. From the profiles of the parent, the common genes of parents are retained to create the profile of a new generation of the OT whereas the residual genes are chosen at random from the parents. Nevertheless, the power network or relay constraint might be violated by the child OT profile; consequently, for examination purposes, whether the profile of the child is under the constraints or not, a feasibility test has been applied. Sometimes the child profiles are assigned to the impracticable zone. Then, the solution of the child, in this case, will be refused and an alternative one will be generated by randomizing the uncommon genes until the feasibility of the child profile is realized. At the initial time and for the initial iterations, the expectation about child profile will be varied and far away from parent OCR operation solutions. Nonetheless, in each iteration, the profiles of both children and parents are nearer to each other, and the search directs closely to the optimum OCRs operation time profile. Achieving the greatest number of iterations or reaching the proposed threshold is the goal of this process, which will be repeated many times until meeting this goal.


#### **Table 2.** The procedures of the GA technique.

3.2.2. A Hybrid Algorithm Gravitational Search Algorithm–Sequential Quadratic Programming (GSA–SQP)

The GSA–SQP algorithm is presented by refs. [8,48] as a powerful optimization solver for OCR coordination. Firstly, the GSA–SQP algorithm is presented as a multipoint method of search that is based on probability through using the gravitational search algorithm (GSA). Secondly, non-linear programing (NLP) techniques such as sequential quadratic programming (SQP), which are the single-point method of search, have the disadvantage of getting trapped in a local optimum point when the first option is closer to the local optimum. The NLP techniques offer a globally optimal solution if the correct first choice is made [48]. The study by ref. [48] suggested a hybrid of GSA with SQP to take advantage of the methods while overcoming their drawbacks. The SQP routine is introduced in GSA as a local technique of search to boost the convergence. Initially, the GSA method is performed and the best fitness for each generation is chosen in each interaction. From this, the corresponding agent is set as the initial value of the variables in the SQPP technique. The SQP routine is then executed according to the local search's adopted probability of local search (αLS), improving the best fitness obtained from GSA in the current interaction. This is how the algorithm of GSA–SQP offers the global optimal solution. For calculating the optimal setting of the OCRs, several agents that represent a complete solution set are presented as the control variable of the OCR coordination problem, *X*.

$$X = \left[TMS\_{\dot{\jmath}}^1, \dots, TMS\_{\dot{\jmath}}^m, \operatorname{Ip}\_{\dot{\jmath}}^1, \dots, \operatorname{Ip}\_{\dot{\jmath}}^m, A\_{\dot{\jmath}}^1, \dots, A\_{\dot{\jmath}}^m \right] \tag{11}$$

where N is the population size (agents in the system), *j* = 1, 2, ... ; N and m are the numbers of the relay in the grid. The process of the GSA–SQP started with a set of the first-generation OCR operation time profiles based on the power network and fault calculation data. Then, for each OCR operation time profile, the objective function (Equation (6)) is used as an evaluation and fitness approach in this work. Thus, the best and worst solutions will be selected. For the next generation, a random number will be generated and compared to the constant αLS. In the case that the random number is less than the αLS, the model will calculate the gravitational constant at time t, G(t), masses of agents, M(t), and the total force that acts on the i-th agent at time t, F(t), to update the velocity and position of the searching agent. In case of a random number larger than the αLS, the SQP method will be used to update the next generation by selecting the new agent as the best agent. Finally, the GSA–SQP model will select the optimal solution among all solutions which is helped to achieve the global solution as shown in Figure 6. The parameters of the algorithm applied for the optimal coordination problem in this paper are: constant G0, the initial gravitational which is set to 100, and constant α, a user-specified value which is adjusted to 20. Both

constants G0 and α control the GSA performance. t is the current iteration while *tmax* is the maximum iteration number which is set to 200; N is adjusted to 50; αLS is 95. For miscoordination problems, β has been used. Miscoordination decreases with increasing β; however, the relay OTs rise. Thus, for omitting the miscoordination, a fit β value should be selected. In addition, there are other parameters related to local search that should be calculated throughout the process which are: G(t), the gravitational constant at time t, M(t), the masses of agents, F(t), the total force that acts on the *i*-th agent at time t, and a(t), the acceleration of the *i*-th agent. For meshed network case studies, the weighting factors are chosen as α<sup>1</sup> and α<sup>2</sup> which are set to 2 and 15, respectively. IEEE 9-bus system β is set to 500 and the IEEE 30-bus system is set to 1000.

**Figure 6.** The flowchart of the GSA–SQP algorithm.

#### **4. Simulation Results and Discussion**

This section aims to present the results of the proposed nonstandard OCR coordination approach, NSTCC, using radial and meshed distribution systems and under different operating scenarios. Throughout this section, the NSTCC will be compared to the conventional OCR coordination scheme and nonstandard OCR scheme developed by ref. [25]. For solving the OCR protection coordination problem, GA and hybrid GSA–SQP optimization techniques are used in this study based on the following network scenarios:

