3.2.2. Learning Phase

Interactive learning between students in each classroom can develop the student's performance then develop the performance of the classroom. The learning phase is given by following steps:


$$X\_{new}^{p}(j) = X\_{old}^{p}(j) + r \left[ X\_{old}^{p}(j) - X^{q}(j) \right],\tag{18}$$

Otherwise,

$$X\_{n \text{rev}}^p(j) = X\_{old}^p(j) + r \left[ X^q(j) - X\_{old}^p(j) \right] \tag{19}$$

where *r* is a random number between [0, 1].

This phase moves student *p* towards student *q* if student *q* has a better solution; while, if student *p* has a better solution, it will move away from student *q* [42].

#### *3.3. Modified SBO Algorithm*

The original SBO algorithm was modified, as shown in its flowchart in Figure 5. That is based on two main points, in order to improve its ability to explore and exploit in the original algorithm. The first point is about the learning phase, which was discussed in the previous section. This part is modified by changing the techniques of learning between students by three additional steps, discussed below. The second point is to select more than one teacher, via a roulette wheel, in order to speed the process up and obtain a better knowledge transfer process inside the class (and with other classes).

#### 3.3.1. First Point: A Modified Learning Phase

This point has been modified to exploit students in each classroom to reach new points within a limited search area that has better fitness values, by using the following steps:


3.3.2. Second Point: Teacher Selected

The original algorithm selected one teacher, but the improved algorithm selected more than one. This point increased the knowledge transfer process between classrooms. In the original algorithm selected, one teacher from another classrooms carried knowledge from it; however, after that, each classroom takes knowledge from many classrooms and then selected new points after evaluating the fitness values, in order to accept the best fitness value between new points affected by teachers. This improved the teacher phase's equation used previously but repeated with each teacher. Teachers were distributed to classrooms by roulette wheel and this modified was used, too, but selected many teachers for each classroom. The number of teachers for each classroom was selected by users and, in this paper, double teachers were selected.

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

The optimization setting of TDS, IP, and TZ2 were tuned by the MATLAB program, used for both SBO and MSBO to solve the optimization problem. These algorithms, discussed in previous sections, used population, classrooms, and maximum iterations, with values are 300, 25, and 1000, respectively. The algorithms were successfully tested in coordination tested systems, i.e., the IEEE 8-bus test system and the IEEE 14-bus distribution network. Each test system has two varying cases: the first is the normal topological grid and the second is after added external power generation for the original grid.

The optimum settings were used to calculate the operation time of the primary and backup protection relays at the near-end and the far-end. These points were tested to succeed in the optimal solution, in order to pass system constraints. The protection devices, assumed with digital relays and CTI, must be greater than or equal to 0.2 s. Relays with normal characteristics constants are α, β, and γ, with values of 0.14, 0.02, and 1.0, respectively, maximum and minimum TDS values of 1.1 s and 0.1 s, respectively, maximum and minimum PS were 4 and 0.5, respectively, and the maximum time for operating the primary DOCRs or distance relays was 1.5 s [21].

MATLAB R2016a was used on a computer with a CPU of 1.70 GHz processor and 4 GB DDR3 RAM, for tuned optimum settings, while ETAP 12.6.0 was used for the calculation three phase fault currents.

#### *4.1. Test System I: IEEE 8-Bus Test System*

The APS was tested on the IEEE 8-bus test system, as shown in Figure 6, for the original topological system, with an external grid linked in bus number 4. This system consists of 8 buses, which are connected with 7 lines and used 14 relays on the ends of the lines to protect these transmission lines. This system has two synchronous generators to feed 4 loads, in addition to the 400 MW for external grid entry and out-of-work [21,43].

**Figure 6.** The single line diagram of IEEE 8-Bus.

This was a highly constrained, nonlinear optimization problem. It had 42 variables of design, which were tuned by optimization algorithms, in each case. The optimal solution was limited with minimum and maximum TDS, IP, TZ2, and T operate limiters. Additionally, they were constrained with a CTI value between the operation time of pairs primary and backup constraints. These constraints were 32 between DOCRs and equal to 40 between DOCRS and distance relays in the normal grid, while the external grid, on

the state the constraints, became 34 between DOCRS and was still equal to 40 between the DOCRs and distance relays.

The ETAP program used to calculate three-phase fault currents is presented as Appendix A Table A1 for the normal grid. Additionally, for the second case, data was extracted from [43].

Table 1 lists the optimal settings for protection relays using both SBO and MSBO in normal topological settings, and the external grid is on. This table proved the MSBO has optimum solutions that are better than the optimum solution of SBO.


**Table 1.** IEEE 8-bus's relays setting.

The normal case of the IEEE 8-bus test system constraints, which occur by optimum solution, was tabulated in Table 2. This table is for primary and backup operation time of DOCRs pairs relay in both near- and far-end. Addition to for constraints between DOCRs and distance relays. Table 3 has the same description as previous Table 2 but deal with another case in which the network is linked with the external grid. These tables show that modified algorithm satisfied all constraints.

**Table 2.** IEEE 8-bus's operation times of Relay's pairs in normal grid by MSBO.



**Table 3.** IEEE 8-bus's operation times of relay's pairs in case with extrnal grid by MSBO.

The convergence characteristics curves of SBO and MSBO for the normal case and the other case are presented in Figures 7 and 8, respectively. And the penalty occurred by SBO and MSBO during running the optimum algorithm shown in Figure 9. For the normal case while the state of the external grid is shown in Figure 10. These figures showed the convergence of MSBO is better and faster than the original SBO convergence. And the ability of MSBO to avoid penalty and pass constraints quickly.

**Figure 7.** Convergence characteristics of SBO and MSBO in normal case of IEEE 8-bus.

**Figure 8.** Convergence characteristics of SBO and MSBO in external grid on case of IEEE 8-bus.

**Figure 9.** Penalty between SBO and MSBO of IEEE 8-bus test system normal case.

**Figure 10.** Penalty between SBO and MSBO of IEEE 8-bus test system with external grid on work.

In the normal case, the original SBO has OF with value 33.705 s while MSBO has OF with value 28.072 s and MSBO has 33.705 s after 300 iterations and MSBO passed penalty after 12 iterations while original SBO continuous to iteration 32 to pass system's constraints. For another case, the external grid stat on operation OF becomes 32.601 s and 35.388 s for MSBO and SBO respectively. MSBO reached 35.350 s after 477 iterations. The penalty passed after 11 iterations in the case of SBO while MSBO passed after three iterations. All of these prove the ability of MSBO to increase its exploration and exploitation more than the original algorithm.

#### *4.2. Test System II: IEEE 14-Bus Distribution Network*

The IEEE 14-bus distribution network which is shown in Figure 11. Which is a downstream section of IEEE 14-bus. This distribution network has two distribution transformers connected at buses number 1 and 2 to supply it. Each transmission line has a protection relay at every end of the line to form 16 relays [38,44].

**Figure 11.** The single line diagram for 14 bus distribution network.

Test system modified with addition 2 DGs connected at buses number 5 and 7 with power equals 5MVA and power factor nominally is 0.9 lagging and their type are synchronous. This modification is from [45] and 3 phase short circuit currents at both near-end and far-end from [38].

The current transformer's ratios of relays are 120, 120, 120, 40, 120, 40, 120, 120, 120, 80, 80, 80, 40, 40, 80, and 80, for relays from 1 to 16, respectively [38].

In this test system, optimization algorithms tuned 48 variables that are limited by minimum and maximum values. Then constrained between operation time values of relays by CTI. This test system is more constrained than the previous test system by 41 between primary and backup DOCRs and 44 between DOCRs and distance relays, in both ends (near and far).

Optimal settings tuned by SBO and MSBO algorithms. Those were tabulated in Table 4 for the normal case and another case. These optimization solutions passed CTI constraints between relays pairs in normal case in Table 5. Then, Table 6 proved the ability of optimization solutions to pass the CTI constraint between relays pairs in DGs working case.

Figure 12 shows the convergence characteristics curve of both SBO and MSBO algorithms in the normal case while in another case after DGs work is shown in Figure 13. During the tuning process for relays setting by optimization algorithms SBO and MSBO, the penalty of both are shown in Figures 14 and 15 for the normal case and the other DGs case, respectively.

In the normal case, MSBO has OF with a value of 34.806 s and is better than SBO with 2.05 s. MSBO reached 36.860 s faster than SBO by 328 iterations and passed penalty after 22 iterations the original SBO passed after 71 iterations. In another case, MSBO reaches SBO's OF after 482 iterations and at the end of the run reaches 51.068 s as OF and better than SBO by 6.2 s. MSBO passed constraints penalty after 113 iterations while SBO still penalty to 183 iterations.


**Table 4.** IEEE 14-bus distribution network's relays setting.


**Table 5.** IEEE 14-bus distribution network's operation times of Relay's pairs in normal case by MSBO.

**Table 6.** IEEE 14-bus distribution network's operation times of relays pairs with DGs by MSBO.


**Figure 12.** Convergence characteristics of SBO and MSBO in normal case of IEEE 14-bus distribution network.

**Figure 13.** Convergence characteristics of SBO and MSBO with DGs case of IEEE 14-bus distribution network.

**Figure 14.** Penalty between SBO and MSBO of IEEE 14-bus distribution network normal case.

**Figure 15.** Penalty between SBO and MSBO of IEEE 14-bus distribution network with DGs.

#### *4.3. Varification of MSBO Using Etap 12.6.0*

Etap is used to verify the results obtained by the proposed algorithm MSBO on 8 bus normal grid, three-phase fault at transmission line between third and fourth bus-bars. This fault applied in both the near end and far end. As simulation by Etap as shown in Figure 16. Relay 3 is the primary relay that operates at 0.535 s and 0.615 s in the near and far end, respectively. While relay 2 is its backup relay which operates at 0.736 s and 0.943 in near and far ends, respectively. And these verify the CTI is more than or equal to 0.2 s and DOCRs without miscoordination. That simulation is also done at the transmission line between the fifth and sixth busbars additional to relays 5 as primary relay and 4 as backup re-lay, the operation time at both ends near and far of this pair relay as 0.318 s, 0.519 s, 0.717 s, and 1.738 s, respectively. The simulation is presented in Figure 17 proved that there is no miscoordination between DOCRs.

**Figure 16.** Operating times for relays 3 and 2.

**Figure 17.** Operating times for relays 5 and 4.

Finally, simulation is done at the transmission line which is connected between the first and third busbars. It is noticed from Figure 18. Operating times at the near end for primary (relay 9), and backup (relay 10) are 0.298 s, and 0.498 s, respectively. At the far end the operating time of primary and backup relays are 0.661 s, and 1.216 s, respectively. This case avoids miscoordination too.

**Figure 18.** Operating times for relays 9 and 10.
