**1. Introduction**

Nowadays, the protection field is one of the more indexing issues in power systems. Directional overcurrent relays (DOCRs) and distance relays are both commonly used for protecting transmission lines. These protection devices monitor the transmission lines from both ends of the lines for faults that cause trip scenarios to be activated.

Overcurrent relays (OCRs) generally work by the magnitude of the fault current, which is set inside relay's parameters, while in DOCRs, adding the direction of the passing current through transmission lines. This direction is determined by voltage phasor from the potential transformer. So, DOCRs are more expensive than normal OCRs but more effective than OCRs. These relays must be operating in the backup case, with a delay time higher than the primary relay [1].

The second protection is distance relays, which have two main zones. The first one works immediately after fault detection. This zone covers 80% of the transmission line to ignore calculation errors. Then, the second zone covers up to 120% of the transmission line by delay time; this wide area covers a part of another transmission line [2].

**Citation:** Abdelhamid, M.; Kamel, S.; Korashy, A.; Tostado-Véliz, M.; Banakhr, F.A.; Mosaad, M.I. An Adaptive Protection Scheme for Coordination of Distance and Directional Overcurrent Relays in Distribution Systems Based on a Modified School-Based Optimizer. *Electronics* **2021**, *10*, 2628. https:// doi.org/10.3390/electronics10212628

Academic Editors: Marinko Barukˇci´c, Nebojša Raiˇcevi´c and Vasilija Šarac

Received: 9 September 2021 Accepted: 19 October 2021 Published: 27 October 2021

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The main problem in this paper regards reducing the protection relay's operation times, to provide the ability for protection devices to isolate the fault area. This saves the lifetime of power system components, and the power system becomes healthier and more reliable. However, the coordination problem of DOCRs and distance relays is more complex and highly constrained, owing to constraints between DOCRs pairs and DOCRs and distance relays pairs. The miscoordination of these protection relays overlap protection operates and does not utilize the advantages of both distance and DOCRs relays [3,4].

The impact of RES-based DGs adds to the distribution system. RES, such as solar energy and wind energy sources, are integrated with the power system. DGs and the coordination problem present many challenges, such as the change of fault current magnitude and flow of direction [5].

This coordination challenge, which is the result of DGs, needs a flexible structure. This paper discussed adaptive protection systems (APS), in order to solve this protection coordination problem. APS gives the ability to change relays settings for both DOCRs and distance relays, according to change in network states, based on the DG's on/off states, using predetermined settings. APS was tested with various scenarios, which are probably tripped in-network, and the optimal settings for protection relays in each scenario were determined. This gives the protection system the ability to minimize miscoordination and malfunction. The main advantage of APS is making the protection system more selective and reliable than conventional or fixed systems [6]. APS's settings group of protection relays is determined by computing optimal settings using an optimization algorithm for each scenario, which is based on the DG's states [7].

In recent years, many optimization algorithms are used for solving coordination problems in literature, of DOCRs coordination, such as the particle swarm optimizer (PSO) and modified PSO in [8], genetic algorithm (GA) and hybrid GA in [9], biogeographybased optimization algorithms (BBO) in [10], differential evolution algorithm (DE) and trigonometric DE algorithm (Tri-DE) in [11], firefly algorithm (FA) and improved FA (IFA) in [12], hybridized whale optimization algorithm (WOA), and hybridized WOA in [13], Jaya Algorithm and oppositional Jaya algorithm (OJaya) in [14], moth–flame optimization (MFO) and improved MFO (IMFO) in [15], political optimization algorithm (PO) in [1], artificial optimizing algorithm(AEO) in [16], and evaporation rate water cycle algorithm in [17].

Then, for the coordination of both the DOCRs and distance, such as the genetic algorithm (GA) in [18,19], water cycle algorithm (WCA) [19], Jaya optimization algorithm [20], grey wolf optimization (GWO) [19], ant colony optimization (ACO), and hybrid ACO algorithm in [21].

The adaptive protection scheme is important for coordinating the protection relays, in order to deal with the change in topology of the distribution network, which results from the DG's on/off status. This topological change causes a change in the short-circuit current. Hence, modern protection systems, which deal with DGs or RES, are needed for an adaptive scheme.

APS is basically dependent on the communication network between the smart grid's components, as a part of information and communication technologies (ICT), or it is dependent on SCADA. These communication networks give APS the ability to set relays remotely.

Because of the real-time performance of the revolution of optimization algorithms (in terms of millisecond or microseconds), as well as high computerized performance, in many research papers, APS is shown to be dependent on the optimization algorithms to coordinate DOCRs, such as using the: particle swarm optimization (PSO) in [22], genetic algorithm (GA) in [23], differential evolution algorithm (DEA) in [24], ant colony optimization (ACO) [25], gravitational search algorithm (GSA) in [26], firefly algorithm (FA) in [27], manta ray foraging optimization (MRFO) in [7], and hybrid Harris hawks optimization (HHO) in [28].

Metaheuristic optimization algorithms usually generate random initial values, as its population within search space limiters then improves the population fitness within a systematic process. The standard of metaheuristic optimization algorithms is always formed by intrapopulation collaboration. The original SBO algorithm utilized subgroups of the parallel populations, with independent values that collaborate. Increase the capability of exploration of the algorithm and improve the overall efficiency. SBO is a collaborative, multi-population framework utilized by TLBO. This algorithm used two stages: the first stage is about a series of metaheuristics works, independent for exploring the different areas of the search space. Then, the second stage concentrated the search on the sub-region within the best solutions. This type of algorithm has many challenges; one of them is selecting and implementing the first stage termination criterion. The terminal criterion introduces parameters that need to be tuned for a specific problem [29].

SBO extends the basic model of TLBO, with both learning and teaching phases; however, MSBO used TLBO with a modified learning phase. Then, teachers can be rearranged with a roulette wheel role to other classrooms to share their knowledge; while, MSBO used multiple teachers for each classroom to improve share knowledge processes between classrooms and increased the exploitation of the population into the teaching phase [30].

SBO is applied to solve many other engineering optimization problems, such as steel frame design in [29,31] and solar cell parameters estimation in [32]. SBO is effective in solving these optimization problems.

Other methods are suggested to deal with APS, such as multi-agents in [33,34] and Q-learning with an environment APS in [35].

Contributions of this paper are as follows:


The rest of the paper is as follows: Section 2 is about the mathematical modelling of coordination problems. Section 3 presents the proposed protection scheme. Then, in Section 4, the performance of both SBO and MSBO, for solving the coordination problem in IEEE 8-bus and IEEE 14-bus distribution networks, is presented. Finally, Section 5 shows the conclusions.

#### **2. The Mathematical Modelling of Coordination Problem**

The main goal of this paper is to ge<sup>t</sup> the optimal coordination of DOCRs and distance relays. The optimal solution to this problem is minimizing the total operation time of DOCRs at both ends of the near-end (*TNR*) and far-end (*TFR*), in addition to the second zone time of distance relays ( *TZ*2). The minimum total operation time is the objective function (*OF*), shown as following [21,36,37]:

$$OF = \min\left(\sum\_{i=1}^{n} TNR\_i + \sum\_{i=1}^{n} TFR\_i + \sum\_{i=1}^{n} T\_{Z2}i + F^{Pen}\right),\tag{1}$$

The standard time inverse DOCRs characteristics, depending on the international electrotechnical commission (IEC) standards, are presented by the following equation [16]:

$$T\_i = \frac{\infty \ast TDS\_i}{\left(\frac{I\_f}{I\_{pi}}\right)^{\beta} - \gamma} \, \, \, \tag{2}$$

where *Ti* is the operation time of relay at any end of transmission line for *i* relay, *TDS* is its time dial setting, and *Ip* is its pick-up current. The other α, *β*, and *γ* are constants with 0.14, 0.02, and 1, respectively [1].

#### *2.1. The Problem's Limiters*

The main limiter of any protection relay is the maximum operation time (*Tmax*) to prevent bad operation, which saves the power system component's lifetime. That limiter must be lower than2s[16].

Any relay settings, in coordination with the problem, have minimum and maximum limiters, as shown in the following equations [21]:

$$TDS\_{\min} \le TDS \le TDS\_{\max} \tag{3}$$

$$Ip\_{\min} \le Ip \le Ip\_{\max} \tag{4}$$

$$\text{Tr}\, \mathbf{2}\_{\text{min}} \le \text{Tr}\, \mathbf{2} \le \text{Tr}\, \mathbf{2}\_{\text{max}} \, \text{ .} \tag{5}$$

#### *2.2. The Problem's Constraints*

The proposed optimization problem becomes a higher constraint problem, via the constraints between the primary and backup pair of DOCRs, in addition to the relationship between the DOCRs, distance, and pairs relay at both ends (near and far). Those constraints are used to avoid miscoordination, which may happen during faults between protection relays.

The relationship between DOCRs pair relays, at any end, as shown in Figure 1, must deal with the backup relay (*tb*), operated with a delay on the primary relay (*tp*). This delay time is called coordination time interval (CTI). The value of CTI is determined according to the type of protection relays. For electromagnetic relays, the CTI value must be more than 0.3 s, while, in the case of digital relays, more than 0.2 s; the digital relays are used in this paper [38]. The following equation shows these constraints [21]:

$$\|\mathbf{t}\_b^{f1} - \mathbf{t}\_p^{f1}\| > \text{CTI}\_\prime \tag{6}$$

$$t\_b f^2 - t\_p f^2 > CTI,\tag{7}$$

**Figure 1.** The relationship between primary and backup DOCRs.

The relationship between DOCRs and distance pair relays is shown in Figure 2. The backup distance relay aliasing, with the primary DOCRs relay at the near end, and TZ2b must delay on *tp f* 1, with the CTI as described in Equation (8); Equation (9) describes the relationship between distance and DOCRs at the far end. At the far end, the second zone of primary distance relay (TZ2p) must delay on primary DOCRs operation time *tp f* 1 with CTI [21].

$$T\_{Z2b} - t\_p{}^{f1} > \text{CTI}\_r \tag{8}$$

**Figure 2.** The relationship between DOCRs and Distance pair relays.

This relationship was developed to specify the minimum value of the second zone of the distance relay, based on the operation time of the primary relay at both ends near and far. This idea is discussed in [39]. Equations (8) and (9) are rearranged to Equations (10) and (11). Then, the maximum value of these equations is used as the specific second zone of distance relay's time. This point helps to reduce the penalty and constraints.

$$T\_{Z2b} = t\_p{}^{f1} + \mathbb{C}T I\_r \tag{10}$$

 (9)

$$T\_{Z2p} = t\_p f^2 + \mathcal{C}T I\_\prime \tag{11}$$

$$T\_{Z2} = \max\{T\_{Z2\mathfrak{b}\prime}, T\_{Z2\mathfrak{p}}\},\tag{12}$$

The penalty function is recommended for use in the main goal of eliminating miscoordinations, as in the following equation [40]:

$$F^{\rm pcu} = \mu \ast \begin{cases} 1 \text{ if } T^{\rm backup} - T^{\rm primary} < CTI \\ 0 \text{ if } T^{\rm backup} - T^{\rm primary} \ge CTI \end{cases} \tag{13}$$

When miscoordination occurs in this penalty function, *Fpen* increases the total time of OF. As a result, the optimization algorithm attempts to eliminate miscoordination, in order to reduce the size of OF; *μ* is the weighting factor in this penalty function [37].

#### **3. The Proposed Protection Scheme**

*3.1. Smart Grid and Adaptive Protection Scheme (APS)*

In this research work, the proposed scheme is based on optimization solutions by an optimization technique. In this paper, the school-based optimization algorithm, used to evaluate the optimization solutions, in addition to this paper, included modifications for that algorithm, in order to improve its convergence characteristics and ability to find better optimization solution, as described in the next section.

The flow diagram (Figure 3) presents APS, considering DG's impact. The centralized processing server is used to optimize SCADA data. These data will be generated by APSproposed algorithms, for resetting the DOCRs and distance relays. The following steps refer to the main points of the proposed APS flow chart.

**Figure 3.** Flow diagram of APS.

The first point determined the actual distribution network topology, especially the state, location, and size of the DGs. Check for a change of distribution network topology. In case of no change, the APS stays with the current protection relay's settings; in the case of a change in topology, the APS moves to the next point.

In the second point, APS identifies the short current through CBs, ETAP was used in this paper for this mission. Then, check the ability of the current relay's settings, in order to save the protection system without loss-coordination of protection relays or miscoordination between protection relays. In case of the ability of the current setting to protect the distribution network, the APS returns to the previous point. However, it will move to the next point in the case that the relay's setting misses their job to protect the distribution network.

In the third point, APS calls the proposed optimized algorithm. Then, the algorithm searches for optimal solutions that are suitable to cover the changes in the distribution network, without miscoordination or loss-coordination. Finally, the APS reports the optimal solution of protection relay's settings and sends them through ICT and in-distribution network update IEDs. APS will stick to new changes in the distribution network [41].

#### *3.2. Original School-Based Optimization Algorithm*

SBO is a metaheuristic algorithm, as shown in its flowchart in Figure 4. SBO is formed from many classrooms and has many teachers. Each classroom used the TLBO algorithm, in order to be built. Each classroom has a teacher, which is the population with the best fitness. Teachers are joining to a pool of teachers. In this pool, teachers are distributed by a roulette wheel to a new classroom, in order to transfer the knowledge between them.

**Figure 4.** Flow chart of SBO algorithm.

The TLBO algorithm was inspired by the educational process in the classroom. That algorithm has two main phases. These phases are about the educational process and exchanging knowledge. The first phase is called the teacher phase. In this phase, the knowledge is transferred from teacher to students. The other phase is called the learning phase. That phase simulates the cooperative learning between students [29].

## 3.2.1. Teaching Phase

In this phase, the optimization algorithm simulates the teaching process to students who are trying to update themselves by knowledge transfer from their teacher. That representation is mathematically as follows:

$$X\_{new}^{k}(j) = X\_{old}^{k}(j) \; \pm \; \Delta(j) \; , \tag{14}$$

$$
\Delta(j) = T\_F \times r|M(j) - T(j)|,\tag{15}
$$

where *X<sup>k</sup>*(*j*) refers to the solution as a student with index *j*th, Δ(*j*) is the difference between the teacher and the mean of the class, *TF* is a teaching factor and equal to 2, *r* is a random value between [0, 1], *T*(*j*) is the solution as a teacher, and *M*(*j*) is the mean of the classroom and is represented as follows [30]:

$$M(j) = \frac{1}{N} \sum\_{k=1}^{N} X^k(j),\tag{16}$$

$$M(j) = \frac{\sum\_{k=1}^{N} \frac{X^k(j)}{F^k}}{\sum\_{k=1}^{N} \frac{1}{F^k}},\tag{17}$$

where *N* is the population. *F<sup>k</sup>* is the penalized fitness of student solution with indexing *k*th.

Equation (17) is about the fitness-based mean. This formula gives more emphasis to students and improves the performance of the TLBO algorithm [42].

At the end of the iteration, the solution that has the best fitness is chosen as a new teacher in the next iteration.
