Introduction

Motivation and purpose

As the globe struggles with climate change and environmental sustainability, green energy is becoming more and more significant. Reducing carbon emissions and the negative environmental effects of traditional fossil fuels requires a switch to renewable energy sources1. Microgrids are important because they offer sustainable, dependable, and efficient local energy solutions. By combining cutting-edge control and storage technologies with renewable energy sources, microgrids allow communities to optimize energy use and lessen their dependency on centralized power grids. Microgrids are an essential part of the green energy revolution because they improve energy security and resilience in addition to helping to conserve the environment. However, because of variations in fault currents, bidirectional power flows, and changing short-circuit levels, incorporating distributed energy resources (DERs) poses challenges to current protection approaches2. Deploying distributed energy sources near the customer end has drawn a lot of interest lately3. Microgrids have been widely deployed in several nations to meet the increasing demand for dependable and secure power supplies for consumers. Critical loads like hospitals, bank servers, and sensitive defence locations are finding that microgrids are a blessing. Microgrids are increasingly demonstrating their value in today’s distribution infrastructure. Over-current relays are frequently used to secure these distribution networks since they are more cost-effective and do not require expensive communication channels4. In theory, OCR protection detects faults by using the high fault current level characteristic. The safety of microgrids in islanded mode, where fault current levels are significantly lower, is one of the most important concerns regarding their operation. Because of their current control methods, inverter-based distributed generation (IBDG) sources limit the fault current to a maximum of 2 p.u5. This problem, along with variations in the direction and amount of fault currents brought on by changes in grid configuration, renders traditional protection techniques ineffective. In order to address this issue, OCR standard characteristics must be modified to be used with different microgrid operating modes.

Overcurrent relay’s coordinated operation is essential for maintaining a dependable power system. OCR needs to be running at optimal settings in order to detect and fix a fault instance in the shortest amount of time. OCR coordination optimization is a non-linear problem. OCR’s operating time is influenced by two key settings: the Plug Setting Multiplier (PSM) and the Time Multiplier Setting (TMS). The primary relay must isolate the fault effect inside its operational zone in order to keep it localised. The backup relay must only function after a predetermined amount of time, known as the CTI, if the primary relay fails. Therefore, maintaining the CTI for a primary-backup relay pair and minimising operational time are the major goals of optimising OCR coordination.

Literature review

A review of the literature demonstrates that researchers employ a variety of optimization strategies to attain the best OCR coordination6. Initial directional OCR (DOCR) coordination strategies utilized trial and error, which resulted in high computing requirements and a low convergence rate7. Following that, relay coordination was attempted using linear optimization, with the value of the DOCR plug setting determined using previous research8. Researchers have efficiently employed non-linear approaches to optimize OCR settings9. In10, the sequential quadratic programming method was used to optimize DOCR parameters simultaneously. Since the previous decade, artificial intelligence (AI) has emerged as a cornerstone in the field of relay coordination. It outperforms standard optimization methods. AI-based methods such as particle swarm optimization11, GA12, grey wolf optimization13, TLBO14, and the Moth-Flame methodology15 have proven to be very effective for OCR coordination16. describes machine-learning-based DOCR settings in microgrids that use double inverse characteristics. The Firefly algorithm17 and modified Firefly algorithm have also been used to achieve optimal settings of OCR18. uses optimal relay coordination in ring distribution network based on hybrid optimization techniques. The water cycle algorithm has been used to solve OCR coordination problems in microgrids19.The vast majority of AI based algorithms have been applied in traditional distribution networks. However, there is still room to adopt a more effective heuristic method to microgrid protection coordination. The various optimization techniques which have been used for relay coordination as mentioned in literature survey above have been summarized in Table 1.

One solution considers the non-standard properties of OCR and incorporates an additional restriction that accounts for PSM and sets the maximum value of PSM to 2020. A similar strategy21 takes advantage of this increased value of PSM at 100. Further improvements have been proposed in22, in which non-standard characteristics are supplemented by assigning a variable to the PSM maximum value rather than leaving it as a parameter. This study uses non-standard OCR features with a PSM constraint, a topic that has been less investigated in previous research.

Table 1 Literature survey summary.
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The fundamental goal of this research is to optimize TMS settings for better OCR coordination for microgrid protection. The study employs the SCA and mod WOA approach for coordination of over-current relays with non-standard characteristics, used in a microgrid. Efficacy of proposed algorithms is analysed by using the IEC microgird benchmark network. This study also compares the proposed approach to previously reported methods from standard literature using GA20,21 with reference to TMS values, overall operating time and CTI. The optimization is done in MATLAB 2019b and to simulate various fault scenarios DIgSILENT Powerfactory 2018 is used. Some AI based techniques which have been recently used in literature for optimization problems have also been reported in23,24,25. These techniques may further be explored for OCR coordination problem.

Contribution of the paper is as follows.

  1. (a)

    Study and implementation of SCA and mod WOA to IEC benchmark microgrid model for solving the OCRs coordination problem.

  2. (b)

    Though AI based algorithms have been applied earlier for OCR coordination but using these algorithms for coordination of OCRs with non-standard characteristics in a microgrid is less investigated in literature.

  3. (c)

    The population-based technique, SCA is employed to address extremely nonlinear relay-coordination problem and is found more effective than GA20,21 and applied mod WOA.

  4. (d)

    It is found that the total time of operation (top) of relays reduces to 5.17 s for operating mode 1(OM1), to 14.84 s for operating mode 2 (OM2) and to 13.95 s for operating mode 3 (OM3) by using SCA as compared to20,21. Reduction in total operating time implies that the fault will be isolated in minimum time, which is important feature of any sensitive and reliable protection system.

  5. (e)

    The top as well as the TMS values of all individual relays in all the OMs is reduced in case of SCA as compared to the standard literature20,21. At the same time the CTI for all relay pairs is maintained greater than 0.3 s, which is essential for relay coordination.

  6. (f)

    If we compare the results of applied mod WOA in terms of top with20,21, it is found that for OM1 overall top reduces to 5.11 s but no such reduction is seen in OM2 and OM3. In terms of TMS values and top of individual relays there is reduction only in OM1 but not in OM2 and OM3.

Hence it can be concluded that the propose SCA is efficient in solving the relay coordination problem in a microgrid for its various operating modes, as compared to mentioned standard literature20,21 and mod WOA.

The structure of this Paper is as follows. Section 2 describes the mathematical formulation of relay coordination problem and identifies the constraints used. Section 3 describes the working principles of SCA (3.1) and mod WOA (3.2) along with their respective flowcharts. Section 4 elucidates the simulation set up, results obtained and its comparison with other techniques. Section 5 sums up with conclusion and scope of future work.

Relay coordination problem: (mathematical formulation and coordination constraints)

Objective function

Plug setting multiplier (PSM) and TMS values are parameters related to OCR coordination that must be computed. The minimum fault current value and the maximum load current value determine the relay’s settings26,27. As previously stated, many heuristic optimization strategies have been employed to determine the best TMS settings for every relay.The objective function (OF) for the OCR coordination problem is the total operating time of all OCRs, which we have to minimize.

$$\:Min\left(OF\right)=\:\sum\:_{q=1}^{m}{\lambda\:}_{q\:}h\left({I}_{p},\:{I}_{q}\right)\times\:TMS$$
(1)
$$\:Min\left(OF\right)=\:\sum\:_{q=1}^{m}{\lambda\:}_{q}{t}_{q,r}$$
(2)

Where, m is total relays, tq, r is of qth relay operating time, rth zone fault. λq is assigned weight of qth relay operating time. Pick-up current is denoted by Ip, and fault current is denoted by Iq, for a qth relay. For instances of varying feeder lengths being same, λq = 1.

Relay characteristics

The total operating time of the relays is OF whose value depends upon the relay characteristics, as stated below:

$$\:g\left({I}_{p},{I}_{q}\right)=\:\frac{\varphi\:}{{P}^{\beta\:}-1}\:+N$$
(3)

where β determines the slope of the relay characteristic curve and P stands for PSM. For this investigation, OCR using a standard inverse curve has been taken into consideration. Values of β = 0.02, ϕ = 0.14 and N = 011.

Constraints on relay operating time

Operating time should be restricted to values between top_min and top_max for all OCRs.

$$\:{t}_{op\_min\:}<{t}_{op}<{t}_{op\_max}$$
(4)

Constraints on time multiplier setting

As TMS plays a significant role in OCR operating time, the following restrictions are placed on it for OCR coordination.

$$\:{TMS}_{qmin}\le\:\:{TMS}_{q}\:\le\:\:{TMS}_{qmax}$$
(5)

Where TMSqmin = 0.025 sec and TMSqmax = 1.2 s.

Bounds on PSM (nonstandard characteristics)

When calculating TMS for individual relays, the maximum PSM value should be taken into account. PSMqmax is the IEC inverse curve’s peak current level in an industrial relay prior to it entering the definite time region of its characteristics curve. The relay’s PSMqmax should therefore be limited when employing any optimization method. The PSM constraint can be described as

$$\:{PSM}_{qmin}\le\:\:{PSM}_{q,r}\:\le\:\:{PSM}_{qmax}$$
(6)
$$\:{PSM}_{q,r}=\:{I}_{fq}/\:{I}_{pickup}$$
(7)

For standard OCR characteristic this range of PSMqmax is usually set between 1.1 and 20. For this work the value of PSMqmax is taken as 100.

Constraints on relay pickup current

The lower and upper limits of the pickup current \(\:{I}_{p}\), are shown in Eq. (8) below and are represented by the symbols \(\:{I}_{pickupmin}\) and \(\:{I}_{pickupmax}\), respectively.

$$\:{I}_{pickupmin}<{I}_{p}<{I}_{pickupmax}$$
(8)

Coordination criteria

Both the primary relay and the backup relay detect faults. Prior reaching the backup relay, the primary relay detects the problem, ensuring that the system is disconnected as minimum as possible. The backup relay should be able to identify the fault after a finite amount of time (CTI) if the primary relay fails. 0.2 to 0.5 s is the range of CTI for OCR coordination. In this investigation, it has been assumed to be 0.3 s.

$$\:{t}_{br}-\:{t}_{qr}\:\ge\:\:0.3$$
(9)

Optimisation techniques used

Sine cosine algorithm

SCA was initially presented in28 and is based on sinusoidal functions and co-sinusoidal functions. A random population set is generated that oscillates inwards and outwards and optimal solution is obtained utilizing a fundamental mathematical method based on sine and cosine functions. SCA incorporates a number of adaptive random variables that make optimal use of search space exploration & exploitation. A favourable region of the search space can be identified during the initial phase, since the rate of randomness of the arbitrary variables is high. After the potential zone has been explored, rate of randomness decreases and the arbitrary variable begins to fluctuate gradually, allowing for the exploitation of the promising region. After the potential zone has been explored, rate of randomness decreases and the arbitrary variable begins to fluctuate gradually, allowing for the exploitation of the promising region.

$$\:{P}_{q}^{r+1}={P}_{q}^{r}+{n}_{1}\text{sin}{n}_{2\:}\times\:\:\left|{n}_{3}{D}_{q}^{r}-\:{P}_{q}^{r}\right|$$
(10)
$$\:{\:P}_{q}^{r+1}={P}_{q}^{r}+{n}_{1}\text{cos}{n}_{2\:}\times\:\left|{n}_{3}{D}_{q}^{r}-\:{P}_{q}^{r}\right|$$
(11)

where \(\:{D}_{q}^{r}\) is the location of the target point in qth dimension for rth iteration, n1, n2, and n3 are random values, and \(\:{P}_{q}^{r}\) is the location of the current solution in qth dimension at the rth iteration. Adding a fourth variablen4, which fluctuates between 0 and 1, hence moving the search from one stage to the next.When n4 is smaller than 0.5, the present solution will lay on the sine curve whereas when n4 is more than or equal to 0.5, the current solution will stand on the cosine curve. The combined equation can be expressed as:

$$\:{P}_{q}^{r+1}=\left\{\begin{array}{c}{P}_{q}^{r}+{n}_{1}{sin}{n}_{2\:}\times\:\:\left|{n}_{3}{D}_{q}^{r}-\:{P}_{q}^{r}\right|,\:{n}_{4}<0.5\\\:{P}_{q}^{r}+{n}_{1}{cos}{n}_{2\:}\times\:\left|{n}_{3}{D}_{q}^{r}-\:{P}_{q}^{r}\right|,{n}_{4}\ge\:0.5\end{array}\right.$$
(12)

When the limiting values of the sine or cosine function are violated, SCA has the tremendous advantage of exploring a different search area whereas when the values fall inside the limit then the exploitation of that promising region takes place. SCA likes to use adaptive variables for quick transition from exploration to exploitation and vice versa. Here variable n1 is used to adaptively alter the range of the sine and cosine functions and is controlled by Eq. (13) as given below.

$$\:{n}_{1}=c-r\left(\frac{C}{N}\right)$$
(13)

where, maximum number of iterations is N, Cis a constant and the value of present iteration is r.

In order to prevent the optimal solution from disappearing during optimization, SCA saves it in a variable as the destination point. It then updates the subsequent position in relation to the destination point as shown in Fig. 1.

Fig. 1
figure 1

Flowchart for SCA.

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Modified Whale algorithm

Mirjalili created the whale optimization algorithm (WOA) in 201629 as a novel heuristic approach inspired by nature to address various mathematical optimization problems as well as engineering-related ones. This optimization method was inspired by humpback whales’ bubble net hunting strategy, which involves following a circular path to hunt small fish close to the surface. This optimization stands out from other nature-inspired optimization techniques because the process of feeding is a characteristic activity of humpback whales. WOA involves the following three steps:

Encircling prey

The humpback whales recognize and encircle the target and prey’s position. The entity closest to the ideal plan is expected to reveal the best candidate guidance currently in place, as not all whales initially exhibit the perfect technique for finding the prey in the search region. The best search agent’s characteristics are used to guide other search agents in that direction. This strategy can be represented as follows:

$$\:\overrightarrow{G}=\left|\overrightarrow{F}\bullet\:{\overrightarrow{P}}_{\left(q\right)}^{*}\:-{\overrightarrow{P}}_{\left(q\right)}\right|$$
(14)
$$\:\overrightarrow{{P}_{(q+1)}}={\overrightarrow{P}}_{\left(q\right)}^{*}-\overrightarrow{E}\bullet\:\overrightarrow{G}$$
(15)

where q is the iteration that is currently running;\(\:{\overrightarrow{\:P}}_{\left(q\right)}^{*}\)represents the best available solution in the position vector \(\:{\overrightarrow{P}}_{\left(q\right)}^{*}\) and the coefficient vectors are \(\:\overrightarrow{E}\) and \(\:\overrightarrow{F}\). Note that each iteration will change\(\:{\overrightarrow{P}}_{\left(q\right)}^{*}\), where \(\:\overrightarrow{G}\) is the distance between the rth whale and the prey. Furthermore, the vectors \(\:\overrightarrow{E}\) and\(\:\overrightarrow{F}\) are computed as follows, using Eqs. (16) and (17), respectively:

$$\:\overrightarrow{E}=2\overrightarrow{m}\bullet\:\overrightarrow{n}-\overrightarrow{m}$$
(16)
$$\:\overrightarrow{F}=2\overrightarrow{n}$$
(17)

where the value of \(\:\overrightarrow{m\:}\)is decreased from two to zero during the exploitation and exploration steps, and \(\:\overrightarrow{n}\) is an arbitrarily selected vector with a range between zero and one.

Bubble net attacking method

The hump back whales employ two techniques to model this attacking method-.

Shrinking encircling mechanism

This behaviour is caused by a decrease from two to zero in the estimation of \(\:\overrightarrow{m\:}\) through the repetitions of Eq. (15). Similarly, by reducing the value of \(\:\overrightarrow{m\:}\), a value selected at random in [− m, m], the scope of modification for \(\:\overrightarrow{E}\) is reduced. By selecting irregular attributes for \(\:\overrightarrow{E}\) in the interval [− 1, 1], the initial location of search agents is selected from among each agent’s primary location and the position of the best agent.

Spiral updating of position

This procedure establishes the distance between the prey, which is positioned at (P*, W*), and the whale, which is positioned at (P, W). From then on, a helix condition is generated between the whale and the prey locations, in order to replicate the movement of humpback whales which is spiral in shape:

$$\:\overrightarrow{{P}_{(q+1)}}=\overrightarrow{G{\prime\:}}\bullet\:\:{e}^{st}\bullet\:\:\text{cos}2\pi\:t+\overrightarrow{{P}_{\left(q\right)}^{*}}$$
(18)

Where \(\:\overrightarrow{\text{G}{\prime\:}}\)determines the location or distance of whale r to the prey and is determined as

$$\:\overrightarrow{G}{\prime\:}=\:\overrightarrow{G}\bullet\:\:{e}^{st}\bullet\:\:{cos}2\pi\:t$$
(19)

In addition, t is an arbitrary value between [-1, 1] and s is a constant that represents the logarithmic helix’s state. Given that the humpback whales are swimming in a contracting loop around the prey and forming a helix, the equal chance of selecting the helix approach or the shrinking surrounding technique can be summed up as follows:

$$\:\overrightarrow{{P}_{(q+1)}}=\left\{\begin{array}{c}{\overrightarrow{P}}_{\left(q\right)}-\overrightarrow{E}\bullet\:\overrightarrow{G},\:\:u<0.5\\\:\overrightarrow{G{\prime\:}}\bullet\:\:{e}^{st}\bullet\:\:{cos}2\pi\:t+\overrightarrow{{P}_{\left(q\right)}^{*}},\:\:u\ge\:0.5\end{array}\right.$$
(20)

and u is a random number ranging between zero & one.

Fig. 2
figure 2

Flowchart for mod WOA.

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Search for prey

A similar method that relies on the vector \(\:\overrightarrow{E}\)’s heterogeneity can be used, when looking for the prey (exploration). A random survey of humpback whales reveals that they may be identified and are in view of one another. Similarly, it is anticipated that a moving search agent located far from a reference whale will be proficient in the behaviour where |\(\:\overrightarrow{E}\)| > 1. Furthermore, a search agent’s status during the exploration phase is modified based on an arbitrary search agent rather than the most effective pursuit agent discovered thus far as shown in Fig. 2. In terms of mathematical equations, it can be expressed as:

$$\:\overrightarrow{\:G}=\left|\overrightarrow{F}\bullet\:{\overrightarrow{P}}_{rand}^{*}\:-\overrightarrow{P}\right|$$
(20)
$$\:\overrightarrow{{\:P}_{(q+1)}}=\:\overrightarrow{{P}_{rand}}-\:\:\overrightarrow{E}\bullet\:\:\overrightarrow{G}$$
(21)

Simulation setup and results

DIgSILENT Powerfactory simulation software is used to simulate a benchmark IEC microgrid model that includes several distributed generating systems. Microgrid model is depicted in Fig. 3 and its parameter details are given in30. Three operating modes are considered, as shown in Table 1. Based on the network’s maximum loading capacity, load flow calculations are used to determine each relay’s current transformer ratio and plug setting.The short circuit calculation then generates five three-phase faults on different lines to accommodate for different operating conditions. Figure 4 displays the short circuit currents on different lines in various operating modes. The three-phase faults considered are F1, F2, F3, F4 & F5, on the lines DL-5, DL-4, DL-2, and DL-1and DL-3 respectively. During all the operating modes, CB – LOOP1 is kept open.

Fig. 3
figure 3

IEC benchmark microgrid.

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Fig. 4
figure 4

Three phase fault current values for various operating modes.

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Coding for SCA & mod WOA algorithm is done in MATLAB software and used to obtain the optimal TMS values for all the relays. The results obtained using the proposed algorithms are compared with those reported in20,21. The current transformer ratios and the values of pick-up current, for various relays are shown in the Tables 2 and 3.

Table 2 Operating modes of microgrid.
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Table 3 CT ratio and I pick up for relays.
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The coordination time interval (CTI) is the time difference between primary and back-up relay operating time. CTI must be greater than or equal to 0.2 s, according to IEEE standard 242 recommendations31. For this paper, CTI value considered is 0.3 s. For calculating the time of operation of various relays, IEC standard inverse characteristic is considered, with β and ϕ values of 0.02 and 0.14 respectively. The location of the 15 relays considered, numbered from 1 to 15, is shown in Fig. 3. The primary relay is depicted as (P) and the back relay is depicted as (B), during various operating modes and under different fault conditions. SCA & mod WOA algorithm is then implemented using various constraints mentioned in Sect. 3.

Operating mode 1

In operating mode 1 (OM1), all DG sources are disconnected and the microgrid is powered by the main grid as depicted in Table 2. Five different faults, F1, F2, F3, F4 and F5 are created at various locations as shown in IEC benchmark microgrid model (Fig. 3). The simulation is run in Digsilent powerfactory software and fault currents are obtained for OM1, for various relays operational in this mode (Fig. 4). SCA & WOA algorithm codes developed in Matlab software are used to find the Optimal TMS values for all the relays. Table 4 compares the results obtained with SCA and mod WOA with the ones using GA reported in20,21. It is seen that the total time of operation of all the relays in OM1, which is the objective function value shown as O.F. (s), is minimum and equal to 5.167 s in case of SCA as compared to the others. As is evident from Table 4 that the TMS values for all the relays in case of SCA has been reduced as compared to20,21 and are lesser as compared to mod WOA. Table 5 shows the operating time of each relay for each of the faults that were taken into consideration. It is seen that the operating time of each relay in case of SCA is lesser as compared to other algorithms. As seen in Fig. 5, the CTI of every primary and backup relay pair is maintained at or above 0.3s which is a necessary condition for relay coordination.

For OM1, an initial population of 30 is taken and the algorithm converges within 2000 iterations for SCA and mod WOA. Figure 6 displays the convergence characteristics for OM1 for both the algorithms implemented.

Table 4 TMS settings for OM1.
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Table 5 TOP for OM1.
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Fig. 5
figure 5

CTI of various primary backup relay pairs in OM 1.

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Fig. 6
figure 6

Convergence graph for OM1.

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Operating mode 2

In operating mode 2 (OM2), the microgrid is powered by all DG sources and the main grid. Once again five different faults, F1, F2, F3, F4 and F5 are created at various locations as shown in IEC benchmark microgrid model (Fig. 3) for finding the fault current values for various relays in OM2 by running the simulation in Digsilent powerfactory software (Fig. 4). SCA & WOA algorithm codes developed in Matlab software are again used to find the overall operating time (O. F. value), Optimal TMS values and operating time for all the relays for this operating mode. Table 6 compares the results for TMS values obtained with SCA and mod WOA with the ones reported in20,21. It is seen that the total time of operation of all the relays in OM2 is minimum and equal to 14.8376 s in case of SCA as compared to the others. As is evident from Table 6 that the TMS values for all the relays in case of SCA has been reduced as compared to GA20,21 and are lesser as compared to mod WOA. Table 7 shows the operating time of each relay for each of the faults that were taken into consideration. It is seen that the operating time of each relay in case of SCA is lesser as compared to other algorithms. A CTI greater than or equal to 0.3 s is maintained for all primary and back-up relay pairs as is evident from Fig. 7., thereby satisfying the necessary condition for OCR coordination.

For OM2 an initial population of 30 is taken and the algorithm converges within 3000 iterations for SCA as well as for mod WOA. Figure 8 displays the convergence characteristics for OM1 for both the algorithms implemented. The results obtained by SCA are more optimized in terms of reduction of total operating time of all relays (O.F. value), TMS values of OCRs and also as per the reduction in operating time of individual relays, as is evident from Tables 6 and 7 respectively.

Table 6 TMS settings for OM2.
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Table 7 TOP for OM2.
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Fig. 7
figure 7

CTI of various primary-backup relay pairs, in OM2.

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Fig. 8
figure 8

Convergence graph for OM 2.

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Operating mode 3

In operating mode 3 (OM3), the microgrid is powered by all the DG sources while the main utility grid is cut off. F1, F2, F3, F4 and F5 are the five faults considered and are created at various locations as shown in IEC benchmark microgrid model (Fig. 3). The short circuit analysis is then done to obtain the fault current values for various relays in OM3 by running the simulation in Digsilent powerfactory software (Fig. 4). The values of overall operating time (O. F. value), optimal TMS values and operating time for all the relays are obtained for this operating mode utilizing the Matlab codes developed for SCA and mod WOA. Table 8 compares the results for TMS values obtained with SCA and mod WOA with the ones using GA reported in20,21. It is seen that the total time of operation of all the relays in OM3 is minimum and equal to 13.9448 s in case of SCA as compared to the others. As is evident from Table 8 that the TMS values for all the relays in case of SCA has been reduced as compared to20,21 and are lesser as compared to mod WOA. Table 9 shows the operating time of each relay for each of the faults that were taken into consideration. It is seen that the operating time of each relay in case of SCA is lesser as compared to other algorithms. A CTI greater than or equal to 0.3 s is maintained for all primary and back-up relay pairs as is evident from Fig. 9., thereby satisfying the necessary condition for OCR coordination. The results obtained by SCA are more optimized in terms of reduction of total operating time of all relays (O.F. value), TMS values of OCRs and also as per the reduction in operating time of individual relays, as is evident from Tables 8 and 9.

For OM3, initial population for SCA is taken as 30 and the algorithm converges within 3000 iterations. For mod WOA initial population of 30 is taken and the algorithm converges within 50,000 iterations. Figure 10 displays the convergence characteristics for OM3 for both the algorithms implemented.

Table 8 TMS settings for OM3.
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Table 9 TOP for OM3.
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Fig. 9
figure 9

CTI of various primary-backup relay pairs in OM3.

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Fig. 10
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Convergence graph for OM 3.

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Fig. 11
figure 11

Comparison of objective function value (s).

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Figure 11 compares the total operating time (objective function value) for each of the three operating modes utilizing the suggested algorithm with20,21. It is found that the total time of operation (top) of relays reduces to 5.1676 s for operating mode 1(OM1), to 14.8376 s for operating mode 2 (OM2) and to 13.9448 s for operating mode 3 (OM3) by using SCA as compared to20,21. Reduction in total operating time implies that the fault will be isolated in minimum time, which is important feature of any sensitive and reliable protection system. The top as well as the TMS values of all individual relays in all the OMs is reduced in case of SCA as compared to the standard literature20,21. At the same time the CTI for all relay pairs is maintained greater than 0.3 s, which is essential for relay coordination for all operating modes. If we compare the results of applied mod WOA in terms of top with20,21, it is found that for OM1 overall top reduces to 5.11 s but no such reduction is seen in OM2 and OM3. In terms of TMS values and top of individual relays there is reduction only in OM1 but not in OM2 and OM3.

Hence it can be concluded that the proposed SCA is efficient in solving the relay coordination problem in a microgrid for its various operating modes. But the applied mod WOA is not that effective to solve this problem of relay coordination when applied to different operating modes. SCA has also got the limitation that the total time taken by the algorithm is more as compared to mod WOA for all OMs. Till the time the total convergence time is very not high, a small change in its value doesn’t makes a big difference, as these optimized TMS settings obtained using SCA algorithm can be stored and can be chosen as per the operating mode of microgrid, for ensuring the OCR coordination.

Furthermore the statistical analysis and comparison of the applied algorithms with the standard literature considered here20,21 is summarized as follows-.

  1. (i)

    For SCA the reduction in the value of objective function i.e. the overall operating time of all relays when compared with20, for OM1 is 31.37%, for OM2 is 22.64% and for OM3 is 10.39%.

  2. (ii)

    For SCA the reduction in the value of objective function i.e. the overall operating time of all relays when compared with21, for OM1 is 22.18%, for OM2 is 15.11% and for OM3 is 10.39%.

  3. (iii)

    For mod WOA the reduction in the value of objective function i.e. the overall operating time of all relays when compared with20, for OM1 is 32.10%, for OM2 is 3.44% and for OM3 is − 44.87% (means increase in overall top).

  4. (iv)

    For mod WOA the reduction in the value of objective function i.e. the overall operating time of all relays when compared with21, for OM1 is 23%, for OM2 is -5.96% and for OM3 is -44.87% (means increase in overall top for OM2 and OM3).

Conclusion and future prospects

Newer and more intelligent protection methods are required as DG penetration increases and microgrids are introduced. OCR miscoordination may result from variations in fault current levels and direction, brought on by modifications in the microgrid’s operating mode. As the fault current values are lower in islanded mode, the OCR malfunctions. As a result, AI-based methods have become more and more common for solving relay coordination issues. Finding a proper balance between exploration and exploitation is the most challenging task in the development of any meta-heuristic algorithm due to the stochastic nature of the optimization process. The cyclic pattern of sine and cosine function allows a solution to be re-positioned around another solution. This ensures that the space between solutions is exploited. The effectiveness of SCA in solving the optimal coordination problems of OCRs is tested on IEC benchmark microgrid model. This study develops the Matlab codes using SCA & mod WOA to solve the relay coordination problem in an IEC benchmark microgrid model and attain optimal relay settings (TMS). It is found that the minimum value of overall operating time as well as the TMS settings are obtained using SCA while comparing it with GA20,21 application or mod WOA, considering non-standard characteristics of OCR. The results show the effectiveness of SCA in attaining relay coordination. Relay coordination is acheived in all operating modes of the microgrid model under consideration by maintaining a CTI of 0.3 s or more between the pairs of primary-backup relays. Hence it is recommended to use SCA for solving OCR coordination problem, in a microgrid.

The power grid will become increasingly complex in the future due to the growth of DC and AC-DC hybrid microgrids, the expansion of generator capacity, and the rising penetration of DGs. In future AI and machine learning based algorithms and some hybrid algorithms can be explored further to enhance the precision and adaptability of OCR settings. Further different non-conventional relay characteristic curves may be exploited for various operating modes of microgrid and relay setting groups can be developed. So, the scope of future work lies in developing more intelligent protection techniques for better OCR coordination, which befits and adapts to all kinds of changes in network configuration.