© The Author(s), published by EDP Sciences, 2023

1 Introduction

In recent years, renewable distributed energy sources plays an energetic role in meeting the world’s energy consumption needs and they have more benefits than fossil fuels. Generally, the generators are linked to the grid in normal conditions and islanding occurs when the grid is disconnected during abnormal conditions [1]. Unintentional islanding causes damage to the system and also utility workers are affected when they are exposed to the shocks [2, 3]. The islanding is considered a component of the electrical system that occurs at the time of interruption is needed to resolve in a short time [4]. Any fluctuation in frequency and voltage affects the electrical equipment connected to the islanded segment. The islanding techniques are classified into several types according to the local and communication practices. Detection methods such as passive, active, and hybrid islanding are differentiated from local islanding detection approaches [5–7]. One of the islanding techniques called communication islanding is more complicated and the cost is very high but it has great dependability [8]. The transient variation of parameters present in the Power Control Circuit (PCC) current, voltage, phase shift, frequency, and harmonic distortion influence the passive islanding operation [9–11]. The islanding detection takes place by detecting the fluctuation in the output signal and also by allowing a signal at the PCC for certain cycles [12–14]. The active method is used to detect the islanding detection is preferable to the passive methods because they have more ability to enhance the power quality [15–17]. DQ controller of inverter-based distributed generation is utilized to inject a low-frequency current into Non-Detection Zone (NDZ) [18, 19]. Many standard algorithms such as ANNs [20, 21], Decision Tree models (DTs) [22], and Support Vector Machines (SVMs) [23] are employed for differentiating islanding and non-islanding events. These popular algorithms use a real-time approach and maintain the minimum NDZ even though the control circuits of these active methods are complicated. The communication-oriented solutions are very effective and have no side effects on the system’s power quality but they are complicated and more expensive compared to other models. The islanding detection on the utility’s side and DG’s side are determined by the remote islanding detection method, which makes use of PLCC and SCADA. The PLCC monitors signals arriving from the utility grid is absent in any case resulting in islanding. SCADA utilizes the Circuit breaker auxiliary contacts to detect islanding. Here, if the passive way suspects the islanding then the active system will confirm it. In addition, low NDZ affects the power quality of the system [24]. The organization of work is illustrated in Figure 1.

Fig. 1 Organization of the work.

2 Recent research work

More research has been earlier implemented, which is linked to islanding detection on distributed generation with various techniques and features. Some of them reviewed are as follows.

Kolli and Ghaffarzadeh [25] have illustrated islanding detection using a novel signal processing methodology depending on the phaselet algorithm. The phaselets were significantly used in the computation of phasors over data windows and very effective in the integer multiplication of half-cycle. The islanded and non-islanded situation were found in the absence of allowing any disturbance or a high-frequency signal. The feature did not exist a power quality problem and it makes the method more reliable and provides the optimal result. Here, the variable filtering window capability was utilized to determine the negative sequence component of voltage and current waveform. Paiva et al. [26] have explained a modification in CWT to achieve Real-Time execution (RT-CWT) of non-stationary signal analysis to execute a Wavelet-Based Hybrid Island Detection Scheme (WB-HIDS). Here, power quality-related such as power grid voltage, grid impedance, and power angles were evaluated to detect the islanding condition or fault occurrence.

Özcanlı and Baysal [27] have suggested a novel passive Island Detection Method (IDM) of synchronous and inverter-interfaced MGs. The microgrid played an important role in the future energy system may operate in island mode or connected to the grid by integrating RES like photovoltaic power, wind power, and hydropower. Unintentional islanding causes system issues like power quality, voltage stability, and security risks. The harmonic distortion of voltage and current was calculated at the Point of Common Coupling (PCC) of MG using multi-length short-term memory architecture. In the analysis process, the distorted main grid with various operating conditions was considered. Various simulations were implemented on MATLAB/Simulink. The comparative analysis of the introduced system using intelligent IDMs was estimated to authenticate its effectiveness.

Nayak et al. [28] have found a novel islanding detection technique to notice the islanding condition in distributed generation systems to assure the safety of personnel and equipment. Initially, a raw signal was collected using EMD and converted into Intrinsic Mode Functions (IMFs) using dissimilar frequency scales. This signal is rebuilt allowing for IMFs also be used in the analysis according to the correlation coefficients. The hybrid method was used mainly to minimize the detection time and improve accuracy. For different PQs, disturbance, and islanding events were replicated to check the performance and efficiency of the system.

Markovic et al. [29] have introduced a popular interface protection method called Loss of Mains (LoM) protection for Distribution Generation (DGs). Here, the technique finds the island at the connection point and disconnects DG to avoid the system. The high penetration of DG with inverter interface and decommissioning of synchronous generators combine to reduce system inertia. In addition, quicker changes and greater voltage and frequency deviations were achieved through this method. According to the local measurement, the injected active and reactive power was modified under inverter-based DGs and was considered to support the network. A developed analytic formulation was used in the paper to determine the NDZ of LoM protection. Performance analysis was taken place and detailed dynamic simulation was done and the new requirements of the inverter on the operation of LoM protections were tested. Khair et al. [30] have advised that the improvement in the wind turbine, solar PhotoVoltaic (PV), and fuel cell joined using enhanced power electronics emerges the renewable energy sources. The ever-increasing load demand was satisfied by switching the distributed generation. In the distribution generation islanding took place a part of the distribution system was disengaged as the repose of the grid. It was necessary to disconnect all the distribution generation once the islanding occurred. It was important to consider in order to protect the operating personnel and avoid power quality problems. In the paper detection of islanding was considered the main objective. Hence, the DG was designed using a suitable anti-islanding detection system. The Phasor Measurement Unit (PMU)-based islanding detection system was introduced and relatively significant results of the industry were obtained using MATLAB/Simulink site.

Elshrief et al. [31] have found an island phenomenon and passive systems employed to secure it. The key objective of the work was island detection based on time and accuracy with a Rate Of Change Of Power (ROCOP) system depending Terminal Voltage (TV) (ROCOP-TV) of the PhotoVoltaic (PV) inverter. Actually, islanding means providing energy to the load from DG during disconnection from the utility grid at PCC. The result of this system was examined through MATLAB/Simulink platform. ROCOP-TV system was likened to using different sorts of passive sensing relays after synchronization.

2.1 Background of research work

The review of the investigation included the detection of island problems is an important contribution component under DG. This islanding condition occurs on microgrids through expanding distributed generation due to line fault and leads the system into danger. This islanding influences the normal operation of the DG. Different islanding area strategies such as communication-based, active, passive, and hybrid systems deal with these unsettling influences. Compared to other strategies communication-based strategies are the most expensive due to the reconfiguration of the protection plot. The specific parameters such as voltage, reactive power, and frequency are estimated using localized algorithms. The passive strategies are used to reduce the islanding condition when the system contains a low power imbalance. These active techniques are considered dangerous and in the passive strategy, the threshold values are assigned experimentally but cause misdirection and problems. The harmonic condition occurs due to the change in the connection/disconnection of nonlinear loads. A high amount of 3rd harmonic is generated using the no-load transformer. By injecting a clean currently, the DG inverter increases the voltage distortion. The main issues of islanding detection in applications are the choice of parameters, choice of threshold, and discrimination of harmonic pollution generated by grid, loads, and DG unit. The hybrid artificial intelligence strategies influence the negligible negative downside of the passive and active techniques for example ANN, ANFIS, FL, and some joined with active/passive methods. To determine the islanding problem trend-setting innovation is used. In interrelated works, the systems used to determine islanding issues are discussed and the recent research reference motivated to do this investigation work.

3 Configuration of the proposed system

The proposed system consists of synca hronous Phase-Locked Loop (PLL), synchronized solar PhotoVoltaic DG (PVDG), and an RLC load (R = 0.2Ω, L = 530 H, C = 13 260 F) connected in parallel with PVDG and the grid. The way of connecting the solar system using the capacity of 100 kW through DC to DC converter, voltage source inverter, CB, and transmission line to a 120 KV main network is shown in Figure 2. The system of solar consists of 330 solar panels with 66 strings in it. Every solar panel is made up of five series-related strings in the shunt (66*5*305.2 W = 100.7 KW). Also, every panel contains a 5.96 A short circuit current and 64.2 V open-circuit voltage at 1000 W/m² solar irradiation 250° C ambient heat. The solar panels with a DC/DC construction deliver higher output voltage via MPPT. For this instance, this organization develops incremental conductance and integral regulator technique.

Fig. 2 Proposed grid-connected solar PV system.

The DC–DC boost converter produces an output voltage that is increased to 500 volts and is given to the inverter. The inverter output is converted into a DC voltage of 500 V into an AC voltage of 260 V. PWM (Pulse Width Modulation) controller generates pulses which are used to switch VSC (Voltage Source Converter) and it is used to run the PVDG in constant PQ control mode. The voltage and current harmonics are detached once passing through the filter. It is necessary to step up the voltage to 120 kV to integrate the voltage into 25 kV feeders and 120 kV. The block diagram for presenting the process of the proposed scheme portrays in Figure 3.

Fig. 3 Block diagram for presenting the process of proposed system.

The islanding is considered the most dangerous situation on grid-tied PV systems and it affects the PV system and grid in the DG. Also, the grid voltage and frequency are not constant due to islanding circumstances. If a circuit breaker is linked among the grid and PCC fault is neglected and the condition varies reference values of the grid using the final objective. In case of CB is not able to open the circuit and the DG keeps providing power to the load. The unfamiliar interference of the grid is the reason for islanding activity and this situation allows the voltage shutdown and short-circuits to happen.

3.1 Mathematic model of DG unit

Islanding on PV power generation system consists of three standard segments such as solar PV, DC–DC converter, PV inverter along with the filter. The mathematic model of the three main regions is discussed below.

3.1.1 PV array

PV cell is used to convert the photon energy of sunlight into power and the cell material generates stable open circuit voltage. The PV system modeling is represented in Figure 4.

Fig. 4 PV system modeling.

The current (I_{PV (cell)}) flowing through load according to light energy (photons) expressed as:(1)

The indices n and m are assigned and the above equation is changed for the PV array is illustrated in the following equation,(2)

The I_ph subject with parameters, like ambient temperature and solar irradiance articulated below,(3)

3.1.2. DC–DC converter

An ideal bus voltage is obtained by the DC–DC converter and the passive element of the converter is derived which is illustrated below equation,(4) (5)

The duty cycle D is expressed as,(6)

It is known from the beyond equation, ∆I _i considers input current 10% and ∆v considered output voltage 3%.

3.1.3. PV inverter

Three-phase voltage source converter is utilized to transform DC into AC voltage. Six Insulated Gate Bipolar Transistors (IGBTs) consist of a two-level photovoltaic inverter according to a fixed and rotating frame derived as [32]:(7) (8)

The following equation derives the active and reactive power,(9) (10)

4 Proposed (GBDT-JS) technique for islanding detection on distributed generating system

4.1 Data generation

The test law is used to establish a number of islands and non-island actions in order to provide categories of the variance of generous data. The DER’s power and the power consumed by the neighborhood loads are used to explain the islanding occasion. The less and great power mismatches (0–30%) (30–100%) are considered as two active and reactive power mismatches. It is difficult to identify the island in this circumstance, on the ground the small power is superfluous [33]. Load switching, capacitor bank switching, motor switching, etc., on every bus are considered occasions without operation on the island.

4.2 Feature extraction using Discrete Wavelet Transform (DWT)

The feature extraction process is set after the data generation process is used to collect the voltage signal features that have the ability to determine drawbacks in the DG. The framework, including the islanding period, is developed using DG and loads. When the current supplied by the utility side is interjected, the DG starts to sustain the load. Therefore, to minimize the total power, the generator begins to slow down its rotor speed. The terminal voltage and angle for a reference are exaggerated. In this way, the proposed technique extracts five variables. These variables are used to extract the features by the Standard Deviation (SD) within a sliding data window that has width ΔT. With this system, the characteristics of five network variables, like capacitor switch, load switch, and so on, are removed under islanding and non-islanding circumstances. The five characteristics expressed in the below equation,(11) (12) (13) (14) (15)

Thus, the feature vector is assessed below,(16)where T represents the transpose operator.

A wavelet transform is the best choice for the signal and speech processing application and it includes the location and scale of two basic components [34, 35]. The wavelet transform includes a succession of wavelet functions of various sizes. The HPF and LPF are used to generate lower-resolution components. The decomposition process continues until the entire component is generated. The objective signal (S) is sent via the HPF and LPF. The wavelet transform is classified into two types such as Continuous Wavelet Transform (CWT) and Discrete Wavelet Transform (DWT).

A CWT signal expressed as,(17)where x represents the scale (dilation) constant, y denotes the translation (time shift) constant and the mother wavelet is denoted by ψ ^*. A DWT signal denoted as,(18)

The x and y terms in equation (17) are replaced by using integer variables and . The signal properties in the wavelet function are stored by HPF, whereas the LPF represents the coarser information of the approximation signal. In this procedure, the Daubechies level 4 filter is used by DWT analysis (d-4).

4.3 Gradient Boosting Decision Tree (GBDT)

GBDT is employed to find the power which is explained in this subsection. The GBDT method utilized stage-wise fashion in the model designing and allows the optimization function and the model to be generalized [36]. The decision tree with the constant size is utilized as base learners on a gradient boosting system. In the regression and classification problems, gradient boosting is considered a machine learning technique that provides a prediction model in terms of a weak prediction model as a decision tree. The GBDT’s main work is to raise the weak base classifiers collected in the robust classifier. It can be also used to make the global convergence of the algorithm. The inspiration diagram of the GBDT approach portrays in Figure 5.

Fig. 5 Inspiration diagram of GBDT approach.

4.3.1 Steps for GBDT

• Step 1: Initialization

At the initialization process input vectors as the duty cycle of the DC to DC converter are initialized:(19)where H(x) defines the basic learner of the system and p represents the number of predicted variables and Y _i mentions the predicted label.

• Step 2: Assessment of objective function

The evaluation of the objective takes the actual and reference battery power into the consideration for obtaining the objective function and can be described by,(20)

• Step 3: Boosting function

In the boosting function, the iteration is increased. Let C denotes the iteration number and is written as C = 1, 2, 3, …, n, and it is necessary to perform the following two steps to compute the negative gradient among the loss function of the current model using the below equation,(21)

• Step 4: Fit the sample data

In this step, the better-fit value of sample α _m is evaluated for every leaf node y _t and can be expressed by,(22)

Considering y _t as the novel label of sample x _i to obtain novel sample data h[(x _i ; a_,m )i = 1, 2, …, n], and innovative tree model contains N _m (j = 1, 2, …, j).

• Step 5: Find the fitness function

The loss of function is reduced in order to determine the fitness function and can be expressed as,(23)

• Step 6: Updation

In the updation process, the value is efficient according to the following equation,(24)

Depending on the fitness function GBDT is operated and the optimal output is found.

4.4 Jelly Fish Search algorithm

The mathematical model for the jellyfish algorithm is established according to three significant rules [37] which are illustrated in the following and also the flowchart for the JS algorithm is represented in Figure 6.

• The jellyfish considers the ocean current and moves within the swarm and its time control mechanism.

• In the case of searching for food, the jellyfish move in the ocean is very excited and attracted towards the place wherever the availability of food is high.

• The amount of food is employed using location and their equivalent function.

• Step 1: Ocean current

Fig. 6 Flow chart of Jelly Fish (JS) algorithm.

Ocean currents consist of a lot of nutrients due to this jellyfish has attraction towards the ocean. The ocean current is found by taking an average of vectors of each and every jellyfish that are present both in the ocean and in the current best location and can be expressed by the following equation,(25)

Considered,(26)

Hence, can be calculated as,(27)where the number of jellyfish is represented as η_pop, the jellyfish current best position on swarm is noted as x ^*, E _c is defined as factor governs attraction, the mean position of entire jellyfish marked as μ, df is described as the difference among the current best position of e jellyfish and mean of entire jellyfish:(28) (29) (30)

Equation (30) can be modified as,(31) (32)

Thus,(33)

The novel position of the jellyfish is expressed,(34)

Equation (34) may be denoted,(35)Here, β > 0 is known as the distribution coefficient), β = 3 is determined by considering the consequences of sensitivity analysis under numeric tests.

• Step 2: Jelly Fish Swarm

In the jellyfish swarm, there are two types of jellyfish motion are available which are passive and active motion. They can be considered as type A and B. In type A the jellyfish are available at their own location is represented,(36)Here, the upper and lower bound of search spaces marked as U _b and L _b , γ > 0 refer motion coefficient relates to the duration of movement around jellyfish’s positions, γ = 0.1 is found according to the outcomes of sensitivity analysis. The movement is defined as the actual exploitation of local search space,(37)Here,(38) (39)Here, the objective function of location x is represented as f. Thus,(40)

The type of motion over time is determined by using the time control mechanism. This control mechanism is also employed for evaluating that type A and B motions on swarm and movements of jellyfish towards ocean current controls are controlled using this mechanism.

• Step 3: Time control mechanism

The time control mechanism is defined as a random value that varies from 0 to 1 over time and it involves control function c(t) and constant c₀. Equation (41) represents the time control function,(41)Here, t represents the time identified iteration number and a maximal number of iterations is represented as max_iter, which is an initialized parameter.

• Step 4: Population initialization

In this step, the population of jellyfish is initialized according to a random manner that has influenced such as slow convergence and little population diversity. Recover that initial population called a logistic, tent, and liebovitch map using different chaotic maps,(42)Here, x _i defines the logistic chaotic value of ith jellyfish utilized to generate the initial population of jellyfish.

• Step 5: Boundary condition

Oceans are available all over the world and the earth’s shape is a sphere. In such a case, the jellyfish go back to the opposite bound when its moves outside the bounded search area and which can be expressed in equation (35),(43)here i _d denotes the position of ith jellyfish on dth dimension, x _i.d represents that modernized position after checking boundary restrictions.

5 Result and discussion

This section briefly explained system performance in different loading conditions which are categorized into five cases. The simulation results occurred as the proposed GBDT-JS system is likened using existing procedures like Support Vector Machine (SVM), Decision Tree, and Naïve Bayesian classifier.

The occurrence of islanding was developed at 0.2 s in all the cases explained below by tripping the circuit breaker on the grid side. After the islanding instant, the frequency of the microgrid started to change from the grid frequency. The result proves that the difference in frequency parameter started to diverge from zero at t = 0.3525 portrayed in Figure 7a. The d-axis voltage is a local measurement as it begins to change at t = 0.2 s which is illustrated in Figure 7b. When f _d approaches Th₁ (0.33), disturbance current is inserted via inverter current controller for a brief period of 0.3 s. The islanding is detected when the RCPABPSVAC value surpasses the threshold value Th₂ (0.02 pu) which is shown in Figure 7c. The trip signals are developed for several power mismatch situations which are illustrated in Figure 7d. The proposed methodology is implemented using MATLAB/Simulink. Analysis of Discrete Wavelet Transform is performed Python programming is used up to level 4 and the GBDT-JS Methodology is employed for numerous case studies to predict islanding. Figures 7, 9, 11, 13, and 15 represents the frequency deviation, d-axis voltage, RCPABPSVAC, and the trip signal generated at the DG side circuit breaker. Similarly, Figures 8, 10, 12, and 14 represent Daubechies wavelet approximate and detailed coefficient up to level 4 for various fault conditions.

• Case 1: Conditions of normal loading

Fig. 7 System performance under normal loading conditions, (a) frequency deviation versus time, (b) d-axis voltage versus time, (c) RCPABPSVAS versus time, and (d) trip signal versus time.

Fig. 8 System performance under normal loading conditions.

Fig. 9 System performance under balanced loading conditions, (a) frequency deviation versus time, (b) d-axis voltage versus time, (c) RCPABPSVAS versus time, and (d) trip signal versus time.

Fig. 10 System performance under balanced loading conditions.

Fig. 11 System performance under overloading conditions, (a) frequency deviation versus time, (b) d-axis voltage versus time, (c) RCPABPSVAS versus time, and (d) trip signal versus time.

Fig. 12 System performance under overloading conditions.

Fig. 13 System performance through Inductive load switching, (a) frequency deviation versus time, (b) d-axis voltage versus time, (c) RCPABPSVAS versus time, and (d) trip signal versus time.

Fig. 14 System performance during Inductive load switching.

Fig. 15 System performance during capacitor switching, (a) frequency deviation versus time, (b) d-axis voltage versus time, (c) RCPABPSVAS versus time, and (d) trip signal versus time.

Coefficients of the Daubechies wavelet family approximately and in detail up to level 4 for 70 percent loading conditions are shown in Figures 8a–8e. The timing samples data was reduced when the wavelet propagated from level 1 to level 4, making testing data more reliable for detecting the islanding condition. Under normal circumstances, islanding occurs at 17.9 ms based on the GBDT-JS model.

• Case 2: Balanced loading conditions

Detailed and Approximate coefficients of the Wavelet family for the Daubechies model up to level 4 are shown in Figures 10a–10e under very few loading scenarios when the capacity of the load is 100 percent of the capacity of distributed generator. Under normal circumstances, the prediction of the islanding condition is done using the GBDT-JS model and it would occur at 16.98 ms.

• Case 3: Conditions of overloading

Figures 12a–12e shows the coefficients of approximation and detail of the Up to level 4 of the Daubechies wavelet family for overloading conditions with a load capacity of 120 percent of the distributed generator capacity (overloading). The GBDT-JS model anticipated that the islanding condition will occur at 16.54 ms under these conditions.

• Case 4: Switching conditions for inductive loads (50 HP) (non-islanding)

Figures 14a–14e depicts the Daubechies wavelet family’s estimated and detailed coefficients up to level 4 when the inductive load circuit breaker is switched on for 1.5 s. Wavelet coefficients are resolute up to level 4 under the scenario. Under balanced conditions, the GBDT-JS model predicted the non-islanding condition in 17.86 s. Power is continuously delivered to the load when non-islanding conditions exist.

• Case 5: Switching condition of a capacitor (10 KVA) (Non-islanding)

Wavelet coefficients from the Daubechies family up to level 4 in the approximate and detailed form are shown in Figures 16a–16e for the proposed technique RCPABPSVSAC during rapid capacitor switching at 1.5 s. Wavelet coefficients are also resolute up to level 4 under the scenario. Under a balanced case, predation of the non-islanding condition of the GBDT-JS model is done at 17.89 ms.

Fig. 16 System performance during capacitor switching.

5.1 Comparative statement

In this paper, the GBDT-JS-based frequency disturbance triggered passive islanding detection scheme gradually decreased at a level 4 below 18 ms due to a reduction in the number of samples. MSE also determined for various case studies, the lower the value of MSE better will be the accuracy. As shown in Table 1, the results are based on the minimum square error for each case study. The injected current in the current controller has not produced sinusoidal d-axis voltage during both balanced and non-islanding conditions which will affect islanding detection time. So, this method detects islanding even under balanced load conditions also. Table 2 indicates proposed method has a better detection time likened to existing procedures. Table 3 illustrates the detection results of the proposed technique.

The efficiency comparison of the proposed system using the existing one during island failure for 50, 100, and 150 test numbers is outlined in Figures 17–19, including accuracy, specificity, recall, and accuracy. Over 50 trial numbers, the proposed system contains an accuracy of 1.24, a specificity of 1.54, a recall of 1.97, and a precision of 1.54. In the existing system mentioned above, the ranges refer to 0.56, 0.6, 0.7, and 0.53 correspondingly. At SVM refer to 0.76, 0.72, 0.9, and 0.73 correspondingly. At DT, ranges denote 0.86, 0.82, 0.89, and 0.83, correspondingly. At FAT, the ranges refer to 0.91, 0.89 1, and 0.89. At OCSO, accuracy, specificity, recall, and precision refer to 0.92, 0.95, 1.52, and 0.97. Over 100 trial numbers, the proposed system has an accuracy of 1.42, a specificity of 0.97, a recall of 0.91, and a precision of 1.42. In the existing system mentioned above, the ranges denote 0.7, 0.54, 0.58, and 0.56 correspondingly. At SVM, the range denotes 0.69, 0.64, 0.59, and 0.66 correspondingly.

Fig. 17 Performance comparison of proposed using existing system for 50 trials.

Fig. 18 Performance comparison of proposed using existing system for 100 trials.

Fig. 19 Analysis comparison of proposed using existing system for 150 trials.

At DT, ranges for accuracy, specificity, recall, and precision denotes 0.89, 0.76, 0.86, and 0.73. At FAT, the ranges for accuracy, specificity, recall, and precision refer to 0.92, 0.86, 0.79, and 0.97. At OCSO, ranges refer to 0.92, 0.89, 0.86, and 0.97. At 150 trials, the proposed system contains an accuracy of 1.34, a specificity of 0.98, a recall of 1.50, and a precision of 1.08. In the existing system mentioned above, the ranges refer to 0.77, 0.57, 0.66, and 0.59 correspondingly. At SVM, ranges refer to 0.79, 0.72, 0.88, and 0.73 correspondingly. At DT, ranges refer to 0.79, 0.88, 0.75, and 0.73, correspondingly. At FAT, ranges refer to 0.98, 0.88, 0.87, and 0.85. At OCSO, ranges denote 0.88, 0.91, 0.93, and 0.97, correspondingly. Likened to the existing mentioned above, the proposed scheme works precisely and accurately.

Figures 20 and 21 portray statistical evaluation of the proposed and existing system through 50 and 100 tests. To assess the general efficiency of the proposed system, the RFMFO island detection methodology is likened to using existing classification strategies like ANN, SVM, RF, DT, and the naive Bayesian classifier. At 50 trial numbers, the RMSE, MAPE, and MBE range of the proposed system implies 7.64, 0.94, 1.24 time of the proposed system refers 1.98 (s) and the existing system RMSE range of ANN implies 8.53, MAPE refers 0.98, MBE implies 1.79 and consumption 2.97. The RF refers to 10.66, MAPE implies 1, MBE refers to 2.88, and time consumption implies 5.55. The DT implies 23.44, MAPE refers to 13.55, MBE implies 5.74, and consumption time refers to 8.66. The SVM implies 18.92, MAPE refers to 6.77, MBE implies 2.79, and consumption time refers to 6.68. The Naïve Bayesian classifier refers to 25.44, MAPE implies 18.24, MBE refers to 7.57, and consumption time implies 7.68 likened to an existing system, the consumption time of the proposed system is low. At 100 route numbers, the RMSE, MAPE, and MBE range of the proposed system refers to 8.66, 0.68, 2.68, and the time consumption of the proposed system refers to 22.59 (s) and the existing system RMSE range of ANN implies 9.37, MAPE implies 1, MBE refers 3.88, and consumption time refers 2.97. The RF implies 14.68, MAPE implies 2.57, MBE implies 5.76, and time implies 6. DT RMSE implies 26.79, MAPE refers to 14.68, MBE refers to 8.87, and consumption time implies 8.36. The SVM implies 21.56, MAPE refers to 7.76, MBE refers to 5.59, and consumption implies 7.45. The RMSE range of the Naïve Bayesian classifier implies 28.79, MAPE refers to 19.56, MBE implies 10, and time consumption refers to 8.78. Likened to existing methodologies, the proposed system has fewer errors and much less time consumption.

Fig. 20 Statistic evaluation of proposed using existing system through island for 50 trials.

Fig. 21 Statistic evaluation of proposed using existing system through island for 100 trials.

6 Conclusion

The research provides a negative sequence islanding detection technique based on GBDT-JS that utilizes mean square error to detect islanding conditions for various wavelet coefficients. The energy content, as well as the standard deviation, are measured and fed into the GBDT-JS Model. It deals with islanding detection time using an accuracy of 88–92 percent of varied loads. In balanced conditions with 0% NDZ, the suggested islanding technique can also detect islanding and overload conditions in a short amount of time. Advanced approaches such as multiple regressions, recurrent neural networks, and others can be used to implement the recommended approach for detecting islands without sacrificing accuracy in the future.

Funding information

This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.

Ethical approval

This article does not contain any studies with human participants performed by any of the authors.

References

All Tables

All Figures

	Fig. 1 Organization of the work.
In the text

	Fig. 2 Proposed grid-connected solar PV system.
In the text

	Fig. 3 Block diagram for presenting the process of proposed system.
In the text

	Fig. 4 PV system modeling.
In the text

	Fig. 5 Inspiration diagram of GBDT approach.
In the text

	Fig. 6 Flow chart of Jelly Fish (JS) algorithm.
In the text

	Fig. 7 System performance under normal loading conditions, (a) frequency deviation versus time, (b) d-axis voltage versus time, (c) RCPABPSVAS versus time, and (d) trip signal versus time.
In the text

	Fig. 8 System performance under normal loading conditions.
In the text

	Fig. 9 System performance under balanced loading conditions, (a) frequency deviation versus time, (b) d-axis voltage versus time, (c) RCPABPSVAS versus time, and (d) trip signal versus time.
In the text

	Fig. 10 System performance under balanced loading conditions.
In the text

	Fig. 11 System performance under overloading conditions, (a) frequency deviation versus time, (b) d-axis voltage versus time, (c) RCPABPSVAS versus time, and (d) trip signal versus time.
In the text

	Fig. 12 System performance under overloading conditions.
In the text

	Fig. 13 System performance through Inductive load switching, (a) frequency deviation versus time, (b) d-axis voltage versus time, (c) RCPABPSVAS versus time, and (d) trip signal versus time.
In the text

	Fig. 14 System performance during Inductive load switching.
In the text

	Fig. 15 System performance during capacitor switching, (a) frequency deviation versus time, (b) d-axis voltage versus time, (c) RCPABPSVAS versus time, and (d) trip signal versus time.
In the text

	Fig. 16 System performance during capacitor switching.
In the text

	Fig. 17 Performance comparison of proposed using existing system for 50 trials.
In the text

	Fig. 18 Performance comparison of proposed using existing system for 100 trials.
In the text

	Fig. 19 Analysis comparison of proposed using existing system for 150 trials.
In the text

	Fig. 20 Statistic evaluation of proposed using existing system through island for 50 trials.
In the text

	Fig. 21 Statistic evaluation of proposed using existing system through island for 100 trials.
In the text