1. Introduction
The demand for electrical energy is a useful tool for measurement in the economy of any country around the world. Energy demands have become more complex as a result of the rising standards of living worldwide. By 2050, the urban population is anticipated to rise from 55% to 69%, resulting in a massive energy demand [
1,
2]. Moreover, the energy sector’s continuous urbanization and growth has significantly increased the load on the electric grid, leading to frequent grid failures. All of these elements have paved the way to the installation of distributed generation (DG) systems, which will lessen the reliance on the utility grid [
3]. Hence, local energy-producing facilities based on renewable energy are added to the conventional central utility system [
4,
5]. Over the past several years, improvements in distributed generators (DGs) have been essential in addressing problems with traditional power system networks. A probable solution to the unavailability and exhaustion of fossil fuels, as well as to the rapid increase in electric load, environmental pollution, and the high costs of petroleum products and gases, may be found in the significant rise of DGs. A range of technological, governmental, and current issues in the conventional electric system have been successfully addressed by DGs [
6]. This ground-breaking technology has led to the replacement of the conventional electric power system with microgrids, which are low-voltage active distribution systems. A microgrid (MG) is a network of energy storage, distributed generation (DG), and various loads that can be managed by monitoring and protection systems. Circuit breakers are typically used at the point of common connection to link microgrids to the main grid on the distribution side (PCC). The MG is synchronized with the utility under normal operating conditions and will be disconnected from the utility grid and operate in an autonomous mode to meet high energy demands if it experiences any problems, such as voltage or frequency variations [
7]. The DG units in a microgrid have substantially less capacity than the enormous generators used in traditional systems; the MG is vulnerable to climate change due to its lower energy density and dependency on regional topographical considerations. Because of their proximity to consumers, they can supply electricity and heat loads with the proper voltage and frequency while minimizing transmission losses, preventing the power network from becoming congested. By keeping the lights on when the regular power source is available, they raise the technical standards, economic benefits, and environmental reliability of the current power system. These interruptions might cause significant changes in some system characteristics, which might result in instability in the power system. Therefore, it is important to identify and fix any disturbances as soon as possible to maintain the continuity of the power supply. Several utilities view the islanded operation mode of DG units as a feasible strategy to preserve continuity and reliability due to the significant diffusion of renewable energy resources (RES) in distribution systems. However, islanding operations require a quick, accurate, and economical islanding detection method, which has no impact on the supply’s quality. As a result, several islanding control mechanisms have been created and implemented on these DG units. According to IEEE Std. 1547-2003 [
8], islanding must be identified within 2 s of it taking place. The following are the literature works that have discussed the islanding techniques that are used in a microgrid system.
The authors of [
9] proposed a hybrid method for islanding detection to identify the islanding phenomenon in a distribution system. The proposed approach is a hybrid technique that combines a passive approach and a remote detection approach. The next stage is the proposal of an adaptive control method to guarantee the steady operation of islanded subsections. The proposed technique makes use of error rates for system parameters such as voltage and power to re-adjust generator controls and keep the system stable. In [
10], the researchers suggest a unique islanding detection approach based on an adaptive neuro-fuzzy inference system (ANFIS) that is integrated with various passive monitoring strategies. One of the objectives of this study is to minimize the negative effects of the islanding detection (IDT) approach on PQ, while preserving the detection accuracy and minimizing the non-detection zone (NDZ). The suggested method’s main component is data mining, which enables all necessary data to be obtained using relay metering sensors installed on the PCC. To create a decentralized IDT for numerous and hybrid DG-based microgrids, each DG connected at the PCC in [
11] injects a low-frequency disturbance signal through a d-axis current controller that is integrated with the suggested hybrid analysis technique. The suggested approach is capable of identifying island formation due to (1) individual DGs becoming isolated from the rest of the system, with or without a load, and (2) additional DGs becoming isolated from the grid with or without a load. The study in [
12] suggests a novel method for the quick identification of islanding events in a microgrid (MG). The suggested method consists of two steps, the first of which is to extract certain useful features from the voltage and current information. The discrete Fourier transform is used to examine these signals for the second harmonic termination (DFT). LSTM is a novel artificial intelligence method that uses a unique recurrent neural network structure. In [
13], a passive IDT based on the rate of change of frequency deviation technique is investigated within the MG under various levels of power imbalance. Moreover, [
14] demonstrates the phenomenon as quickly and accurately as possible using the rate of change of power technique based on the terminal voltage of a photovoltaic inverter. However, in [
15], the authors extracted electrical feature quantities that had a strong correlation with islanding detection. In addition, an islanding detection method based on CatBoost was proposed for an MG in this paper to effectively determine the thresholds of multiple electrical feature quantities and reduce the dead zone in the islanding detection process. The authors in [
16] used the superimposed angle of negative sequence impedance for the detection of islands in a reconfigurable system. The authors in [
17] used a combinatorial strategy combining various passive schemes in an attempt to reduce the detection time and the non-detection zone (NDZ). However, the authors in [
18] proposed a hybrid active and passive islanding technique. The method was used to obtain a solution for the NDZ by using fuzzy classifiers and applying a suitable active or passive method. An approach to unplanned island detection in a microgrid with a micro-phasor measurement unit is suggested in [
19]. To determine if an island or fault will develop, the unit extracts specific features from recorded voltage data utilizing the discrete fractional Fourier transform’s multi-domain nature.
From the literature, it is identified that the development of knowledge-based classifiers frequently relies on classification methods based on decision tree, Bayes classification, and SVM approaches. Deep learning methodologies are now most frequently used when creating classification algorithms. When there are enormous amounts of data accessible, these strategies are highly useful. However, gathering such information for educational purposes might be challenging. Thus, one of the best ways to visualize a decision in these situations is through a decision tree. When the next step in the decision-making process depends on the information analysis from previous steps, a decision tree can be interpreted as a representation of regular human reasoning. Moreover, studies in the literature have focused on implementing classification methods to determine islanding in single microgrid systems. Thus, by keeping these aspects in view, this paper proposes a decision-tree-based fuzzy controller for effective islanding detection with an improved transient response in a multi-microgrid system, which is formed by integrating two adjacent microgrids in an urban community.
The remainder of the article is structured as follows.
Section 2 presents the description of the system under study and also the modeling of the various constituent units of the system;
Section 3 discusses the proposed decision-tree-based fuzzy logic controller;
Section 4 presents a discussion of the simulation findings; and the conclusions are presented in
Section 5.
3. Proposed Decision-Tree-Based Fuzzy Logic (DT-FL) Controller
The proposed decision-tree-based fuzzy logic controller adopts a passive method by taking the data mining methodology into account for islanding detection in a multi-microgrid cluster. This process involves creating a straightforward and reliable fuzzy classifier with an initial decision tree for islanding detection. It becomes vital to address structural problems with the identification of classifier systems as a result of the complexity and dimensionality of the classification problems arising. The identification of the appropriate initial partition of the input domain and the choice of pertinent features are important considerations. Moreover, when the classifier is recognized as a component of an expert system, language interpretability is another crucial factor that needs to be taken into consideration. While the interpretability factor is frequently unnoticed, the first two aspects are frequently tackled through educated estimates. When the significance of each of these factors is understood, automatic data-based classification systems that are accurate, compact, and understandable may be identified.
The input space is divided into rectangles by DT-based classifiers, whereas fuzzy models produce non-axis parallel decision boundaries. Because of this, rule-based classifiers have more flexible decision bounds than crisp DTs, which is their main advantage. As a result, fuzzy classifiers may be easier to understand than DT classifiers. The suggested method is implemented mainly in two stages: (1) features are extracted in the first stage, and (2) a classification task is carried out in the second stage to detect islands. Hence, one of the crucial responsibilities associated with the suggested approach is feature selection. Thus, we have obtained the change in frequency deviation, change in voltage deviation, and rate of change in frequency at the point of common coupling of the MMG. The decision tree uses the extracted features as inputs to select the most important aspects that contribute to the decision-making process and the initial categorization limits. Trapezoidal fuzzy membership functions are generated from the DT classification boundaries of the most significant features, and a corresponding rule base is formed for classification. However, depending on the similarity measure, certain fuzzy MFs are combined, which lowers the overall number of fuzzy MFs. A streamlined fuzzy rule basis for islanding detection is created from the fuzzy MFs that have been decreased in size. A DT is a high-dimensional classifier DT, in which each branch of the tree indicates the result of a test, while each internal node evaluates the usefulness of a predictor. The leaf nodes, also known as the ending nodes, reflect the classification. The classification problem’s dimension is indicated by how many predictors are utilized. The confidence in the decision is connected to each decision (tree leaf). In simple terms, this is the ratio of the specific class to all the other classes in the dataset for a given node [
22].
A robust, accessible data mining and analysis workbench called “Insightful Miner” enables enterprises to provide tailored predictive intelligence whenever required. Its user-friendly interface was created with statisticians and business analysts, who lack specialist programming skills, in mind. With Insightful Miner, one can identify the solutions that one needs to tackle particular business problems quickly and effortlessly and share one’s findings with one’s colleagues throughout the company. Insightful Miner performs better in this scenario by offering a strong statistical analysis and visualization capacity, as typical data mining tools become less and less effective as the data sets grow in size. Hence, for the suggested study, this has been chosen to develop the DT structure. The most relevant characteristics that are used in the decision-making process are produced by the DT analysis using the best splitting setting, which includes the extracted features at the PCC. In this study, a total of 11 features are extracted at the PCC of the multi-microgrid system, which are given in
Table 4. However, in the end, the classification tree shown in
Figure 5 is developed using only three features. As a result, DT only gives information on the three most important features that influence the decision making, rendering the remaining eight features superfluous. Fuzzy membership functions are created from the categorization boundaries of the most significant characteristics produced by DT and used in the fuzzy rule basis for islanding.
After obtaining the DT’s partition boundaries from the classification, we create fuzzy membership functions and the DT is converted into a fuzzy rule base. Rectangular MFs are created for each independent variable from the DT boundaries. The process of fuzzification replaces a numerical attribute
with a fuzzy attribute
(
k = 1, 2, 3 …
i) described by
linguistic terms. We refer to these linguistic concepts as fuzzy sets. As the numerical attribute values are defined as a vector of real numeric values, we have ‘
M’ instances of these values
. Each
numerical value of this vector
is fuzzified into membership degrees of
linguistic terms. As a result, these values of the membership function of each
linguistic concept define the value of each instance of the fuzzy attribute. Thus, the
linguistic term of
is designated as
. Fuzzy set
with respect to
is defined by a membership function
. Formally, a fuzzy set
is described in terms of a pair of sets given by
[
23]. The DT output obtained from the aforementioned DT-fuzzy transformation method is changed into the corresponding fuzzy rule base. Three input parameters extracted from the PCC of the MMG cluster are designated as ‘X
1’, which is a change in frequency deviation, ‘X
2’, which is a change in voltage deviation, and ‘X
3’, which is the rate of change in the frequency deviation. For islanding detection, the categorization borders are determined based on the values of the above three variables, as mentioned in
Appendix A. The contour plot of the input parameters extracted at the PCC of the system considered for testing and the output parameter is shown in
Figure 6.
The developed membership functions for X
1 are (P
1, P
2), for X
2 are (Q
1, Q
2, Q
3), and for X
3 are (R
1, R
2). Rectangular shapes characterize the fuzzy MFs produced by the DT classification boundaries. However, the rectangular borders are somewhat warped by heuristic adjustment, which adds fuzziness to the membership functions. Following tests on numerous values in the vicinity of the starting values produced from the DT, the coordinates of the trapezoidal fuzzy MFs are adopted. The fuzzy membership function plots of the input and output variables are shown in
Figure 7. The flow chart implementation for the proposed DT-based fuzzy logic controller is shown in
Figure 8.
The corresponding fuzzy rules are formed as follows.
- –
Rule 1: if X1 is P1 and X2 is Q2, then an island occurs.
- –
Rule 2: if X1 is P2 and X2 is Q3, then an island occurs.
- –
Rule 3: if X1 is P2 and X2 is Q1 and X3 is R1, then an island occurs.
- –
Rule 4: if X1 is P2 and X2 is Q1 and X3 is R2, then no island occurs.