Advanced Deep Learning Based Predictive Maintenance of DC Microgrids: Correlative Analysis

Abstract

This paper presents advanced frameworks for microgrid predictive maintenance by performing a comprehensive correlative analysis of advanced recurrent neural network (RNN) architectures, i.e., RNNs, Long Short-Term Memory (LSTM), and Gated Recurrent Units (GRUs) for photovoltaic (PV) based DC microgrids (MGs). Key contributions of this analysis are development of advanced architectures based on RNN, GRU and LSTM, their correlative performance analysis, and integrating adaptive threshold technique with the algorithms to detect faulty operations of inverters which is indispensable for ensuring the reliability and sustainability of distributed energy resources (DERs) in modern MG systems. The proposed models are trained and evaluated with a dataset of diverse real-world operational scenarios and environmental conditions. Moreover, the performances of those advanced models have been compared with the conventional RNN-based techniques. The achieved decremental MAE scores from 12.102 (advanced RNN) to 10.182 (advanced GRU) to 8.263 (advanced LSTM) and incremental R² scores from 0.941 (advanced RNN) to 0.958 (advanced GRU), and finally to 0.971 (advanced LSTM) demonstrate strong predictive capabilities of all, while the proposed advanced LSTM method outperforming other counterparts. This study can contribute to the emerging technology for predictive maintenance of MGs and provide significant insights into the modeling and performance of RNN architectures for improving fault detection in MG systems. The findings can have noteworthy implications to enhance the efficiency and resilience in MG systems, thereby evolving the renewable energy technologies in power sector and contributing to the sustainable and greener energy landscape.

1. Introduction

The modern energy landscape is experiencing a profound transformation, following an unprecedented shift towards sustainability with the unification of renewable energy sources (RES) into power systems at present. In this dynamic context, DC microgrids are emerging as a pivotal advancement in this modern energy infrastructure, providing an efficient platform towards the seamless integration of these large number of RES and loads within the broader network of AC grids [1]. These DC microgrid (MG) systems can play a significant role in achieving technological innovation in power systems with promising improvements in terms of energy resiliency, efficiency as well as economic viability [2,3].

Remarkably, the appeal of DC microgrids is increasing for their unique features, including improved efficiency, reduced losses and immunity to the harmonics and synchronization issues frequently plaguing AC grids [4,5]. The ability to overcome these limitations places DC microgrids at the forefront of this evolving energy paradigm, offering a versatile resolution in the context of the integration of distributed energy resources (DERs) to facilitate the transition towards sustainable, resilient power systems. Solar photovoltaic (SPV) systems stand out in this context as an outstanding generation source within the spectrum of RES by contributing to the evolution of MG systems through harnessing the abundant, clean, and renewable energy from the sun [4,6]. The scalability and cost-effectiveness of SPV generations have fuelled its recent widespread deployment, placing it a top role in the global push towards the renewable energy adoption. Nevertheless, the variable and intermittent attribute of solar energy, influenced by diverse factors like solar irradiation and ambient temperature, brings many inherent challenges, mainly in terms of maintaining the stability of the power output from these SPVs into MG systems.

Machine learning (ML) methods have emerged as a powerful tool in recent times in order to detect and respond to different types of power system faults, offering the potential of enhancing predictive maintenance and upgrading the resilience of the MG system. The application of ML-based data-driven [7] predictive maintenance models is getting widely adopted by different industries such as healthcare [8], transportation [9], and manufacturing [10,11]. Nevertheless, its implementation on MG systems is still a relatively new area which requires further exploration.

Besides, most of the latest researched areas regarding MG are based on energy management [12], and economic dispatching [13]. Study has been conducted by [14] on MG digital twin focused on the energy management of MG. Another work [15] explored the MG challenges regarding cyber attack detection. Study conducted in [16] investigated digital twin technology for the capacity estimation of battery energy storage of MGs. A convolutional-LSTM based model has been explored in [17] for predicting the voltage stability of MG. Research conducted by [18] discussed various DERs scheduling issues on MG, Monte Carlo simulation integrated genetic algorithm technique based on sensor networks has been investigated in [19] for MG risk assessment, and [20] explored different experimental platforms for the energy management of hydrogen-based microgrids.

A protection technique for low-voltage AC MG based on voltage sags, current magnitudes as well as direction of active power flow was proposed in [21] using MATLAB/Simulink platform, which shown a good performance specifically for low impedance faults. Another study [22] explored high and low resistance DC faults based on the relay ground current and inductor voltage for low-voltage MG network using PSCAD/EMTDC platform. In addition, ref. [23] investigated a protection strategy for islanded MG incorporating short-circuit fault identification using PSCAD/EMTDC platform. Study conducted in [24] investigated MG fault identification under both high and low impedance operating conditions based on power quality control technique using PSCAD/EMTDC platform. There are limited studies based on advanced ML techniques for MG predictive maintenance specifically on fault detection of MG inverters in the present literature.

Recently, the susceptibility to anomalies within the power system escalates as MG architectures have become more complex by integrating diverse DERs and inverters. Inverters, functioning as the essential components of MG systems, play an utmost role in terms of converting the DC power generated by RES into AC power compatible with grid integration as well as end-user consumption. Anomalies or faults, characterized by the deviations from the expected or normal measurements, can manifest because of various factors such as inverter faults, load fluctuations, or system oscillations. The detection of faults has become vital for ensuring safe and resilient power supply [25,26]. For ensuring uninterrupted and reliable energy flow, developing advanced ML-based predictive model focusing on inverter fault detection for MG applications has become crucial.

Besides, deep learning (DL) methods are gaining a great attention in recent times [27]. Having powerful feature vectors with higher dimension and deeper network structure, DL-based architectures can be excellent avenue for predictive analytics-based fault detection applications compared with traditional ML techniques. Because, the learning algorithms of traditional artificial neural networks (ANN)-based techniques converge slowly and in terms of fault detection, these traditional techniques have poor interpretability [28]. Motivated by the enormous potential of DL in the realm of MG operations, this study explores the application of advanced recurrent neural network (RNN) based DL architectures as well as their comparative performances in order to identify anomalies from the power signals of DC microgrid inverters. The goal of this work lies in providing a comprehensive correlative analysis of these methods, illuminating their respective strengths in terms of MG predictive analytics based fault detection. The contributions of this paper are threefold through the following key points:

• ▪. Advanced DL-based PdM algorithms for MG: For identifying microgrid inverter anomalies under different real-world exogenous factors, three advanced architectures based on RNN, GRU and LSTM have been presented in this article. The loss function of the advanced algorithms has been leveraged for optimizing the error rates which enhances the generalizability of the algorithms and capabilities of capturing both short and long term temporal dependencies from the complex MG data-points. The adaptability of those techniques to the changing patterns of inverter power signals gets increased consequently. As a result, the overall efficacy of the anomaly detection algorithms gets enhanced.

• ▪. Advanced RNN-based correlative analysis: In the context of MG inverter fault detection, a correlative study among advanced RNN-based DL architectures has been introduced in this research work. For capturing the temporal dependencies as well as patterns in the inverter data-points, each of the advanced DL architectures has been leveraged, providing a comprehensive evaluation of the performances of the implemented and conventional approaches in terms of identifying anomalies from MG inverter data.

• ▪. Adaptive threshold integration: An adaptive threshold-integrated anomaly detection procedure has been implemented with the advanced DL architectures. Based on the statistical properties of the prediction errors of the deployed DL architectures, the threshold level gets adjusted by the proposed technique. Consequently, the sensitivity to anomalies of those models gets enhanced, which enables an efficient detection of deviations from the MG inverter power signals.

The following presents the remaining structure of this work. Section 2 describes the problem statement. Methodology of this study has been presented in Section 3. Section 4 describes the findings with simulation results. The discussion with a correlative analysis of the results has been presented in Section 5. Finally, the article has been concluded in Section 6 with remarks.

2. Problem Statement

A new era has emerged in the spectrum of sustainable energy through the rapid adoption of RES into MG systems specifically by the promising SPVs as the DER. Nevertheless, this magnificent transformation in power systems comes with challenges. Specifically, for ensuring the resilient and efficient power generation and distribution through MGs which are equipped with [29] diverse inverter-based resources (IBRs), it is crucial to monitor the inverter performances through anomaly detection. Figure 1 depicts the overview of a DC MG system possessing battery energy storage systems (BESS), some local loads, and SPVs as the DER.

One of the key challenges of the MG’s DERs specifically SPVs is the inherent highly dependency on environmental aspects like ambient temperature and irradiation. Any fluctuations impacting by these aspects may cause faults or anomalies in terms of the AC output power yielded from the inverters. Besides, different system complexities and load fluctuations can amplify the possibilities of anomalies. To ensure the stability of the system and prevent any unexpected power losses, maintaining the operational efficacy and reliability of MG inverters is significant. Consequently, to enhance the longevity and stable operation of MG architectures, the significance of detecting these inverter anomalies effectively is paramount.

For addressing these exclusive challenges risen through the dynamic nature of modern MG systems, the conventional techniques are not effective enough to identify MG inverter anomalies proactively for maintaining the system performance and reducing downtime. Conventional techniques are not capable of adapting to diverse fault scenarios and evolving conditions in case of real-world modern MG scenarios [30]. The overall system efficiency and power quality are directly impacted by these inverter performances within the MG network. Anomalies or faults encountered in MG inverters can be identified by analyzing the fluctuation patterns of the AC power, that are influenced greatly by few factors.

The non-linear power characteristics of SPVs, and temporal dependencies are the most critical factors. Consequently, the inverter output AC power is dynamic, which is highly influenced by time-series dependencies such as variations in the temperature and irradiation patterns. Conventional techniques [31] might not be able to identify the intricate temporal dependencies and external factors present in modern MG networks and might not be effective enough without explicit domain knowledge. These limitations emphasize the modeling of more advanced techniques that possess adaptive detection capabilities along with addressing these nuanced patterns in the MG inverter performances.

Having inherent memory capabilities, advanced techniques based on RNN, GRU, and LSTM can be tailored to learn these complex temporal dependencies. Nevertheless, the implementation of these models for correlative performance analysis in PdM applications for DC microgrids still remains unexplored. For identifying the intricacies encountered in terms of MG inverter fault detection, the integration of advanced RNN-based DL architectures such as RNN, GRU, and LSTM can be a promising avenue. Moreover, there is no recent study of comprehensive comparative analysis focused on these DL techniques in the context of fault detection scenarios of MG inverters in the present literature. Furthermore, study [32] describes that in terms of power grid applications, the performance comparisons of LSTM and GRU architectures are still an unexplored research area.

By exploring an in-depth analysis focused on the advanced RNN-based fault detection architectures, this study aims to bridge this gap. This research work focuses on evaluating the efficacies of the advanced RNN-based DL architectures, compared with the conventional methods in the context of fault detection scenarios of MG inverters under different operational conditions through implementing real-world data. The findings from this research work can provide significant insights regarding the pros and cons of the techniques which can pave the way for developing advanced maintenance strategies in future for the continuation of more resilient and efficient evolution of DC microgrid systems.

In this advanced RNN, GRU, and LSTM-based correlative analysis, the critical environmental factors that affect the output AC power from inverters have been utilized in the feature vector $X\left(t\right)$ for modeling these algorithms where $I_{irr}\left(t\right),T_m\left(t\right),T_a\left(t\right),$ and $P_{AC}\left(t\right)$ represent the irradiance, module, ambient temperatures, and AC power respectively:

(1)$X\left(t\right)=[I_{irr}\left(t\right),T_m\left(t\right),T_a\left(t\right),P_{AC}\left(t\right)]$

For identifying the temporal dependencies properly, the historical patterns of the vector have been fed into the algorithms:

(2)$\mathbf{X}=\left[X\right(t),X(t-1),X(t-2),\dots ,X(t-n\left)\right]$

The predicted output power ($A{C}_{\mathrm{Predicted}}$) has been modeled by implementing the advanced RNN, GRU, and LSTM algorithms according to the following equation where f is the learning function for the temporal sequence and ${\theta }_t$ indicates the optimized model parameters of the advanced algorithms.

(3)$A{C}_{\mathrm{Predicted}}\left(t\right)=f(\mathbf{X};{\theta }_t)$

3. Proposed Methodology

A brief overview on the utilized data set and data processing for this study, proposed advanced RNN-based DL architectures: RNN, GRU, and LSTM integrated with an adaptive threshold-based approach has been introduced in this section to identify anomalies from the DC microgrid inverters. Figure 2 illustrates the proposed structure of the advanced DL based correlative analysis on MG inverter fault detection.

3.1. Data Set

A real-world dataset incorporating a DC microgrid has been implemented for this comparative study. The data had been collected for 30 days from December 2022 to January 2023 with timestamp of 15 min interval. Reflecting the intrinsic challenges in real world scenarios, this dataset comprises diverse operational conditions. Capturing the dynamics of a complex real world DC MG, key attributes of environmental parameters such as irradiation (W/m²), ambient and module temperatures (°C), and electrical parameters such as produced DC power (kW) from the DER and converted AC power (kW) from the inverters had been recorded.

Python programming language has been implemented for this correlative analysis. Python 3.10, Intel Core i7-1185G7 (Santa Clara, CA, USA), 3.00 GHz processor on 11th Gen machine with 16 GB RAM, 64-bit OS with kernel version 22H2 and build 19045.5487 specifications have been used while developing the algorithms. Different Python libraries and frameworks like Pandas, Matplotlib, TensorFlow, scikit-learn, NumPy, and Keras have been utilized, which enabled tasks like data cleaning, data visualization, statistical analysis, and model building and implementation.

3.2. Data Processing

For improving the performance of the algorithms, it is crucial to choose the most important features from the data [33]. For finding the most significant features from this dataset, a statistical technique has been implemented. For calculating the linear associations among various features within the dataset, the correlation analysis has been performed. The correlation coefficient (${\gamma }_{RZ}$), indicating the linear association between two features R and Z, has been enumerated using the following equation:

(4)${\gamma }_{RZ}={\displaystyle \frac{\sum (R_i-\overline{R})(Z_i-\overline{Z})}{\sqrt{\sum {(R_i-\overline{R})}^2\sum {(Z_i-\overline{Z})}^2}}}$

Here, $R_i$ and $Z_i$ indicate the individual data points of features R and Z, $\overline{R}$ and $\overline{Z}$ denote the means of R and Z respectively.

The correlations (${\gamma }_{XY}$) from each pair of features X and Y from the dataset have been computed. This analysis helps find the redundant features from dataset. A high positive value ($\gamma \approx 1$) indicates a high linear association between the features. Figure 3 illustrates the correlation (${\gamma }_{XY}$) coefficients among each pair of features. From the figure, it can be seen that (${\gamma }_{\mathrm{DC},\mathrm{AC}}=1$), which indicates the strongest positive correlation between the features AC and DC powers. As a result, the DC power feature has been omitted during model training. This helps reduce the complexity by improving the model interpretability as well as performance while minimizing multi-collinearity.

After this, data with the selected features has been prepared for training the advanced DL models as can be seen from Algorithm 1. Data (X) was scaled and then divided into sequences (T) with test size ($T_s$).    

Algorithm 1: Data Preparation for the Advanced DL Algorithms

Input: $X,T,T_s$ Output: $X_{\mathrm{Train}}$, $X_{\mathrm{Valid}}$, $X_{\mathrm{Test}}$ 1. $ScaleData:X_{\mathrm{Scaled}}\to (X-X_{\min })/(X_{\max }-X_{\min })$ 2. $DivideintoSequences\to X_{\mathrm{Seq}}$ 3. $X_{\mathrm{Seq}}\leftarrow [X_{\mathrm{Scaled}}[i:i+T]$ for i in range $(length\left(X_{\mathrm{Scaled}}\right)-T+1)]$ 4. $Splitinto\to X_{\mathrm{Train}},X_{\mathrm{Valid}},X_{\mathrm{Test}}$ 5. $X_{\mathrm{Train}},X_{\mathrm{Valid}},X_{\mathrm{Test}}\to Train.Test.Split(X_{\mathrm{Seq}}$, Ts = 0.2)

3.3. Advanced RNN Architecture

RNN is a type of DL architecture which includes internal memories that enable capturing the sequential dependencies from the data through recurrent connections. Temporal orders of the input sequences are considered in the RNN architectures, enabling them to be a suitable candidate for processing sequential information [34]. In the context of anomaly detection in MG inverters, an advanced RNN architecture has been leveraged in this study for predicting the deviations from the AC power signals.

Figure 4 illustrates the internal architecture of the implemented advanced RNN model for the MG inverter fault detection. The equation for the implemented advanced RNN algorithm integrated with ReLU activation function is:

(5)$H_t=\mathrm{ReLU}(M_{ih}·X_t+M_{hh}·H_{t-1}+b_h)$

Here, for the time step t, the input and the updated hidden state are indicated by $X_t$, and $H_t$ respectively. Previous hidden state is represented by $H_{t-1}$ for the time step ($t-1$). Hidden layer bias is $b_h$, and the utilized weight matrices are denoted by $M_{ih}$ and $M_{hh}$ for input-to-hidden and hidden-to-hidden layers, respectively. ReLU indicates the rectified linear unit activation function implemented in the algorithm. $Y_t$ indicates the model output at the time step t as follows:

(6)$Y_t=H_t$

3.4. Advanced LSTM Architecture

LSTM technique can be an excellent approach in the context of MG inverter fault detection. This is a version of neural network which is connected to RNN family. Having a number of layers for processing each time step, LSTM architectures have proven to be more efficient than the traditional RNNs [35]. LSTM is capable of retaining long-term dependencies of data from many time steps before, making it well-suited for time-series data like inverter power analysis. Figure 5 illustrates the internal architecture of the implemented advanced LSTM model for the MG inverter fault detection.

Here, at each time step t, the input $\left(x_t\right)$ and hidden state $\left(h_{t-1}\right)$ get processed by the advanced LSTM cell from previous time state to generate a new hidden state $\left(h_t\right)$. The forget, input, and output gates are responsible for deciding what information to discard or retain from previous hidden state $\left(h_{t-1}\right)$ as well as the current input. Forget gate $\left(f_t\right)$ decides what information to drop from previous hidden state, while input gate $\left(i_t\right)$ and the candidate cell state ${\tilde{C}}_t$ determine which new information to add to the current hidden state. Corresponding equations utilized for this advanced LSTM architecture are described as follows:

(7)$f_t={\sigma }_1(M_f[h_{t-1},x_t]+b_f)$

Here, $h_{t-1}$ denotes the output in time step $(t-1)$, $M_f$ and $b_f$ represent the weight matrix and the bias, and ${\sigma }_1$ indicates the sigmoid activation function.

(8)$i_t={\sigma }_2(M_i[h_{t-1},x_t]+b_i)$

Here, $(M_i,b_i)$ denote the weight matrix and the bias.

(9)${\tilde{C}}_t=tanh(M_c[h_{t-1},x_t]+b_c)$

Here, for the candidate cell state, $(M_c,b_c)$ indicate the weight matrix and the bias, and tanh is the hyperbolic tangent activation function.

(10)$C_t=f_t{C}_{t-1}+i_t{\tilde{C}}_t$

Here, $C_{t-1}$ indicates the previous cell state.

In these equations, ${\sigma }_i$ represents sigmoid activation function, $(M,b)$ represent the weight matrix and the bias respectively, for the corresponding gates and state. Finally, which information to process from current cell state gets determined by the output gate $\left(y_t\right)$, and the next hidden state $\left(h_t\right)$ is computed by multiplying the cell state passed through the tanh activation function and the output gate. The corresponding equations of the output and next hidden state $\left(h_t\right)$ of this advanced LSTM layer are as follows:

(11)$y_t={\sigma }_3(M_y[h_{t-1},x_t]+b_y)$

(12)$h_t=y_{t}tanh\left(C_t\right)$

3.5. Advanced GRU Architecture

GRU is a part of RNN and variant of LSTM architecture. In the context of MG inverter fault detection, GRU is capable of both capturing long-term dependencies and addressing gradient vanishing issues. Moreover, in terms of processing smaller dataset, GRU could be a more appropriate technique than LSTM which has been reported in the study conducted in [36]. Figure 6 illustrates the basic structure of the proposed advanced GRU architecure which has been leveraged for detecting the MG inverter faulty operations. For governing the model operations, this advanced GRU architecture possesses a number of equations as well as parameters which have been defined as follows:

(13)$U_t={\sigma }_u(M_u·[H_{t-1},X_t]+b_u)$

(14)$R_t={\sigma }_r(M_r·[H_{t-1},X_t]+b_r)$

(15)${\tilde{H}}_t=\tan \mathrm{h}(M_h·[R_t·H_{t-1},X_t]+b_h)$

(16)$H_t=(1-U_t)·H_{t-1}+U_t·{\tilde{H}}_t$

(17)$Y_t={\sigma }_o(M_o·H_t+b_o)$

Here, for time step t, $X_t$ and $Y_t$ indicate the input and output vectors; the update and reset gates, candidate and latest hidden states are represented by $U_t$, $R_t$, and ${\tilde{H}}_t$, $H_t$, respectively; ${\sigma }_i$ denotes the sigmoid activation function; $H_{t-1}$ denotes the previous hidden state obtained from the previous time step ($t-1$); the vector concatenation between $H_{t-1}$ and $X_t$ has been indicated through $[H_{t-1},X_t]$; $b_u,b_r,b_h,b_o$ are the corresponding bias vectors, and $M_u,M_r,M_h,M_o$ are the respective weight matrices for update and reset gates, hidden state of candidate and the output.

3.6. Adaptive Optimization of Error

For training the learning parameters of the implemented advanced DL architectures, adaptive stochastic techniques can be outstanding solutions. This can be computationally effective optimization technique [37] with less memory requirements for finding the optimal points and can be core of various engineering applications. An adaptive stochastic optimization technique has been implemented in the advanced DL algorithms for optimizing the error functions. It adapts the learning rates for each parameter during training, providing an effective optimization strategy in scenarios with changing data distributions or model parameters.

In mathematical terms, the adaptive learning rates are calculated using two moving averages: exponentially decaying averages of both past gradients ($d_t$) and past squared gradients ($r_t$). The decay rates regarding these moving averages get controlled by the parameters ${\alpha }_1$ and ${\alpha }_2$. The model parameters ($\theta$) of this adaptive stochastic technique are then updated based on the following equations:

(18)$d_t={\alpha }_1·d_{t-1}+(1-{\alpha }_1)·L_t$

(19)$r_t={\alpha }_2·r_{t-1}+(1-{\alpha }_2)·L_t^2$

Here, the gradient of the loss at time step t is represented by $L_t$ with respect to the parameters. After that, the moving averages get bias-corrected through the following implemented equations:

(20)${\widehat{d}}_t={\displaystyle \frac{d_t}{1-{\alpha }_1^t}}$

(21)${\widehat{r}}_t={\displaystyle \frac{r_t}{1-{\alpha }_2^t}}$

Here, ${\alpha }_1^t$ and ${\alpha }_2^t$ are the bias-corrected parameters. The model parameters then get updated finally using the following equation:

(22)${\theta }_t={\theta }_{t-1}-{\displaystyle \frac{\eta }{\sqrt{{\widehat{r}}_t}+ϵ}}·{\widehat{d}}_t$

Here, the learning rate is indicated by $\eta$, and for preventing the division by zero, a small constant has been applied which is denoted by $ϵ$.

3.7. Adaptive Threshold for MG Fault Detection

In this work, a scenario has been considered where $S_c$ denotes the differences between real AC power ($A{C}_{\mathrm{Real}}$) and the predicted output ($A{C}_{\mathrm{Predicted}}$) as follows:

(23)$S_c=\left|A{C}_{\mathrm{Real}}-A{C}_{\mathrm{Predicted}}\right|$

An adaptive threshold ($T_h$) based anomaly detection procedure has been implemented which can be enumerated based on the statistical analysis of $S_c$. The mean and standard deviation of $S_c$ have been utilized to identify the anomalous data points from the AC signal as follows:

(24)$T_h=\mu +k·\sigma$

Here, $\mu$, and $\sigma$ indicate the mean and standard deviation of $S_c$, respectively; k is a constant regarding the sensitivity of $T_h$. With the $T_h$ value enumerated, faults can be detected based on whether the $S_c$ value of the AC signal exceed this adaptive threshold point by the following equation:

(25)$\mathrm{Fault}=\left\{\begin{array}{cc}1\hfill & \mathrm{if}{S}_c>T_h\hfill \\ 0\hfill & \mathrm{Normal}\hfill \end{array}\right.$

This adaptive threshold approach allows for a dynamic identification of anomalies based on the statistical properties of the prediction errors. It’s crucial to fine-tune the value of k based on the characteristics of the implemented data and the algorithm parameters.

4. Results

In this section, the process of model training, compilation as well as evaluation for this study have been discussed briefly with results.

4.1. Model Training

This step includes feeding the training data to the advanced DL algorithms as well as updating the parameters iteratively till the DL architectures converge to minimum error. For all the models, 100 epochs with batch size 10 have been utilized. To handle the overfitting issue, a 0.2 validation split was employed, allocating 20% of the training data for validation purposes during model training and enhancing the generalizability of the advanced algorithms to new data.

Figure 7 depicts the training and validation of the DL architectures capturing the differences between model predictions and real values. A significant decrease of errors can be observed through the adaptive stochastic optization of the error functions from Figure 7a for advanced RNN, Figure 7b for advanced GRU, and Figure 7c for advanced LSTM after several epochs (x-axis). The trained architectures are then implemented in model compilation for detecting MG inverter faults from the real AC signal.

4.2. Model Compilation and Evaluation

The implemented advanced RNN, LSTM, and GRU architectures are guided into the parameter space efficiently by the implemented adaptive stochastic optimization technique which helps to achieve an enhanced adaptability to changing patterns of inverter’s AC power signals during fault detection. For identifying the anomalous points from the inverter’s AC output power, the proposed adaptive threshold technique is implemented. Figure 8 illustrates the identification of the anomalous data points by integrating the adaptive threshold technique by the algorithm for each of the advanced DL architectures between the actual and predicted AC power. The red, black, and purple pentagrams from Figure 8a, Figure 8b and Figure 8c indicate the identification of probable anomalous data points by integrating the adaptive threshold technique with advanced RNN, GRU, and LSTM, respectively.

The threshold levels of the implemented advanced DL frameworks get adjusted dynamically based on the statistical properties of the optimized prediction errors of the DL architectures. The highlighted stars are the potential anomalous data points from the real AC power signal identified by the advanced algorithms based on the adaptive threshold. The threshold lines can be seen at different positions that were adjusted dynamically by the algorithms. In Figure 8a, for the advanced RNN model, the dynamic threshold (black line) is lower than the advanced LSTM and GRU models. Hence, it captured more data points to be faulty on 22, 24, 30 and 31 December which have been highlighted in red stars by the algorithm. In Figure 8b, for the advanced GRU model, the threshold (green line) is a bit higher than the advanced RNN model and it identified a bit less data points than the advanced RNN model but a bit more data points than the advanced LSTM model to be faulty (highlighted black stars) on 22, 24 and 31 December. In Figure 8c, for the advanced LSTM model, the threshold (black line) had been adjusted by the algorithm dynamically at a bit higher point than the advanced RNN and GRU models, and identified a bit less data points from the real AC power signal to be faulty (highlighted purple stars) on 22, 24 and 31 December than other counterparts.

Figure 9 and Figure 10 illustrate the detected inverter faults from the proposed advanced and traditional DL methods, respectively. The red, black, and purple circles from Figure 9 and Figure 10 indicate the detected inverter faults from the proposed advanced RNN (Figure 9a), advanced GRU (Figure 9b), advanced LSTM (Figure 9c), and conventional RNN (Figure 10a), conventional GRU (Figure 10b), and conventional LSTM (Figure 10c), respectively. For the adaptive threshold integration, the sensitivity to anomalies of those models becomes enhanced, enabling efficient detection of deviations from the MG inverter power signals. The models identified the faults denoted by dotted points which were encountered on 22, 24, and 31 December, 2022 from the dataset.

For evaluating the performances of the implemented DL methods, the R-squared (R²) and mean absolute error (MAE) matrices have been utilized for this analysis. The matrices have been enumerated through the following equations:

(26)$R^2=1-{\displaystyle \frac{{\sum }_{i=1}^N{(Y_i-{\widehat{Y}}_i)}^2}{{\sum }_{i=1}^N{(Y_i-\overline{Y})}^2}}$

(27)$MAE={\displaystyle \frac{1}{N}}\sum _{i=1}^N|Y_i-{\widehat{Y}}_i|$

Here, N indicates the total number of samples; $Y_i$, and ${\widehat{Y}}_i$ denote the real values from the AC signal and the predicted values by the models, respectively; $\overline{Y}$ indicates the mean of the real values.

5. Discussion

The implemented advanced DL techniques shown better performances than the conventional methods in terms of detecting MG inverter anomalies. Each of the implemented architectures went through a careful training and evaluation. The developed advanced LSTM architecture demonstrated a correlative superiority over other methods in terms of both prediction accuracy and deviation from real values. The proposed advanced LSTM, GRU, and RNN model achieved R² scores of 0.971, 0.958, and 0.941, MAE scores of 8.263, 10.182, and 12.102, respectively; whereas the traditional LSTM, GRU, and RNN methods achieved R² scores of 0.949, 0.937, and 0.911, MAE scores of 11.847, 12.545, and 15.188, respectively. Table 1 enlists the performances of the DL architectures in terms of detecting MG inverter faults. The findings from here demonstrate a progressive correlative improvement from conventional to developed advanced RNN to GRU and LSTM method in the context of error reduction as well as prediction accuracy.

A satisfactory performance was achieved from the advanced RNN method with R² score of 0.941 and MAE scores of 12.102. Nevertheless, it possesses some limitations while capturing long-term dependencies from the sequential MG data. Because of less capability of tackling gradient vanishing issues than other two counterparts while processing long sequences, it’s performance was affected when retaining and compiling long-term dependencies from the MG inverter power signals. This resonates with the need for models that have improved memory capabilities and possess better capturing capabilities of temporal patterns, which are very significant in terms of discerning subtle deviations from the output AC power trends with respect to the external factors.

Having capabilities of handling gradient vanishing issues, the advanced GRU architecture provided better performance of a higher R² value: 0.958 and lower MAE: 10.182 than the advanced RNN and traditional LSTM, GRU, and RNN methods. This enhanced performance was achieved through the architectural improvement with two gating mechanisms for an enhanced regulation of information flow. The relevant past information regarding irradiation, temperature variations, and output AC power were retained whereas the redundant data were discarded through the update gate. Consequently, the sequential temporal dependencies of the MG inverter power outputs with complex environmental factors were better processed by this method. With a better capturing capability of temporal dependencies in the time series data, this model can be more efficient in the context of MG fault detection.

The advanced LSTM method outperformed with the lowest MAE: 8.263 and highest R² value: 0.971, compared to other DL counterparts. Advanced LSTM architecture incorporated gating mechanisms as well as cell states, allowing most enhanced memory retention and discarding of redundant information. The inherent gradient vanishing problem of standard RNN was handled by the cell state mechanism through retaining the long-term dependencies into the model. Consequently, the significant historical patterns which impact the output AC power with variations due to environmental factors like irradiance, temperatures were better preserved than other methods. This allows an enhanced reduction of noise sensitivity as well as output AC power fluctuations which can be caused by external factors or transient faults. As a result, this method was capable of differentiating between normal deviations in power generation with the external factors and real anomalies more precisely, enhancing the predictive maintenance capabilities thereby.

In the context of predictive maintenance, a lower MAE score demonstrates more precise identification of anomalies, indicating reduction of both false negatives which cause missed faults and false positives which cause unnecessary maintenance triggers. The advanced LSTM algorithm outperformed other counterparts with the lowest MAE. Besides, the incremental enhancement of R² scores from 0.941 (advanced RNN) to 0.958 (advanced GRU) to 0.971 demonstrates that the advanced LSTM model is more accurate than other DL methods in terms of modeling intricate temporal dependencies from the MG inverter performance with respect to the external factors. From the correlative performance analysis, it can be said that the advanced LSTM algorithm can be more robust with the capabilities of capturing both short and long-term dependencies from the complex datapoints for identifying anomalies in MG applications to minimize unexpected failure risks and ensure consistent power flow through the MG network to improve overall system efficiency and stability.

6. Conclusions

This correlative study advances the DL-based avenues for the inverter fault detection in microgrid applications by conducting a comprehensive correlative performance analysis on advanced and conventional RNN, GRU, and LSTM architectures. The proposed adaptive threshold-based technique enhanced the performance of the anomaly detection algorithms through adjusting the threshold point dynamically. Both adaptability of the model to changing patterns and training efficacy were improved through the implementation of adaptive stochastic optimization technique. The achieved incremental enhancement of R² scores from 0.941 (advanced RNN) to 0.958 (advanced GRU), and finally to 0.971 (advanced LSTM) suggest that the advanced LSTM model is more accurate and robust than other counterparts in minimizing prediction errors while processing intricate temporal dependencies from the MG inverter power signals with respect to complex environmental factors. The applicability of these DL methods is promising, but still has challenges in terms of generalization through diverse MG scenarios for an enhanced malfunction diagnosis to improve overall MG energy efficiency by minimizing downtime. Besides, some limitations of this research consist of computational complexity, data dependency as DL architectures highly depend on historical high-quality data and in the case of missing values or inconsistencies in the data set the prediction accuracies can be affected, and some factor variability as in this analysis some other factors such as SPV module aging, MG topology variations, cloud cover variations were not considered, which can affect the performance of MG inverters over time. Developing more advanced hybrid architectures considering these limitations, with more enhanced interpretability and error reduction capabilities with IoT setups can be an excellent avenue for real-time implications of diverse large-scale MG scenarios. Future studies can focus on exploring real-time implementation, enhancing robustness with respect to intricate external factors, integration of multiple data sources through diverse DER scenarios, and addressing scalability concerns while deploying on large-scale, diverse MG setups.

Author Contributions

Conceptualization, M.Y.A.; methodology, M.Y.A.; software, M.Y.A.; validation, M.Y.A.; formal analysis, M.Y.A.; investigation, M.Y.A. and M.J.H.; resources, M.Y.A. and M.J.H.; data curation, M.Y.A.; writing—original draft preparation, M.Y.A.; writing—review and editing, M.J.H. and L.L.; visualization, M.Y.A., M.J.H. and L.L.; supervision, M.J.H. and L.L.; project administration, M.J.H.; funding acquisition, M.J.H. All authors have read and agreed to the published version of the manuscript.

Data Availability Statement

This work uses confidential data which could be shared upon request subject to approvals and restrictions.

Conflicts of Interest

The authors declare no conflicts of interest.

Nomenclature

$T_m\left(t\right)$	Module Temperature
$P_{AC}\left(t\right)$	AC Power
$T_a\left(t\right)$	Ambient Temperature
$X\left(t\right)$	Feature Vector
$I_{irr}\left(t\right)$	Irradiance
$A{C}_{\mathrm{Predicted}}\left(t\right)$	Predicted Output AC Power
${\theta }_t$	Optimized Model Parameters of the Advanced Algorithms
${\gamma }_{RZ}$	Correlation Coefficient for Features R and Z
${\gamma }_{DC,AC}$	Correlation Between AC and DC Power
T	Data Sequence
$T_s$	Test Size
$X_{Scaled:}$	Scaled Data Vector
$X_{Seq:}$	Divided Data Vector into Sequences
$X_{Train:}$	Training Vector
$X_{Test:}$	Testing Vector
$X_{Valid:}$	Validation Vector
M	Weight Matrix
b	Bias
${\sigma }_i$	Sigmoid Activation Function
${\tilde{C}}_t$	Candidate Cell State
$tanh$	Hyperbolic Tangent Activation Function
$d_t$	Moving Average for Past Gradients
$r_t$	Moving Average for Past Squared Gradients
$L_t$	Gradient of the Loss Function
$\eta$	Learning Rate
$ϵ$	Constant Preventing Division by Zero
$T_h$	Adaptive Threshold

Footnotes

Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content.

Figures and Table

Figure 1. Illustration of a DC microgrid network.

Figure 2. Overview of the proposed work.

Figure 3. Correlation Heat-map of Features.

Figure 4. Advanced RNN Layer for Microgrid PdM.

Figure 5. Advanced LSTM Cell for Microgrid PdM.

Figure 6. Advanced GRU Layer for Microgrid PdM.

Figure 7. Training, Validation Loss of the advanced DL Algorithms: (a) Advanced RNN method. (b) Advanced GRU method. (c) Advanced LSTM method.

Figure 8. Adaptive Threshold Integrated Method With: (a) Advanced RNN model. (b) Advanced GRU model. (c) Advanced LSTM model.

Figure 9. Identification of MG Inverter Faults by the Proposed: (a) Advanced RNN architecture. (b) Advanced GRU architecture. (c) Advanced LSTM architecture.

Figure 10. Detected MG Inverter Faults by the: (a) Conventional RNN Method. (b) Conventional GRU Method. (c) Conventional LSTM Method.

Table 1

Correlative Permormance Evaluation of Different DL Models.

Methods	R2 Score	MAE
Advanced RNN	$0.941$	$12.102$
Advanced GRU	$0.958$	$10.182$
Advanced LSTM	$0.971$	$8.263$
Conventional RNN	$0.911$	$15.188$
Conventional GRU	$0.937$	$12.545$
Conventional LSTM	$0.949$	$11.847$

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