RNN-BiLSTM-CRF based amalgamated deep learning model for electricity theft detection to secure smart grids

Data collection

This research study utilized three distinct datasets. The first dataset was obtained from the State Grid Corporation of China (SGCC) and consisted of real power usage data from customers (Yi-Chong, 2018). The dataset was presented in a numerical format and included the customer ID, the days of the week, Land Classification and the quantities of energy consumed by each customer over a 2-year period. It also included labeled classes indicating whether the users were normal users (8,562) or theft users (1,394). The dataset also provided numerical information for any missing or faulty data. The second dataset was obtained from Haq et al. (2023) through a public request. It contained records of energy usage from 560,640 industrial and residential customers. The dataset included one normal class and six different theft classes, with varying numbers of instances in each class. The data was collected over a 10-min interval using smart meters from May 2019 to April 2020.The third dataset was collected by Badr et al. (2023) from the Ausgrid dataset and the SOLCAST website. The Ausgrid dataset, provided by Ausgrid, the largest electricity distributor along the eastern coast of Australia, consisted of real measurements of power usage and generation. The data was recorded every 30 min by a group of consumers located in Sydney and New South Wales, Australia. These consumers had solar panels installed on their rooftops. The readings covered the time period from 1 July 2021 to 30 June 2022. These datasets includes both one-dimensional and two-dimensional electricity consumption data. Table 1 provides statistical information for each of the three datasets mentioned above.

Data preprocessing

Electricity consumption data is typically extensive, but it often contains noise and missing values due to the susceptibility of smart meters (Liu et al., 2021). Consequently, it is necessary to clean the data before conducting analysis. To address the issue of missing values, an interpolation method is employed. This method operates on the principle of arithmetic mean, whereby the missing value is replaced with the average of its preceding and succeeding values. The following is the equation that should be used for the interpolation technique:

(1) $$\mathrm{I}(y_j)=\sum ▒〖((y_{j-1}+y_{j+1})/2)〗$$where $y_j$ represents the value that is absent, $y_{j-1}$ represents the value that came before it, and $y_{j+1}$ represents the value that will come after it. In addition, we used an empirical rule to recover the erroneous data, which is known as the three-sigma rule. This rule makes use of three different standard deviation methodologies to recover the erroneous data.

(2) $$\mathrm{S}\left(y_j\right)=\mathrm{a}\mathrm{v}\mathrm{g}\left(\mathrm{y}\right)+2\cdot \mathrm{s}\mathrm{t}\mathrm{d}\left(\mathrm{y}\right);$$

$$\mathrm{\forall }{y}_j>avg\left(\mathrm{y}\right)+2\cdot \mathrm{s}\mathrm{t}\mathrm{d}\left(\mathrm{y}\right)$$where $y_j$ stands for the incorrect value, std(y) represents the standard deviation of the data, and avg(y) represents the average of the information that was used.

As a result, when we had finished removing any outliers and cleaning up the noisy data, we continued to normalize the data that was left by using the MAX-MIN scaling approach. This method makes use of a linear transformation methodology, in which the data are converted based on the extraction of the highest and lowest values from the transformed dataset. This technique is called “linear transformation.” After that, the predetermined MAX-MIN mathematical equation is applied to each and every one of the dataset’s values in order to make a substitution.

(3) $$\mathrm{M}\left(y_j\right)=(y_j-min\left(y\right))/\left(max\left(y\right)-min\left(y\right)\right)$$where min(y) indicates the absolute least value and max(y) indicates the absolute greatest value.

Data balancing

In real-world scenarios, it is commonly observed that the number of regular electricity customers is higher compared to those with unusual consumption patterns. This leads to imbalanced data distribution, which poses challenges for deep learning models in terms of efficiency. The problem becomes more pronounced as it introduces bias towards the larger class in classification models. To address this issue, a technique called SMOTE (Synthetic Minority Oversampling Technique) can be employed. SMOTE generates new instances by modifying existing data points using a synthetic oversampling approach for the minority class (Chawla et al., 2002). The method identifies neighboring data points in the up-sampled data and calculates their distance from each other. By adding a random number, denoted as k, to this distance, the sample is expanded to create synthetic examples. This results in a more balanced distribution of generated features, which can be effectively utilized in the system layer. The algorithm for data balancing using SMOTE is shown in Algorithm 1.

Feature extraction

The feature extraction process is crucial to the accurate classification. In this work the services of well know algorithm recurrent neural network (RNNA) recurrent neural network (RNN) is a sort of artificial neural network that enables the output of particular nodes to impact future input to those same nodes by virtue of the fact that the connections between the nodes create a cycle (Zhu et al., 2022). This characteristic allows RNNs to display temporal dynamics, meaning they can effectively handle sequences of inputs with varying lengths by utilizing their internal state, or memory. As a result, RNNs find utility in tasks such as extracting features.

RNNs, in contrast to deep neural networks, incorporate hidden states as learning parameters (Sridhar et al., 2022). These hidden states play a crucial role in processing sequential data. During training, the hidden states are kept up to date by taking into account the information that came before as well as the information that is now available from the sequential data.

This phase involves extracting features from both one-dimensional (1-D) time-series data and two-dimensional (2-D) spatial data. For the 1-D aspect, we focus on extracting time series features. In the case of 2-D data, we concentrate on attributes such as Population Density, Land Classification (Urban/Rural), and Environmental Conditions. Additionally, we incorporate combined features, specifically Energy Efficiency Ratings and Peak Demand Times, to enhance the feature extraction process. These meticulously extracted features are pivotal in enabling our model to proficiently handle and analyze both one-dimensional (1-D) and two-dimensional (2-D) aspects of electricity consumption data.

The hidden state and the output $y_t$ of the recurrent layer, where $\mathrm{t}\in \{1,\dots ,\mathrm{T}\}$ denotes the index of the frame, are calculated as follows:

The hidden state, denoted by $h_t$, and the output of the recurrent layer, denoted by $y_t$, are computed in the following manner, where t represents the index of the frame and $\mathrm{t}\in \{1,\dots ,\mathrm{T}\}$.

The hidden state, denoted by $h_t$, and the output of the recurrent layer, denoted by $y_t$, are computed in the following manner, where $\mathrm{t}\in \{1,\dots ,\mathrm{T}\}$ respectively:

(4) $$h_t=\tanh (W_{hh}{h}_{t-1}+W_{xh}{x}_t+b_h)$$

(5) $$y_t=W_{hy}{h}_t+b_y$$where W and b, respectively, describe the weights and biases that are applied between the items.

The current input $x_t$, as well as the prior hidden state, $h_{t-1}$, are both used in the process of updating the hidden state $h_t$. Therefore, given sequential data, the information that came before it has an effect on the neural network’s computation of the information that comes after it. Through the use of Eq. (2), the output values of the recurrent layer may be determined.

BiLSTM-CRF framework

Long short-term memory is an example of recurrent neural network (RNN) architecture, which was developed in order to solve the issue of disappearing gradients (Zha et al., 2022). This issue was the motivation for its creation. Because LSTMs are able to learn and remember information across extended sequences, they are well suited for tasks that include sequential or time-series data. Some examples of such tasks include voice recognition, natural language processing, machine translation, and sentiment analysis. Memory cells are an essential component of LSTM networks. These cells enable the network to retain information and retrieve it even after it has been dormant for a significant amount of time. These memory cells are made up of a cell state and three different kinds of gates, which are the input gate, the forget gate, and the output gate respectively. The entry and exit of information into and from the memory cells is controlled by these gates. LSTM has the benefit of selectively reading and writing information, which helps it considerably compensate for the shortcomings of gradient explosion and gradient disappearance. Although LSTM is effective at solving the issue of long-term dependencies, it is difficult to make use of the contextual information provided by the text. The fundamental idea behind the construction of the BiLSTM model is that the feature data collected at time t should simultaneously include information about both the past and the future (Park et al., 2023). Both the forward LSTM and the reverse LSTM have the capability of acquiring the aforementioned information on the input sequence. In order to retrieve the complete representation of the hidden layer, the context information of the input sequence is first computed, and then vector splicing is used. It is important to point out that the parameters of the LSTM neural network used in BiLSTM are not reliant on one another in any way; the only thing they have in common is the word vector list used for word embedding (Wu et al., 2023).

By processing the input sequence in both the forward and the backward direction, BiLSTMs are able to accomplish their purpose of capturing contextual information. They are able to describe relationships between neighboring tokens in a sequence as a result of this. They do not, however, clearly describe global dependencies for the whole of the sequence. This restriction is addressed by the CRF layer, which takes into account the joint probability of all potential label sequences (Meng et al., 2022). Additionally, it takes into consideration the interactions that occur between labels that are located in various places. Because of this, the model is able to account for long-range relationships and provide forecasts that are more grounded in reality.

Baseline method

Using the data sets displayed in Table 2, we evaluate the performance of the proposed model by comparing it to the baseline models provided below.

• Baseline 1: Ullah et al. (2022) proposed a technique that were based on AdaBoost, AlexNet and Artificial Bee models.

• Baseline 2: Ahir & Chakraborty (2022) proposed a technique for detection of electricity theft using context-aware approach and pattern based approach.

• Baseline 3: Hasan et al. (2019) presented a method based on deep CNN and LSTM computations for the detection of power theft in smart grids.

Performance matrices

The effectiveness of the suggested strategy is assessed using three different types of performance criteria.

Experimentation results

By evaluating the precision, accuracy, and recall of the suggested method for electricity theft detection, the first experiment demonstrates its effectiveness. It can be witnessed that proposed technique scored highly across all datasets, as shown in Fig. 3, indicating outstanding results in terms of recall, precision, and accuracy for each dataset.

In comparison to testing the algorithm on synthetic data, the model was unable to effectively classify the fraud users when unbalanced data was supplied to it. Table 2 provides information on performance metrics for both imbalanced and synthetic data. The suggested technique scored highly across all datasets, as shown in Fig. 3, indicating outstanding results in terms of recall, precision, and accuracy for each dataset.

Another widely used statistic for binary classification is the MCC, which we utilize in this experiment. Figure 4 shows three more performance measures in relation to the number of epochs. While the validation loss grew and accuracy showed a declining trend, the train loss and accuracy increased as the number of epochs increased. The model overfits in this situation because it was not generalized for the unknowable input.

When the datasets in question are unbalanced, the MCC is frequently used. The accuracy figures for regular users and theft users who do not employ SMOTE are incongruent with one another, as seen in Table 2. Despite the fact that overall accuracy was essentially the same before and after SMOTE was adopted, this is the case. This is due to the fact that, despite the model’s high degree of accuracy, the test dataset’s uneven distribution hinders the model from correctly identifying the data. The model is then trained using the newly created dataset after the SMOTE has been set up to produce synthetic data. Figure 4 illustrates the training results using the balanced dataset. The train set and the test set do not contain any diverging patterns for patterns that are identical to one another. After the first 500 epochs, the test’s accuracy pattern remained consistent, and after the first 600 epochs, it had an accuracy rate of 89%. The test loss also appeared to be unchanged after the same number of epochs. The test set’s MCC also yielded a value of 0.82, indicating that the model is capable of making precise predictions.

Comparison to existing models

According to what was previously stated in the baseline techniques sections, the performance of the proposed model was compared to baseline models.

Table 3, gives insight of the performance comparison of a proposed technique with a baseline technique (Ullah et al., 2022; Ahir & Chakraborty, 2022; Hasan et al., 2019). The proposed technique attained a precision of 90.02%, recall of 84.18%. The F-score was calculated to be 86.62%. The accuracy of our proposed model was 93.05%. The Baseline one model, on the other hand gained an accuracy of 87.94%, a precision of 86.05%, a recall of 84.21%, and an F-score of 83.20%. The improved results show the effectiveness of proposed model in terms of used measures.

The proposed module utilizes an amalgamated model based on deep learning, which is achieved by combining the architectures of bidirectional long short-term memory (BiLSTM) and recurrent neural networks (RNN). The astute amalgamation of RNN and BiLSTM components in this model improves its capacity to comprehend contextual details and sequential dependencies present in the data. Recurrent neural networks (RNNs) are highly suitable for processing sequential data, whereas BiLSTM networks, by virtue of their bidirectional architecture, demonstrate exceptional proficiency in capturing information from both past and future contexts. By amalgamating these two formidable components, our suggested module capitalizes on the respective merits of each architecture, thereby producing an all-encompassing and efficient framework for the designated application. The performance of the module is enhanced by this novel combination, which distinguishes it from traditional models that depend on a solitary architecture.

As demonstrated in Fig. 5, the proposed model performs better than the baseline models (Ullah et al., 2022; Ahir & Chakraborty, 2022; Hasan et al., 2019) in terms of precision, recall, F-score, and accuracy. These findings suggest that the suggested approach has promise and might work for the current project. However, more research and testing are required to confirm its advantages and establish its practicality for practical applications.