The improved integrated Exponential Smoothing based CNN-LSTM algorithm to forecast the day ahead electricity price

Abstract

The deregulation of electricity market has led to the development of the short-term electricity market. The power generators and consumers can sell and purchase the electricity in the day ahead terms. The market clearing electricity price varies throughout the day due to the increase in the consumers bidding for electricity. Forecasting of the electricity in the day ahead market is of significance for appropriate bidding. To predict the electricity price the modified method of Exponential Smoothing-CNN-LSTM is proposed based on the time series method of Exponential Smoothing and Deep Learning methods of Convolutional Neural Network (CNN) and Long Short-Term Memory (LSTM). The dataset used for assessment of the forecasting algorithms is collected from the day ahead electricity market at the Indian Energy Exchange (IEX). The forecasting results of the Exponential Smoothing-CNN-LSTM method evaluated in terms of Mean Absolute Error (MAE) as 0.11, Root Mean Squared Error (RMSE) as 0.17 and Mean Absolute Percentage Error (MAPE) as 1.53 % indicates improved performance. The proposed algorithm can be used to forecast the time series in other domains as finance, retail, healthcare, manufacturing.

• •The method of Exponential Smoothing-CNN-LSTM is proposed for forecasting the electricity price a day ahead for accurate bidding for the short-term electricity market participants.
• •The forecasting results indicate the better performance of the proposed method than the existing techniques of Exponential Smoothing, LSTM and CNN-LSTM due to the advantages of the Exponential Smoothing to extract the levels and seasonality and with the CNN-LSTM methods ability to model the complex spatial and temporal dependencies in the time series.

Graphical abstract

Specifications Table

More specific subject area:	Forecasting
Name of your method:	Exponential Smoothing based CNN-LSTM
Name and reference of original method:	The proposed methodology of Exponential Smoothing-CNN-LSTM is designed using the existing Exponential Smoothing [[27], [28], [29]] and CNN-LSTM [31]
Resource availability:	https://doi.org/10.17632/7t5jg4ms99.1

Background

The electricity sector in many countries has adopted the recent developments that has led the electricity market to become dynamic. The increasing demand of electricity has made it necessary to include measures that have made the electricity market deregulated [1]. The power generating companies can now trade their electricity more competitively. The distribution companies and consumers are increasingly purchasing the power from the short-term market. The sale of electricity that was initially limited to long term and medium term has now expanded to short term. The day ahead market schedules power with the unit electricity price that keeps on varying throughout the day based on the bids of the power generators and the consumers. These bids are selected competitively based on the availability of power and demand requirement and the bid quote. The bids are made by the consumers for the power requirement at a specific bid price and by the power suppliers for the power supply at a bid price for every time interval for the 24 h. The power exchange market operator selects the bids based on the algorithm that sorts the bids made by the power suppliers and consumers for every time interval and selects the bids based on the demand and supply equilibrium that sets the electricity price for every time interval. The selected bids are checked for the transmission corridor availability that sets the market clearing price for every regional area and the electricity is dispatched the next day. The bids made by the power generators and consumers get selected on the availability of the power and the bid price. The availability of the electricity price forecast is necessary for the suppliers and consumers to appropriately bid in power market. This gives the prediction of electricity price immense significance [2].

The applications of the electricity price forecasting are numerous, that allow the market participants and the utilities to take informed decisions [3,4]. The Demand response market bidding is a mechanism to improve the electrical grid reliability [5]. The utilities, power suppliers and consumers can competitively bid for the electricity and improve the cost benefits. The variable electricity price schemes can reduce the peak demand on the grid by encouraging the consumers to consume more electricity during the off-peak durations and reduce the consumption during the peak demand durations [6]. In this context the forecast of electricity price is very important for the participants to take informed decisions. The significance of the research is that it would benefit the utilities and participants to take price-based decisions that can positively affect the electrical grid operations. The market-based demand response can actively motivate the integration of the distributed energy reserves in the electricity market that can improve the system reliability.

The electricity price forecasting can be done using the time series forecasting techniques, there are different techniques discussed in the literature such as statistical, artificial intelligence-based techniques. The different time series methods are used to forecast electricity price [7]. The authors in their paper used the ARIMA (Autoregressive Integrated Moving Average) model to forecast time series of day-ahead electricity prices from EPEX power exchange [8]. There are machine learning algorithms being used to forecast electricity price, the Artificial Neural Network (ANN) models can be trained to forecast day ahead electricity price, by using non-linear correlative and autocorrelative time series properties in electricity price forecasting [9]. The approaches like Convolutional Neural Network (CNN) are employed by the authors in their research, which introduces a forecasting model that integrates with graph based convolutional network and time-based CNN variant, where graph construction module automatically extracts relations between price areas [10]. There are other machine learning models that identify and create clusters in data that is used by the authors to develop a model using the fuzzy C-mean clustering to forecast the short-term electricity price [11]. The authors in their paper propose a time-sharing electricity price forecasting model using the heuristic method that considers the effect of renewable energy on the electricity prices [12]. In the paper the authors have used three different machine learning techniques K-Nearest Neighbour, Support Vector Regression (SVR) and ANN to forecast electricity prices in the Spanish electricity market [13]. The statistical methods and machine learning models have limited application when modelling increased system complexity, in that case the deep learning models are used, the authors in their paper [14] have proposed a deep learning network called GHTnet for electricity price forecasting, which outperforms traditional statistical methods and machine learning algorithms. There are Recurrent Neural Network (RNN), authors in the paper proposes using multi-layer Gated Recurrent Units (GRUs) for electricity price forecasting and compares them with other neural network structures and statistical techniques [15]. The authors in their paper have compared the SVR and the Deep Learning (DL) models for electricity price forecasting, with DL outperforming SVR [16]. The authors in their paper propose a novel two-stage supervised learning approach that diversifies the data sources, as the correlated power data. The results demonstrate that, when renewable energy sources are considered, the method gives improved results compared to existing approaches, which use neural networks, polynomial regression, SVR, and deep neural networks [17]. In their paper, authors have compared different forecasting models and selected the most promising as input for clearing price prediction of the short-term electricity market. that comprises in simulating regression methods [18]. In their work, to explore the complex dependence structure of multivariate EPF model, the authors have suggested employing deep recurrent neural networks (DRNNs) for day-ahead electricity price forecasting in deregulated electric market [19]. The authors in their paper have used the technique of quantile regression for forecasting of the electricity prices from the Australian electricity market [20]. The authors in their work have used different time series forecasting techniques to forecast the electricity demand by dividing the time series data into deterministic and stochastic components [21]. The electricity price at the Italian electricity market is forecasted using the functional autoregressive forecasting methods [22,23] and the authors use the method of semi-parametric methods to forecast the deterministic component of the electricity price and time series and machine learning algorithms for the stochastic component [[24], [25], [26]].

The important contribution of this research is the development of the novel Exponential Smoothing-CNN-LSTM technique to predict the electricity price in short term electricity market. The article is organized as follows: The method details section explains the working of the existing methods and proposed method, the method validation section discusses the parameters and settings used in the research, the results and discussion section show the simulation results and discusses the results and the concluding section includes the summary of the research and the limitations and future scope.

Method details

Exponential Smoothing

Exponential Smoothing is a forecasting technique suitable for short-term forecasts and based on univariate time series data. It marks decreasing weights of historical data points in an exponentially declining pattern. The assumption of this method is focused on the identification of the “level,” which represents the average value that the data oscillates around. It is based on the fact that the near future will mimic the immediate past. Exponential Smoothing is an uncomplicated method of forecasting a time series that works well if the most current historical data is predictive of the immediate future. Exponential Smoothing is a method used for prediction of demand and other time-based patterns because it is a supple framework that may be fitted to a wide range of complexity.

There are different forms of models ranging from simple models to complex ones, and each is good in different data elements, like trends and seasonal fluctuations. Simple Exponential Smoothing, Holt's linear Exponential Smoothing, and Holt-Winters Exponential Smoothing are the three of the versions that incorporate more elements of trends and seasonality of the data. The Exponential Smoothing version used in our analysis to predict the day-ahead pricing is consistent with Holt-Winters Seasonal Methods. This cluster of techniques is highly known to identify trends and seasonality in a time series clearly. The following Eqs. (1) to (6) explain the terms related to the forecasting [[27], [28], [29]].

The Simple Exponential Smoothing includes the levels components in the forecast and the forecast value is given by Eq. (1).

$$S_t=\alpha *y_{t-1}+\left(1-\alpha \right)*S_{t-1}$$ (1)

Here $y_{t-1}$ is the actual value for the previous period, $S_{t-1}$ is the forecasted value for the previous period. The $\alpha$ value is selected between 0 and 1, that assigns weight to the past values and is selected with the Levenberg-Marquardt algorithm.

The Holt's linear Exponential Smoothing includes the trend and levels components in the forecast and is modelled with the (2), (3).

$$S_t=\alpha *y_{t-1}+\left(1-\alpha \right)*(S_{t-1}+b_{t-1})$$ (2)

$$b_t=\beta *\left(S_t-S_{t-1}\right)+\left(1-\beta \right)*b_{t-1}$$ (3)

Here $\beta$ is a constant, selected with the Levenberg-Marquardt algorithm, $S_t$ and $S_{t-1}$ are the forecasts for the current and previous periods and $b_{t-1}$ is the trend for the previous period.

The Holt-Winters Exponential Smoothing includes the seasonality, trend and levels components in the forecast and the forecast values are given using Eqs. (4), (5), (6).

$$S_t=\alpha *\frac{y_{t-1}}{l_{t-L}}+\left(1-\alpha \right)*(S_{t-1}+b_{t-1})$$ (4)

$$l_t=\gamma *\frac{y_t}{S_t}+\left(1-\gamma \right)*l_{t-L}$$ (5)

$$F_{t+m}=S_t+m*b_t+l_{t-L+m}$$ (6)

Here $y_t$ is the actual value and $S_t$ is the predicted value for the current period. $\gamma$ is a constant selected to give least MSE. $l_{t-L+m}$ is the seasonal index for the $m$ periods ahead and $L$ is number of seasons. $F_{t+m}$ is the forecasted value for $m$ periods ahead.

LSTM

Long short-term memory networks are a type of recurrent neural networks with more preserved and well-functioning gating mechanisms [30]. Gates allow LSTMs to memorize or forget past observation information, allowing them to more efficiently model large data sequences. LSTMs have the ability to find out which prior data are more or less relevant instead of ignoring them uniformly like other RNNs. LSTMs are more stable due to their gating mechanism compared to traditional RNNs. They are more stable due to the limitations of conventional RNNs because they rectify the vulnerabilities, they have that are the vanishing and exploding gradients.

The LSTM architecture has been designed to manage the intricate patterns within the electricity price data's temporal dynamics. Through the use of memory cells that regulate the information flow, the model learns from data sequences that may take an extended amount of time to materialize. Specifically, the ability to forecast electricity expenditure is largely dependant on combining historical information with seasonal sharing and undue forage waves.

LSTM memory cell is shown in Fig. 1 with the summing and multiplying operators and the tanh and sigmoid functions that process the data from different inputs. There are different gates in the LSTM memory cell that determine the information that is to be removed, added, and given as output from the memory cell, after taking the input from the various inputs to the memory cell. The different inputs that the LSTM cell takes are as follows; $C_{t-1}$ is the previous memory cell state, $h_{t-1}$ is the output of the hidden layer of the previous memory cell, and the current input data $x_t$. The gates are used to regulate the information as forget gate $f_t$ for the data that is removed, the input gate $i_t$ for the data that is added, and the output gate $o_t$for the data that is output from the memory cell. LSTM cell uses these gates to control the data to be stored or discarded, that are governed by the following equations,

$$f_t=\sigma \left(W_f·\left[h_{t-1},x_t\right]+b_f\right)$$ (7)

$$i_t=\sigma \left(W_i·\left[h_{t-1},x_t\right]+b_i\right)$$ (8)

$$o_t=\sigma \left(W_o·\left[h_{t-1},x_t\right]+b_o\right)$$ (9)

$${\tilde{\mathrm{C}}}_t=\text{tanh}\left(W_c·\left[h_{t-1},x_t\right]+b_c\right)$$ (10)

$$C_t=f_t·C_{t-1}+i_t·{\tilde{\mathrm{C}}}_t$$ (11)

$$h_t=o_t·\text{tanh}\left(C_t\right)$$ (12)

where, σ denotes the sigmoidal function giving output in terms of 0 and 1, $C_t$ is the cell state, and ${\tilde{\mathrm{C}}}_t$ denotes the candidate value of the cell state. The LSTM network consists of the neurons having weight matrices that update the input for the gates as forget, input, output, and the cell denoted as $W_f$, $W_i$, $W_o$, and $W_c$ respectively and $b_f$, $b_i$, $b_o$, and $b_c$ denote the biases respectively.

Fig. 1.

A graphical illustration of a single LSTM cell.

CNN-LSTM

CNN-LSTM neural network interprets time series data by integrating convolutional neural layers and recurrent neural layers. The architecture includes the convolution layer to extract features of input data, and the LSTM layer detects time-dependant representative of the derived features. Because the model can figure out both short-term and long-term serial information, it is suitable for univariate time series forecasting. The CNN-LSTM model reads the spatial and temporal pattern of the input data and is able to forecast the future sequence based on past observations. The authors applied the CNN-LSTM model to predict the electricity prices [31].

In the CNN architecture the convolutional layers and pooling layers form the fundamental components. The convolutional layer extracts the features from the data. During this process the dimensionality of the convolutional layer output increases. The dimensionality reduction of the extracted features, is done with pooling layer, that reduces the computational costs during the training process. Fig. 2 illustrates the CNN-LSTM model structure, comprising of the input layer, convolutional layer, max pooling layer from the CNN structure and the LSTM cells are used to forecast the sequential data after the flattening layer.

Fig. 2.

CNN-LSTM model architecture.

Exponential smoothing-CNN-LSTM

The authors propose the technique of Exponential Smoothing-CNN-LSTM, that combines the Exponential Smoothing, CNN and LSTM networks to provide a comprehensive and sophisticated method. The technique merges the feature extraction capabilities of CNN and sequence modelling capabilities of LSTM with the Exponential Smoothing techniques method to model the trend, seasonality components in the input sequential data. This technique combination captures the intricate temporal patterns and inherent trend and seasonality component in the input data that influence the fluctuations in the time series data.

The Fig. 3 depicts the flowchart outlining the proposed Exponential Smoothing-CNN-LSTM model. Initially the Exponential Smoothing algorithm calculates the smoothed output of the input electricity price data with the chosen alpha value. The smoothed output of the Exponential Smoothing algorithm is normalized and split into the training and test datasets. The CNN model trains on the data and can extract the features in the data. The LSTM model follows the CNN model and then gives the output through the dense layer. The model performance is evaluated using the test dataset in terms of the MAE, MSE, RMSE and MAPE.

Fig. 3.

Flowchart of the Exponential Smoothing-CNN-LSTM algorithm.

Method validation

Exponential smoothing

The exponential smoothing model takes the electricity price data as the input vector and is tuned on the hyperparameters as the configuration of the seasonal component, that is set to additive. This setting models the seasonality variations in the data that are integral to the trend and imply that the seasonal effects remain present in the time series irrespective of the trend strength.

The model seasonal interval is set to 365, indicating that the daily price values represent a yearly seasonality cycle. The additive seasonality component demonstrates that the data has a consistent amplitude of seasonal fluctuations. The 365-day seasonal period is deliberate choice that captures the inherent annual rhythmicity observed in daily data as the electricity price. The electricity price data displays the cyclic variation influenced by various factors as the seasonal holidays and weather conditions.

LSTM

The LSTM model is tuned on the following hyperparameters:

• •LSTM Units (50 units): Choosing 50 LSTM units for these layers is a middle-of-the-road approach to model complexity. It means that the model grasps the subtle patterns in electricity price data despite the danger of overfitting. The proper selection of units is critical, as it affects how much the model can extrapolate from the historical data to the future prices.
• •Activation function: ‘ReLU’ as it accelerates the convergence of the training process and solves the vanishing gradient dilemma.
• •Optimizer (Adam): Adam optimizer is utilized to optimize the model's weights. It has gained popularity due to its effectiveness with large amounts of data and adaptiveness to the learning rate. Thus, in our case, it speeds up the model's convergence to the optimal performance indicator. Since electricity prices are fluctuating, this choice is suitable due to Adam's behaviour in a large number of samples
• •Loss Function (Mean Squared Error - MSE): Utilizing MSE as the loss function aligns with the objective of reducing the discrepancy between the forecasted and actual electricity prices. This metric is instrumental in guiding the model towards accurate forecasts by quantitatively assessing prediction errors.

CNN-LSTM

The CNN-LSTM model is tuned on the following hyperparameters:

Model architecture and configuration overview:

• •Convolutional layer: The CNN architecture employs a 1-D convolutional layer and it features 64 filters and has a kernel of size 3 and the ReLU activation function. The convolution layer forms a significant part that extracts the information from the input data to enable further analysis.
• •Pooling layer: There is feature dimensionality reduction layer known as pooling layer. The Max pooling layer of pool size 2. This dimensionality reduction is attained by retaining only the maximum value of every selection, and allows the model to represent the information is a more condensed form without losing its important characteristics. This reduces the computational costs and risks of overfitting the training data.
• •LSTM layer: The LSTM comprises of the 50 units using the ReLU activation function to process the input data from the CNN part. The capability of the LSTM layer to model the long-term dependencies is of particular importance in electricity price forecasting for the sequences ranging over the varied lengths of time in the past.
• •Dense layer: The final part of the architecture is the dense layer that enables the model to give a single output with using a single unit. This layer synthesizes the processed and feature enriched data from the previous layers. Although the number of hidden dense layers vary, in this research the single dense layer is used.

Hyperparameters and training configuration:

• •Optimizer: The Adam optimizer is employed for its adaptability, automatically adjusting the learning rate based on the data, thus facilitating efficient and effective model training.
• •Loss Function (Mean squared error): During the training the algorithm uses the MSE as the loss function to minimize the discrepancy between the forecasted and actual electricity prices and guides the model towards accurate forecasts by quantitatively assessing prediction errors.
• •Batch Size: Training is initially with a batch size of 32, striking a balance of learning granularity with computational effectiveness. This setup ensures that the model iteratively learns from the data in manageable portions, gradually refining its predictions.
• •Early Stopping: To prevent overtraining and ensure model generalizability, an early stopping mechanism monitors validation loss with a patience of 10 epochs. This approach halts training if no improvement is observed, reverting the model to the weights that yielded the best performance on validation data.

Exponential smoothing-CNN-LSTM

The model architecture used for the Exponential smoothing, CNN-LSTM is used in the proposed model of Exponential smoothing-CNN-LSTM and the similar hyperparameters settings and values are used to tune the model. Overall, this hybrid model leveraged the initial preprocessing and normalization of the data to enable CNN and LSTM layers to function at the optimal capacity. By identifying and visualising the additive seasonality and existence of a peak around years, the CNN-LSTM architecture allowed better readings and predictions of the electricity rate. The design of the hybrid model apart from adjusting to the characteristics of the data, allowed more thorough reading of the relationships between seasonal trends, short-term fluctuations and long-term trends.

Results and discussion

The proposed method is used to predict the electricity price from the Indian electricity market IEX in day ahead terms. The electricity price in the day ahead market at IEX varies every 15 min through the 24 h of the day. The electricity price data is collected from the year January 2020 to December 2022. The IEX is the electricity market for the consumers to purchase electricity and generators to sell electricity at a bid price. The market operator selects the bids from the buyers and sellers and dispatches to the generators based on the availability of the power and the transmission constraints at the calculated area marginal clearing electricity prices every 15 min.

The Table 1 provides the descriptive statistics of the day ahead electricity price data. The data has a mean of 4.86, standard error of 0.0123, median of 3.65, mode of 12, standard deviation and sample variance as 3.24 and 10.52 respectively. The skewness is 1.97, range is 19.4 and minimum and maximum values are 0.59 and 20 respectively.

Table 1.

Descriptive statistic of the electricity price data.

Descriptive statistic	Value
Mean	4.86 Rs./ kWh
Standard error	0.0123 Rs./ kWh
Median	3.65 Rs./ kWh
Mode	12 Rs./ kWh
Standard deviation	3.24 Rs./ kWh
Sample variance	10.52 ${\left(\text{Rs}./\text{kWh}\right)}^2$
Skewness	1.97
Range	19.4 Rs./ kWh
Minimum	0.59 Rs./ kWh
Maximum	20 Rs./ kWh

The electricity price data is available for 96 time intervals in the day, similarly for the total duration of 2 years there are 70,080 data values. The 80 % of the data comprising of 56,064 data values are used to train the models and the remaining 20 % data with 14,016 data values is used for testing the models. The dataset is available in the repository [32]. The electricity price data is initially standardized with the Min-Max scaler and arranged as a vector and then given as input to the Exponential Smoothing model. The Exponential Smoothing method forecasts the time series data and the data is divided into dataset to train and test. The training set data is given to the CNN-LSTM model and is then used to test on the testing data. For comparing the forecasting results with the existing methods, the total dataset is initially divided in the training set and testing set and the data is standardized, and the algorithms are trained on the data.

The parameters and the architecture for the existing models Exponential Smoothing, LSTM and CNN-LSTM and for the proposed model Exponential Smoothing-CNN-LSTM are set as discussed in the previous section. The numerical results shown in the Table 2, indicate the performance of the proposed and existing techniques in terms of the error evaluation metrics of Mean Absolute Error (MAE), Mean Squared Error (MSE), Root Mean Squared Error (RMSE) and Mean Absolute Percentage Error (MAPE). The error metrics are highest for the Exponential Smoothing model followed by the LSTM model and the CNN-LSTM model. The error metrics values are least for the proposed technique of Exponential Smoothing-CNN-LSTM. The MAE for the proposed technique is 0.11, MSE is 0.028, RMSE is 0.17 and MAPE is 1.53 %. The R squared values indicate the model fit, closer the value to 1 better the model fit. The accuracy of forecasting for the LSTM and CNN-LSTM are comparable with the proposed technique Exponential Smoothing-CNN-LSTM.

Table 2.

Numerical results of the simulations for the existing and proposed model for different evaluation metrics.

Model	R Squared	Mean Absolute Error (MAE)	Mean Squared Error (MSE)	Root Mean Squared Error (RMSE)	Mean Absolute Percentage Error (MAPE)%
Exponential Smoothing	−0.1576	2.8919	12.003	3.4644	52.83
LSTM	0.9496	0.5849	0.7471	0.8644	7.12
CNN-LSTM	0.9472	0.4989	0.7098	0.8425	6.56
Exponential Smoothing-CNN-LSTM	0.9973	0.1094	0.0288	0.1697	1.53

The deviations in the actual and the forecasted electricity price are significantly higher for the Exponential Smoothing method as the electricity price data is non-linear and non-stationary and the parameters for the model are fewer. As a result, the model is less accurate as it is unable to model the pattern of the change in the time series sequential data. For the LSTM and CNN-LSTM the error is comparatively lesser as the LSTM units, neural network and the convolutional layers effectively model the underlying changes in the time series data with the sophisticated learning method to update the weights. The proposed method has the least error as the advantages of Exponential Smoothing to exponentially assign weights to the past data and the CNN-LSTM model capability to learn spatial and temporal patterns make the method more accurate.

The Fig. 4 shows the graphical representation of the results given in Table 3, that depicts the improved forecasting accuracy of the proposed algorithm in terms of the error metrics of MAE, MSE, RMSE and MAPE. The results are also shown as a plot of the actual electricity price and the forecasted electricity price in the Fig. 5 for the Exponential Smoothing, LSTM, CNN-LSTM and the proposed technique of Exponential Smoothing-CNN-LSTM. The electricity prices forecasted with the LSTM and CNN-LSTM show spikes on the extreme values, but with the Exponential Smoothing-CNN-LSTM the spikes are reduced and the forecast is comparable to the actual electricity price.

Fig. 4.

Performance of the forecasting algorithms with the evaluation error metrics.

Table 3.

Diebold-Mariano (DM) test and Harvey-Leybourne-Newbold (HLN) test results in terms of p-values, ${\mathit{H}}_{\mathit{o}}$: there is no significant difference in forecasting accuracy between the model 1 and model 2, ${\mathit{H}}_{\mathit{a}}$: the model 1 predicts with greater accuracy than the model 2.

Model 1	Model 2	p-values
		DM	HLN
LSTM	Exponential Smoothing	< 0.00068	< 0.00035
CNN-LSTM	Exponential Smoothing	< 0.00072	< 0.00037
Exponential Smoothing-CNN-LSTM	Exponential Smoothing	< 0.00053	< 0.00027
CNN-LSTM	LSTM	0.22288	0.20302
Exponential Smoothing-CNN-LSTM	LSTM	< 0.00206	< 0.00112
Exponential Smoothing-CNN-LSTM	CNN-LSTM	< 0.00206	< 0.00113

Fig. 5.

The actual and predicted electricity price for the different forecasting models.

To validate the significance of the difference between the results for the different methods the Diebold-Mariano test and Harvey-Leybourne-Newbold test is performed [[33], [34], [35]]. The error between the actual value and the predicted value of the electricity price data is calculated for the Exponential Smoothing, LSTM, CNN-LSTM and Exponential Smoothing-CNN-LSTM methods. The Table 3 shows the Diebold-Mariano test and Harvey-Leybourne-Newbold test results in terms of the p-values for the testing the difference in forecasting accuracy between methods. The forecasting accuracy between the model 1 and model 2 having no significant difference is the null hypothesis. The p-values for the tests that are less than the significant value of 0.05 indicate that the prediction accuracy of the model 1 is greater than the model 2.

The proposed method of Exponential Smoothing-CNN-LSTM performs better than the existing techniques of CNN-LSTM, LSTM and Exponential Smoothing as the proposed method combines the advantages of the Exponential Smoothing, CNN and LSTM techniques. The electricity price data has the trend and seasonality component that can be modelled with these techniques, the Exponential Smoothing technique is used to remove the noise component in the original signal. The Exponential Smoothing technique, uses the parameters to smooth the data and model the original data based on the past data. The existing techniques of LSTM, CNN-LSTM have been used to forecast the electricity price. The LSTM technique is better to model the temporal dependencies in the data, the technique combined with the CNN improves the forecasting as the CNN has feature extraction and dimensionality reduction layers incorporated. Using the CNN technique, the underlying features that are imbibed in the data are captured. The forecasting result generated by the proposed technique is improved than the existing techniques as the advantages of every component technique improves the forecasting accuracy. The limitations and drawbacks of the other existing time series forecasting methods as Autoregressive (AR) and Moving average (MA) are that if the time series data is non-stationary then it has to made stationary before using the forecasting methods and the selection of the order of the models as AR, MA needs to be determined from other methods.

The electricity price variation is non-linear with random fluctuations. To forecast the electricity price the proposed technique is advantageous as it models the intricate pattern in the data with the Exponential Smoothing model and with the deep learning CNN-LSTM model. The method very accurately predicts the future electricity price with the least error. The model trains on the data from the IEX and can accurately forecast the random variation in the electricity price. This electricity forecast can definitely be used to take informed decisions by the electricity market participants to bid in the day ahead electricity market. The significance of the accurate forecast is that the electricity price quote bid for the electrical power by the consumers in the day ahead electricity market is selected only if it is greater than the market clearing price, that is calculated based on the demand supply equilibrium. For all the bid prices quoted less than the market clearing price the bid is not selected. Therefore, accurate forecasting is highly essential for appropriate bidding.

Conclusion

This paper discusses about the novel forecasting technique of Exponential Smoothing-CNN-LSTM to predict the time varying electricity rates. The objective of this research was to better the performance accuracy of the time series forecasting for the benefit of the electricity market bidding in day ahead electricity market. The electricity price demonstrates nonlinearity and non-stationarity. The time series models and deep learning techniques are better at modelling the intricate long-term dependencies in the data. The proposed model of Exponential Smoothing-CNN-LSTM was used to predict the electricity price in day ahead terms and the performance was measured with the error metrics as MAE, MSE, RMSE and MAPE. The proposed technique gives the least error as compared to the existing techniques of Exponential Smoothing, LSTM and CNN-LSTM with the MAE as 0.11, MSE as 0.028, RMSE as 0.17 and MAPE as 1.53 %. The simulation results indicate that the forecasting accuracy of proposed method has improved than that of the existing techniques, that combines the advantages of the Exponential Smoothing technique and the CNN-LSTM technique. The advantage of Exponential Smoothing technique is that it is better at generating short term forecast, whereas the CNN is better at identifying the spatial, local patterns and LSTM is used to identify the long-range dependencies. Although the proposed model is computationally extensive it is comparatively accurate than the existing models.

The limitations of the Exponential Smoothing technique are that the tuning of the parameter is to be done with trial and error, the technique does not forecast accurately for the non-stationary time series and the time horizon to accurately forecast is less. Although the LSTM and CNN-LSTM requires large dataset to train and more hyperparameters to tune, the forecasting accuracy is better as compared to the Exponential Smoothing, and by integration with the Exponential Smoothing the accuracy improves further. This research forecasted for the dataset from the IEX day ahead electricity market, similarly can be used for other electricity markets.

The future scope of the research would be to develop other time series forecasting techniques using transformation methods that do better time series components analysis that with the deep learning techniques can better the forecasting accuracy.

Limitations

Not applicable.

Ethics statements

Not applicable.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Data availability

• The data is available in the repository.