International Journal of Electrical and Computer Engineering (IJECE) Vol.
No.
October 2025, pp.
ISSN: 2088-8708.
DOI: 10.
11591/ijece.
A hybrid extreme learning machine and sine cosine algorithm model for accurate electricity price forecasting Udaiyakumar Sambathkumar.
Sangeetha Shanmugam.
Kannayeram Ganapathiya Pillai Department of Electrical and Electronics Engineering.
Sri Ramakrishna Institute of Technology.
Anna University.
Chennai.
India
Article Info
ABSTRACT
Article history:
Electricity demand is continually rising due to the advancement of new technology, the switch to greener energy, and the popularity of electric vehicles over conventional ones.
The proliferation of businesses in the generation and distribution sectors has increased competition in the electricity market.
Forecasting electricity prices enables consumers to control their monthly electricity bills and consumer-owned distributed generation by knowing the forecasted hourly price.
For demand management, generation scheduling, and bidding price quotations, electricity price forecasting is crucial for buyers, generation businesses, and bidders Electricity price data is highly nonlinear and affected by numerous factors because of which EPF models are more complex, highly volatile and slow in convergence.
A range of neural network models, training algorithms, and hybrid systems comprising two or more models have been suggested for precise and efficient electricity price forecasting by researchers over the This study involves the development of a hybrid neural network model with two intelligent algorithms sine cosine algorithm (SCA) and extreme learning machine (ELM) to predict electricity price for a particular The newly developed network model is trained and tested with real-time Indian electricity price data from the year 2022.
The selected annual price data set is divided into three different sets to explore seasonal variations and all the sets are given as the input to the model for training and testing to obtain the effective price forecasting.
Received Aug 29, 2024 Revised May 28, 2025 Accepted Jun 30, 2025 Keywords:
Dynamic electricity pricing Electrical price forecasting Extreme learning machine Neural network Sine cosine algorithm This is an open access article under the CC BY-SA license.
Corresponding Author:
Udaiyakumar Sambathkumar Department of Electrical and Electronics Engineering.
Sri Ramakrishna Institute of Technology.
Anna University Pachapalayam (Pos.
Perur Chettipalayam.
Coimbatore - 641 010.
India Email: udaiyakumar.
e@sritcbe.
INTRODUCTION
The price of power that is fixed for various consumers is different from the price of other supplies because it has certain characteristics, such as the need to balance supply and demand, demand fluctuation, accurate and unexpected generation, particularly from renewable energy sources, and non-storability.
Both producers and customers must forecast electricity prices in the current competitive electricity market.
They can also use it to plan facility management, negotiate bilateral contracts, allocate assets, and mitigate hazards.
Participants in the market can also use the same value to forecast different power market indices and thus comprehend the behaviors of both operators and loads.
The idea of dynamic energy pricing necessitates the real-time calculation of the cost of the power to be sold to various users .
Ae.
Since its inception.
Electricity boards established by state governments will control all aspects of the entire power system.
It integrates the production, transmission, and distribution of power within their Journal homepage: http://ijece.
Int J Elec & Comp Eng
ISSN: 2088-8708
The regulatory commission, which the board appointed, determined tariffs and frequently took into account issues other than economics.
The power industry's deregulation separated transmission from generation, ensuring the power system's dependable and effective functioning.
As a result, power trading has gradually grown to be an essential aspect of the power sector.
The availability of hydroelectric power and other renewable energy outputs, fuel prices, power exchange between local and regional markets through long-term contracts, and system load demand are parameters to be considered for forecasting electricity prices.
The aforementioned variables can be utilized as input variables to the market clearing price (MCP) to obtain accurate forecasts.
Regression, linear curve fitting, and state-space methods are the traditional techniques for predicting the price of electricity .
Ae.
Accurate pricing prediction with many more limitations is made possible by the development of contemporary approaches.
RELATED WORKS
Among the tools now available for prediction assignments, artificial neural networks (ANN) are a well-known technique that has drawn increasing interest.
The reason is that it performs well, is simple to implement, and has a clear modeling technique .
Ae.
This method uses past data to identify the characteristics that would suit a predetermined mathematical formula and then uses the generated models to project future energy prices.
The actual inputs fed to the model are going to determine the forecast.
Although this approach is relatively simple to use, it is unable to account for temporal differences such as congestion and contingency .
, .
In the pursuit of accurate electricity price forecasting for a minimal time, a novel adaptive hybrid model has been proposed by combining variational mode decomposition (VMD), self-adaptive PSO, seasonal autoregressive integrated moving average (SARIMA), and deep belief network (DBN) algorithms and forecasted results were analyzed in Zhang et al.
Empirical evaluations demonstrate that this integrated approach significantly enhances forecasting accuracy and stability.
Concurrently.
Wang et al.
has developed an innovative outlier-robust neural network model for electricity price forecasting (EPF), which synergizes a robust forecasting engine based on an outlier-resistant extreme learning machine (ELM) model with three novel algorithms.
A key component of this model is a newly formulated sine cosine algorithm (SCA) to optimize the selected variables for phase space reconstruction.
Additionally, the authors discussed the new feature selection technique that facilitates to creation of the most relevant feature set for modeling electricity prices accurately.
From the literature, it is found that ANNs are popularly adopted for price prediction of electricity since they work effectively for nonlinear relationship problems.
However, conventional methods such as the back-propagation (BP) algorithm used for training ANNs suffer from the problem of slow convergence rates and the potential to become trapped in local optima.
Addressing these limitations.
Chen et al.
has introduced a quick price prediction method for the electricity market using ELM, a recently emerged learning algorithm for single-layer feedforward neural network (SLFN), which overcomes the inherent drawbacks of the BP algorithm.
Mirjalili .
proposed a SCA which works efficiently on complicated optimization problems.
initializes numerous random variables and attains the solution toward the global optimum through the functions based on sine and cosine equations.
Empirical results and performance metrics demonstrate the SCA's ability to explore diverse regions of the search space effectively, avoid premature convergence to local optima, and efficiently exploit promising regions, making it a widely adopted optimization technique in various research domains in Rizk-Allah and Hassanien .
An SCA algorithm with a multi-mechanism variant that can solve the multidimensional problem is developed to address the premature convergence while deriving a solution for six constrained nonlinear problems.
The results are compared with results from the experimental setup to check the quality of the proposed method in Yang et al.
A hybrid model is designed by combining the SCA and hill climbing optimizer to find load dispatch patterns.
The proposed hybrid model improves its exploitation ability for SCA to effectively solve the load dispatch problem, this model is tested with various real-time problems and results were compared in Al-Betar et al.
A hybrid network by combining the SCA and marine predator algorithms is built to choose the best-suited value of the parameters for hybrid active power filters.
The performance evaluation of the developed network is analyzed with results of already proven network models in Ali et al.
Similarly, during the past years, researchers have merged and applied a variety of neural network and optimization algorithms for forecasting and prediction applications in Udaiyakumar and Victorie .
hybrid model with multilayer perceptron which is trained by ELM and optimized by PSO is recommended for predicting the cost of electricity, its results were compared with various other forecasting methods in Udaiyakumar et al.
For the prediction of IranAos daily electricity price, a new algorithm by combining the convolutional neural network and long short-term memory network is proposed and found to produce A hybrid extreme learning machine and sine cosine algorithm model for A (Udaiyakumar Sambathkuma.
A ISSN: 2088-8708 accurate prediction in Heidarpanah .
In this paper, we are going to discuss the modeling of a novel algorithm that is developed by combining the ELM and SCA for electricity price forecasting, both are selected due to their simplicity, high problem-solving ability and number of various models availability.
THEORETICAL BACKGROUND
The network model which is feed-forward .
consists of six input layers of neurons, three hidden layers each with fifteen neurons, and one neuron as an output layer is modeled to solve the considered problem statement of electricity forecasting.
Figure 1 depicts the proposed neural network's topology.
A new model is developed by combining an ELM and SCA to train the network.
This section describes in detail the working of ELM and SCA.
ELM is selected because of its simple yet powerful generalization capability also the training speed is very high when compared with most of the neural network training algorithms.
ELM gives flexibility in choosing the weights and bias of expecting the final hidden layer.
to effectively optimize these weights and the bias optimization algorithm comes into play.
In this paper Sine Cosine Algorithm is used as an optimization algorithm because of its higher variable handling capacity, faster convergence and simple Figure 1.
Neural network model for EPF Extreme learning machine The following is the equation of the output layer function with the input variable be ycuycn , yc be the network's final output for Ea number of hidden neurons, yc = yc.
ca OcEayc=1 ycyc ycyc ) .
the variable ycycnyc , ycayc , yciyc (.
) denotes the weight assigned between the input layer and hidden layer, hidden layer bias and activation function respectively for n number of input variables.
In addition, new variable ycyc is assigned for the weight of the connections between the hidden layer and output layer .
The equation of the hidden layer neurons output is given as .
, ycyc = yciyc .
cayc Ocycuycn=1 ycycnyc ycuycn ) .
The activation function of the output neuron is given by the .
and the vector form of the .
is given by the .
Int J Elec & Comp Eng.
Vol.
No.
October 2025: 4366-4375
Int J Elec & Comp Eng
ISSN: 2088-8708
yc = OcEayc=1 ycyc ycyc ycU = .
cOycuycN ycO)ycN .
The network output vector is ycU = .
, yc.
U , yc.
cA)]ycN and the weight vector is ycOycu = .
c1 , yc2 .
U , ycEa ]ycN .
The matrix of the hidden layer output is given by .
and the Input weight and bias matrix are framed as shown in .
ycO=[ U ycEa .
ycEa .
ycO=[ U cA) U ] ycEa .
cA) ycaEa Output weight is estimated as shown in .
, where ycO A the generalized inverse of the output matrix is developed by the Moore-Penrose and ycycc = .
, ycycc .
U , ycycc .
cA)]ycN is the desired output and it is given by .
yc0 = ycO A ycycc ycO A = .
cO ycN ycO)Oe1 ycO ycN By substituting .
yc0 is estimated by least-squares solution.
yc0 = .
cO ycN ycO)Oe1 ycO ycN ycycc Sine cosine algorithm A new population-based algorithm called as sine cosine algorithm (SCA) is developed by incorporating the concept of basic waveforms of sine and cos functions.
This algorithm is widely used by researchers due it its simplicity and its powerful optimization .
Ae.
SCA is carefully designed to adjust the weights of the connection established between input and hidden layers to improve the forecasting capability of the proposed hybrid model.
In this technique, the randomly selected particles travel towards the best possible solution.
The following equation is used to randomly initialize the appropriate population size.
ycIycoyco = yayayco .
cOyayco Oe yayayco ) y yc Where Rkl is variable.
LL is the lower limit and UL upper limit.
r is assigned as the random number whose value lies between 0 and 1.
Each variable is initialized and the same is used to calculate the output from which the best variable is selected.
Then each variable is updated using the sine cosine function which is shown in .
ycIycn 1 = ycIycn yc1 y ycycnycu.
c2 ) y .
c3 ycIyca Oe ycIycn | .
ycIycn 1 = ycIycn yc1 y ycaycuyc.
c2 ) y .
c3 ycIyca Oe ycIycn | .
In .
Ri is the current iteration variable.
Rb is the overall best variable, and yc1 , yc2 , and yc3 are random variables chosen between 0 and 1.
For the implementation of a random selection of sin or cosine function, equations .
are combined as .
ycI yc1 y ycycnycu.
c2 ) y .
c3 ycIyca Oe ycIycn |, yc4 < 0.
ycIycn 1 = { ycn ycIycn yc1 y ycaycuyc.
c2 ) y .
c3 ycIyca Oe ycIycn |, yc4 Ou 0.
The value of yc4 is chosen between 0 and 1.
The updated variable is used in the next iteration and all the steps are carried out until a specified number of iterations are carried out.
A hybrid extreme learning machine and sine cosine algorithm model for A (Udaiyakumar Sambathkuma.
A ISSN: 2088-8708
PROPOSED HYBRID ALGORITHM
ELM and SCA algorithms are combined in such a way to form a hybrid forecasting model with high Both algorithms have specific roles to play with their highlights.
The weights between the hidden layer and output layer are calculated using the ELM technique while the weights of the link between the input and hidden layers are randomly generated, which are optimized by SCA, and by this both ELM and SCA are combined to form the powerful hybrid forecasting model.
This evaluation of the best value of weight between the hidden layer and the output layer is a minimization problem .
The Euclidean norm used to find the minimum norm is given by the equation.
ycoycnycu(Anyc Oe ycycc An2 ) The equation .
can be modified by adding the output weight matrix with the regularization parameter yu which will be always greater than zero, it is given in .
and its solution is given in .
ycoycnycu(Anyc Oe ycycc An2 yuAnyc0 An2 ) .
yc0 = .
cO ycN ycO yuy.
Oe1 ycO ycN ycycc Where ya is the identity matrix.
The optimization problem of the proposed SLFN is the minimization function whose objective function is as given in .
yue = yaycycoycyce .
c, ycycc ) By estimating the error function for actual output .
and predicted output .
the accuracy of the proposed algorithm for price forecasting.
Root mean square error (RMSE) is calculated by .
c, ycycc ) = Oo OcycA yco=1.
Oe ycycc .
] ycA During the execution of optimization, individual parameters will be constituted by .
in which sj is an integer variable that defines the activation function.
Output layer activation function fj is given as .
ycEyco = .
U , yc1Ea , yca1 .
U , ycaEa , yc1 .
U , ycEa , y.
ycN E0 E1 / .
e(Oe.
) EE
f j .
= E .
Oe e(Oe.
) / .
e(Oe.
) E .
Oe e(Oe2.
)/ .
) E
EEv if s j = 0 if s j = 1 if s j = 2 if s j = 3 if s j = 4 The hidden layer can be adjusted based on the value assigned to the parameter sj, the following activation function is selected for various values of s when sj=0 that particular neuron is not considered, sigmoid function, tangent function, hyperbolic function, and linear is selected as activation function with sj as 1, 2, 3, 4 respectively.
Implementation of the adjustable hidden layer by five different activation functions and a combination of SCA and ELM are the novelty of this work.
The flowchart of the proposed hybrid extreme learning machineAesine cosine algorithm (ELMAeSCA) algorithm is shown in the Figure 2.
Selection of training data In this paper hybridization of SCA and ELM algorithms is used for training the proposed neural network model.
The annual electricity price pattern data set for the year 2022 has been chosen to validate the proposed network model and algorithm.
The price data for 12 months are divided into three sets of data involving seasonal variations, for the inclusion of the regional variation Indian electricity market price is The first set of data is electricity prices for January.
February, and March Indian electricity marked for the year 2022 and it is shown in Figure 3.
Similarly, the second data include the price data set of May.
June, and July and is shown in Figure 4, and the price of September.
October, and November comprises the third data set which is shown in Figure 4.
The training data will be the data for three months and price forecasting is done for next month for one week for each set.
In this research three sets of data are trained and shown in Figures 3, 4, 5 respectively.
The graph obtained shows the pattern, the variation of electricity price with to time in hours for a three-month duration of 2,160 hours .
Int J Elec & Comp Eng.
Vol.
No.
October 2025: 4366-4375
Int J Elec & Comp Eng
ISSN: 2088-8708
Figure 2.
Flowchart of the proposed hybrid algorithm Figure 3.
Electricity price data for training .
ata set .
Figure 4.
Electricity price data for training .
ata set .
A hybrid extreme learning machine and sine cosine algorithm model for A (Udaiyakumar Sambathkuma.
A ISSN: 2088-8708 Figure 5.
Electricity price data for training .
ata set .
RESULTS AND DISCUSSION The electricity price forecasting is done using the proposed hybrid model using MATLAB R2021a in Windows 10 with Intel core i5 7th generation and 16 GB RAM.
Since the proposed hybrid network model is simple and powerful, moderate computational devices are enough to run the proposed model and the device used smoothly runs the proposed model.
One week of data is forecasted and various error metrics are calculated by using the forecasted electricity price value and original electricity price value.
These metrics are the parameters generally used for the evaluation of the accuracy of forecasted prices.
The price forecasting is obtained and the above-mentioned error metrics were calculated based on the training set data of 2160 hours with three methods namely the back-propagation (BP) algorithm, the Extreme learning method (ELM), and also proposed hybrid model.
The comparison plot is shown in the Figure 6 for April month 168 From Table 1 the error metrics MSE and RMSE were found to be reduced thus promising good accuracy in prediction.
The price forecasting and error metrics are evaluated based on the training set data of the next three months (May.
June, and Jul.
with the same model as the previous data set.
The comparison plot is shown in Figure 7 for the first week of August month.
From Table 2 it is found that for this particular set, error metrics are less than the BP algorithm but slightly greater than ELM.
The RMSE of the proposed method was reduced by more than 10 percent when compared with other models.
Figure 6.
Comparison plots for data set 1 Table 1.
Error metrics comparison of data set 1
Error metrics/methods MAE
MSE
RMSE
MARE
MSRE
RMSRE
ELM
ARIMA
Int J Elec & Comp Eng.
Vol.
No.
October 2025: 4366-4375
LSTM
Proposed Int J Elec & Comp Eng
ISSN: 2088-8708
Figure 7.
Comparison plots for data set 2 Table 2.
Error metrics comparison of data set 2
Error Metrics/Methods MAE
MSE
RMSE
MARE
MSRE
RMSRE
ELM
ARIMA
LSTM
Proposed The prediction of electricity price and error metrics are assessed based on the last set of training data (September.
October, and November month dat.
with all models as previous data sets.
The comparison plot is shown in Figure 8 for the first week of December.
Table 3 with error metrics and different algorithm results illustrates the reduction in error metrics that assures the improved accuracy of prediction.
In this research, electricity forecasting was done for one year .
of data with the formation of the three sections of data sets.
The predicted value of electricity prices is assessed for its accuracy of prediction with the different error metrics.
The process is carried on backpropagation.
ELM, and hybrid model and output is compared with the original value of the price that existed in the planning horizon.
From the graph obtained and error metric comparison table, it is found the proposed has enhanced prediction capability which serves the purpose.
Figure 8.
Comparison plots for data set 3 Table 3.
Error metrics comparison of data set 3
Error Metrics/Methods MAE
MSE
RMSE
MARE
MSRE
RMSRE
ELM
ARIMA
LSTM
Proposed A hybrid extreme learning machine and sine cosine algorithm model for A (Udaiyakumar Sambathkuma.
A ISSN: 2088-8708
CONCLUSION
The forecasting models such as the back-propagation algorithm, extreme learning machine, autoregressive integrated moving average, and proposed ELM-SCA model are simulated and results were It is evident from the comparison graph and error metrics comparison that the hybrid versions of the suggested neural network model produce more accurate forecasts.
The main benefit of this technique is their speedy calculation times, which allow them to efficiently extract more precise results from extremely volatile pricing data sets by creating the variable hidden layer neurons and independently selecting the various activation functions for each neuron for all the hidden layers.
The outcomes demonstrate the efficacy of this suggested method for accurate online price forecasting in spot market analysis.
It is found that the variables influencing price prediction are time and the pattern of electricity demand.
This sort of real-world accurate electricity price forecasting will help the electricity market participants in a better bidding and selling process and for the consumer as a reduced electricity bill.
REFERENCES