The application of machine learning models for the assessment of off and on-grid connected individual or hybrid renewable energy sources nowadays burning research areas as the need for electrical supply is increasing day by day (Kamran et al., 2018). Some of the recent works concerning this issue have been quoted in Table 1.

The contribution made in this research article can be summarized as:

• A multilevel-tuned deep learning method has been developed for the prediction of both solar irradiation and wind speed forecasting.

The paper has been organized as the first section contains the introduction, literature survey and the contribution made. The second section has focused about the methodology and data preprocessing methods. The theory about the deep learning models, optimization method applied and performance metrics has been explained in section 3rd, 4th and 5th respectively. The next section is about HRES modelling followed by the result and discussion section. Finally, the overall research work has been concluded in the last section.

An artificial neural network type called a recurrent neural network (RNN) was introduced in the 1990s by Elman to handle sequential data by retaining the internal state or history of the observations. RNNs can display dynamic temporal behavior because they have connections that loop around on themselves, in contrast to feed-forward neural networks, which only process data in a single direction. To put it another way, an RNN gives neural network a memory function, which helps the neural network perform well while analyzing time series data (Miao and Yokota, 2024).

The present state of a hidden layer of an RNN unit can be determined using the current input state and the prior hidden state as per the Equation 2: H t = f w H I × I t + w H H × H t − 1 + b H (2) where H t and H t − 1 are the current and previous hidden state, f   and g   show the nonlinear activation function, I t and T t are the input and output state at time t , b H and b T are the bias added to the hidden and output state respectively. w H I , w H H , and w H T are the weights of the input state, hidden state and output state respectively. The corresponding target or output variable state can be obtained using Equation 3 given below: T t = g w H T × H t + b T (3)

The problem of dealing with long-term dependencies in sequential data has led to the development of LSTM, an upgraded version of recurrent neural network (RNN) (Xu et al., 2024). Since its first introduction by (Hochreiter and Schmidhuber, 1997), it has been widely utilized in several domains, such as time series analysis, natural language processing, and speech recognition.

The LSTM cell unit structure can be explained with the following three gate:

I. Forget gate: It decides which data or information needs to be erased from the memory as in Equation 4.

The expression for the other states like temporary cell state, current cell state and the hidden layer state can be presented using Equations 7–9. C S t ¯ = tan ⁡ h × W c × H t − 1 + D t + B c (7) C S t = F g t ⊗ C S t − 1 + I g t ⊗ C S t ¯ (8) H t = O g t ⊗ tan ⁡ h C S t (9)

1D-CNN is a type of deep neural network that has become well-known for its exceptional capacity to identify and evaluate intricate patterns within huge datasets (Teng et al., 2024). Sequential data is processed by a one-dimensional CNN by convolving the input sequence using learnable filters. A feature map is produced by the convolution process, which calculates the dot product between the input sequence and the filter at each place (Namdari et al., 2023). Let’s have an input sequence of one dimension x = x 1 , x 2 , x 3 , x 4 … . . x n and learnable filters of w = w 1 , w 2 , w 3 , w 4 … . . w n having f length. The feature map associated with filter W p as Z p , which is calculated using Equation 10 described below: Z p q = ∑ r = 0 f − 1 x q + r × W p r (10) here Z p q indicates that in the input sequence, the filter W p has been activated at position q . The output of the filter can be obtained if we add a sigmoid function and a bias term as shown in Equation 11 below: Y p q = σ ⋅ Z p q + b p (11)

The significant features are then usually extracted from the feature maps Y by down-sampling them using methods like average or max-pooling, which lower dimensionality. The final output of the CNN is usually formed by concatenating or combining the outputs of all filters, which are further processed through fully connected layers for tasks involving regression or classification. The basic processing of the 1D-CNN model has been shown in Figure 2.

In machine learning and deep learning, stacking—also referred to as stacked generalization or meta-ensembling is an effective approach that combines numerous models to enhance prediction performance. Stacking is the process of training many neural networks and integrating their predictions to generate a better ensemble model in the context of deep learning (Lazzarini et al., 2023). The procedure for the stacking of ML or DL modes can be represented with the pseudo-code of Algorithm 1 which is as follows:

Algorithm 1

Stacking pseudo code.

Input: X (input variables) and Y (target variable), Training data d = X j , Y j j = 1 n , number of deep learning models n

The stacked model considered in this article consists of RNN, LSTM and 1DCNN as the base learner and linear regression as the meta-learner model or final prediction model. First, the hyperparameters of the base learners are tuned using Bayesian optimization and the overall stacking structure is presented in Figure 3.

Like other population-based optimization techniques, RIME starts by initializing the population. The population is made up of m rime agents R u as per Equation 12 and each agent consist of D rime particles y u v . Thus the population P with the rime particles can be represented with Equation 13: P = R 1 R 2 … R u ;   R u = y u 1 , , y u 2 , … . . y u v (12) P = y 11 … p 1 v ⋮ ⋱ ⋮ y u 1 ⋯ p u v (13)

In this case, u for the rime agent’s ordinal number, and v the rime particle’s ordinal number. The rate of progress of every agent is represented by f R u , indicates the fitness value.

Soft-rime growth grows slowly in the same direction but is very unpredictable and may stick to most object surfaces. RIME may efficiently prevent local stagnation and explore widely in initial iterations thanks to the soft-rime search technique, which is based on these growth qualities. The following is the updating procedure for rime particles: P n e w u v = P b e s t v + R 1 ⋅ cos ⁡ θ ⋅ α ⋅ H ⋅ u b u v − l b u v + l b u v , R 2 < E (14)

In the above equation, the new position of the v t h particle of the u t h agent is P n e w u v . P b e s t v refers to the best agent position for the present iteration. The direction of particle movement is determined by the control parameter R 1 , which has a random value between the predefined bounds of [−1, 1] and R 2 shows any number between 0 and 1. The degree of adhesion, or H , is a random quantity in the interval (0, 1) that regulates the separation of two rime-particle centres. The parameter cos ⁡ θ varies with the number of iterations, and is obtained using Equation 15: θ = π ⋅ i / 10 ⋅ I (15) where I is the algorithm’s maximum is the number of iterations and i is the number of iterations that is currently in process. As seen in Equation 16, α the environmental component, which comes after the number of iterations to mimic the impact of the external environment is utilized to guarantee the algorithm’s convergence. α = 1 − W ⋅ i I / W (16)

In order to regulate the number of segments of the step function, the default value W has been taken as 5. The factor E represents the probability of condensation which has been shown in Equation 17: E = i / I (17)

The pseudo code of the above analysis of the soft rime method has been shown in Algorithm 2.

Algorithm 2

Soft-Rime Searching Pseudo Code.

1. Initialization of Rime population (P)

Like rime puncture, hard rime frequently intersects because it expands in the same direction. By imitating this technique, rime agents can share information, improving convergence and avoiding entrapment in local optima as described in Equation 18 below: P n e w u v = P b e s t v , R 3 < f N R u (18) where the R 3 can have any random value between [−1, 1] that regulates the exchange procedure and the probability that the i t h rime-agent will be chosen is shown by the normalized value of the agent fitness value, denoted as f N R u . The flow of the procedure of the hard rime has been shown as pseudo code in Algorithm 3.

Algorithm 3

Hard Rime Puncture Pseudo Code.

1. Initialization of Rime population (P)

In contrast to traditional greedy selection, RIME takes an aggressive stance, which improves the algorithm’s exploration and exploitation. It contrasts the fitness values of updated and non-updated search agents, swapping out the latter for updated agents that perform better. By enhancing the search agents’ general quality, this strategy drives the population closer to optimum with each repetition. The Algorithm 4 has represented the steps of the positive greedy selection in the form of pseudo code.

Algorithm 4

Positive Greedy Selection Pseudo Code.

1. Initialization of Rime population (P)

Algorithm 5 provides a concise overview of the RIME algorithm, including its operational phases and pseudo-code and also the flow diagram of the algorithm has been shown in Figure 4.

Algorithm 5

Rime Pseudo Code.

1. Initialization of Rime population initialization (P)

The optimization is better than the other traditional or state of art optimization techniques due to following reasons:

1. The soft rime strategy allows the algorithm to simultaneously consider the breadth and depth when searching for the optimal solution, alternating between large-scale exploration and small-scale exploitation.

The system considered for the analysis consists of the four major resources which are solar array, wind turbine, battery storage system and diesel generators. The mathematical design of the individual system components has been discussed separately.

The energy management system of the suggested hybrid/integrated renewable energy system handles issues with robustness, stability, and technological dependability. The duties covered in this area include managing rural communities, achieving technological performance, allocating resources optimally, and operating in a resilient manner. The main goal of energy management is to govern the flow of energy in the hybrid energy system for rural communities by making effective decisions that take into account the technological capabilities and constraints of each system component. Here the strategies for the energy flow have been categorized into three scenarios which are as follows:

Scenario 1: When RES power is greater than the load, then battery charges according to the Equations 26–28. P S P V i + P W T i ≥ P l i   ∀ i ∈ H r (26) P c h i = P S P V i + P W T i − P l i   ∀ i ∈ H r (27) E b i = E b i − 1 + P c h b i × 1 H r   ∀ i ∈ H r (28)

Scenario 2: When RES power is less than the load power, then the BSS supplies the deficit load according to Equations 29–31. P d i b i = P l i − P S P V i + P W T i   ∀ i ∈ H r (29) E b i = E b i − 1 − P d i b i ⋅ 1 H r   ∀ i ∈ H r (30)

Scenario 3: “When RES and BSS are both unable to supply the load, then power will be supplied by the grid according to Equation 31. P g r i d i = P l i − P S P V i + P W T i − E b i η c o n   ∀ i ∈ H r (31)

Several economic criteria are employed in the literature to analyze the economic feasibility of localized renewable energy systems. The life cycle cost, total annualized cost, and cost of energy are some of these factors. The economical method, which takes into account the life cycle, initial cost, operation and maintenance costs, and replacement costs of each subsystem, is established in this section for system configurations depending on the Total Net Present Cost (TNPC) and Energy Cost (EC).

The minimization of the COE for the proposed HRES is the main concern of this study which can be expressed using Equation 32 expressed below: min C O E R s . / k W h = T N P C ∑ H r = 1 8760 P l ⋅ C R F (32) where, CRF denotes the capital recovery factor which can be calculated using Equation 33 expressed below: C R F = r 1 + r p / 1 + r p − 1 (33) where r is the actual rate of interest which is 7 percent here and the project period is generally considered equal to the PV panel life span.

To evaluate an investment project’s economic feasibility, one important financial metric is the TNPC which consists of all system components’ capital cost, their maintenance and operating cost and the cost of replacement of any particular component.

Similar to TNPC one more key parameter that has been analyzed here is the renewable fraction (RF) refers to a limit that establishes how much energy is imported by the grid concerning a renewable generator. The perfect system using exclusively renewable resources is indicated by the renewable factor of 100%. On the other hand, the renewable factor of 0% indicates that the power imported by the grid is equal to the power generated by renewable resources. The RF can be obtained using Equation 34 shown below: R F Max % = 1 − ∑ P g r i d ∑ P S P V + ∑ P W T ⋅ 100 (34)

The constraints taken for each objective function are the maximum and minimum number of PV panels, wind turbines and battery systems.

Earmarking the sustainable development, the environment impact and social development have to be a concern to consider while designing any HRES system. The environmental benefits on by reducing the Carbon emission should be prioritize and employment of the local for rural community enhancement must be taken into the consideration. This paper has introduced the socio-environmental index while designment HRES system and formulating the objective functions.

The following Equation 35 computes the total employment that could be created by deployment of the proposed HRES system (Kumar et al., 2023): J C t o t a l = J C S P V * P W T + J C t o t a l * P W T + J C B S S * E B S S + J C g r i d *   P g r i d (35) where, J C t o t a l is the total job creation, J C S P V , J C t o t a l , J C B S S , J C g r i d are perhaps the number of job may offered per KW power generated or consumed by the Solar, wind, storage system and grid respectively. Researcher have come up with job creation estimations with criteria for the renewable based hybrid system so that the study may simplify.

Table 3 below display the input parameter as employment variables considered in this paper. Furthermore, this paper also includes the environmental index which highlights that the following system have attained reduction in carbon emission in comparison with the traditional diesel generator or grid. The carbon emission is calculated by the emission factor mentioned in the Table 3 and power generated by each component of the system and the total emission can be determined by the following Equation 36. C O 2 = ∑ i = 1 8760 α S P V * P S P V + α W T * P W T + α g r i d * P g r i d (36) where α S P V , α W T , α g r i d are the C O 2 emission factor per kWh energy generation.

The 5 years of data obtained from the NREL have been taken for the analysis and the five performance parameters have been calculated to highlight the efficiency of the model. There are so many parameters associated with each deep learning model which generally affect the performance of the model if properly not selected. For this reason, the hyperparameters of each deep learning model have been optimized with Bayesian optimization and a further stacking process has been accomplished.

The hyperparameters range and chosen values for the optimization have been shown in Table 4 and the Table 5 shows the output of the Bayesian Optimization. The statistical errors of the stacked model with the optimized parameters for the GHI and the wind speed prediction have been represented in Table 6. The regression analysis has been done between the predicted and the true values of both targeted variables and has been shown with the scatter plot in Figure 6A for GHI and in Figure 6B for wind speed.

This paper examines and presents quantitative experiment results related to resilient planning and evaluation of the integrated multi-agent hybrid energy system that was created. The solar radiation and wind speed data utilized in this study is primarily anticipated using the stacked deep learning method, followed by the planning and distribution of the hourly rural local load consumption profile. In order to create a strong and practical techno-socio-economic architecture RIME optimization is applied and compared with other prominent optimization techniques.

The residential load profile for the entire year has been plotted in Figure 7 where it can be noted that the load is generally low in the morning and night but at the peak in the afternoon. Also, if we analyze the entire year the summer season has maximum demand as compared to the winter. The monthly profile of the solar irradiance and temperature has been shown in Figure 8 and the wind speed in Figure 9 respectively.