1 Introduction

India has planned to install 500 GW of non-fossil fuel-based power capacity by 2030 [1], wherein Renewable Energy, like solar and wind energy capacity, will be around 80 percent and more. Due to high cost and inherent issues, the adoption of renewable energy faces challenges. Reliability is also important which is caused by intermittent and variability of the electricity produced by renewable energy sources. One approach is to use Hybrid Renewable Energy Systems (HRES), which involves integrating various renewable sources. The objective of this study is to address these challenges using the HRES method in the state of Karnataka in India. The state of Karnataka is rich in potential for both Solar and Wind energy. In Karnataka, the total installed capacity of Renewable Energy is 16,318 MW as of 31st March 2024. It has the capacity to generate 8267 MW from solar power and 5273 MW from wind. The goal of the state’s renewable energy program is to increase its generation capacity to 10 GW within the next five years from Renewable Energy sources. However, due to cloudy weather during the 2023 monsoon, Karnataka generated only 4238 MW of solar energy which is around half of the total installed capacity during the peak daytime, while wind energy generation fell drastically to 600 MW. This situation has arisen due to various structural factors. This study would solve reliability and cost-related issues faced by the state of Karnataka.

The design and optimization of a hybrid renewable energy system (HRES) for the Indian state of Karnataka are the primary focus of this case study. The following highlights the importance of this case study:

1.1 Renewable energy transition

To lessen climate change and lessen reliance on fossil fuels, there has been a drive recently on a worldwide scale to switch to renewable energy sources. Like many other nations, India has set high goals for using renewable energy to meet its expanding energy needs and cut greenhouse gas emissions.

1.2 Challenges of RE

Renewable energy has many advantages, but widespread implementation is hampered by intermittency, variability, and high upfront prices. These difficulties may impact the affordability and dependability of renewable energy systems, especially in areas with varying climates like Karnataka.

1.3 Reliability and cost-effectiveness

Especially in areas where industry and agriculture play a major role, reliability is essential to guaranteeing a steady and continuous power supply. Furthermore, to make renewable energy sources financially feasible and appealing to investors and customers, they must be cost-effective.

1.4 HRES approach

The issues of intermittency and variability related to particular renewable energy sources can be effectively addressed by HRES. HRES can improve dependability and optimize energy use by combining various renewable energy sources, such as solar, wind, and hydroelectric power, with energy storage technologies, such as batteries.

2 Literature review

One major challenge faced by Renewable Energy Sector is reliability as electricity is generated based on natural climate conditions such as solar radiation and wind speed. Another challenge is high cost of electricity. To solve these problems an approach called Hybrid Renewable Energy method is used and then optimization technique is used. To generate ideas, the following literature is used.

In the first stage, the ideas related to Hybrid Renewable Energy Systems are explored from literature. In this context, a study by Hongxing et al. [2] is relevant, which has shown an ideal design concept with battery storage for hybrid solar-wind systems with the goal of obtaining a stable and affordable energy source. Five important factors are mentioned to build the model of this study: battery capacity, wind turbine number, wind turbine installation height, PV module number, and PV module slope angle. An implementation of this approach to a relay station for communications is done in Southeast China and shows how successful it was. The results demonstrated that solar and wind energy sources complement each other; the hybrid system offered a consistent power supply all year round with few instances of battery over-discharge. This method emphasizes how crucial strategic design and optimization are to meeting particular power supply needs in renewable energy systems whileminimizing costs.

Then, the work of Dawoud was explored to gather more insights into HRES systems. This study has shown how a hybrid renewable energy system can be formed using solar photovoltaics, wind turbine generators, diesel engines, and batteries [3]. This paper also gives ideas on how to simulate different Hybrid Renewable Energy System combinations using HOMER software.

At the second stage of idea generation, it was explored how AI/ML techniques can be integrated with the HRES approach. The work of Bhandari et al. has helped in it. This study has highlighted the difficulties and factors to be considered when optimizing hybrid renewable energy systems (HRES) with accuracy [4]. It has explored the impact of weather on the reliability of PV and wind systems, and they can be very unpredictable without sufficient storage or backup systems. Reliability can be greatly improved by incorporating solar PV and Wind Turbine generators into a hybrid design with enough battery capacity. To guarantee that the HRES can meet energy demands even during low renewable energy output, optimal system component sizing is essential. This study provides a comprehensive analysis of recent developments in renewable energy usage trends, physical modeling of these systems, and optimization techniques. The focus placed on artificial intelligence’s (AI) contribution to HRES optimization. By identifying trends and modifying the system in real-time, artificial intelligence (AI) and machine learning approaches can accelerate the optimization process even in the lack of long-term meteorological data.

To understand more usage of Machine Learning Techniques in HRES, the work of Rahman et al. was explored/useful. This study has mentioned how different advance Machine Learning algorithms like artificial neural networks (ANNs), multi-layer perceptron (MLP), recurrent neural network (RNN), convolutional neural network (CNN), long-short-term memory (LSTM) models can be utilized in building HRES of Solar PV and Wind sources [5]. How these techniques can be used in forecasting of output, and how efficiency and reliability of HRES systems can be increased using these techniques.

To gather more insights on ML techniques usage in HRES approach, the work by Roselinea et al. is explored. It has discussed the vital role that predictive models play in the renewable energy industry, particularly to tackle global warming and climate change issues [6]. Here, a modern technique of artificial neural network (ANN) is used to model the HRES approach. The modeling is done to estimate energy generation from photovoltaic (PV) and hybrid PV-wind systems. Such ANN models can greatly improve the accuracy of energy forecasts, which is necessary for the effective operation of smart grids, by considering a variety of weather parameters.

Further, to understand how the Adaptive Neuro-Fuzzy Inference System (ANFIS) technique can be utilized to develop the HRES system, the work of Rajkumar et al. is explored. It has discussed the significance of maximizing resource utilization and cost-effectiveness by optimizing the scale of hybrid renewable energy systems [7]. A primary area of focus for this study is optimizing cost and efficiency through appropriate system sizing. The three main matrices utilized in this case are the Cost of Energy (COE), Capital Recovery Factor (CRF), and Loss of Power Supply Probability (LPSP). The Adaptive Neuro-Fuzzy Inference System (ANFIS) technique has demonstrated great accuracy when compared to other available software like HOMER and HOGA in this context. The simulated result of ANFIS shown better results compared to data generated from these softwares.

At the third stage of idea generation the usage of chemical reaction optimization (CRO) algorithm has been explored. To understand it, the work of Alatas has been considered. It talked about the Artificial Chemical Reaction Optimization Algorithm (CRO), a fascinating strategy that builds a reliable computer method by taking cues from the effectiveness of chemical reactions [8]. Objective of this study is to reduce the number of parameters and boost the robustness of a computational algorithm by utilizing the natural events and processes of chemical reactions. It is also mentioned that CRO Algorithm is used in a variety of fields, including data mining, benchmark functions, and multiple-sequence alignment, which indicates how adaptable and efficient it is at handling challenging issues. The focus of CRO Algorithm is to provide an effective tool for optimization problems across a range of domains by imitating the dynamic and adaptable character of chemical reactions.

Next, to understand more about CRO algorithm and its usage, the work of Siddique et al. is explored. This study gives a thorough explanation of how chemical reactions are viewed within the context of optimization, goes over the Chemical Reaction Optimization (CRO) algorithm and its variations, and gives advice on how to choose efficient CRO parameters to solve different kinds of optimization problems [9]. It serves as an illustration of how nature-inspired algorithms, like CRO, have gained popularity in domains like cognitive computing and machine learning, providing fresh methods for handling challenging problems.

Further, to get an understanding and usage of the CRO algorithm, the study by Luo et al. has been explored. This study talked about the introduction of the novel IMCRO Chemical Reaction Optimization (CRO) method, which aims to solve the Shortest Common Super-sequence (SCS) problem [10] more effectively. Because of its computational complexity, the SCS problem is categorized as NP-hard and is usually solved using heuristic techniques. Adding two new operators—a circular shift operator in the decomposition reaction and a two-step crossover operator in the intermolecular ineffective collision reaction—to the standard CRO, IMCRO improves upon it.

Finally, to understand how CRO algorithm can be combined with advanced ML algorithms, the study by Nayak et al. has been explored. It has focused on the integration of a sophisticated machine learning algorithm, such as the Adaptive Neuro-Fuzzy Inference System (ANFIS), with the Chemical Reaction Optimization algorithm [11]. This paper has introduced a new method for predicting the behavior of the stock market by enhancing a neuro-fuzzy network model using Chemical Reaction Optimization (CRO). By using appropriate metrics, this model seeks to increase the accuracy of financial forecasts.

From the above, the idea of how HRES models can be built using advanced ML algorithms like Feed Forward Neural Network (FNN), ANFIS, Random Forest etc. is explored. But it has been found that no study has tried to integrate advanced ML techniques with Chemical Reaction Optimization algorithm to build HRES systems. Since CRO is a technique thatneeds lesser number of parameters and deliveres efficient and effective results in optimization use cases, it has been conceptualized to use in this case. The present study is focused onfilling the gap, and modeling is done on the idea of building one HRES system using the FNN algorithm and then optimizing it using CRO algorithm.

3 Research questions

  1. a.

    How can we effectively integrate solar PV, wind energy, and Hydropower to achieve reliable and stable power supply?

  2. b.

    What are the economic implications of this HRES configuration?

4 Research objective

Intermittency and variability are two key characteristics of Renewable Energy that affect the reliability of electric power supply. To address intermittency and variability, one approach is to use Hybrid Renewable Energy Systems, which involves integrating various renewable sources. The objective of this study is to address these challenges by the HRES method in the state of Karnataka. This study will also provide a mechanism to optimize the following parameters:

  1. a.

    Cost of electricity

  2. b.

    Capacity of power sources

5 Methodology

5.1 HRES approach

In order to build a more durable and dependable energy generation system, the Hybrid Renewable Energy Systems (HRES) strategy integrates several renewable energy sources. HRES systems integrate two or more renewable energy sources—such as hydro, solar, wind, and occasionally geothermal or biomass energy—to maximize their respective advantages and minimize their drawbacks. HRES systems improve system resilience and dependability by reducing reliance on a single energy type through the diversification of energy sources. When it comes to resource availability and generating patterns, many renewable energy sources complement one another. For instance, wind power may peak at night or during times of low solar irradiance, but solar power output peaks during the day when sunlight is abundant. HRES systems can reduce the variability associated with individual sources and deliver more constant and balanced energy production by integrating sources with complementary generation patterns. To optimize resource consumption and provide a consistent power supply, HRES systems need advanced optimization and energy management techniques. In order to maximize the performance of various energy sources, storage systems, and grid connections in real time, sophisticated control algorithms and prediction models are frequently employed. Energy management systems seek to balance the supply and demand for energy, give priority to the use of renewable energy sources, and reduce dependency on fossil fuels and grid power.

Batteries, pumped hydro storage, thermal energy storage, and other energy storage technologies are essential components of HRES systems. Storage systems store extra energy produced during high production times so they can be used later on during low production or high demand periods. For extended periods of low renewable energy generation, backup devices like diesel generators or grid connections offer more stability and a fallback alternative. HRES systems can be expanded and adjusted to meet changing energy needs, regional climates, and technological breakthroughs. They can be implemented to achieve particular energy needs and resilience objectives in a variety of contexts, such as isolated off-grid locations, metropolitan settings, or hybrid microgrids.

5.2 Model development

A two-step method for forecasting and optimizing power generation from solar, wind, and hydropower sources combines the Feedforward Neural Network (FNN) model with the Chemical Reaction Optimization (CRO) Algorithm. By combining these two methods, it is possible to effectively optimize the power generation system using the CRO algorithm and anticipate power generation from renewable sources with accuracy using the FNN model. While the CRO algorithm optimizes the system configuration to achieve the intended goals, such as decreasing the cost of energy or optimizing the exploitation of renewable energy sources, the FNN model offers the necessary forecasts. The details of model development and algorithm is explained below.

5.2.1 FFNN model

A feed-forward neural network (FFNN) transfers data in a single direction across one or more layers, from the input to the output layer. After receiving input from the neurons in the layer above, each hidden layer neuron adds an activation function to the weighted sum of its inputs. Until the output layer is reached, the output of each neuron in a hidden layer is sent as input to the neurons in the subsequent hidden layer. The final output of the neural network, which is usually a class label or a numerical value, is produced by the output layer.

Strong relationships between inputs and outputs can be modeled by FFNNs, which is advantageous since it allows them to be used for jobs where traditional statistical models might not work well. These models are particularly useful in the intricate energy system, which is connected to many other economic areas. Furthermore, the industry dynamics are rapidly evolving, which complicates any statistical strategy meant to capture all the constraints and theories that exist at a given time.

In our case, to estimate total power generation based on multiple inputs, a single hidden layer of five neurons is incorporated into the neural network design. SSE is used as the loss function, resilient backpropagation is used for effective training, and logistic activation functions are used for non-linearity. This configuration is designed to depict the intricate interactions that exist between technical and environmental factors and the power output produced by renewable energy sources.

Activation function

It’s represented by the sigmoid function

$$f\left( x \right) = \frac{1}{{1 + e^{ - x} }}$$
(1)

The weighted sum of the inputs at every neuron in the hidden layer and the output layer is subjected to this function.

The logistic function adds non-linearity to the model and is utilized as the activation function. The logistic function produces values between 0 and 1 and has an S-shaped curve. The network’s ability to capture intricate patterns surpasses that of linear models due to its non-linearity. The output of FNN in R software which is shown in Fig. 1 below:

Fig. 1
figure 1

FFNN model output in R

Full size image

Error function/loss function

Sum of Squared Errors (SSE): Each data point’s error is squared before being totaled.

$$E = \mathop \sum \limits_{i = 1}^{n} \left( {y_{i} - \hat{y}} \right)^{2}$$
(2)

The loss function of the model is the sum of squared deviations between the actual targets and the expected outputs. Model accuracy is increased during training by minimizing this value.

Hidden layer configuration

Hidden Layers: Neuron activations in the model are dependent on weighted inputs and occur in a single hidden layer, which is an intermediate layer between inputs and outputs.

Neurons: This hidden layer contains 5 neurons. During training, each neuron picks up unique information about how the input properties and the target relate to one another. The decision to use 5 neurons in the model design strikes a compromise between learning capacity and complexity.

Learning algorithm

Resilient Backpropagation: Based on the error determined by the loss function, the method modifies the weights in the neural network. It makes use of the Rprop + algorithm’s principles to update the weights.

This improved backpropagation algorithm is intended for quicker convergence. It modifies the weights based on the gradient’s sign, as opposed to ordinary backpropagation, which modifies them in proportion to the error’s gradient. This makes the update magnitude independent of the gradient’s magnitude. This may result in more rapid training and improved performance on challenging tasks.

5.2.1.1 Hybrid renewable energy system model

It takes a lot of steps to develop a Hybrid Renewable Energy System (HRES) that uses the Feedforward Neural Network (FNN) algorithm to integrate solar, wind, and hydropower. These steps are gathering of data, modelling of the system, FNN model training, mode evaluation, and optimization.

A Hybrid Renewable Energy System (HRES) that integrates solar, wind, and hydropower can be efficiently planned, optimized, and controlled to produce sustainable and dependable energy generation by following the previously mentioned processes and utilizing the FNN algorithm’s capabilities.

At first separate FNN models for Solar energy, wind energy, Hydropower energy are developed and tested. Then separate FNN models are combined into one single FNN model using R software. The details of algorithm, forecasting results and performance metrics are explained and shown below.

Algorithm 1
figure a

FFNN model for solar, wind and hydro power

Full size image

Solar Electricity generation, Wind Electricity Generation and Hydropower Electricity generation data are used to train the model.

5.2.1.2 Forecasting & performance metrics

On the predictor’s data frame, predictions are made using the trained FFNN model. The model’s prediction accuracy is assessed using the Root Mean Squared Error (RMSE) and mean absolute percentage error (MAPE). The difference between the expected and actual values is measured by RMSE.

RMSE Root Mean Squared Error is referred to as RMSE. It’s a metric used, especially in regression analysis, to assess a prediction model’s accuracy. The square root of the average of the squared discrepancies between the expected and actual values is known as the root mean square error, or RMSE. It offers an indicator of how well the model’s predictions agree with the actual data points. Greater agreement between expected and actual values is shown by a lower RMSE.

The following represents the RMSE formula:

$$RMSE = \sqrt {\frac{1}{n}\sum\limits_{{i = 1}}^{n} {\left( {y_{i} - \widehat{{y_{i} }}} \right)^{2} } }$$
(3)

MAPE Mean Absolute Percentage Error is referred to as MAPE. It’s a statistic for assessing a predictive model’s accuracy, especially in forecasting applications. The average of the absolute percentage errors between the actual and anticipated values is known as the MAPE. It offers an indicator of how well the model’s predictions match the actual values. Better agreement between anticipated and actual values is indicated by a lower MAPE.

The following represents the MAPE formula:

$$MAPE = 100/n\mathop \sum \limits_{i = 1}^{n} \left( {y_{i} - \widehat{{y_{i} }}} \right)/y_{i}$$
(4)
Algorithm 2
figure b

Code snippet for RMSE and MAPE

Full size image

5.2.2 Optimization technique

The hybrid system’s optimization technique is used for the optimization of the PV, wind and Hydropower electricity. In the first step, FFNN model determines the total power generated by the wind, Solar PV and Hydropower and after then following Techno-Economic parameters are used for optimization:

  1. 1.

    Loss of power supply probability (LPSP)

  2. 2.

    Capital recovery factor (CRF)

  3. 3.

    Cost of energy (CoE)

5.2.2.1 LPSP

In the hybrid system, LPSP is defined as the probability of an unmet load compared to the total energy produced. LPSP is zero when the load is always met and LPSP is 1 when load never met. To determine the unmet load, the difference in power between the load and all of its available energy sources is used. In this case study, unmet load may be found by subtracting the sum total of load from the solar, wind, hydro from the sum total of load and adding the minimum power available from all other sources. In this way, LPSP is found with the below equation:

$$LPSP = \frac{{\sum {\left( {P_{Load} - P_{pv} - P_{wind} - P_{Hydel} + P_{SOC,min} } \right)} }}{{\sum {P_{load} } }}$$
(5)
Algorithm 3
figure c

Code snippet of LPSP function

Full size image
5.2.2.2 Capital recovery factor

The capital recovery factor, or CRF for short, is a ratio used to determine the components’ present value while accounting for interest rates.

$$CRF = \frac{{interest*\left( {1 + interest} \right)^{usage remaining} }}{{\left( {1 + interest} \right)^{usage reamining} - 1}}$$
(6)
Algorithm 4
figure d

Code snippet of CRF function

Full size image
5.2.2.3 Cost of energy

The cost of energy produced by the hybrid system per unit is known as the levelized cost of energy. Written alternatively, it represents the proportion of the total annualized system cost to the total energy produced by the HRES.

$$COE\left( {RM\, per\, {\text{kW}}} \right) = \frac{{\left[ {\left( {present\, cost + \frac{o}{m}cost + replacement\, cost} \right)*CRF} \right]}}{{P_{load,total} }}$$
(7)
Algorithm 5
figure e

Code snippet of COE function

Full size image

5.3 CRO algorithm

The characteristics of chemical reactions and mathematical optimization approaches are loosely coupled in the idea of CRO. The natural process of changing unstable chemical compounds (reactants/molecules) into stable ones is called a chemical reaction. An excessively energetic, unstable molecule is the first step in any chemical process. Through a series of basic reactions, the molecules interact with one another to produce intermediate chemical compounds. They are ultimately transformed into molecules that need the least amount of energy to survive. Enthalpy (minimization problem) and/or entropy (maximization problem) are terms used to describe the energy associated with a molecule.

This energy fluctuates during a chemical reaction in response to a reactant’s changing intra-molecular structure before stabilizing at a certain point. Depending on the number of reactants involved, these reactions can be either monomolecular or bimolecular. An initial set of reactants in a solution is where the CRO algorithm starts. Subsequently, reactants are used up and produced through chemical processes. When the termination requirement is satisfied, the algorithm ends, akin to the situation in which no more responses are possible (inert solution). The molecule and the elementary reactions are the two main parts of CRO.

Molecules with different energy levels participate in chemical processes, move through a series of simple reactions, and end up as products with the least amount of energy. The CRO’s operators are the basic reactions. These reactions are divided into uni-molecular and multi-molecular reactions.

5.3.1 Chemical reaction operations

Unimolecular reactions:

  1. (i)

    Ineffective collisions on walls

  2. (ii)

    Decomposition

Multiple molecular processes:

  1. (iii)

    Inter-molecular ineffective collision

  2. (iv)

    Synthesis

Algorithm 6
figure f

CRO-initiate parameters and chemical reaction operations

Full size image

5.3.2 On-wall ineffective collision operation

This kind of activity involves just one molecule. The molecule doesn’t interact with other molecules chemically. When molecule x collides with a wall and bounces back, PE and KE are altered. x′ is used to represent the new value. As a result, it is known as an on-wall ineffective collision.

5.3.3 Decomposition operation

Such a process involves a single molecule. The molecule doesn’t interact with other molecules chemically. Two molecules, × 1 and × 2, are created when a molecule, x, collides with a wall. In addition, the molecule has the ability to split into several molecules.

5.3.4 Inter-molecular ineffective collision operation

This kind of process involves two molecules. When two molecules, × 1 and × 2, collide, the two molecules become perturbed and transform into x′1 and x′2. Potential energies {PE(× 1), PE(× 2)} and kinetic energies {KE(× 1), KE(× 2)} are thus altered as a result of the collision.

5.3.5 Synthesis operation

This kind of activity involves two or more molecules. After colliding, two molecules, × 1 and × 2, fuse to form molecule x′. The energy released during fusion is enormous. Therefore, during the synthesis procedure, there is a significant energy change.

The CRO algorithm’s operators are the on-wall ineffective and intermolecular ineffective collision operations, which generate solutions from the neighborhood structure for searching the search space, and the decomposition and synthesis operations, which act as mechanisms for producing new solutions for exploring the search space. The operators for synthesis and decomposition serve as diversification, and the operators for ineffective and intermolecular ineffective collisions serve as algorithmic intensification.

In CRO, there are four primary parameters. These include starting KE, fraction of unimolecular reaction, population size, and KE loss rate. The initial number of randomly produced solutions in the solution space is known as the population size, or PopSize. KELossRate is the maximum percentage of KE lost to the environment during on-wall unsuccessful collisions. It is the loss rate of KE during the reaction. The fraction of molecules that experience uni- or intermolecular reactions is known as the fraction of uni-molecular reaction, or MoleColl. An unimolecular collision occurs if MoleColl is less than a random number, ρ. If not, there will be an intermolecular collision. It should be emphasized that when there is just one molecule left in the population, a uni-molecular collision will always occur. The initial value that is assigned to every element of KE during the initialization step is known as Initial KE, or KE0.

Algorithm 7
figure g

CRO function and optimization loop

Full size image

6 Model development for the study in Karnataka

6.1 Data collection

Data has been collected for the Month of September 2023 from Renewable Energy Management Centers (REMC), Bangalore and Regional State Load Dispatch Centers (SLDC), Karnataka.

REMC-Renewable Energy Management Centers (REMC) serves as a central hub for monitoring, controlling, and optimizing the integration of renewable energy sources into the power grid. Its primary function is to ensure the efficient and reliable operation of renewable energy systems while maintaining grid stability. The REMCs are equipped with artificial intelligence-based RE forecasting and scheduling tools and provide greater visualization and enhanced situational awareness to the grid operators. REMCs are co-located with RLDCs and SLDCs in various states. In Karnataka also, REMC and SLDC areco-located.

6.2 Model implementation

Solar, Wind and Hydropower generation data at 15 min interval was collected in excel format and combined and fitted in our model. At first, the data is cleaned and applied with appropriate technique. 15 days Generation data is used to train the FNN model and used to forecast 16th day data.

The forecasted result of FNN algorithm can be seen below in Fig. 2.

Fig. 2
figure 2

Forecasted output of FNN

Full size image

Then the forecasted result is measured through RMSE and MAPE. The results can be seen below in the Fig. 3.

Fig. 3
figure 3

RMSE and MAPE output of FNN

Full size image

The average magnitude of the errors between projected and actual values is measured by the Root Mean Square Error (RMSE). The discrepancy between expected and observed values is quantified. The RMSE for total generation in this instance is roughly 190.609. The average error in predicting the entire generation is indicated by this value, which is the standard deviation of the prediction errors.As a proportion of the actual values, the MAPE calculates how accurate the predictions are.

An average of 3.46% separates the FNN model’s predictions from the actual total generation values, according to a MAPE value of roughly 3.462135%. Because MAPE is a relative metric, it is simpler to understand how accurate forecasts are, regardless of the size of the data. Next the output of the FNN algorithm is used to get optimum capacity and optimum COE. As tariff rate data was unable to be received within the stipulated time, those rates are assumed from historic data. For COE, a combination of different wind generators, PV module and hydel power was used to match the renewable energy generation with the load. Energy generation with the load was matched on hourly basis with an average of 15 min time block. This was done for a day on 16th September, 2023, with the data collected from REMC and SLDC, Karnataka. The data is available at the appendix. The unmet energy in each time of block is provided by conventional energy or battery. The data for 4:30 PM to 5:30 PM of 16th September is used for the calculation, which is shown in the Table 1.

Table 1 Demand and generation from hydel, solar and wind
Full size table

The first column shows the date and time, the second column showsthe demand at that time block, the third column is for the energy generation of the hydel power, the fourth column shows the energy generation of Solar, and the fifth column shows wind generation. It is not possible for renewable energy to meet the unmet energy directly; for this purpose conventional sources or a storage system, i.e. batteries are needed. Here, for the sake of simplicity, it is called battery storage. It is also assumed that the ability to store excess energy produced by renewable sources (such as solar and wind) during times of high output for use later during times of low production is represented by the battery component in this CRO algorithm. In order to reduce the cost of producing energy, this algorithm optimizes the distribution of energy resources, including battery capacity. The program aims to create the best possible balance between energy generation, storage, and use by modifying the size of the battery in conjunction with other renewable and conventional energy sources.

It has been further assumed that to get a virtual HRES system consisting of PV, Wind, Hydropower and Battery storage. The goal of the optimization process is to determine how best to arrange these capacities to satisfy energy demand while minimizing the cost of energy (COE). The finding of CRO iteration is shown below in Fig. 4.

Fig. 4
figure 4

COE iterations of CRO

Full size image

7 Results

The findings show that the algorithm is getting closer to identifying a solution with reduced energy costs as the Best COE declines over rounds. These numbers stand for the best capacity of the battery storage system and each renewable energy source (photovoltaic, wind, and hydro), respectively, that produce the lowest cost of energy (best COE). Depending on the problem setting or the method used to scale the data, the capacities are expressed in the appropriate units. The total cost (including capital cost and maintenance cost, replacement cost, and operation cost) and LPSP were calculated for each combination. The total lifetime of the system is assumed to be 20 years.

Figure 5 depicts the output of the CRO function. The optimization was done for loss of power supply probability of zero, i.e., the generation will always satisfy the demand. According to the findings, the battery size is roughly 1.937 GW, the best wind capacity is roughly 2.591 GW, the best hydro capacity is approximately 2.591 GW, and the best PV capacity is roughly 3.548 GW that satisfies LPSP of zero value with minimum cost. The demand on 16th September 2023, from 4:30 PM to 5:30 PM was on average, 10.359 GW, which is taken from Table 1. This provides information for the various inputs of different RE sources for a reliable power system.

Fig. 5
figure 5

CRO output for individual capacities

Full size image

8 Discussion

The Renewable Energy Sector faces significant challenges related to reliability and cost. Due to this, Renewable Energy curtailment was observed in the state of Karnataka. Hybrid Renewable Energy Systems (HRES) combined with optimization techniques have emerged as a promising solution to address this. Literature explores several strategies and innovations in this field. For instance, Hongxing et al. highlighted that combining solar and wind energy with battery storage could provide a stable and cost-effective energy supply, as evidenced by a successful implementation in Southeast China [2]. Their findings showed that strategic design could address the variability of renewable sources and minimize costs. While this study demonstrated the effectiveness of integrating solar and wind energy, it primarily focused on a specific implementation in Southeast China. The generalizability of these results to other regions with different climate conditions or energy needs could be a limitation. Dawoud further demonstrated this by exploring the integration of solar photovoltaics, wind turbines, and diesel engines with simulations performed using HOMER software [3]. While the use of HOMER software for simulations offers valuable insights, the integration of fossil fuels may not align with the goal of achieving a fully sustainable energy system. The integration of AI and machine learning techniques, as discussed by Bhandari et al. and Rahman et al., represents a significant advancement in optimizing HRES. Bhandari et al. [4] highlighted how AI can improve reliability by optimizing system component sizing and adapting to real-time data. Rahman et al. [5] demonstrated that machine learning algorithms like ANN can enhance forecasting and efficiency. These techniques address the unpredictability of renewable sources and improve system performance. Roselinea et al. [6] further emphasized the role of predictive models, particularly ANNs, in improving energy forecasts for smart grids. While these advances are promising, they often require extensive data and may face challenges in real-world implementation, such as data quality and availability. Furthermore, the Adaptive Neuro-Fuzzy Inference System (ANFIS) technique, as discussed by Rajkumar et al. [7], has shown promise in optimizing cost and efficiency. The Chemical Reaction Optimization (CRO) algorithm, inspired by natural processes, offers a novel approach to solving optimization problems, as detailed in studies by Alatas [8] and Siddique et al. [9]. As Nayak et al. [11] proposed, combining CRO with machine learning could enhance predictive accuracy and optimization efficiency. The application of the CRO algorithm, as discussed by Alatas [8], Siddique et al. [9], and Luo et al. [10], introduces an innovative approach to optimization. CRO’s ability to handle complex problems with fewer parameters and its adaptability across different fields are valuable. The integration of CRO with advanced machine learning algorithms, as explored by Nayak et al. [11], presents an exciting opportunity for enhancing predictive accuracy and optimization in HRES. This study integrates advanced machine learning techniques like Feed Forward Neural Networks with CRO to develop an optimized HRES model. The results indicate that this approach has provided reliability while increasing the share of Solar, Wind, and Hydro Power in the power system. As the power demand is 10.359 GW from 4:30 PM to 5:30 PM on 16th September 2023, the result of the study suggests using the wind of 2.591 GW and solar power of 3.548 GW which is the higher share of Solar and Wind energy. Thus, this study improved resource utilization by optimizing the sizing and configuration of renewable energy components like Solar and Wind in the power system in the state of Karnataka. However, further validation is needed to assess the generalizability of these findings and the practical implementation of this integrated approach. Future research should focus on validating these techniques across diverse conditions and refining methodologies to enhance the practicality and sustainability of HRES solutions.

9 Conclusion

The first research question was to find a mechanism to integrate effectively Solar PV, Wind Energy, and Hydropower to achieve reliable and stable power supply. For this, the research offers valuable perspectives on the ideal arrangement of a hybrid renewable energy system that includes photovoltaic (PV), wind, hydro, andbattery storage elements. These results can be used to create and put into place dependable, reasonably priced renewable energy systems that are suited to certain regions and profiles of energy consumption. For the second research question, the economic implications of the HRES configuration used in this research, the findings show how to best arrange battery storage and renewable energy components in the hybrid renewable energy system to reduce energy production costs, as determined by the CRO algorithm. The method gradually converges to the least expensive solution by iteratively modifying each component’s capacities in response to their interactions and assessing their effect on the total cost of energy. From the results, it can be observed that this study provides a prototype algorithm for developing HRES systems using FNN and CRO techniques.

The dynamic character of the optimization process is highlighted by the variation in cost of energy (COE) figures throughout several rounds. In comparison to conventional optimization methods, researchers can draw the conclusion that the CRO algorithm dynamically explores the solution space, possibly resulting in increased convergence and solution quality.

The distribution of capabilities among photovoltaic, wind, hydro, and battery storage components show how each contributes differently to reaching the best possible system performance. Scholars can deduce information about how various parts interact with one another and how that affects the overall cost and dependability of the system.

The study emphasizes the difficulties in combining cost, reliability, and performance issues in hybrid renewable energy system optimization. To address these issues and improve the efficacy and efficiency of the deployment of renewable energy, it also offers chances for more research and development. The findings emphasize the significance of reliable optimization techniques that can manage the complexity and unpredictability present in the design and operation of hybrid renewable energy systems. This research will help in reduction in the curtailment of wind energy in the state of Karnataka. However, the same model is difficult to be implemented in other geographical area as the wind energy and solar energy both are dependent on different geographical and climatic conditions. To create and improve optimization algorithms that can accurately and quickly find the best solutions under a range of operational restrictions and settings, more research is necessary in the development of models which are not dependent on geographical and climatic conditions. Research Flow Diagram:

figure h