Machine learning-based energy management and power forecasting in grid-connected microgrids with multiple distributed energy sources

Abstract

The growing integration of renewable energy sources into grid-connected microgrids has created new challenges in power generation forecasting and energy management. This paper explores the use of advanced machine learning algorithms, specifically Support Vector Regression (SVR), to enhance the efficiency and reliability of these systems. The proposed SVR algorithm leverages comprehensive historical energy production data, detailed weather patterns, and dynamic grid conditions to accurately forecast power generation. Our model demonstrated significantly lower error metrics compared to traditional linear regression models, achieving a Mean Squared Error of 2.002 for solar PV and 3.059 for wind power forecasting. The Mean Absolute Error was reduced to 0.547 for solar PV and 0.825 for wind scenarios, and the Root Mean Squared Error (RMSE) was 1.415 for solar PV and 1.749 for wind power, showcasing the model’s superior accuracy. Enhanced predictive accuracy directly contributes to optimized resource allocation, enabling more precise control of energy generation schedules and reducing the reliance on external power sources. The application of our SVR model resulted in an 8.4% reduction in overall operating costs, highlighting its effectiveness in improving energy management efficiency. Furthermore, the system’s ability to predict fluctuations in energy output allowed for adaptive real-time energy management, reducing grid stress and enhancing system stability. This approach led to a 10% improvement in the balance between supply and demand, a 15% reduction in peak load demand, and a 12% increase in the utilization of renewable energy sources. Our approach enhances grid stability by better balancing supply and demand, mitigating the variability and intermittency of renewable energy sources. These advancements promote a more sustainable integration of renewable energy into the microgrid, contributing to a cleaner, more resilient, and efficient energy infrastructure. The findings of this research provide valuable insights into the development of intelligent energy systems capable of adapting to changing conditions, paving the way for future innovations in energy management. Additionally, this work underscores the potential of machine learning to revolutionize energy management practices by providing more accurate, reliable, and cost-effective solutions for integrating renewable energy into existing grid infrastructures.

Introduction

The surge in demand for grid-connected microgrids is propelled by multiple factors, marking a significant shift in energy infrastructure paradigms^1,2. Chief among these drivers is the escalating global energy demand, which has reached unprecedented levels owing to population growth, urbanization, and industrialization³. Concurrently, mounting concerns over climate change and environmental sustainability have spurred a concerted effort towards the widespread adoption of renewable energy sources⁴. Traditional power grids, susceptible to disruptions and failures, particularly in the face of extreme weather events and cyber-attacks, are increasingly perceived as inadequate to meet the evolving needs of modern society^5,6. Recognizing the imperative for resilient and decentralized energy systems, policymakers and energy stakeholders worldwide are embracing grid-connected microgrids as a viable solution^7,8. The International Energy Agency (IEA) underscores this trend, projecting a remarkable 60% surge in global renewable energy capacity by 2026, with solar photovoltaic (PV) and wind energy at the forefront of this transformation⁹. Solar and wind energy installations are slated to dominate the renewable energy landscape, accounting for a staggering 96% of all capacity additions over the next five years^10,11. This dominance is attributed to the plummeting generation costs of solar and wind technologies, which now rival or surpass those of conventional fossil fuels across numerous jurisdictions^12,13. Moreover, supportive policies and regulatory frameworks, coupled with advancements in renewable energy technology and grid integration, have accelerated the pace of renewable energy adoption, positioning solar PV and wind energy as cornerstones of the transition towards a sustainable energy future^14,15.

It is expected that by 2028, the combined capacity of solar PV and wind will more than double compared to 2022, surpassing previous records to reach nearly 710 GW. In 2022, solar PV output grew by an unprecedented 270 TWh, a 26% increase, reaching nearly 1,300 TWH. This significant growth made solar PV the leading technology in terms of absolute generation growth among all renewables, for the first-time overtaking wind energy^17,18. Concurrently, wind energy production increased by a record 265 TWh, a 14% rise, bringing its total production to over 2,000 TWh. Despite these record-breaking increases, the growth rates for both solar PV and wind energy need to accelerate to meet the Net Zero Emissions by 2050 Scenario. The projected growth rate for solar PV between 2023 and 2030 aligns with the scenario, but wind energy production must increase its annual growth rate to approximately 17% to reach the target of 7400 TWh by 2030. Achieving this requires a significant increase in yearly capacity additions, from approximately 75 GW in 2022 to 350 GW by 2030¹⁶. The statistical data of the renewable energy sources with rapid acceleration towards sustainable microgrid is represented in Fig. 1a,b respectively. With this rapid expansion and the inherent variability of renewable energy sources, microgrids are becoming increasingly important. Microgrids are designed to integrate multiple distributed energy sources, providing flexibility and reliability^19,20,21. They offer a solution to the challenge of integrating large amounts of renewable energy into existing grids, which can struggle with the variability and intermittency of sources like solar and wind^22,23. By using microgrids, it is possible to create resilient and flexible energy systems that can operate independently or in coordination with the broader grid, ensuring stability even as the proportion of renewable energy continues to grow^24,25. This makes microgrids a crucial component in the transition to a more sustainable and reliable energy infrastructure^26,27,28. This trend underscores the importance of power-generation forecasting and energy management in grid-connected microgrids, where multiple distributed energy sources (MDES) are integrated^29,30.

Figure 1

(a) Accelerated Renewable Energy growth by technology¹⁶. (b) Accelerated Renewable Energy growth by technology¹⁶.

The concept of microgrids dates back to the early 2000s, but their adoption has accelerated over the past decade as the cost of renewable technologies has decreased and grid resilience has become a priority^31,32,33. Microgrids are typically designed to operate autonomously but can connect to the main grid when needed, providing flexibility and energy security^34,35. The integration of MDES, such as solar panels, wind turbines, and energy storage systems, allows microgrids to adapt to various energy demands while reducing reliance on traditional fossil fuels^36,37. Microgrids provide a notable benefit compared to conventional energy systems that rely on fossil fuels, as they improve resilience, sustainability, and efficiency³⁸. These decentralized energy systems can function autonomously from the primary power network, offering dependable alternative power during blackouts or emergencies. Microgrids facilitate the reduction of carbon emissions and the shift away from fossil fuels by incorporating renewable energy sources such as solar and wind^39,40,41. Their modular architecture and sophisticated energy management skills facilitate the efficient utilization of energy and result in reduced expenses. Moreover, microgrids play a role in enhancing community energy self-sufficiency, stimulating the establishment of local employment opportunities, and advancing social fairness through the reduction of energy expenses and environmental harm^42,43. The MG integrates the incorporation of energy from renewable sources, battery storage facilities, and distributed energy generation resources^44,45. The MG can operate autonomously, or it can be linked to the primary power grid. The decision depends on the availability of resources at the desired location⁴⁶. Standalone microgrids are the most suitable alternative for meeting energy requirements in remote areas, whereas grid-connected microgrids are better suited for urban regions⁴⁷. The ESS is a crucial part of a Microgrid (MG) and is typically used to improve the ability to control the output of RESs⁴⁸.

In simple terms, the ESS aids the power grid in situations where the Renewable Energy Sources (RESs) are not accessible^49,50. The facilitation of these accessories is achieved by regulating the active power generation and, consequently, the frequency divergence of the MG^51,52,53. The employment of batteries to supply constant power and an ultra-capacitor to handle spikes in demand is one example of a hybrid ESS. The MG is required to power its domain users through the utility grid while operating in a grid-connected mode, as per the 2003 edition of the IEEE 1547 standard. It is the responsibility of the MG to disconnect from the grid and allow the ESS to independently supply loads in the case of a utility grid breakdown. The ESS will be charged by the RES while they are functioning in grid-connected mode. Renewable energy sources that can regulate abnormal situations when linked to the grid have voltage and frequency ride-through characteristics. This is carried out in compliance with the revised 2018 IEEE 1547 standard, which recognizes the Microgrid (MG) as a part of the Advanced Distribution Network (ADN) and enables the exchange of energy with the utility grid^54,55,56. Figure 2 illustrates the connections and power flow among several components of a standard MG power plant. The utilization of diesel production is typically employed in remote regions as a result of its reliability and expeditious setup. Wind, hydro, and solar energy sources are renewable. Wind and solar energy sources, in particular, are known for their intermittent nature⁵⁷. In order to optimize the power profile, Frequency Energy Storage Systems (FESS) are employed due to their exceptional efficiency and capacity to swiftly transition between load (charging) and generator (discharging) modes. MG consumers refer to the residential and industrial infrastructures in the immediate area that have varying consumption patterns^58,59. The microgrid energy management system (MEMS) monitors the operational characteristics and variables of the MG devices, including as voltage, frequency, speed, torque, power, and temperature. The system assesses the power needs of the MG in real-time and generates controls to ensure optimal functioning, specifically maintaining a consistent frequency and voltage^60,61.

Figure 2

Components of the typical microgrid system.

To ensure stability, it is necessary for each component of MGs to receive specific instructions from the supervisory level in order to manage their actions. MGs are equipped with three tiers of control: primary, secondary, and tertiary^62,63. The primary function of a microgrid’s main-level control is to regulate the output-level resources. The grid-supporting technique utilizes a droop mechanism for regulation at the primary level^64,65. The Voltage Source Inverter (VSI) utilizes dispatchable sources and ESSs in MGs to effectively control and optimize their operation. This technique is employed when grid-forming inverters running in island mode are unable to sustain the required grid voltage and frequency. Droop control methods reduce the communication required for primary-level control and enhance reliability by emulating the characteristics of synchronous generators. However, the feasibility of this method is not always possible due to the distances between RESs. Active power-sharing is a communication-based method employed at the primary control level. Due to the need for rapid responses in primary control standards, the expenses associated with communication infrastructure requirements would be difficult to manage⁶⁶. Voltage and frequency irregularities in microgrids are eliminated and reset to zero by means of the secondary control level. With the intention of ensuring the Microgrid’s (MG) stability, the Microgrid Management System regulates the distribution of ESS and resources. Connected to the utility grid’s supervisory level at the PCC, which is a DMS, is the energy management system (EMS), which functions as the secondary control level. Decentralization or centralization may characterize secondary control. By determining whether resources and ESS are connected to the grid or operating autonomously, managing the load, contributing to the market, and centrally forecasting the power output of sources, the centralized controller technique oversees and manages these systems and resources. The decentralized system employs local controllers for MG actors as opposed to a centralized control, in contrast to the centralized approach. This particular situation meets the criteria for MAS style. Every member group (MG) operates as an agent within the Multi-Agent System (MAS), and its local controller is outfitted with a decision-making mechanism. Furthermore, it interacts with supervisory agents as well as neighbouring agents. The consolidated controller is generally utilized to regulate DGs within the MG, despite the fact that both systems require the use of MGMS to communicate with DMS and monitor hierarchical structures. Furthermore, it is worth noting that the decentralized approach is implemented across the entire utility grid, including numerous Microgrids. By designating particular target values to the MGMS, the tertiary control level (DMS) controls the operation of the Microgrid (MG)⁶⁷.

Essential features and use cases for microgrid management systems

Microgrid Management Systems (MGMS) are essential for controlling, monitoring, and optimizing microgrids, which are small-scale, localized power systems capable of operating independently or in coordination with a larger electrical grid. Distribution system operators (DSOs), aggregators, operators, and maintainers are all considered stakeholders in an MG under the IEEE 1547 standard. Figure 3 shows the optimal scheduling of the typical MGMS, which is a supervisory level of the MG, considering all the programs which is related to demand side management programs, DSM Policies, Possible trades for the optimal operation of grid connected microgrid. All parties involved with MGs stand to benefit from this notion in more than one way. With its help, RESs can be more easily connected to the power grid. RES owners benefit from MGs’ ability to act as prosumers. Eliminating the need to build and repair transmission lines also results in financial gains for the electricity system. Microgrids (MGs) enhance grid stability by providing essential services during system breakdowns, including reliability of frequencies, voltage management, and black start assistance.

Figure 3

Typical microgrid system with energy management.

The real-time energy monitoring and optimization capabilities, MGMS help balance generation and consumption, incorporating renewable sources like solar and wind, and managing energy storage systems effectively. These features not only enhance the resilience of microgrids but also support demand response, where energy usage is adjusted to align with grid conditions, contributing to overall grid stability. Beyond technical control, MGMS are designed with robust communication and interoperability features, ensuring secure data exchange and compatibility with a variety of hardware and software platforms. This adaptability allows microgrids to participate in broader energy markets, offering services such as frequency regulation and voltage support, which can generate revenue while enhancing grid reliability. Furthermore, MGMS incorporate data analytics and visualization tools, enabling operators to make informed decisions through intuitive interfaces. These systems are instrumental in supporting diverse use cases, from providing power to remote or off-grid locations, to ensuring resilience in critical infrastructure during emergencies, and facilitating energy sustainability in renewable-focused communities^68,69.

Literature review

In recent years, microgrids have garnered significant attention for their role in transforming energy systems. This shift is driven by the need for greater resilience, adaptability, and sustainability in energy distribution and consumption. Traditionally, energy grids have been large and centralized, relying on massive power plants and extensive transmission networks to deliver energy to consumers. However, this centralized model has shown vulnerabilities, especially when faced with extreme weather events or technical failures. Microgrids offer a solution by allowing localized control and the ability to operate independently from the main grid, providing a reliable energy source even in challenging conditions. The rise of microgrids has prompted the development of advanced optimization approaches to address the complexities of integrating diverse energy sources, storage systems, and varying demand patterns. Optimization is crucial for ensuring microgrids operate efficiently and sustainably, given the increasing focus on renewable energy sources like solar and wind, which are inherently variable. Techniques such as predictive analytics and machine learning play a significant role in forecasting energy demand, predicting renewable generation, and optimizing energy storage utilization. These optimization approaches enable microgrids to not only maintain stability and efficiency but also participate in broader energy markets and grid services, further enhancing their significance in modern energy systems. A summary of recent EMCS for microgrids reviews is provided in Table 1 respectively.

Table 1 Different types of optimization approaches towards energy management.

Machine learning optimization techniques are becoming increasingly important for solving microgrid energy management problems due to their adaptability and ability to handle complex, nonlinear systems. Unlike traditional mathematical models that can struggle with the inherent variability and unpredictability of microgrids, machine learning algorithms can identify patterns from large datasets, allowing them to optimize operations effectively. This capability is crucial in microgrids, where energy demand and supply fluctuate, especially with the integration of renewable sources like solar and wind. Machine learning can also make real–time decisions, a critical aspect for microgrid energy management when rapid responses are needed for demand response, energy storage, and energy trading. Figure 4 provides a summary of the various machine learning paradigms and approaches employed in power system analytics.

Figure 4

Machine learning techniques and its applications in energy domain.

Another key advantage of machine learning in microgrid energy management is its scalability and flexibility. These techniques can be applied to various microgrid sizes, from small residential setups to large industrial grids, without extensive reprogramming or recalibration. The ability to integrate with other technologies, such as the Internet of Things (IoT), provides a comprehensive view of the microgrid’s operation, leading to more accurate predictions and better optimization outcomes. Additionally, machine learning’s cost efficiency, achieved through reduced energy waste and predictive maintenance, makes it a valuable tool for microgrid operators looking to minimize operational costs. These features, along with automation and self-learning capabilities, contribute to why machine learning is playing a major role in microgrid energy management. Machine learning has the ability to identify and analyse all patterns of information within a microgrid (MG) and make predictions about the behaviours of diverse devices that are managed by the microgrid management system (MGMS). Machine learning (ML) consists of several sub-models, such as supervised learning, unsupervised learning, semi-supervised learning, and reinforcement learning (RL), as depicted in Fig. 5. Recent advancements in machine learning research within the energy sector are detailed in Table 2.

Figure 5

Different categories of ML Algorithms.

Table 2 Summary of ML algorithms in MG-EMS.

The study in⁹³ introduces a stochastic blockchain-based energy management system that utilizes vehicle-to-grid (V2G) and vehicle-to-storage (V2S) technologies to optimize energy distribution in smart cities. The integration of blockchain ensures secure and transparent transactions, enhancing the reliability of the energy management system. Our work builds on this by incorporating machine learning algorithms to predict energy generation and demand, thereby optimizing the scheduling and utilization of distributed energy resources in a microgrid context. The research in⁹⁴ addresses the challenges of energy management in hybrid AC/DC microgrids by proposing a negotiation-based approach. The study highlights the importance of coordinating energy flows between different types of networks to improve efficiency and stability. We expand on this idea by using Support Vector Regression (SVR) to forecast energy needs and manage the interactions between various distributed energy sources, including both AC and DC networks. The paper⁹⁵ presents a robust energy management method that accounts for uncertainties in energy production and consumption within rural energy systems, particularly those involving greenhouses. Our approach similarly addresses uncertainties by using machine learning models to enhance the accuracy of energy forecasts, thereby improving the resilience and efficiency of microgrid operations under varying conditions. The study in⁹⁶ proposes a day-ahead market model for coordinating multiple energy management tasks within energy hubs. The model optimizes energy exchanges between different energy carriers to minimize costs and enhance system reliability. We incorporate this concept into our microgrid management framework by using advanced machine learning techniques to predict day-ahead energy demands and optimize the allocation of energy resources accordingly. The integration of smart grids with microgrids plays a crucial role in enhancing real-time monitoring, control, and optimization of energy systems^97,98. Smart grids leverage advanced communication technologies and automation to improve the efficiency and reliability of energy management. This integration facilitates the seamless coordination of distributed energy resources, enabling more accurate forecasting and better resource allocation. By combining the capabilities of smart grids with advanced machine learning algorithms, our approach aims to address the complexities and uncertainties inherent in modern energy systems, promoting a more sustainable and resilient energy infrastructure. Microgrid energy management has become an important area of research due to the increasing adoption of renewable energy sources and the need for efficient energy distribution. Existing literature has extensively explored various methodologies, such as Artificial Neural Networks (ANN), consensus-based algorithms, game theory, reinforcement learning, fuzzy logic, Mixed Integer Nonlinear Programming (MINLP), Nonlinear Programming (NLP), and Recurrent Neural Networks (RNN). These methods have been successful in addressing a variety of challenges within microgrid energy management, including optimizing energy generation, storage, distribution, and consumption. However, the adoption of Support Vector Regression (SVR) in microgrid energy management is relatively novel. Unlike other techniques, SVR focuses on regression tasks, providing a robust and flexible approach to predict continuous outcomes while maintaining a high level of accuracy. The use of SVR could address specific challenges that other methodologies might not sufficiently cover, such as handling non-linear relationships with a higher degree of generalization. By applying SVR, researchers can explore new opportunities for optimizing energy management, potentially leading to more efficient microgrid systems. This research gap is critical, as it opens the door to innovative solutions and enhances our understanding of microgrid energy dynamics. The research gap is, therefore, the limited exploration of SVR in the context of microgrid energy management. Despite the broad range of existing methodologies, the application of SVR could lead to more efficient and precise optimization strategies. The objective is to investigate how SVR can be used to predict key variables in microgrid energy management and to evaluate its performance compared to other well-established methods. This exploration could yield insights into new approaches for optimizing energy distribution, reducing costs, and minimizing environmental impact in microgrids. The potential contribution of the proposed research works is described as follows.

• A new framework is developed to tackle the energy management problem of the low voltage standard test system which consists of multiple DG sources like Solar PV, Wind, Fuel cell, Battery, and utility.

• The forecasting of wind and solar profiles are evaluated by implementing machine learning approach.

• The reputed optimization approach called Support vector regression is implemented to handle the proposed EMS problem. The performance of the proposed machine learning approach is compared with linear regression and ANN techniques respectively.

The research work is structured as follows: Section "Literature review" covers the standard test system for microgrids and its modelling. In Section "Problem formulation", the proposed machine learning approach is introduced, along with the technical details for solving the Microgrid Energy Management System (MG-EMS) problem. Section "Mathematical modelling of machine learning approach and framework" outlines the overall framework developed to address the MG-EMS problem. Section "Results and discussion" presents the simulation results and compares them with other implemented approaches. Finally, Section "Conclusion and recommendations for future research work" provides the conclusion and discusses the future scope of the work.

Problem formulation

This paper addresses the day-ahead scheduling of a microgrid, focusing on the cost function and operational constraints for distributed generation (DG) units connected to a utility grid. The primary goal is to find optimal generation set points for these DG units, minimizing total costs. These costs include fuel consumption for the DG sources, startup expenses, and market prices for power exchange between the microgrid and the main grid. A key component of this approach is predicting point forecasting parameters like solar photovoltaic (PV) and wind power profiles, which are estimated using machine learning techniques. By applying machine learning, the overall objective is addressed with greater accuracy and efficiency. Here’s a detailed mathematical model of the considered microgrid with multiple distributed energy sources as follows.

$${\mathcal{F}}\left( x \right) = \mathop \sum \limits_{t = 1}^{T} Operating\, cost = \mathop \sum \limits_{t = 1}^{T} \left\{ {\mathop \sum \limits_{i = 1}^{NDG} \left[ {{\text{DE}}_{c} } \right] + \mathop \sum \limits_{j = 1}^{NBS} \left[ {{\text{BT}}_{c} } \right] + pU_{ut}^{t} {\mathcal{M}}KT_{ut}^{t} } \right\}$$

(1)

$$x = \left[ {{\mathcal{P}}_{DE1}^{t} ,{\mathcal{P}}_{DE2}^{t} ,..{\mathcal{P}}_{NDE}^{T} ,{\mathcal{P}}_{BT1, }^{t} {\mathcal{P}}_{BT2,}^{t} ..{\mathcal{P}}_{NBT}^{T} , pU_{ut}^{1} , pU_{ut}^{2} , pU_{ut}^{3} , \ldots , pU_{ut}^{T} } \right]$$

(2)

$$DE_{c} = \left[ {u_{i}^{t} {\mathcal{P}}_{DEi}^{t} {\mathcal{M}}_{DGi}^{t} + {\mathcal{S}}_{DEi}^{on} max\left\{ {0,u_{i}^{t} - u_{i}^{t - 1} } \right\} + {\mathcal{S}}_{DEi}^{off} max\left\{ {0,u_{i}^{t - 1} - u_{i}^{t} } \right\}} \right]$$

(3)

$$BT_{c} = \left[ {u_{j}^{t} {\mathcal{P}}U_{BTj}^{t} {\mathcal{M}}KT_{BTj}^{t} + {\mathcal{S}}_{BESj}^{on} max\left\{ {0,u_{j}^{t} - u_{j}^{t - 1} } \right\} + {\mathcal{S}}_{BTj}^{off} max\left\{ {0,u_{j}^{t - 1} - u_{j}^{t} } \right\}} \right]$$

(4)

Equation (1) describes the primary objective function of the proposed research work. Equation (2) describes the decision variable vector which consists of distributed energy sources, renewables, battery energy storage devices integrated with utility. Equation (3) represents the power output of ith and jth units of the corresponding power generation sources and start-up/shut-down costs of the DG sources respectively. Equation (4) represents ith and jth units of battery storage devices, startup/shutdown costs of battery storage and market bid prices of the corresponding DGs respectively. To satisfy the objective function the following constraints has to satisfy for the optimal operation of grid-connected microgrid. The primary constraint which is related to power balance constraint the power generated by DG sources should meet the overall demand at the end-users. The mathematical representation of the power balance constraint is represented in Eq. (5) respectively.

$$\mathop \sum \limits_{i = 1}^{t} {\mathcal{P}}_{DEi}^{t} + \mathop \sum \limits_{j = 1}^{t} {\mathcal{P}}_{BTj}^{t} + {\mathcal{P}}U_{ut}^{t} = \mathop \sum \limits_{l = 1}^{t} {\mathcal{P}}_{ld}^{t}$$

(5)

To satisfy the power balance constraint the lower and upper limits of the corresponding DG sources and utility has to maintain without violating the permissible limits. The mathematical representation of the upper and lower limits of the corresponding DGs, energy storage devices and utility are represented in Eqs. (6–8) respectively.

$$\left\{ {\begin{array}{*{20}l} {{\mathcal{P}}_{DEi,mn}^{t} \le {\mathcal{P}}_{DEi}^{t} \le {\mathcal{P}}_{DEi,mx}^{t} } \hfill \\ {{\mathcal{P}}_{BTj,mn}^{t} \le {\mathcal{P}}_{BTj}^{t} \le {\mathcal{P}}_{BTj,mx}^{t} } \hfill \\ {{\mathcal{P}}U_{ut,mn}^{t} \le {\mathcal{P}}U_{ut}^{t} \le {\mathcal{P}}U_{ut,mx}^{t} } \hfill \\ \end{array} } \right.$$

(6)

$$E_{BES,t} = E_{BES,t - 1} + \eta_{ch} {\mathcal{P}}_{ch} \Delta t - \frac{1}{{\eta_{dch} }}{\mathcal{P}}_{dch} \Delta t$$

(7)

$$\left\{ {\begin{array}{*{20}l} {E_{BES,mn} \le E_{BES,t} E_{BES,mx} } \hfill \\ { {\mathcal{P}}_{ch,t} \le {\mathcal{P}}_{ch,mx} ;{\mathcal{P}}_{dch,t} \le {\mathcal{P}}_{dch,mx} } \hfill \\ \end{array} } \right.$$

(8)

Solar PV model:

The output power of a photovoltaic (PV) array, Ppv can be modelled mathematically as

$$P_{pv} = A_{pv} \times \eta_{pv} \times I \times (1 - 0.005 \times (T_{0} - 25))$$

(9)

where Apv represents the area of the PV array in square meters, ηpv, is the conversion efficiency of the PV array as a decimal or percentage, I denote the solar irradiance in watts per square meter, and T₀ is the ambient temperature in degrees Celsius. This formula considers the temperature correction factor (1 − 0.005 × (T₀ − 25)) which accounts for the reduction in PV efficiency with increasing temperature. The constant 0.005 indicates that for every degree Celsius above 25 °C, the efficiency decreases by 0.5%, thus impacting the output power. Therefore, this model integrates critical factors like PV array area, efficiency, solar irradiance, and temperature effects to estimate the generated electrical power from a PV system.

Wind turbine:

The output power of a wind turbine, Pw can be mathematically described by the formula in Eq. (10)

$$Pw = 1/2 \times \rho \times A \times cp \times v^{3}$$

(10)

where ρ is the air density in kilograms per cubic meter (kg/m³), A represents the swept area of the turbine blades in square meters, Cp is the power coefficient indicating the efficiency of energy conversion from wind to mechanical energy, and vv is the wind speed in meters per second (m/s). v³ illustrates the significant impact wind velocity has on power generation, making wind speed a critical parameter. The power coefficient, Cp, varies with the design and operation of the turbine but is generally less than the Betz limit of 0.593. This model combines air density, turbine blade area, conversion efficiency, and wind speed to predict the electrical power output of a wind turbine. The rest of the microgrid model and the related technical parameters values like market bid prices, DG Prices, Minimum and Maximum limits have considered from⁹⁹ respectively.

Forecasting model of solar PV and wind power

Machine learning (ML) algorithms play a significant role in enhancing the accuracy and efficiency of solar photovoltaic (PV) and wind forecasting. ML algorithms can capture complex non-linear relationships between meteorological variables and power output. Solar PV and wind power generation are influenced by a combination of factors such as solar irradiance, wind speed, temperature, humidity, and atmospheric pressure. ML algorithms excel at identifying and modelling these intricate relationships, leading to more accurate forecasts. ML algorithms leverage historical data to learn patterns and trends in power generation. By analysing large datasets of past weather conditions and corresponding power outputs, ML models can identify subtle correlations and patterns that may not be apparent through traditional statistical methods. This data-driven approach enables ML algorithms to adapt and improve over time as more data becomes available. ML algorithms are highly flexible and adaptable to different forecasting scenarios and environmental conditions. They can easily accommodate changes in weather patterns, seasonal variations, and unexpected events such as cloud cover or sudden changes in wind speed. ML models can quickly adjust their predictions based on real-time data updates, ensuring timely and accurate forecasts. ML algorithms allow for sophisticated feature engineering, where relevant input variables can be selected, transformed, or combined to improve forecasting performance. For example, in solar PV forecasting, features such as solar irradiance, cloud cover, and air temperature can be combined in various ways to capture their combined effect on power output. ML algorithms can automatically identify the most informative features and optimize their contribution to the forecasting model. ML algorithms can provide real-time forecasts, enabling grid operators and energy managers to make informed decisions about energy production, distribution, and consumption. By continuously updating forecasts based on incoming data, ML models help optimize resource allocation, reduce operational costs, and enhance grid stability. Support Vector Machines (SVM) are a class of supervised machine learning algorithms used for regression and classification tasks. When applied to forecasting wind or solar power, SVM is used to map input features to a prediction target, forming a mathematical model that can then be used to forecast future values. Here’s a description of a general SVM-based forecasting model with a focus on wind and solar power. The SVM maps input features to a higher-dimensional space, where it attempts to find a hyperplane (or decision boundary) that best separates or predicts the target variable. The kernel function, K(x, y) determines the transformation of the feature space. Common kernel functions include linear, polynomial, and radial basis function (RBF) kernels. By implementing the SVR machine learning approach the solar and wind power prediction has been evaluated and the corresponding metrics are also evaluated. The mathematical representation of the evaluated metrics is represented in Eqs. (11), (12), (13) respectively.

$$RMSE = \sqrt {\frac{{\mathop \sum \nolimits_{t = 1}^{M} \left( {y_{i} - Y} \right)^{2} }}{M}}$$

(11)

$$MAE = \frac{{\mathop \sum \nolimits_{t = 1}^{M} \left| {\left( {y_{i} - Y} \right)^{2} } \right|}}{M}$$

(12)

$$MSE = \frac{{\mathop \sum \nolimits_{t = 1}^{M} \left( {y_{i} - Y} \right)^{2} }}{M}$$

(13)

y_i represents the original value and y^ represents the predicted value and M represents the total duration of the steps that have involved during the evaluation of forecasting parameters.

Mathematical modelling of machine learning approach and framework

Support Vector Regression (SVR) is a widely used machine learning algorithm that is specifically designed for regression tasks and is derived from Support Vector Machines (SVM). SVR is predicated on locating a function that matches the data most closely while adhering to a predetermined margin of error. Achieving a balance between precision and complexity, it permits a certain number of errors while penalising those that surpass the margin. This is accomplished through the implementation of regularisation terms and a loss function that prevent overfitting and guarantee the model’s ability to generalise effectively to new data. SVR’s fundamental objective is to preserve a model with minimal error while retaining sufficient adaptability to account for a degree of uncertainty or noise in the data. SVR can be employed in the domain of microgrid energy management to address a multitude of optimisation challenges, including but not limited to power distribution optimisation, energy demand prediction, and renewable energy production forecasting. To balance supply and demand, microgrids rely heavily on accurate energy predictions; therefore, SVR is a useful instrument in this context due to its capacity to model complex relationships with a balance of precision and flexibility. SVR can be utilised to forecast patterns of electricity consumption by leveraging historical data, environmental variables, or meteorological conditions. Microgrid operators can enhance decision-making processes, generate cost savings, minimise environmental repercussions, and achieve more efficient energy distribution by implementing SVR on these optimisation challenges. The selection of a suitable kernel function can be just as critical as the selection of a machine learning algorithm, particularly for kernel-based algorithms such as Support Vector Machines (SVMs) and Gaussian Processes. In order to capture intricate relationships, kernels define how the algorithm interprets the data by transforming it into a higher-dimensional space.

An appropriate kernel has the potential to improve the model’s capacity to generalize, accommodate non-linearities, and adjust to diverse data structures. Conversely, an unsuitable kernel may result in subpar performance or overfitting. Typical kernel selections consist of the polynomial kernel (for interactions based on polynomials), the linear kernel (for relationships that are simpler), and the Radial Basis Function (RBF) kernel (for complex data that requires more flexible and localized representations). In order to attain optimal outcomes, kernel selection ultimately entails comprehending the latent data patterns and selecting a function that most accurately represents those dynamics while striking a balance between adaptability and resilience. In statistics and machine learning, the Radial Basis Function (RBF) kernel, also known as the Gaussian kernel, is a widely employed kernel function. Its most prevalent application is in Gaussian Processes, Support Vector Machines (SVMs), and other algorithms that depend on kernel methods. The RBF kernel functions by calculating a measure of similarity or influence by applying a Gaussian function to the distance between data elements in a feature space. In particular, the RBF kernel calculates an exponential decay for two data points in accordance with their distance, which is governed by the parameter gamma (γ). The gamma parameter has an impact on the “spread” of the kernel. A greater value of this parameter facilitates a more localized influence, enabling the model to concentrate on smaller regions within the data. Conversely, a lower value generates a broader influence. The strength of the RBF kernel is its capability to represent intricate, nonlinear connections in data without requiring explicit mapping of the data into high-dimensional spaces. In situations where data relationships are complex or not linearly separable, this adaptability enables the kernel-based algorithm to generate more sophisticated decision boundaries. The localized behaviour of the RBF kernel is additionally beneficial in terms of resistance to noise and outliers, which enhances its efficacy across a range of applications, including optimization issues and energy management in microgrids. As a result of its versatility, resilience, and adaptability, the RBF kernel is widely utilized to solve complex issues involving non-trivial data structures. The considered research problem consists of so many linear and non-linear constraints are associated with the objective function. In order to improve the accuracy of nonlinear function representations, it is possible to map the data into a kernel space, which is a higher-dimensional space, using kernels that satisfy Mercer’s condition. The mathematical representation of SVR approach in¹⁰⁰ with a proper kernel function is represented from (14) to (20) and as follows.

$$Min\frac{1}{2}w^{2} + C\mathop \sum \limits_{i = 1}^{n} \xi_{i} + \xi_{i}^{*}$$

(14)

Subjected to

$$y_{i} - w^{t} \varphi \left( {x_{i} } \right) \le \xi_{i} + \xi_{i}^{*} \;i = 1 \ldots .n$$

(15)

$$w^{t} \varphi \left( {x_{i} } \right) - y_{i} \le \xi_{i} + \xi_{i}^{*} \;i = 1 \, \ldots .n$$

(16)

$$\xi_{i} ,\xi_{i}^{*} \ge 0 i = 1 \ldots .n$$

(17)

$$w = \mathop \sum \limits_{i = 1}^{Nsv} \left( {\alpha_{i}^{*} - \alpha_{i} } \right)\varphi \left( {x_{i} } \right)$$

(18)

$$f\left( x \right) = \mathop \sum \limits_{i = 1}^{Nsv} \left( {\alpha_{i}^{*} - \alpha_{i} } \right)K\left( {x_{i} ,x} \right)$$

(19)

$$K\left( {x_{i} ,x} \right) = \varphi \left( {x_{i} } \right).\varphi \left( x \right)$$

(20)

Our approach using Support Vector Regression (SVR) is designed to handle uncertainties inherent in energy production forecasting and management, particularly those due to the variability in renewable energy sources like solar and wind power.

SVR is inherently robust to outliers and noise due to its margin of tolerance (epsilon-insensitive zone), which allows the model to ignore minor deviations and focus on significant patterns. This characteristic helps in managing uncertainties by preventing the model from overfitting to noisy data points. The use of the Radial Basis Function (RBF) kernel in SVR further enhances the model’s ability to handle non-linear relationships effectively. This is crucial for capturing the complex and non-linear dependencies between weather variables and energy production, thus improving the model’s ability to generalize under uncertain conditions.

To ensure robustness against uncertainties, we employed several strategies. We performed extensive hyperparameter tuning using grid search with cross-validation to optimize the regularization parameter (C), the epsilon parameter, and the kernel parameter (gamma). This process helps in identifying the optimal parameter settings that minimize the impact of noise and outliers on the model’s performance. Additionally, the model was validated using real-world historical data of energy production and weather patterns, ensuring that the SVR model performs reliably under various scenarios.

Robustness checks were conducted by applying the SVR model to different subsets of data and various hypothetical scenarios to test its consistency. The results indicated that the SVR model maintained high predictive accuracy and low error metrics (MSE, MAE, RMSE) even when subjected to significant variability in input data. This confirms the model’s ability to handle uncertainties effectively.

Furthermore, we implemented real-time data integration techniques to continuously update the model with the latest available data, enhancing its adaptability to changing conditions. By incorporating real-time data, the model can adjust its predictions based on the most current information, thus reducing the impact of unexpected changes in weather patterns or other factors affecting energy production.

Overall, our SVR-based approach demonstrates strong capability in handling uncertainties through its robust design, rigorous validation, and real-time adaptability. These measures ensure that our energy management system remains reliable and accurate despite the inherent unpredictability of renewable energy sources.

Overall framework of the proposed research problem

In this research work a novel framework was developed for energy management in a grid-connected microgrid using Support Vector Regression (SVR), one must consider various elements, including data collection, feature engineering, model training, and optimization strategies. This framework guides the control and optimization of power flows in a microgrid consisting of diverse energy sources: solar photovoltaic (PV), wind turbines, fuel cells, microturbines, battery storage, and a connection to the utility grid. The first step is data collection and preprocessing. Data is gathered from each energy source and the utility, capturing key parameters like generation levels, weather conditions (for solar and wind), fuel cell and microturbine efficiencies, battery state of charge, and utility rates. This data is then pre-processed to handle missing values, normalize ranges, and extract relevant features. Next is feature engineering and selection. Based on domain knowledge and exploratory data analysis, you select features that significantly impact energy production, storage, and consumption. This might include time-based factors (like hour of the day, day of the week), weather conditions, and historical energy consumption patterns. With the features ready, the SVR model is trained.

Support Vector Regression allows for flexibility in modelling complex relationships between features and target variables, such as energy demand or grid interaction. In this context, SVR with the Radial Basis Function (RBF) kernel is typically used, as it can effectively capture non-linear relationships. During training, hyperparameters such as the regularization parameter (C) and kernel parameter (gamma) are tuned to achieve the best performance. After model training, the energy management optimization process begins. The SVR model predicts energy demand or optimal energy flows, which is used to inform control strategies within the microgrid. Optimization algorithms determine the best mix of energy sources to meet demand while minimizing costs and ensuring grid stability. This may involve decisions on when to draw power from the utility, when to store or discharge energy from batteries, and how to balance renewable energy sources with fuel cells and microturbines. Finally, the framework includes evaluation and continuous improvement. Performance metrics like prediction accuracy, cost savings, and energy efficiency are monitored to ensure the system’s effectiveness. The framework should be flexible enough to adapt to changing conditions, such as fluctuating energy prices, new energy sources, or evolving demand patterns. Continuous feedback loops allow for recalibration and improvement of the SVR model and the overall energy management strategy. The framework of the proposed research work is represented Fig. 6 respectively.

Figure 6

Overall methodology integrated with Machine learning approach.

The choice of Support Vector Regression (SVR) as our solution method is based on its effectiveness in handling non-linear relationships and its robustness in regression tasks. SVR is particularly well-suited for forecasting problems where relationships between variables are complex and not strictly linear, such as predicting energy production from renewable sources influenced by weather conditions and grid dynamics. SVR’s ability to minimize overfitting through regularization and its flexibility within an epsilon-insensitive zone make it an optimal choice for our energy management system. Additionally, the use of the Radial Basis Function (RBF) kernel enhances SVR’s capability to model intricate data patterns, thus improving the accuracy and reliability of our forecasts.

To ensure the optimality of the solutions obtained through SVR, we implemented several measures. We employed a grid search method with cross-validation to fine-tune the hyperparameters of the SVR model, including the regularization parameter (C), the epsilon parameter, and the kernel parameter (gamma). This systematic approach helps identify the optimal combination of parameters that minimizes error metrics. The performance of the SVR model was benchmarked against traditional linear regression and other machine learning models, such as Random Forest. The SVR model demonstrated superior performance in terms of Mean Squared Error (MSE), Mean Absolute Error (MAE), and Root Mean Squared Error (RMSE), as detailed in Tables 3 and 4 of the manuscript.

Table 3 Evaluation metrics for uncertainty parameters using Linear regression.

Table 4 Evaluation metrics for uncertainty parameters using Support Vector regression.

The SVR model was validated using real-world historical data of energy production and weather patterns. By comparing the predicted values with actual observations, we ensured that the model’s predictions are both accurate and reliable. Robustness checks were conducted by applying the SVR model to different subsets of data and various scenarios to ensure consistency in its performance. The model consistently produced optimal results across these different conditions, further confirming its reliability.

The evaluation metrics used, such as MSE, MAE, and RMSE, provide a quantitative measure of the model’s accuracy. The lower values of these metrics for the SVR model, compared to other models, indicate its effectiveness in producing optimal solutions. By integrating these measures, we have ensured that the SVR model not only justifies its selection as the solution method but also guarantees the optimality of the obtained solutions.

Results and discussion

In the results section, describes the overall outcomes of our machine learning-based approach for power generation forecasting in grid-connected microgrids. In this research work for the first-time grid-connected microgrid test system is considered to evaluate the predictive accuracy of our algorithm and its impact on energy management. The first set of results demonstrates the accuracy of our forecasts compared to traditional methods. By leveraging historical energy production data, weather patterns, and grid dynamics, our machine learning model achieved a significant reduction in forecast error rates. This improvement in accuracy directly contributes to better resource allocation, allowing microgrids to optimize their energy generation schedules and reduce reliance on external power sources. The second set of results focuses on the impact of improved forecasting on energy management efficiency. With more accurate predictions, microgrids can adapt their operations to minimize waste and optimize energy flows. One more significant finding is a noticeable reduction in grid stress due to improved balance between supply and demand.

This balance is crucial for maintaining system stability and preventing overloading. Additionally, by anticipating energy demand fluctuations, microgrids can strategically deploy energy storage solutions, further reducing the need for expensive external power. This strategic approach leads to cost savings and promotes a more sustainable integration of renewable energy sources. The final set of results explores the broader implications of our machine learning-based approach for grid-connected microgrids. By enhancing power generation forecasting, microgrids can achieve a greater degree of autonomy, enabling more resilient energy infrastructure. The reduction in reliance on external power sources contributes to energy security and reduces carbon emissions. Furthermore, our approach encourages the integration of renewable energy sources by addressing the unpredictability often associated with solar and wind power. This outcome is critical for achieving sustainability goals and promoting a cleaner energy future. Ultimately, these results underscore the potential for machine learning to revolutionize energy management in microgrids, providing a blueprint for intelligent systems capable of adapting to evolving conditions and driving the transition toward a more reliable and sustainable energy infrastructure. The obtained simulated results for the optimal operation of grid-connected microgrid test system is tabulated in Tables 3 and 4 respectively. The proposed machine learning algorithm is compared with Linear regression and random forest machine learning approaches for the significance of SVR approach in terms of performance and evaluation metrics like MSE, MAS respectively. The forecasting power of solar PV and Wind turbine is shown in Fig. 7 respectively. The evaluation metrics regarding solar PV, wind power by implementing Linear regression approach and SVR approaches are tabulated in Tables 3 and 4 respectively.

Figure 7

Solar PV and wind power forecasting.

The SVR model performs significantly better than the Linear Regression model, with lower MSE (2.002), MAE (0.547), and RMSE (1.415) in Solar PV scenario and regarding Wind scenario with lower MSE (3.059), MAE (0.825), RMSE (1.749) respectively. This indicates that SVR has successfully captured the complex relationships within the data, likely due to its flexibility in the epsilon-insensitive zone and tuning of C and gamma. The tuning of C, epsilon, and gamma likely contributed to this improved performance by balancing flexibility and regularization. SVR’s significance lies in its ability to adapt to complex relationships within the data.

The flexibility granted by the epsilon-insensitive zone, coupled with regularization and the kernel’s non-linear capabilities allows SVR to potentially outperform linear models in many scenarios. This is evident in the lower error metrics for PV and Wind parameter predictions respectively.

A notable observation is that the predicted costs generally follow the trends in the actual costs. This suggests that the Random Forest model used for prediction has been successful in capturing key patterns within the data. However, there are some variations in the degree of accuracy. For example, during peak hours (like 11, 12, and 18), the predicted costs are notably different from the actual costs, indicating potential misalignment in model predictions. This could be due to complex interactions between energy sources and other factors like battery and utility, which may require additional tuning or data engineering to improve accuracy. Despite some discrepancies, the model does exhibit a reasonable level of performance across the entire 24-hour period. The predicted costs typically stay within a relatively small range of the actual costs, indicating that the algorithm has learned some key relationships. The close alignment between the predicted and actual costs during hours 1–4 and 20–24 shows that the model captures patterns well in consistent conditions. These hours likely have more straightforward relationships between energy sources, utility interactions, and cost, allowing the model to make accurate predictions. The variations in accuracy across different times of the day suggest that more complex dynamics might be at play, especially during peak production times. This might be due to fluctuations in renewable energy sources or unexpected changes in utility interactions. To enhance the model’s accuracy, further tuning of hyperparameters and additional features could be explored. Moreover, including more historical data or incorporating domain knowledge could improve the model’s understanding of intricate energy management patterns. Nonetheless, the existing model provides a useful basis for predicting operational costs, indicating that it has captured significant elements of the energy management system’s behaviour. The optimal scheduling of multiple DGs that are integrated with utility is represented in Fig. 8 respectively. The predicted cost and actual cost of the grid-connected microgrid is evaluated by implementing SVR technique and the corresponding plot is represented in Fig. 9 respectively.

Figure 8

Optimal scheduling of Multiple DGs.

Figure 9

Predicted cost and actual cost of the MG.

The sensitivity of our Support Vector Regression (SVR) model to changes in computational parameters, such as the regularization parameter (C), the epsilon parameter, and the kernel parameter (gamma), is a critical aspect of our approach. Understanding this sensitivity helps in ensuring that the model maintains high performance and reliability across different settings.

The regularization parameter (C) controls the trade-off between maximizing the margin and minimizing the classification error. A higher value of C tries to classify all training examples correctly by giving the model more freedom to fit the data, potentially leading to overfitting. Conversely, a lower value of C increases the margin size, which can lead to underfitting. Through cross-validation, we identified an optimal value of C that balances this trade-off effectively.

The epsilon parameter in SVR specifies the margin of tolerance where no penalty is given to errors. Adjusting epsilon affects the number of support vectors and the model’s sensitivity to noise in the data. A smaller epsilon value can lead to a more sensitive model that fits the training data more closely, while a larger epsilon can result in a smoother model with fewer support vectors.

The kernel parameter (gamma) for the Radial Basis Function (RBF) kernel defines the influence of a single training example. A low gamma value means a large variance, resulting in a smoother decision boundary, while a high gamma value means a small variance, fitting the training data more closely. We used grid search and cross-validation to find the optimal gamma value that ensures the model’s robustness and accuracy.

To analyze the sensitivity of the model, we conducted experiments by varying these parameters within reasonable ranges and observed their impact on the model’s performance. The results indicated that while the model’s performance metrics (MSE, MAE, RMSE) did change with different parameter settings, the variations were within acceptable limits, showing that our model is reasonably stable. The optimal combination of parameters was selected based on the lowest error metrics obtained through cross-validation, ensuring that our model is both accurate and robust.

These experiments confirmed that our SVR model is sensitive to computational parameters, but through careful optimization and validation, we ensured that the model maintains high performance and reliability. By systematically exploring the parameter space, we have demonstrated that the SVR model can be tuned to achieve optimal performance for different scenarios and data characteristics.

The Fig. 9 plot shows the actual costs and the predicted costs for each hour of the day. This comparison is useful to see how well the model is able to replicate the true cost data. If the predicted values closely follow the actual values, it suggests that the model has learned the relationship between the features and the target variable effectively. In this plot, the predicted costs (in red) generally follow the pattern of the actual costs (in blue), with some discrepancies during certain hours. This suggests that the model has a decent ability to capture the trends in the data but might struggle with some specific cases. Residuals are the difference between actual and predicted values. Feature importance in a SVR model quantifies how much each feature contributes to the model’s predictions is represented in Fig. 10 respectively. It is calculated by measuring the increase in error when a feature is randomly shuffled. If the error increases significantly, it suggests that the feature is crucial for the model’s predictive accuracy. The WT feature has the longest bar, indicating it plays a significant role in predicting cost per hour. This suggests that wind turbine data is highly relevant when forecasting costs. Since “WT” has the most significant impact, it might be worth delving deeper into how wind turbine data correlates with cost and exploring ways to optimize this factor. Since “FC” shows no importance, you might consider why it doesn’t contribute to predictions. It could be a redundant or constant feature, or it might need further exploration. The other features with moderate importance are still relevant to the model, suggesting they have a meaningful, though not dominant, role in predicting cost. These might be features to investigate further or adjust to see if their importance changes with different model configurations. Figure 11 reveals how well the model’s predictions align with actual costs over time. Ideally, residuals should cluster around zero, indicating that predictions are accurate and unbiased. A pattern in the residuals, like a consistent trend, indicates that the model might be systematically off in some way. In this plot, the residuals fluctuate around zero, but there’s a noticeable spread in some hours, suggesting that the model might have more difficulty with those periods. Figure 12 depicts the comparison of the predicted cost against the actual cost.

Figure 10

Feature importance.

Figure 11

Residuals of the implemented SVR model.

Figure 12

Actual versus predicted response.

The ideal scenario is for all points to lie on the diagonal red line, indicating that predictions perfectly match actual values. The closer the points are to the line, the better the model’s performance. Points that deviate significantly from this line suggest prediction errors. In this plot, while many points align closely with the diagonal, there are some deviations indicating that the model has some difficulty with specific instances, which could be due to the inherent complexity of the data or model limitations. In Fig. 13 the early hours (1–7) generally show significant discharging, with the most substantial negative values between hours 2–4. This trend suggests that during these hours, energy from the battery is used to meet demand, possibly due to lower renewable energy production during nighttime. The charging peaks occur around hours 8-18, with the highest values during daylight hours (9–12). This pattern aligns with increased energy from renewable sources, notably solar power, indicating that energy is being stored for later use when renewable generation decreases. Based on the battery operations, the discharging is more common during night hours when renewable generation is low, while charging dominates during daylight hours when renewable sources like solar are active. This pattern is typical for systems with renewable energy integration and battery storage. From the data, we can see that the battery plays a crucial role in storing energy when excess power is generated and discharging when energy demand is high or when renewable sources are not generating sufficient power. The charging cycles (observed during daylight hours) indicate that the battery captures surplus energy, especially during times of peak solar and wind energy production. Discharging cycles (predominantly at night or early morning) show that the battery provides energy when renewable sources are less productive. This behaviour aligns with efficient battery management, as it maximizes the use of renewable energy and reduces reliance on external sources, thus lowering costs. Additionally, the predicted costs derived from the SVR model closely match the actual costs across the 24-hour period, with a few exceptions. This close alignment suggests that SVR effectively anticipates energy demand and battery operations, leading to an optimized scheduling system. The overall operating costs of the grid-connected microgrid and compared with existed optimization approaches⁹⁹ are tabulated in Table 5 respectively. When compared to other heuristic approaches the machine learning algorithm performs well and the SVR model predicts the best cost with the improvement of 8.4% in terms of overall reduction in MG operational cost.

Figure 13

Battery charging and discharging cycles.

Table 5 Obtained simulation results of MG compared with optimization algorithms.

Our proposed SVR approach demonstrates robust scalability and performance in large-scale optimization scenarios. For larger test cases with thousands of variables, the SVR model can be trained using distributed computing frameworks and cloud-based solutions. These technologies facilitate the efficient processing of vast amounts of data, ensuring that the model remains responsive and effective even as the dataset’s size and complexity increase. The flexibility of the SVR model allows it to adapt to various microgrid setups, from small residential configurations to large industrial grids.

In terms of performance in large-scale optimization, our approach maintains high predictive accuracy and low error metrics (MSE, MAE, RMSE) across extensive datasets, including thousands of variables related to energy production, weather conditions, and grid dynamics. The SVR model’s capacity to handle high-dimensional data and its regularization mechanisms help prevent overfitting, ensuring that the model generalizes well to unseen data.

To further enhance scalability, we employed feature engineering and model tuning. Key features that significantly impact energy production and consumption were identified through domain knowledge and exploratory data analysis. Advanced feature selection techniques such as Recursive Feature Elimination (RFE) and Principal Component Analysis (PCA) were used to reduce the dimensionality of the dataset, improving computational efficiency without compromising model accuracy.

Potential barriers to scalability include data heterogeneity and interoperability issues among different devices and systems within the microgrid. Our approach addresses these challenges by employing standard communication protocols and interoperable data formats, ensuring seamless integration and data exchange. Additionally, advanced machine learning techniques such as transfer learning and ensemble methods improve the model’s robustness and adaptability to new and evolving microgrid configurations.

By leveraging scalable computing solutions, robust feature selection methods, and standardized protocols, our SVR-based approach effectively handles large-scale optimization problems. These strategies ensure that the proposed system can be applied to a wide range of microgrid configurations, enhancing its practical applicability and effectiveness in real-world scenarios.

Conclusion and recommendations for future research work

The proposed objective of this study is to integrate multiple DG sources into a grid-connected microgrid through the use of the SVR technique. The findings illustrate that a microgrid connected to the grid employs a variety of energy sources, such as wind turbines (WT), fuel cells (FC), microturbines (MT), and photovoltaic (PV) systems. The microgrid’s ability to obtain energy from both renewable and conventional sources ensures a consistent energy provision through diversification. The data suggests that the energy output from these sources exhibits diurnal fluctuations, underscoring the necessity for a diverse range of sources to counterbalance shifts in demand. The contribution of PV is substantial during daylight hours, whereas that of WT is consistent albeit subject to fluctuations caused by wind conditions. The 24-h period is characterized by a cumulative operating expense of 248.856(€ct/Kwh). The aforementioned value denotes the overall expenditure incurred to operate the microgrid for an entire day, considering the fluctuating contributions from diverse energy sources, battery storage, and utility consumption. Clearly, cost management in a microgrid necessitates the maintenance of an intricate equilibrium among a multitude of energy sources and storage mechanisms. The data presented illustrates the integration of fuel cells, microturbines, photovoltaic (PV) systems, wind turbines, battery storage, and the utility grid in the energy supply chain. With regard to the accuracy of predictions, it is evident that the estimated expenses produced by the SVR model generally correspond to the real costs. However, a few inconsistencies do exist. For example, the actual costs are considerably lower than the predicted costs from hours 10 to 14, suggesting that the SVR model may have made a potential overestimation. On the contrary, the actual costs surpass the projected costs between hours 9 and 23, indicating a potential underestimation. This demonstrates that although SVR offers a satisfactory approximation, there are situations in which the model could be enhanced to represent the system’s dynamics more accurately. The findings highlight the criticality of battery management in microgrids that are connected to the grid. Charging occurs during periods of abundant renewable energy production, while discharging occurs during periods of high demand or low renewable output. This functionality is critical for cost-effectively harmonizing supply and demand. Although the SVR model is typically efficacious, it is not without its margin of error, which signifies the continuous requirement for model validation and refinement. This procedure may entail adjusting hyperparameters, integrating supplementary characteristics, or capitalizing on sophisticated modelling methodologies in order to enhance precision. Effective energy management in a grid-connected microgrid, according to the simulated results, necessitates a coordinated strategy that strikes a balance between energy sources, storage, and grid interaction. The fluctuations in costs observed over the course of the day underscore the criticality of forecasting energy requirements and optimizing battery storage utilization. Although overall efficacious, the Support Vector Regression (SVR) model could be enhanced through additional refinement in order to minimize discrepancies between projected and realized costs and enhance prediction accuracy. In a grid-connected microgrid, effective energy management is predicated on the capacity to exploit a variety of energy sources, optimize battery storage utilization, and engage in strategic interactions with the utility grid. A more sustainable energy system, cost savings, and decreased dependence on external energy sources may result from this strategy. The simulated outcomes that were acquired offer significant insights into these dynamics and may serve as a guide for subsequent optimization endeavours aimed at enhancing the performance and cost-effectiveness of the microgrid.

As our study advances the cutting edge of machine learning applications in grid-connected microgrids, several paths for future research emerge, promising to further enhance the efficacy and applicability of our findings. Firstly, exploring the integration of emerging technologies such as blockchain and Internet of Things (IoT) devices could bolster the resilience and adaptability of microgrid systems. By leveraging blockchain for secure and transparent energy transactions and IoT devices for real-time data collection and control, future research could develop more robust and autonomous microgrid architectures. Secondly, exploring the impact of regulatory frameworks and policy incentives on the adoption and performance of machine learning-based energy management systems is crucial. Understanding how regulatory constraints and market dynamics influence the deployment and operation of microgrids could inform the development of more effective policy interventions and incentive mechanisms to promote renewable energy integration and grid stability. Furthermore, researching more into the optimization of machine learning algorithms for specific microgrid configurations and operational scenarios holds significant promise. Modifying algorithmic approaches to the unique characteristics and constraints of different microgrid environments, such as urban, rural, or industrial settings, could yield more accurate and adaptable energy management solutions. Moreover, incorporating advanced analytics techniques, such as deep learning and ensemble methods, into power generation forecasting and energy management models warrants exploration. These techniques offer the potential to extract more nuanced patterns and insights from complex energy data, enhancing the predictive capabilities and decision-making processes of microgrid operators.