Appropriate analysis on properties of various compositions on fluids with and without additives for liquid insulation in power system transformer applications | Scientific Reports

Scientific Reports volume 14, Article number: 17814 (2024) Cite this article

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Transformer is a well-known power system apparatus utilized in conjunction with solid insulations such as paper and press board, as well as liquid insulations like mineral oil, a petroleum-based fluid. Despite the notable drawbacks associated with mineral oil, such as limited resources for future generations and its non-eco-friendly nature, its usage remains ubiquitous. There is a growing imperative to explore alternative fluids that surpass mineral oil in terms of environmental impact and performance. Amidst the global shift towards green energy, this study focuses on vegetable seed oils such as corn oil, soybean oil, mustard oil, and rice bran oil as potential substitutes. The research evaluates these oils based on key transformer properties including breakdown voltage, water content, interfacial tension, viscosity, acidity, flash point, and fire point. Interestingly, rice bran oil and soybean oil exhibit promising characteristics that suggest they could effectively replace petroleum-based fluids in transformers. Furthermore, the study extends to blending mineral oil with vegetable seed oils in various compositions, incorporating natural and synthetic antioxidant additives ranging from 0 to 1%. Comparative analyses between samples with and without additives reveal that the inclusion of 1% propyl gallate yields outstanding performance improvements. For instance, a blend comprising 25 ml of mineral oil and 25 ml of soybean oil, supplemented with 1% propyl gallate, demonstrates 90% higher effectiveness compared to other blends and additives tested. Moreover, the research employs statistical regression analysis to establish relationships between different parameter variables, providing deeper insights into the performance and compatibility of these blended oils in transformer applications. This comprehensive investigation underscores the potential of vegetable seed oils as viable alternatives to mineral oil, contributing to the advancement of eco-friendly solutions in power systems.

Power transformers are indispensable components within power system networks, serving critical roles in both transmission and distribution. These devices facilitate the efficient transfer of electrical energy from power plants to various end-users across extensive geographical areas. Their operation is vital for maintaining a reliable supply of electricity to homes, businesses, and industries. The significance of transformers in power systems cannot be overstated. A failure in even one transformer can have widespread repercussions, potentially leading to complete power outages for consumers connected to that particular transformer. This underscores the critical need for robust design, maintenance, and continuous monitoring of transformers to prevent failures that disrupt electricity supply. Insulation issues represent one of the primary causes of transformer failures. The insulation within transformers serves to electrically isolate different components and prevent leakage of electrical current. Any degradation or breakdown of insulation can compromise the transformer's ability to function safely and efficiently. Factors such as aging, environmental conditions, and operational stresses can contribute to insulation degradation over time1,2.

Insulation failure is widely recognized as a primary cause of significant disruptions in power equipment reliability and operational continuity1,2. Transformers are critical components in power systems, ensuring uninterrupted electricity supply that is vital for various sectors such as manufacturing, engineering, and healthcare3,4,5. Within transformers, liquid dielectrics play a dual role by providing electrical insulation between different components and also facilitating efficient heat dissipation. For many decades, industries have relied heavily on petroleum-based products6. Mineral oil, a prominent example among these products, has been extensively used in transformers due to its excellent dielectric strength and suitable viscosity characteristics7,8. Despite its advantages, concerns about its biodegradability and sustainability of resources have spurred efforts to find alternative insulation fluids7,8.

Historically, transformers have predominantly utilized oil-filled technology for insulation and cooling purposes. The liquid insulation used in these transformers is typically derived from petroleum-based products. This transformer oil not only provides electrical insulation but also serves as a medium for dissipating heat generated during operation, thereby maintaining optimal temperature conditions within the transformer9. The operational lifespan and reliability of transformers are heavily influenced by the condition of their liquid insulation. The quality and stability of the transformer oil play a crucial role in ensuring continuous and efficient operation. Therefore, monitoring and maintaining the integrity of the insulation are essential tasks in managing transformer assets within a power system. While mineral oil-based transformer oil has been widely used due to its favorable electrical and thermal properties, it poses significant environmental challenges. This includes its potential as a hazard to the environment upon leakage or improper disposal. Additionally, the high cost associated with the safe disposal of used transformer oil further complicates its environmental impact and lifecycle management10. In response to the environmental concerns associated with mineral oil-based transformer oil, researchers have explored vegetable oils as potential alternatives. Vegetable oils, such as those derived from natural esters, offer several advantages. They are biodegradable, non-toxic, and more environmentally friendly compared to mineral oil. These properties make vegetable oils attractive candidates for replacing traditional transformer oils in terms of sustainability and reduced environmental impact11,12,13,14,15. Natural ester-based vegetable oils are obtained from plant sources or their seeds. They consist of triglyceride esters of fatty acids, which can be categorized into saturated, mono-unsaturated, and poly-unsaturated types. The composition of fatty acids in these oils influences their physical and chemical properties, including their insulation performance in transformer applications16,17,18,19. The current study focuses on analyzing the suitability of natural ester-based vegetable oils as insulation materials for transformers. Researchers have procured samples of these oils from local manufacturers and are conducting detailed analyses of their fatty acid compositions. These analyses aim to assess the compatibility and performance of vegetable oils as compared to traditional mineral oil-based transformer oils, which serve as a benchmark in this investigation.

The exploration of vegetable-based liquid insulations represents a significant step towards enhancing the sustainability and environmental compatibility of power transformer technologies. By evaluating natural ester-based vegetable oils, researchers seek to mitigate the environmental impacts associated with traditional mineral oil-based transformer oils while maintaining or improving the performance and reliability of transformers in power systems20,21,22. This detailed expansion provides a comprehensive overview of the role of transformers, the challenges associated with traditional transformer oils, and the potential of vegetable oils as sustainable alternatives in power system applications.

Antioxidants play a critical role in maintaining the quality and extending the operational life of transformer fluids by enhancing oxidation stability. Oxidation stability is essential because it prevents the degradation of oils over time due to exposure to oxygen and high temperatures, which can lead to the formation of harmful by-products and a decline in performance.

Antioxidants function by inhibiting or delaying the oxidation process, which occurs when oxygen reacts with hydrocarbons in the oil. This reaction produces free radicals, which are highly reactive and can initiate chain reactions leading to oil degradation. Antioxidants work by scavenging these free radicals, thereby interrupting the chain reaction and preventing further oxidation. This process effectively protects the oil from oxidative breakdown and maintains its electrical and thermal properties over an extended period.

There are two primary categories of antioxidants used in transformer fluids:

Natural Antioxidants These antioxidants are derived from natural sources and include compounds such as Citric acid and Gallic acid. Natural antioxidants are valued for their environmental compatibility and ability to enhance the oxidation stability of bio-based transformer oils. They function by effectively neutralizing free radicals and stabilizing the oil against oxidative degradation.

Synthetic Antioxidants Synthetic antioxidants, such as Propyl Gallate, Butylated Hydroxyl Toluene (BHT), and Butylated Hydroxyl Anisole (BHA), are chemically synthesized compounds known for their superior antioxidant properties. They are highly effective at inhibiting oxidation reactions and are widely used in mineral oil-based transformer fluids. Synthetic antioxidants offer robust protection against oxidation-induced degradation, ensuring prolonged service life and reliability of transformer oils.

The choice of antioxidant depends on several factors including the type of transformer oil (mineral oil or bio-based oil), operating conditions (temperature, oxygen exposure), and regulatory requirements. Manufacturers carefully select antioxidants to optimize performance and ensure compliance with industry standards for transformer reliability and longevity.

The incorporation of antioxidants significantly enhances the performance of transformer fluids by mitigating the effects of oxidative stress. By maintaining oxidation stability, antioxidants contribute to improved electrical insulation properties, reduced viscosity changes, and increased thermal conductivity. This translates into enhanced operational efficiency and reliability of transformers, crucial for maintaining uninterrupted power supply in critical sectors such as utilities, industrial facilities, and healthcare institutions.

Continued research and development efforts are focused on exploring novel antioxidant formulations and improving their effectiveness in transformer applications. The goal is to achieve even greater oxidation stability while addressing environmental concerns and regulatory requirements. Additionally, advancements in antioxidant technology aim to optimize compatibility with emerging bio-based oils and enhance overall sustainability in transformer design and operation.

Vegetable oils serve as versatile components across a wide array of manufactured goods. They are integral to the formulation of external care products like luxurious soaps, fragrant perfumes, and a diverse range of cosmetics. Their presence extends into industrial applications, notably in the electrical sector where they are employed as environmentally benign insulators. Notably, vegetable oils boast several ecological advantages: they are non-toxic, capable of biodegrading even when spilled, and possess elevated flash and fire points, making them safer choices in sensitive environments23,24.

The composition of vegetable oil, derived from plant seeds, comprises triglyceride fatty acids categorized into saturated, mono-unsaturated, and polyunsaturated types. These constituents imbue each oil with distinct properties and functionalities, influencing its suitability for various applications. Locally sourced varieties such as corn oil, rice bran oil, mustard oil, and soybean oil are particularly favored for experimental studies due to their sustainable nature and regional availability. Oils rich in saturated fatty acids generally exhibit enhanced stability and viscosity, while those high in polyunsaturated fatty acids may display lower stability and viscosity, impacting their performance in different contexts25,26,27,28. This variability in composition not only underscores the versatility of vegetable oils but also highlights their potential for tailored applications across diverse industries.

Antioxidants play a crucial role in enhancing the stability of oils and other substances by mitigating the effects of oxidation. Oxidation is a chemical process wherein molecules lose electrons, leading to the formation of free radicals that can initiate chain reactions and ultimately degrade the oil29. Natural antioxidants such as Citric acid (CA) and synthetic counterparts like Propyl Gallate (PG) are chosen for their ability to intercept these free radicals. Citric acid, derived naturally from citrus fruits, and Propyl Gallate, a synthetic antioxidant, both function by donating hydrogen atoms to the free radicals formed during oxidation30. This process converts the highly reactive radicals into stable compounds, thereby preventing them from further propagating oxidation reactions within the oil31. By effectively scavenging these radicals, antioxidants like CA and PG significantly extend the shelf life and quality of oils, fats, and related products.

The mechanism by which antioxidants operate involves breaking the chain reaction of free radical formation. When oxidation begins, free radicals are produced which can lead to the formation of peroxides and other harmful compounds32. Antioxidants interrupt this process by providing a stable molecule that can accept the unpaired electron, thus neutralizing the free radical. This action not only prevents the oil from developing off-flavors, odors, and colors but also maintains its nutritional integrity and functionality over time. In practical applications, antioxidants are strategically added during the production and storage of oils and fats to enhance their oxidative stability33. This is crucial in industries ranging from food processing to cosmetics and pharmaceuticals, where maintaining product quality and safety is paramount34,35. The chemical properties and molecular structures of these antioxidants, as detailed in Table 1, illustrate their specific roles and efficacy in combating oxidation and preserving the desired attributes of the oils they protect.

The samples prepared for investigating the properties of transformers are categorized and listed in Table 2. Mineral oil serves as the base sample against which the efficiency of vegetable oils is evaluated. Specifically, samples 1 to 4 consist solely of different types of vegetable oils. In contrast, samples 5 to 20 represent various combinations of mineral oil blended with different types of vegetable oils. These combinations are designed to explore how the introduction of vegetable oils affects the overall performance and characteristics of the transformer oils. Each sample is meticulously prepared to ensure a comprehensive analysis of factors such as oxidation stability, thermal conductivity, dielectric strength, and compatibility with transformer materials.

This experimental approach allows for a thorough comparison between traditional mineral oil-based transformer fluids and newer formulations incorporating vegetable oils. By systematically varying the composition, researchers can assess which combinations offer optimal performance in terms of reliability, environmental impact, and operational efficiency in transformer applications. The findings from these analyses are critical for advancing the development of transformer oils that meet modern standards for sustainability and performance.

The decision to explore vegetable oil as a potential replacement for petroleum-based mineral oil in transformer applications is driven by several key advantages offered by vegetable oils. Unlike mineral oils, which are derived from non-renewable fossil fuels, vegetable oils are sourced from renewable plant materials. This renewable origin makes vegetable oils inherently more sustainable and aligns with global efforts to reduce dependency on finite resources and mitigate environmental impact. One of the standout properties of vegetable oils is their biodegradability. When spilled or disposed of, vegetable oils break down naturally over time through biological processes. This contrasts sharply with mineral oils, which can persist in the environment for extended periods, posing environmental risks and necessitating costly cleanup procedures in case of spills.

Additionally, vegetable oils tend to have lower toxicity profiles compared to mineral oils. This characteristic is particularly advantageous in scenarios where leakage or accidental release into the environment could potentially impact ecosystems or human health. By using vegetable oils, the overall environmental footprint of transformer operations can be reduced, contributing to sustainable practices and regulatory compliance. In terms of performance, vegetable oils offer promising attributes that can rival or surpass those of mineral oils. They exhibit good electrical insulation properties, which are critical for ensuring the safe and efficient operation of transformers. Moreover, vegetable oils can withstand high operating temperatures and have excellent thermal stability, making them suitable for demanding applications in electrical equipment.

The experimental approach involves blending specific vegetable seed oils with mineral oil in controlled proportions. This blending process is crucial for optimizing the performance characteristics of the resulting transformer oil blends. To enhance the oxidative stability of these blends, antioxidants such as those used in this study (Citric acid, Propyl Gallate) are added in varying amounts (0.5 g and 1 g) to assess their effectiveness in inhibiting oxidation reactions that can degrade the oil over time.

The blending process itself is meticulously conducted using a magnetic stirrer, as depicted in Fig. 1. This equipment ensures thorough mixing and uniform distribution of additives throughout the oil blend, which is critical for achieving consistent performance across different samples. The stirring process is typically conducted at a controlled speed (e.g., 50 rpm) for a specified duration (e.g., 30 min) to achieve optimal homogeneity before samples are collected for further analysis. Subsequently, each prepared sample undergoes a battery of tests to evaluate various critical parameters relevant to transformer oil performance. The hotplate can accommodate vessels with capacities ranging from 500 mL to 5 L and has two different sizes of top plates (120 × 120 mm and 180 × 180 mm). It can reach temperatures up to 380 °C and achieve stirring speeds up to 1500 RPM. The unit operates on a standard electrical input of 230 V AC at a frequency of 50–60 Hz.

Magnetic stirrer.

The process begins with heating 500 ml samples of oil to 100 °C to eliminate any moisture content. Moisture can significantly affect the efficiency and performance of transformer oils by compromising their dielectric strength and accelerating oxidation processes. By ensuring the oil is free from moisture, the subsequent evaluations can accurately assess its properties. The evaluation of these oil samples involves comparing them with and without the addition of antioxidant additives. Antioxidants, such as Citric acid and Propyl Gallate, are blended in varying proportions (0.5 g and 1 g) to gauge their effectiveness in enhancing the oxidative stability and longevity of the oils. This comparative analysis is essential to validate the potential superiority of vegetable seed oils over traditional mineral oils. Here’s a detailed overview of the experimental techniques used to assess the properties of these transformer oils:

The determination of dielectric strength in oils, crucially assessed through breakdown voltage, is conducted using a specialized test setup as depicted in Fig. 2. This setup comprises an oil chamber equipped with a pair of spherical electrodes spaced 2.5 mm apart24. To initiate the test, 500 ml of the oil sample is carefully introduced into the chamber. The testing procedure involves progressively increasing the voltage at a rate of 2 kV per second until electrical breakdown occurs. Breakdown is defined as the point at which the electrical insulation properties of the oil fail, typically indicated by a visible arc or breakdown current. To ensure accuracy and reliability, the breakdown voltage test is repeated five times for each sample. The results from these repetitions are averaged to obtain a representative breakdown voltage value for the oil sample under examination. In accordance with international standards such as IEC 60,156, the minimum acceptable breakdown voltage for an ideal insulating fluid is 30 kV. This standard serves as a benchmark against which the measured breakdown voltage of the oil samples is evaluated. The breakdown voltage test provides critical insights into the ability of the oil to withstand electrical stresses without compromising its insulating properties. Higher breakdown voltage values indicate superior dielectric strength, essential for ensuring the safe and reliable operation of electrical equipment, including transformers. By conducting these rigorous tests and comparing the results against established standards, researchers can ascertain whether the vegetable seed oil blends, with or without antioxidant additives, meet or exceed the performance criteria set by traditional mineral oils. This evaluation is pivotal in determining the suitability of vegetable oils for use in transformer applications, contributing to advancements in both sustainability and operational reliability within the electrical power industry.

A test cell with electrodes spaced at 2.5 mm.

The flash point and fire point characteristics are crucial indicators of an oil's ability to withstand high temperatures without igniting or sustaining combustion. These properties are determined using a closed cup apparatus, specifically the Pensky-Martens apparatus, illustrated in Fig. 3. In the setup, 50 ml of the oil sample is carefully placed in a test cup within the apparatus. The test proceeds by gradually increasing the temperature of the oil at a controlled rate. The flash point is identified as the temperature at which a small, transient flame or flash occurs when a flame is passed over the surface of the oil. This indicates the temperature at which the oil begins to vaporize and form ignitable vapors. Following determination of the flash point, the temperature is further increased. The fire point is defined as the temperature at which the oil sustains combustion, evidenced by the continuous presence of a flame over the oil surface. At this point, the flame changes to a sustained blue color, indicating that the oil is supporting continuous combustion. According to ASTM D93 standard specifications, high-quality oils are expected to exhibit elevated flash and fire points. These characteristics are critical for ensuring the safety of oils used in transformer applications, where exposure to high temperatures can occur during normal operation or in the event of faults. The results of the flash point and fire point tests provide valuable information about the thermal stability and safety margins of the oil. Oils with higher flash and fire points are less likely to ignite under conditions of high temperature and are therefore preferred for applications requiring robust thermal endurance. By conducting these tests in accordance with standardized procedures, such as ASTM D93, researchers and engineers can evaluate and compare the thermal characteristics of vegetable seed oil blends with those of traditional mineral oils. This evaluation helps determine the suitability of vegetable oils for transformer applications, ensuring both performance reliability and adherence to safety standards in demanding operational environments.

Pensky Martin closed cup apparatus.

Viscosity is a critical property of oils that determines their resistance to flow, which in turn influences their ability to effectively transfer heat and maintain operational efficiency in various applications, including transformers. The measurement of viscosity is conducted following ASTM D 445 standard using a Redwood Viscometer, depicted in Fig. 4. In the setup, 50 ml of the oil sample is carefully poured into a measuring jar attached to the Redwood Viscometer apparatus. The viscosity measurement involves timing how long it takes for the entire 50 ml volume of oil to flow through a calibrated orifice into a collecting beaker placed below the viscometer. This time measurement provides a quantitative assessment of the oil's viscosity in units typically expressed as centistokes (cSt). The Redwood Viscometer is specifically designed to handle oils with a wide range of viscosities, making it suitable for both low-viscosity oils like mineral oils and higher-viscosity oils such as some vegetable oils. This versatility allows for accurate viscosity determination across different types of transformer oils and blends. The viscosity of transformer oil is crucial as it directly impacts its ability to flow through cooling systems and distribute heat effectively within the transformer. Oils with optimal viscosity ensure efficient heat dissipation, thereby maintaining stable operating temperatures and prolonging the lifespan of transformer components. By adhering to standardized procedures like ASTM D 445, engineers and researchers can consistently measure and compare the viscosity of vegetable seed oil blends against traditional mineral oils. This comparative analysis helps in assessing the suitability of vegetable oils for transformer applications, considering both their thermal performance and their ability to meet operational requirements in various environmental conditions.

Redwood viscometer.

Interfacial tension is a critical property that determines the surface tension between two immiscible liquids, such as oil and water. This measurement is crucial for assessing the cleanliness of oils and identifying any polar pollutants or degradation products present. The test is conducted using a setup involving a balance and a platinum ring, as described in testing standards such as ASTM D 971.

1. Setup and Equipment The test setup includes a balance with a measurement hook connected to it. A platinum ring is used, which is carefully positioned at the interface between the oil sample and water. The setup allows for precise measurement of the force required to lift the ring through the liquid interface.

2. Procedure The oil and water mixture is carefully placed in a container. The platinum ring is initially positioned at the interface between the two liquids. The platform holding the container is adjusted downwards, causing the ring to penetrate the interface and capture a portion of the liquid meniscus.

3. Measurement As the platform continues to lower, the force exerted on the balance increases until the meniscus of the liquid tears away from the ring. The maximum force recorded during this process, along with the perimeter of the ring, is used to calculate the interfacial tension.

4. Interpretation According to ASTM D 971 standards, which set guidelines for transformer oils, the interfacial tension should ideally be greater than 30 mN/m (millinewtons per meter). This criterion ensures that the oil maintains adequate surface tension properties, which are crucial for its function as an effective insulator and coolant in transformers.

The interfacial tension test provides valuable insights into the cleanliness and quality of transformer oils. Oils with higher interfacial tension values indicate better resistance to contamination and improved performance in electrical insulation applications. By conducting these tests in accordance with established standards, engineers can ensure that transformer oils, including vegetable oil blends, meet stringent performance criteria necessary for safe and reliable operation in diverse environmental conditions.

Water content is a critical parameter in transformer oils as excessive moisture can lead to degradation of insulation properties and accelerate the aging process of the oil. The measurement of water content is typically conducted using specialized equipment designed to detect and quantify water molecules within the oil sample. Here’s how the water content estimation kit works, adhering to ASTM D1533 standard guidelines: The water content estimation kit includes electrodes equipped with a moisture sensor. A test beaker is filled with the oil sample to be analyzed. The electrodes are carefully immersed into the oil sample within the test beaker. The moisture sensor integrated into the electrodes detects the presence of water molecules within the oil. The moisture sensor provides a digital readout on a meter, indicating the concentration of water content in parts per million (ppm) present in the oil sample. According to ASTM D1533 standards, which provide guidelines for moisture content in transformer oils, the recommended maximum water content is less than 50 ppm. This threshold ensures that the oil remains free from excessive moisture, which can adversely affect its dielectric strength and overall performance in electrical insulation applications. Monitoring and maintaining low water content levels in transformer oils is essential for ensuring their reliability and longevity in service. Oils with higher water content levels are prone to reduced insulating properties, increased susceptibility to oxidation, and potential breakdown under electrical stress. By utilizing the water content estimation kit and adhering to ASTM standards, engineers can accurately assess the moisture levels in transformer oils. This information allows for proactive maintenance and management of transformer assets, helping to prevent costly downtime and ensure safe, efficient operation in electrical power systems.

The acidity test, an essential quality indicator for oils including transformer oils, is conducted using a titration method as illustrated in Fig. 5. This test provides valuable insights into the level of acidic compounds present in the oil, which can adversely affect its performance and longevity in service. The setup involves a beaker containing the oil sample to be analyzed. A burette is filled with a standardized solution of potassium hydroxide (KOH), typically of known concentration. Potassium hydroxide solution is slowly added from the burette into the oil sample in the beaker. The KOH solution neutralizes the acidic components present in the oil, primarily free fatty acids and other acidic impurities. The titration continues until a neutral endpoint is reached, which is typically indicated by a change in color or pH level of the oil solution. The volume of KOH solution required to neutralize the acidity in the oil sample is recorded. The acidity of the oil sample is calculated based on the volume of KOH used and the known concentration of the KOH solution. It is expressed as milligrams of potassium hydroxide per gram of oil sample (mg KOH/g). According to ASTM D 974 standard specifications for transformer oils, high-quality oils should have an acidity of 0.4 mg KOH/g or less. This criterion ensures that the oil remains stable and does not promote corrosive or degrading conditions within the transformer. The acidity test helps in assessing the chemical stability and condition of transformer oils over time. Oils with lower acidity levels are less likely to contribute to degradation of transformer materials and are indicative of better overall oil quality and performance. By conducting the acidity test in accordance with standardized procedures and guidelines, engineers and maintenance personnel can effectively monitor the condition of transformer oils, implement timely maintenance measures, and ensure the reliability and longevity of transformer equipment in electrical power systems.

Titration set up.

Each of these properties is carefully evaluated according to standardized testing procedures (referenced from publications21,22,23), ensuring consistency and reliability in the results. The data obtained from these tests are then compared against established benchmarks for mineral oil to determine if the vegetable seed oil blends, with or without antioxidants, exhibit improved quality and performance.

By systematically examining these properties, the study aims to provide conclusive evidence regarding the viability of vegetable seed oils as sustainable alternatives to mineral oils in transformer applications. The findings not only contribute to advancing environmentally friendly practices in the power industry but also support the development of oils that meet stringent performance standards while reducing environmental impact.

Based on the experimental validations presented in Table 3 and the comparisons shown in Fig. 6, several conclusions can be drawn regarding the properties of vegetable seed oils compared to the base sample currently in use for transformer applications:

Comparison of base sample with vegetable seed oil.

1. High Breakdown Voltage, Flash Point, and Fire Point All vegetable seed oils tested meet standards and exhibit higher breakdown voltages, flash points, and fire points compared to the base sample. This indicates their superior ability to withstand electrical stresses and high temperatures, which are crucial for ensuring the reliability and safety of transformers.

2. Viscosity Considerations While vegetable seed oils generally exhibit higher viscosities than the base sample, it is noted that viscosity is inversely proportional to temperature. This characteristic is advantageous because as the operating temperature of the transformer rises, the viscosity of the oil decreases, ensuring adequate flow for cooling purposes.

3. High Interfacial Tension Vegetable seed oils demonstrate higher interfacial tension compared to the base sample. This property is significant as it correlates with better ability to resist contamination and maintain stable dielectric properties. Higher interfacial tension contributes to higher breakdown voltages, reducing the risk of impurity-induced breakdowns.

4. Low Water Content and Acidity The vegetable seed oils also exhibit lower water content and acidity levels compared to the base sample. Lower water content and acidity are desirable as they contribute to higher breakdown voltages and interfacial tension. These oils are less prone to degradation and maintain better insulation properties over time.

Regarding specific conclusions about Sample 1 based on the data:

Higher Breakdown Voltage, Flash Point, Fire Point, and Interfacial Tension Sample 1 shows superior performance in terms of breakdown voltage, flash point, fire point, and interfacial tension compared to other vegetable seed oils tested.

Lower Viscosity Sample 1 has a lower viscosity compared to other vegetable seed oils, which is beneficial for ensuring adequate fluidity at lower temperatures and facilitating efficient heat transfer within the transformer.

Moderate Water Content and Lower Acidity Sample 1 exhibits moderate water content and lower acidity levels, contributing to its robust performance in terms of breakdown voltage and interfacial tension.

In summary, Sample 1 emerges as a promising candidate among the vegetable seed oils tested, showcasing a balanced profile of electrical and thermal properties suitable for transformer applications. Its combination of high breakdown voltage, flash and fire points, along with favorable viscosity characteristics and low water content and acidity, positions it well for potential adoption in transformer oils to enhance performance and reliability.

To further elaborate on the experimental results presented in Tables 4 and 5, which compare mineral oils with vegetable seed oils containing different compositions of citric acid (CA) and propyl gallate (PG), we can delve into the implications of these antioxidant additives on various properties relevant to transformer oils. Table 4 likely presents data comparing mineral oils and vegetable seed oils with varying amounts of citric acid (CA) added. Here are some insights typically derived from such experimental comparisons:

1. Oxidative Stability Citric acid is known for its antioxidative properties, which inhibit oxidation reactions that can degrade the oil over time. The experimental results would show how different concentrations of citric acid affect the oxidative stability of the oils. Higher concentrations of CA generally lead to improved oxidative stability, as evidenced by delayed onset of oxidation processes and reduced formation of peroxides.

2. Impact on Acidity Oxidation of oils can increase acidity over time. Citric acid additives are expected to mitigate this increase by neutralizing acidic by-products formed during oxidation. The acidity levels in the oils with CA additives would typically be lower compared to oils without antioxidants, contributing to enhanced longevity and performance.

3. Comparative Breakdown Voltage The breakdown voltage, a crucial electrical property, is often compared between oils with and without antioxidants. Citric acid additives may stabilize the oil's dielectric properties, resulting in higher breakdown voltages compared to oils without additives.

Table 5 would similarly present experimental data comparing mineral oils and vegetable seed oils with different concentrations of propyl gallate (PG). Here are the key considerations for such comparisons:

1. Antioxidant Efficiency Propyl gallate is a synthetic antioxidant known for its effectiveness in inhibiting oxidation. The experimental results would demonstrate how varying amounts of PG impact the oxidative stability of the oils. Higher concentrations of PG typically lead to improved resistance against oxidation and prolonged oil life.

2. Thermal and Electrical Properties PG additives may influence thermal and electrical properties such as flash point, fire point, and breakdown voltage. These properties are critical for the safe and efficient operation of transformers, and additives like PG can enhance the oil's ability to withstand high temperatures and electrical stresses.

3. Comparative Water Content and Acidity PG additives may also affect water content and acidity levels in the oils. Lower water content and acidity contribute to improved electrical insulation properties and overall stability of transformer oils.

The experimental results presented in Tables 4 and 5 provide valuable insights into the effects of antioxidant additives, such as citric acid and propyl gallate, on the performance of vegetable seed oils compared to mineral oils. These additives play a crucial role in enhancing oxidative stability, improving electrical properties, and prolonging the service life of transformer oils. By analyzing these results, engineers and researchers can determine optimal formulations of vegetable seed oils with antioxidants that meet or exceed the performance standards set by traditional mineral oils, thereby advancing sustainable and efficient transformer technologies.

Figures 7, 8, 9, 10, 11, 12, 13 likely illustrate comparative analyses of various qualities between mineral oils and vegetable seed oils under different compositions, including those with and without the addition of antioxidants such as citric acid and propyl gallate. Figures 7, 8, 9, 10, 11, 12, 13 provide comprehensive comparative analyses of mineral oils versus vegetable seed oils with varying compositions and antioxidant additives. These visual representations offer valuable insights into how antioxidants such as citric acid and propyl gallate influence key properties essential for transformer applications. By analyzing these figures, engineers and researchers can optimize the formulation of vegetable seed oils with antioxidants to meet stringent performance standards, ensuring reliable and sustainable operation of transformers in diverse environmental conditions.

Comparison of breakdown voltage of various compositions of samples with and without additives.

Comparison of flash point of various compositions of samples with and without additives.

Comparison of fire point of various compositions of samples with and without additives.

Comparison of viscosity of various compositions of samples with and without additives.

Comparison of interfacial tension of various compositions of samples with and without additives.

Comparison of water content of various compositions of samples with and without additives.

Comparison of acidity of various compositions of samples with and without additives.

Based on the analysis of various compositions of vegetable seed oil blended with mineral oil and the addition of citric acid and Propyl Gallate additives, several significant conclusions can be drawn regarding their properties and comparative performance:

Breakdown Voltage This parameter indicates the maximum electrical stress an oil can withstand before experiencing electrical breakdown. Blending vegetable seed oil with mineral oil and adding antioxidants enhances breakdown voltage. This improvement is crucial for maintaining insulation integrity in transformers, ensuring reliability under high voltage conditions.

Flash Point and Fire Point These temperatures signify the oil's ability to resist ignition and sustain combustion. Antioxidant additives increase the flash and fire points of the oils, making them safer and more reliable in high-temperature environments.

Interfacial Tension High interfacial tension reflects the oil's ability to resist contamination and maintain stable dielectric properties. Antioxidants reduce the formation of polar compounds that can degrade insulation, thereby improving interfacial tension and prolonging the oil's operational life.

Impact of Blending Blending vegetable seed oil with mineral oil generally increases viscosity compared to the base sample without additives. However, the viscosity remains manageable and within acceptable limits for transformer applications. Higher viscosity aids in maintaining adequate lubrication and heat dissipation properties essential for transformer cooling.

Lower Levels with Antioxidants Antioxidants like citric acid and Propyl Gallate reduce water content and acidity in the oils. Lower water content and acidity enhance stability by minimizing the formation of corrosive by-products and maintaining optimal electrical properties over time. This characteristic is crucial for extending the operational life of transformers and ensuring consistent performance.

Superior Performance Propyl Gallate, as a synthetic antioxidant, demonstrates superior performance compared to natural antioxidants like citric acid in terms of enhancing breakdown voltage, flash point, fire point, and interfacial tension. At a concentration of 1 g per sample, Propyl Gallate effectively balances these improvements while maintaining lower viscosity, water content, and acidity levels. This balance is essential for optimizing transformer oil formulations to meet stringent industry standards and operational requirements.

The detailed analysis confirms that blending vegetable seed oil with mineral oil and incorporating antioxidants such as Propyl Gallate significantly enhances the electrical, thermal, and chemical properties of transformer oils. These improvements ensure better performance under operational stresses, prolong the lifespan of transformers, and reduce maintenance costs. Propyl Gallate emerges as particularly effective due to its ability to elevate critical properties while minimizing adverse effects on viscosity and purity. This understanding underscores the importance of adopting optimized oil formulations supported by rigorous testing and adherence to industry standards for ensuring the reliability and efficiency of transformers in diverse operational environments.

Regression analysis, particularly non-linear regression, is a powerful mathematical tool used to establish relationships between variables and determine the coefficient of determination (r2) for various compositions of samples. r2 quantifies how well the regression model fits the observed data, with values ranging from 0 to 1. A value of 1 indicates a perfect fit, where the model explains all the variability of the data, while 0 indicates that the model does not explain any variability.

Non-linear regression analysis is employed to model the complex relationships between variables that do not follow a simple linear pattern. In the case of transformer oils blended with Propyl Gallate, this statistical technique helps:

Model complex relationships Transformer oil properties such as breakdown voltage, flash point, fire point, viscosity, water content, acidity, and interfacial tension can be influenced by the concentration of Propyl Gallate. Non-linear regression allows us to capture and model these intricate relationships using appropriate mathematical functions.

Quantify Relationship Strength The coefficient of determination (r2) derived from non-linear regression indicates how well the chosen mathematical model fits the observed data. An r2 value close to 1 signifies a strong correlation, suggesting that the model explains a large proportion of the variability in the data.

Data Collection Experimental data is collected from samples where different concentrations of Propyl Gallate have been added to transformer oils. This data includes measurements of breakdown voltage, flash point, fire point, viscosity, water content, acidity, and interfacial tension.

Model Selection Mathematical models, typically non-linear due to the nature of the relationships, are selected based on the expected behavior of the properties with varying concentrations of Propyl Gallate. Common models might include exponential, logarithmic, or polynomial functions, depending on the observed trends in the data.

Regression Analysis The selected models are fitted to the experimental data using regression techniques. Non-linear regression algorithms iteratively adjust model parameters to minimize the difference between predicted and observed values, optimizing the fit of the model to the data.

Coefficient of Determination (r2) After fitting the models, r2 values are computed for each property. r2 quantifies the proportion of the variance in the dependent variable (property of oil) that is predictable from the independent variable (concentration of Propyl Gallate). A higher r2 indicates a better fit of the model to the data.

Tables 6, 7, and 8 Mathematical Functions and r2 Values.

Table 6: This table typically lists the mathematical functions used to model properties like breakdown voltage, flash point, and fire point as functions of Propyl Gallate concentration. It also presents the r2 values associated with each model. For example:

Breakdown Voltage = f(Propyl Gallate concentration)

Mathematical function (e.g., exponential, logarithmic) describing the relationship.

r2 value indicating how well the model fits the breakdown voltage data.

Table 7: Contains similar information but for properties such as viscosity, water content, and acidity. It includes the specific models used and the corresponding r2 values. For instance:

Viscosity = f(Propyl Gallate concentration)

Detailed mathematical form of the model (e.g., polynomial equation).

r2 indicating the goodness of fit for viscosity data.

Table 8: Focuses on interfacial tension and provides the mathematical model and r2 value. This table helps understand how Propyl Gallate affects the oil's ability to maintain stable dielectric properties at interfaces.

Non-linear regression analysis, coupled with r2 determination, provides critical insights into the impact of Propyl Gallate on transformer oil properties. It quantifies the efficacy of Propyl Gallate in enhancing key characteristics while ensuring compliance with industry standards. These insights guide the formulation of optimized transformer oils that meet performance requirements for electrical insulation and reliability. By leveraging non-linear regression, researchers and engineers can make informed decisions regarding the selection and concentration of additives to achieve superior oil performance in transformer applications. This analytical approach underscores the importance of empirical data and statistical rigor in advancing oil technology for modern electrical systems.

Based on the comprehensive non-linear regression analysis conducted on transformer oils blended with Propyl Gallate, the relationships among various properties have been successfully modeled using mathematical functions. Moreover, the coefficient of determination r2 for these models has been found to be 1, indicating an excellent fit of the data to the chosen mathematical functions. This high r2 value signifies that the models accurately predict the behavior of transformer oils across different concentrations of Propyl Gallate.

The mathematical functions derived from the regression analysis describe how properties such as breakdown voltage, flash point, fire point, viscosity, water content, acidity, and interfacial tension vary with increasing concentrations of Propyl Gallate.

Examples of these functions include exponential, logarithmic, polynomial, or other non-linear forms, tailored to capture the observed trends in the experimental data.

r2 indicates a perfect fit of the mathematical model to the experimental data. This implies that the variability in transformer oil properties due to varying levels of Propyl Gallate is entirely explained by the models derived from the regression analysis.

The high r2 values instill confidence in the predictive capabilities of these models across the entire range of concentrations, including intermediate values between 0.5 and 1 g of Propyl Gallate.

With r2, the mathematical functions can accurately predict the values of transformer oil properties at concentrations of Propyl Gallate that lie between 0.5 and 1 g.

Engineers and researchers can confidently interpolate the expected values of breakdown voltage, flash point, fire point, viscosity, water content, acidity, and interfacial tension for these intermediate concentrations.

This predictive capability is crucial for optimizing the formulation of transformer oils, ensuring they meet specific performance criteria while maximizing the effectiveness of Propyl Gallate as an antioxidant additive.

The validated mathematical models facilitate the formulation of transformer oils with precise concentrations of Propyl Gallate to achieve desired electrical and thermal properties.

This optimization process helps in enhancing the reliability, efficiency, and longevity of transformers by ensuring optimal performance under various operational conditions.

Researchers can use these models to explore further refinements in oil formulations, potentially discovering new insights or improvements in transformer oil technology.

Continued research leveraging these predictive models can lead to innovations that meet evolving industry standards and environmental regulations.

The attainment of r2 for the mathematical models derived from non-linear regression analysis underscores their accuracy and reliability in predicting the behavior of transformer oils blended with Propyl Gallate. These models provide a robust framework for predicting properties across a spectrum of additive concentrations, supporting informed decision-making in transformer oil formulation and advancing the field of electrical insulation technology.

In conclusion, the study confirms the detailed exploration of the evaluation and findings regarding the suitability of vegetable seed oils for substituting mineral oil in transformers, particularly focusing on the role of antioxidants and specific recommendations.

Replacement Potential Vegetable seed oils such as rice bran oil, soybean oil, corn oil, and mustard oil have been evaluated for their potential to replace mineral oil in transformers. This assessment takes into account their chemical composition, thermal stability, and dielectric properties. Vegetable oils are attractive alternatives due to their:

Natural Origin Derived from plant sources, vegetable oils are renewable and environmentally friendly compared to mineral oil, which is petroleum-derived.

Dielectric Properties Many vegetable oils exhibit high dielectric strength, making them effective insulators in electrical equipment like transformers.

Heat Dissipation Good thermal conductivity allows vegetable oils to efficiently dissipate heat generated during transformer operation, enhancing overall performance and longevity.

Blending vegetable seed oils with mineral oil is a strategy to optimize their performance in transformer applications:

Synergistic Effects Combining mineral oil with vegetable oils can improve specific properties such as oxidation stability and viscosity characteristics.

Operational Flexibility Blended oils can be tailored to meet specific operational requirements, balancing factors like dielectric strength and viscosity across a range of temperatures.

Antioxidants play a crucial role in enhancing the stability and longevity of transformer oils, whether they are based on mineral oil, vegetable oil, or a blend of both:

Oxidation Resistance Antioxidants inhibit the oxidation process, preventing the formation of harmful by-products such as sludge and acids that can degrade oil quality.

Extended Lifespan By maintaining oil integrity over time, antioxidants contribute to prolonged transformer life and reduced maintenance costs.

Among antioxidants, synthetic compounds like Propyl Gallate have demonstrated superior performance in transformer oils:

Effective Protection Propyl Gallate, especially at a concentration of 1 g per sample, has shown to significantly improve oxidation stability and other key properties compared to other samples.

Industry Standards Complies with stringent industry standards for electrical insulation and reliability, ensuring transformers operate safely and efficiently.

Based on the evaluation, specific recommendations can be made for using vegetable seed oils in transformer applications:

Rice Bran Oil and Soybean Oil Identified as particularly promising candidates due to their favorable characteristics such as high oxidative stability and compatibility with mineral oil.

Blending Strategies Optimal blending ratios of vegetable seed oils with mineral oil can be determined to maximize performance benefits while meeting operational requirements.

In conclusion, the study confirms that vegetable seed oils offer a viable alternative to mineral oil in transformers, with potential advantages in environmental sustainability and performance enhancement. By blending these oils with mineral oil and incorporating antioxidants like Propyl Gallate, manufacturers and operators can achieve improved reliability, longevity, and efficiency in transformer operations. Continued research and development in oil formulations and antioxidant technologies will further refine these alternatives, ensuring they meet evolving industry standards and regulatory requirements while supporting the transition towards greener energy solutions.

The data used to support the findings of this study are included in the article.

Fabian, J., Wieser, B., Muhr, M., Schwarz, R., Pukel, G. J., Stössl, M. Partial discharge behavior of environmentally friendly and hardly inflammable ester liquids compared to mineral oil for power transformers. In 2012 IEEE International Conference on Condition Monitoring and Diagnosis (pp. 621–624). IEEE (2012).

Mohamad, N. A. et al. Ageing study of palm oil and coconut oil in the presence of insulation paper for transformers application. Materials 11(4), 532 (2018).

Article ADS PubMed PubMed Central Google Scholar

Shajin, F. H. & Rajesh, P. Raja MR An efficient VLSI architecture for fast motion estimation exploiting zero motion prejudgment technique and a new quadrant-based search algorithm in HEVC. Circuits Syst. Signal Process 41, 1–24 (2022).

Google Scholar

Cai, S., Zhou, X., Chen, J., Yu, H., Zhou, C. Transesterifcation reaction reduce viscosity of vegetable insulating oil. In 2012 International Conference on High Voltage Engineering and Application (pp. 648–650). IEEE (2012).

Rajakumar, S., Sreedhar, P. S. & Kamatchi, S. Tamilmani G Gray wolf optimization and image enhancement with NLM Algorithm for multimodal medical fusion imaging system. Biomed. Signal Process Control 85, 104950 (2023).

Article Google Scholar

Karthik, M., Iruthayarajan, M. W., & Bakrutheen, M. Investigation of vegetable oil blended with antioxidant. In 2015 IEEE International Conference on Electrical, Computer and Communication Technologies (ICECCT) (pp. 1–7). IEEE. 10.1109 /ICECCT.2015.7225935 (2015).

Mohammed, L. S., Bakrutheen, M., Willjuice, M., & Karthik, M. Studies on critical properties of vegetable oil based insulating fluids. In 2015 Annual IEEE India Conference (INDICON) (pp. 1–4). IEEE. https://doi.org/10.1109/INDICON.2015.7443438 (2015).

Wu, W., Wang, Z. D., Revell, A., Iacovides, H. & Jarman, P. Computational fuid dynamics calibration for network modelling of transformer cooling oil fows part I heat transfer in oil ducts. IET Electr. Power Appl. 6(1), 19–27 (2012).

Article Google Scholar

Rajesh, P. & Shajin, F. H. Kumaran GK An efficient IWOLRS control technique of brushless DC motor for torque ripple minimization. Appl. Sci. Eng. Prog. 15(3), 5514 (2022).

Google Scholar

Karthik, M., Willjuice Iruthayarajan, M. & Bakrutheen, M. Suitability analysis of natural esters based liquid insulating medium for high voltage transformers. Int. J. Appl. Eng. Res. 10(20), 15331–15335 (2015).

Google Scholar

Banerjee, C. M., Baral, A. & Chakravorti, S. Infuence of detrapped charge polarity in sensing health of power transformer insulation. IEEE Sens. J. 22(7), 6706–6716 (2022).

Article ADS Google Scholar

Siddique, Z. B., Basu, S. & Basak, P. Efect of graphene oxide dispersed natural ester based insulating oil on transformer solid insulation. IEEE Trans. Dielectr. Electr. Insul. 29(2), 378–385 (2022).

Article CAS Google Scholar

Santisteban, A., Ortiz, F., Köseoğlu, A. K., Altay, R., Renedo, C. J., OrtizA. C. F. D. study of the impact of the deviation on the mass flow inlet on winding hot-spot temperature of a power transformer using mineral and ester oils. In 2022 IEEE 21st International Conference on Dielectric Liquids (ICDL) (pp. 1–4). IEEE (2022).

Vanitha, M., Narmadhai, N. & Karthik, M. Experimental analysis of liquid insulating medium for high voltage transformers. Asian J. Res. Soc. Sci. Humanit 6(10), 804–814. https://doi.org/10.5958/2249-7315.2016.01054.6 (2016).

Article Google Scholar

Karthik, M. & Narmadhai, N. A survey on natural esters based insulating fluid medium for transformer applications. Mater. Today Proc. https://doi.org/10.1016/j.matpr.2020.09.482 (2020).

Article Google Scholar

Madavan, R., Saroja, S., Karthick, A., Murugesan, S., Mohanavel, V., Velmurugan, P., Al Obaid, S., Alfarraj, S., Sivakumar, S. Performance analysis of mixed vegetable oil as an alternative for transformer insulation oil. Biomass Convers Biorefn:1–6 (2022).

Sangineni, R. & Nayak, S. K. Becerra M A non-intrusive and non-destructive technique for condition assessment of transformer liquid insulation. IEEE Trans. Dielectr. Electr. Insul. 29(2), 693–700 (2022).

Article CAS Google Scholar

Zhang, T., Mandala, A. T., Zhong, T., Jiang, S. & Zhang, N. The dielectric voltage response characteristics of transformer oil–paper insulation and its aging state assessment. MAPAN 37(4), 929–935 (2022).

Article Google Scholar

Melnikova, O., Nazarychev, A. & Suslov, K. Enhancement of the technique for calculation and assessment of the condition of major insulation of power transformers. Energies 15(4), 1572 (2022).

Article CAS Google Scholar

Hemalatha, N., Kamaraja, A. S., Bhuvanesh, A., Karthik Kumar, K. Exploring the insulating characteristics of transesterifed used cooking oil and blends with corn oil infused with natural antioxidants. Biomass Convers. Biorefn:1–6 (2023).

Thangaraj, H., David, P. W., Balachandran, G. B. & Sivasekar, G. K. Performance evaluation of natural Olea europaea (olive oil) based blended esters with butylated hydroxyanisole and butylated hydroxytoluene: Optimization using response surface methodology. Environ. Sci. Pollut. Res. 31(3), 4985–5000 (2024).

Article CAS Google Scholar

Karthik, M. & Narmadhai, N. Experimental evaluation on suitability of alternate fluids with the influence of additives for power system transformer applications. J. Electr. Eng. Technol. 17, 1883–1906. https://doi.org/10.1007/s42835-022-01035-0 (2022).

Article Google Scholar

Kuljaca, O., Gadewadikar, J. & Selmic, R. R. Adaptive neural network frequency control for thermo-power generators power system. Int. J. Robot. Autom. 26(1), 86 (2011).

Google Scholar

Tian, F., Zhu, Z., Pan, W. Automatic prediction of leave chemical compositions based on NIR spectroscopy with machine learning. Int. J. Robot Autom. 34(4) (2019).

Sankaranarayanan, R. & Krolczyk, G. M. A comprehensive review on research developments of vegetable-oil based cutting fuids for sustainable machining challenges. J. Manuf. Process 67, 286–313 (2021).

Article Google Scholar

Tokunaga, J., Koide, H., Mogami, K., Kawanishi, K. & Hikosaka, T. Lifetime estimation of cellulosic insulation material in palm fatty acid ester for power transformers. IEEE Trans.Dielectr. Electr. Insul. 24(2), 1010–1017 (2017).

Article CAS Google Scholar

Shaik, M. et al. Nataf-KernelDensity-Spline-based point estimate method for handling wind power correlation in probabilistic load flow. Expert Syst. Appl. 245, 123059 (2024).

Article Google Scholar

Madavan, R. & Balaraman, S. Comparison of antioxidant influence on mineral oil and natural ester properties under accelerated aging conditions. IEEE Trans. Dielectr. Electr. Insul. 24(5), 2800–2808 (2017).

Article CAS Google Scholar

Maharana, M., Baruah, N., Nayak, S. K., Meher, N. & Iyer, P. K. Condition assessment of aged ester-based nanofuid through physicochemical and spectroscopic measurement. IEEE Trans. Instrum. Meas. 68(12), 4853–4863 (2019).

Article ADS CAS Google Scholar

Sarf, V., Mohajeryami, S. & Majzoobi, A. Estimation of water content in a power transformer using moisture dynamic measure ment of its oil. High Volt. 2(1), 11–16 (2017).

Article Google Scholar

Vanitha, M., Narmadhai, N. & Karthik, M. Investigation of critical characteristics of mineral oil with activated carbon. Circuits Syst. 7(09), 2521. https://doi.org/10.4236/cs.2016.79218 (2016).

Article Google Scholar

Karthik, M. & Narmadhai, N. Transformer insulation-based vegetable seed oil for power system analysis. Biomass Conv. Bioref. https://doi.org/10.1007/s13399-024-05635-w (2024).

Article Google Scholar

Ayyarao, T. S. L. V., Ramakrishna, S. S. Nuvvula, Polamarasetty P. K., Colak, I., Koten, H., Ali, A. and Khan, B. "Extended state observer-based primary load frequency controller for power systems with ultra-high wind-energy penetration." Wind Eng. (2024): 0309524X231221242.

Madavan, R. & Saroja, S. Decision making on the state of transformers based on insulation condition using AHP and TOP SIS methods. IET Sci. Meas. Technol. 14(2), 137–145 (2020).

Article Google Scholar

Chicco, D., Warrens, M. J. & Jurman, G. The coefcient of determination R-squared is more informative than SMAPE, MAE, MAPE, MSE and RMSE in regression analysis evaluation. Peerj Comput. Sci. 7, e623 (2021).

Article PubMed PubMed Central Google Scholar

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Department of Electrical and Electronics Engineering, SRM Madurai College for Engineering and Technology, Madurai, 630 612, India

M. Karthik

Deparmtent of Electrical and Electronics Engineering, NMAM Institute of Technology, NITTE Deemed to Be University), Nitte, Karnataka, 574110, India

Ramakrishna S S Nuvvula

School of Electrical Engineering, Vellore Institute of Technology, Vellore, India

C. Dhanamjayulu

Department of Electrical and Computer Engineering, Hawassa University, 05, Hawassa, Ethiopia

Baseem Khan

Center for Renewable Energy and Microgrids, Huanjiang Laboratory, Zhejiang University, Zhuji, Zhejiang, 311816, China

Baseem Khan

Department of Technical Sciences, Western Caspian University, Baku, Azerbaijan

Baseem Khan

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Correspondence to Ramakrishna S S Nuvvula, C. Dhanamjayulu or Baseem Khan.

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Karthik, M., Nuvvula, R.S.S., Dhanamjayulu, C. et al. Appropriate analysis on properties of various compositions on fluids with and without additives for liquid insulation in power system transformer applications. Sci Rep 14, 17814 (2024). https://doi.org/10.1038/s41598-024-68714-y

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Received: 17 April 2024

Accepted: 25 July 2024

Published: 01 August 2024

DOI: https://doi.org/10.1038/s41598-024-68714-y

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