Quantitative Evaluation Method of Insulation Performance for Mineral Insulating Oil Used in Power Transformers

Quantitative Evaluation Method of Insulation Performance for Mineral Insulating Oil Used in Power Transformers | Authorea try { document.documentElement.classList.add('js'); } catch (e) { } var _gaq = _gaq || []; _gaq.push(['_setAccount', 'G-8VDV14Y67G']); _gaq.push(['_trackPageview']); (function() { var ga = document.createElement('script'); ga.type = 'text/javascript'; ga.async = true; ga.src = ('https:' == document.location.protocol ? 'https://ssl' : 'http://www') + '.google-analytics.com/ga.js'; var s = document.getElementsByTagName('script')[0]; s.parentNode.insertBefore(ga, s); })(); Skip to main content Preprints Collections Wiley Open Research IET Open Research Ecological Society of Japan All Collections About About Authorea FAQs Contact Us Quick Search anywhere Search for preprint articles, keywords, etc. Search Search ADVANCED SEARCH SCROLL This is a preprint and has not been peer reviewed. Data may be preliminary. 17 March 2026 V1 Latest version Share on Quantitative Evaluation Method of Insulation Performance for Mineral Insulating Oil Used in Power Transformers Authors : Congcong Chen 0000-0002-0818-7784 , Bo Qi 0000-0001-8001-5824 [email protected] , Chunjia Gao 0000-0001-6921-6190 , Chunyu Zhang , and Chengrong Li Authors Info & Affiliations https://doi.org/10.22541/au.177371676.62937819/v1 123 views 42 downloads Contents Abstract INTRODUCTION Selection of evaluation parameters Acquisition of Measurement Data for Evaluation Parameters Test of PDIV Test of , tan , and Construction of the original data matrix Preprocessing of the original data Determination of parameter weights Determination of objective weights Comprehensive performance evaluation APPLICATION OF QUANTITATIVE EVALUATION METHOD Construction of the original data matrix Preprocessing of the original data Determination of parameter weights Comprehensive Performance Evaluation Evaluation results verification CONCLUSION Data Availability Statement Supplementary Material Information & Authors Metrics & Citations View Options References Figures Tables Media Share Abstract To overcome the binary “qualified/unqualified” evaluation inherent in current standards, a quantitative insulation performance evaluation method for mineral insulating oils is proposed in this paper. Ten indicators are selected. Five of them are intrinsic electrical parameters, namely partial discharge inception voltage (PDIV), breakdown voltage (BDV), relative permittivity (εr), dielectric dissipation factor (tanδ), and DC resistivity (ρ). The remaining five indicators are their aging-induced relative variations, denoted as ΔPDIV, ΔBDV, Δεr, Δtanδ, and Δρ, which characterize degradation behavior. Objective weights are obtained from inter-sample standard deviations and incorporated into the Analytic Hierarchy Process. Three widely used oils, labeled A, B, and C, are subjected to 35-day thermal aging at 90 °C and subsequently evaluated. Their comprehensive scores are determined as A (7.934) > B (0.778) > C (0.725), which is consistent with the evolution of oil color during aging. The proposed method overcomes the binary evaluation in current standards, enabling objective and reproducible evaluation of oil performance. It is particularly suitable for evaluating the long-term operational characteristics of oils and provides valuable guidance for material selection in engineering applications. A R T I C L E C A T E G O R Y Quantitative Evaluation Method of Insulation Performance for Mineral Insulating Oil Used in Power Transformers Congcong Chen 1 Bo Qi 1 Chunjia Gao 1 Chunyu Zhang 2 Chengrong Li 1 1 State Key Laboratory of Alternate Electrical Power System with Renewable Energy Sources, North China Electric Power University, Beijing, China 2 Zhejiang Provincial Key Laboratory of Island Green Energy and New Materials, Taizhou University, Taizhou, China Correspondence Bo Qi ( [email protected] ) Funding informatio n This work was supported by the National Key Research and Development Program of China (Grant 2023YFB2407000) Abstract To overcome the binary “qualified/unqualified” evaluation inherent in current standards, a quantitative insulation performance evaluation method for mineral insulating oils is proposed in this paper. Ten indicators are selected. Five of them are intrinsic electrical parameters, namely partial discharge inception voltage (PDIV), breakdown voltage (BDV), relative permittivity ( ε r ), dielectric dissipation factor (tan δ ), and DC resistivity ( ρ ). The remaining five indicators are their aging-induced relative variations, denoted as ΔPDIV, ΔBDV, Δ ε r , Δtan δ , and Δ ρ , which characterize degradation behavior. Objective weights are obtained from inter-sample standard deviations and incorporated into the Analytic Hierarchy Process. Three widely used oils, labeled A, B, and C, are subjected to 35-day thermal aging at 90 °C and subsequently evaluated. Their comprehensive scores are determined as A (7.934) > B (0.778) > C (0.725), which is consistent with the evolution of oil color during aging. The proposed method overcomes the binary evaluation in current standards, enabling objective and reproducible evaluation of oil performance. It is particularly suitable for evaluating the long-term operational characteristics of oils and provides valuable guidance for material selection in engineering applications. INTRODUCTION China is actively advancing the development of ultra-high-voltage transmission systems, whereas the supply of mineral insulating oil remains insufficient, necessitating the use of different oil types in engineering practice. As a critical insulating medium in power transformers, the insulation performance of mineral oil directly affects transformer service life and long-term reliability [1]. At present, the performance of insulating oils is typically evaluated through physicochemical properties and dielectric characteristics, each governed by corresponding standards [2]. However, existing standards face three major limitations in practical applications. First, both IEC and national specifications predominantly adopt a binary “qualified/unqualified” evaluation approach, which only determines whether an oil meets basic threshold requirements but fails to provide quantitative differentiation of insulation superiority. For example, although different oils may satisfy qualification criteria, their dielectric and breakdown behaviors can differ significantly, and current standards cannot identify which oil is more suitable for specific engineering contexts. Second, performance judgment in engineering practice often relies on expert experience, yet conclusions frequently diverge, boundaries remain ambiguous, and reproducibility is poor. Third, current standards mainly target unused oils and pay insufficient attention to performance evolution under long-term operating conditions. These limitations result in performance assessment that still depends on subjective judgment, lacks objective quantification, and constrains scientific validity. With the increasing deployment of oil-immersed equipment such as transformers and reactors in modern power systems, issues related to insulation performance evaluation of mineral oils are becoming increasingly pronounced. Therefore, the development of a quantitative method to evaluate the insulation performance superiority of mineral insulating oils is urgently required. At present, existing comprehensive material performance evaluation methods [3-4] primarily include the weighted average method (WAM), principal component analysis (PCA), analytic hierarchy process (AHP), technique for order preference by similarity to ideal solution (TOPSIS), and combined evaluation method (CEM). These approaches differ in applicability and inherent characteristics. The WAM is simple and intuitive, yet its weight assignment is highly subjective and fails to objectively reflect intrinsic correlations among indicators. The PCA can eliminate information redundancy through dimensionality reduction, but the physical meaning of the extracted principal components is unclear, resulting in weak engineering interpretability. The AHP determines weights through pairwise comparison within a hierarchical structure, providing explicit indicator relationships, but it still relies on expert judgment for weight assignment. The TOPSIS performs well in ranking multiple alternatives, although its results are sensitive to weight distribution and extreme data. The CEM attempts to integrate multiple approaches to enhance robustness, yet it suffers from computational complexity and a lack of unified integration rules. Overall, existing methods are largely “data-driven” or “experience-driven” and have not effectively addressed the balance between subjective weight determination and alignment of evaluation results with physical meaning in engineering applications. Current IEC standards and several national specifications have established requirements and test procedures for evaluating the insulation performance of mineral insulating oils. For example, GB/T 14542 [5] specifies guidelines for the maintenance and management of mineral insulating oils, particularly defining technical requirements for breakdown voltage (BDV), dielectric dissipation factor (tan δ ), and DC resistivity ( ρ ). Standards GB/T 17648 [6] and GB/T 507 [7] prescribe test procedures for determining partial discharge inception voltage (PDIV) and BDV of insulating liquids, respectively, which can be used to assess the partial discharge and breakdown characteristics of mineral oils. IEC 60422 [8] provides detailed procedures for monitoring and maintaining in-service mineral insulating oils and specifies requirements for BDV. IEC 60296 [2] addresses unused mineral insulating oils, clarifies their classification for application in electrical equipment, and defines standard test requirements for moisture content, BDV, and tan δ . IEC 60247 [9] provides standard methods for measuring relative permittivity ( ε r ), tan δ , and ρ of liquid insulating materials, enabling dielectric characterization of mineral oils. In addition, IEC 60156 [10] specifies the standard test method for dielectric strength under power-frequency voltage and details electrode configurations and parameters for BDV testing. IEC TR 61294 [11] further outlines general procedures for determining PDIV of mineral insulating oils and specifies criteria for discharge inception determination. These standards collectively form the fundamental framework for testing the insulation performance of mineral oils. However, they are mainly intended for qualification judgment and lack quantitative bases for comparative evaluation. In addition to existing standards, numerous studies have been conducted to advance the evaluation of oil performance. For example, Borin [12] et al. proposed a multivariate quality-control technique for lubricating oils based on Fourier-transform infrared spectroscopy and PCA, enabling rapid and nondestructive discrimination of oil quality and providing methodological reference for the performance assessment of mineral insulating oils. Rengaraj [13] et al. developed a multi-criteria performance classification method for mineral insulating oils containing antioxidants using the AHP and TOPSIS, and its feasibility was verified under accelerated aging conditions. Luo [14] et al. investigated the effects of temperature and electric-field strength on the electrical properties of mineral insulating oils and introduced an evaluation approach based on an aging model. Wang [15] et al. developed a diagnostic technique for identifying oil aging states using n-butanol and methanol as detection markers. In addition, several studies [16] have attempted to evaluate oil performance from the perspective of the overall insulation condition of the oil–paper system. In summary, existing comprehensive evaluation approaches invariably retain subjective components; expert-based judgments exhibit ambiguous boundaries, limited repeatability, and insufficient alignment with underlying engineering physics. Although current standards and related studies provide valuable reference for assessing the insulation performance of mineral oils, prevailing evaluation practices remain predominantly qualitative and lack quantitative analysis of long-term operational characteristics. To address these issues, a quantitative evaluation method based on the analytic hierarchy process is proposed in this paper, in which key insulation performance parameters of mineral oils constitute the evaluation basis. Relative importance is determined through inter-sample standard deviations, thereby overcoming the subjectivity inherent in conventional weight assignment and ensuring fully objective weighting. In parameter selection, relative variation during the aging process is incorporated as a supplementary indicator, enabling explicit consideration of performance evolution throughout long-term operation. Finally, three widely used mineral insulating oils are selected as representative samples to validate the practical effectiveness of the proposed method. SELECTION OF EVALUATION PARAMETERS AND ACQUISITION OF MEASUREMENT DATA Selection of evaluation parameters To enable scientific and objective evaluation of mineral insulating oil performance, appropriate selection of representative indicators forms the basis of the assessment methodology. In this paper, three fundamental principles are followed during parameter selection: (i) each indicator must possess clear physical meaning related to electrical insulation characteristics; (ii) it must effectively differentiate performance among different oil types; and (iii) it must reflect both initial properties and long-term operational behavior of insulating oils. Based on these principles, typical test parameters closely associated with oil insulation performance were first extracted from existing IEC and GB/T standards, such as PDIV and BDV. Second, key indicators capable of directly characterizing insulation condition were identified by referring to reported research on aging behavior and electrical degradation patterns of insulating oils. Finally, experimental testing was conducted to obtain parameter values, and the final set of indicators was determined according to their discriminatory performance among oil samples. Five electrical performance parameters were ultimately selected as primary indicators: PDIV, BDV, ρ , ε r , and tan δ . These parameters are fundamental test items specified in IEC/GB standards and directly reflect breakdown, conduction, and dielectric characteristics of mineral oils. Their explicit physical meaning and direct correlation with insulation strength satisfy Principle (i). Specifically, PDIV and BDV are central metrics in insulation system design. PDIV is typically determined based on a Weibull distribution corresponding to a partial discharge probability below 0.1%, whereas BDV is obtained via an extreme-value distribution corresponding to a breakdown probability below 0.01%. Allowable field stress is then derived by combining these values with safety margins and service conditions [17]. ρ and ε r are also key quantities used in insulation design and essential representations of oil insulation performance. Under a DC electric field, the steady-state electrical stress is proportional to ρ , whereas under an AC field it varies inversely with ε r . Meanwhile, tanδ characterizes dielectric loss in AC fields and directly influences thermal behavior of the oil. In addition, ρ , BDV, and PDIV display the strongest sensitivity to oil-type variation, yielding relatively large inter-sample standard deviations, thereby enabling effective quantification of performance differences among mineral oils. For example, PDIV differentiates partial discharge endurance among oils, while ρ distinguishes conduction characteristics. These properties satisfy Principle (ii) of parameter selection. Beyond the five aforementioned parameters, long-term operating characteristics of mineral insulating oils must also be incorporated into the evaluation framework. During prolonged transformer operation, top-oil temperatures can reach up to 95 °C [18] due to core losses, dielectric losses, and winding Joule heating. As an organic insulating material, mineral oil inevitably undergoes thermal degradation when exposed to high-temperature environments for extended periods, potentially affecting the overall insulation performance [19]. Studies have shown that insulation margin design based solely on initial properties may reduce actual transformer lifetime by 30%–40% [20]. Therefore, long-term behavior represents an essential dimension in insulation performance assessment of mineral oils. To address this, relative change rates of the five base parameters during aging—ΔPDIV, ΔBDV, Δ ε r , Δtan δ , and Δ ρ —are introduced as supplementary evaluation indicators. These metrics quantify performance degradation before and after aging and enhance the model’s ability to capture long-term operational characteristics, satisfying Principle (iii). The relative change indicators also carry explicit physical meaning. ΔPDIV reflects changes in discharge activity during the early stage of electrical aging and serves as an early warning parameter. ΔBDV quantifies the degradation trend of macroscopic insulation strength and is a key indicator for end-of-life evaluation. Δ ρ reveals deterioration in electrical conduction properties under coupled electrical-thermal stress. Δ ε r is sensitive to chemical oxidation processes and captures polarity evolution of the oil. Δtan δ reflects changes in dielectric losses during long-term operation and characterizes energy dissipation behavior. It should be noted that the five base electrical parameters selected in this work—PDIV, BDV, ε r , tan δ , and ρ —originate from core IEC/GB test specifications and represent the initial insulation behavior of mineral oils. To further incorporate aging effects, relative change rates (ΔPDIV, ΔBDV, Δ ε r , Δtan δ , and Δ ρ ) were defined for each base parameter to characterize degradation sensitivity. Accordingly, ten indicators were established as the core evaluation set, providing a comprehensive basis for quantitatively assessing insulation performance superiority among mineral insulating oils. Acquisition of Measurement Data for Evaluation Parameters Three types of mineral insulating oils from mainstream suppliers were selected in this paper and labeled as A, B, and C. The oil samples were collected from in-service converter transformers with similar service durations and load conditions to ensure consistent impurity and moisture levels, thereby improving the representativeness and comparability of the samples. Prior to testing, all oil samples underwent a rigorous pretreatment process. Specifically, each oil was filtered three times using a 0.45 μm microporous membrane, followed by dehydration and degassing at 85 °C under 100 Pa vacuum for 24 hours, and then cooled to room temperature. After treatment, the moisture content of the samples was controlled below 10 mg/L, meeting the operational standards for transformer oil [8]. To simulate long-term operational aging, the pretreated mineral oil samples were placed in separate beakers and subjected to thermal aging at a constant temperature of 110 °C. Samples were taken on the 1st and 35th day of aging to measure five key insulation performance parameters. The performance change rates from day 1 to day 35 were then calculated, yielding a total of 10 parameters for subsequent quantitative analysis. According to [18], the top-oil temperature of oil-immersed transformers should generally not exceed 85 °C during long-term operation. Taking 85 °C as the reference for normal operating temperature, and based on the thermal aging ”six-degree rule,” aging at 110 °C for one day is approximately equivalent to 18.8 days of actual service. Accordingly, 35 days of aging at 110 °C corresponds to about 1.8 years of transformer operation. It is worth noting that all parameter measurements were conducted under a controlled room temperature of 26 °C. The parameter testing procedures—including sample selection, electrode configuration, test plan design, and test platform setup—were carried out in strict accordance with the standards IEC 60422 [8], IEC 60296 [2], IEC 60247 [9], IEC 60156 [10], IEC TR 61294 [11], ensuring procedural consistency and accuracy of the test data. Test of BDV The BDV test was conducted in accordance with the IEC 60156-2025 [10]. A pair of spherical electrodes with a diameter of 36 mm and a gap distance of 2.5 mm was used. During the test, the transformer oil samples were poured into a dry and clean standard test cell and left to stand for 10 minutes to eliminate air bubbles. An AC voltage at power frequency was then applied to the electrodes at a ramp rate of 3 kV/s until breakdown occurred, and the corresponding breakdown voltage was recorded. Each sample underwent five independent tests, with a 5-minute interval between successive tests. The final breakdown voltage result was calculated as the average of the maximum and minimum values from the five tests. If the difference between the maximum and minimum values exceeded 25% of the minimum value, the test was repeated. To prevent residual conductive channels between the electrodes from affecting subsequent measurements, a clean glass rod was used to gently tap the gap after each breakdown to destroy any newly formed electric bridges. The oil sample was then allowed to rest for 5 minutes before the next test. Additionally, since the first test result may be lower due to possible contamination on the electrode surface, a sixth test was performed to ensure the reliability and representativeness of the average result. FIGURE 1 | Standard oil cup for BDV test Test of PDIV The PDIV test was conducted in accordance with IEC TR 61294-1993 [11], which defines PDIV as the AC voltage at which partial discharges exceeding 100 pC are first detected. A needle-to-sphere electrode configuration was used in this paper. The sphere electrode had a diameter of 13 mm, while the needle electrode was 25 mm long with a tip curvature radius of 3 μm. The gap between the electrodes was set to 50 mm. Partial discharge signals were detected using an LDS-6 PD detector with a bandwidth of 100–500 kHz. All tests were conducted in a shielded room, and the background interference of the system was less than 3 pC at 40 kV. Following the IEC TR 61294-1993 [11] recommended procedure, the voltage was initially increased at a rate of 1 kV/s until a discharge level of 70 pC was detected. The voltage ramp was then reduced to 1 kV/min until the discharge magnitude reached 100 pC. The corresponding voltage at this point was recorded as the PDIV. The voltage was then brought back to the initial state, and the sample was allowed to rest for 10 minutes before repeating the test. This procedure was repeated 10 times, and the average of the recorded values was taken as the final PDIV result. FIGURE 2 | Schematic diagram of PDIV test circuit Test of, tan, and The ε r , tan δ , and ρ of the three mineral insulating oils were measured using a Haefely 2830/2831 solid-liquid dielectric analyzer. Each parameter was tested using at least five specimens, and the average value was recorded as the result. The instrument has a measurement range of 1 to 30 for ε r and offers a precision of 0.001 pF, making it suitable for high-accuracy characterization of insulating materials. Both the measurement principle and testing procedure are fully compliant with the IEC 60247-2004 [9]. QUANTITATIVE EVALUATION METHOD OF INSULATION PERFORMANCE Construction of the original data matrix Among the ten evaluation indicators considered in this paper, seven represent relative change rates. It should be noted that the computation of these rates differs among parameters. Compared with the results after 1 day of aging, the relative changes of ε r and tan δ after 35 days were calculated using an increment form, as expressed in Equation (1). () For the remaining insulation parameters, degradation occurred with increasing aging time; therefore, their relative changes were computed in a decrement form, as shown in Equation (2). () This treatment ensures that all change rates reflect performance degradation in a consistent direction, facilitating subsequent normalization and comprehensive evaluation. Given the multiple evaluation indicators and evaluation objects involved, a matrix representation was adopted to integrate the original experimental data with differing physical dimensions, enabling unified multidimensional data processing, as defined in Equation (3). () Where \(\mathbf{X}_{n\times m}\) denotes the original data evaluation matrix, n represents the number of evaluation objects, m denotes the number of evaluation indicators, and x ij corresponds to the measured value of the j -th parameter for the i -th object. In this paper, three mineral insulating oils are selected as evaluation objects, and ten indicators are used, hence n = 3 and m = 10. Preprocessing of the original data Because the evaluation indicators differ in dimension and magnitude—for example, ρ is expressed in Ω·m whereas ε r is dimensionless—direct utilization of raw data would lead to inconsistent units and impede effective computation. In addition, some parameters exhibit large numerical values (e.g., ρ typically reaches the order of 10 10 ), whereas others are comparatively small (e.g., tan δ is generally below 1). Without appropriate treatment, indicators with large magnitudes would be overly emphasized, while those with smaller scales may be neglected, resulting in inaccurate evaluation outcomes. Therefore, dimensional normalization is required to eliminate the influence of unit and magnitude discrepancies. Common normalization techniques include range normalization, vector normalization, and Z -score standardization. Vector normalization divides each sample value by the square root of the sum of squares of all samples for that parameter, converting each column into a unit vector. This method features simple computation, stable outcomes, and preservation of parameter proportional relationships. Accordingly, vector normalization is adopted in this paper. The transformation for the j -th indicator is expressed in Equation (4). () where x ij denotes the raw value of the j -th parameter and represents the normalized dimensionless quantity obtained via vector normalization. In insulation performance assessment, indicator directions differ: some parameters benefit from higher values (e.g., PDIV, BDV), whereas others benefit from lower values (e.g., tan δ ). To unify the evaluation system, directional consistency must be established through a monotonic transformation. Common techniques include range-based conversion, linear mapping, and reciprocal transformation. The reciprocal transformation is concise, computationally efficient, preserves relative proportional relations, and avoids negative or excessively amplified values, making it suitable for parameters with strictly positive magnitudes. Therefore, reciprocal transformation is adopted in this paper, with its formulation given in Equation (5). () where denotes the direction-aligned result. After preprocessing, the standardized data matrix is obtained as expressed in Equation (6). () Determination of parameter weights When multiple evaluation indicators exhibit independence or mutual conflict, ranking, selecting, or comprehensively assessing several alternatives constitutes a multi-criteria decision-making (MCDM) problem [21]. The insulation performance assessment of mineral insulating oils in this paper is a typical MCDM task, because it involves multiple performance indicators with differing dimensionality and significance, requiring mathematical integration into a unified evaluation framework to enable rational and comparable judgment. In essence, the mathematical nature of insulation performance assessment lies in transforming an originally qualitative, ambiguous, and preference-influenced multi-parameter evaluation process into a quantifiable, comparable, and boundary-explicit decision system through mathematical modeling. Operations research offers various approaches to address this problem, including AHP, entropy weight methods, and FCE. Among them, the AHP provides a systematic, quantifiable, and consistency-verifiable approach for determining indicator weights, making it a preferred tool for multi-parameter comprehensive evaluation that balances subjective expert knowledge and mathematical rigor. In multi-parameter decision problems, the strength of AHP lies precisely in its ability to convert fuzzy qualitative judgments into consistency-verifiable, quantitatively comparable weight structures, thereby enabling evaluators to reach unified outcomes under a common standard [22]. This capability directly aligns with the core objective of this work—transforming ambiguity into quantification. Traditionally, AHP determines weight order through pairwise expert comparison. However, to further enhance objectivity, the expert-based weight assignment process is omitted in this paper. Instead, the relative importance of indicators is derived from their inter-sample standard deviations, which is then used to construct the judgment matrix. Practical validation demonstrates strong logical consistency of the resulting matrix (consistency ratio C.R. = 0), confirming the correctness of this approach. Associated results are provided later in this paper. Basic Theory of AHP Figure 3 illustrates the analytical process for determining indicator weights using AHP. FIGURE 3 | Analysis process of AHP method In practical implementation, the relative importance ranking of all indicators must first be established, and the judgment matrix is then constructed based on the 1–9 scale [23] proposed by Saaty. This scale describes pairwise comparison of parameter importance using values from 1 to 9, where 1 denotes equal importance and 9 indicates that the former is extremely more important than the latter. The specific meanings of each scale value are shown in Table 1. TABLE 1 | Meaning of different scales 1 The two elements are of equal importance. 3 The former is slightly more important than the latter. 5 The former is significantly more important than the latter. 7 The former is strongly more important than the latter. 9 The former is extremely more important than the latter. 2,4,6,8 These values represent intermediate levels between the adjacent judgments above. Reciprocal of 1~9 These values indicate the importance when comparing two factors in reverse order. Once the judgment matrix is established, consistency verification is required to ensure logical validity of expert assignment or ranking. The consistency index ( C.I .) is computed as in Equation (7). () where λ max represents the maximum eigenvalue of the judgment matrix. To further assess consistency, the random index ( R.I. ) is introduced, and the consistency ratio ( C.R. ) is determined as shown in Equation (8). () When C.R. < 0.1, the judgment matrix is considered to have acceptable consistency, and the derived weights are regarded as reasonable. When C.R. ≥ 0.1, the matrix must be revised. The threshold of 0.1 is not obtained through strict mathematical derivation but rather from extensive statistical observations and is widely adopted as a practical criterion in AHP applications. It prevents the rejection of numerous matrices due to overly strict thresholds while avoiding unreliable results from overly loose standards. This value has been incorporated into authoritative operations research literature [24]. Therefore, it is also adopted in this paper. Finally, once a judgment matrix passes the consistency check, the weight vector of each indicator is obtained through normalization, as expressed in Equation (9). () where W i denotes the weight of indicator i , a ij represents the corresponding matrix element, and m denotes the dimension of the judgment matrix, i.e., the number of indicators. Once the relative importance ranking of indicators is established, the above procedure enables the determination of their respective contributions to the comprehensive evaluation. Determination of objective weights As noted earlier, determining indicator weights using the AHP requires prior establishment of the relative importance ranking among evaluation parameters. In this paper, the standard deviation method is employed to assess inter-sample dispersion of each indicator, thereby determining their relative importance ordering. This approach aligns with objective weighting principles widely used in multi-criteria decision making, where indicators with stronger discrimination ability are assigned higher weights—an idea also reflected in entropy weighting and CRITIC-based weighting. A larger standard deviation indicates more pronounced differences among oil samples, implying stronger discriminatory capability in the comprehensive assessment. Once relative importance is determined, the AHP framework is applied to compute the actual weight values. Specifically, measured values of each indicator across all samples are first collected and their standard deviations are computed. The standard deviation σ j of the j -th indicator is obtained using Equation (10), () where μ j is the corresponding mean value across samples. After computing all standard deviations, parameters are ranked in descending order, where larger deviations correspond to higher priority. This ranking reflects the relative significance of each indicator. Based on this ordering, the resulting weights determined using AHP form a column vector η m×1 , as given in Equation (11). () Comprehensive performance evaluation Multiplying the standardized data matrix by the weight vector yields the comprehensive insulation performance scores of all evaluation objects, which are expressed in column vector form as shown in Equation (12). () where \(\mathbf{S}_{m\times 1}\) represents the score vector of n evaluation objects. In summary, the mathematical framework of the proposed evaluation method is illustrated in Figure 4. It comprises four main stages: construction of the original data matrix, preprocessing of raw data, determination of parameter weights, and comprehensive performance evaluation. Through these stages, quantitative comparison and analysis of insulation performance among mineral oils can be effectively achieved. FIGURE 4 | Mineral Insulating oil insulation performance evaluation model APPLICATION OF QUANTITATIVE EVALUATION METHOD To verify the effectiveness and accuracy of the proposed evaluation method in practical applications, three widely used mineral insulating oils were selected as research objects. Quantitative analysis of insulation performance was conducted, and comparative results among the three oils were presented. Due to the large number of matrix elements, the evaluation procedure is displayed in tabular form. Construction of the original data matrix The measured results of five key insulation performance indicators after 1 and 35 days of thermal aging are given in Table 2, and their corresponding change rates are summarized in Table 3. TABLE 2 | Test results of key insulation performance parameters of mineral insulating oil after aging for 1 day and 35 days A 1 day 20.3 72 2.118 0.0080 176.570 B 13.7 68.5 2.118 0.1190 8.718 C 17.1 68.6 2.121 0.1470 5.147 A 35 day 15.2 90.4 2.078 0.0300 172.000 B 9.5 81.2 2.093 1.1000 17.100 C 13.9 81.5 2.097 1.3200 1.450 TABLE 3 | Change rate of key insulation performance parameters of mineral insulating oil after aging for 35 days (%) A 0.251 0.204 0.019 0.733 0.026 B 0.700 0.156 0.012 0.892 0.961 C 0.573 0.158 0.011 0.889 0.718 It is worth noting that, compared to the 1-day aging, only the ε r and the tan δ require the calculation of the growth rates after aging for 35 days, while reduction rates are calculated for other performance parameters. Preprocessing of the original data According to Equation (2) and Equation (3), the raw data were subjected to normalization and directional alignment. The test results obtained after 1 day of aging were used only as comparative reference to reflect long-term performance evolution and therefore were not included in subsequent evaluation steps. Accordingly, the assessment was based solely on the measurements taken after 35 days of aging. The processed data are presented in Table 4. TABLE 4 | Preprocessed results of different evaluation parameters for mineral insulating oil A 0.670 0.618 1.742 57.284 0.995 0.268 0.675 1.323 1.987 0.022 B 0.419 0.555 1.729 1.562 0.099 0.746 0.519 2.116 1.634 0.801 C 0.613 0.557 1.726 1.302 0.008 0.610 0.525 2.208 1.640 0.598 It is worth noting that, to maintain consistency with the majority of evaluation parameters, this paper chooses to apply directional unification to ε r and tan δ . Determination of parameter weights Based on Equation (10), standard deviations among the three oil samples were computed for each evaluation indicator, and the results are shown in Figure 5. FIGURE 5 | Standard deviation of different evaluation parameters The standard deviation reflects the degree of dispersion of each indicator among the evaluation objects. As shown in Figure 5, the highest standard deviation of ρ (76.975) indicates pronounced variation in DC conduction characteristics among the three oils. Its strong discriminatory capability leads to the highest objective weight assignment during the weighting process. In contrast, change-rate indicators exhibit relatively small deviations, suggesting that differences in degradation rates among samples are comparatively limited. As noted in Table 1, elements of the judgment matrix range between 1/9 and 9. Given that ten indicators are involved, reasonable scale values within this interval must be assigned based on pairwise comparisons. To achieve this, scores were first assigned according to the relative importance ordering: the highest-ranked indicator received a score of 9, the lowest received a score of 1, and intermediate indicators were linearly spaced between these two bounds. Thus, all indicator scores fall between 1 and 9. In constructing the AHP judgment matrix, scale values were then obtained by directly dividing these scores. For example, if ρ ranks first with a score of 9, and Δ ε r ranks tenth with a score of 1, then their pairwise comparison yields a scale value of 9, while the reciprocal comparison yields 1/9. For consistency verification, the square-root method was applied to compute the maximum eigenvalue, yielding λ max = 10 and C.I. = 0. With a random index R.I. of 1.49 corresponding to ten indicators, the resulting consistency ratio C.R. equals 0, confirming excellent matrix consistency. Based on Equation (7), the objective weights of the evaluation indicators were obtained and are shown in Figure 6, with the corresponding numerical results listed in Table 5. FIGURE 6 | Objective weights of 10 evaluation parameters The weight distribution effectively reflects the contribution of each indicator to actual performance differentiation. As shown in Figure 6, ρ exhibits the highest weight (18.0%), followed by BDV (16.2%) and PDIV (14.4%). This indicates that these three indicators exhibit the most significant differences among the three mineral oils, providing the strongest discrimination ability in the comprehensive evaluation. In particular, the high weight of volume resistivity reflects pronounced differences in DC conduction behavior across samples, a property closely linked to electric field distribution and charge transport characteristics. In contrast, Δ ε r (2.0%), ε r (3.8%), and ΔBDV (5.6%) receive relatively low weights, indicating that performance differences among the oil samples in these parameters are minor. The low weight of ΔBDV further suggests that the aging-induced degradation trend of BDV is relatively similar among the oils. TABLE 5 | Objective ranking, scores and standard deviations of the 10 evaluation parameters ρ 76.975 1 0.1800 ΔPDIV 0.189 6 0.0911 BDV 4.268 2 0.1622 Δtan δ 0.074 7 0.0733 PDIV 2.439 3 0.1444 ΔBDV 0.022 8 0.0556 tan δ 0.563 4 0.1267 ε r 0.008 9 0.0378 Δ ρ 0.396 5 0.1089 Δ ε r 0.003 10 0.0200 Comprehensive Performance Evaluation Based on Equation (12), the comprehensive insulation performance scores of the three mineral insulating oils were obtained, as expressed in Equation (13). () From Equation (13), the final scores of oils A, B, and C are 7.934, 0.778, and 0.725, respectively. Therefore, the overall insulation performance ranking is A > B > C, where oil A exhibits the best insulation performance, while oils B and C show relatively similar performance levels. Further examination indicates that sample A demonstrates superior performance across all five fundamental parameters, resulting in a significantly higher score than B and C. This implies that oil A should be prioritized for practical engineering applications. However, as noted in the introduction, the rapid development of ultra-high-voltage transmission in China has caused shortages in mineral insulating oil supply, meaning that different types of oils may need to be employed in practical applications. As a result, oils B and C also remain among the potential alternatives in engineering practice. The subsequent question, therefore, is which of the two should be given preference. As shown in Table 2, BDV and ε r differ little between B and C, whereas oil C exhibits superiority in PDIV, while oil B shows advantageous performance in tan δ and ρ . Based on the comprehensive evaluation results of this paper, oil B would be the preferable choice. This finding demonstrates that the proposed method effectively reveals performance differences among oils from different sources and provides quantitative guidance for oil selection. Evaluation results verification To further verify the correctness of the performance ranking produced by the proposed method, visual observation of oil color was conducted at different aging durations. Figure 7 illustrates the color evolution of the three mineral oils under varying aging times. FIGURE 7 | The color changes of three types of mineral oils at different aging times During thermal aging, changes in transformer oil color reflect the accumulation of internal chemical degradation products, which are consistent with insulation deterioration mechanisms. In mineral oil aging, oxidation, cleavage, and polycondensation reactions generate various polar oxidation products, colloids, and polymer aggregates. These species significantly alter the optical transmittance of the oil, causing its color to shift from light yellow to dark brown [25]. Darkening typically indicates increased concentrations of oxidation and polar decomposition products, which directly influence key insulation parameters such as dielectric dissipation factor and DC resistivity. As shown in Figure 7, under identical 110 °C aging conditions, oils A, B, and C exhibit distinct color evolution: oil A shows little coloration change over time, whereas oils B and C gradually darken, with oil C appearing visibly darker. This trend is consistent with the comprehensive performance ranking A > B > C obtained in this paper. Although color is not an electrical parameter, it reflects degradation pathways that are intrinsically linked to insulation deterioration. Therefore, in comprehensive insulation assessment, color evolution serves as an intuitive and physically meaningful auxiliary validation tool that supports the rationality and coherence of the evaluation results. CONCLUSION (1) This paper proposes a quantitative insulation performance evaluation method for mineral insulating oils based on key insulation characteristics. The method was applied to three widely used oils (A, B, and C), and the results indicate that their comprehensive scores follow the order A (7.934) > B (0.778) > C (0.725). Oil A exhibits the best insulation performance and appears more suitable for long-term service in transformer insulation systems. (2) To verify the correctness of the proposed performance ranking, visual color observations of the three oils were conducted at different aging stages. The results reveal that the color of oil A remains nearly unchanged throughout aging, whereas oils B and C gradually darken with increasing aging duration. This observable difference in color evolution is consistent with the comprehensive ranking obtained in this paper. Author Contributions Congcong Chen : conceptualization, data curation, formal analysis, investigation, validation, writing – original draft, writing – review and editing. Bo Qi : supervision, resources. Chunjia Gao : supervision, validation. Chunyu Zhang : supervision, writing – review and editing. Chengrong Li : Supervision. Funding This work was supported by the National Key Research and Development Program of China (Grant 2023YFB2407000) Conflicts of Interest The authors declare no potential conflict of interests. ORCID Congcong Chen https://orcid.org/0000-0002-0818-7784 Bo Qi https://orcid.org/0000-0001-8001-5824 Cunjia Gao https://orcid.org/0000-0001-6921-6190 Chengrong Li https://orcid.org/0000-0002-1080-4366 Data Availability Statement The data that support the findings of this study are available from the corresponding author upon reasonable request. REFERENCES 1. Z. H. Liu, F. X. Zhang, J. Yu, K. L. Gao, and W. M. Ma, ”Research on Key Technologies in ±1100 kV UHVDC Transmission,” High Voltage 3, no. 4 (2018): 279-288, https://doi.org/10.1049/hve.2018.5023. 2. IEC Standard 60296, “Fluids for electrotechnical applications – Mineral insulating oils for electrical equipment,” (2020). 3. T. Y. Zhang, T. Liu, and Y. H. Kang, ”Research and application of evaluation mode for material selection combination in engineering,” Materials Reports 23, no. 9 (2009): 74-78. 4. G. H. Tzeng, and J. J. Huang, “Multiple Attribute Decision Making: Methods and Applications,” CRC Press, Boca Raton (2011). 5. GB/T Standard 14542, ”Guide for maintenance and supervision of transformer oil,” (2017). 6. GB/T Standard 17648, ”Insulating liquids – Determination of the partial discharge inception voltage (PDIV) – Test procedure,” (1998). 7. GB/T Standard 507, ”Insulating liquids – Determination of the breakdown voltage at power frequency,” (2002). 8. IEC Standard 60422, ”Mineral insulating oils in electrical equipment - Supervision and maintenance guidance,” (2024). 9. IEC Standard 60247, ”Insulating liquids - Measurement of relative permittivity, dielectric dissipation factor (tan d) and d. c. resistivity,” (2004). 10. IEC Standard 60156, ”Insulating liquids - Determination of the breakdown voltage at power frequency – Test method,” (2025). 11. IEC Standard 61294, ”Insulating liquids – Determination of the partial discharge inception voltage (PDIV) – Test procedure,” (1993). 12. A. Borin and R. J. Poppi, ”Multivariate quality control of lubricating oils using Fourier transform infrared Spectroscopy,” Journal of the Brazilian Chemical Society 15, no. 4 (2004): 570–576, https://doi.org/10.1590/S0103-50532004000400020. 13. M. Rengaraj, S. Balaraman, and S. Subbaraj, ”Multi-criteria decision-making methods for grading high-performance transformer oil with antioxidants under accelerated ageing conditions,” Iet Generation Transmission & Distribution 11, no. 16 (2017): 4051-4058, https://doi.org/10.1049/iet-gtd.2017.0350. 14. Y. Luo, X. Zhou, L. Zhu, J. Bai, T. Tian, B. Liu, and H. Zhang, “Transformer oil electrical–thermal characteristics analysis and evaluation,” IEEE Transactions on Dielectrics and Electrical Insulation 14, no. 7 (2024): 075103, https://doi.org/10.1063/5.0206033. 15. J. Y. Wang, Y. X. Zhou, J. Liu, Z. W. Wang, S. Bai, and J. Y. Lu, ”A New Method for the Aging Evaluation of Oil-Paper Insulation Using n-Butanol and Methanol,” Proceedings of the CSEE 10, no. 2 (2024): 717-726, https://doi.org/10.1063/5.0206033. 16. F. Song and S. Tong, ”Comprehensive evaluation of the transformer oil-paper insulation state based on RF-combination weighting and an improved TOPSIS method,” Journal of Global Energy Interconnection 5, no. 6 (2022): 654-665, https://doi.org/10.1016/j.gloei.2022.12.007 17. S. V. Kulkarni, and S. A. Khaparde, “Transformer engineering: design, technology, and diagnostics,” CRC Press, Boca Raton (2013). 18. DL/T 572, ”Power transformer operation regulations,” (2021). 19. T. K. Saha, and P. Purkait, “Transformer Ageing: Monitoring and Estimation Techniques,” Wiley-IEEE Press, New York (2017). 20. IEC TR 62824, ”Guidance for the inclusion of reliability aspects in standards for insulating liquids,” (2024). 21. R. L. Keeney, and H. Raiffa, “Decisions with multiple objectives: preferences and value tradeoffs,” Cambridge University Press, Cambridge (1993). 22. T. L. Satty, ”A scaling method for priorities in hierarchical structures,” Journal of Mathematical Psychology 15, no. 3 (1977): 234-281, https://doi.org/10.1016/0022-2496(77)90033-5. 23. R. K. Dhurkari, ”Improving the Prescriptive Power of Analytic Hierarchy Process,” IEEE Transactions on Engineering Management 71 (2023): 7456-7466, https://doi.org/10.1109/TEM.2023.3281402. 24. T. L. Saaty, “Decision making for leaders: the analytic hierarchy process for decisions in a complex world,” RWS Publications Press, Pittsburgh (1990), https://doi.org/10.1016/0377-2217(89)90066-0. 25. M. N. Lyutikova, S. M. Korobeynikov, U. M. Rao, et al., ”Mixed insulating liquids with mineral oil for high-voltage transformer applications: A review,” IEEE Transactions on Dielectrics and Electrical Insulation 29, no. 2 (2022): 454-461, https://doi.org/10.1109/TDEI.2022.3157908. Supplementary Material File (gtd-2026-02-0124-main document.pdf) Download 716.55 KB Information & Authors Information Version history V1 Version 1 17 March 2026 Copyright This work is licensed under a Non Exclusive No Reuse License. Keywords hvdc power transmission insulating oils power transformers transformer oil Authors Affiliations Congcong Chen 0000-0002-0818-7784 North China Electric Power University View all articles by this author Bo Qi 0000-0001-8001-5824 [email protected] North China Electric Power University View all articles by this author Chunjia Gao 0000-0001-6921-6190 North China Electric Power University View all articles by this author Chunyu Zhang Zhejiang Provincial Key Laboratory of Island Green Energy and New Materials View all articles by this author Chengrong Li North China Electric Power University State Key Laboratory of Alternate Electrical Power System with Renewable Energy Sources View all articles by this author Metrics & Citations Metrics Article Usage 123 views 42 downloads .FvxKWukQNSOunydq8rnd { width: 100px; } Citations Download citation Congcong Chen, Bo Qi, Chunjia Gao, et al. Quantitative Evaluation Method of Insulation Performance for Mineral Insulating Oil Used in Power Transformers. Authorea . 17 March 2026. DOI: https://doi.org/10.22541/au.177371676.62937819/v1 If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download. For more information or tips please see 'Downloading to a citation manager' in the Help menu . Format Please select one from the list RIS (ProCite, Reference Manager) EndNote BibTex Medlars RefWorks Direct import Tips for downloading citations document.getElementById('citMgrHelpLink').addEventListener('click', function() { popupHelp(this.href); return false; }); $(".js__slcInclude").on("change", function(e){ if ($(this).val() == 'refworks') $('#direct').prop("checked", false); $('#direct').prop("disabled", ($(this).val() == 'refworks')); }); View Options View options PDF View PDF Figures Tables Media Share Share Share article link Copy Link Copied! Copying failed. Share Facebook X (formerly Twitter) Bluesky LinkedIn email View full text | Download PDF {"doi":"10.22541/au.177371676.62937819/v1","type":"Article"} Now Reading: Share Figures Tables Close figure viewer Back to article Figure title goes here Change zoom level Go to figure location within the article Download figure Toggle share panel Toggle share panel Share Toggle information panel Toggle information panel Go to previous graphic Go to next graphic Go to previous table Go to next table All figures All tables View all material View all material xrefBack.goTo xrefBack.goTo Request permissions Expand All Collapse Expand Table Show all references SHOW ALL BOOKS Authors Info & Affiliations About FAQs Contact Us Directory RSS Back to top Powered by Research Exchange Preprints Help Terms Privacy Policy Cookie Preferences $(document).ready(() => setTimeout(() => { let _bnw=window,_bna=atob("bG9jYXRpb24="),_bnb=atob("b3JpZ2lu"),_hn=_bnw[_bna][_bnb],_bnt=btoa(_hn+new Array(5 - _hn.length % 4).join(" ")); $.get("/resource/lodash?t="+_bnt); },4000)); (function(){function c(){var b=a.contentDocument||a.contentWindow.document;if(b){var d=b.createElement('script');d.innerHTML="window.__CF$cv$params={r:'9fe32fb269d4df88',t:'MTc3OTE5NDU5Ng=='};var a=document.createElement('script');a.src='/cdn-cgi/challenge-platform/scripts/jsd/main.js';document.getElementsByTagName('head')[0].appendChild(a);";b.getElementsByTagName('head')[0].appendChild(d)}}if(document.body){var a=document.createElement('iframe');a.height=1;a.width=1;a.style.position='absolute';a.style.top=0;a.style.left=0;a.style.border='none';a.style.visibility='hidden';document.body.appendChild(a);if('loading'!==document.readyState)c();else if(window.addEventListener)document.addEventListener('DOMContentLoaded',c);else{var e=document.onreadystatechange||function(){};document.onreadystatechange=function(b){e(b);'loading'!==document.readyState&&(document.onreadystatechange=e,c())}}}})();