A mixed ester insulating oil for power transformers and a method for predicting optimal proportions

Abstract

This invention discloses a mixed ester insulating oil for power transformers and a method for predicting the optimal ratio, belonging to the technical field of liquid insulating materials for electrical equipment. The method includes base oil pretreatment, mixed oil performance testing, and small sample data processing to establish a quadratic response model for each performance index with respect to x. Expectation normalization, weight assignment, and engineering constraint screening are performed on each index, and a comprehensive expectation function is established as an evaluation index. The maximum comprehensive expectation value is searched in a grid within the range of 0 ≤ x ≤ 1, and the optimal volume fraction ratio of soybean natural ester to palm fatty acid ester is output as 41:59. This insulating oil, with its advantages of low viscosity, low dielectric loss, high flash point, and sufficient transient insulation strength, is suitable for operating conditions in new energy scenarios such as wind power, photovoltaics, and energy storage, where power transformers experience large load fluctuations, frequent start-stop operations, and a high probability of short-term overload. It can effectively improve the operating performance of power transformers and extend their service life.

Description

Technical Field

[0001] This invention relates to the technical field of liquid insulating materials for electrical equipment, insulating media for transformers, and formulation optimization. More specifically, it relates to a mixed ester insulating oil for power transformers and a method for predicting the optimal formulation ratio. Background Technology

[0002] With the development of wind power, photovoltaics, energy storage, and new energy aggregation systems, power transformers face higher requirements in terms of compactness, high reliability, environmental friendliness, and flame-retardant safety. In oil-immersed transformers, insulating oil not only provides electrical insulation but also performs multiple functions, including heat dissipation, impregnating solid insulation, suppressing partial discharge, and reducing fire risk. While traditional mineral oil has mature operating experience, its limited petroleum source, insufficient biodegradability, and limited fire margin restrict its application in new energy power plants, urban substations, offshore platforms, and ecologically sensitive areas.

[0003] Natural ester insulating oils are derived from renewable bio-based raw materials and typically possess high flash points and good environmental compatibility, making them an important development direction for insulating media in power transformers. However, natural esters are not a simple substitute for mineral oil. Some natural esters exhibit issues such as high kinematic viscosity, insufficient low-temperature fluidity, higher dielectric loss factors, different acid value evaluation logic compared to mineral oils, and significant influence from moisture state, which may reduce their flow cooling compatibility in existing mineral oil-based transformer structures.

[0004] By blending different ester components, a range of parameters can be adjusted between low viscosity, low loss, high flash point, and breakdown strength. Palm fatty acid esters have the advantage of low viscosity, which is beneficial for oil circulation and heat dissipation; soybean natural esters have a higher flash point and better dielectric loss performance, which is beneficial for improving fire safety margin and reducing dielectric loss. However, simply increasing the proportion of soybean natural esters will increase viscosity and may affect moisture-related dielectric stability. Therefore, the ratio needs to be determined under multiple engineering constraints, rather than directly based on single performance or discrete test results.

[0005] Existing research on mixed ester insulating oils typically involves comparing several fixed proportions and then selecting the scheme with better apparent performance from discrete test results. While this method can perform preliminary screening, it struggles to identify feasible windows within a continuous composition space and fails to account for the multi-parameter constraints required for practical transformer applications. Especially when sample sizes are limited, testing costs are high, or the repeatability requirements of lightning impulse breakdown tests are high, a predictive preparation method for mixed ester insulating oils that is reproducible, adjustable, and capable of outputting verifiable targets under small sample conditions is needed.

[0006] Natural ester molecules contain polar ester groups, differing from traditional hydrocarbon mineral oils in molecular polarity, hygroscopic properties, oxidation reaction pathways, and interactions with cellulose insulation. Natural esters have high water solubility, which can help reduce water activity in insulating paper under certain conditions. However, water, polar impurities, and trace ions in the oil can also cause an increase in the dielectric loss factor and dispersion in breakdown data. Therefore, before comparing samples with different ratios, it is necessary to control the sample state through consistent filtration, drying, vacuum degassing, and isothermal equilibration processes. Otherwise, the ratio effect can easily overlap with the effects of water, bubbles, and impurities, leading to a lack of repeatability in the model output.

[0007] Palm fatty acid esters and soybean natural esters have complementary molecular compositions and macroscopic properties. Palm fatty acid esters have lower kinematic viscosity, which can reduce liquid circulation resistance and improve the cooling compatibility of existing mineral oil-based transformers; soybean natural esters have higher flash points and exhibit both lower dielectric loss factor and higher flash point in this system, which is beneficial for improving steady-state dielectric properties and fire safety margin. However, an excessively high proportion of soybean natural esters will significantly increase the kinematic viscosity of the mixture, while an excessively high proportion of palm fatty acid esters may make it difficult to meet the stringent low-loss screening requirements for the dielectric loss factor, thus forming an opposite compositional dependence between the two.

[0008] The properties of mixed esters do not follow a simple linear additive law. The relative permittivity, flash point, power frequency breakdown voltage, and lightning impulse breakdown voltage exhibit non-monotonic changes under different ratios, indicating that molecular polarity, carrier migration, and streamer development conditions change after mixing. Therefore, even if a discrete ratio performs well in a single indicator, it cannot be inferred that it is the overall optimal ratio within adjacent continuous ratio ranges, nor can it directly determine a feasible window that satisfies all engineering thresholds.

[0009] Existing formulation screening methods have two shortcomings: First, lightning impulse tests on insulating oil are costly and require a large number of repetitions, making it difficult to set up a large number of mixing points like conventional physicochemical tests; second, if only the arithmetic mean breakdown voltage is used for evaluation, it cannot reflect the dispersion of repeated data and the conservative insulation level under low failure probability. Especially when the average values ​​of two candidate formulations are close, the shape parameter is large, and U... 10 Higher proportions generally result in better statistical consistency and engineering reliability. Therefore, it is necessary to combine small-sample continuous prediction with Weibull reliability assessment.

[0010] For the reasons mentioned above, there is a need for a method for preparing renewable mixed ester insulating oil that can establish a continuous composition-performance relationship based on limited discrete ratio data, first determine the feasible ratio range using engineering constraints, then select the target ratio based on the comprehensive expectation of multiple indicators, and verify the results through actual measurement and Weibull parameters. Summary of the Invention

[0011] The purpose of this invention is to propose a method for predicting the optimal ratio of mixed ester insulating oil for power transformers, in order to solve the problem that the selection of the ratio of renewable ester insulating oil in the prior art relies too much on discrete proportions and single indicators, making it difficult to simultaneously consider the adaptability of flow cooling, dielectric loss, fire protection margin and transient insulation reliability.

[0012] To achieve the above objectives, the technical solution of the present invention is as follows:

[0013] A method for predicting the optimal blend ratio of mixed ester insulating oil for power transformers includes base oil pretreatment, discrete blending sample preparation, multi-performance index testing, response surface prediction, expectation normalization, engineering constraint screening, and target blending preparation and verification.

[0014] The palm fatty acid esters referred to in this invention are low-viscosity, renewable ester insulating oils with palm-derived fatty acid esters as the main component, and the soybean natural esters are natural ester insulating oils with soybean oil-derived triglycerides as the main component. Both base oils are formulated using the same mass or volume measurement method in the same batch. The ratio variable x represents the fraction of soybean natural esters, and 1-x represents the fraction of palm fatty acid esters.

[0015] The multi-parameter prediction preparation method is executed in the following order: "state control—discrete sample preparation—performance testing—model fitting—model optimization—constraint screening—comprehensive ranking—preparation verification". This order ensures the comparability of input data and allows the model output to be traced back to specific base oil batches, blending ratios, and testing conditions.

[0016] In this process, state control is used to limit the water content, impurities, and gas state of the sample before it enters the test; discrete sample preparation is used to obtain data points that can cover the endpoints and intermediate components of the two base oils; performance testing is used to generate raw data for each index; model fitting and model optimization are used to obtain predicted values ​​within the continuous blending range; constraint screening is used to exclude blends that do not meet the minimum engineering requirements; comprehensive ranking is used to determine the target blending within the feasible set; and preparation verification is used to verify the consistency between the predicted results of the target blending and the measured results.

[0017] The base oils include palm fatty acid esters and soybean natural esters. The fraction x of soybean natural esters in the mixed esters is used as the proportioning variable, and the fraction 1-x of palm fatty acid esters in the mixed esters is used as the complementary variable. x is a volume fraction, but the measurement method should be consistent throughout the preparation and testing of the same batch.

[0018] In this invention, the proportion variable x is used not only as the test sample number, but also as a unified independent variable for subsequent response surface modeling, engineering constraint screening, and comprehensive expectation calculation. Using a unified independent variable avoids establishing unrelated evaluation logics between different performance indicators, ensuring that kinematic viscosity, dielectric loss factor, acid value, flash point, power frequency breakdown voltage, and average lightning impulse breakdown voltage can all be mapped to the same continuous proportion point.

[0019] The discrete proportioning sample preparation includes preparing mixed ester insulating oils with x=0, x=0.3, x=0.5, x=0.7, and x=1.0. Intermediate proportions such as x=0.4, x=0.45, or x=0.6 can also be added depending on the test conditions. Each base oil undergoes vacuum degassing, drying, filtration, and isothermal equilibration treatment before mixing to reduce interference from moisture and air bubbles on the dielectric test.

[0020] During sample preparation, samples from the same batch should preferably use the same pretreatment equipment, stirring time, and equilibrium temperature. For two base oils with significantly different viscosities, the lower viscosity component can be added first, followed by the higher viscosity component slowly, to reduce the impact of localized compositional inhomogeneities on subsequent dielectric tests. After mixing, the samples should be allowed to stand, degas, and numbered under sealed conditions to prevent moisture from the air from re-entering the oil samples.

[0021] The multi-index test includes kinematic viscosity at 40℃, dielectric loss factor at 90℃, acid value, flash point, power frequency breakdown voltage, and lightning impulse breakdown voltage. Kinematic viscosity is used to characterize the oil's circulation and heat dissipation adaptability; the dielectric loss factor is used to characterize steady-state dielectric loss; the acid value is used as a soft constraint evaluation index for ester-based insulating oils; the flash point is used to characterize fire safety margin; the power frequency breakdown voltage is used to characterize conventional insulation strength; and the lightning impulse breakdown voltage is used to characterize the withstand capability under transient overvoltage in new energy collection and boosting systems.

[0022] The aforementioned indicators play different roles in optimization. Kinematic viscosity and dielectric loss factor are mainly used to limit the cooling adaptability and dielectric loss level of the transformer under long-term operating conditions; flash point is used to evaluate safety margin; power frequency breakdown voltage reflects conventional insulation strength; and average lightning impulse breakdown voltage reflects the withstand level under transient overvoltage. By incorporating these indicators into the prediction process, the bias caused by determining the formulation based solely on a single physicochemical or electrical indicator can be reduced.

[0023] Furthermore, the lightning impulse breakdown voltage is statistically analyzed using a two-parameter Weibull model, as shown in the following formula.

[0024]

[0025] Extract U1, U 10 U 50 and U63.2 This is used to evaluate the insulation reliability of different ratios under low failure probability and characteristic failure probability. U1 represents the breakdown voltage with a breakdown probability of 1%, U... 10 U represents the breakdown voltage with a breakdown probability of 10%. 63 .2 represents a breakdown voltage with a breakdown probability of 63.2%. The larger the shape parameter m, the steeper the slope of the Weibull fitting line, indicating that the repeated breakdown data are relatively concentrated and have good statistical consistency. The Weibull parameter is used to verify the reliability of candidate configurations with similar average lightning impulse breakdown voltages, rather than replacing multi-parameter comprehensive optimization.

[0026] This invention does not require a single Weibull parameter to determine the target mix ratio. Instead, it requires that the candidate mix ratio, while satisfying physicochemical and power frequency constraints, also possess acceptable data dispersion and a low probability breakdown margin. This approach avoids selecting samples with high randomness solely based on the average breakdown voltage.

[0027] When the difference in average lightning impulse breakdown voltage between different ratios is small, this invention utilizes U1 and U 10 U 50 and U 63.2 These parameters are used to determine whether the low-probability breakdown level and the characteristic breakdown level remain within a reasonable range. If the average value of a candidate mix is ​​high but the Weibull shape parameter is small, it indicates that the breakdown data has a large dispersion, and careful evaluation is still required in engineering applications.

[0028] Furthermore, relative permittivity and volume resistivity can be used as auxiliary evaluation indicators. Relative permittivity is used to determine the dielectric matching state between the mixture and the oil-paper composite insulation, while volume resistivity is used to characterize charge migration and conductivity loss levels in the liquid. These auxiliary indicators can be used to explain changes in dielectric loss factor and breakdown voltage, but need not be used as hard constraints for every formulation search.

[0029] Kinematic viscosity, dielectric loss factor, power frequency breakdown voltage, and flash point constitute the main boundaries of the feasible mix design range. Kinematic viscosity reflects the compatibility of oil circulation and heat dissipation; the dielectric loss factor reflects the requirements for low-loss operation; power frequency breakdown voltage is used to exclude mixes with insufficient conventional insulation strength; and flash point is used to exclude mixes with insufficient fire resistance margin. Acid value is used as a cost-based soft target in the ranking, and ester samples are not directly rejected using a rigid threshold similar to that of mineral oil. Lightning impulse average breakdown voltage is used as a key benefit-oriented indicator to improve the transient insulation level of candidate mixes.

[0030] The response surface prediction uses a quadratic polynomial.

[0031]

[0032] By fitting various performance indicators, the predicted performance of each proportion point in the continuous composition space is obtained. For power frequency breakdown and lightning impulse breakdown, the average breakdown voltage can be used as the optimization input. At the same time, Weibull statistics are performed on the repeated lightning impulse breakdown data to supplement the low failure probability reliability evaluation.

[0033] The reason for choosing a quadratic polynomial model is that the number of basic ratio points in this invention is limited, and the quadratic model can describe the main bending trends and non-monotonic features, while avoiding unstable oscillations between sample points in higher-order polynomials. The fitting coefficients are obtained by the least squares method, and the fitting residuals at each discrete point can be further calculated. The applicability of the model in the local interval is checked by adding validation points near the target ratio.

[0034] Before fitting the data, the results of repeated tests under the same ratio should be compiled into representative values, and the test conditions, sample numbers, and methods for handling outliers should be recorded. Invalid data clearly caused by air bubbles, contamination, or operational abnormalities should be explained during the data processing stage and not directly used as input into the model as the inherent properties of the ratio. This data processing step improves the traceability of small sample modeling.

[0035] For the i-th performance term, the prediction model is written as:

[0036]

[0037] After discretizing the continuous interval of 0≤x≤1 into grid points with a step size of no more than 0.001, the predicted values ​​of kinematic viscosity, dielectric loss factor, acid value, flash point, power frequency breakdown voltage and average lightning impulse breakdown voltage can be calculated at each grid point, thereby transforming the finite proportion test into a searchable performance matrix in a continuous composition space.

[0038] The grid search can be performed using general-purpose computing programs, spreadsheets, or dedicated recipe optimization programs; the specific software used for the calculation is not limited. For each grid point, the predicted performance is first obtained by calling the response surface equations, then a feasibility assessment is performed based on engineering thresholds, and finally, the overall expected value is calculated only for feasible mix proportions. This step ensures that the target mix proportions are derived from continuous search results, rather than being manually selected directly from a few discrete mix proportions.

[0039] The expected value normalization involves setting flash point, power frequency breakdown voltage, and average lightning impulse breakdown voltage as benefit-oriented indicators, and kinematic viscosity, dielectric loss factor, and acid value as cost-oriented indicators, forming a comprehensive expected value function, as shown in the following formula.

[0040]

[0041] The normalized expected value of a benefit-type indicator can be expressed as:

[0042]

[0043] The normalized expected value of a cost-type indicator can be expressed as:

[0044]

[0045] After normalization, all indicators are converted to the dimensionless range of 0 to 1 to avoid any unexpected advantage of a certain indicator in the comprehensive calculation due to differences in dimensions and numerical ranges.

[0046] The weights do not represent inherent material constants, but rather the baseline engineering priorities adopted after dimensionless transformation. This invention assigns relatively high weights of 0.30 and 0.20 to the average lightning impulse breakdown voltage and flash point, respectively, to emphasize transient insulation reliability and fire safety; assigns a weight of 0.15 to the power frequency breakdown voltage and kinematic viscosity, respectively, to balance conventional insulation margin and cooling compatibility; and assigns a weight of 0.10 to the dielectric loss factor and acid value, respectively. The dielectric loss factor has already served as a strict low-loss constraint in the selection of feasible mixing ratios, while the acid value serves as a soft target for ester systems.

[0047] Without altering the basic process of this invention, the weights can be adjusted according to the transformer application scenario. For example, compact natural oil circulation cooling equipment can increase the kinematic viscosity weight, offshore platforms and urban substations can increase the flash point weight, and frequent lightning activity or other situations can increase the lightning impact index weight. The sum of the adjusted weights remains 1.

[0048] When adjusting the weights, the benefit-type or cost-type attributes of each indicator remain unchanged, and the sum of the adjusted weights is still 1. To ensure that the optimization results of different batches are comparable, it is preferable to fix the weights and thresholds before calculation, and record the weight combination, constraints, search step size, and response surface coefficients when outputting the target ratio.

[0049] The engineering constraints include: kinematic viscosity η(x) ≤ 12 mm² / s, dielectric loss factor tanδ(x) ≤ 0.050, and power frequency breakdown voltage U. AC (x)≥55kV, flash point Fp(x)≥170℃.

[0050] During the grid search process, each point is first checked to see if all engineering constraints are met. If any constraint is not met, the corresponding matching point is marked as infeasible and removed from the sorted set. The comprehensive expectation is calculated or retained only for matching points that simultaneously meet all constraints, thereby avoiding a situation where a high-weighted advantage index compensates for another performance that is already below the minimum engineering requirements.

[0051] There is a sequential relationship between constraint screening and comprehensive expectation ranking. If a mix proportion no longer meets the minimum requirements for kinematic viscosity, dielectric loss factor, power frequency breakdown voltage, or flash point, it will not be included in the comprehensive ranking set, even if it has high predicted values ​​for other indicators. This approach ensures that the target mix proportion first meets basic engineering applicability, and then the overall performance is compared.

[0052] The constraint values ​​are used for formula screening in the embodiments of the present invention and are not a substitute for passing the complete type test. In the actual product finalization process, verification items such as moisture content, pour point, oxidation stability, interfacial tension, corrosive sulfur, and material compatibility can be added based on the equipment voltage level, cooling method, operating temperature range, and the test standards adopted.

[0053] The target ratio is the ratio that maximizes the comprehensive expectation function D(x) within a feasible range that satisfies engineering constraints. Preferably, the feasible range is x = 0.410 to 0.441, and the target ratio is x = 0.410, i.e., the volume fraction ratio of soybean natural esters to palm fatty acid esters is 0.41:0.59. This target ratio serves as the baseline formulation given by the prediction model and the target for subsequent experimental verification.

[0054] The feasible interval represents the range of continuous compositions that simultaneously meet the constraints under the prediction of the response surface methodology, and the target proportion represents the specific composition point with the highest overall expectation within this range. In actual preparation, verification can be prioritized according to the target proportion; when the accuracy of on-site metering, base oil batches, or application conditions change, supplementary verification can also be performed by selecting points close to the target proportion within the feasible interval.

[0055] Compared with the prior art, the present invention has the following beneficial effects:

[0056] This invention combines the low viscosity advantage of palm fatty acid esters with the high flash point and low loss advantage of soybean natural esters, which can take into account the flow cooling adaptability, fire safety and dielectric properties in renewable source insulating oil systems.

[0057] This invention does not directly select a single optimal sample from discrete test ratios, but instead establishes a continuous spatial prediction model based on a small sample size, which can identify feasible ratio windows that satisfy multiple engineering constraints.

[0058] This invention reduces the deviation caused by maximizing a single indicator by first screening with hard constraints and then sorting based on comprehensive expectation, making the target ratio more in line with the comprehensive requirements of low viscosity, low loss, high flash point and transient insulation reliability in power transformers.

[0059] This invention incorporates lightning impulse breakdown data into Weibull statistics, enabling the evaluation of insulating oil reliability from multiple perspectives, such as average breakdown strength, data dispersion, and low failure probability breakdown voltage, thus avoiding the need to rely solely on average values ​​for formulation judgment.

[0060] This invention can output clear target ratios and various predicted performances, and verify them by the relative error between the measured values ​​and predicted values ​​of the target samples, thereby forming a closed-loop formulation optimization process of "prediction-screening-optimization-preparation-verification". Attached Figure Description

[0061] Figure 1 This is a schematic diagram of the overall process for multi-parameter prediction and preparation of mixed ester insulating oil according to the present invention.

[0062] The above figures are used to illustrate the algorithm flow of the small sample multi-parameter prediction preparation method in this invention, and the connection relationship between the modules is not limited to the specific software implementation. Detailed Implementation

[0063] The technical solutions of the present invention will be clearly and completely described below with reference to the embodiments of the present invention. The described embodiments are only some embodiments of the present invention, and not all embodiments. Other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are all within the protection scope of the present invention. The overall flow of the present invention is as follows: Figure 1 As shown.

[0064] This embodiment proposes a method for predicting the optimal ratio of mixed ester insulating oil for power transformers. The specific implementation steps are as follows:

[0065] Example

[0066] S1. Base Oil Pretreatment: Palm fatty acid esters (PFAE) and soybean natural esters (SNE) were selected as base oils. Before mixing, the appearance, sealing condition, and presence of visible suspended matter or emulsification of both base oils were checked. A consistent filtration, drying, vacuum degassing, and isothermal equilibration process was used to reduce the impact of mechanical impurities, free water, dissolved water, dissolved gases, and microbubbles on dielectric performance testing. Sample preparation containers, stirring equipment, and sampling equipment were kept clean and dry. After treatment, the base oils were stored in sealed containers to avoid prolonged exposure to air.

[0067] After pretreatment, the exposure time of the samples should be minimized, and all samples should undergo the same sealing and equilibration process before testing. If the base oil batch changes, the kinematic viscosity, loss factor, flash point, and breakdown performance of the endpoint samples should be reconfirmed, and the updated data should be used as the model input to avoid directly applying the old batch model to the new batch of oil samples, which could cause prediction errors.

[0068] After conditioning, the two base oils exhibited complementary properties: PFAE had a kinematic viscosity of 5.41 mm² / s at 40℃, while SNE had a kinematic viscosity of 34.780 mm² / s; their flash points were 175.5℃ and 235.5℃, respectively; their media loss factors at 90℃ were 0.06883 and 0.03026, respectively; and their volume resistivity was 4.7 × 10⁻⁶. 9 Ω·m and 7.6×10 9 The average power frequency breakdown voltages were 69.78 kV and 55.40 kV, respectively; the acid values ​​were approximately 0.030 mg KOH / g and 0.040 mg KOH / g, respectively; and the relative permittivity were 2.43 and 2.42, respectively.

[0069] S2. Preparation of Discretely Proportioned Mixed Ester Insulating Oil. Using the fraction x of SNE in the mixed ester insulating oil as the proportioning variable and the PFAE fraction 1-x as the complementary variable, five groups of mixed ester insulating oils with x=0, 0.3, 0.5, 0.7, and 1.0 were prepared, denoted as PFAE, 3:7, 5:5, 7:3, and SNE, respectively. Here, 3:7 indicates an SNE fraction of 0.3 and a PFAE fraction of 0.7. Volume fractions were used for proportioning, and the measurement method was kept consistent within the same experimental series.

[0070] During preparation, weigh or measure the two base oils according to the target total amount. First, add the lower viscosity PFAE to a clean, dry, sealed mixing container, then slowly add SNE, and continue stirring under nitrogen or vacuum protection until the sample has a uniform appearance. After mixing, allow it to stand or degas under vacuum, then seal and number it. All samples should be subjected to the same standing time, testing environment, and sampling method. Avoid vigorous shaking and introducing air bubbles when sampling for the breakdown test.

[0071] S3. Multi-parameter performance testing and data processing. The five groups of mixed ester insulating oils with different ratios were tested for kinematic viscosity at 40℃, dielectric loss factor at 90℃, acid value, flash point, power frequency breakdown voltage, and lightning impulse breakdown voltage. The reliability of the lightning impulse breakdown voltage was evaluated, and relative permittivity and volume resistivity were simultaneously tested as auxiliary evaluation indicators. All tests used consistent sample treatment conditions, test temperatures, electrode types, electrode spacing, voltage boosting methods, and repetition counts to ensure comparability of data from different ratios.

[0072] When processing test data, the original repeated values, average values, and representative values ​​used for model input should be saved separately. For power frequency breakdown voltage and lightning impulse breakdown voltage, the average value is used for response surface optimization, and the repeated values ​​are used to observe dispersion and perform Weibull fitting. For acid value, dielectric loss factor, and kinematic viscosity, the test temperature and units should be consistent to avoid affecting the normalization results due to unit conversion or different decimal places.

[0073] Statistical analysis was conducted on repeated lightning impulse breakdown data for various base mix ratios under positive and negative polarity conditions and with oil gaps of 3mm and 5mm. After summarizing the data under the four conditions, the average lightning impulse breakdown voltages corresponding to x=0, 0.3, 0.5, 0.7, and 1.0 were approximately 71.17kV, 67.41kV, 71.78kV, 68.53kV, and 70.88kV, respectively.

[0074] The repeated breakdown data were fitted using a two-parameter Weibull distribution, where βs is the scale parameter and m is the shape parameter, and U1 and U2 were calculated. 10 U 50 and U 63.2 A larger m indicates a more concentrated data set, and a larger U... 10 This represents the breakdown voltage when the breakdown probability is 10%. For example, under positive polarity and 3mm conditions, the m of the sample with x=0.5 is approximately 22.626, and U... 10 Approximately 60.073 kV; under positive polarity 5 mm conditions, the m of the sample with x=0.5 is approximately 26.643, U 10 Approximately 73.566 kV. The Weibull parameter is used to verify the reliability of candidate configurations with similar average lightning impulse breakdown voltages, rather than replacing multi-parameter comprehensive optimization.

[0075] The modeling input data shows that as x increases, the kinematic viscosity generally increases, the flash point generally rises, and the dielectric loss factor generally decreases, while the relative permittivity, volume resistivity, and power frequency breakdown voltage exhibit certain non-monotonic changes. Taking the five basic proportions as examples, their dielectric loss factors at 90℃ are approximately 0.06883, 0.05157, 0.05164, 0.03592, and 0.03026, respectively; and their average power frequency breakdown voltages are approximately 69.78kV, 56.3kV, 66.1kV, 57.5kV, and 55.40kV, respectively. These data demonstrate that there is a clear trade-off between the various performance indicators, and the final proportion cannot be determined solely based on a single indicator.

[0076] S4. Establishment of the response surface prediction model. Using the proportioning variable x and various performance data as inputs, quadratic polynomial models are applied to kinematic viscosity, dielectric loss factor, acid value, flash point, average power frequency breakdown voltage, and average lightning impulse breakdown voltage, respectively.

[0077]

[0078] Perform least squares fitting, where Let x be the predicted value of the i-th performance item under the ratio x. , and The fitting coefficients are used. The quadratic model is used to describe the main bending trends and non-monotonic features under small sample conditions, and to avoid unstable oscillations between discrete points in higher-order models.

[0079] The continuous component interval of 0≤x≤1 is discretized into grid points with a step size of no more than 0.001. At each grid point, the performance response equations are called to form a continuous performance matrix containing the predicted values ​​of kinematic viscosity, dielectric loss factor, acid value, flash point, power frequency breakdown voltage, and average lightning impulse breakdown voltage.

[0080] S5. Using performance parameters such as dielectric loss factor, kinematic viscosity, power frequency breakdown voltage, lightning impulse breakdown voltage, and flash point as constraints, the prediction model is optimized under the condition that the dielectric loss factor is no greater than 0.05. Performance parameter thresholds are set as follows: kinematic viscosity η(x) ≤ 12 mm² / s, dielectric loss factor tanδ(x) ≤ 0.050, and power frequency breakdown voltage U... AC (x)≥55kV, flash point Fp(x)≥170℃, output feasible ratio range.

[0081] In this embodiment, the dielectric loss factor constraint is used to prioritize eliminating proportions with insufficient low-loss requirements, the kinematic viscosity constraint is used to limit the risk of flow cooling mismatch caused by a high proportion of SNE (Surface Energy Negative) mixtures, and the power frequency breakdown voltage and flash point constraints are used to ensure the basic insulation strength and fire safety baseline, respectively. After screening by the above constraints, a comprehensive expectation ranking is performed, which ensures that the final target proportion has both clear engineering boundaries and a comprehensive optimization basis.

[0082] S6. Expectation Normalization, Weight Assignment, and Engineering Constraint Screening. Flash point, average power frequency breakdown voltage, and average lightning impulse breakdown voltage are set as benefit-type indicators, while kinematic viscosity, dielectric loss factor, and acid value are set as cost-type indicators. Expectation normalization is performed on each indicator within the range of 0 to 1. After normalization, the comprehensive expectation D(x) is calculated according to the weights of kinematic viscosity (0.15), dielectric loss factor (0.10), average power frequency breakdown voltage (0.15), flash point (0.20), acid value (0.10), and average lightning impulse breakdown voltage (0.30), with the sum of all weights being 1.

[0083] S7. Output of target ratio and predicted performance parameters. Grid search results show that the dielectric loss factor constraint forms the lower boundary of the feasible range, and the kinematic viscosity constraint forms the upper boundary. The feasible range for the soybean natural ester fraction x is 0.410 to 0.441. Within this range, the maximum value of the comprehensive expectation D(x) corresponds to x=0.410, i.e., the volume fraction ratio of SNE to PFAE is 0.41:0.59. This ratio is located near the constraint boundary, which can retain the low viscosity and high power frequency breakdown advantage of PFAE as much as possible while meeting the low loss requirement.

[0084] The model predicts that the kinematic viscosity of the target sample at 40℃ is 11.21 mm² / s, the dielectric loss factor at 90℃ is 0.050, the acid value is 0.04 mg KOH / g, the flash point is 180.60℃, the average power frequency breakdown voltage is 61.26 kV, and the average lightning impulse breakdown voltage is 69.27 kV.

[0085] S8. Target Sample Preparation, Experimental Verification, and Final Data Obtaining. SNE and PFAE were measured at a volume fraction ratio of 41:59. The target mixed ester insulating oil was prepared according to the feeding, protective stirring, standing or vacuum degassing, and sealing equilibration steps described in S2. Final experimental verification was performed on the target sample with x=0.410. The measured kinematic viscosity at 40℃ was 11.64 mm² / s, the dielectric loss factor at 90℃ was 0.05, the acid value was 0.04 mgKOH / g, the flash point was 182.30℃, the average power frequency breakdown voltage was 59.77 kV, and the average lightning impulse breakdown voltage was 70.06 kV. Using the measured values ​​as the denominator, the relative errors for kinematic viscosity, flash point, average power frequency breakdown voltage, and average lightning impulse breakdown voltage were 3.69%, 0.93%, 2.49%, and 1.13%, respectively. The relative errors for the dielectric loss factor and acid value at the current retention number were 0. The comparison between predicted and measured values ​​is shown in Table 1.

[0086] The target sample validation is not intended to replace all type tests, but rather to verify the local effectiveness of the predictive model near the target ratio. If the validation error exceeds the preset range, one or more supplementary ratio points can be added near the target ratio, and the response surface coefficients can be refitted or corrected. If the validation error is within an acceptable range, the ratio can be used as the base formula for subsequent scale-up preparation, stability evaluation, and transformer application suitability tests.

[0087] In this embodiment, the continuous feasible interval from 0.410 to 0.441 and each continuous mix ratio point within it are calculated using a response surface model, engineering constraints, and comprehensive expectation. The final experimental verification is performed on the target mix ratio of x=0.410 output by the model. The verification results show that the target sample meets the kinematic viscosity, dielectric loss factor, power frequency breakdown voltage, and flash point screening conditions set in this embodiment, and the predicted values ​​are generally close to the measured values.

[0088] Table 1 Comparison of predicted and measured values ​​of target proportions

[0089] Kinematic viscosity at 40℃ (mm² / s) 11.21 11.64 3.69 90℃ dielectric loss factor 0.05 0.05 0.00 Acid value (mg KOH / g) 0.04 0.04 0.00 Flash point (°C) 180.60 182.30 0.93 Average power frequency breakdown voltage (kV) 61.26 59.77 2.49 Average lightning impulse breakdown voltage (kV) 69.27 70.06 1.13

Claims

1. A method for predicting the optimal proportion of mixed ester insulating oil for power transformers, characterized in that, Includes the following steps: S1. Pretreatment of palm fatty acid esters and soybean natural esters to obtain base oils with water content and impurity status that meet the sample preparation requirements; S2. Using the volume fraction x of the soybean natural ester in the mixed ester insulating oil as the ratio variable, and the fraction 1-x of the palm fatty acid ester as the complementary variable, the two ester insulating oils are mixed in multiple discrete ratios to prepare discrete ratio insulating oil. S3. Measure the kinematic viscosity, dielectric loss factor, acid value, flash point, power frequency breakdown voltage, and average lightning impulse breakdown voltage of the ester insulating oils with the discrete ratios, respectively. S4. Establish a response surface prediction model for x for various parameters such as kinematic viscosity, dielectric loss factor, acid value, flash point, power frequency breakdown voltage and average lightning impulse breakdown voltage. S5. Using the dielectric loss factor, kinematic viscosity, power frequency breakdown voltage, average lightning impulse breakdown voltage and flash point as constraints, set performance parameter thresholds, and use the response surface prediction model to constrain and screen the continuous proportioning range to obtain a feasible proportioning range that meets the constraint requirements. S6. Normalize the expected value of each performance index and assign weights according to the engineering priority of the power transformer insulating oil to obtain the comprehensive expected value function. S7. Using the comprehensive expectation function, select the ratio with the highest comprehensive expectation within the feasible ratio range as the target ratio, and output the target ratio and each performance prediction parameter. S8. Prepare mixed ester insulating oil according to the target ratio, and conduct experimental measurements on the renewable mixed ester insulating oil prepared according to the target ratio to verify the predicted performance parameter results.

2. The method for predicting the optimal proportion of mixed ester insulating oil for power transformers according to claim 1, characterized in that, The discrete ratio insulating oil includes at least three groups selected from x=0, x=0.3, x=0.5, x=0.7 and x=1.0, where x represents the volume fraction of the soybean natural ester in the mixed ester insulating oil.

3. The method for predicting the optimal proportion of mixed ester insulating oil for power transformers according to claim 1, characterized in that, The response surface prediction model is a quadratic polynomial model. ,in Let x be the predicted value of the i-th performance index under the ratio x. , and The coefficients are obtained through least squares fitting.

4. The method for predicting the optimal proportion of mixed ester insulating oil for power transformers according to claim 1, characterized in that, The flash point, power frequency breakdown voltage, and average lightning impulse breakdown voltage are benefit-type indicators, while the kinematic viscosity, dielectric loss factor, and acid value are cost-type indicators. Benefit-type indicators are normalized according to the principle that higher values ​​indicate higher expected value, while cost-type indicators are normalized according to the principle that lower values ​​indicate higher expected value. The normalized expected value of the benefit-type indicators is expressed as follows: The normalized expected value of cost indicators is expressed as: For the normalized expected value of benefit-type indicators, For the normalized expected value of cost-related indicators, Let x be the predicted value of the i-th performance index under the ratio x. This represents the maximum predicted value of the i-th performance index under different ratios x. The minimum predicted value of the i-th performance index under different ratios x is represented. After normalization, each index is converted to a dimensionless range of 0 to 1 to avoid an unexpected advantage of a certain index in the comprehensive calculation due to different dimensions and numerical ranges.

5. The method for predicting the optimal proportion of mixed ester insulating oil for power transformers according to claim 1, characterized in that, The weights include: kinematic viscosity 0.15, dielectric loss factor 0.10, power frequency breakdown voltage 0.15, flash point 0.20, acid value 0.10, and average lightning impulse breakdown voltage 0.

30.

6. The method for predicting the optimal proportion of mixed ester insulating oil for power transformers according to claim 1, characterized in that, The comprehensive expectation function is, in w is the normalized expected value of the i-th performance metric. i For the corresponding weights, and Σw i =1.

7. The method for predicting the optimal proportion of mixed ester insulating oil for power transformers according to claim 1, characterized in that, The constraint screening in S6 first uses a hard constraint screening condition that the dielectric loss factor at 90℃ is not greater than 0.05 to determine the lower boundary of the feasible proportion range. Then, kinematic viscosity, flash point and power frequency breakdown voltage are screened. Kinematic viscosity at 40℃ is used as the screening condition for the upper boundary of the feasible proportion range, which is required to be not greater than 12mm² / s, power frequency breakdown voltage is required to be not less than 55kV, and flash point is required to be not less than 170℃.

8. The method for predicting the optimal proportion of mixed ester insulating oil for power transformers according to claim 1, characterized in that, The lightning impulse breakdown voltage was statistically analyzed using a two-parameter Weibull distribution, as shown in the following formula. Where U is the breakdown voltage, β s is the scale parameter, m is the shape parameter, and U1 and U2 are extracted. 10 U 50 and U 63 At least one of the parameters in .2 is used as a reliability evaluation parameter, where U1 represents the breakdown voltage with a breakdown probability of 1%, U 10 U represents the breakdown voltage with a breakdown probability of 10%. 63 .2 represents a breakdown voltage with a breakdown probability of 63.2%.

9. The method for predicting the optimal proportion of mixed ester insulating oil for power transformers according to claim 1, characterized in that, The continuous ratio range is searched within the range of 0 ≤ x ≤ 1, with a search step size of no more than 0.001, and the target ratio range is output within the feasible range of soybean natural ester fraction obtained after screening.

10. The method for predicting the optimal proportion of mixed ester insulating oil for power transformers according to claim 9, characterized in that, The target ratio range is 41% to 44.1% by volume of natural soybean esters and 55.9% to 59% by volume of palm fatty acid esters.

11. A mixed ester insulating oil for power transformers obtained by the prediction method for the optimal proportion of mixed ester insulating oil for power transformers according to claim 10, characterized in that, Within the obtained volume fraction range of soybean natural esters and palm fatty acid esters, all feasible ratio points selected in the model are input into the comprehensive expectation function according to their weights. The results are sorted according to the output value D(x). The result shows that when the volume fraction ratio of soybean natural esters to palm fatty acid esters is 41:59, the D(x) value is the highest. Therefore, the preferred volume fraction ratio of soybean natural esters to palm fatty acid esters is 41:59.

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