Performance Assessment of Oil-Immersed Cellulose Insulator Materials Using Time–Domain Spectroscopy under Varying Temperature and Humidity Conditions
Abstract
:1. Introduction
2. The Theoretical Analysis of Power Series
3. The Preparation and Testing Process of Oil-Immersed Cellulose Pressboards
4. The Novel Method for Calculating the PTC Data at Various Temperatures
4.1. The Feature Parameters Extraction on the PTC Data Based on the Power Series Theory
4.2. Research on Temperature Conversion Method.
5. Verification Experiments in the Laboratory
6. Conclusions
- A functional model based on the power series theory is applied to fitting the PTC curve of oil-immersed cellulose pressboards. A sixth-order power function model is used by including the proper fitting accuracy and overfitting prophylactic measure. The average value of goodness-of-fit measure exceeding 0.99, which indicates that the sixth-order power series model can be used to describe the PTC curve accurately;
- The coefficient θj (i = 0, 1, ..., 6) used in the sixth power series model is related to both the moisture inside the oil-immersed cellulose and the test temperature. The mathematical model among the normalized parameters (τj) of coefficient θj, the moisture inside the oil-immersed cellulose and the test temperature can be established by depth fitting technique;
- Relying on the computed parameters τj(mc%, T) and θj-tes by using the mentioned mathematical model and Equation (14), the PTC curve at any temperature can be calculated by the sixth-order power series model and the conversion of PTC curve between different temperatures is thus realized;
- Findings reveal that the obtained relative error of the temperature correction is less than 20%, which proves the feasibility of the proposed method. In particular, the proposed model outperforms the “master curve” technique which does not take into account the effects of moisture content;
- This work provides a novel method to correct the temperature effect on the PTC data, which is expected to promote the evaluation of aging or wetness of transformer cellulose insulating material.
Author Contributions
Funding
Conflicts of Interest
References
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Cellulous Pressboard | Insulating Oil | ||
---|---|---|---|
Brand | T4 pressboard | Brand | Karamay no. 25 mineral oil |
Thickness | 0.5 mm | tan δ | 4 × 10−4 |
Density | 0.96 g/cm3 | Pour point | ≤−45 °C |
TS | MD: 98 MPa, CMD: 47 MPa | Flash point | 135 °C |
j | 4 | 5 | 6 | 7 |
---|---|---|---|---|
Average R2 | 0.9752 | 0.9836 | 0.9950 | 0.9990 |
Coefficient | 45 °C | 60 °C | 75 °C | 90 °C |
---|---|---|---|---|
θ0 | 1.816 × 10−9 | 3.926 × 10−9 | 7.323 × 10−9 | 3.941 × 10−8 |
θ1 | −6.088 × 10−8 | −1.905 × 10−7 | −2.985 × 10−7 | −9.346 × 10−7 |
θ2 | 2.098 × 10−7 | 6.798 × 10−7 | 1.059 × 10−6 | 3.101 × 10−6 |
θ3 | −2.421 × 10−7 | −8.632 × 10−7 | −1.316 × 10−6 | −3.626 × 10−6 |
θ4 | 1.315 × 10−7 | 4.842 × 10−7 | 7.305 × 10−7 | 1.944 × 10−6 |
θ5 | −3.350 × 10−8 | −1.197 × 10−7 | −1.823 × 10−7 | −4.907 × 10−7 |
θ6 | 3.402 × 10−9 | 1.133 × 10−8 | 1.801 × 10−8 | 5.011 × 10−8 |
Normalized Parameter | mc% = 1.13% | Normalized Parameter | mc% = 1.94% | ||||||
---|---|---|---|---|---|---|---|---|---|
45 | 60 | 75 | 90 | 45 | 60 | 75 | 90 | ||
τ0(1.13, T) | 1.00 | 2.16 | 4.03 | 21.71 | τ0(1.94, T) | 1.00 | 4.01 | 9.04 | 23.48 |
τ1(1.13, T) | 1.00 | 3.13 | 4.90 | 15.35 | τ1(1.94, T) | 1.00 | 3.93 | 5.43 | 16.60 |
τ2(1.13, T) | 1.00 | 3.24 | 5.05 | 14.78 | τ2(1.94, T) | 1.00 | 3.71 | 6.25 | 17.11 |
τ3(1.13, T) | 1.00 | 3.57 | 5.44 | 14.98 | τ3(1.94, T) | 1.00 | 3.75 | 6.44 | 17.58 |
τ4(1.13, T) | 1.00 | 3.68 | 5.56 | 14.78 | τ4(1.94, T) | 1.00 | 3.80 | 6.55 | 17.75 |
τ5(1.13, T) | 1.00 | 3.57 | 5.44 | 14.65 | τ5(1.94, T) | 1.00 | 3.72 | 6.69 | 17.53 |
τ6(1.13, T) | 1.00 | 3.33 | 5.29 | 14.73 | τ6(1.94, T) | 1.00 | 3.88 | 6.93 | 17.01 |
Normalized Parameter | mc% = 2.28% | Normalized Parameter | mc% = 3.36% | ||||||
---|---|---|---|---|---|---|---|---|---|
45 | 60 | 75 | 90 | 45 | 60 | 75 | 90 | ||
τ0(2.28, T) | 1.00 | 8.50 | 12.817 | 25.07 | τ0(3.36, T) | 1.00 | 7.65 | 16.09 | 30.94 |
τ1(2.28, T) | 1.00 | 5.11 | 9.28 | 21.46 | τ1(3.36, T) | 1.00 | 5.65 | 11.82 | 25.79 |
τ2(2.28, T) | 1.00 | 4.63 | 8.74 | 21.54 | τ2(3.36, T) | 1.00 | 4.97 | 11.88 | 34.70 |
τ3(2.28, T) | 1.00 | 4.32 | 8.60 | 21.72 | τ3(3.36, T) | 1.00 | 4.75 | 11.94 | 31.89 |
τ4(2.28, T) | 1.00 | 4.06 | 8.47 | 21.71 | τ4(3.36, T) | 1.00 | 4.67 | 12.13 | 30.65 |
τ5(2.28, T) | 1.00 | 4.05 | 8.35 | 21.55 | τ5(3.36, T) | 1.00 | 4.79 | 12.52 | 31.69 |
τ6(2.28, T) | 1.00 | 4.30 | 8.47 | 21.56 | τ6(3.36, T) | 1.00 | 4.95 | 12.75 | 30.73 |
τ0(mc%, T) = (Z0 + Z1 × x + Z2 × y + Z3 × y2 + Z4 × x × y)/(1 + Z5 × x + Z6 × y + Z7 × x2 + Z8 × y2 + Z9 × x × y) | |||||
Z0 | −27.913 | Z4 | −9.697 | Z8 | 0.023 |
Z1 | 439.417 | Z5 | 11.631 | Z9 | −0.461 |
Z2 | −6.778 | Z6 | −1.769 | Precision | 10−15 |
Z3 | 0.143 | Z7 | 3.443 | R-square | 0.981 |
τ1(mc%, T) = (Z0 + Z1 × x + Z2 × y + Z3 × y2 + Z4 × x × y)/(1 + Z5 × x + Z6 × y + Z7 × x2 + Z8 × y2 + Z9 × x × y) | |||||
Z0 | 106.976 | Z4 | −2.179 | Z8 | 0.010 |
Z1 | 102.418 | Z5 | −0.412 | Z9 | −0.097 |
Z2 | −5.820 | Z6 | −0.822 | Precision | 10−15 |
Z3 | 0.062 | Z7 | 1.306 | R-square | 0.986 |
τ2(mc%, T) = (Z0 + Z1 × x + Z2 × y + Z3 × y2 + Z4 × x × y)/(1 + Z5 × x + Z6 × y + Z7 × x2 + Z8 × y2 + Z9 × x × y) | |||||
Z0 | 300.999 | Z4 | −4.186 | Z8 | 0.015 |
Z1 | 186.128 | Z5 | −26.097 | Z9 | 0.022 |
Z2 | −13.769 | Z6 | −1.166 | Precision | 10−15 |
Z3 | 0.134 | Z7 | 4.419 | R-square | 0.998 |
τ3(mc%, T) = (Z0 + Z1 × x + Z2 × y + Z3 × y2 + Z4 × x × y)/(1 + Z5 × x + Z6 × y + Z7 × x2 + Z8 × y2 + Z9 × x × y) | |||||
Z0 | 63.104 | Z4 | −2.233 | Z8 | 0.007 |
Z1 | 102.893 | Z5 | −12.176 | Z9 | 0.022 |
Z2 | −3.988 | Z6 | −0.577 | Precision | 10−15 |
Z3 | 0.042 | Z7 | 1.791 | R-square | 0.996 |
τ4(mc%, T) = (Z0 + Z1 × x + Z2 × y + Z3 × y2 + Z4 × x × y)/(1 + Z5 × x + Z6 × y + Z7 × x2 + Z8 × y2 + Z9 × x × y) | |||||
Z0 | 1.707 | Z4 | −1.121 × 105 | Z8 | −1.796 × 107 |
Z1 | 1.531 × 108 | Z5 | 4.741 × 108 | Z9 | 9.063 × 104 |
Z2 | −9.448 × 108 | Z6 | 3.469 × 107 | Precision | 10−15 |
Z3 | 1.735 × 107 | Z7 | −2.017 × 108 | R-square | 0.994 |
τ5(mc%, T) = (Z0+ Z1 × x + Z2 × y + Z3 × y2 + Z4 × y3)/(1 + Z5 × x + Z6 × x2 + Z7 × x3 + Z8 × y + Z9 × y2) | |||||
Z0 | 1729.159 | Z4 | −0.011 | Z8 | −0.642 |
Z1 | 13.202 | Z5 | −17.428 | Z9 | 0.002 |
Z2 | −94.237 | Z6 | 13.771 | Precision | 10−15 |
Z3 | 1.690 | Z7 | −2.067 | R-square | 0.991 |
τ6(mc%, T) = (Z0 + Z1 × x + Z2 × y + Z3 × y2 + Z4 × x × y)/(1 + Z5 × x + Z6 × y + Z7 × x2 + Z8 × y2 + Z9 × x × y) | |||||
Z0 | 8.690 × 109 | Z4 | −5.492 × 108 | Z8 | 1.190 × 106 |
Z1 | 2.465 × 1010 | Z5 | −3.370 × 109 | Z9 | 6.167 × 106 |
Z2 | −7.284 × 108 | Z6 | −8.614 × 107 | Precision | 10−15 |
Z3 | 9.238 × 106 | Z7 | 4.837 × 108 | R-square | 0.996 |
τ0(mc%, T) | mc% = 1.51% | ||
---|---|---|---|
60 °C | 75 °C | 90 °C | |
τ0(1.51, T) | 3.58 | 6.08 | 20.65 |
τ1(1.51, T) | 3.32 | 5.53 | 15.94 |
τ2(1.51, T) | 3.32 | 5.85 | 15.04 |
τ3(1.51, T) | 3.08 | 6.21 | 15.54 |
τ4(1.51, T) | 3.36 | 6.26 | 15.81 |
τ5(1.51, T) | 2.86 | 6.35 | 15.57 |
τ6(1.51, T) | 3.31 | 6.20 | 15.37 |
RMSE | 60 °C | 75 °C | 90 °C |
---|---|---|---|
PTC | 0.32 | 0.37 | 0.31 |
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Lai, B.; Yang, S.; Zhang, H.; Zhang, Y.; Fan, X.; Liu, J. Performance Assessment of Oil-Immersed Cellulose Insulator Materials Using Time–Domain Spectroscopy under Varying Temperature and Humidity Conditions. Energies 2020, 13, 4426. https://doi.org/10.3390/en13174426
Lai B, Yang S, Zhang H, Zhang Y, Fan X, Liu J. Performance Assessment of Oil-Immersed Cellulose Insulator Materials Using Time–Domain Spectroscopy under Varying Temperature and Humidity Conditions. Energies. 2020; 13(17):4426. https://doi.org/10.3390/en13174426
Chicago/Turabian StyleLai, Benhui, Shichang Yang, Heng Zhang, Yiyi Zhang, Xianhao Fan, and Jiefeng Liu. 2020. "Performance Assessment of Oil-Immersed Cellulose Insulator Materials Using Time–Domain Spectroscopy under Varying Temperature and Humidity Conditions" Energies 13, no. 17: 4426. https://doi.org/10.3390/en13174426