# UV-Vis Spectroscopy: A New Approach for Assessing the Color Index of Transformer Insulating Oil

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Sampling and Sample Design

#### 2.2. Optical Measurement Setup

_{10}(S

_{λ}− B

_{λ}/ R

_{λ}− B

_{λ}) = ε

_{λ}• c • l,

_{λ}is the transmittance of light passing through the sample in sampling slot, R

_{λ}is the transmittance of light passing through the sample in reference slot, B

_{λ}is the baseline, ε

_{λ}is the absorbance coefficient of the absorbing sample at a certain wavelength, c is the concentration of the absorbing sample, and l is the path-length traversed by the light.

#### 2.3. Initial Results and Modification

_{λ}to R

_{λ}is extremely low, Abs will be extremely high, resulting in noises due to the fluctuation of S

_{λ}. In order to increase the ratio of S

_{λ}to R

_{λ}, S

_{λ}has to be increased or R

_{λ}has to be decreased. S

_{λ}cannot be increased further as the brightness of the light source in the spectrometer affects both sample and reference sides. Therefore, R

_{λ}needs to be decreased to remove the noises. To reduce R

_{λ}, a neutral density (ND) filter (model: FNDU-20C02-0.1), which provides significant optical attenuation (Transmittance = 1%–3%) in the UV-Vis region, was applied at the reference slot of the spectrometer. The noises can also be reduced by decreasing l, which means a shorter path-length cuvette is used. However this method reduces the interaction of light with the oil samples, thus reducing the sensitivity of the measurement. Due to the shortcomings of a shorter path-length, the ND filter was chosen to reduce the measurement noise. The outcome is shown in Figure 2, where the noises at the peaks (top) of absorbance spectral response of the same four oil samples in Figure 1, are eliminated and clear smooth optical absorbance spectrum can be observed.

## 3. Final Results and Data Analysis

#### 3.1. Absorbance Spectra of Transformer Oil Samples

#### 3.2. Mathematical Modeling

^{2}), adjusted R

^{2}, and standard error of estimate (S) were calculated. R

^{2}provides a descriptive measure of how well the regression line makes the prediction [38] while the adjusted R

^{2}is a modified version of R

^{2}that has been adjusted for the number of predictors in the model [40]. The range of both R

^{2}and adjusted R

^{2}are between 0 and 1, where 0 indicates that the measured data is far from the regression line while 1 indicates that all measured data is on the regression line. S measures the average distance that the measured data fall from the regression line. A smaller S value generally indicates that the data are closer to the regression line. Table 2 shows the analysis results of the three regression methods used.

^{2}and adjusted R

^{2}, and the lowest S value compared to linear and paraboloid regressions. Therefore, Gaussian regression was chosen for the mathematical model. Figure 5 shows a 3-dimentional plot of CW vs. CI vs. Abs of the transformer oil with the Gaussian regression plane.

^{2}value of 0.9412, adjusted R

^{2}value of 0.9412, and S value of 55.8578. The mathematical model that describes the relationship between the Area and CI of transformer oil is as Equation (3).

#### 3.3. Verification of Mathematical Modeling

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Initial optical absorbance spectrums of four oil samples with different color indices (CI) based on ASTM D 1500.

**Figure 2.**Optical absorbance spectrums of four oil samples with different CI based on ASTM D 1500 after applying ND filter.

**Figure 4.**(

**a**) CW verses CI of transformer oil samples at Abs = 0.5; 1.0 and 1.5, (

**b**) Area verses CI of transformer oil samples.

**Figure 5.**Graph of CW vs. CI of transformer oil samples vs. Abs (Red Circles with black borders) with Gaussian regression (White plane).

**Figure 7.**Plot of average absolute difference and maximum absolute difference at different Abs value.

**Table 1.**Guideline for interpretation of strength of relationship for absolute values of correlation.

Absolute Value of r, |r| | Strength of Relationship |
---|---|

0–0.19 | Very Weak |

0.20–0.39 | Weak |

0.40–0.59 | Moderate |

0.60–0.79 | Strong |

0.80–1.00 | Very Strong |

Regression Method | R^{2} | Adjusted R^{2} | S |
---|---|---|---|

Linear | 0.9563 | 0.9553 | 0.3670 |

Paraboloid | 0.9651 | 0.9635 | 0.3317 |

Gaussian | 0.9802 | 0.9793 | 0.2499 |

Sample | Measured CI ^{1} | Measured Cutoff Wavelength (nm) | Calculated CI ^{2} | Difference in CI ^{3} | Standard Deviation | Standard Error |
---|---|---|---|---|---|---|

S1 | 0.5 | 352 | 0.7 | 0.2 | 0.0733 | 0.033 |

S2 | 0.5 | 357 | 0.8 | 0.3 | ||

S3 | 0.5 | 346 | 0.6 | 0.1 | ||

S4 | 0.5 | 361 | 0.8 | 0.3 | ||

S5 | 0.5 | 345 | 0.6 | 0.1 | ||

S6 | 1.0 | 371 | 0.9 | −0.1 | 0.1174 | 0.053 |

S7 | 1.0 | 370 | 0.9 | −0.1 | ||

S8 | 1.0 | 379 | 1.0 | 0.0 | ||

S9 | 1.0 | 385 | 1.1 | 0.1 | ||

S10 | 1.0 | 389 | 1.2 | 0.2 | ||

S11 | 1.5 | 427 | 1.9 | 0.4 | 0.2238 | 0.100 |

S12 | 1.5 | 409 | 1.5 | 0.0 | ||

S13 | 1.5 | 402 | 1.4 | −0.1 | ||

S14 | 1.5 | 425 | 1.9 | 0.4 | ||

S15 | 1.5 | 425 | 1.9 | 0.4 | ||

S16 | 2.0 | 447 | 2.4 | 0.4 | 0.1839 | 0.082 |

S17 | 2.0 | 447 | 2.4 | 0.4 | ||

S18 | 2.0 | 440 | 2.2 | 0.2 | ||

S19 | 2.0 | 440 | 2.2 | 0.2 | ||

S20 | 2.0 | 428 | 1.9 | −0.1 | ||

S21 | 2.5 | 451 | 2.5 | 0.0 | 0.0777 | 0.035 |

S22 | 2.5 | 458 | 2.7 | 0.2 | ||

S23 | 2.5 | 456 | 2.6 | 0.1 | ||

S24 | 2.5 | 453 | 2.5 | 0.0 | ||

S25 | 2.5 | 452 | 2.5 | 0.0 | ||

S26 | 3.0 | 467 | 2.9 | −0.1 | 0.1723 | 0.077 |

S27 | 3.0 | 477 | 3.2 | 0.2 | ||

S28 | 3.0 | 477 | 3.2 | 0.2 | ||

S29 | 3.0 | 471 | 3.0 | 0.0 | ||

S30 | 3.0 | 464 | 2.8 | −0.2 | ||

S31 | 3.5 | 487 | 3.5 | 0.0 | - | - |

S32 | 3.5 | 495 | 3.8 | 0.3 | - | - |

S33 | 4.0 | 504 | 4.1 | 0.1 | - | - |

S34 | 4.0 | 495 | 3.8 | −0.2 | - | - |

S35 | 4.5 | 511 | 4.3 | −0.2 | - | - |

S36 | 4.5 | 513 | 4.4 | −0.1 | - | - |

S37 | 5.0 | 523 | 4.8 | −0.2 | - | - |

S38 | 5.5 | 538 | 5.3 | −0.2 | - | - |

S39 | 5.5 | 536 | 5.2 | −0.3 | - | - |

S40 | 6.5 | 568 | 6.4 | −0.1 | - | - |

S41 | 7.0 | 582 | 7.0 | 0.0 | - | - |

S42 | 7.5 | 592 | 7.3 | −0.2 | - | - |

^{1}Color index based on measurement in accordance of ASTM D 1500,

^{2}Color index calculated based on Equation (2),

^{3}Difference in CI = Calculated CI – Measured CI.

Sample | Measured CI ^{1} | Area^{2} | Calculated CI ^{3} | Difference in CI ^{4} | Standard Deviation | Standard Error |
---|---|---|---|---|---|---|

S1 | 0.5 | 11.7707 | 0.1 | −0.4 | 0.0480 | 0.021 |

S2 | 0.5 | 11.3844 | 0.1 | −0.4 | ||

S3 | 0.5 | 4.0164 | 0.0 | −0.5 | ||

S4 | 0.5 | 16.6769 | 0.2 | −0.3 | ||

S5 | 0.5 | 4.6769 | 0.0 | −0.5 | ||

S6 | 1.0 | 48.885 | 0.4 | −0.6 | 0.0872 | 0.039 |

S7 | 1.0 | 37.4572 | 0.3 | −0.7 | ||

S8 | 1.0 | 46.276 | 0.4 | −0.6 | ||

S9 | 1.0 | 56.0387 | 0.5 | −0.5 | ||

S10 | 1.0 | 62.8738 | 0.6 | −0.4 | ||

S11 | 1.5 | 148.5237 | 1.3 | −0.2 | 0.2465 | 0.110 |

S12 | 1.5 | 103.449 | 0.9 | −0.6 | ||

S13 | 1.5 | 83.9942 | 0.8 | −0.7 | ||

S14 | 1.5 | 138.809 | 1.3 | −0.2 | ||

S15 | 1.5 | 136.7029 | 1.2 | −0.3 | ||

S16 | 2.0 | 236.6137 | 2.1 | 0.1 | 0.3090 | 0.138 |

S17 | 2.0 | 236.3961 | 2.1 | 0.1 | ||

S18 | 2.0 | 198.7913 | 1.8 | −0.2 | ||

S19 | 2.0 | 209.3838 | 1.9 | −0.1 | ||

S20 | 2.0 | 153.3042 | 1.4 | −0.6 | ||

S21 | 2.5 | 246.3 | 2.2 | −0.3 | 0.1903 | 0.085 |

S22 | 2.5 | 296.6479 | 2.7 | 0.2 | ||

S23 | 2.5 | 274.906 | 2.5 | 0.0 | ||

S24 | 2.5 | 264.5622 | 2.4 | −0.1 | ||

S25 | 2.5 | 246.69 | 2.2 | −0.3 | ||

S26 | 3.0 | 503.8327 | 4.5 | 1.5 | 0.6625 | 0.296 |

S27 | 3.0 | 355.9228 | 3.2 | 0.2 | ||

S28 | 3.0 | 374.7372 | 3.4 | 0.4 | ||

S29 | 3.0 | 343.9266 | 3.1 | 0.1 | ||

S30 | 3.0 | 313.9438 | 2.8 | −0.2 | ||

S31 | 3.5 | 435.9306 | 3.9 | 0.4 | - | - |

S32 | 3.5 | 580.9014 | 5.2 | 1.7 | - | - |

S33 | 4.0 | 538.9002 | 4.9 | 0.9 | - | - |

S34 | 4.0 | 430.8067 | 3.9 | −0.1 | - | - |

S35 | 4.5 | 547.1639 | 4.9 | 0.4 | - | - |

S36 | 4.5 | 345.1915 | 3.1 | −1.4 | - | - |

S37 | 5.0 | 572.1769 | 5.2 | 0.2 | - | - |

S38 | 5.5 | 805.9143 | 7.3 | 1.8 | - | - |

S39 | 5.5 | 624.9499 | 5.6 | 0.1 | - | - |

S40 | 6.5 | 743.9695 | 6.7 | 0.2 | - | - |

S41 | 7.0 | 821.1863 | 7.4 | 0.4 | - | - |

S42 | 7.5 | 901.6618 | 8.1 | 0.6 | - | - |

^{1}Color index based on measurement in accordance of ASTM D 1500,

^{2}Integration of area under the graph from 360 nm to 600 nm,

^{3}Color index calculated based on Equation (3),

^{4}Difference in CI = Calculated CI – Measured CI.

**Table 5.**Maximum absolute difference, average absolute difference, and RMSE value for verification data.

Abs | Maximum Absolute Difference | Average Absolute Difference | RMSE | |
---|---|---|---|---|

For Equation (2) | 0.25 | 0.8 | 0.3413 | 0.3972 |

0.50 | 0.6 | 0.1752 | 0.2235 | |

0.75 | 0.4 | 0.1632 | 0.1961 | |

1.00 | 0.4 | 0.1798 | 0.2144 | |

1.25 | 0.6 | 0.2247 | 0.2747 | |

1.50 | 0.8 | 0.2350 | 0.2981 | |

1.75 | 0.9 | 0.2493 | 0.3163 | |

2.00 | 0.9 | 0.2574 | 0.3249 | |

For Equation (3) | - | 1.8 | 0.4647 | 0.6274 |

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## Share and Cite

**MDPI and ACS Style**

Leong, Y.S.; Ker, P.J.; Jamaludin, M.Z.; M. Nomanbhay, S.; Ismail, A.; Abdullah, F.; Looe, H.M.; Lo, C.K.
UV-Vis Spectroscopy: A New Approach for Assessing the Color Index of Transformer Insulating Oil. *Sensors* **2018**, *18*, 2175.
https://doi.org/10.3390/s18072175

**AMA Style**

Leong YS, Ker PJ, Jamaludin MZ, M. Nomanbhay S, Ismail A, Abdullah F, Looe HM, Lo CK.
UV-Vis Spectroscopy: A New Approach for Assessing the Color Index of Transformer Insulating Oil. *Sensors*. 2018; 18(7):2175.
https://doi.org/10.3390/s18072175

**Chicago/Turabian Style**

Leong, Yang Sing, Pin Jern Ker, M. Z. Jamaludin, Saifuddin M. Nomanbhay, Aiman Ismail, Fairuz Abdullah, Hui Mun Looe, and Chin Kim Lo.
2018. "UV-Vis Spectroscopy: A New Approach for Assessing the Color Index of Transformer Insulating Oil" *Sensors* 18, no. 7: 2175.
https://doi.org/10.3390/s18072175