Prediction of the Degree of Polymerization in Transformer Cellulose Insulation Using the Feedforward Backpropagation Artificial Neural Network

Abstract

The life expectancy of power transformers is primarily determined by the integrity of the insulating oil and cellulose paper between the conductor turns, phases and phase to earth. During the course of their in-service lifetime, the solid insulating system of windings is contingent on long-standing ageing and decomposition. The decomposition of the cellulose paper insulation is strikingly grievous, as it reduces the tensile strength of the cellulose paper and can trigger premature failure. The latter can trigger premature failure, and to realize at which point during the operational life this may occur is a daunting task. Various methods of estimating the DP have been proposed in the literature; however, these methods yield different results, making it difficult to accurately estimate a reliable DP. In this work, a novel approach based on the Feedforward Backpropagation Artificial Neural Network has been proposed to predict the amount of DP in transformer cellulose insulation. Presently, no ANN model has been proposed to predict the remaining DP using 2FAL concentration. A databank comprising 100 data sets—70 for training and 30 for testing—is used to develop the proposed ANN using 2-furaldehyde (2FAL) as an input and DP as an output. The proposed model yields a correlation coefficient of 0.958 for training, 0.915 for validation, 0.996 for testing and an overall correlation of 0.958 for the model.

1. Introduction

The staunch operation of power transformers is essential to safeguard the transmission and distribution of energy in an electrical power network. The optimal operation of these transformers ensures cost-effective and staunch energy distribution [1]. In view of the deregulation of the energy market, utilities are pressed to reduce the energy tariffs and are lumbered with an alternative for operating electrical equipment close to their nameplate rated parameters [2,3]. This overrating and often sporadically short overloading of transformers coerces their health, causing deterioration attributable to electrical and thermal stresses. Therefore, adequate maintenance of the transformer is imperative in monitoring the condition of the unit in service. The designed lifecycle of a power transformer is typically projected to be approximately 25 to 30 years [4,5]. However, there are electrical transformers still in service after 30 years in the grid on account of thorough condition monitoring and the application of remnant lifecycle evaluation techniques [5]. These methods impede unforeseen interruptions and consequently save revenue in a power system. The insulation system of power transformers is comprised of cellulose paper and dielectric oil. The quality of this insulation system characterizes the condition of the respective units during service, as there are a number of variables that may impact the ageing mechanism in a power transformer.

Variables affecting the ageing mechanics of the transformer insulation system are excessive heating, prolonged overloading conditions, oxidation, moisture, distorted harmonic load currents, etc. [6,7]. Moisture, oxygen, temperature and solid impurities are the most notable triggers of the ageing mechanics of the insulation system. Oxidation fast-tracks the decomposition of cellulose paper [7]. The oil submerging the transformer active components degenerates as a result of elevated dissolved gas concentrations including carbon dioxide, hydrogen acetylene, ethane, ethylene and methane. However, the byproducts of the aging mechanism of the cellulose paper are mainly furan compounds (2-Furaldehyde) and carbon dioxide. These gases can be detected by Dissolved Gas Analysis (DGA) [8,9]. In addition, the transformer oil comprises furan compounds (2-Furaldehyde and derivates) which are the main byproducts of cellulose aging and can be ascertained in the laboratory to give insight into the condition of the cellulose paper [10,11,12]. The methods of predicting the cellulose paper remnant lifecycle are reliant on the information collected in the in-service oil samples. Furan compound information (specifically, 2FAL) collected in the dielectric oil furan test has been used to predict the degree of Polymerization (DP) in the cellulose paper by means of models and, also, by a Machine Learning approach [12,13,14,15,16]. In [14], ANN was applied to identify winding deformations on a 1.2 MVA transformer. An accuracy of about 95.4% was reported. The application of ANN has also been pushed in the prediction of hotspot temperature [15] and in the detection of transmission line faults [16].

In this work, an appraisal of the existing DP models has been presented. However, these methods yield different results, making it difficult to accurately estimate a reliable DP for new and in-service transformers. As a result, a novel approach based on the Feedforward Backpropagation Artificial Neural Network has been proposed to predict the amount of DP in transformer cellulose insulation. Presently, no ANN model has been proposed to predict the remaining DP using 2FAL concentration. A databank comprising 100 data sets—70 for training and 30 for testing—is used to develop the proposed ANN using 2-furaldehyde (2FAL) as an input and DP as an output.

2. Materials and Methods

2.1. Furan Formation and Correlation between 2-FAL and DP

The solid insulation scheme of electrical transformers comprises cellulose paper, and, when susceptible to temperature rises exceeding 100 °C as a result of plentiful operational conditions, it will produce by-products of deterioration, and a few cases are dissolvable in oil [17,18,19]. These by-products are a sequel to the ageing mechanics and become dissolved in the transformer oil; hence, the dielectric oil can be assessed by furan concentration. The latter can be fluently monitored during routine site testing and can be employed as ageing indexes. The high-performance liquid chromatography is generally employed as an oil laboratory for preforming the furan analysis test. Recent investigation formulates a theory that the furan compounds that are produced as a result of electrical discharges have adverse effects on the cellulose paper, although in lower amounts [20,21]. Electrical discharges will generally reduce the degree of polymerization of the cellulose paper, resulting in increased levels of furans being released into the dielectric oil. On account of the thermal stresses, Furanic compounds of large concentrations can be produced, as these cellulosic insulating materials are susceptible to a hotspot temperature exceeding 120 °C [19]. The rate at which these Furanic compounds are produced can be characterized as a function of numerous ageing indexes including oxygen and moisture content. The measurement of Furanic compounds is carried out in micrograms per litre (ug/L). While there are several Furanic compounds, a vast majority of them are not stable over time in the dissolvent. Commonly used Furanic compounds that are employed in the symptomatic assessment of cellulose paper insulation are summarized below:

• 2-Furaldehyde (2FAL).
• 5-Methyl-2-Furaldehyde (5M2F).
• 5-Hydroxymethyl-2-Furaldehyde (5H2F).
• 2-Acetyl Furan (2ACF).
• 2-Furfuryl Alcohol (2FOL).

The sources for the production of these Furanic compounds into the dielectric oil are demonstrated in Figure 1.

The constancy of Furanic compounds intrigues the transformer manufacturing industry in view of the fact that they are of service in arriving at conclusions based on the concentration levels present in the dielectric oil. However, inconsistent Furanic compounds may bring about an erroneous conclusion to manufacturers. In practice, the above-mentioned compounds may be holistically useful in predicting the condition of cellulose paper.

From the observational data presented by various researchers, it has been convincingly observed that 2-furaldehyde (2FAL) is the most stable furan compound in assessing the condition of cellulose paper. As a result, it has been adopted by the transformer manufacturing industry as an index that can conclusively predict the DP in cellulose paper. The condition of the transformer cellulose paper based on 2FAL has been demonstrated in Figure 2 using the inhouse empirical data of mineral-based transformers ranging between 1500 kVA and 40 MVA. These units are based on the south African power utility specification.

Recent research [23,24] has established that, by analyzing dielectric oil samples by means of the furan test for 2FAL concentration dissolved into the oil throughout the ageing process, the indirect measurement of the cellulose paper sample can be carried out. During the transformer’s intended operational lifetime, 2FAL compounds are released from the cellulose paper into the oil, and, by analyzing the oil, the DP value can be predicted. The measurement of the 2FAL from the oil can be fairly easy in the laboratory; however, the interpretation is intricate. As mentioned, there are miscellaneous ageing indexes that are involved. Several works [25,26,27] have examined the ageing mechanics of cellulose paper and have established some correlation between 2FAL and the amount of DP present.

The above models have been formulated based on a fleet of power transformers and by collecting the oil samples for laboratory analysis. The models were validated by units that were taken out of service for repair and refurbishment, at which point the actual cellulose paper samples were extracted.

In Equation (1), a DP model proposed by Chendong et al., has been presented [25]. This model was formulated based upon empirical data collected from transformers that are insulated with normal Kraft paper.

$$\mathrm{DP}=\frac{{\log }_{10}2\mathrm{FAL}-1.51}{-0.0035}$$

(1)

In Equation (2), a DP model reported in [26] by Stebbins et al., is presented. This model was established based on empirical data from Kraft paper and by carrying out hermetical ageing experimentations under high thermal conditions.

$$\mathrm{DP}=\frac{2.6-{\log }_{10}2\mathrm{FAL}}{0.0049}$$

(2)

In Equation (3), a DP model proposed by De Pablo et al., in [27] is presented.

This model is an alternative to the conventional Chendong et al., and Vaurchex et al., models. The degradation of a polymer main chain theory was employed in deriving the model.

$$\mathrm{DP}=\frac{1850}{2\mathrm{FAL}+2.3}$$

(3)

A comparison of these models is demonstrated in Figure 3, with the 2FAL concentration ranging from about 0.1 to 7 parts per million (ppm). It can be observed that the prediction of the DP is based solely on the 2FAL concentration.

The main drawback of these models is primarily based on the fact that they are based on a specific type of transformer, viz. the type of cellulose paper insulating the transformer. However, they do have the advantage of using the cellulose paper by-product as opposed to using the hotspot temperature in the oil, which has influenced a multitude of health indexes.

In addition, the DP can be employed to further predict the consumed lifetime at the point at which the oil sample was taken. A model proposed in [28] is expressed as follows in Equation (4).

$${ \mathrm{Life}}_{\mathrm{consumed}}=20.5\times \ln \left(\frac{1100}{\mathrm{DP}}\right)$$

(4)

The above equation is formulated based on one parameter, i.e., the predicted DP of the cellulose paper. The consumed lifetime of the transformer can therefore be calculated.

2.2. Artificial Neural Network

An Artificial Neural Network (ANN) is assembled from a multitude of neurons. These neurons are grouped into a number of layers. Further, the neurons in the respective layers are interconnected to neurons in other layers. The latter do not appeal to the input and output layers but rather to the intermediary layers. The intelligence perceived at the input layer is continued from one layer to another until it reaches the ANN output layer.

The layer that links up the input and output of an ANN is referred to as the hidden layer. ANNs are valuable tools for addressing daunting challenges in the transformer manufacturing industry. Various researchers have employed the ANN technique for predicting many transformer conditions, such as the identification of incipient faults using Dissolved Gas Analysis (DGA) [29,30,31]. Presently, there is no ANN model that has been proposed to predict the remaining DP using 2FAL concentration.

In this work, a databank comprising 100 data sets—70 for training and 30 for testing—is used to develop the proposed ANN using 2-furaldehyde as an input and DP as an output. An ANN has been selected in this work because of its ability to self-learn, model non-linear problems and produce an output not limited to the input fed, which is significant for the problem of cellulose paper for transformer manufacturers. A schematic drawing that will be used to formulate the proposed ANN model for predicting DP is shown in Figure 4.

In this work, the empirical data are ascertained to be significantly divergent from the results of the existing DP models. Subsequently, an ANN-based model is proposed to predict the DP in the paper for new and existing transformers given the 2FAL concentration. The data have been obtained from different mineral-oil-based transformers that range from 1500 kVA to 40 MVA, with a maximum voltage of 132 kV on the HV winding.

2.3. Proposed Artificial Neural Network Model

In this work, the proposed ANN model has been developed in the MATLAB R2018a platform. The multilayer feedforward backpropagation has been selected as the ANN structure in view of the fact that it is the most prevalently accepted structure [32] and that it is relevant to the current research scope. This model is comprised of three-layer networks. The respective network is achieved by means of one input layer for the measured 2FAL concentration, ten hidden layers and one output layer for the DP prediction.

The proposed model will produce the network output target of a new dataset based on the input (2FAL) and the targeted DP output fed to the ANN network. Figure 5 illustrates a comprehensive flowchart employed in developing the proposed ANN model. By and large, the methodology for formulating an ANN model is segmented into the training and testing stage.

2.3.1. ANN Training

In the course of the ANN training stage, the network is furnished with data consisting of the 2FAL concentrations and the transformer DP as the targeted output. The training stage is a critical process in designing the proposed ANN model. Factors that can affect the performance of the ANN network include the network type, training function, adoption learning function, performance function, number of layers and transfer function. Some challenges that may result from this stage include overfitting and underfitting. The problems of overfitting arise when the dataset loaded for training learns too many details in the training dataset, including the noise from the data, which results in the poor performance of the network. Early stopping of the network has been employed as a method for alleviating network overfitting. Nonetheless, in the proposed model, the databank for the training stage has been segmented into the training input, target and testing data.

2.3.2. ANN Testing

During the ANN testing, an unfamiliar dataset is introduced to the network to appraise the performance of the trained network. At this stage, the ANN network is assessed by employing linear regression modelling. The correlation coefficient (R) is calculated to examine the correlation between the ANN network outputs and the targeted output. Ideally, a good network will yield an R close to 1, demonstrating a significant correlation between the ANN network output and the targeted output. The overall performance of the ANN network is based upon the value of R that is ascertained. The most suitable ANN network is selected based on the nearest correlation value to 1.

Figure 6 demonstrates the proposed network performance plot. It can be observed that the proposed network has the capability to generalize well, yielding a correlation coefficient of 0.958 for the training, 0.915 for the validation, 0.996 for the testing and an overall correlation of 0.958 for the model. Separate samples of 10 units were used in the validation of the proposed model.

In the proposed network, 100 databanks, where 70 datasets are intended for the training stage and 30 are aimed at the testing stage, are considered. The algorithmic rules employed in the proposed ANN model are tabulated in

Table 1. ANN algorithm summary.

Sample	2FAL
Data division	Random
Training	Levenberg–Marquardt
Performance	Mean Square Error
Calculations	MEX

.

The Levenberg–Marquardt (LM) training technique was employed on account of it being suggested in the MATLAB platform as the preferred supervised algorithm given that it has the highest degree of training time. The Mean Square Error (MSE) plot of the proposed ANN is demonstrated in Figure 7.

It can be observed that, initially, the network yields a significant MSE, but there is a gradual decrease as the training progresses to eight epochs. The best MSE was ascertained at Epoch 2, as indicated above.

The summary of the training state for the proposed model is demonstrated as follows in Figure 8.

The gradient, which is the square of the error function, can be observed to be 41.32 at Epoch 8. Additionally, the network control parameter denoted as “mu” is observed to be 0.0001 at Epoch 8. This is a good indication that the network has holistically converged. Further, it can be observed that there are six “val fail” validation checks at Epoch 8. This prevents the network from performing poorly while learning.

3. Results

This section presents nine transformer case studies unfamiliar with the proposed ANN model. The DP and, consequently, the consumed life will be predicted, and the proposed ANN model and the existing models will be tested in terms of performance against the practical data.

3.1. Degree of Polymerization

The DP present in the cellulose paper is evaluated in this subsection. For the ANN results, these case studies are fed into the network for prediction. On the existing methods, Equations (1)–(3) are employed. The DP of the considered case studies are tabulated in

Table 2. Transformer case studies: DP.

Sample	2FAL	Measured	ANN	Chendong	Vaurchex	De Pablo
1	1.778	389.2	388.581	360.021	479.606	453.654
2	2.377	352.2	353.234	323.992	453.872	395.553
3	3	321.8	325.068	295.108	433.241	349.057
4	1.601	403.5	401.054	373.031	488.810	474.237
5	0.676	514.8	505.379	480.015	565.317	621.641
6	0.231	640.8	635.306	613.254	660.487	730.936
7	0.143	693.5	676.561	672.761	702.992	757.266
8	1.513	411.6	407.895	380.046	493.910	485.182
9	1.563	410.6	403.961	376.012	491.029	478.902

.

The error margin of the measured DP against the prediction techniques is tabulated in

Table 3. Transformer case studies: Error margin.

Sample	ANN	Chendong	Vaurchex	De Pablo
1	0.16%	7.50%	23.23%	16.56%
2	0.29%	8.01%	28.87%	12.31%
3	1.02%	8.29%	34.63%	8.47%
4	0.61%	7.55%	21.14%	17.53%
5	1.83%	6.76%	9.81%	20.75%
6	0.86%	4.30%	3.07%	14.07%
7	2.44%	2.99%	1.37%	9.19%
8	0.90%	7.67%	20.00%	17.88%
9	1.62%	8.42%	19.59%	16.63%

. It can be observed that the proposed ANN model yields the lowest error margin in comparison to the measured data.

3.2. Consumed Lifetime

Additionally, the corresponding consumed lifetimes of the transformers at the time the oil samples were taken at the site are tabulated as shown in

Table 4. Transformer case studies: Consumed Lifetime.

Sample	Actual	ANN	Chendong	Vaurchex	De Pablo
1	21.299	21.332	22.897	17.017	18.157
2	23.347	23.287	25.058	18.148	20.967
3	25.197	24.990	26.972	19.101	23.531
4	20.559	20.684	22.169	16.627	17.248
5	15.565	15.944	17.000	13.646	11.699
6	11.077	11.254	11.978	10.457	8.379
7	9.457	9.964	10.079	9.178	7.654
8	20.152	20.337	21.787	16.415	16.780
9	20.202	20.536	22.006	16.535	17.047

using Equation (4).

Consequently, the error margin of the actually consumed lifetime against the predicted values by employing the proposed model and the existing methods is tabulated in

Table 5. Transformer case studies: Error margin.

Sample	ANN	Chendong	Vaurchex	De Pablo
1	0.15%	7.50%	20.10%	14.75%
2	0.26%	7.33%	22.27%	10.19%
3	0.82%	7.04%	24.19%	6.61%
4	0.61%	7.83%	19.12%	16.11%
5	2.43%	9.21%	12.33%	24.84%
6	1.59%	8.13%	5.60%	24.36%
7	5.36%	6.58%	2.95%	19.07%
8	0.92%	8.11%	18.55%	16.73%
9	1.65%	8.93%	18.15%	15.61%

.

It can be observed that the proposed technique remains superior in comparison to the existing models.

4. Conclusions

In this work, a model of a multilayer Feedforward Backpropagation Artificial Neural Network is successfully developed to predict the DP of cellulose insulation in a power transformer using the 2FAL concentration measured from oil samples. A well-generalized network is developed by employing a databank that consists of 100 2FAL and DP datasets. The robustness of the developed network is verified by testing the network using unfamiliar data consisting of nine 2FAL samples in the testing stage. As a result, the prediction of the DP of the cellulose paper of a power transformer can be triumphantly carried out by using the proposed Artificial Neural Network. Presently, no ANN model has been proposed to predict the remaining DP using 2FAL concentration. The proposed model yields a correlation coefficient of 0.958 for the training, 0.915 for the validation, 0.996 for the testing and an overall correlation of 0.958 for the model.

The proposed method can be applied to predict the DP in power transformers, as the empirical data have revealed the superiority of the proposed technique.

This work can assist manufacturers in accurately assessing the condition of transformers in comparison to the existing DP models. Future work may involve the development of remnant transformers’ lifetimes by employing a multilayer Feedforward Backpropagation Artificial Neural Network using 2FAL and DP as inputs.