**7. Summary**

Cognitive science research suggests that musicians may possess distinct advantages in divergent thinking tasks. Divergent thinking skill may result from utilizing a particular method of classical guitar study. Thus, anyone who is interested in creativity training and classical guitar study could develop divergent thinking expertise through long-term, focused practice. In this article I have presented conceptual evidence to support my suggestion that classical guitar study may benefit and enhance the creativity and innovative behavior of managers and entrepreneurs. A future research goal is to empirically test this hypothesis.

**Funding:** This research received no external funding.

**Acknowledgments:** The author is grateful to the reviewers and editors for their valuable feedback and helpful suggestions.

**Conflicts of Interest:** The author declares no conflict of interest.

#### **References and Notes**

© 2018 by the author. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

#### *Review* **Creativity in Business Education: A Review of Creative Self-Belief Theories and Arts-Based Methods**

#### **Sogol Homayoun 1 and Danah Henriksen 2,\***

Received: 8 September 2018; Accepted: 13 November 2018; Published: 20 November 2018

**Abstract:** Creativity has become one of the most sought-after skills from graduates across business and industry. It is therefore imperative to infuse creativity training within business programs of study and professional development experiences, to remind people of their eternally curious and creative nature. The objective of this paper is to explore the literature around theories of creative potential and performance—including creative identity, creative mindset, and creative self-efficacy. We consider perspectives that reveal that creativity is a mindset predicated on beliefs and ways of thinking. Educational psychology literature and theories of creative self-belief illustrate how creative identity, mindset, and self-efficacy form the core of an individual's belief system to think, act, and develop creatively in the world. This connects to the potential of arts-based methods as a means to infuse creative learning into business education. We illustrate how our findings can be put into practice by sharing an example of an arts-based intervention that is currently in progress to develop creative capacity among students in an internationally known business program. We conclude with the idea that its incumbent upon business education, professional development, and training to incorporate methodologies that enhance creative capacity by initially eliminating or minimizing self-perceived limitations in people, such as fear, negative personal judgement, and chattering of the mind—and theories of creative self-belief provide a foundation that can undergird arts-based methods toward this goal.

**Keywords:** creativity; business; education; training; professional development; creative thinking; theories; arts; arts-based methods; innovation


**Author details**

Rajesh Kumar Yadav1 \*, Bandana Kumari1 , Pritanjali Singh2 , Asgar Ali1 , Sadhana Sharma1 \* and Krishnan Hajela3

1 Department of Biochemistry, All India Institute of Medical Sciences, Patna, India

2 Department of Radiotherapy, All India Institute of Medical Sciences, Patna, India

3 School of Life Sciences, Devi Ahilya Vishwavidyalaya, Indore, MP, India

\*Address all correspondence to<EMAIL_ADDRESS>and<EMAIL_ADDRESS>
© 2021 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


2.2.1. Boundary-Aware Feature Extraction (BAFF)

The traditional feature extraction is implemented across the entire 2D space without distinguishing direction, i.e., four boundary directions including the *x*-left, *x*-right, *y*-top, and *y*-down. As a result, important boundary-sensitive features are not extracted. Thus, BAFF is arranged to solve this problem so as to ensure the subsequent boundary localization accuracy.

Figure 12 shows the implementation of BAFE. BAFE contains two parallel branches, i.e., *x*-boundary feature extraction and *y*-boundary feature extraction. Here, we take the *x*-boundary feature extraction as an example to introduce details. The same can be reasoned for the *y*-boundary feature extraction. First, we use a convolutional block attention module (CBAM) [61] to better capture direction-specific information of the ROI region. Then, a 1 × 1 conv with a softmax activation is used to normalize the attention map which will be weighted to the raw feature maps by the matrix element-wise multiplication. Afterwards, we sum features along the *y*-direction and use a 1 × 3 asymmetric conv to achieve the features along *x*-direction *Fx*. The above can be described by

$$F\_{\rm x} = \sum\_{y} F\_{\rm CCIM-Block}(y\_{\prime}; \cdot) \* M\_{\rm x}(y\_{\prime}; \cdot) \tag{6}$$

where *Mx* denotes the attention map of the x-boundary. Finally, *Fx* is split into two subsets evenly, i.e., *Fx*−*right* and *Fx*−*lef t*, to represent the features of the right and left boundaries.

**Figure 12.** Implementation of the boundary-aware feature extraction (BAFE) used in BABP-Block.

Figure 13 shows the implementation of CBAM. Let its input be *F*GCIM−Block ∈ R*H*×*W*×*C* where H and W are the height and width of feature maps and *C* is the channel number, then the channel attention is responsible for generating a channel-dimension weight matrix *WCA* ∈ R1×1×*C* to measure the important levels of *C* channels; the space attention is responsible for generating a space-dimension weight matrix *WSA* ∈ R*H*×*W*×1 to measure the important levels of space-elements across the entire *H* × *W* space. They both range from 0 to 1 by a sigmoid activation which can enrich nonlinearity of neural networks for better performance, suggested by [61]. The result of the channel attention is denoted by *FCA* = *F* × *WCA*. The result of the space attention is denoted by *FSA* = *FCA* × *WSA*. It should be noted that here, the space attention is executed following the channel attention. It is also feasible to change their order.

**Figure 13.** Implementation of the convolutional block attention module (CBAM) used in BAFE.

For the channel attention, a max-pooling (MaxPool) is used to capture its local response, and an average-pooling (AvgPool) is used to capture its global response. A multi-layer perceptron (MLP) is used to refine them for better fusion between the local and global responses. Finally, the results are normalized by a sigmoid function to obtain *WCA*. The above is described by

$$\mathcal{W}\_{\complement A} = \sigma\{\text{MLP}[\text{MaxPool}(F)] + \text{MLP}[\text{AvgPool}(F)]\}\tag{7}$$

where *σ* denotes the sigmoid activation defined by 1/(1 + *e*−*x*).

For the space attention, MaxPool and AvgPool are also used. Still, differently, they both operate on the channel dimension to achieve 2D feature maps. Their results are concatenated directly and convolved by a common conv layer, producing the 2D spatial

attention map. Finally, the results are normalized by a sigmoid activation to obtain *WSA*. The above is described by

$$\mathcal{W}\_{SA} = \sigma \{ f\_{\mathcal{T} \times \mathcal{T}}([\text{MaxPool}(F\_{CA}), \text{AvgPool}(F\_{CA})]) \} \tag{8}$$

where *f* 7×7 is a 7 × 7 conv recommended by their original report [61].

### 2.2.2. Boundary Bucketing Coarse Localization (BBCL)

After boundary-sensitive features are achieved by the previous BAFE stage, we follow the bucketing idea [62] to predict the box boundary, referred to as BBCL. The specific implementation scheme is consistent with Wang et al. [59]. This scheme divides the target space into multiple buckets, or called discrete grid cells [60]. This coarse boundary localization is completed by searching for the correct bucket, i.e., the one in which the boundary resides. Figure 14 shows the implementation of BBCL. The candidate regions are divided into 2*k* buckets on both *x*-direction and *y*-direction, with *k* buckets corresponding to each boundary. Here, *k* is equal to 14, because the feature map's size is 14 × 14. From Figure 14, we adopt a fully-connected (FC) layer to serve as a binary classifier to predict whether the boundary is located in or is the closest to the bucket on each side, based on the ship boundary-aware features *Fx*−*right*, *Fx*−*lef t*, *Fy*−*right*, and *Fy*−*lef t*. We achieve the boundary probabilities of four sides, denoted by *sx*−*right*, *sx*−*lef t*, *sy*−*right*, and *sy*−*lef t*. It should be noted that the boundary probabilities of four sides, i.e., *sx*−*right*, *sx*−*lef t*, *sy*−*right*, and *sy*−*lef t* will be utilized for the final boundary-guided classification rescoring, which will be introduced in the next sections. Afterwards, the maximum activation value is then projected into the raw feature maps to achieve the corresponding index value. Finally, the four boundary positions are obtained, i.e., *x*-right, *x*-left, *y*-right, and *y*-left. In this way, the coarse boundary of a ship is predicted successfully.

**Figure 14.** Implementation of the boundary bucketing coarse localization (BBCL) used in BABP-Block.

2.2.3. Boundary Regression Fine Localization (BRFL)

After the coarse boundary of a ship is obtained, we need to finely adjust the box close to the GT box in order to eliminate the boundary effects of buckets, as shown in Figure 15. This process is the same as the traditional bounding box regression scheme. Specifically, we adopt a 4-way FC layer to complete this task, i.e., the center point correction and width-height adjustment. Since this process is operated in the predicted boundary box,

the distance between the initial box and the GT box becomes smaller. Consequently, such a regression task will become more relaxing to deal with the cross-scale effect, because the positioning difficulty is shared by the previous boundary prediction stage.

**Figure 15.** Implementation of the boundary regression fine localization (BRFL) used in BABP-Block.

Up to this point, we have achieved bounding box regression results by the regression branch in Figure 11.

### 2.2.4. Boundary-Guided Classification Rescoring (BGCR)

BBCL offers the localization reliability of the predicted boundary box, that is, the boundary probabilities of four sides *sx*−*right*, *sx*−*lef t*, *sy*−*right*, and *sy*−*lef t* as previously introduced. The idea of rescoring is also shown in FCOS [63] where the final classification score is computed by using the predicted center-ness score and the raw classification score together. And it is a direct intuition that it should be conducive to maintaining the optimum box with both high classification confidence and accurate localization if fully leveraging them. Thus, we arrange a boundary-guided classification rescoring (BGCR) strategy to reach this aim, which is described by

$$\mathbf{s}' = \mathbf{a} \cdot \mathbf{s} + \beta \cdot \frac{1}{4} \left( \mathbf{s}\_{x-right} + \mathbf{s}\_{x-left} + \mathbf{s}\_{y-right} + \mathbf{s}\_{y-left} + \mathbf{s}\_{y-left} \right) \tag{9}$$

where *s* denotes the original confidence score of the classification network (i.e., two FC layers in Figure 11), *s* denotes the final confidence score, *α* denotes the weight coefficient of the original confidence score and *β* denotes the weight coefficient of the localization reliability. In our work, *α* and *β* are both set to 0.5 considering the trade-off between the spatial localization reliability and the classification reliability [64,65]. Here, in terms of the total localization reliability, we directly average the four sides' boundary probabilities, because they seem to be equally important. Finally, the resulting score *s* will be inputted to the non-maximum suppression (NMS) algorithm [48] to remove repeated detections.


**4. Conclusions**

the EGM96 geoid undulations when computing the terrain correction with the TC

In Eq. (4), as previously stated, the orthometric height *H* is derived via the EGM96 geoid undulation and the Bouguer plate is accounted for by using Eq. (1).

Given the three different terrain corrections, by applying Eq. (4), three different

and the normal gravity in a point *Q* of latitude *φQ* on the ellipsoid is given by the

Although this formula has an accuracy of 0.1 mGal (see [16]), it can be used in the context of this relative comparison among different terrain correction compu-

**Table 7** summarizes the statistics of the Bouguer anomalies obtained with the

Comments similar to those given on **Table 3** hold for the Bouguer values in **Table 7**. The Bouguer anomalies obtained by applying the three methods have quite similar statistics. Those computed via TC-GRAVSOFT software have the smallest standard deviation and the highest mean while those obtained with the other two methods have smaller mean and higher standard deviations. If the RMSs are considered, one can see that the Bouguer anomalies based on the flat tesseroid have the smallest value. However, as pointed out before, even the largest difference among

**Δ***gB* **μ [mGal] σ [mGal] RMS [mGal] Min [mGal] Max [mGal]** TC (GRAVSOFT) �137.846 16.131 138.786 �168.873 �90.511 TESSEROID (UNIPOL) �137.074 16.205 138.028 �166.337 �90.299 FLAT TESSEROID (FT) �136.894 16.221 137.852 �166.262 �90.069

*∂h* ¼ �0*:*30877 *mGal=m* (14)

2*φQ*

*φQ* � 0*:*0000058 *sin* 2

*mGal* (15)

software of the GRAVSOFT package.

GRS80 normal gravity formula [16]:

three terrain correction methods.

*The statistics of the Bouguer anomalies.*

*γ*ð Þ¼ *Q* 978032*:*7 1 þ 0*:*0053024 *sin* 2

We further assumed that

**Figure 7.**

tation methods.

**Table 7.**

**54**

sets of Bouguer anomalies have been derived.

*The DTM (AREA\_2) and the points for TC computation.*

*Geodetic Sciences - Theory, Applications and Recent Developments*

*∂γ*

Three different methods for terrain correction have been compared in two areas over the Alps. The standard computation given by the TC-GRAVSOFT program has been compared with the terrain corrections evaluated via spherical tesseroid and flat tesseroid formulas. In the first test, the SRTM DTM was clipped in a 1° 1° window and *TC* effect was computed in a set of gridded points in the same area. In the second test, observed gravity values in a 1° 1° area have been used in the computation of Bouguer anomalies considering the 3° 3° SRTM DTM values centered on the area containing the gravity data. Despite the fact that the topography in the two selected DTM windows is quite rough, no significant differences among the methods have been revealed. The statistics of the values obtained by modeling in different ways the shape of the discretized topography elements are practically equivalent. Differences among *TC* effects and Bouguer anomalies computed with parallelepiped, spherical tesseroid and flat tesseroid amount to maximum values that are around 1 and 3 mGal respectively. As a matter of fact, there are other error sources (e.g., density heterogeneities, DTM and gravity point heights mismatch) that can have impacts on the terrain correction computation larger than 3 mGal. However, if in the second test on Bouguer computation we consider the values *per se*, spherical tesseroid and flat tesseroid models perform slightly better when RMS values are compared, i.e. the spherical tesseroid and flat tesseroid based Bouguer anomalies are smoother.

Finally, we remark that the concept applied in the flat tesseroid modeling can be adapted to the terrain effect computation when shaping the topography according to the Triangulated Irregular Network model [17]. In this way, a more detailed terrain effect evaluation will be possible, particularly in the neighbor of the computational points, by better modeling the terrain slopes.


**1. Introduction**

In today's rapidly evolving business landscape, organizations confront unprecedented challenges driven by the volatile, uncertain, complex, and ambiguous (VUCA) nature of the world [1]. These challenges necessitate a fundamental reevaluation of conventional approaches to strategy implementation and performance

management [2]. Within this context, the roles played by employee behavior and organizational culture have emerged as pivotal factors that can significantly influence an organization's success in navigating the complexities of a VUCA world [3].

The primary objective of this chapter is to delve into the intricate relationship between employee behavior, organizational culture, strategy implementation, and performance within the VUCA framework. It seeks to provide a comprehensive understanding of how these interconnected elements influence one another and, in turn, shape an organization's ability to thrive in an environment characterized by volatility, uncertainty, complexity, and ambiguity.

The contemporary business landscape is characterized by unprecedented levels of volatility, uncertainty, complexity, and ambiguity (VUCA) [4, 5]. Rapid technological advancements, shifting consumer preferences, global economic fluctuations, and political uncertainties create a challenging environment for organizations across industries [2]. In this dynamic context, effective strategy implementation becomes paramount for organizations to navigate uncertainties, capitalize on opportunities, and achieve sustainable performance [6, 7].

The success of strategy implementation is contingent upon the behavior of employees and the prevailing organizational culture [8, 9]. Employee behavior plays a pivotal role in translating strategic objectives into actions and outcomes [10, 11]. It encompasses the attitudes, actions, and decisions made by individuals at all levels of the organization [12, 13]. Similarly, organizational culture, defined as the shared values, beliefs, and norms that guide behavior within an organization [14, 15], influences the collective mindset, behaviors, and actions of employees during strategy execution [16, 17].

Understanding the interplay between employee behavior, organizational culture, and strategy implementation is essential for organizations to effectively navigate the VUCA world. By aligning employee behavior with strategic objectives and fostering a culture that supports strategy execution, organizations can enhance their ability to adapt, innovate, and achieve superior performance outcomes [18].

While prior research has examined the individual effects of employee behavior and organizational culture on strategy implementation, there is a need for a comprehensive conceptual framework that integrates these two critical factors [19]. This conceptual paper aims to fill this gap by synthesizing recent literature and theoretical frameworks to develop a holistic understanding of the role of employee behavior and organizational culture in strategy implementation and performance in the VUCA world.

The paper is structured as follows: Firstly, the theories surrounding employee behavior and its impact on strategy implementation will be explored. Social cognitive theory, which emphasizes the role of cognitive processes, self-efficacy, and observational learning in shaping employee behavior [20] will be discussed. Additionally, goal-setting theory will be delved into, which highlights the importance of setting clear and challenging goals, providing feedback, and fostering employee motivation [21]. Furthermore, we will examine self-determination theory, which emphasizes the role of intrinsic motivation, autonomy, competence, and relatedness in driving employee engagement and commitment to strategic initiatives [22].

Secondly, the literature on organizational culture and its influence on strategy execution will be delved into. The Competing Values Framework is explored, which categorizes organizational culture into four types: clan, adhocracy, hierarchy, and market, each with distinct characteristics and implications for strategy implementation [3]. Additionally, organizational socialization theory is discussed, which

## *The Role of Employee Behavior and Organizational Culture in Strategy Implementation… DOI: http://dx.doi.org/10.5772/intechopen.113830*

highlights the role of socialization processes and organizational rituals in shaping employees' beliefs, values, and behaviors [23]. Moreover, Schein's model of organizational culture is explored, which emphasizes the existence of three levels of culture (artifacts, espoused values, and basic underlying assumptions) and their impact on strategy implementation [15].

Next, there will be an integration of these factors to examine their mutual influence and their joint impact on strategy implementation outcomes. Personorganization fit theory will be discussed, which emphasizes the importance of aligning individual values and behaviors with the organizational culture to enhance strategy execution [24]. Furthermore, cultural congruence theory is explored, highlighting how a strong alignment between employee behavior, organizational culture, and strategic goals leads to improved performance [25]. Additionally, social exchange theory is examined, which explores the reciprocal relationship between employees and the organization, emphasizing the role of trust, reciprocity, and commitment in fostering desired behaviors during strategy implementation [26].

Recognizing the challenges organizations face in a VUCA world, strategies to overcome them will be discussed. Sensemaking theory is explored, emphasizing the role of employee behavior and organizational culture in making sense of ambiguity and complexity during strategy implementation [27]. Additionally, discussing change management theories, including Lewin's change model and Kotter's 8-step model, offering frameworks for addressing resistance, fostering employee buy-in, and adapting to dynamic VUCA conditions [28, 29]. Moreover, discussing resilience theory, underscoring the importance of individual and organizational resilience in navigating the uncertainties and disruptions associated with a VUCA world [30].

Lastly, highlighting the importance of measuring and evaluating strategy implementation and performance. The balanced scorecard approach will be discussed, which offers a comprehensive set of metrics and indicators across financial, customer, internal processes, and learning and growth perspectives to assess strategy outcomes [31]. Furthermore, exploring organizational network analysis, a valuable tool for understanding communication patterns, social networks, and the influence of employee behavior and organizational culture on strategy execution [32]. Additionally, considering employee engagement theories and measurement tools, recognizing the impact of engaged employees on strategy implementation success [33].

This paper's relevance and importance are underscored by several key considerations:


**Laboratory Model Studies on the Drying E**ffi**ciency of Transformer Cellulose Insulation Using Synthetic Ester**

### **Piotr Przybylek \* , Hubert Moranda , Hanna Moscicka-Grzesiak and Mateusz Cybulski**

Institute of Electric Power Engineering, Poznan University of Technology, Piotrowo 3A, 61-138 Poznan, Poland<EMAIL_ADDRESS>(H.M<EMAIL_ADDRESS>(H.M.-G<EMAIL_ADDRESS>(M.C.)

**\*** Correspondence<EMAIL_ADDRESS>Tel.: +48-061-665-2018

Received: 25 May 2020; Accepted: 30 June 2020; Published: 4 July 2020

**Abstract:** This paper presents the results of laboratory tests of cellulose insulation drying with the use of synthetic ester. The effectiveness of the drying process was investigated depending on the initial moisture of cellulose samples (2%, 3%, and 4%), ester temperature (55, 70, and 85 ◦C), initial moisture of the ester (70, 140, and 220 ppm), drying time (48, 96, and 168 h), and the weight ratio of cellulosic materials to ester (0.067 and 0.033). A large influence of temperature and time of drying on the efficiency of the drying process was found. This is important information due to the application of the results in the transformers drying procedure. The heating and drying ester unit should provide the highest possible temperature. For the assumed experiment conditions the initial moisture of the ester had little effect on the drying efficiency. An ester with a moisture content below 140 ppm can still be considered as meeting the requirements for drying cellulose with significant moisture. The weight ratio of cellulose products to ester has no major effect on drying efficiency during cellulose drying by circulating dry ester.

**Keywords:** transformer; oil–paper insulation; moisture; drying; synthetic ester

#### **1. Introduction**

The main insulation of the vast majority of power transformers is based on paper/ pressboard-mineral oil system. During the operation of the transformer, its insulation system is constantly aging. High temperature and the presence of an electric field significantly accelerate the aging process.

One of the effects of aging is the increase of moisture content in cellulose insulation. The main cause of the moisture contamination process is the chemical decomposition of cellulose, which is accompanied by water formation. Looseness of the transformer tank plays a smaller role in the insulation moistening process than chemical cellulose degradation. It was found that, with the passage of transformer years of use, the annual increase in cellulose moisture increases [1,2].

Moisture in the transformer's cellulose insulation depends on the transformer's power and operating conditions. Figure 1 shows the water content in cellulose insulation depending on the transformer years of operation. The figure shows data obtained from grid transformers (160, 250, 330, and 500 MVA) and generator transformers, investigated in three countries [3]. The colors on the graph correspond to the moisture classification according to [4]. The figure shows that insulation with water content above 2% should be treated as wet, and above 4% as excessively wet.

**Figure 1.** Dependence of water content in cellulose insulation on transformer age in the whole investigated population divided into three moisture ranges as per IEEE classification, on the basis of data from [3].

One of the dangerous effects of high moisture content in cellulose insulation is the occurrence of the bubble effect phenomenon. It involves the rapid release of water adsorbed on cellulose fibers after exceeding the critical temperature. This leads to an increase in the pressure in the transformer's tank even above its tearing strength, which can result in an explosion and fire [5,6].

#### **2. Drying Methods for Cellulose Insulation**

Drying of transformer insulation is carried out during the production and operation. During the production process, stationary devices in the factory are used. On the other hand, drying of insulation during operation is carried out at the place of the unit installation with the use of a mobile device or in a repair plant—if the general condition of the transformer requires major renovation [7].

The drying methods used so far require heating the insulation and creating a vacuum in the tank. The insulation is heated with hot oil, hot air, or electric current flow. The LFH (low frequency heating) method has the best opinion. In this method, three-phase high voltage winding is supplied and the low voltage winding is shorted. The frequency of the supply voltage is reduced to the lowest possible value at which the transformation effect still occurs. It is usually between 0.4 and 2 Hz [8]. The tank design must allow for the creation of an appropriate vacuum. The method is very effective, but unfortunately very expensive. For a network transformer, the service costs are about € 150,000.

#### **3. Drying Cellulose Insulation Using Synthetic Ester**

The use of an ester as a drying medium is possible due to the huge solubility of water in the ester. Figure 2 shows a comparison of the water saturation limit of three selected liquids used for filling transformers. Such great possibilities of dissolving water in the ester result from the fact that one molecule of the ester is able to attach, on the basis of hydrogen bonds, as many as four molecules of water.

**Figure 2.** Comparison of the water saturation limit of four selected insulating liquids, on the basis of data from [9].

If wet cellulose is surrounded by dry ester, then there is an intensive migration of water from cellulose to the ester until the moisture equilibrium between cellulose and ester is achieved. The closer to equilibrium, the smaller the dynamics of water migration. The dynamics of water migration depend, to varying degrees, on many factors. The main ones are: initial moisture content in cellulose insulation, moisture of the ester, the mass ratio of cellulosic materials to liquid, insulation temperature, and thickness of cellulosic materials [10].

#### **4. Research Results and Discussion**

#### *4.1. Introduction*

In the earlier research, described in publication [11], the effect of cellulose sample thickness on the efficiency and dynamics of their drying with the use of synthetic ester was investigated. During the experiment 0.05, 0.5, 3.0, and 5.0 mm thickness samples were tested.

In this experiment, the drying process of 3 mm thick pressboard samples with three different moisture levels, about 2%, 3%, and 4%, was studied. The effects of drying temperature (55, 70, and 85 ◦C), initial moisture of the ester (70, 140, and 220 ppm) and the mass ratio of cellulose products to synthetic ester (0.067 and 0.033) were studied. These mass ratios are found in grid and distribution transformers.

#### *4.2. Sample Preparation*

Sample preparation was multi-stage. In the first stage the pressboard samples were dried at 85–95 ◦C for 26–29 h in a vacuum of 0.2–0.4 mbar to reduce the water content to less than 0.1%. Then the samples were conditioned in a climatic chamber to achieve the assumed water content. In the third stage, pressboard samples were degassed and impregnated with mineral oil. The air trapped in the samples was rapidly released from the cellulose materials, causing oil bubbling, which stopped after about 15 min from the moment of applying the vacuum. Next, the pressboard samples were placed in the climatic chamber for 144 h for their further impregnation and stabilization. In final stage, the water content (WCPi ) in the samples was measured by Karl Fischer titration (KFT) method [12]. All parameters of sample preparations and sample moisture contents are presented in Table 1. The samples prepared in this way were subjected to a drying process using a synthetic ester.

(\*) temperature fluctuation ≤ 1.3 ◦C; relative humidity fluctuation ≤ 2.5% RH.

Different water content in the synthetic ester was obtained by mixing in an appropriate proportion the dry ester (50 ppm) with the moistened ester (950 ppm). In this way, a synthetic ester with an initial moisture level (WCEi ) of 70, 140, and 220 ppm was prepared.

#### *4.3. Expermental Procedure*

The experimental procedure is presented in Figure 3. At the beginning the cellulose samples of initial water content WCPi impregnated with mineral oil were placed in a glass bottles filled with synthetic ester of water content WCEi . The bottles were placed in a thermal chamber, which kept the drying temperature T constant (Figure 4). The motion of the ester inside the bottles was forced by a magnetic stirrer.

**Figure 3.** Drying procedure; WCE—water content in ester; WCP—water content in pressboard.

The first drying stage lasted 48 h. After this time, the water content in synthetic ester WCEI was measured using the KFT method (Figure 5), and the moistened ester was replaced with a dry one. After a further 48 h of drying, the water content in ester WCEII was measured again and the ester was replaced with dry one. The third and final drying stage ended after 168 h. After this time, the water content in ester WCEIII was measured last time. The final water content in the pressboard (WCPf ) was also measured using the KFT method.

**Figure 4.** Measurement setup used for drying pressboard samples by means of synthetic ester.

**Figure 5.** Instrument for measuring water content by Karl Fischer coulometric titration method.

Based on the measured water content in the synthetic ester (WCEI , WCEII) and the mass of cellulose and the mass of ester it was possible to calculate the water content in pressboard samples after drying time equal to 48 h and 96 h, respectively.

#### *4.4. Investigation Results*

Figure 6 shows the water loss in cellulose during its drying, depending on the initial moisture content of the cellulose. The curves are made for three values of drying temperature (55, 70, and 85 ◦C). The thickness of the samples was 3 mm. Dry synthetic ester (with a moisture content of 50 to 70 ppm) was introduced into the cellulose sample chambers three times. The first portion of the ester was kept in the chamber in the time range of 0–48 h, the second in the time range of 48–96 h, and the third in the range of 96–168 h. It should be noted that the introduction of the ester three times, according to our estimates, gives a similar effect to drying continuously. Under real conditions, continuous drying corresponds to the circulation of the ester between the transformer tank and the ester heating and drying unit. Figure 6a refers to the mass ratio of cellulose to ester 0.033, while Figure 6b to the mass ratio 0.067. A very large influence of temperature on the intensity of the drying process can be seen. The amount of water removed from cellulose in the described conditions is approximately proportional to its initial moisture. The effect of the mass ratio of cellulose to ester on the intensity of the drying process is small.

**Figure 6.** Water loss in samples depending on the initial moisture content of the cellulose at different temperatures; sample thickness 3 mm; initial moisture of the ester 70 ppm; total drying time 168 h—with the three times introduction of the ester; mass ratio of cellulose to ester of 0.033 (**a**) and 0.067 (**b**).

Figure 7 shows the water content of cellulose samples depending on the drying time, with three times the introduction of a dry synthetic ester with an initial moisture content of 70 ppm. The temperature was 85 ◦C. A decrease can be observed in the dynamics of the drying process with the time and reduction of moisture in cellulose.

**Figure 7.** Water content in cellulose samples depending on drying time for three different values of initial moisture of cellulose; mass ratio of cellulose to ester 0.067, samples thickness 3 mm, temperature 85 ◦C; triple introduction of an ester with moisture content of 70 ppm.

When starting the research, it was assumed that the initial moisture content of the ester has a significant impact on the cellulose drying process efficiency. Figure 8 shows the water loss in cellulose samples, in percentage points, depending on the initial moisture content of the ester. The weight ratio of cellulose to ester was 0.067, the thickness of the samples was 3 mm, and the drying time was 168 h, while the temperature was 70 ◦C (Figure 8a) and 85 ◦C (Figure 8b).

**Figure 8.** Water loss in cellulose in percentage points depending on the initial moisture of the three times introduced ester; initial moisture of cellulose 2%, 3%, and 4%, insulation thickness 3 mm, mass ratio of cellulose to ester 0.067, drying time 168 h; temperature 70 ◦C (**a**) and 85 ◦C (**b**).

It is easier to assess the drying efficiency by analyzing the percentage water loss, as shown in Figure 9. For example, a 3% moisture cellulose sample dried for 168 h with a 70 ppm moisture ester at 85 ◦C loses about 40% of water, and if a 220 ppm moisture ester is used, cellulose may lose about 34% of water. The influence of different ester moistures within the tested limits (70–220 ppm) is not significant. This can be explained by using Figure 10, prepared on the basis of CIGRE documents [2]. This figure shows the moisture of the ester in equilibrium state depending on the cellulose moisture. It can be seen that the moisture content of the ester used in the experiment is far from equilibrium state at which the cellulose drying process ends.

**Figure 9.** Percentage water loss in cellulose depending on the initial moisture of the three times introduced ester; initial moisture of cellulose 2%, 3%, and 4%, insulation thickness 3 mm, mass ratio of cellulose to ester 0.067, total drying time 168 h; temperature 70 ◦C (**a**) and 85 ◦C (**b**).

A good illustration of the large impact of temperature on the efficiency of the drying process is Figure 11. However, Figure 12 shows that the effectiveness of this process is slightly dependent on the moisture of the ester. Therefore, when planning the transformer drying procedure, the highest possible temperature should be provided. On the other hand, an ester with a moisture content of even 220 ppm will fulfill its task—under the condition that we ensure its high temperature (at least 85 ◦C).

**Figure 10.** Moisture of the ester in the equilibrium state of the cellulose-ester system depending on the moisture content of cellulose for various temperatures; prepared on the basis of data from [2].

**Figure 11.** Cellulose moisture depending on the drying time for three temperatures (55, 70, and 85 ◦C); sample thickness 3 mm, ester with a moisture content of 70 ppm was introduced three times, the mass ratio of cellulose to ester 0.067.

**Figure 12.** Cellulose moisture depending on the drying time for three initial values of moisture of the ester introduced three times (70, 140, and 220 ppm); sample thickness 3 mm, temperature 85 ◦C, mass ratio of cellulose to ester 0.067.

The experiments are summarized in Figure 13. The moisture content of cellulose at various drying times (48, 96, and 168 h) is shown for the worst drying parameters (220 ppm, 55 ◦C) and the best (70 ppm, 85 ◦C). For initial moisture of cellulose, about 3% and 4%, after the whole drying process (168 h), differences in cellulose moisture are at the level of about 1 percent point. This fact should be taken into account when planning the transformer drying procedure, paying particular attention to ensure high temperature of the drying process.

**Figure 13.** Cellulose moisture in the drying process depending on the drying time—comparison for the worst (pink color: 220 ppm, 55 ◦C) and best (green color: 70 ppm, 85 ◦C) drying process conditions; initial moisture of cellulose ~3% and ~4%, thickness of samples 3 mm, mass ratio of cellulose to ester 0.067.

#### **5. Conclusions**

There are two groups of methods that allow on-site transformer drying. The first group includes methods consisting of heating the insulation by means of oil, air, solvent vapors, or low-frequency current and applying a vacuum [8,13,14]. To sufficiently dry the transformer insulation a vacuum equal to 1 mbar have to be applied [8,15]. The necessity of vacuum application is the biggest disadvantage of these methods. In cases involving many distribution transformers an underpressure of just 500 mbar can be used, due to the low mechanical strength of their tanks. Moreover, the application of the vacuum may result in deimpregnation of cellulose materials, which leads to deterioration of dielectric parameters of insulation.

The second group of methods is based on the use of mineral oil as a drying medium. These methods are much safer for transformers than vacuum ones, while their biggest drawback is their low drying efficiency. The authors of [16] proved the higher drying efficiency when applying natural ester. It should be pointed out that the water solubility in synthetic ester is much higher than in mineral oil and natural ester; therefore, better drying efficiency should be expected for this liquid.

The method proposed by authors, based on the use of synthetic ester for drying cellulose insulation, is free from disadvantages of methods based on applying vacuum and is much more efficient than drying the insulation by means of mineral oil which was proved in our previous research [10].

The drying efficiency of cellulose insulation using a synthetic ester depends, to varying degrees, on cellulose moisture, insulation temperature, drying time, mass ratio of cellulosic materials to ester, and initial water content in ester which was the subject of the research described in this article. The main conclusions from this research are given below.

The initial moisture content in cellulose is very important. At the temperature used in the experiment, equal to 55, 70, and 85 ◦C, there was water loss (in percentage points) during the drying process, approximately proportional to the initial moisture of cellulose.

A very large influence of temperature on the efficiency of the drying process was found. For example, with a mass ratio cellulose to ester of 0.067, increasing the temperature from 55 to

85 ◦C results in at least a two-fold increase in cellulose water loss for all investigated initial moisture values of cellulose (2%, 3%, and 4%).

With the time of drying its dynamics decreases, which is understandable, as the cellulose-ester system approaches the moisture equilibrium state.

The conducted research shows that when drying a transformer using a synthetic ester, special attention should be paid to ensuring the highest possible process temperature, which may be difficult in winter conditions. In such a situation, thermal insulation of the transformer tank should be used.

It was found that the moisture content of the ester from 70–220 ppm—with significant moisture content of the transformer cellulose insulation, equal to 2%, 3%, and 4%—does not have a significant impact on the intensity of the drying process. However, with a relatively low moisture content of insulation, below 2% at low temperature (below 50 ◦C), the effect of moisture on the ester may be noticeable.

In case of low temperature and thick cellulose insulation, the drying time may exceed 168 h due to low water migration within this material. It is related with moisture diffusion coefficients which were described in [17,18].

On the basis of obtained results, the next study related to drying cellulose by means of ester circulating between the transformer tank and a drying unit is planned. The final result of these investigations will be finding a means to achieve optimal drying conditions on the basis of which a mobile system for on-site drying of transformer's insulation will be developed.

**Author Contributions:** Conceptualization and methodology, P.P., H.M.-G., and H.M.; Validation, P.P. and H.M.; Formal analysis, P.P., H.M.-G., and H.M.; Investigation, P.P., H.M., and M.C.; Resources, P.P. and H.M.; Data curation, P.P.; Writing—original draft, H.M. and H.M.-G.; Writing—review and editing, P.P. and H.M.; Visualization, H.M.; Supervision, P.P. and H.M.; Project administration, H.M.; Funding acquisition, H.M. and P.P. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by the Polish National Center for Research and Development from the funds of Subactivity 4.1.2 "Regional research and development agendas" under the project POIR.04.01.02-00-0045/17-00 entitled "Mobile insulation drying system for distribution transformers using a liquid medium"; the total value of the project is PLN 7,677,957, including co-financing from the National Center for Research and Development PLN 6,084,569.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

*Article*

## **Streaming Electrification of Nycodiel 1255 Synthetic Ester and Trafo EN Mineral Oil Mixtures by Using Rotating Disc Method**

### **Maciej Zdanowski**

Faculty of Electrical Engineering, Automatic Control and Informatics, Opole University of Technology, Prószkowska 76, 45-758 Opole, Poland<EMAIL_ADDRESS>
Received: 19 October 2020; Accepted: 21 November 2020; Published: 24 November 2020 -

**Abstract:** Power transformers are the main element of an electric power system. The service life of these devices depends to a large extent on the technical condition of their insulation system. Replacing mineral oils with natural or synthetic ester (retrofilling process) may increase the efficiency and operational safety of transformers, and also limit their adverse environmental impact. It is technically unfeasible to completely remove mineral oil from a transformer. Its small residues form a mixture with fluid ester, with different physicochemical and electric properties. Streaming electrification is one of the phenomena which, under unfavorable conditions, may damage the insulation system of a forced oil cooled transformer. It is necessary to run prophylactic tests for the ECT (electrostatic charging tendency) of insulating liquid mixtures from the point of view of transformer retrofilling, which is being used more often than before. The article presents the results of studies on selected physicochemical, and electrical properties, and the ECT of mixtures of fresh and aged Trafo EN mineral oil with Nycodiel 1255 synthetic ester. In this regard, the density, the kinematic viscosity, the conductivity, and the relative dielectric constant were measured. The molecular diffusion coefficient was determined using Adamczewski's empirical dependency. The streaming electrification was tested in a rotating disc system. The impact of the rotation time, the diameter, and the disc's rotation speed on the amount of the electrification current generated were analyzed. In addition, the co-relation between the electrification current and the composition of the mixture was determined using fresh and aged mineral oil. On the basis of the electrification model, the volume density of the *qw* charge was calculated, which is a parameter defining the ECT of insulating liquids. Based on the results, it was concluded that the synthetic ester is characterized by a higher susceptibility to electrification than the mineral oil. However, combining synthetic ester with a small amount (up to 20%) of fresh or aged mineral oil significantly reduces its ECT, which is beneficial from the point of view of retrofilling power transformers.

**Keywords:** mineral oil; natural ester; synthetic ester; insulation liquid mixtures; power transformers; retrofilling; streaming electrification; ECT; rotating disc system

#### **1. Introduction**

#### *1.1. Research of Insulating Liquids Mixtures*

Power transformers are a key element of the equipment in power plants, transmission systems, electro-power companies, and large industrial plants. Replacing or repairing these devices as a result of breakdowns involves large financial expenditures [1,2]. A transformer's long and reliable operation strictly depends on the technical condition of its insulation system [3–6]. For economic reasons, the vast majority of transformers is filled with mineral oils with well-known properties [7–9]. Due to tighter fire safety and environmental protection regulations, more often than before the power industry is interested in alternative electro-insulating fluids, which include natural, and synthetic esters [10–13]. Liquid esters are used to fill new or modernized transformers. The process of removing mineral oils from transformers to replace them with liquid esters is defined as retrofilling [14–17]. For technical reasons, it is not possible to completely remove mineral oil from the inside of a transformer. Its small amount (4–7%) usually remains in the paper insulation, the windings, the core, and in places hard to reach in a transformer [18]. Replacing mineral oil with liquid ester creates in a transformer a mixture with properties different than each base fluid. It is necessary to test the properties of insulating liquids generated as a result of retrofilling to ensure long, effective, and safe operation of power transformers. In this regard, the physicochemical and electrical properties, ageing processes, the flammability parameters and the thermal properties of insulating liquid mixtures were examined. Fofana at al. [19,20] presented the research results of two insulating liquids mixtures, proposed as alternatives to mineral oil. The first part of the investigation presented a comparison of the mixed liquids properties with those of pure liquids. The second part of the studies, evaluates the compatibility of the mixed liquids with insulating papers used in power transformers. Perrier et al. [21] showed the test results of heat transfer, breakdown voltage, aging stability and electrostatic charging tendency of different mixtures based on the mineral oil, silicon oil and synthetic ester. It was shown that the best mixture enabling optimization of the power transformer insulation is a mixture containing 20% synthetic ester and 80% mineral oil. Rao et al. [22] presented research results of the 80% mineral oil and 20% synthetic ester mixture in the field of thermal aging processes. The main purpose of the work was to lower the cost of transformer insulation liquid having a good thermal performance and improved oxidation stability. The authors observed that the oxidation rate of the blend of mineral oil with synthetic ester is lower than mineral oil. Yu at al. [23] presented the research results of the electrical and physicochemical parameters of dielectric liquid mixtures based on Envirotemp FR3 natural ester and Karamay No. 25 mineral oil. The tests showed that, with an increase of the natural ester concentration in the mixture, the pour point, acidy, dynamic viscosity, and AC breakdown voltage increased. Beroual et al. [24] showed the test results of AC and DC breakdown voltage of different mixtures based on Midel 7131 synthetic ester, Envirotemp FR3 natural ester and mineral oil. The authors confirmed that the increase in the concentration of both types of esters in a mixture with mineral oil always increases the electrical strength. It has been suggested that transformer retrofilling can be considered with mixtures composed of ester oil (80%) and mineral oil (20%). Hamadi et al. [25] presented a study on the electrical and thermal stability of mixtures of Borak 22 mineral oil and Midel 7131 synthetic ester. The authors showed that the use of synthetic ester in a mixture with mineral oil effectively slows down aging processes of insulating liquids. Dombek and Gielniak [26] investigated the effect of the mixture composition of Nynas Draco mineral oil and Midel 7131 synthetic ester with Envirotemp FR3 natural ester on the flash point, fire point, net calorific value, breakdown voltage, relative permittivity, dissipation factor and conductivity. The authors showed that the content of the mixture significantly determines the change of the tested parameters. Nadolny et al. [27,28] presented the research results of thermal properties of Nytro Taurus mineral oil with Envirotemp FR3 natural ester and Midel 7131 synthetic ester mixtures. The authors showed the measurement results of thermal conductivity, viscosity, specific heat, density, and thermal expansion of the created mixtures in a wide temperature range. The authors showed that the increase in the concentration of esters in the mixture with mineral oil deteriorates the transformer cooling.

#### *1.2. Streaming Electrification Measurement Methods*

Another group of issues are ECT tests of the insulating liquids. For this purpose, a number of measurement methods were prepared to evaluate the risk of streaming electrification in the insulation of transformers. Gao et al. [29] have developed a measurement system with a closed insulating liquid circulation, to simulate the oil flow in a transformer. The electrification current was generated in an insulation system model. The current value was changing depending on the flow rate and the temperature of the mineral oil, and also depending on the values of the DC voltage applied. Zdanowski [30] has prepared a flow system that makes it possible to test the streaming electrification depending on the type of the metering pipe material, the flow rate, and the temperature of the insulating fluid. Zmarzły and Fr ˛acz [31,32] created measuring systems with a plate and an oscillating cylinder. In these systems, the electrification current can be measured in relation to the oscillation frequency of the measuring electrode. Ren et al. [33] used a modified mini-static tester to test electrification. In this system, the electrification current was generated as a result of a flowing sample of mineral oil with a volume of 50 mL at a speed of 1.2 m/s through a cellulose filter. Leblanc et al. [34] used a measurement system with a capillary pipe, developed at the PPRIME institute (Poitiers, France). In this case, two electrometers were used, one of which would measure the leakage of electrical charges from the capillary pipe, and the other from a metal vessel placed in a Faraday cage. Zmarzły and K ˛edzia [35] prepared a system with a rotating electrometer, which makes it possible to record 1/f noise generated by the streaming electrification phenomenon. The electrification current signal obtained could be analyzed in the time domain, frequency domain, and in the time-frequency domain. Zdanowski et al. [36] developed a measurement system with a rotating disc to evaluate the ECT in insulating liquids. The electrification current was measured with an electrometer connected to a tank, in which the disc was placed submerged in the insulating liquid. Electrical charges were generated as a result of the disc being put into rotary motion. In the system, it is possible to measure the electrification current in relation to the rotation time, the diameter, and the rotation speed of the disc. For the disc system, an electrification model was developed, which makes it possible to determine the *qw* charge volume density at the interface between the disc and the liquid. This parameter is a material indicator used to evaluate and compare the ECT of insulating liquids. The main advantages of the disc system is its simple design, the ease of balancing the disc dynamically, the small volume of the liquid being tested, and the possibility of measuring the current continuously.

#### *1.3. Purpose and Scope of Research*

This paper is another stage of the author's research works related to the streaming electrification of insulating liquid mixtures. Zdanowski and Maleska [37,38] showed a high correlation between the electrification current and the composition of Trafo EN mineral oil mixtures with Envirotemp FR3 natural ester, Midel 1204 natural ester and Midel 7131 synthetic ester. The electrification current characteristics significantly depended on the type of mineral oil used in the tests (fresh or aged). The minimum and maximum of the electrification current were observed. This time, the subject was to evaluate the ECT of mixtures of Nycodiel 1255 synthetic ester with fresh and aged Trafo EN mineral oil. Their main purpose of the paper was to specify the most beneficial composition of the mixture in terms of retrofilling transformers. The tests were performed in a rotating disc system, designed and built by the author. In the first stage of the study, the impact of the mixture's composition on its density, kinematic viscosity, molecular diffusion coefficient, conductivity, and relative dielectric constant was determined. Then, the impact of the rotation time, the rotation speed, and the disc's diameter on the electrification current generation in the insulating liquid was examined. In the next stage, the impact of the composition of the mixture of synthetic ester with fresh and aged mineral oil on the form of the electrification current was analyzed. Based on the measurements of the physicochemical and electrical properties, and of the electrification current, the volume density of the *qw* charge was determined using the electrification model, which is a parameter defining the ECT of insulating liquids. The key conclusion from the studies is that a small amount (up to 20%) of fresh and aged Trafo EN effectively reduces the electrification of Nycodiel 1255 synthetic ester. The results show that replacing mineral oil with synthetic ester reduces the risk of streaming electrification in the insulation system of transformers. Running diagnostic tests for the streaming electrification phenomenon may help reduce the effects of possible failures, and thus shorten the time and reduce the costs of repairing power transformers.

#### **2. Materials and Methods**

To prepare the insulating liquid mixtures, Trafo EN (MO) mineral oil from Orlen Oil (Krakov, Poland), and Nycodiel 1255 (SE) synthetic ester from Cargil (Paris, France) were used. In order to simulate the ageing processes that take place in the course of a power transformer's operation, the mineral oil was subjected to accelerated thermal ageing according to standard IEC 1125 (Method C: 164 h, 120 C, copper catalyst—1144 cm2 /kg of oil, air—0.15 L/h). The mixtures based on the synthetic ester, and on the fresh and aged mineral oil were prepared at an ambient temperature, and then cured in tightly sealed bottles for a month. The liquids was mixed with the aid of a magnetic stirrer at a speed of 1100 rpm for about 60 min, according to the procedure proposed by Beroual et al. [24]. The mixture's volume was 1000 mL, and its composition was changing by 10%. The fluid's density was determined by means of a universal glass densimeter according to standard ISO 3675. The kinematic viscosity was measured with a Brookfield DV-II + Pro viscometer on the basis of standard ISO 2555. The electrical parameters were determined according to standard IEC 60,247 with the use of a tri-electrode capacitor. The conductivity was determined by measuring the resistivity with an MR0-4c meter. The relative dielectric constant was determined by measuring the electrical capacity with a Hioki 3522-50 LCR HiTester meter. The molecular diffusion coefficient was determined based on the empirical dependency (1) specified by Adamczewski [39]:

$$D\_m = \frac{3.93 \times 10^{-14} \text{ } T}{\nu\_k \rho} \tag{1}$$

where *T* is temperature, ν*k* kinematic viscosity, and ρ density.

Figure 1 presents the rotating disc system for measuring the electrification current of insulating liquids. The system consisted of an air-tight measurement vessel with a diameter of 100 mm, filled with 500 mL of the liquid, placed on a Teflon insulator. In the vessel, metal discs were installed with diameters of 50, 60, 70, and 80 mm. The discs' rotation speed within the range from 100 to 500 rpm was regulated by means of a type 57BYGH step motor, combined with a system with a controller and a display. Each disc was connected with the motor by means of a metal mandrel, and an isolating clutch, serving as a mechanical and electric separator. The whole system was placed in a metal casing, serving the role of a Faraday cage. The rotary motion of the disc generated electrostatic charges, and their leakage to the ground was measured with a Keithley 6517A electrometer. The half-rack-sized model 6517A has a special low current input amplifier with an input bias current of <3 fA with just 0.75 fA p-p (peak-to-peak) noise and <20 µV burden voltage on the lowest range. The electrometer allows the measurement of current in the range 1 fA to 20 mA. The measurement process was controlled by means of a dedicated software application [40] installed on a portable computer. The measurement process consisted in washing and de-greasing the disc carefully, and then in seasoning it for two hours in the liquid being tested, to stabilize the hydrodynamic and electric conditions in the measuring system. During the tests, the air temperature in the lab was at a level of approx. 20 ◦C. Each point on the current characteristics chart is the average of the 500 values obtained from five measurement series, each of which lasted for 100 s. The error bars were determined based on the average electrification current, the standard deviation, and the significance level α = 0.05. The streaming electrification phenomenon in the measuring system starts to grow as a result of an increase in the disc's rotation speed. Due to the liquid's very complex motion in the measurement vessel, during the disc's activation, transient states are observed, characterized by considerable fluctuations in the form of the electrification current. The transitional processes result from a fast increase in the disc's speed in respect to the adjacent liquid. This results in a lot of slippage, a consequence of which is a rapid growth in the electrification current. This condition disappears within seconds after the speed of the disc and of the adjacent liquid layer become equal. Zmarzły [35] has analyzed the electrification current signal in the transient state. Because of the limited metering capabilities of the Keithley 6517A electrometer applied, the article presents the measurement results, which were recorded after the transient states disappeared.

— — — — — — **Figure 1.** Rotating disc system for the investigation of electrification current of insulation liquids: 1—measuring vessel with liquid and disc, 2—Faraday cage, 3—Keithley 6517A electrometer, 4—portable computer, M—stepper motor and C—controller with display.

#### *Mathematical Model of the Streaming Electrification Phenomenon*

of the model developed by Kędzia [41]. The liquid' ' ' ' ' ' ' ' ' The impact of the hydrodynamic conditions and of the physicochemical properties of the insulation liquids on the electrification process in the rotating disc system is described with the use of the model developed by K ˛edzia [41]. The liquid's motion in the system being discussed is very complex. The liquid adjacent to the disc moves with the disc's angular speed. The centrifugal forces create the liquid's component speeds in the radial direction. At the measurement vessel's wall, the liquid moves vertically. Then, the liquid moves over the disc's upper and lower surface towards its axis. The current in the measurement circuit is the sum of the diffusion current from the *qw* charge spread across the vessel's and the disc's surface, the diffusion current from the *q*0 charge introduced by the disc's rotational movement into the volume of the liquid, and the conductivity current, flowing in the liquid as a result of the electric field created by the charge in the liquid. In the model, it was assumed that the liquid's speed profile is fully developed. It was also assumed that the volumetric density of the *qw* charge in the double electrical layer depends only on the properties of the liquid and of the solid, and does not depend on the hydrodynamic conditions. For this reason, the *qw* parameter can be used to determine and compare the ECT of insulating liquids. The electrification current in the disc system is described with the use of the Equation (2):

0,5

−0,25 2

$$I = \frac{\sigma q\_w V}{\varepsilon\_0 \varepsilon\_r A} + \frac{D\_m q\_w}{\delta A} S\_d - \frac{D\_m q\_w}{\delta} S\_d \tag{2}$$

 Constant *A* is given by the Equation (3):

$$A = \frac{q\_{\rm w}}{q\_0} = 1 + \frac{\delta V}{\lambda^2 \mathcal{S}} \tag{3}$$

 = The thickness of the laminar sublayer is described by the Equation (4):

1

$$\delta = \frac{B\upsilon\_k}{\mathcal{S}\_n \text{\textquotedblleft}\left(\frac{\tau\_w}{\rho}\right)^{0.5}}\tag{4}$$

 = √ 0 The Debye length can be determined from Equation (5):

$$
\lambda = \sqrt{\frac{D\_m \varepsilon\_0 \varepsilon\_r}{\sigma}} \tag{5}
$$

 = 0,0396 The shear stresses are given by Equation (6):

$$
\tau\_w = 0.0396 \text{Re}^{-0.25} \rho v^2 \tag{6}
$$

The Reynolds number is given by Equation (7):

$$Re = \frac{\omega \mathbb{R}^2}{\nu\_k} \tag{7}$$

where *I* denotes the electrification current, *qw*—volume charge density on the phase border, *q0*—volume charge density in the liquid volume, σ—conductivity, ρ—density, ν*k*—kinematic viscosity, ε*0*—vacuum electric permittivity, ε*r*—relative dielectric constant, *Dm*—molecular diffusion coefficient, δ—laminar sublayer thickness, τ*w*—shearing stress, λ—Debye length, ω—angular velocity, *v*—average velocity, *Re*—Reynolds number, *V*—liquid volume, *R*—disc radius, *Sd*—disc surface, *S*—disk and container surface, *Sn*—Schmidt number (*Sn* = ν*k* /*Dm*), and *A*, *B*, *C*—constant (*A* = *qw*/*q*0, *B* = 11.7; *C* = 3).

#### **3. Results**

The density and viscosity are among the most important indicators describing the physicochemical properties of liquid dielectrics. The density of an insulating liquid is used in design calculations to determine a transformer's weight, and the viscosity determines the cooling effectiveness of its active parts. Liquids with lower viscosity are more effective at removing heat from the inside of a transformer into the environment. The conductivity and viscosity depend to a significant extent on the temperature, and thus they affect other properties of the insulating liquids, which include the carrier mobility, molecular diffusion coefficient, relative dielectric constant, and charge relaxation time. The relative dielectric constant influences the stress distribution in a transformer's insulation system, and thus it determines its electric durability [26–28]. When analyzing the data contained in Tables 1 and 2, it can be observed that the ageing processes affect to a different extent the physicochemical and electrical properties of Trafo EN mineral oil. The changes in the density (ρ) and in the relative dielectric constant (ε*r*) do not exceed 1%. The kinematic viscosity (ν*k* ) is characterized by a 9% increase, and the molecular diffusion coefficient (*Dm*) shows a 10% drop. The largest differences are visible in the conductivity (σ), the value of which increases by nearly two orders of magnitude. And when comparing Nycodiel 1255 synthetic ester with Trafo EN mineral oil, we can see that the ester is characterized by a higher density, kinematic viscosity, conductivity, relative dielectric constant, and a lower molecular diffusion coefficient.

**Table 1.** Properties of Nycodiel 1255 synthetic ester and fresh Trafo EN mineral oil mixtures (20 ◦C).

**Table 2.** Properties of Nycodiel 1255 synthetic ester and aged Trafo EN mineral oil mixtures (20 ◦C).

For example, Figures 2a–c and 3a,b present the dependencies that describe the impact of the percentage share of fresh Trafo EN mineral oil and Nycodiel 1255 synthetic ester in the mixtures on the change in the physicochemical and electric parameters. An increase in the content of the mineral oil in the mixture with the synthetic ester caused a linear drop in the density (Figure 2a), and in the relative dielectric constant (Figure 3b), and a non-linear drop in the kinematic viscosity (Figure 2b), and in the conductivity (Figure 3a), and also a non-linear increase in the molecular diffusion coefficient (Figure 2c). Similar parameters are demonstrated by both mixtures of Envirotemp FR3 natural ester with Nytro Taurus [27] and Trafo EN [37] mineral oils, and also mixtures of Midel 7131 synthetic ester with Nytro Draco [26] and Nytro Taurus [28] mineral oils. –

**Figure 2.** *Cont.*

–

−5 −11 −11 −5 −11 −11 −5 −11 −11 −5 −11 −11 −5 −11 −11 −5 −11 −11

**Figure 2.** (**a**) Density, (**b**) kinematic viscosity and (**c**) molecular diffusion coefficient vs. mixing of Nycodiel 1255 synthetic ester with fresh Trafo EN mineral oil.

**Figure 3.** (**a**) Conductivity and (**b**) relative dielectric constant vs. mixing of Nycodiel 1255 synthetic ester with fresh Trafo EN mineral oil.

To sum up, it should be concluded that comparing the properties of synthetic esters with those of mineral oils is important from the point of view of retrofilling power transformers. It is difficult to clearly indicate, which of the insulating liquids discussed is better or worse for use in transformers. The synthetic esters and mineral oils show a number of desired properties, unfortunately they are not free from disadvantages. Undoubtedly, the use of the synthetic esters is supported by environmental and fire safety aspects, and thus the interest in these liquids increases.

' Figure 4a presents the electrification current characteristics of the synthetic ester in relation to the rotation time of the discs with different diameters (50, 60, 70, 80 mm) at a speed of 500 rpm. A change in the disc's rotation speed within the range from 50 to 500 rpm results in a non-linear increase in the electrification current of Nycodiel 1255 insulating liquid (Figure 4b). It was observed

'

that the diameter and the rotation speed of the discs are factors that significantly influence the hydrodynamic conditions in the measurement system, and thus they affect the generation of the streaming electrification phenomenon.

**Figure 4.** Electrification current of Nycodiel 1255 synthetic ester vs. (**a**) rotating time (*v* = 500 rpm) and (**b**) rotational velocity for discs of different diameters (*d* = 50, 60, 70, 80 mm).

Figure 5a presents the dependencies between the electrification current in fresh and aged Trafo EN mineral oil, and Nycodiel 1255 synthetic ester depending on the rotation speed of the disc with the diameter of 80 mm. For each of the liquids, a non-linear increase in the electrification current is observed. The fresh mineral oil electrifies the least. The ageing processes in the mineral oil increase its electrification tendency. The synthetic ester shows an electrification nearly three times higher than that of the fresh Trafo EN oil. At the highest rotation speed (*v* = 500 rpm) of the disc (*d* = 80 mm), the electrification current was 417 pA (fresh Trafo EN oil), 854 pA (aged Trafo EN oil), and 1154 pA (Nycodiel 1255), respectively. Figure 5b presents the impact of the disc's rotation speed on the volume density of the *qw* charge. The average *qw* valueis 0.036 C/m3 (fresh Trafo EN oil), 0.065 C/m3 (aged Trafo EN oil), 0.192 C/m3 (Nycodiel 1255), respectively. When analyzing the charts, it may be stated that this parameter depends to a significant extent on the insulating liquid type. On the other hand, it does not depend on the hydrodynamic conditions prevailing in the measuring system, which is confirmed by its usefulness in determining the ECT of liquid dielectrics. As the study shows, the chemical structure of a liquid and the ageing processes can have a significant effect on the streaming electrification phenomenon in power transformers. In addition, as a result of retrofilling a transformer, a mixture is generated inside with electrostatic features that can be different than those of each base fluid.

'

**Figure 5.** (**a**) Electrification current and (**b**) volume charge density *qw* of insulating liquids vs. rotational velocity of the disc (*d* = 80 mm).

charge volume density and the mixture's composition. The characteristics of the q Figure 6a presents the impact of the composition of the mixtures of Nycodiel 1255 synthetic ester with Trafo EN mineral oil on the electrification current form. In the measurements, a disc with a diameter of 80 mm was used, rotating at a speed of 500 rpm. Significant differences in the form of the current characteristics were demonstrated, depending on the type of the mineral oil admixture (fresh or aged). In the first case, the electrification current decreases and reaches its minimum value (1011 pA), when the content of fresh oil in the mixture is 20%. Increasing the volume of oil in the mixtures results in an intensive growth in the electrification current value. The current characteristic reaches its maximum value (2613 pA) in the mixture consisting of 80% of mineral oil and 20% of synthetic ester. In the second case, the admixture of aged mineral oil of up to approx. 20% leads to lowering the electrification current value. Increasing the percentage share of mineral oil does not lead to any significant changes in the electrification current form anymore. Figure 6b presents the dependencies between the *qw* charge volume density and the mixture's composition. The characteristics of the *qw* charge have a different form than the current characteristics, since the electrification model, apart from the electrification current, takes additionally account of the physical-chemical and electrical properties of the liquids being studied.

**Figure 6.** (**a**) Electrification current and (**b**) volume charge density *qw* vs. mixing of Nycodiel 1255 synthetic ester with fresh and aged Trafo EN mineral oil (*v* = 500 rpm, *d* = 80 mm).

— — —

— —

This leads to a significant conclusion that, in order to specify the ECT of insulating liquids, it is necessary to know both the electrification current and the properties of the liquids. In order to visualize the electrification current value, and the *qw* charge value for selected liquids, their results are presented in the form of bar charts (Figure 7a,b).

— — — — — **Figure 7.** (**a**) Electrification current and (**b**) volume charge density *qw* of: 1—fresh Trafo EN, 2—aged Trafo EN, 3—Nycodiel 1255, 4—20% (SE)—80% (fresh MO) mixture.

The tests performed demonstrated that the type of the mineral oil used (fresh or aged) and the percentage share of the particular components in the mixtures substantially contribute to the generation of the streaming electrification phenomenon. Similar dependencies between the parameters being studied were obtained for the mixtures of Trafo EN mineral oil with Envirotemp FR3 natural ester [37], and with Midel 1204 natural ester and Midel 7131 synthetic ester [38]. Rajab et al. [42] presented the results of their studies on the electrification in mixtures of PFAE (palm fatty acid ester) with fresh and used mineral oil. The authors also observed the characteristic maximum of the electrification current, when the content of PFAE was 80%. It is difficult to clearly explain this phenomenon, since for the density, the kinematic viscosity, the conductivity, or the relative dielectric constant, no maximum or minimum values are observed. The reasons for this type of phenomena can result from different chemical structures of mineral oil and synthetic ester. These liquids differ in, for example, the capacity to absorb water from the environment, which may influence the structure of the electrical double layer, where the charge responsible for electrification in insulating liquids is created.

#### **4. Conclusions**

Due to their complex structure and the role they serve in an electric power system, power transformers should be properly diagnosed, which may be reflected in their effective, reliable, and long operation. For this reason, more often than before, when modernizing transformers, mineral oil is being replaced with synthetic or natural esters. The primary purpose of the paper was to specify the ECT of mixtures of fresh and aged Trafo EN mineral oil with Nycodiel 1255 synthetic ester in the context of retrofiling power transformers. The ECT of the insulating liquids were determined on the basis of the volume density of the *qw* charge created in the double electrical layer at the solid - liquid interface. The *qw* parameter was determined using the electrification model for the disc system, based on the measurements of the density, the kinematic viscosity, the molecular diffusion factor, the conductivity, the relative dielectric constant, and the electrification current in the mixtures. The parameters that affect the size of the electrification current generated are the rotation speed, the disc diameter, and the

mixtures' composition. The study demonstrated that Nycodiel 1255 synthetic ester electrifies more than fresh and aged mineral oil. It was demonstrated that the ECT of the mixtures depends to a significant extent on their composition. The forms of the electrification current in the mixtures with fresh and aged mineral oil are essentially different. In the first case, the minimal electrification current is observed at 20% of oil in the mixture, and the maximum when the oil content reaches 80%. Aged mineral oil (20%) in the mixtures reduces the electrification current value. A further increase in the aged oil content in a mixture with synthetic ester causes no further significant changes in the electrification current. In both the first and second cases, a small amount of Trafo EN mineral oil (up to 20%) effectively reduces the ECT of Nycodiel 1255 synthetic ester. The most important conclusion of the study conducted is the observation that replacing mineral oil with synthetic ester does not increase the risk of streaming electrification in the insulation system of power transformers. This phenomenon is beneficial for transformer retrofilling.

**Funding:** This research received no external funding.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**

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