Electrical Breakdown Mechanism of Transformer Oil with Water Impurity: Molecular Dynamics Simulations and First-Principles Calculations

crystals

Article Electrical Breakdown Mechanism of Transformer Oil with Water Impurity: Molecular Dynamics Simulations and First-Principles Calculations

Bin Cao, Ji-Wei Dong and Ming-He Chi *

Key Laboratory of Engineering Dielectrics and Its Application, Ministry of Education, School of Electrical and Electronic Engineering, Harbin University of Science and Technology, Harbin 150080, China; [email protected] (B.C.); [email protected] (J.-W.D.) * Correspondence: [email protected]; Tel.: +86-045186391605

Abstract: Water impurity is the essential factor of reducing the insulation performance of transformer oil, which directly determines the operating safety and life of a transformer. Molecular dynamics simulations and first-principles electronic-structure calculations are employed to study the diffusion behavior of water molecules and the electrical breakdown mechanism of transformer oil containing water impurities. The molecular dynamics of an oil-water micro-system model demonstrates that the increase of aging acid concentration will exponentially expedite thermal diffusion of water molecules. Density of states (DOS) for a local region model of transformer oil containing water molecules indicates that water molecules can introduce unoccupied localized electron-states with energy levels close to the conduction band minimum of transformer oil, which makes water molecules capable of capturing electrons and transforming them into water ions during thermal diffusion. Subsequently, under a high electric field, water ions collide and impact on oil molecules to break the molecular chain Citation: Cao, B.; Dong, J.-W.; Chi, of transformer oil, engendering carbonized components that introduce a conduction electronic-band M.-H. Electrical Breakdown in the band-gap of oil molecules as a manifestation of forming a conductive region in transformer oil. Mechanism of Transformer Oil with The conduction channel composed of carbonized components will be eventually formed, connecting Water Impurity: Molecular Dynamics two electrodes, with the carbonized components developing rapidly under the impact of water ions, Simulations and First-Principles Calculations. Crystals 2021, 11, 123. based on which a large number of electron carriers will be produced similar to “avalanche” discharge, https://doi.org/10.3390/cryst11020123 leading to an electrical breakdown of transformer oil insulation. The water impurity in oil, as the key factor for forming the carbonized conducting channel, initiates the electric breakdown process Academic Editors: of transformer oil, which is dominated by thermal diffusion of water molecules. The increase of Tomoyuki Hamada and aging acid concentration will significantly promote the thermal diffusion of water impurities and the Paolo Restuccia formation of an initial conducting channel, accounting for the degradation in dielectric strength of Received: 28 December 2020 insulating oil containing water impurities after long-term operation of the transformer. Accepted: 25 January 2021 Published: 27 January 2021 Keywords: transformer oil; electrical breakdown; molecular dynamics; first-principles calculation

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional afﬁl- 1. Introduction iations. Transformer internal insulation is primarily composed of an oil-paper composite system. Transformer oil, as the insulation and cooling fundamental, directly determines the operation safety and life of a transformer [1]. In the manufacturing, transportation, assembly, and operation processes of transformers, water impurities that inevitably existing Copyright: © 2021 by the authors. in transformer oil will reduce the electrical and aging resistance of transformer oil and Licensee MDPI, Basel, Switzerland. even lead to the breakdown infraction of transformer internal insulation [2]. The researches This article is an open access article on the diffusion behavior of water impurities in transformer oil and its effect on the distributed under the terms and conditions of the Creative Commons dielectric breakdown of the transformer can provide a theoretical basis for further exploring Attribution (CC BY) license (https:// dielectric failure mechanisms of transformer oil to improve the safe and stable operation of creativecommons.org/licenses/by/ transformers. 4.0/).

Crystals 2021, 11, 123. https://doi.org/10.3390/cryst11020123 https://www.mdpi.com/journal/crystals Crystals 2021, 11, 123 2 of 10

Distribution and diffusion of water impurities in transformer oil-paper insulation and their influence on dielectric properties has always been of high interest in electrical insulation researches: Zhou reported the steady-state equilibrium relationship of the moisture distribution in oil-paper insulation at different temperatures [3–5]; Dielectric frequency response has been tested in correlation with the transient process of moisture penetration in oil-paper insulation [6,7]; and Liao revealed the changing trend of moisture content and distribution during insulation aging of oil-paper insulation [8,9]. Zhao elucidated the effecting mechanisms of moisture, air bubbles, and cellulose particles on the breakdown characteristics of oil gaps [10,11]. Many scholars have carried out experimental research on the breakdown characteristics of insulating oil. Calcara compared the breakdown voltages of various mineral oils and natural esters under both AC and impulse voltages and described how these two tests reveal the electrical performance of the dielectric liquid [12]. Rao introduced the breakdown theories and different streamer properties of ester fluids and presented a detailed report on the modelling and analysis of the pre-breakdown event (streamer) [13]. Water impurities are also important factors affecting the breakdown characteristics of transformer oil: Miners found that the breakdown strength of oil decreased by approximately 25 percent when the moisture content was increased from 5 ppm to 20 ppm [14]; Krins reports on experimental investigations dealing with the impact of different water contents on the electrical strength of oil gaps [15]; and Guo studied the influences of moisture and a compound electric field on the breakdown characteristics of transformer oil at low temperatures [16]. These studies do not adequately explain micro mechanisms underlying experimental phenomena. Molecular simulation technology provides a powerful approach at the molecule/atom scale. Molecular dynamics (MD) simulations on the diffusion behavior of water molecules in polypropylene laid a foundation for related follow-up research [17]. By calculating the interaction energy, Zhu discussed that the law of binding effect of insulating oil on water changing with temperature [18]. It has been found with the MD method that blending SiO2 nano-particles in oil can reduce the diffusion coefficient of water molecules [19]. Wang found that a rapid temperature rise will cause water molecules to ac- cumulate into clusters through intermolecular hydrogen bonding at the oil-paper interface to form local liquid water [20]. It is also suggested by MD simulations that the formation of a hydrogen bond will impede thermal diffusion and facilitate cohesion of water molecules in oil [21]. Zhang established a complex model containing water molecules, mineral oil molecules, and formic acid molecules and simulated the diffusion and interaction of water and acid in oil at different temperatures [22]. At present, most of the theoretical atomic-level researches of water impurities in transformer oil merely focus on the analyses of diffusion and distribution law, without reckoning on water impurities in the breakdown process of transformer oil. Therefore, in this paper, molecular simulation technology is used to establish the multiple-molecule model of transformer oil with water impurities to calculate mean square displacement and diffusion coefficients of water molecules in transformer oil at different temperatures, based on which the electron properties of the local region containing water molecule in transformer oil are calculated by means of a first-principles method to explore electrical breakdown mechanism of water-containing transformer oil.

2. Model Establishment and Simulation Method 2.1. Transformer Oil Model Naphthenic mineral oil possesses the advantages of having a simple manufacturing process and excellent thermal conductivity, and it has been widely used as the main insulation of transformers. Naphthenic mineral oil consists of naphthenic and chain hydrocarbons with a mass composition, as listed in Table1. The molecular model of ﬁve alkanes in naphthenic mineral oil is established, as shown in Figure1. Employing the amorphous blending method, as implemented by the Amorphous Cell module of Materials Studio software package (Accelrys Inc., Materials Studio v8.0.0.843, San Diego, Crystals 2021, 11, x FOR PEER REVIEW 3 of 11

Crystals 2021, 11, 123 lation of transformers. Naphthenic mineral oil consists of naphthenic and chain hydrocar- 3 of 10 bons with a mass composition, as listed in Table 1. The molecular model of five alkanes in naphthenic mineral oil is established, as shown in Figure 1. Employing the amorphous blending method, as implemented by the Amorphous Cell module of Materials Studio CA, USA) [23], a multiple-molecules system model with a target density of 0.95g/cm−3 software package (Accelrys Inc., Materials Studio v8.0.0.843, San Diego, CA, USA) [23], a was constructed by taking each alkane molecules as a constitute unit in the proportions multiple-molecules system model with a target density of 0.95g/cm−3 was constructed by listed in Table1. taking each alkane molecules as a constitute unit in the proportions listed in Table 1. Table 1. Mass composition of naphthenic mineral oil. Table 1. Mass composition of naphthenic mineral oil. Bicyclic Monocyclic Tricyclic Tetracyclic Component AlkanesBicyclic Monocyclic Tricyclic Al- Tetracyclic Al- Component Alkanes Alkanes Alkanes Alkanes Alkanes Alkanes Alkanes kanes kanes Content 13% 18% 32% 26% 11% Content 13% 18% 32% 26% 11%

Figure 1. MolecularFigure model 1. Molecular of naphthenic model ofmineral naphthenic oil: (a)mineral Alkanes oil: C12 (Ha)26 Alkanes; (b)Monocyclic C12H26 ;(alkanesb) Monocyclic alkanes C14H28; (c) BicyclicC14H alkanes28;(c) Bicyclic C13H24; alkanes (d) Tricyclic C13H alkanes24;(d) Tricyclic C16H28; alkanes(e) Tetracyclic C16H28 alkanes;(e) Tetracyclic C16H26. alkanes C16H26. 2.2. Model of Oil-Water-Acid System 2.2. Model of Oil-Water-Acid System The saturated water content of transformer oil at room temperature is so low as to The saturated water content of transformer oil at room temperature is so low as to be be in the magnitude order of ppm. The basic principle of molecular dynamics are to in the magnitude order of ppm. The basic principle of molecular dynamics are to first first solve the motions of atomic or molecular particles by Newton’s equation to obtain solve the motions of atomic or molecular particles by Newton’s equation to obtain statis- statistical mean values of microscopic parameters and then analyze the macro properties of tical mean values of microscopic parameters and then analyze the macro properties of multiple-molecule systems. If the number of water molecules is too small, the calculated multiple-molecule systems. If the number of water molecules is too small, the calculated parameters cannot represent substantial statistics. Accordingly, based on many simulation parameters cannot represent substantial statistics. Accordingly, based on many simula- practices, the number of water molecules added into the transformer oil model is set as 20 tion practices, the number of water molecules added into the transformer oil model is set to construct the oil-water system model. as 20 to construct the oil-water system model. The diffusion and distribution of water impurities in transformer oil rely on the The diffusionMD simulation and distribution temperature of water of impu targetrities thermodynamics. in transformer oil In long-termrely on the operationMD of the simulation temperaturetransformer, of oil-paper target thermodyna insulation willmics. continue In long-term to age andoperation produce of acidsthe trans- [24]. These acids former, oil-papermainly insulation consists ofwill low continue molecular to organicage and acids, produce such acids as formic [24]. acidThese and acids acetic acid, and mainly consistshigh of molecular low molecular organic organic acids, acids, such assuch stearic as formic acid. In acid oil-paper and acetic insulation, acid, and low molecular high molecularorganic organic acids acids, majorly such distribute as stearic in acid. insulating In oil-paper paper, insulation, while stearic low acid molecular is mainly distributed organic acidsin majorly transformer distribute oil [25 in,26 insulating]. In order topaper, study while the effect stearic of agingacid is acid mainly on the distrib- diffusion behavior uted in transformerof water oil molecules, [25,26]. In four order oil-water-acid to study the system effect models of aging with acid different on the contentsdiffusion of aging acid behavior of waterwere establishedmolecules, byfour individually oil-water-acid mixing system 5~20 models stearic with acid different (SA) molecules contents into of the oil-water aging acid weresystem established model. by individually mixing 5~20 stearic acid (SA) molecules into the oil-water system model. 2.3. Simulation Methods 2.3. Simulation MethodsIn molecular dynamics (MD) simulations, the energy of molecules is approximately In moleculardescribed dynamics by the (MD) space simulations, coordinate function the energy of each of molecules atom with isa approximately series of functions describ- described bying the thespace relationship coordinate between function atoms, of each which atom iswith called a series force of field. functions A COMPASS describ- force field is ing the relationshipbased on between an ab initio atoms, algorithm which is to called present force the field. first A high-quality COMPASS molecularforce field forceis field that based on an unifiesab initio the algorithm parameters to present of organic the first and high-quality inorganic molecules. molecular It force is thus field suitable that to adopt a COMPASS force field for the multiple-molecule model and the dynamic simulations of a transformer oil mixture. For dynamics simulations, van der Waals force and Coulomb interaction are calculated by the atom-based summation method, with a cutoff distance of 15.5Å and a buffer width of 2.0 Å. Temperature and pressure controls adopts algorithms of Crystals 2021, 11, x FOR PEER REVIEW 4 of 11

unifies the parameters of organic and inorganic molecules. It is thus suitable to adopt a COMPASS force field for the multiple-molecule model and the dynamic simulations of a Crystals 2021, 11, 123 4 of 10 transformer oil mixture. For dynamics simulations, van der Waals force and Coulomb interaction are calculated by the atom-based summation method, with a cutoff distance of 15.5Å and a buffer width of 2.0 Å. Temperature and pressure controls adopts algorithms of Andersen and Berendsen,Andersen respectively. and Berendsen, Newtonian respectively. equations Newtonian of motion equations are solved of by motion are solved by the the Velocity Verlet jumpingVelocity frog Verlet method. jumping frog method. Before the dynamics calculations,Before the dynamics it is necessary calculations, to optimize it is necessarythe initial tomodel optimize to reach the initial model to reach a a stable conformation withstable the conformation lowest potent withial theenergy, lowest which potential is called energy, geometry which is optimi- called geometry optimization zation of energy minimization,of energy as minimization, implemented as by implemented the Forcite module by the Forcite of Materials module Studio of Materials Studio software software package. A smartpackage. algorithm A smart is algorithm used for isgeometry used for geometryoptimization optimization to reach tothe reach en- the energy convergence − ergy convergence of 2×10of 2−5 ×kcal/mol.10 5 kcal/mol. The constant The constant particle particle number, number, pressure, pressure, temperature temperature (NPT) ensemble is (NPT) ensemble is usedused in MD in MDsimulations simulations of an of annealing an annealing model model under under atmosphere atmosphere pres- pressure, with temperature sure, with temperaturebeing being gradually gradually increased increased from from 300 300 to to 500 500K K and then decreased to 300 K in steps of 50 K. 300K in steps of 50K. ConsecutiveConsecutive heating heating and and cooling cooling processes areare cycledcycled five five times. times. The constant particle number,The constant volume particle and temperature number, volume (NVT) and ensemble temperature is used (NVT) to ensemble is used to simulate each system modelsimulate under each a COMPASS system model force under field for a COMPASS 5ps, with a force time ﬁeldstep of for 1fs. 5 ps, with a time step of The simulation trajectory1fs. is The output simulation every 250fs trajectory to calculate is output the every dynamic 250 fsparameters. to calculate MD the dynamic parameters. simulation temperatureMD is simulationset to 300K, temperature 500K, and 700K, is set torespectively, 300 K, 500 K,to andinvestigate 700 K, respectively, the to investigate temperature influence theon the temperature displacement inﬂuence and diffusion on the displacement of water impurities. and diffusion Especially of water impurities. Espe- to compare different concentrationscially to compare of SA different molecules, concentrations the simulation of SA temperature molecules, of the oil- simulation temperature water-acid system wasof set oil-water-acid to 343K, which system is the was normal set to oil 343 temperature K, which is theof an normal operating oil temperature of an oper- transformer. Taking asating an example transformer. for an Taking oil-water-acid as an example system, for a thermodynamic an oil-water-acid equi- system, a thermodynamic librium structure with equilibriuma content of structure20 SA molecules with a content at 343K of is 20shown SA molecules in Figure at2. 343 K is shown in Figure2.

Figure 2. Amorphous multiple-moleculesFigure 2. Amorphous model multiple-molecules of oil-water-acid system model with of oil-water-acid 20 stearic acid system (SA) with 20 stearic acid (SA) molecules at 343K. molecules at 343 K.

3. Simulation Results 3.and Simulation Analysis Results and Analysis 3.1. Diffusion Coefficient3.1. Diffusion Coefﬁcient In order to describe theIn orderdisplacement to describe behavior the displacement of particles, behavior the concept of particles, of mean the concept of mean square square displacement (MSD)displacement is introduced, (MSD) which is introduced, is defined which by the is deﬁnedaverage byvalue the of average the value of the square square displacement ofdisplacement particles studied of particles in a certain studied period in a of certain time: period of time: = − 2 D 2E MSD ri (t) ri (0) MSD = |ri(t) − ri(0)| (1) (1)

where ri(t) and ri(0) representwhere r ithe(t) andpositionri(0) representvectors of themolecule position i at vectors the initial of molecule time and i att the initial time and t time, respectively, andtime, brackets respectively, <> denote and thebrackets average <>of the denote particles the average studied. of the particles studied. The diffusion coefficient is an important parameter that is used to characterize the diffusion ability of a substance in a medium. The larger the diffusion coefficient, the smaller the confinement effect of the medium on the diffusion particles. In molecular dynamics simulation, the data can be intercepted from the particle trajectories to calculate the mean square displacement, and then the diffusion coefficient can be obtained by the Einstein relationship as: Crystals 2021, 11, x FOR PEER REVIEW 5 of 11

The diffusion coefficient is an important parameter that is used to characterize the diffusion ability of a substance in a medium. The larger the diffusion coefficient, the smaller the confinement effect of the medium on the diffusion particles. In molecular dy- Crystals 2021namics, 11, 123 simulation, the data can be intercepted from the particle trajectories to calculate 5 of 10 the mean square displacement, and then the diffusion coefficient can be obtained by the Einstein relationship as: 1 d n n = − 2 1 d 2 D lim [ri (t) ri (0)] D = lim [ri(t) − ri(0)] (2) (2) →∞  t→∞ ∑ 6n t dt i=1 6n dt i=1 where n is the numberwhere of diffusingn is the number particles, of and diffusing the differential particles, can and be the approximately differential can be approximately replaced by the slopereplaced a of MSD by thecurves slope to acalculof MSDate curvesdiffusion to calculatecoefficient diffusion D=a/6. Twenty coefficient D = a/6. Twenty water molecules in watereach system molecules model in eachare incorporated system model for are statistic incorporated calculations for statisticwith calculations with Equation (2), accordingEquation to the motion (2), according trajectory to the output motion from trajectory MD processes. output from MD processes. In the initial stage ofIn thermodynamic the initial stage ofsimulation, thermodynamic the transient simulation, temperature the transient of the temperature of the sys- system rises instantaneouslytem rises to instantaneously target temperature to target with temperature an increment with in entropy an increment of mole- in entropy of molecules cules in the system. Atin thethis system.stage, the At sharply this stage, increasing the sharply MSD increasing curves imply MSD that curves the dis- imply that the displace- placements of water mentsmolecules of water have molecules not converged have notinto converged the stable intothermodynamic the stable thermodynamic equi- equilibrium. librium. Thus, the molecularThus, the system molecular should system be equilibrium should be equilibrium for calculating for calculating the diffusion the diffusion coefficient coefficient by the Einsteinby the relationship, Einstein relationship, which means which MSD means increases MSD increaseslinearly with linearly time. with time. Therefore, Therefore, initial datainitial before data 500fs before in the 500 MD fs in process the MD are process discarded are discarded to obtain tothe obtain linearly the linearly fitted MSD fitted MSD for calculatingfor calculating the diffusion the diffusioncoefficient, coefficient, as shown as in shown Figure in 3. FigureTable 32. and Table Fig-2 and Figure4 present ure 4 present the diffusionthe diffusion coefficients coefficients of various of various oil-water-acid oil-water-acid systems. systems.

Figure 3. Mean square Figuredisplacement 3. Mean (MSD) square of displacementwater molecules (MSD) in an of oil-water-acid water molecules system in an with oil-water-acid 20 system with 20 SA molecules at 343K. SA molecules at 343 K.

Table 2. Diffusion coefficient for oil-water-acid systems. Table 2. Diffusion coefficient for oil-water-acid systems. Temperature Diffusion Coefficient Influence factor Temperature Diffusion Coefficient Influence Factor 2 Concentration Concentration/(Å /ps) /(Å2/ps) 300K 0.25851 Temperature 300 K 0.25851 Temperature 500K 500 K0.283708 0.283708 15 SA molecules 15 SA molecules 700K 700 K0.858275 0.858275 5 50.135583 0.135583 SA content SA content10 100.195182 0.195182 at 343K at 343 K15 150.273205 0.273205 20 200.423333 0.423333

When the temperatureWhen of the the oil-water temperature syst ofem the increases oil-water from system 300 increasesto 500K, fromthe diffu- 300 to 500 K, the diffusion sion coefficient of watercoefficient molecules of water shows molecules no evident shows change. no evident By contrast, change. when By contrast, the tem- when the temperature perature rises from 500rises to from700K, 500the todiffusion 700 K, thecoefficient diffusion more coefficient than doubles more to than 0.86 doubles Å2/ps. to 0.86 Å2/ps. It is suggested from an effective fitting that the diffusion coefficient increases exponentially with temperature. The relationship between the diffusion coefficient and temperature can be expressed by the Arrhenius equation as: E D = D exp − (3) 0 RT Crystals 2021, 11, x FOR PEER REVIEW 6 of 11

Crystals 2021, 11, x FOR PEER REVIEW 6 of 11

It is suggested from an effective fitting that the diffusion coefficient increases exponen- It is suggested fromtially an effective with temperature. fitting that the diffusion coefficient increases exponentially with temperature. The relationship between the diffusion coefficient and temperature can be expressed The relationshipby betweenthe Arrhenius the diffusion equation coef as:ficient and temperature can be expressed by the Arrhenius equation as: E DD=−exp (3) =−E 0  DD0 exp RT (3) RT where D0 is the limiting diffusion coefficient, E is the diffusion activation energy, and R = where D0 is the limiting8.314J/(mol diffusion·K) coefficient, is the gas constant. E is the diffusion The relationship activation between energy, andlnD Rand = the reciprocal of tem- 8.314J/(mol·K) is the gas constant. The relationship between lnD and the reciprocal of tem- Crystals 2021, 11, 123 perature can be obtained with Equation (3) as lnD = −(E/R)(1/T) + lnD0, as shown in Figure 6 of 10 perature can be obtained with Equation (3) as lnD = −(E/R)(1/T) + lnD0, as shown in Figure 5. The diffusion activation energy can be calculated from the slope of the two straight 5. The diffusion activation energy can be calculated from the slope of the two straight lines. When the temperature of the oil-water system increases from 300 to 500K, the diffu- lines. When the temperature of the oil-water system increases from 300 to 500K, the diffusion activation energy decreases from 16105.99 J/mol to 579.97 J/mol, which indicates that sion activation energy decreases from 16105.99 J/mol to 579.97 J/mol, which indicates that where D is the limiting diffusion coefﬁcient, E is the diffusion activation energy, and water molecules inwater oil are molecules more0 easily in activatedoil are more and haveeasily a activatedstronger diffusionand have ability a stronger at diffusion ability at · high temperatures. highR = temperatures. 8.314 J/(mol K) is the gas constant. The relationship between lnD and the reciprocal of As shown in FiguretemperatureAs 4b, shown the diffusion canin Figure be behavi obtained 4b, orthe of diffusion withwater Equation molecules behavi (3)oris greatlyof as water lnD affected= molecules−(E/ R)(1/ is greatlyT) + ln Daffected0, as shown by SA concentrationby inin SA Figurethe concentration oil. 5As. Thethe number diffusion in the of oil. SA activation As molecules the number energy is raised of can SA from bemolecules calculated5 to 20, theis raised from from the slope 5 to 20, of the the two diffusion coefficientdiffusion straightrises from coefficient lines. 0.14 to When 43 rises Å2/p the froms, temperature implying 0.14 to that 43 of Å2/pthe the presences, oil-water implying of SA system that mole- the increases presence fromof SA 300 mole- to 500 K, cules will significantlyculesthe promote will diffusion significantly water activation diffusion promote in energy oil. water It can decreases diffusionbe reasonably from in oil. speculated 16,105.99 It can be reasonablythat J/mol to 579.97 speculated J/mol, that which the existence of SA moleculestheindicates existence makes that of SA water the molecules molecu moleculeslar makesstructure in oil the of are molecu transformer morelar easily structure oil activated more of loose, transformer and have oil a stronger more loose, diffusion increases the free volumeincreasesability of at waterthe high free molecules temperatures. volume in of the water oil-water molecules system, in andthe oil-waterprovides moresystem, and provides more space for the diffusionspace of waterfor the molecules. diffusion of water molecules. (a) (a) (b) (b)

Figure 4. Diffusion coefﬁcients of water molecules in (a) oil-water system model at different tempera- Figure 4. Diffusion coefficients of water molecules in (a) oil-water system model at different tem- tures; (b) oil-water-acid system model at different aging acid concentrations. peratures; (b) oil-water-acidFigure system4. Diffusion model coefficients at different ofaging water acid molecules concentrations. in (a) oil-water system model at different temperatures; (b) oil-water-acid system model at different aging acid concentrations.

Figure 5. The relationship between lnD and the reciprocal of temperature. Figure 5. The relationship between lnD and the reciprocal of temperature. As shownFigure in5. The Figure relationship4b, the diffusionbetween lnD behavior and the reciprocal of water of molecules temperature. is greatly affected by SA concentration in the oil. As the number of SA molecules is raised from 5 to 20, the diffusion coefﬁcient rises from 0.14 to 43 Å2/ps, implying that the presence of SA molecules will signiﬁcantly promote water diffusion in oil. It can be reasonably speculated that the existence of SA molecules makes the molecular structure of transformer oil more loose, increases the free volume of water molecules in the oil-water system, and provides more space for the diffusion of water molecules.

3.2. First-Principles Electronic Structure Calculation The electron properties of water molecules in the presence of nearby oil molecules are key factors in the electrical breakdown micro-process of transformer oil, and they determine the macroscopic breakdown characteristics of transformer oil containing water impurities. Due to the small amount of water molecules in the oil-water system model, the basic molecules of oil are evenly distributed around a single water molecule, and the contents of several basic alkane molecules are not very different. Therefore, In order to determine the localized electron state introduced by water molecules and the behavior of charge Crystals 2021, 11, x FOR PEER REVIEW 7 of 11

3.2. First-Principles Electronic Structure Calculation Crystals 2021, 11, x FOR PEER REVIEW 7 of 11 The electron properties of water molecules in the presence of nearby oil molecules are key factors in the electrical breakdown micro-process of transformer oil, and they determine the macroscopic breakdown characteristics of transformer oil containing water 3.2. First-Principles Electronic Structure Calculation Crystalsimpurities.2021, 11 ,Due 123 to the small amount of water molecules in the oil-water system model, 7 of 10 the basic molecules of oil are evenlyThe electr distributedon properties around of watera single molecules water molecule, in the presence and theof nearby oil molecules contents of several basic alkaneare key molecules factors in are the not electrical very different.breakdown Therefore, micro-process In order of transformer to oil, and they determine the localized electrondetermine state theintroduced macroscopic by breakdownwater molecules characteristics and the of behavior transformer of oil containing water impurities. Due to the small amount of water molecules in the oil-water system model, charge transports in oil, we builttransports a simplified in oil, model we built of aan simplified oil-water modelsystem of containing an oil-water one system containing one water the basic molecules of oil are evenly distributed around a single water molecule, and the water molecule and five basicmolecule alkane andmolecules five basic of alkanenaphthenic molecules mineral of naphthenic oil (as shown mineral in oil (as shown in Table1) to contentsfeasibly of simulate several thebasic local alkane region molecules comprising are not water very impurities. different. Therefore, After geometry In order optimization to Table 1) to feasibly simulatedetermine the local regionthe local comprisingized electron water state introducedimpurities. by After water geometry molecules and the behavior of and molecular dynamics simulation, the stable configuration of the simplified model is optimization and molecularcharge dynamics transports simulati in oilon,, we the buil stablet a simplified configuration model of of an the oil -simpli-water system containing one fied model is shown in Figurewatershown 6. The molecul in densities Figuree and6. offive The states basic densities (DOS)alkane of ofmolecules states the local (DOS) of area naphthenic of models the local mineral for area modelsoil (as shown for pure in oil and pure oil and oil-water systemsTableoil-water are 1) calculatedto feasibly systems simulate by are the calculated atom-orbital the local region by the all-electron comprising atom-orbital first-princi- water all-electron impurities. first-principles After geometry method, ples method, as implementedoptimizationas with implemented the DMol3and molecularwith module the DMol3 dynamicsof Materials module simulation, Studio of Materials 8.0. the Gradient stable Studio configuration 8.0. Gradient of the correction correction functional (GGA)simplified functionalis adopted model (GGA)for DF is T is shown exchange-correlation adopted in Figure for DFT 6. The exchange-correlation densitfunctional,ies of andstates self- (DOS) functional, of the and local self-consistent area × −6 consistent field (SCF) tolerancemodelfield iss (SCF) setfor pureas tolerance1 oil× 10 and−6 eV/atom oil is- setwater as insystem 1 first-principles10s are calculatedeV/atom calculations. by in the first-principles atom -orbital all calculations.-electron The first-principles method, as implemented with the DMol3 module of Materials Studio 8.0. The calculation result of DOScalculation is shown result in Figure of DOS 7, is with shown the in highest Figure7 ,occupied with the higheststate occupied state (HOMO) Gbeingradient referenced correction asfunctional energy (GGA) zero. is adopted for DFT exchange-correlation functional, (HOMO) being referenced as energy zero. and self-consistent field (SCF) tolerance is set as 1 × 10−6 eV/atom in first-principles calculations. The calculation result of DOS is shown in Figure 7, with the highest occupied state (HOMO) being referenced as energy zero.

Figure 6.Figure Local 6.regionLocal model region of model an oil-water of an oil-water system. system. Figure 6. Local region model of an oil-water system.

(a) (b) (a) (b) FigureFigure 7. 7. DDensityensity of ofstate state for for(a) pure (a) pure transformer transformer oil and oil (b and) oil- (waterb) oil-water system systemin local region in local region model. Figure 7. Density of state for (amodel) pure. transformer oil and (b) oil-water system in local region model. Compared with DOS results for pure oil and oil-water systems, it is noted that the Compared with DOS results for pure oil and oil-water systems, it is noted that the water molecule introduces a few unoccupied localized electronic-states (electron wave water molecule introduces a few unoccupied localized electronic-states (electron wave Compared with DOS resultsfunction for ispure localized oil and at oil-water the water systems, molecule), it is withnoted the that energy the levels being 0.4 eV lower water molecule introduces athan few the unoccupied conduction localized band bottom electronic-states of transformer (electron oil with wave a band-gap of 6 eV. The small DOS of these localized states from the water molecule is a manifestation of charge traps that capture electron carriers from the conduction band of the transformer oil. Therefore, the electrons injected from electrodes or thermally excited from the valence band of oil molecules are energetically favorable to transit from basic oil molecules to the impurity water molecule, but need to cross over the energy barrier in vacuum between oil and water molecules, which will drop off when water molecule thermally collides with an oil molecule. This electron trapping mechanism leads to a substantial probability of water Crystals 2021, 11, x FOR PEER REVIEW 8 of 11

function is localized at the water molecule), with the energy levels being 0.4 eV lower than the conduction band bottom of transformer oil with a band-gap of 6 eV. The small DOS of these localized states from the water molecule is a manifestation of charge traps that capture electron carriers from the conduction band of the transformer oil. Therefore, the electrons injected from electrodes or thermally excited from the valence band of oil molecules are energetically favorable to transit from basic oil molecules to the impurity water mole- Crystals 2021, 11, 123 8 of 10 cule, but need to cross over the energy barrier in vacuum between oil and water molecules, which will drop off when water molecule thermally collides with an oil molecule. This electron trapping mechanism leads to a substantial probability of water molecules capturing electrons moleculesfrom oil to capturing become water electrons ions, from and this oil to will become be accelerated water ions, to andhigher this will be accelerated to velocity under a highhigher electric velocity field to under impact a highonto electricoil molecules. field to impact onto oil molecules. Guan has reported Guanthe MD has simulation reported study the MD on simulationthe two-phase study system on theof Dodecyl two-phase system of Dodecyl benzene (DDB) insulatingbenzene oil (DDB)with water insulating ions, and oil demonstrated with water ions, that and the demonstratedcollision of water that the collision of water ions with DDB moleculesions with under DDB a moleculeshigh electric under field a will high lead electric to the field fracture will lead of th to eC-C the fracture of th eC-C bond bond and the C-H andbond the in C-Hthe molecular bond in the chain, molecular and produce chain, andunsaturated produce unsaturatedcarbon frag- carbon fragments such ments such as CH, CH3, C3H5, and C7H6 [27]. Accordingly, on the basis of the simplified as CH, CH ,C H , and C H [27]. Accordingly, on the basis of the simplified model shown model shown in Figure 6, we added3 3 the5 above7 unsaturated6 carbon fragments, one of each in Figure6, we added the above unsaturated carbon fragments, one of each type, to build a type, to build a simplized model of transformer oil with carbonized-fragments that are simplized model of transformer oil with carbonized-fragments that are supposed to be the supposed to be the results of water ions impacting on oil molecules. The first-principles results of water ions impacting on oil molecules. The first-principles electronic-structure electronic-structure calculations of this carbonized oil model, as shown by DOS in Figure calculations of this carbonized oil model, as shown by DOS in Figure8, illustrate that a few 8, illustrate that a few impurity bands, in a wide energy range from carbonized-fragments, impurity bands, in a wide energy range from carbonized-fragments, are introduced into are introduced into the band-gap of the transformer oil, through which electrons are estimated to be thermallythe excited band-gap by kT of ( thek and transformer T denote the oil, Boltzmann through which constant electrons and the are tem- estimated to be thermally perature, respectively)excited from by thekT valence(k and Tanddenote conduction the Boltzmann bands of constantthe transformer and the oil temperature, at respectively) ambient temperature.from the valence and conduction bands of the transformer oil at ambient temperature.

Figure 8. DensityFigure of 8.stateDensity for oil of system state forwith oil unsaturated system with carbonized-fragments. unsaturated carbonized-fragments.

The calculation of theThe electron calculation density of of the the electron carbonized density oil ofmodel thecarbonized is shown in oilFigure model is shown in Figure9 . 9. It can be seen thatIt the can iso-surfaces be seen that of the carbonized-fragments iso-surfaces of the carbonized-fragments and the oil molecule is and the oil molecule is connected together,connected which indicates together, that whichthe electron indicates wave that functions the electron of the two wave molecules functions of the two molecules overlap. The electronsoverlap. in the Theconduction electrons band in the and conduction valence band band of andthe oil valence molecule band have of the oil molecule have a a certain probabilitycertain to cross probability the potential to cross barrier the of potential the vacuum barrier molecular of the vacuum gap and molecular tran- gap and transition Crystals 2021,sition 11, x FOR to PEERthe carbonized-fragment. REVIEWto the carbonized-fragment. In summary, the In carbonized summary, components the carbonized from components the frac- from9 the of 11 fracture of

ture of oil moleculesoil will molecules form a local will conductive form a local region conductive in the transformer region in the oil. transformer oil.

(a) (b)

FigureFigure 9. 9.(a)( Isoa) Iso-surfaces-surfaces of electron of electron density density are indicated are indicated with blue with, and blue, the andcarboned the carboned-fragments-fragments are are indicated with red; (b) partial enlarged detail near CH3. indicated with red; (b) partial enlarged detail near CH3. 3.3. Breakdown Mechanism of Transformer Oil with Water Impurities The water molecules in transformer oil collide with oil molecules under thermal diffusion to capture electrons from oil molecules and transform them into water ions. But in the actual electric breakdown test, the electrons captured by the water molecules are preferred from electrode injection with a small amount of thermally excited electrons directly from oil molecules. Therefore, it can be inferred that the concentration of water ions in the high potential region of oil is higher. These water ions can obtain enough kinetic energy under an electric field to break the oil molecular chain and produce unsaturated carbon fragments, which form local conductive regions. Meanwhile, when the negative water ions reach the positive electrode, the charge exchange makes them revert to neutral water molecules. In the subsequent thermal diffusion process, water molecules will be converted into water ions, again due to collision and electron capture, thus repeating the migration process near the positive electrode. With the continuous impact of water-ions under an electric field, the carbonized components generated in the high potential region are extending thermally from the high to the low potential area in oil, and finally form a conductive channel between two electrodes, after which a large amount of electrons will be injected from the electrode to cause an avalanche breakdown, with the conductive channel being rapidly expanded by electron bombardment. Therefore, the thermal diffusion of water impurities in oil and the migration of water ions under an electric field initialize the electric breakdown process of transformer oil. According to MD simulations of water-oil-acid systems, thermal diffusion of water molecules will be significantly exacerbated by the presence of aging acid; we have therefore elucidated the insulation fracture mechanism of transformer oil with water impurities in the longer-term operation that produces the aging acids.

Crystals 2021, 11, 123 9 of 10

3.3. Breakdown Mechanism of Transformer Oil with Water Impurities The water molecules in transformer oil collide with oil molecules under thermal diffusion to capture electrons from oil molecules and transform them into water ions. But in the actual electric breakdown test, the electrons captured by the water molecules are preferred from electrode injection with a small amount of thermally excited electrons directly from oil molecules. Therefore, it can be inferred that the concentration of water ions in the high potential region of oil is higher. These water ions can obtain enough kinetic energy under an electric field to break the oil molecular chain and produce unsaturated carbon fragments, which form local conductive regions. Meanwhile, when the negative water ions reach the positive electrode, the charge exchange makes them revert to neutral water molecules. In the subsequent thermal diffusion process, water molecules will be converted into water ions, again due to collision and electron capture, thus repeating the migration process near the positive electrode. With the continuous impact of water-ions under an electric field, the carbonized components generated in the high potential region are extending thermally from the high to the low potential area in oil, and finally form a conductive channel between two electrodes, after which a large amount of electrons will be injected from the electrode to cause an avalanche breakdown, with the conductive channel being rapidly expanded by electron bombardment. Therefore, the thermal diffusion of water impurities in oil and the migration of water ions under an electric field initialize the electric breakdown process of transformer oil. According to MD simulations of water-oil-acid systems, thermal diffusion of water molecules will be significantly exacerbated by the presence of aging acid; we have therefore elucidated the insulation fracture mechanism of transformer oil with water impurities in the longer-term operation that produces the aging acids.

4. Conclusions The electrical breakdown mechanism of transformer oil that has water impurities and is used in long-term operation has been investigated by molecular dynamics simulations using first-principles electronic-structure calculations. The diffusion processes of water molecules in transformer oil with aging acid at different temperatures were dynamically simulated to evaluate the temperature and aging acid concentration that evidently affected the diffusion coefficient of water molecules in transformer oil. In first-principles calculations, a local area model of a water-oil system was used to theoretically reveal the electrical breakdown mechanism of transformer oil. Water molecules introduce unoccupied local states that capture electrons and transform them into negative water ions that will be accelerated to a high velocity and impact and break oil molecule chains, which can be aggravated by thermal diffusion of the water molecules. Carbonized components introduce impurity conduction mini-bands of electronic-states into the band-gap of oil molecules, which act as conductive regions that will thermally extend to form a conduction channel between electrodes. A large amount of electrons will be injected from the electrode into the conduction channel to discharge in an avalanche process of complete electric breakdown. For transformer oil containing water impurities, the thermal diffusion of water molecules and the high-velocity impact of water ions on oil molecules under a high electric field form conduction channels. Therefore, water impurities, which are expedited by aging acid in diffusion, play a role in initializing the electric breakdown process of transformer oil systems.

Author Contributions: Data curation and Formal analysis, B.C.; investigation and writing, J.-W.D.; project administration, M.-H.C. All authors have read and agreed to the published version of the manuscript. Funding: This research was funded by the National Key Research and Development Program of China (2017YFB0902704), the National Natural Science Foundation of China (Grant No. 51877056 and 51677046). Conﬂicts of Interest: The authors declare no conﬂict of interest. Crystals 2021, 11, 123 10 of 10

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