Fluid Degradation Measurement Based on a Dual Coil Frequency Response Analysis

sensors

Article Fluid Degradation Measurement Based on a Dual Coil Frequency Response Analysis

Jose M. Guerrero 1 , Alejandro E. Castilla 1, José Ángel Sánchez-Fernández 2 and Carlos A. Platero 1,*

1 Department of Automatic Control, Electrical and Electronic Engineering and Industrial Informatics, Universidad Politécnica de Madrid, E-28006 Madrid, Spain; [email protected] (J.M.G.); [email protected] (A.E.C.) 2 Department of Hydraulic, Energy and Environmental Engineering, Universidad Politécnica de Madrid, E-28040 Madrid, Spain; [email protected] * Correspondence: [email protected]

Received: 17 June 2020; Accepted: 23 July 2020; Published: 26 July 2020

Abstract: Electrical industry uses oils for cooling and insulation of several machines, such as power transformers. In addition, it uses water for cooling some synchronous generators. To avoid malfunctions in these assets, fluid quality should be preserved. To contribute to this aim, a sensor that detects changes in fluid composition is presented. The designed sensor is like a single-phase transformer whose magnetic core is the fluid whose properties will be measured. The response of this device to a frequency sweep is recorded. Through a comparison between any measurement and a reference one corresponding to a healthy state, pollutants presence, such as water in oil or salt in water, can be measured. The performance of the sensor was analyzed through simulation. In addition, a prototype was built and tested measuring water concentration in oil and salt content in water. The correlation between pollutant concentration measured with the sensor and known pollutant concentrations is good.

Keywords: degradation; fault diagnosis; frequency response analysis; predictive maintenance; oil insulation; capacitive sensors; magnetic sensors

1. Introduction Fluid degradation is responsible for numerous equipment failures. Since the use of fluids in industrial processes is extended to practically every area [1], its degradation is one of the most important parameters to control in an industrial installation. In many installations, fluids are used to evacuate the heat of an industrial process. For this reason, they are exposed to high temperatures that can cause the breakup of their molecules or at least their cracking [2]. This causes an alteration in the characteristics of the fluid [3] and, therefore, a significant reduction in the performance and efficiency of the industrial processes in what they are applied to. Another problem resulting from fluids degradation is their oxidation [4]. Chemical oxidation reactions take place when a fluid is exposed to air. This oxidation causes an increase in its viscosity [5]. It can even generate sediments [6,7], with the obvious damage the sediments can cause as they are deposited on duct walls or interact with the fluid. In the electrical field, oils are the fluids most widely used to insulate the conductors in high voltage application machines as well as used as a cooler, e.g., in power transformers [8]. In this case, the degradation of oil is mainly caused by the cellulose decomposition in water, which causes a lack of insulation properties in the oil [9].

Sensors 2020, 20, 4155; doi:10.3390/s20154155 www.mdpi.com/journal/sensors Sensors 2020, 20, 4155 2 of 17

Due to the fluid degradation issues mentioned above, continuous monitoring is very useful to know the fluid condition at all times. This knowledge allows the timely removal of the different components formed by fluid degradation through techniques such as decantation or distillation or, in situations with an advanced degradation, replacing the fluid with a new one to avoid possible future failures [10]. There are several measurement techniques currently used to evaluate fluid degradation [11,12]. They can be classified as chemical and electrical. These techniques can be complemented by some intelligent techniques to draw a conclusion about the degradation degree of the fluid under consideration. Although some other techniques have been proposed, they have not gained momentum [13]. Among the chemical techniques, dissolved gas analysis (DGA) is the most used [14,15]. It is usually accomplished through chromatography [16]. There are several methods to draw conclusions from a DGA. Most of them are based on ratios of different compound concentrations, such as the Doernenberg or the Rogers’ method. The Duval’s triangle and pentagons combine several ratios to achieve a diagnostic about transformer oil degradation [17,18]. Another technique used to evaluate fluid degradation is ultraviolet spectrophotometry [19]. It is based on determining the absorbance spectra of a fluid sample. Regarding electrical techniques, they can be classified as time domain and frequency domain [11]. These techniques analyze the dielectric response of the fluids. The polarization and depolarization current (PDC) and the recovery voltage (RV) measurements are time-domain based techniques [20]. The PDC method consists of applying a DC charging voltage to a sample and measuring the polarization current. Then, after removing the DC source, the sample is short-circuited, and the depolarization current is measured [21]. The RV method has a first part similar to the PDC method, i.e., applying a DC voltage to a sample. However, in the RV method, the voltage magnitude applied is measured. Then, the DC source is also removed, and the sample is also short-circuited. After a defined discharging period, the short circuit is cleared, and the remaining voltage is measured [22]. Frequency domain spectroscopy (FDS) consists in measuring the dielectric dissipation factor or loss factor of a sample [23]. From the electrical methods, fluid conductivity can be deduced [24]. It should be taken into account that the values obtained are temperature dependent. Therefore, this parameter should be constant to make comparisons between healthy and degraded fluid samples. Finally, some methods based on frequency response analysis (FRA) are used to diagnosis the state of electrical machines, such as power transformers [25]. FRA makes a frequency sweep injecting a fixed amplitude voltage, usually 1 V or 10 V (root mean square or RMS value), in terminals of the transformer, and analyzes the transfer function between its terminals. Depending on the state of the insulating fluid, i.e., the oil, the transfer function will differ depending on water concentration or temperature. Additionally, impedance polar plots are used [25]. One of the drawbacks of this method is the necessity of stopping the operation to perform the test. Online technologies for fluid degradation include the measurement of the complex permittivity produced by the insulator fluid among electrodes used as sensors, which changes with an increase in pollutant agents [26]. This research focuses on the design of a new sensor for measuring fluid degradation based on frequency response analysis. This sensor has two coils immersed in the fluid under test. Attending to the gain variation within a defined frequency range, the concentration of pollutant agents can be determined. The paper is structured as follows: Section2 explains the design of the proposed sensor. Then, Section3 describes a simulation model of the sensor, and Section4 reports the experimental measurements made to validate the designed sensor. Finally, Section5 presents the main contribution of the paper. Sensors 2020, 20, x FOR PEER REVIEW 3 of 17

Sensors 2020, 20, 4155 3 of 17 2. Materials and Methods SensorsSensors 20202020,, 2020,, xx FORFOR PEERPEER REVIEWREVIEW 33 ofof 1717 The proposed sensor is like a transformer where its windings are two coils, and its magnetic core 2. Materials and Methods is 2.the2. MaterialsMaterials fluid under andand test, MethodsMethods as shown in Figure 1. The voltage applied to the first coil causes the magnetic flux ThecommonTheThe proposed proposedproposed to both sensor sensorsensor coils. is isis like This likelike a a a transformer magnetic transformertransformer flux where wherewhere induces itsititss windingswindings a voltage areare in twotwo two the coils,coils, coils, second andand and itsitscoil. its magneticmagnetic magnetic This induced corecore core isvoltage theisis thethe fluid fluidisfluid measured under underunder test, test,test, by as astheas shown shownshown FRA in test inin Figure FigureFigure equipment.1 . 1.1. The TheThe voltage vovoltageltage applied appliedapplied toto the thethe first firstfirst coilcoil causescauses causes thethe the magneticmagnetic magnetic fluxfluxflux common commoncommon to toto both bothboth coils. coils.coils. This ThisThis magnetic magneticmagnetic flux fluxflux inducesininducesduces aa voltagevoltage in in thethe secondsecond coil.coil. coil. ThisThis This inducedinduced induced voltagevoltagevoltage is measuredisis measuredmeasured by byby the thethe FRA FRAFRA test testtest equipment. equipment.equipment.

Figure 1. Fluid core dual-coil sensor, magnetic flux scheme.

FigureFigure 1. 1.Fluid Fluid core core dual-coil dual-coil sensor,sensor, magneticmagnetic flux flux scheme. scheme. Both windings are alsoFigure capacitively 1. Fluid core coupled. dual-coil sensor, This capacitive magnetic flux coupling scheme. is increasingly important as theBoth frequency windings of are the also applied capacitively voltage coupled.increases. This The capacitive simplified coupling equivalent is increasingly circuit is displayed important in BothBoth windingswindings areare alsoalso capacitivelycapacitively coupled.coupled. ThisThis capacitivecapacitive couplingcoupling isis increasinglyincreasingly importantimportant asFigure the frequency 2. The increase of the or applied decrease voltage in fluid increases. permittivity The simplified implies higher equivalent or lower circuit leakage is displayed currents inin asas thethe frequencyfrequency ofof thethe appliedapplied voltagevoltage increases.increases. TheThe simplifiedsimplified equivalentequivalent circuitcircuit isis displayeddisplayed inin Figure2. The increase or decrease in fluid permittivity implies higher or lower leakage currents in the theFigureFigure system, 2.2. The Theas can increaseincrease be seen oror indecreasedecrease the scheme inin fluidfluid proposed permittivitypermittivity in Figure impliesimplies 2. higherhigher oror lowerlower leakageleakage currentscurrents inin system, as can be seen in the scheme proposed in Figure2. thethe system,system, asas cancan bebe seenseen inin thethe schemescheme proposedproposed inin FigureFigure 2.2.

FigureFigure 2.2. FrequencyFrequency responseresponse analysisanalysis (FRA)(FRA) testtest fluidfluid corecore dual-coildual-coil sensorsensor capacitycapacity couplingscouplings FigureFigure 2.2. FrequencyFrequency responseresponse analysisanalysis (FRA)(FRA) testtest fluidfluid corecore dual-coildual-coil sensorsensor capacitycapacity couplingscouplings simplifiedsimplified circuit. circuit. simplifiedsimplified circuit.circuit. AndAnd finally,finally, the effect effect of of fluid fluid resistivity resistivity (ρ ()ρ modifies) modifies the the energy energy losses losses in these in these couplings. couplings. The AndAnd finally,finally, thethe effecteffect ofof fluidfluid resistivityresistivity ((ρρ)) modifiesmodifies thethe energyenergy losseslosses inin thesethese couplings.couplings. TheThe Theinsulation insulation resistance resistance to ground, to ground, between between the windings the windings and andbetween between turns turns is modified is modified in case in caseof fluid of insulationinsulation resistanceresistance toto ground,ground, betweenbetween thethe windingswindings andand betweenbetween turnsturns isis modifiedmodified inin casecase ofof fluidfluid fluiddegradation. degradation. The simplified The simplified circuit circuit of the of fluid the fluid core coredual dualcoil is coil shown is shown in Figure in Figure 3. 3. degradation.degradation. TheThe simplifiedsimplified circuitcircuit ofof thethe fluidfluid corecore dualdual coilcoil isis shownshown inin FigureFigure 3.3.

Figure 3. FRA test fluid core dual-coil sensor simplified circuit. FigureFigureFigure 3.3. 3.FRA FRA FRA test testtest ﬂuidfluid corecore dual-coil dual-coildual-coil sensor sensor simplified simpliﬁedsimplified circuit. circuit. circuit. Sensors 2020, 20, 4155 4 of 17 Sensors 2020, 20, x FOR PEER REVIEW 4 of 17

ThisThis phenomenon phenomenon is is quite quite difficult difficult to to characteri characterizeze due due to to the the different different compounds present present in in a a fluidfluid [27]. [27]. The The interactions interactions among among these these compounds compounds can can cause resistance chan changes.ges. The The variations variations in in conductivity can be linear functions, such as in H2SO4–H2O electrolytes, logarithmic functions, as in conductivity can be linear functions, such as in H2SO4–H2O electrolytes, logarithmic functions, as in NaCl–H2O electrolytes, etc., which makes its characterization difficult. The design of the fluid core NaCl–H2O electrolytes, etc., which makes its characterization difficult. The design of the fluid core dual-coildual-coil sensor sensor prototype prototype is is show shownn in Figure 44a.a. AA coilcoil waswas placedplaced onon eacheach holder.holder. TheseThese coilscoils hadhad 2 NN == 200200 turns turns each, each, with with a a circular circular conductor conductor section of S = 0.20.2 mm mm2 andand 0.504 0.504 mm mm diameter. diameter. The The two two holdersholders must be placed placed vertically vertically and an empty empty cavi cavityty between between them. This This cavity cavity was was filled filled with with fluid fluid when the sensor was submerged in it. The The number number of of turns turns was was 200 200 to to keep the sensor compact but but with high enough resolution to observe fluidfluid behavior. ThisThis geometry geometry allowed allowed the the fluid fluid to to circulate circulate betw betweeneen both both coils. coils. A 3D A representation 3D representation of the of two the coiltwo holders, coil holders, one for one each for eachwiring wiring confronted confronted in a vertical in a vertical disposition, disposition, is pictured is pictured in Figure in Figure 4b. This4b. dispositionThis disposition allowed allowed the free the fluid free fluidcirculation circulation into the into core the corecolumn. column.

(a) (b)

Figure 4. Dual coil holders’ design (a) Fluid core dual coil holder dimensions. (b) Dual coil holders’ Figuredisposition. 4. Dual They coil were holders’ aligned design vertically (a) Fluid for core thefree dual fluid coil circulationholder dimensions. between them.(b) Dual coil holders’ disposition. They were aligned vertically for the free fluid circulation between them. Once the double coil was submerged in the fluid recipient and this fluid surrounded the sensor, a frequencyOnce the response double coil analyzer was submerged (FRA) test in equipment the fluid recipient was connected and this between fluid surrounded the terminals the sensor, of each acoil, frequency as shown response in Figure analyzer5. The input (FRA) voltage test equipm (U in) wasent was applied connected between between 1 and 1’ the terminals terminals of oneof each coil. coil,The amplitudeas shown in was Figure 1 V, 5. and The the input frequency voltage went (Uin) from was applied 20 Hz to between 20 MHz. 1 Theand voltage1’ terminals in the of other one coil. coil The(Uout amplitude) was measured was 1 byV, theand FRA the frequency test equipment. went from The input 20 Hz impedance to 20 MHz. of The the FRAvoltage test in equipment the other wascoil (Unormallyout) was ameasured 50 Ω resistor. by the FRA test equipment. The input impedance of the FRA test equipment was normally a 50 Ω resistor. The FRA test consisted of contrasting the input with the output voltage in the different frequencies range as (1): Sensors 2020, 20, 4155 5 of 17

SensorsThe 2020 FRA, 20, testx FOR consisted PEER REVIEW of contrasting the input with the output voltage in the diﬀerent frequencies5 of 17 Sensors 2020, 20, x FOR PEER REVIEW 5 of 17 range as (1): 𝑈 ! Uout A𝐴(dB𝑑𝐵)==20·log20 log 𝑈 (1) 𝐴𝑑𝐵 =20·log· Uin𝑈 (1) 𝑈 IfIf the the composition composition of of the the ﬂuid fluid changes, changes, then then the the FRA FRA test test results results will will also also change. change. If the composition of the fluid changes, then the FRA test results will also change.

1 Sensor 2 1 Sensor 2

Uout Uin Z Uout Uin Z

1'1' 2'2'

Figure 5. Frequency response analysis test equipment connections in the fluid core double coil sensor. FigureFigure 5. 5. Frequency Frequency response response analysis testtest equipment equipment connections connections in in the the fluid fluid core core double double coil coil sensor. sensor. To sum up, the Frequency Response Analysis test results, in general, depend on several factors relatedToTo to sum thesum fluidup, up, the asthe magneticFrequency Frequency permeability Response AnalysisAnalysis (µ), permittivity test test results, results, (ε), in andin general, general, resistivity depend depend (ρ). on In onseveral the several case factors of factors fluid degradation,relatedrelated to to the the a changefluid fluid asas in magneticmagnetic its composition permeability occurs, ((µµ),),and, permittivity permittivity therefore, (ε (),ε the ),and and FRA resistivity resistivity test results (ρ ).( ρIn). would Inthe the case change. case of of However,fluidfluid degradation, degradation, it should be aa change notedchange that, inin its in thecomposition cases presented occurs,occurs, (waterand, and, therefore, intherefore, oil and the saltthe FRA inFRA water), test test results thereresults would are would only change. However, it should be noted that, in the cases presented (water in oil and salt in water), there changeschange. inHowever, resistivity. it should be noted that, in the cases presented (water in oil and salt in water), there are only changes in resistivity. are onlyThe inductivechanges in coupling resistivity. will be significant in the low-frequency range. However, the capacitive The inductive coupling will be significant in the low-frequency range. However, the capacitive couplingThe of inductive the windings coupling will will have be more significant importance in the at low-frequency the high-frequency range. range. However, As the the capacitance capacitive coupling of the windings will have more importance at the high-frequency range. As the capacitance increases,coupling of the the impedance windings betweenwill have conductors more importance and ground at the decreases,high-frequency while range. the voltage As the drop capacitance in the increases, the impedance between conductors and ground decreases, while the voltage drop in the increases, the impedance between conductors and ground decreases, while the voltage drop in the systemsystem is lower,is lower, and and the the gain gain response response gets gets higher. higher. system is lower, and the gain response gets higher. Finally,Finally, if waterif water is is added added to to an an insulating insulating fluid, fluid, the the resistivityresistivity shouldshould decrease, making this this fluid fluid a Finally, if water is added to an insulating fluid, the resistivity should decrease, making this fluid bettera better conductor conductor for leakage for leakage currents. currents. This implies This implies a decrease a decrease in fluid resistancein fluid resistance and, by consequence, and, by aa lower consequence,better voltage conductor dropa lower infor the voltage leakage transfer drop function.currents. in the transfer ForThis this implies function. reason, a the Fordecrease gain this obtained reason, in fluid bythe registeringgainresistance obtained Uand,out bywill by consequence, a lower voltage drop in the transfer function. For this reason, the gain obtained by beregistering higher. Uout will be higher. registering Uout will be higher. 3. Simulations3. Simulations 3. Simulations ToTo make make simulations, simulations, a a model model of of the the proposed proposed sensorsensor was needed. needed. This This model model is isshown shown in inFigure Figure 6. 6. TheThe calculationTo calculation make simulations, process process consisted co a nsistedmodel of ofof solving the solving proposed this this circuit senscircuitor for wasfor di ffneeded.differenterent frequencies This frequencie model betweensis betweenshown 20in 20 HzFigure Hz and 6. 20Theand MHz. calculation 20 TheMHz. individual Theprocess individual calculationconsisted calculation of took solving into took account this into circuit account the circuitfor thedifferent parameters, circuit frequencieparameters, the variables betweenthe variable frequency 20 Hz voltageandfrequency 20 source,MHz. voltage andThethe source,individual voltmeter and thecalculation impedance. voltmeter tookimpedance. Therefore, into account theTherefore, Uout thewas the circuit obtained, Uout was parameters, obtained, and circuit andthe gain circuit variable could befrequencygain calculated, could voltage be as calculated, expressed source, asand in expressed Equation the voltmeter in (1). Equation impedance. (1). Therefore, the Uout was obtained, and circuit gainThe couldThe model modelbe calculated, was was based based as on expressedon the the traditional traditional in Equation equivalentequivalent (1). circuit circuit of of a a transformer, transformer, but but included included the the capacitivecapacitiveThe couplingsmodel couplings was and based and insulation insulation on the resistances. traditional resistances. Modelsequivalent Models similar similar circuit to theto of the onea transformer, one presented presented here but here canincluded becan found be the incapacitive thefound literature in thecouplings literature [28–30 ].and [28–30]. insulation resistances. Models similar to the one presented here can be found in the literature [28–30].

Figure 6. Electrical equivalent circuit used for simulations. Figure 6. Electrical equivalent circuit used for simulations.

Figure 6. Electrical equivalent circuit used for simulations. Sensors 2020, 20, 4155 6 of 17

The parameters of the equivalent circuit were calculated, attending to the geometrical coil disposition and materials, using well-known formulae. Later, they were ﬁne-tuned, attending to the initial conditions of an FRA test in the unpolluted main ﬂuid. The parameters of the equivalent circuit were: The coils resistances RCu1 and RCu2 were calculated from copper resistivity, wire section, length, and number of turns, as can be seen in Equation (2):

N lCu RCu = ρCu · (2) · SCu

2 where lCu was, according to Figure4, 0.167 m, the wire section (S Cu) was 0.2 mm , and the resistivity at 25 C was 0.0171 Ω mm2/m. ◦ · The initial values for the induction L1 and L2 were calculated as in (3):

N2 L = L = (3) 1 2 1 l µ · S where l was the average length of the magnetic circuit: 0.0867 m (2 times the length of the sensor limbs and the top and bottom yokes), and S was the section of the empty window of the sensor where the ﬂuid circulates (3.93 10 4 m2). × − Additionally, the capacitance between the sensor to the ground was estimated as the interaction between two equivalent wires of diameter, d, 0.504 mm in the middle of each coil, and using a relative electrical permittivity of 80.5, which corresponded to distillated water. Then (4) can be expressed as:

εrεo Cﬂuid = (4) DCu1Cu2 ln d where DCu1Cu2 was the distance between equivalent wires. The capacitance between turns has been calculated as the capacitance between two adjacent wires 2 µm apart and using the known expression below, (5):

εrεo Cturns = (5) 2d+2 [µm] ln d

On the other hand, the resistances between turns (Rturns1,Rturns2) and between coils were considered through the fluid (Rfluid). So, they were calculated as a direct multiplication between the fluid electrical resistivity (distillated water = 3 MΩ/cm) and the insulation length between cables or between equivalent cables. The magnetizing induction was initially considered 5 times lower than L1 and L2 to provoke high magnetizing currents. Finally, the parameters were adjusted, taking as reference the response to a test of the sensor submerged in a healthy fluid. The adjusted parameters are shown in Table1.

Table 1. Simulation model, initial parameters.

Parameter Value Units

RCu1 2.86 Ω 4 L1 9.87 10 H × − RCu2 2.86 Ω 4 L2 9.87 10 H × − Rturns1 2000 Ω 10 Cturns1 9.05 10 F × − Rturns2 2000 Ω 10 Cturns2 9.05 10− F × 7 Rﬂuid 2 10 Ω × 4 Lµ 1.97 10− H × 10 Cﬂuid 1.63 10 F × − Sensors 2020, 20, x FOR PEER REVIEW 7 of 17

Finally, the parameters were adjusted, taking as reference the response to a test of the sensor Sensors 2020, 20, 4155 7 of 17 submerged in a healthy fluid. The adjusted parameters are shown in Table 1. To verify the proposed methodology, circa 200 simulations were performed based on the already To verify the proposed methodology, circa 200 simulations were performed based on the already described equivalent circuit varying Rturns1, Rturns2, Cturns1, Cturns2, Lμ, Rfluid and Cfluid to achieve the described equivalent circuit varying R ,R ,C ,C ,L ,R and C to achieve the healthy-state fluid transfer function. Theturns1 fittingturns2 processturns1 was turns2done byµ comparingfluid thefluid simulation with healthy-state fluid transfer function. The fitting process was done by comparing the simulation with an experimental healthy-state salt in the water test, taking as reference the gain value in the plateau an experimental healthy-state salt in the water test, taking as reference the gain value in the plateau (between 200 Hz and 10 kHz) and the first resonance gain (between 200 and 500 kHz), in dB. As (between 200 Hz and 10 kHz) and the first resonance gain (between 200 and 500 kHz), in dB. As shown shown in Table 1, the impedances of the equivalent circuit of the proposed sensor were different from in Table1, the impedances of the equivalent circuit of the proposed sensor were di fferent from the the usual ones of iron core transformers. usual ones of iron core transformers. The simulations were performed, varying different parameters of the equivalent circuit. They The simulations were performed, varying different parameters of the equivalent circuit. They took took into account variations of the core-magnetizing inductance, fluid resistance, and capacitance into account variations of the core-magnetizing inductance, fluid resistance, and capacitance with the with the addition of component B into a fluid A. The simulations corresponded to the case of water addition of component B into a fluid A. The simulations corresponded to the case of water polluted with polluted with salt. Therefore, different salt (component B) quantities were added to water (main salt. Therefore, different salt (component B) quantities were added to water (main fluid). Increasing fluid). Increasing the frequency from 20 Hz to 20 MHz, emulating the sweeping stages of FRA the frequency from 20 Hz to 20 MHz, emulating the sweeping stages of FRA equipment, the following equipment, the following results were achieved varying the fluid resistance, inductance, and results were achieved varying the fluid resistance, inductance, and capacitance for salt additions of capacitance for salt additions of 0, 10, 20, 30 …, up to 100 ppm weight of salt in 1 L of water and 0, 10, 20, 30 ... , up to 100 ppm weight of salt in 1 L of water and registering Uout (see Figure7). registering Uout (see Figure 7). Furthermore, the values of the parameters that depend one fluid Furthermore, the values of the parameters that depend one fluid composition are displayed in Table2 composition are displayed in Table 2 for concentrations of 10, 20, 50, and 100 ppm of salt in water. for concentrations of 10, 20, 50, and 100 ppm of salt in water.

Figure 7. Simulation results for diﬀerent salt in water concentrations, from 0 ppm up to 100 ppm. Figure 7. Simulation results for different salt in water concentrations, from 0 ppm up to 100 ppm. In these simulations, where salt was added to water, the resistance parameter was highly aﬀected In these simulations, where salt was added to water, the resistance parameter was highly by the addition of the pollutant agent. This was caused by the ions that appeared when salt dissolved in affected by the addition of the pollutant agent. This was caused by the ions that appeared when salt distilled water. Then, the variation of Rturns1 and Rturns2 were the main factors of the resonant frequency dissolved in distilled water. Then, the variation of Rturns1 and Rturns2 were the main factors of the displacement. A lower value of these parameters implies a softer and lower-frequency resonance. resonant frequency displacement. A lower value of these parameters implies a softer and lower- frequencyTable resonance. 2. Simulation model, parameters’ evolution when the salt concentration in water varies.

TableParameter 2. Simulation model, 10 ppmparameters’ evolution 20 ppm when the salt 50 concentration ppm in 100 water ppm varies. 4 4 4 4 L1 (H) 9.87 10− 9.87 10− 9.87 10− 9.87 10− Parameter 10× ppm4 20 ppm× 4 50 ppm× 4 100 ppm× 4 L2 (H) 9.87 10− 9.87 10− 9.87 10− 9.87 10− L1 (H) 9.87× × 10−4 9.87 × 10−4 9.87 × 10× −4 9.87 × 10−4× Rturns1 (Ω) 780 612 446 349 C (F)L2 (H) 9.059.8710 × 1010−4 9.879.05 × 10 −410 9.879.05 × 1010−4 10 9.87 ×9.05 10−4 10 10 turns1 × − × − × − × − Rturns2R(turns1Ω) (Ω) 780780 612 612 446 446 349 349 10 10 10 10 C (F) 9.05 10 −10 9.05 10−10 9.05 −1100 9.05−10 10 turns2Cturns1 (F) 9.0×5 × −10 9.05 × 10− 9.05 × 10× − 9.05 × 10 × − R (Ω) 7.80 106 6.12 106 4.46 106 3.49 106 fluidRturns2 (Ω) ×780 612× 446 × 349 × L (H) 4 4 4 4 µ 1.97 10− −10 1.97 10−1−0 1.97 −1100 − 1.97−10 10− Cturns2 (F) 9.0×5 × 1010 9.05 ×× 10 10 9.05 × 10× 10 9.05 × 10 × 10 Cfluid (Ω) 1.63 10− 1.63 10− 1.63 10− 1.637 10− Rfluid (Ω) 7.×80 × 106 6.12× × 106 4.46 × ×106 3.49 × 106× Lμ (H) 1.97 × 10−4 1.97 × 10−4 1.97 × 10−4 1.97 × 10−4 The brine achieved implies an exponential reduction in water resistance or fast growth of the Cfluid (Ω) 1.63 × 10−10 1.63 × 10−10 1.63 × 10−10 1.637 × 10−10 conductivity that increased from 0.5 µS/cm to approximately 5000 µS/cm for a 0.05 mol/L at a standard Sensors 2020, 20, x FOR PEER REVIEW 8 of 17 Sensors 2020, 20, 4155 8 of 17 The brine achieved implies an exponential reduction in water resistance or fast growth of the conductivity that increased from 0.5 μS/cm to approximately 5000 μS/cm for a 0.05 mol/L at a standardtemperature temperature of 25 ◦C dissolution of 25 °C dissolution according to accord [27]. Theing capacitanceto [27]. The and capacitance inductance and had inductance small changes. had Thesmall capacitance changes. becameThe capacitance lower than became in healthy lower conditions than in because healthy the conditions relative permittivity because the of a relative 2 mol/L permittivitybrine was 55 of versus a 2 mol/L 80.5 ofbrine distilled was 55 water. versus However, 80.5 of distilled the differences water. However, were extremely the differences low due towere the extremelysmall variations low due in saltto the concentrations. small variations The in inductive salt concentrations. part of the systemThe inductive also remained part of nearlythe system constant, also remainedbeing salt nearly a diamagnetic constant, material. being salt a diamagnetic material. Although different different concentrations of pollutant pr producedoduced different different results in the FRA tests that lead to didifferentfferent R,R, L,L, CC values, values, the the minimum minimum peak peak achieved achieved in in every every frequency frequency sweep sweep was was located located in inthe the same same frequency frequency range range (20 (20 kHz–200 kHz–200 kHz), kHz), as as shown shown in in Figure Figure7 .7. This This di differencefference between relative minimums allowedallowed thethe sensorsensor to to distinguish distinguish the the extent extent to to which which the the polluting polluting agent agent was was affecting affecting the themain main fluid. fluid. To thisTo this aim, aim, the the FRA FRA results results from from a polluting a polluting agent agent concentration concentration should should be be compared compared to tothe the corresponding corresponding healthy healthy state state FRA FRA test test (0 ppm(0 ppm of saltof salt in water).in water). As thethe interactioninteraction between between fluids fluids alters alters the the frequency frequency response, response, a database a database should should be created be created with withdifferent different fluid fluid contaminations contaminations depending depending on the on application the application of fluid of monitored.fluid monitored. The simulations The simulations were performedwere performed for salt for in salt water. in water. Other Other fluids fluids were notwere simulated. not simulated. Once the simulations were carried out, some expe experimentalrimental tests in a prototype must be done to validate the proposedproposed sensor. In addition,addition, thethe parametersparameters thatthat changechange withwith contaminationscontaminations shouldshould be determined.

4. Experimental Experimental Setup According to the proposed methodology, impuritiesimpurities or degradation symptoms in fluidsfluids could be detected by performing an FRA test with the pr proposedoposed sensor. However, the fluid fluid must be tested previously in reference conditions. This firstfirst test is considered a reference test. Future tests should be compared to the reference testtest toto determinedetermine ifif therethere isis anyany changechange inin fluidfluid composition.composition. In the firstfirst setset ofof tests, tests, some some quantities quantities of of NaCl NaCl were were added added to waterto water to modifyto modify its properties.its properties. In the In thesecond second set of set tests, of sometests, quantitiessome quantities of water of were water added were to transformeradded to transformer oil, emulating oil, theemulating degradation the degradationin a real power in a transformer. real power transformer. Before the experiments, an experimental setup waswas prepared. It consisted of the proposed proposed sensor that was going to be submerged in the tested fluidfluid (See FigureFigure8 8).). InIn thethe firstfirst coil,coil, aa voltagevoltage sourcesource applied a 1 VRMS sinusoidalsinusoidal wave. wave. The The frequency frequency of of the the voltag voltagee source source varied varied from from 20 20 Hz Hz to to 20 20 MHz. MHz. The voltagevoltage inin thethe second second coil coil was was measured measured and and compared compared to theto the voltage voltage applied applied to the to firstthe first one. one. The TheFRA FRA test equipment’stest equipment’s main main characteristics characteristics are displayed are displayed in Table in Table3. 3.

Figure 8. FluidFluid core double coil sensor used in the experimental setup.

Once the connectionsconnections werewere done,done, thethe sensor sensor was was submerged submerged in in a a two-liter two-liter container, container, as as shown shown in inFigure Figure9. The 9. The container container was ﬁlledwas filled with thewith ﬂuid the under fluid test,under while test, a secondwhile a dissolution second dissolution was prepared was preparedoutside with outside the pollutant with the agent.pollutant agent. Sensors 2020, 20, x FOR PEER REVIEW 9 of 17

Sensors 2020,, 20,, 4155x FOR PEER REVIEW 9 of 17 Table 3. Frequency response analysis (FRA) equipment’s main characteristics. Table 3. Frequency response analysis (FRA) equipment’s main characteristics. Parameter Value Table 3. Frequency response analysis (FRA) equipment’s main characteristics. FrequencyParameter range 10 Hz–20Value MHz OutputFrequencyParameter Impedance range 10 Hz–20 Value50 Ω MHz AccuracyOutputFrequency (down Impedance rangeto −80 dB) 10 Hz–20< 500.1 Ω dBMHz AccuracyAccuracyOutput (down (down Impedance to to − 80−100 dB) < 0.1 50 Ω dB Accuracy (down to 80 dB) << 0.30.1 dB Accuracy (downdB) to− −100 Accuracy (down to 100 dB) << 0.30.3 dB dB) −

Figure 9. Two-liter container with the fluid core double coil sensor. Figure 9. Two-liter container with the fluid core double coil sensor. Figure 9. Two-liter container with the fluid core double coil sensor. The tests were performed at constant temperature conditions. The container was placed in a The tests were performed at constant temperature conditions. The container was placed in a controlledThe tests temperature were performed tank (see at Figure constant 10). temperat The tempureerature conditions. of the referenceThe container test should was placed be close in toa controlled temperature tank (see Figure 10). The temperature of the reference test should be close controlledthe normal temperature condition operatingtank (see Figuretemperature, 10). The e.g. temp, oilerature and waterof the referencetests, emulating test should a transformer be close to to the normal condition operating temperature, e.g., oil and water tests, emulating a transformer thecellulose normal decomposition condition operating from the temperature,insulation materials, e.g., oil were and performedwater tests, at emulating70 °C. Then, a thetransformer addition cellulose decomposition from the insulation materials, were performed at 70 ◦C. Then, the addition of celluloseof a second decomposition component wasfrom done the insulation with the aimmaterials, of carrying were performedout different at 70FRA °C. tests Then, with the differentaddition a second component was done with the aim of carrying out different FRA tests with different pollutant ofpollutant a second agent component concentrations. was done The with FRA the connections aim of carrying to the experimentout different are FRA displayed tests with in Figure different 11, agent concentrations. The FRA connections to the experiment are displayed in Figure 11, where the pollutantwhere the agent whole concentrations. system can be The observed FRA connections (from left to to right: the experiment FRA Equipment, are displayed computer in Figurefor signal 11, whole system can be observed (from left to right: FRA Equipment, computer for signal monitoring, wheremonitoring, the whole and the system recipient can bewith observed the tested (from flui leftd). Onceto right: the FRAconnections Equipment, were computerdone, the forFRA signal tests and the recipient with the tested fluid). Once the connections were done, the FRA tests were performed, monitoring,were performed, and thetaking recipient around with 5 min the per tested test. flui d). Once the connections were done, the FRA tests taking around 5 min per test. were performed, taking around 5 min per test.

Figure 10. Controlled temperature of the dissolution of oil and water at 70 C. Figure 10. Controlled temperature of the dissolution of oil and water at 70 ◦°C. Figure 10. Controlled temperature of the dissolution of oil and water at 70 °C. Sensors 2020, 20, x FOR PEER REVIEW 10 of 17

Sensors 2020, 20, 4155x FOR PEER REVIEW 10 of 17

Figure 11. FRA test connections to the two-liter container. No thermostable bath was done in this test. Figure 11. FRA test connections to the two-liter container. No thermostable bath was done in this test. Figure 11. FRA test connections to the two-liter container. No thermostable bath was done in this test. As electric conductivity depends on temperature [31], the FRA test results will be affected by As electric conductivity depends on temperature [31], the FRA test results will be affected by operatingAs electric temperature. conductivity Therefore depends, the ontemperature temperature of the[31], different the FRA tests test shouldresults bewill constant. be affected Hence, by operating temperature. Therefore, the temperature of the different tests should be constant. Hence, operatingcontrasting temperature. the tests and Therefore, the reference the testtemperature can be done. of the In differentthis paper, tests only should one-constant be constant. temperature Hence, contrasting the tests and the reference test can be done. In this paper, only one-constant temperature contrastingtests were carried the tests out. and the reference test can be done. In this paper, only one-constant temperature tests were carried out. tests were carried out. 4.1. Distilled Water Contaminated with Salt Experimental Tests 4.1. Distilled Water Contaminated with Salt Experimental Tests 4.1. DistilledFirstly, Watera set of Contaminated experiments with with Salt pure Experimental distilled water Tests with additions of salt was conducted. The Firstly, a set of experiments with pure distilled water with additions of salt was conducted. tests were performed with 1.7 L of water in a recipient. An additional dissolution of salt in 1 L of The testsFirstly, were a set performed of experiments with 1.7 with L ofpure water distil inled a recipient. water with An additions additional of dissolutionsalt was conducted. of salt in The 1 L water was used to add small ppms of salt to the first recipient. With those recipients, the addition of testsof water were was performed used to add with small 1.7 L ppms of water of salt in toa therecipi firstent. recipient. An additional With those dissolution recipients, of salt the in addition 1 L of the brine in the first container was progressive, then only 2.7 L of water and less than 1 g of NaCl waterof the was brine used in the to firstadd containersmall ppms was of progressive,salt to the firs thent recipient. only 2.7 With L of those water recipients, and less than the 1addition g of NaCl of were used. werethe brine used. in the first container was progressive, then only 2.7 L of water and less than 1 g of NaCl They consisted of filling the container with pure distilled water and dive the sensor in the wereThey used. consisted of filling the container with pure distilled water and dive the sensor in the container. After this, an FRA test was performed, obtaining the results shown in Figure 12. In this container.They consisted After this, of an filling FRA testthe wascontainer performed, with pu obtainingre distilled the resultswater and shown dive in the Figure sensor 12. Inin thisthe figure, the frequency response of pure distilled water can be seen. This test corresponded to a healthy container.figure, the frequencyAfter this, responsean FRA test of pure was distilled performed, water obtaining can be seen. the results This test shown corresponded in Figure to 12. a healthyIn this state of the fluid, and it has been be considered as the reference test. The frequency of test injection figure,state of the the frequency fluid, and response it has been of pure be considered distilled water as the can reference be seen. test. This Thetest frequencycorresponded of test to a injection healthy equipment went from 20 Hz up to 20 MHz. stateequipment of the wentfluid, fromand it 20 has Hz been up to be 20 considered MHz. as the reference test. The frequency of test injection equipment went from 20 Hz up to 20 MHz.

Figure 12. FRA test results with pure distillated water. Reference test. Figure 12. FRA test results with pure distillated water. Reference test. Figure 12. FRA test results with pure distillated water. Reference test. Sensors 2020, 20, x FOR PEER REVIEW 11 of 17

Sensors 2020, 20, 4155 11 of 17 SensorsThe 2020 next, 20, x stepFOR PEERwas REVIEWthe addition of salt at an approximate ratio of 15 ppm. The effects 11in ofthe 17 frequency response can be observed in Figures 13 and 14. In them, the results of tests for salt The next step was the addition of salt at an approximate ratio of 15 ppm. The effects in the concentrationsThe next stepvarying was from the addition 15 ppm to of 305 salt ppm at an are approximate shown. The ratio FRA of results 15 ppm. were The clearly eﬀects different in the frequency response can be observed in Figures 13 and 14. In them, the results of tests for salt frequencydepending responseon the quantity can be of observedsalt in water. in FiguresAs can be13 observed and 14., the In them,resonant the frequency results of and tests amplitude for salt concentrations varying from 15 ppm to 305 ppm are shown. The FRA results were clearly different concentrationschanged in a monotonic varying fromway. 15This ppm is an to important 305 ppm are fact shown. to determine The FRA theresults quantity were of salt clearly in the di ﬀwater.erent depending on the quantity of salt in water. As can be observed, the resonant frequency and amplitude dependingIn these experimental on the quantity tests, of a saltreso inlution water. of As15 ppm can be was observed, corroborated the resonant. frequency and amplitude changed in a monotonic way. This is an important fact to determine the quantity of salt in the water. changed in a monotonic way. This is an important fact to determine the quantity of salt in the water. In these experimental tests, a resolution of 15 ppm was corroborated. In these experimental tests, a resolution of 15 ppm was corroborated.

Figure 13. FRA test results from 15 ppm up to 305 ppm of salt in water. Figure 13. FRA test results from 15 ppm up to 305 ppm of salt in water. Figure 13. FRA test results from 15 ppm up to 305 ppm of salt in water.

Figure 14. FRA test results from 15 ppm up to 305 ppm of salt in water. Zoom (100 kHz to 500 kHz). Figure 14. FRA test results from 15 ppm up to 305 ppm of salt in water. Zoom (100 kHz to 500 kHz). A comparison of the last test, with water polluted at 305 ppm of salt, and the reference test, Figure 14. FRA test results from 15 ppm up to 305 ppm of salt in water. Zoom (100 kHz to 500 kHz). with pureA comparison distilled water, of the is last presented test, with inFigure water 15polluted. It can beat 305 clearly ppm observed of salt, and how the the reference frequency test response, with pure distilled water, is presented in Figure 15. It can be clearly observed how the frequency response variedA incomparison the range ofof 100–500the last test kHz, with (see Figurewater polluted14). However, at 305 atppm low of frequencies, salt, and the impedance reference remainedtest, with varied in the range of 100–500 kHz (see Figure 14). However, at low frequencies, impedance remained almostpure distilled constant, water and, is the presented FRA results in Figure were not15. I influencedt can be clearly by the observed addition how of salt. the frequency response almost constant, and the FRA results were not influenced by the addition of salt. varieInd in Figure the range 15, of a 10 second0–500 kHz resonance (see Figure appeared 14). However, that should at low be frequencies, provoked impedance by the added remain salt.ed WhenalmostIn comparing constantFigure 15,, and thisa second the figure FRA resonance with results Figure were appeared 13 not, this influe secondthatn shouldced resonant by thebe provokedaddition peak did of notby salt appearthe. added in simulations. salt. When Thiscomparing is because this thisfigure model with hasFigure been 13, fitted this tosecond get an resonant optimum peak response did not in app theear frequency in simulations. range of This up In Figure 15, a second resonance appeared that should be provoked by the added salt. When tois because 500 kHz. this model has been fitted to get an optimum response in the frequency range of up to 500 kHz. comparingTo estimate this figure the salt with quantity Figure by 13, the this analysis second of resonant the FRA results,peak did the not gains app atear the in resonant simulations. frequency This wereis because used. this These model gains has correspondedbeen fitted to get to thean optimum minimum response gains in in the the frequency frequency rangerange fromof up 100to 500 kHz kHz. to 500 kHz. The minimum gains vary in a monotonic way, as shown in Figure 16. Sensors 2020, 20, x FOR PEER REVIEW 12 of 17

SensorsSensors 20202020,,20 20,, 4155x FOR PEER REVIEW 1212 ofof 1717

Figure 15. FRA tests for a transformer with distillated water core with salt. Tests compare distilled water and water with 305 ppm of salt.

To estimate the salt quantity by the analysis of the FRA results, the gains at the resonant frequencyFigure were 15. FRA used tests. These for a gains transformer correspond with distillateded to the waterminimum core withgains salt. in the Tests frequency compare distilledrange from Figure 15. FRA tests for a transformer with distillated water core with salt. Tests compare distilled 100 kHzwater to and500 waterkHz. withThe 305minimum ppm of salt.gains vary in a monotonic way, as shown in Figure 16. water and water with 305 ppm of salt.

To estimate the salt quantity by the analysis of the FRA results, the gains at the resonant frequency were used. These gains corresponded to the minimum gains in the frequency range from 100 kHz to 500 kHz. The minimum gains vary in a monotonic way, as shown in Figure 16.

Figure 16. Measures of the minimum value of gains in the range of 100 kHz up to 500 kHz and the Figure 16. Measures of the minimum value of gains in the range of 100 kHz up to 500 kHz and the fitted curve. fitted curve. Data presented in Figure 16 can be fitted by Equation (6) achieving a coefficient of determination, Data presented in Figure 16 can be fitted by Equation (6) achieving a coefficient of determination, R2, of 0.9987: 2 R , of 0.9987: α A β A C[ppm] = f (A[dB]) = k e · + k e · (6) Figure 16. Measures of the minimum value of gains in 1the· range2 of· 100 kHz up to 500 kHz and the 퐶[ppm] = 푓(퐴[dB]) = 푘 · 푒훼·퐴 + 푘 · 푒훽·퐴 (6) wherefitted curve. 1 2 5 Where k1 = 1.102 10 ; k2 = 24.13 ; α = 0.1512 ; β = 0.01762 Data presented in Figure 16× can be fitted− by Equation (6) achieving− a coefficient of determination, 5 R2, ofThese 0.9987 results: corroborate푘1 = 1.102 × the10 possibility ; 푘2 = −24 of.13 characterizing ; 훼 = 0.1512 ; water훽 = −0 contamination.01762 with salt by FRA analysis. These results corroborate the possibility of characterizing훼·퐴 water contamination훽·퐴 with salt by FRA 퐶[ppm] = 푓(퐴[dB]) = 푘1 · 푒 + 푘2 · 푒 (6) analysis. 4.2.Where Oil Contaminated with Water Experimental Tests 4.2. OilThese Contaminated second laboratory with Water experimentalExperimental5 Tests tests aimed to detect water in power transformer oil. 푘1 = 1.102 × 10 ; 푘2 = −24.13 ; 훼 = 0.1512 ; 훽 = −0.01762 During the lifetime of power transformers, insulation degrades, especially at the end of their useful life. These second laboratory experimental tests aimed to detect water in power transformer oil. DuringThese results this process, corroborate water the is releasedpossibility from of cellulose,characterizing which water is one contamination of the main components with salt by of FRA the During the lifetime of power transformers, insulation degrades, especially at the end of their useful life. insulationanalysis. system of a power transformer. In addition, water is mixed with oil; therefore, it is essential During this process, water is released from cellulose, which is one of the main components of to monitor the content of water in oil. High concentrations of water can initiate partial discharges and the4.2. insulation Oil Contaminated system withof a Waterpower Experimental transformer. Tests In addition, water is mixed with oil; therefore, it is even cause catastrophic failures in power transformers. These phenomena occur when the cellulose of essential to monitor the content of water in oil. High concentrations of water can initiate partial the insulatingThese second Kraft laboratory paper decomposes. experimental tests aimed to detect water in power transformer oil. DuringIn thisthe life case,time the of tests power were transformers, performed insulation with 1.7 L degrade of oil ands, especially an additional at the dissolution end of their of useful 1 gram life of. waterDuring in 1 L ofthis oil process, that allowed water the is additionreleased offrom water cellulose, in 1 or 10which ppm is increments one of the tomain the maincomponents recipient. of the insulation system of a power transformer. In addition, water is mixed with oil; therefore, it is essential to monitor the content of water in oil. High concentrations of water can initiate partial Sensors 2020, 20, x FOR PEER REVIEW 13 of 17 Sensors 2020, 20, x FOR PEER REVIEW 13 of 17 discharges and even cause catastrophic failures in power transformers. These phenomena occur discharges and even cause catastrophic failures in power transformers. These phenomena occur when the cellulose of the insulating Kraft paper decomposes. when the cellulose of the insulating Kraft paper decomposes. In this case, the tests were performed with 1.7 L of oil and an additional dissolution of 1 gram of SensorsIn2020 this, 20 case,, 4155 the tests were performed with 1.7 L of oil and an additional dissolution of 1 gram13 of of 17 water in 1 L of oil that allowed the addition of water in 1 or 10 ppm increments to the main recipient. water in 1 L of oil that allowed the addition of water in 1 or 10 ppm increments to the main recipient. The objective of these experimental tests was to measure in ppm the concentration of water in The objective of these experimental tests was to measure in ppm the concentration of water in oil usingThe objectiveFRA tests of. these experimental tests was to measure in ppm the concentration of water in oil oil using FRA tests. usingNumerous FRA tests. tests with oil and water were performed. The test results are displayed in Figure 17. Numerous tests with oil and water were performed. The test results are displayed in Figure 17. The pNumerousrocedure was tests similar with oil toand the waterprevious were tests performed.. However, The now test the results pollutant are displayed agent was in water. Figure The 17. The procedure was similar to the previous tests. However, now the pollutant agent was water. The Thetests procedure were carried was out similar from to 1 the ppm previous up to 1000 tests. ppm However, of water now in the 1.7 pollutant L of oil. agentThe water was water. contamination The tests tests were carried out from 1 ppm up to 1000 ppm of water in 1.7 L of oil. The water contamination wereaddition carried steps out were from 1, 1 2 ppm … up up to to 10 1000 ppm, ppm 10, of 20 water … up in to 1.7 100 L ofand oil. finally The water 100, 200 contamination … up to 1000 addition ppm. addition steps were 1, 2 … up to 10 ppm, 10, 20 … up to 100 and finally 100, 200 … up to 1000 ppm. steps were 1, 2 ... up to 10 ppm, 10, 20 ... up to 100 and finally 100, 200 ... up to 1000 ppm.

Figure 17. FFRARA test results for dissolutionsdissolutions of oil and water from 1 toto 10001000 ppmppm ofof waterwater inin oil.oil. Figure 17. FRA test results for dissolutions of oil and water from 1 to 1000 ppm of water in oil. InIn thesethese tests,tests, thethe resonant frequencyfrequency rangerange wentwent fromfrom 33 MHzMHz upup toto 44 MHzMHz because of the higherhigher In these tests, the resonant frequency range went from 3 MHz up to 4 MHz because of the higher insulationinsulation capacitycapacity andand resistanceresistance ofof oiloil comparedcompared withwith water.water. InIn thisthis range,range, thethe variationvariation inin gain was insulation capacity and resistance of oil compared with water. In this range, the variation in gain was smallsmall but but not not negligible. negligible. Comparing Comparing Figure Figure 17 with 17 with Figure Figure 15, in oil 15, and in water oil and mixtures, water mixtures, the frequency the small but not negligible. Comparing Figure 17 with Figure 15, in oil and water mixtures, the resonancefrequency was resonance already was present already in a healthy present state, in a andhealthy water state addition, and smoothed water addition it. However, smooth ined salt it. frequency resonance was already present in a healthy state, and water addition smoothed it. andHowever, water mixtures,in salt and the water behavior mixtures was, the behavior opposite. was the opposite. However, in salt and water mixtures, the behavior was the opposite. The evidenceevidence of how the FRA variedvaried due to the additionaddition of water is shown in FigureFigure 1818,, wherewhere The evidence of how the FRA varied due to the addition of water is shown in Figure 18, where thethe gaingain waswas plottedplotted againstagainst thethe concentrationconcentration ofof waterwater inin oil.oil. In these experiments, 1 ppm resolution the gain was plotted against the concentration of water in oil. In these experiments, 1 ppm resolution waswas achieved.achieved. To To get thisthis sensitivity,sensitivity, aa good good ﬂuidfluid circulation circulation and and homogenization homogenization of the the mixture mixture was achieved. To get this sensitivity, a good fluid circulation and homogenization of the mixture waswas required.required. was required.

Figure 18. Measures of the minimum value of gain in the range of 3 MHz up to 4 MHz and the Figure 18. Measures of the minimum value of gain in the range of 3 MHz up to 4 MHz and the fitted curve. ﬁttedFigure curve. 18. Measures of the minimum value of gain in the range of 3 MHz up to 4 MHz and the fitted curve.

In this case, the most accurate model adjustment was a model of gain from water concentration, as shown in (7) γ C δ C A[dB] = f (C[ppm]) = k0 e · + k0 e · (7) 1· 2· Sensors 2020, 20, 4155 14 of 17

Afterward, the concentration could be estimated thanks to a lookup table made from the previous model. In this case, the model parameters were:

5 k0 = 5.279 ; k0 = 72.72 ; γ = 0.07425 ; δ = 4.391 10− 1 − 2 − − × with a regression coeﬃcient of 0.9843. Due to the low conductivity of the transformer oil, the accuracy of the method was lower than in the previous cases with water and salt. However, thanks to the 3.4 MHz minimum peak, the concentration of water in oil could be calculated.

5. Conclusions Fluid degradation is the cause of failure in many industrial processes or machines. For example, in the field of electrical machines, power transformers and large turbo-generators need pure oil and water, respectively. In power transformers, the oil, used as cooling and insulating medium, should not be contaminated with water. Otherwise, insulation failures can take place with severe consequences. In large generators, the cooling systems comprise pure water to directly cool down the stator windings. This water should have an extremely low conductivity; otherwise, an internal fault could take place. In the paper, the design of a fluid core double coil sensor prototype was presented. The prototype was manufactured, and numerous experimental tests were performed to detect contamination of pure water with salt and contamination of transformer oil with water. In both cases, it was possible not only to detect contamination but also to estimate the amount of contaminant. For this, the minimum gain in the transfer function, corresponding to the resonant frequency was analyzed. Monotonic behaviors were observed in both cases. Hence, fit curves were calculated. In addition, a simulation model was presented. The simulation model was based on the equivalent electric circuit of the double coil sensor. In this case, pure water contaminated with salt was used for the simulations. Numerous simulations were carried out, varying the components of the equivalent electric circuit of the model according to the salt quantity in the water. Similar results to the experimental tests were obtained. In this paper, a novel sensor to detect fluid degradation or contamination was presented. The diagnosis technique was based on analyzing the frequency response analysis (FRA) of the sensor immersed in the tested fluid. The sensor comprised two coils with an open core. The first coil was fed at constant voltage with variable frequency (from 20 Hz to 20 MHz), while the voltage in the second coil was recorded. Afterward, its transfer function was calculated, dividing the voltage measured in the second coil with the voltage injected in the first one. The FRA test performed in normal operating conditions was considered as the reference test. The changes in the FRA tests were due to variations in the magnetic permeability, electric permittivity, and resistivity of the fluid. Therefore, if there is a contamination or degradation in the fluid, it can be detected by comparing an FRA test with the FRA reference test. In terms of future research, the double-coil sensor dived in the power transformer tank must be tested with higher voltages, so as to create higher fluxes that would induce larger voltages in the second coil and improve the sensitivity of the method. Besides, temperature influence will be considered and corrected with experimental parameters to standard ranges. For this, numerous experimental FRA tests must be conducted for different temperatures and pollution sweeps. These improvements can be important for developing a sensor that allows online fluid degradation measurement.

6. Patents As a result of this work, a patent has been applied for, Spanish Patent P202030539 “Sistema y método de medición de degradación o contaminación de ﬂuidos mediante un sensor inductivo de núcleo hueco”. Sensors 2020, 20, 4155 15 of 17

Author Contributions: Conceptualization, C.A.P.; methodology, J.M.G.; validation, A.E.C.; formal analysis, J.M.G. and A.E.C.; investigation, J.M.G., A.E.C., J.Á.S.-F., and C.A.P.; resources, A.E.C. and C.A.P.; writing—original draft preparation, A.E.C. and J.M.G.; writing—review and editing J.M.G., J.Á.S.-F., and C.A.P.; supervision, J.Á.S.-F. and C.A.P.; project administration, J.Á.S.-F. All authors have read and agreed to the published version of the manuscript. Funding: This research was funded by Universidad Politécnica de Madrid, grant number RP1604330010. Acknowledgments: The authors gratefully acknowledge the contributions of Allani, Díaz, Talavera, Peña, and Martín for their implication in this work. Conﬂicts of Interest: The authors declare no conﬂict of interest.

Nomenclature

A Gain α Mathematical coefficient (salt in water model) β Mathematical coefficient (salt in water model) C Pollutant agent concentration Cfluid Fluid capacitance between coils and ground Cturns1 Capacitance between turns in first coil Cturns2 Capacitance between turns in second coil γ Mathematical coefficient (water in oil model) d Wire diameter DCu1Cu2 Distance between equivalent conductors δ Mathematical coefficient (water in oil model) ε Electric permittivity k1 Mathematical coefficient (salt in water model) k2 Mathematical coefficient (salt in water model) 0 k1 Mathematical coefficient (water in oil model) 0 k2 Mathematical coefficient (water in oil model) l Average length of the magnetic circuit L1 First coil inductance L2 Second coil inductance lCu Conductor’s length Lµ Magnetizing inductance N Turns number µ Magnetic permeability RCu1 First coil wire resistance RCu2 Second coil wire resistance Rfluid Fluid resistance between coils and ground Rturns1 Resistance between turns in first coil Rturns2 Resistance between turns in second coil ρ Electric resistivity S Magnetic gap section SCu Conductor’s section Uin Input voltage Uout Output voltage Z Impedance

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