Design Implication of a Distribution Transformer in Solar Power Plants Based on Its Harmonic Profile

energies

Article Design Implication of a Distribution Transformer in Solar Power Plants Based on Its Harmonic Proﬁle

Iván Rafael Macías Ruiz 1, Luis Alonso Trujillo Guajardo 2,* , Luis Humberto Rodríguez Alfaro 2 , Fernando Salinas Salinas 2 , Johnny Rodríguez Maldonado 2 and Mario Alberto González Vázquez 2

1 PROLEC GE, Blvd Carlos Salinas Km. 7, Apodaca N.L. C.P. 66600, Mexico; [email protected] 2 Universidad Autónoma de Nuevo Leon, UANL, FIME, Av. Universidad S/N Ciudad Universitaria, San Nicolás de los Garza N.L. C.P. 66451, Mexico; [email protected] (L.H.R.A.); [email protected] (F.S.S.); [email protected] (J.R.M.); [email protected] (M.A.G.V.) * Correspondence: [email protected]; Tel.: +52-81-83294020

Abstract: This article presents a comparative analysis for the design considerations for a solar power generation transformer. One of the main existing problems in transformer manufacturing is in the renewable energy field, specifically the solar power generation, where the transformer connected to the inverter is operated under a certain harmonic content and operating conditions. The operating conditions of the transformer connected to the inverter are particularly unknown for each solar power plant; thus, the transformer will be subject to a particular harmonic content, which is defined by the inverter of the solar power plant. First, the fundamental calculations for solar power plant transformer and the proposed methodology for the design calculation of the distribution pad-mounted three phase transformer are presented. Then, a design study case is Citation: Macías Ruiz, I.R.; Trujillo described where a distribution transformer and an inverter of a particular solar power plant are Guajardo, L.A.; Rodríguez Alfaro, used for the analysis. Next, the transformer under analysis is modeled using finite element analysis L.H.; Salinas Salinas, F.; Rodríguez ® Maldonado, J.; González Vázquez, in ANSYS Maxwell software, where the transformer will be designed for a non-harmonic and M.A. Design Implication of a Distribution harmonic content application. Lastly, the main design parameters, flux density, the core losses Transformer in Solar Power Plants and the winding excitation voltage of the transformer are calculated and presented in results and Based on Its Harmonic Profile. discussion section. Energies 2021, 14, 1362. https:// doi.org/10.3390/en14051362 Keywords: renewable energy; solar power generation transformer; finite element analysis; harmonics

Academic Editor: Sérgio Cruz

Received: 3 February 2021 1. Introduction Accepted: 26 February 2021 The operation conditions and grid integration of solar power generation (SPG) are Published: 2 March 2021 very particular, similarly to other renewable energy generation systems such as wind power plants (WPP). Solar power generation using photovoltaics involves several technical Publisher’s Note: MDPI stays neutral specifications for its primary equipment, mainly for the selection and sizing of the power with regard to jurisdictional claims in transformer connected to the inverter of the solar power plant (SPP). One main aspect of the published maps and institutional affil- iations. power transformer operation in SPP is the current harmonic content caused by the inverter. The power transformer should be designed for specific operation conditions of SPP generation, specifically the harmonic frequencies generated by the inverter. Thus, this is the main interest of performing this study. As is well known, the study of harmonics in transformers is not a new topic in the field of research. Previous work has already used correction factors Copyright: © 2021 by the authors. for transformer losses [1] as a tool to demonstrate how these are increased due to harmonic Licensee MDPI, Basel, Switzerland. content and thus achieve a better understanding of the operation of the device under these This article is an open access article conditions [2,3]; Yazdani-Asrami et al. [4] evaluate the effects of harmonic distortion on distributed under the terms and conditions of the Creative Commons the performance of the transformers and other electrical elements are analyzed, as well as Attribution (CC BY) license (https:// the effect harmonics have in various electrical elements that affect the electrical systems; creativecommons.org/licenses/by/ Yazdani-Asrami et al. [5] studied the harmonics impacts on alternating current (AC) losses 4.0/). of superconductors. Sadati, S.B. et al. [6], estimated and evaluated the losses, the remained

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lifetime and loadability on the transformer considering the effects of current harmonics and ambient temperature. The impact of harmonics in transformer lifetime is important because the lifetime can be affected if the correction factors show a significant change in losses [1]. Additionally, finite element analysis software has been used to simulate the aforementioned correction factors, and to corroborate the calculation of the increase in losses and currents for a transformer [7,8], Yazdani-Asrami et al. [9] uses simulation of finite element method (FEM) to analyze non-sinusoidal voltage effects on no-load loss of transformers, such as different electromagnetic parameters such as flux lines, flux density, losses under different input sources and with high accuracy. The proposed methodology in this work will include the results of the correction factors in the manufacturer’s design system, particularly in the estimation calculation of loss increase, the volts per turn for each winding, the magnetic field density, and the induction currents. If the RMS value of the load current increases due to a non-sinusoidal load with specific harmonic content, the losses increase. If the losses increase, the flux density in the magnetic core increases, so it will behave as an internal source of harmonic generation, causing a reduction in the power factor [10]. Thus, it is feasible that the design will require an oversize of the magnetic core and coil based on a “k factor” to withstand the increase in flux density and prevent premature transformer failure [11,12]. However, the purpose of this research is to show that a “k factor” is not necessary, and considering the proposed methodology, the SPP transformer design can withstand the inverter harmonic load. The proposed methodology included in the manufacturer’s design system with the use of ANSYS Maxwell® (specialized simulation software in finite element method) will enable evaluation of whether the dimensions and quantity of the materials proposed for the magnetic core and coils of a transformer design are affected due to specific harmonic content of an inverter of an SPP, so the manufacturer can assure the efficiency and stability of the transformer during operation in an SPP. Another important aspect is that an SPP could be connected and disconnected at least three times a day, and also a disconnection of the SPP at full load or partial load condition of the transformer could occur, so the design of an SPP transformer must accomplish the operation requirements of a specific SPP. In a specific SPP design, the use of electrostatic shield between primary and secondary winding should also be considered to reduce the probability of an insulation failure due to voltage distortion, which can reduce the lifetime of a step-up transformer in an SPP [13]. The electrostatic shielding it is aimed to attenuate noise and transients and reduce high frequency components transferred between windings in the transformer. Therefore, the SPP transformers in comparison with standard design transformers should be designed to withstand these conditions. However, in the case for distribution transformers, there is a debate about the use of electrostatic shields and its performance, arguing that they could add unwanted capacitance causing potential resonances during transients, it has already been proven that a ground connection in the secondary winding is enough to avoid the most damaging harmonics and the use of electrostatic shield only reduces the remaining noise [14]. Said, D.M et al. [1,2] clarifies how the shielding tends to reduce capacitive values between the windings resulting in less heating, less conduction of eddy currents, and consequently, a harmonic filtering. However, it is clarified that the electrostatic shield should be considered in the design, if an analysis for a particular transformer design is performed previously, and preferably considered for those applications where the secondary winding has no ground connection. Existing research has analyzed the impact of solar panels and its harmonic effects on transformers and distribution networks through software simulations and laboratory tests [15,16]. Queiroz, H. et al. [17] shows the impacts of distributed generation in order to reduce transformer aging in a distribution transformer. Fortes, R.R.A et al. [18] and Ayub, M. et al. [19], analyze the impact of photovoltaic (PV) inverters in distribution networks and reinforces that PV inverters’ current harmonic injection should be considered for analysis. Additionally, Gray, M.K. et al. [20] evaluates the effect of rooftop solar photovoltaic penetrations and its impact in distribution transformers, and the results Energies 2021, 14, 1362 3 of 17

presented reveal that solar photovoltaic generation reduces transformer aging without significant reductions in neutral current. Thus, the main contribution of this article is to establish and validate the design methodology for SPP transformers which will work under a specific harmonic content (mostly when the third, fifth and seventh harmonics are dominant) due to operation requirements of an SPP.

2. Fundamental Calculations Required for SPP In this section, fundamental calculations required for the transformer design of an 2 SPP will be presented. The total losses of a transformer (PLL) involve the I R losses (P), the winding eddy–current losses (PEC), and other stray losses (POSL)[1,2]. The equation for total losses in a transformer is presented in Equation (1):

PLL = P + PEC + POSL (1)

In Equation (2), the per-unit load loss (PLL-R), under rated conditions is calculated per unit, considering the sum of the per-unit I2R losses (1 p.u.), the per-unit winding eddy–current loss (PEC-R), and the per-unit other stray loss (POSL-R).

PLL−R(pu) = 1 + PEC−R(pu) + POSL−R(pu) (2)

The winding eddy–current losses under rated conditions (PEC-R), are deﬁned as a portion of the total stray loss under rated conditions (PTSL-R), where 33% of the total stray loss is assumed to be winding eddy losses for liquid-ﬁlled transformers and 67% for dry-type transformers [2]. Nevertheless, it should be mentioned that in this analysis the winding eddy current losses under rated conditions (PEC-R) and other stray losses (POSL-R) will be calculated with the design tool of the transformer manufacturer. In order to estimate the increase in winding eddy current stray losses and other stray losses due to non-sinusoidal load, two correction factors for each type of loss (FHL) are used, which is the ratio of the total winding eddy current losses due to the harmonics (PEC), to the winding eddy current losses at the power frequency, when no harmonic currents exist (PEC−O), and the harmonic loss factor for other stray losses (FHL−STR)[2]. The harmonic loss factor equations are presented in Equations (3) and (4):

h i2 h=hmax Ih 2 ∑h=1 I h F = (3) HL h i2 h=hmax Ih ∑h=1 I

h i2 h=hmax Ih 0.8 ∑h=1 I h F = (4) HL−STR h i2 h=hmax Ih ∑h=1 I

where Ih is the RMS current at harmonic order “h”, hmax is the highest signiﬁcant harmonic number, I is the RMS load current, and I1 is the RMS fundamental load current. As a result of considering the harmonic loss correction factors, the per-unit total load loss in Equation (2) now becomes Equation (5):

PLL−R(pu) = (1 + FHL ∗ PEC−R(pu) + FHL−STR ∗ POSL−R(pu)) (5)

Consequently, the maximum current in the windings needs to be obtained, and therefore the maximum current of the winding is calculated with Equation (6). It should be mentioned that other stray losses do not exist in the windings, so (FHL−STR ∗ POSL−R(pu)) is not considered in Equation (6). s PLL−R(pu) Imax(pu) = (6) 1 + FHL ∗ PEC−R(pu) Energies 2021, 14, 1362 4 of 17

Non-sinusoidal loads with a particular harmonic content, can provoke an increase in the magnetic ﬂux of a transformer [7,8]; with this consideration and knowing that in the software design tool of the manufacturer the magnetic ﬂux density (B) directly affects the no-load losses (PNLL), as shown in Equation (7), the calculation of the PNLL must be updated integrating the harmonic content in the calculation of B.

PNLL = B ∗ Manufacturer Material Factor (7)

where the Manufacturer Material Factor (MMF) is a calculation from the software design tool based on the core properties. For the integration of the harmonic content in B, ﬁrst, the calculation of B is shown in Equation (8). Vper−turn B = (Tesla) (8) 4.44 ∗ f ∗ Ac

where Ac is the cross-sectional area of the magnetic core, and Vper−turn is the volts per turn in the winding, whether it is high voltage (HV) winding or low voltage (LV) winding [21]. Then, in order to obtain the volts per turn, the current increase in the windings due to the maximum current in pu presented in Equation (6) is considered; this current, deﬁned as Imax(winding), creates a minimum but measurable increase in the winding voltage which is needed to ascertain the volts per phase (Vper−phase), and consecutively the volts per turn (Vper−turn). The volts per turn directly affect B and is used as an input for the ﬁnite element modeling (FEM). The Imax(winding) for both windings is also an input for the FEM simulation, and it is shown in Equation (9): Imax(winding) = Iwinding ∗ Imax(pu) (9)

where Iwinding is the calculated current using the software design tool under rated conditions for each winding (high or low voltage). The volts per phase of the windings (Vper−phase) can be obtained by using Equation (10):

1000 ∗ Smax Vper−phase = (10) (Number of phases) ∗ Imax(winding)

where Smax is the max apparent power resulting from the calculation of the maximum current in per-unit, and the Number of phases is three for a three-phase transformer. The volts per turn of the windings (Vper−turn) are calculated using Equation (11).

Vper−phase V − = (11) per turn Number of winding turns

It should be mentioned that the Number of winding turns, from the primary and secondary winding, respectively, is obtained according to the winding dimensions calculated from the software design tool of the manufacturer. In Figure1, the proposed methodology for SPP transformer design for a specific harmonic profile is presented. In the spreadsheet section of Figure1, the calculation of new variables are included in the design software tool for the SPP transformer. The proposed methodology in Figure1 consists, in the first step, of obtaining values for core, winding and tank losses from the design tool of the manufacturer for the standard transformer design (also obtaining the efficiency, apparent power, impedance and data of interest), this without altering the default calculations of the design tool. In the second step, based on equations from Richard Marek et al. [2], the equations are adapted into the design tool formulas for the winding current and voltage values to arithmetically estimate the increase in the magnetic flux density due to the harmonic load profile, and thus obtain the increase in core losses. Consequently, changes in the winding and tank losses will be reflected, obtaining new values for efficiency, apparent power, and other data of interest. Both sets of values will serve as input data for the FEM simulations, and finally the data results Energies 2021, 14, x FOR PEER REVIEW 5 of 18

Energies 2021, 14, 1362 the increase in the magnetic flux density due to the harmonic load profile,5 of and 17 thus obtain the increase in core losses. Consequently, changes in the winding and tank losses will be reflected, obtaining new values for efficiency, apparent power, and other data of interest. Both sets of values will serve as input data for the FEM simulations, and finally the data for both scenariosresults (with for andboth without scenarios harmonic (with and loading) withou aret obtainedharmonic for loading) its comparison are obtained for its and analysis. comparison and analysis.

Figure 1.Figure Proposed 1. Proposed methodology methodology for solar power for solar plant power (SPP) plant transformer (SPP) transformer design with design a specific with harmonic a specific profile. harmonic profile. 3. Study Case for SPP Transformer Design 3. Study Case for SPPIn this Transformer section, a study Design case of a transformer design using the proposed methodology In this section,is presented. a study First, case ofthe a sp transformerecification designdata of usingan inverter the proposed and its maximum methodology harmonic profile is presented. First,is required the specification (see Appendix data of A, an Tables inverter A1 and and its maximumA3). With harmonicthis information, profile the design is required (seesoftware Appendix toolA ,can Table be A1updated and Table and A3).a specific With design this information, for a particular the design application can be software tool canachieved be updated and meet and the a specified specific designoperation for requirements; a particular application for this particular can be case, the flux achieved and meetdensity the should specified be operation1.72 Tesla requirements;as the minimu form design this particular requirement, case, the the efficiency flux should density shouldbe be above 1.72 Teslaof 99%, as and the minimumthe percentage design impeda requirement,nce should the be efficiency 5.75 ± 7.5%. should In the following be above of 99%,sections, and the the percentage analysis isimpedance based on an should actual be standard 5.75 ± 7.5%.transformer In the followingdesign (see Table A2), sections, the analysiswhere the is basedcalculated on an variables actual standard for a standard transformer design design are compared (see Table with A2), the calculated where the calculatedvariables variables of a specific for a design standard which design considers are compared the inclusion with theof the calculated maximum harmonic variables of aprofile specific required design whichaccording considers to the proposed the inclusion methodology of the maximum in Figure harmonic 1. profile required according to the proposed methodology in Figure1. 3.1. Assessment of Standard Design vs. Specific Harmonic Profile Design 3.1. Assessment3.1.1. of Standard Standard Design Design vs. Specific Harmonic Profile Design 3.1.1. Standard Design The data required for the analysis are as follows, inverter data, transformer The data requirednameplate for data, the analysis and transformer are as follows, core magnet inverterizing data, data transformer curves. Th nameplatee detailed information data, and transformerof data required core magnetizing for the analysis data is curves. presented The in detailed the Appendix information A. of data required for the analysisIn Table is presented A2, the nameplate in the Appendix data forA a. standard design are presented. The standard In Table A2,design the used nameplate for the dataanalysis for ais standardmodeled designin ANSYS are Maxwell presented.®, where The standardthe design geometries ® design used forrequired the analysis for the is modeledsoftware inare ANSYS the interior Maxwell dimensions, where theof core, design coil, geometries and steel holders and required for the software are the interior dimensions of core, coil, and steel holders and hardware, so a model can be stablished for FEM analysis. In Figure2, the 3D model of the standard design for analysis is presented.

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Energies 2021, 14, 1362 6 of 17 hardware, so a model can be stablished for FEM analysis. In Figure 2, the 3D model of the standard design for analysis is presented.

(a) (b)

FigureFigure 2. 2.StandardStandard design design transformer transformer 3D 3D model model for for analysis: analysis: ( (aa)) transformer transformer geometry geometry using design designsystem system tool of tool the of manufacturer; the manufacturer; (b) equivalent (b) equivalent geometry geometry of the of transformer the transformer in ANSYS in ANSYS Maxwell ®. Maxwell®. First, loss calculations of the transformer were performed in the manufacturer’s designFirst, system loss calculations tool, and the totalof the losses transformer at no load were and loadperformed conditions in the were manufacturer’s obtained before designapplying system the correctiontool, and factors.the total The losses calculated at no load losses and are load presented conditions in Table were1. obtained before applying the correction factors. The calculated losses are presented in Table 1. Table 1. Transformer standard design calculated losses. Table 1. Transformer standard design calculated losses. Losses Watts Losses Watts P 4088.4 NLL𝑃 4088.4 P 635.8 ECL𝑃 635.8 P 14,407.8 𝑃 14,407.8 POSL 1768 𝑃 1768 Total Losses 20,900 𝑇𝑜𝑡𝑎𝑙 𝐿𝑜𝑠𝑠𝑒𝑠 20,900

ForFor the the calculation calculation of of specific specific harmonic harmonic prof profileile transformer transformer design, design, first, first, the the standard standard designdesign calculated calculated losses losses are are obtained obtained in in Se Sectionction 3.1.1. 3.1.1 .Then, Then, the the manufacturer’s manufacturer’s design design systemsystem tool tool is is used used again again and and the the 𝐹FHL andand 𝐹FHL−STR correctioncorrection factors, factors, 𝑃PLL−(R𝑝𝑢(pu) )andand 𝐼Imax(𝑝𝑢(pu),) are, are calculated. calculated. Additionally, Additionally, the the increase increase in in the the apparent apparent power power is is calculated, calculated, multiplyingmultiplying the the nominal nominal apparent powerpower byby the the calculated calculatedImax 𝐼(pu()𝑝𝑢in) order in order to subse- to subsequentlyquently obtain obtain the increasethe increase in the in the HV HV winding winding and and LV LV winding winding currents, currents, which which are are the ® theinputs inputs required required for for the the finite finite element element simulation simulation inin ANSYSANSYS MaxwellMaxwell®.. The The calculated calculated apparentapparent power power and and HV HV and and LV LV winding winding currents currents are are presented presented in in Table Table 2.2.

TableTable 2. 2.ApparentApparent power power and and winding winding currents currents in the in transformer the transformer design design calculated calculated under under the the harmonicharmonic profile. proﬁle.

DesignDesign Parameters Parameters Value Value Apparent Power 2781.057 kVA Apparent Power 2781.057 kVA HighHigh voltage voltage (HV) (HV) winding winding current. current. 26.866 26.866 A A LowLow voltage voltage (LV) (LV) winding winding current. current. 2428.53 2428.53 A A

With the calculated apparent power and winding currents, the 𝑉 and With the calculated apparent power and winding currents, the V and V 𝑉 can be obtained using Equations (10) and (11); it should beper mentioned−phase thatper− forturn can be obtained using Equations (10) and (11); it should be mentioned that for this design, this design, the number of turns of secondary winding was nine. The calculated 𝑉 the number of turns of secondary winding was nine. The calculated Vper−turn was 42.41 V, was 42.41 V, and the 𝑉 results are presented in Table 3. By using Equation (8) and the Vper−phase results are presented in Table3. By using Equation (8) and considering and considering the 𝑉 calculated, the flux density B was 1.7989 T. Next, the the Vper−turn calculated, the flux density B was 1.7989 T. Next, the transformer losses transformerincluding the losses harmonic including profile the were harmonic calculated profile and were are presentedcalculated in and Table are4 .presented Additionally, in Tablethe transformer 4. Additionally, efficiency the was transformer calculated byef usingficiency the manufacturerwas calculated design by softwareusing the tool considering different load percentages to ensure the proper operation under different conditions. The results are presented in Table5.

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manufacturer design software tool considering different load percentages to ensure the Table 3. Transformer winding voltages calculated under the harmonic proﬁle. proper operation under different conditions. The results are presented in Table 5.

Transformer Winding Vper−phase Table 3. Transformer winding voltages calculated under the harmonic profile. HV winding 36,211.7 V TransformerLV winding Winding 𝑽𝒑𝒆𝒓𝒑𝒉𝒂𝒔𝒆 381.72 V HV winding 36,211.7 V LV winding 381.72 V Table 4. Transformer losses with harmonic proﬁle design calculated.

Table 4. TransformerLosses losses with harmonic profile design calculated. Watts

PNLLLosses 5135.15Watts P 642.18 ECL𝑃 5135.15 P 14,407.8 𝑃 642.18 P 1769.07 OSL 𝑃 14,407.8

Total Losses𝑃 21,954.21769.07 𝑇𝑜𝑡𝑎𝑙 𝐿𝑜𝑠𝑠𝑒𝑠 21,954.2 Table 5. Transformer efficiency with harmonic profile calculated. Table 5. Transformer efficiency with harmonic profile calculated. Transformer Load (%) Harmonic Profile Efficiency (%) Transformer Load (%) Harmonic Profile Efficiency (%) 25 99.12 25 99.12 50 99.33 50 99.33 75 99.30 10075 99.2199.30 100 99.21

3.1.2.3.1.2. ManufacturerManufacturer DesignDesign SystemSystem Parameters Results TheThe calculationcalculation results results for for standard standard design des andign harmonic and harmonic proﬁle designprofileare design presented. are Inpresented. Figure3, theIn resultsFigure obtained3, the results are summarized obtained are and summarized presented for and both presented designs, standardfor both anddesigns, harmonic standard proﬁle. and harmonic profile.

FigureFigure 3.3.Percentage Percentage changeschanges betweenbetween transformer stan standarddard design and and harm harmoniconic profile proﬁle design. design.

AsAs shownshown inin FigureFigure3 3,, the the Harmonic Harmonic ProfileProfile DesignDesign showedshowed a differencedifference in all the designdesign parametersparameters consideredconsidered includingincluding the ca calculatedlculated impedance percentage, percentage, which which was was 4.274.27 forfor standardstandard designdesign andand 4.174.17 forfor harmonicharmonic profileprofile design. InIn FigureFigure4 4,, a a percentage percentage change change in in losseslosses calculationcalculation cancan be observed; this percentage percentage changechange forfor HarmonicHarmonic ProfileProfile DesignDesign is adequateadequate and meets the the re requirementsquirements for for this this particularparticular SPP.SPP. Therefore, Therefore, thethe minimumminimum designdesign requirements are fulfilled fulfilled for for this this stage stage of of thethe design. design.

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FigureFigure 4. PercentagePercentage changes changes in losses in lossesbetween between transformer transformer standard design standard and designharmonic and profile harmonic design. proﬁle design.

® 3.1.3.3.1.3. FEM Analysis Using Using ANSYS ANSYS Maxwell Maxwell ® FEMFEM analysisanalysis usingusing the the input input variables variables from from the previousthe previous section section such assuchNumber as o f 𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑤𝑖𝑛𝑑𝑖𝑛𝑔 turns, 𝐼 () in Equation (9) and 𝑉 in Equation (11) winding turns, I in Equation (9) and Vper−turn in Equation (11) was performed max(winding) ® was performed using ANSYS® Maxwell . The objective was that the meshed models of the usingcore, winding, ANSYS Maxwelltank, and steel. The holders objective were was generated that the correctly, meshed modelsso the winding of the core,voltages, winding, tank,the flux and density, steel holders and the werecore losses generated could correctly, be calculated so the by windingthe software voltages, and a final the fluxdesign density, andcould the be core defined losses by could comparing be calculated the results by from the softwareANSYS Maxwell and a final® and design the manufacturer could be defined ® byDesign comparing System. the results from ANSYS Maxwell and the manufacturer Design System. ® FiniteFinite element solvers solvers such such as as ANSYS ANSYS Maxwell Maxwell® havehave their their own own methodology methodology and and formulationformulation to to converge converge into into a aresult result in in electromagnetic electromagnetic problems. problems. For this For work, this work, the the formulationformulation A-phi A-phi [22] [22 ]offered offered by by ANSYS ANSYS Maxwell Maxwell® was® was used used as a assolver a solver in the in study, the study, which,which, inin itsits mathematicalmathematical formulation,formulation, convergesconverges Maxwell’s equations equations for for its its solution solution [23]. [23]. For the meshing, based on the type of data of interest for the study, the adaptive meshFor with the tetrahedral meshing, based elements on the offered type of bydata ANSYS of interest Maxwell for the® study,was used,the adaptive ensuring mesh that the meshingwith tetrahedral was identical elements for eachoffered simulation. by ANSYS Maxwell® was used, ensuring that the meshing was identical for each simulation. 3.1.4. Simulation Results for a Standard Design 3.1.4.The Simulation simulation Results was for performed a Standard using, Design as input data, the parameters obtained from the manufacturerThe simulation design was system performed software. using, In as Figure input5 ,data, the winding the parameters excitation obtained voltage from results Energies 2021, 14, x FOR PEER REVIEWthe manufacturer design system software. In Figure 5, the winding excitation voltage9 of 18 from the simulation are presented, where the maximum peak value for HV winding is 33.75results kV from and forthe LVsimulation winding are is 500presente V. Thesed, where results the are maximum adequate, peak mainly value because for HV they are similarwinding to is the 33.75 nominal kV and voltages for LV ofwinding the study is 500 case V. transformer These results in are Table adequate, A2. mainly because they are similar to the nominal voltages of the study case transformer in Table A2.

(a)

Figure 5. Cont.

(b) Figure 5. Winding voltage waveforms of the standard design transformer: (a) HV winding; (b) LV winding.

In Figure 6, it can be observed the generated meshed model of the transformer under study (see Appendix A, Table A2 and Figure A1). The flux density simulation distribution in the core of the transformer had a maximum value of 1.7911 Tesla and the maximum value of flux density in the tank was 7.43 Tesla. In Figure 6a, the maximum value is observed between phase A and phase B in the upper and lower interval core section; this occurs mainly due to magnetic induction concentration in the core due to the current flow through the windings of each phase. During the continuous simulation results, it could be seen how the magnetic induction concentrates and alternates between phase A and B and then concentrates between phase B and C, which is how the transformer works during operation. In Figure 6, the images presented are considered only in a time frame, which allows us to appreciate the maximum value of magnetic flux density in the core.

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(a)

(b)

FigureFigure 5. 5. WindingWinding voltage voltage waveforms waveforms of the ofstandard the standard design transformer: design transformer: (a) HV winding; (a) HV (b) winding; LV winding.(b) LV winding.

InIn Figure Figure 6,6, it it can can be be observed observed the the generated generated meshed meshed model model of ofthe the transformer transformer under under studystudy (see (see Appendix Appendix A,A ,Table Table A2 A2 and and Figure Figure A1). A1). The The flux flux density density simulation simulation distribution distribution inin the the core core of of the the transformer transformer had had a amaxi maximummum value value of of1.7911 1.7911 Tesla Tesla and and the themaximum maximum valuevalue of of flux flux density density in in the the tank tank was was 7.43 7.43 Tesla. Tesla. In InFigure Figure 6a,6 a,the the maximum maximum value value is is observedobserved between between phase phase A A and and phase phase B Bin inthe the upper upper and and lower lower interval interval core core section; section; this this occursoccurs mainly mainly due due to to magnetic magnetic induction induction concen concentrationtration in the in the core core due due to the to thecurrent current flow flow throughthrough the the windings windings of ofeach each phase. phase. During During the continuous the continuous simulation simulation results, results, it could it be could seenbe seen how how the magnetic the magnetic induction induction concentrates concentrates and alternates and alternates between between phase A phase and B A and and B thenand thenconcentrates concentrates between between phase phase B and B andC, which C, which is how is how the transformer the transformer works works during during Energies 2021, 14, x FOR PEER REVIEWoperation.operation. In In Figure Figure 6,6 ,the the images images presented presented are are considered considered only only in ina time a time frame, frame, which10 whichof 18

allowsallows us us to to appreciate appreciate the the maximum maximum value value of ofmagnetic magnetic flux ﬂux density density in the in thecore. core.

(a) (b)

FigureFigure 6. 6. FluxFlux density density simulations simulations of of standard standard design design transformer: transformer: (a ()a core;) core; (b ()b tank.) tank.

AsAs shown shown in in Figure Figure 7,7 ,the the total total losses losses (Core (Core Loss), Loss), eddy eddy current current losses, losses, and and hysteresis hysteresis losseslosses are are calculated. calculated. The The total total losses losses calculation calculation had had a amaximum maximum value value of of 1.04 1.04 kW. kW.

Figure 7. Core losses of standard design transformer.

3.1.5. Simulation Result for Harmonic Profile Design In this section, the simulation was performed using the harmonic profile design data parameters obtained from the manufacturer design system software in Section 3. In Figure 8, the winding excitation voltage results from the simulation are presented, where the maximum peak value for HV winding is 36.25 kV and for LV winding is 512 V. These results are adequate because they present a similar percentage increase according to the previous calculation in the design system manufacturer’s tool.

Energies 2021, 14, x FOR PEER REVIEW 10 of 18

(a) (b) Figure 6. Flux density simulations of standard design transformer: (a) core; (b) tank. Energies 2021, 14, 1362 10 of 17 As shown in Figure 7, the total losses (Core Loss), eddy current losses, and hysteresis losses are calculated. The total losses calculation had a maximum value of 1.04 kW.

FigureFigure 7. Core losses of of standard standard design design transformer. transformer.

3.1.5.3.1.5. Simulation Result Result for for Harmonic Harmonic Profile Profile Design Design InIn this this section, section, the the simulation simulation was was perfor performedmed using using the harmonic the harmonic profile profile design designdata dataparameters parameters obtained obtained from the from manufacturer the manufacturer design designsystem systemsoftware software in Section in 3. Section In Figure3. In Figure8, the 8winding, the winding excitation excitation voltage voltage results resultsfrom the from simulation the simulation are presented, are presented, where wherethe themaximum maximum peak peak value value for forHV HVwinding winding is 36.25 is 36.25 kV kVand and for forLV LVwinding winding is 512 is 512 V. V.These These resultsresults are adequate because because they they present present a a si similarmilar percentage percentage increase increase according according to tothe the previousprevious calculation in the design design system system manufacturer’s manufacturer’s tool. tool. As presented in Figure9, the flux density simulation distribution in the core of the transformer has a maximum value of 1.8614 Tesla and the maximum value of flux density in the tank is 7.8069 Tesla. In Figure9a, the maximum value is observed between phase A and phase B in the upper and lower interval core section; this occurs during the continuous simulation results as described in Section 3.1.5, where the magnetic induction is concentrated and alternated between phases. As shown in Figure 10, the total losses (CoreLoss), eddy current losses, and hysteresis losses are calculated. The total loss calculation had a maximum value of 1.12 kW. The data results obtained in FEM simulation were compared between the standard design and harmonic profile design to obtain a percentage change, as shown in Figure 11. The results show a similarity with the results using the manufacturer’s design software in Figures3 and4, where an increase in magnetic flux density and loss is noticed, mainly in the core losses. It should be noted that the increase in total losses in the FEM analysis is 4.72% (close to 5.04% when using manufacturer’s design system tool calculations shown in Figure3) and is an indication that the design will meet the required efficiency even with the harmonic profile considered. Additionally, in Figure 11, the FEM simulation results show an increase in the percentage of flux and are similar to the value calculated by the manufacturer’s design system tool in Figure3. However, the increase in the flux density in the core, calculated in both cases, could be dangerous for the core’s material type. This may be an indication that other considerations in the design such as the electrostatic shielding could be required. These results evidence the requirement of analyzing different types of core material for SPP distribution transformer design for future studies or field experiments and knowledge of how the core material behaves for a particular harmonic profile. Energies 2021, 14, 1362 11 of 17 Energies 2021, 14, x FOR PEER REVIEW 11 of 18

(a)

(b) Energies 2021, 14, x FOR PEER REVIEW 12 of 18

Figure 8. WindingWinding voltage waveforms of harmonic profile proﬁle design transformer: (a) HV winding; (b) LV winding.winding.

As presented in Figure 9, the flux density simulation distribution in the core of the transformer has a maximum value of 1.8614 Tesla and the maximum value of flux density in the tank is 7.8069 Tesla. In Figure 9a, the maximum value is observed between phase A and phase B in the upper and lower interval core section; this occurs during the continuous simulation results as described in Section 3.1.5, where the magnetic induction is concentrated and alternated between phases.

(a) (b)

FigureFigure 9.9. FluxFlux densitydensity simulationsimulation ofof harmonicharmonic proﬁleprofiledesign designtransformer: transformer: ((aa)) core;core; ( (bb)) tank. tank.

As shown in Figure 10, the total losses (CoreLoss), eddy current losses, and hysteresis losses are calculated. The total loss calculation had a maximum value of 1.12 kW.

Figure 10. Core losses of harmonic profile design transformer.

Energies 2021, 14, x FOR PEER REVIEW 12 of 18

(a) (b) Figure 9. Flux density simulation of harmonic profile design transformer: (a) core; (b) tank.

Energies 2021, 14, 1362 12 of 17 As shown in Figure 10, the total losses (CoreLoss), eddy current losses, and hysteresis losses are calculated. The total loss calculation had a maximum value of 1.12 kW.

Energies 2021, 14, x FOR PEER REVIEW 13 of 18

SPP distribution transformer design for future studies or field experiments and knowledge of howFigure theFigure core 10. 10. Core materialCore losses losses behavesof of harmonic harmonic for proﬁleprofile a particular design design transformer. transformer. harmonic profile.

The data results obtained in FEM simulation were compared between the standard design and harmonic profile design to obtain a percentage change, as shown in Figure 11. The results show a similarity with the results using the manufacturer’s design software in Figures 3 and 4, where an increase in magnetic flux density and loss is noticed, mainly in the core losses. It should be noted that the increase in total losses in the FEM analysis is 4.72% (close to 5.04% when using manufacturer’s design system tool calculations shown in Figure 3) and is an indication that the design will meet the required efficiency even with the harmonic profile considered. Additionally, in Figure 11, the FEM simulation results show an increase in the percentage of flux and are similar to the value calculated by the manufacturer’s design system tool in Figure 3. However, the increase in the flux density in the core, calculated in both cases, could be dangerous for the core’s material type. This may be an indication that other considerations in the design such as the electrostatic shielding could be required. These results evidence the requirement of analyzing different types of core material for FigureFigure 11. 11.Ansys Ansys Maxwell Maxwell® percentage® percentage changes changes in main design in main parameters design betweenparameters transformer between standard transformer design and harmonicstandard profile design design. and harmonic profile design. 4. Results and Discussion 4. Results and Discussion The magnetic flux density in the core is the parameter that stands out in the design, and The magnetic fluxaccording density to the in calculations the core is performed the parameter by the manufacturer’s that stands designout in system the design, in Section 3, and according to theit is observedcalculations that during performed rated operating by the conditions manufacturer’s with the harmonic design profilesystem presented in the transformer design meets the material specifications, where the flux density is below Section 3, it is observedthe maximum that during flux density rated ofoperating the core material conditions (see Figure with A1).the Inharmonic Table6, a summaryprofile of presented the transformerresults for design main designmeets parameters the material for thespecifications, standard design where and harmonic the flux profile density design is below the maximumis presented. flux density of the core material (see Figure A1). In Table 6, a ® summary of results forThe main percentage design difference paramete resultsrs for from the ANSYS standard Maxwell designsimulation and inharmonic Figure 11 corroborate the proportionality of change in the analysis, which concludes that the harmonic profile design is presented.profile of the inverter does not represent a major problem for the transformer efficiency during rated operating conditions. However, the proposed methodology for SPP distribution Table 6. Summarytransformers, of design where parameter the harmonic results. profile current injection of the inverter (see Table A3) is used in the analysis, could affect the volt per turn in the windings; the results indicate an Harmonic Profile Harmonic Profile Std Design Main Final Design Std Design Design Design Design System Parameters ANSYS Maxwell Design ANSYS Tool System Tool Maxwell B (Tesla) 1.7141 1.7911 1.798 1.8614 Total Losses (W) 20,900 24,991 21.954 26,170 ɳ (%) 99.25 - 99.21 - HV winding max voltage 34,505 34,705 36,211 36,410 LV winding max voltage 363 520 381 530 Vper-turn 40.42 40.42 42.41 42.41

𝐼(𝑝𝑢) 1 1 1.04945 1.049

The percentage difference results from ANSYS Maxwell® simulation in Figure 11 corroborate the proportionality of change in the analysis, which concludes that the harmonic profile of the inverter does not represent a major problem for the transformer efficiency during rated operating conditions. However, the proposed methodology for SPP distribution transformers, where the harmonic profile current injection of the inverter (see Table A3) is used in the analysis, could affect the volt per turn in the windings; the results indicate an increase in the magnetic flux density above 1.72 Tesla, which is the minimum requirement for the design. Regarding the comparison of the obtained results in this proposal with respect to other works, we find the following: in [24], the technical requirements for a step-up transformer in a photovoltaic distribution system are outlined and the design characteristics that must be considered to guarantee the correct operation of the transformer are included. However, the percentage variation in aspects such as capacity,

Energies 2021, 14, 1362 13 of 17

increase in the magnetic flux density above 1.72 Tesla, which is the minimum requirement for the design. Regarding the comparison of the obtained results in this proposal with respect to other works, we find the following: in [24], the technical requirements for a step-up transformer in a photovoltaic distribution system are outlined and the design characteristics that must be considered to guarantee the correct operation of the transformer are included. However, the percentage variation in aspects such as capacity, magnetic flux, total losses, efficiency and impedance of the proposed design with respect to a conventional design is not reported. In this work, the percentage variation is considered (see Figure 11), so we cannot contrast the benefits or deficiencies of this work with the mentioned reference.

Table 6. Summary of design parameter results.

Harmonic Proﬁle Harmonic Proﬁle Design Main Final Design Std Design Std Design Design ANSYS Parameters Design System Tool ANSYS Maxwell Design System Tool Maxwell B (Tesla) 1.7141 1.7911 1.798 1.8614 Total Losses (W) 20,900 24,991 21.954 26,170 ï (%) 99.25 - 99.21 - HV winding max voltage 34,505 34,705 36,211 36,410 LV winding max voltage 363 520 381 530 Vper-turn 40.42 40.42 42.41 42.41 Imax(pu) 1 1 1.04945 1.049

5. Conclusions The calculations and analysis carried out in this work indicate that the harmonic profile considered in the design process (see Figure1) concludes that the final transformer design will operate correctly at the particular operating conditions in an SPP being considered without the requirement of a “k” factor design and without any filter inside the transformer. For a specific harmonic profile design, it is suggested to use the loss correction factors mentioned in Section2 to estimate the increase in apparent power and loss of the transformer design, and the harmonic profile should be indicated by the user of the SPP distribution transformer. For future work and recommendations, it is suggested to perform physical experimen- tation for the designs. The scope of ANSYS Maxwell® software can add greater value if it is correlated with laboratory tests. Additionally, it should be mentioned that, in this type of transformer, an electrostatic shield is usually considered to reduce the harmonic effect into the core and coil. With the appropriate shield design, the transformer design could be robust enough to withstand harmonic loads for SPP applications. Nevertheless, in this work the electrostatic shield was not considered in the design, and the use of an electrostatic shield could be analyzed in future work, including ANSYS Maxwell® simulations in order to determine the effect of the shield in the magnetic flux density. Therefore, physical tests on transformers designed for SPP with and without electrostatic shields with a star delta connection should be performed to evaluate their performance. In the same way, an integration of the FEM simulations is recommended as an external module in the design system tool of the transformer manufacturer.

Author Contributions: Conceptualization, methodology, software, validation, resources, data curation, visualization, investigation, writing—original draft preparation, writing—review and editing, I.R.M.R.; supervision, investigation, writing—original draft preparation, writing—review and editing, L.A.T.G.; data curation, visualization, investigation, writing—review and editing. L.H.R.A., F.S.S., J.R.M. and M.A.G.V. All authors have read and agreed to the published version of the manuscript. Funding: This research received no external funding. Institutional Review Board Statement: Not applicable. Informed Consent Statement: Not applicable. Data Availability Statement: Not applicable. Energies 2021, 14, 1362 14 of 17

Acknowledgments: The authors would like to thank PROLEC GE for allowing us to model one of their distribution transformers, as well as the use of their design system tool for the correspond- ing analysis. This work was supported by the Ministry of Public Education of Mexico in accor- dance with the financial support of the PRODEP project Fortalecimiento de Cuerpos Académicos 2019 UANL-CA-432. Conflicts of Interest: The authors declare no conflict of interest.

Abbreviations Abbreviation Deﬁnition B Magnetic Flux Density FEM Finite Element Modeling FHL Correction Factor for Winding Eddy–Current Losses FHL−STR Correction Factor for Other Stray Losses HV High Voltage I Current R Resistance LV Low Voltage MMF Manufacturer Material Factor PI2R Losses PEC Winding Eddy–Current Losses PEC−R Per-unit Winding Eddy–Current Losses PEC−O Winding Eddy–Current Losses when no Harmonic Currents exist PLL Total Losses of a Transformer PLL−R Per-unit Load Losses PNLL No Load Losses POSL Other Stray Losses POSL−R Per-unit Other Stray Losses PTSL−R Per-unit Total Stray Losses PV Photovoltaic RMS Root Mean Square or Effective S Apparent Power SPG Solar Power Generation SPP Solar Power Plant V Voltage W Watts WPP Wind Power Plants

Appendix A

Table A1. Inverter data.

Rated Power 2.7/2.7 MW/MVA AC Rated Voltage (3-Phase) 600 + 10% V Rated Frequency 60/50 Hz Rated Current 2598 A RMS AC Output Side Power Factor 0.926 Lead/Lag Maximum Current 2598 A RMS Maximum Efﬁciency 98.80 % Rated Efﬁciency 98.50 % Maximum DC voltage 1500 V DC Input Side DC Voltage operation range 875–1200 V

Table A2. Distribution transformer required data.

Distribution Transformer Data Operation Conﬁguration Step-up low voltage input and high voltage output Rated Voltage 34.5/0.630 kV Energies 2021, 14, 1362 15 of 17

Table A2. Cont.

Distribution Transformer Data Rated Power 2.7 MVA Rise Temperature 65 ◦C Rated Frequency 60 Hz Impedance 4.27 % Efﬁciency 99.25 % Connection Delta/Star-Grounded HV and LV Winding material Aluminum

Table A3. Inverter data—harmonic proﬁle.

Harmonic Phase A Phase A Phase B Phase B Phase C Phase C Order (A) (%) (A) (%) (A) (%) 1 2610.37 99.988 2572.83 99.981 2661.82 99.989 2 10.93 0.418 21.5 0.835 6.45 0.242 3 15.14 0.58 25.49 0.991 20.7 0.778 4 3.57 0.137 5.84 0.227 6.05 0.227 5 31.78 1.217 32.94 1.28 29.07 1.092 6 1.51 0.058 1.86 0.072 1.16 0.044 7 9.96 0.382 9.89 0.384 11.33 0.426 8 3.9 0.149 2.06 0.08 2.48 0.093 9 0.8 0.031 1.03 0.04 1.69 0.064 10 0.3 0.011 2.24 0.087 1.93 0.073 11 4.81 0.184 5.0 0.195 4.4 0.165 12 0.86 0.033 1.02 0.04 0.76 0.028 13 1.31 0.05 0.77 0.03 1.47 0.055 14 0.19 0.007 1.94 0.075 2.12 0.08 15 0.5 0.019 1.04 0.04 1.23 0.046 16 1.18 0.045 1.08 0.042 2.01 0.075 17 2.27 0.087 3.05 0.118 0.77 0.029 18 0.75 0.029 0.22 0.009 0.94 0.035 19 2.53 0.097 4.09 0.159 2.91 0.109 20 2.9 0.111 1.69 0.066 1.67 0.063 21 1.08 0.041 1.02 0.04 0.07 0.003 22 3.34 0.128 3.78 0.147 3.22 0.121 23 0.9 0.034 1.16 0.045 0.43 0.016 24 0.13 0.005 0.43 0.017 0.46 0.017 25 0.63 0.024 0.57 0.022 0.46 0.017 26 1.76 0.067 2.15 0.084 2.02 0.076 27 0.24 0.009 0.27 0.011 0.31 0.011 28 0.54 0.021 0.98 0.038 0.89 0.034 29 0.22 0.008 0.25 0.01 0.05 0.002 30 0.09 0.003 0.26 0.01 0.28 0.011 31 0.09 0.003 0.11 0.004 0.05 0.002 32 0.22 0.009 0.21 0.008 0.32 0.012 33 0.12 0.005 0.02 0.001 0.15 0.006 34 0.05 0.002 0.22 0.009 0.21 0.008 35 0.03 0.001 0.07 0.003 0.08 0.003 36 0.17 0.006 0.14 0.005 0.16 0.006 37 0.13 0.005 0.23 0.009 0.19 0.007 38 0.19 0.007 0.26 0.01 0.18 0.007 39 0.05 0.002 0.06 0.002 0.08 0.003 40 0.1 0.004 0.25 0.01 0.25 0.01 41 0.12 0.005 0.1 0.004 0.15 0.006 42 0.07 0.002 0.04 0.001 0.03 0.001 43 0.1 0.004 0.12 0.005 0.07 0.003 44 0.25 0.01 0.22 0.009 0.24 0.009 45 0.06 0.002 0.08 0.003 0.01 0 46 0.81 0.031 0.94 0.037 0.81 0.03 47 0.06 0.002 0.06 0.002 0.06 0.002 Energies 2021, 14, 1362 16 of 17 Energies 2021, 14, x FOR PEER REVIEW 17 of 18

(a) (b) Figure A1. Magnetization curves of selected transformer magnetic core: (a) magnetization curve Figure A1. Magnetization curves of selected transformer magnetic core: (a) magnetization curve (hysteresis); (b) magnetization curve (material quantity relationship). (hysteresis); (b) magnetization curve (material quantity relationship).

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