Zheng Zhao, Lingfei Xiong, Kuan Zheng
View Full Paper
[1] X. Zhou, Y. Luo, L. Zhu, J. Bai, T. Tian, B. Liu, Y. Xu, andW. Zhao, “Analysis of Fine Fault Electrothermal Characteris-tics of Converter Transformer Reduced-Scale Model,” Energies,vol. 17, no. 5, 2024. [2] Y. Wang, K. Liu, M. Lin, H. Tang, X. Li, and G. Wu, “Analysisof electrical–thermal-stress characteristics for eccentric contactstrip in the valve-side bushing of converter transformer,” HighVoltage, vol. 10, no. 1, pp. 106–115, 2024. [3] J. Peiyu, Z. Zhanlong, D. Zijian, W. Yongye, X. Rui, D. Jun, andP. Zhicheng, “Research on distribution characteristics of vibra-tion signals of ±500 kV HVDC converter transformer windingbased on load test,” International Journal of Electrical Powerand Energy Systems, vol. 132, p. 107200, 2021. [4] P. Huang, T. Shen, Z. Liu, R. Dian, X. Wanlun, and D. Wang,“Thermal characteristics analysis of medium frequency trans-former under multiple working conditions,” Thermal Science,vol. 28, no. 1B, pp. 599–609, 2024. [6]-[9] have studied the factors affecting the overload ca-pacity of the converter transformer and, through param-eter research, demonstrated the specific impact of thesefactors on the transformer’s overload capacity, providing abasis for the safe operation, fault diagnosis, aging research,1and cooling scheme design of the converter transformer.Reference [10] considered the impact of the load signalof the converter transformer on its voice signal character-istics and selected the converter transformer of an 800 kVconverter station as the research object. It collected faultsignals including voice signals and current signals underoverload conditions (such as DC bias) and constructed asample library through historical playback. By introduc-ing the load signal segmentation diagnosis interval, a jointfeature vector was formed to improve the accuracy of faultdiagnosis. The operation process of the converter trans-former was divided into different load intervals, enablingthe separate diagnosis of core faults and winding faults, ef-fectively overcoming the problem of overlapping core andwinding faults and improving the accuracy of fault identi-fication.Reference [11] detailly analyzed the operational capacityof the converter transformer under different overload con-ditions, including continuous overload, hour-level overload,and other states, and proposed corresponding calculationmodels and methods for each state. Under the continu-ous overload state, the transformer environment was builtaccording to the designed wiring method, and the opera-tional capacity data of the transformer under continuousoverload conditions were collected and compared with thecalculated values by the algorithm. The results showedthat when the error was within ±0.02p.u., the proposedalgorithm met the calculation accuracy requirements. Sta-tistical results indicated that when the transformer’s op-erating environment temperature did not reach 25◦C, theoperational capacity remained unchanged under continu-ous overload conditions; as the temperature increased, theoperational capacity gradually decreased, and there wasa linear relationship between the two. Under the hour-level overload state, different initial load rates (1.05p.u.,1.15p.u., 1.25p.u.) were used as analysis conditions, andthe hour-level overload capacity was calculated using theproposed algorithm. The results showed that under dif-ferent initial load rates, when the temperature remainedconstant, the overload capacity was positively correlatedwith the duration; when the initial load rate and over-load capacity were the same, as the temperature increased,the duration gradually decreased. Under three initial loadrate conditions, the overload capacity decreases as the ini-tial overload rate increases, and the duration will also beshortened.Reference [12] conducted an in-depth study on the vibra-tion characteristics of ±800 kV converter transformers un-der overload conditions. Through full-load thermal stabil-ity tests, important information such as vibration, voltage,and current under different load conditions was collected,and features such as vibration amplitude, vibration spec-trum, main frequency, vibration power ratio in differentfrequency bands, vibration power entropy, and odd-evenharmonic ratio were analyzed to evaluate the vibrationstate. Under overload conditions, the vibration amplitudeof the converter transformer significantly increases, mainlydue to the electromagnetic force generated by the load cur-rent in the windings. Theoretical analysis shows that theelectromagnetic force is proportional to the square of theload current, so the vibration amplitude increases quadrat-ically with the increase in the load rate. The vibrationpower ratio in different frequency bands changes, reflectingthe shift of the vibration source from the core to the wind-ings. The vibration power ratio in the low-frequency band(0-400 Hz) decreases from light load to medium load butincreases from medium load to heavy load, while the op-posite occurs in the high-frequency band. Under overloadconditions, the vibration power entropy decreases, indicat-ing a reduction in the complexity of the vibration signal.The odd-even harmonic ratio decreases with the increasein the load rate under overload conditions, which is relatedto the operating state of the filter.Reference [13] analyzed the temperature distribution lawof the windings of ±800 kV converter transformers underthe influence of different harmonic currents through a two-dimensional refined simulation model. It was pointed outthat as the load rate increases, the vibration amplitude ofthe converter transformer significantly increases, mainlydue to the electromagnetic force generated by the loadcurrent in the windings. The vibration frequency of theconverter transformer gradually shifts from 200 Hz to 300Hz or 400 Hz, indicating that under overload conditions,the vibration of the windings gradually replaces the vibra-tion of the core as the dominant vibration source. In addi-tion, the temperature rise caused by harmonic currents in-creases the hot spot temperature of the windings, therebyaffecting the mechanical performance and stress distribu-tion of the windings. High-frequency harmonic currentscause the equivalent resistance of the windings to gradu-ally increase, intensifying the losses and further raising thetemperature of the windings. Under overload conditions,the stress distribution and temperature distribution of thewindings become more complex, and the coupling effect ofharmonic currents and temperature rise needs to be com-prehensively considered. The final research shows that asthe content and frequency of harmonic currents increase,the hot spot temperature and stress of the windings signif-icantly increase. The proposed winding stress calculationmodel can accurately reflect the influence of harmonic cur-rents and temperature rise on the stress of the windings,providing important technical guidance for the design andmaintenance of converter transformers.Reference [14] studied the stress distribution characteris-tics of the windings of ±800 kV converter transformers un-der the influence of harmonic currents through simulation,revealing the thermal characteristics and stress changes ofthe transformer under overload conditions. The researchshows that harmonic currents cause the temperature ofthe windings to rise, with uneven temperature distribu-tion, and the hot spots are mainly concentrated in theupper part of the windings. Under 250 Hz harmonics, asthe harmonic current content increases from 0% to 20%,the hot spot temperature of the grid side winding risesfrom 87.2◦C to 99.2◦C, and that of the valve side risesfrom 98.1◦C to 108.7◦C; under 650 Hz harmonics, thetemperature rise of the grid side hot spot is more signif-icant. At the same time, the stress distribution of the2windings is affected by temperature and shifts towards theoil channels and the center area of the windings, with themaximum stress increasing in a power function relation-ship with the harmonic current content. The research alsoshows that the temperature rise caused by harmonic cur-rents increases the equivalent resistance of the windings,intensifying losses and temperature rise, and the changesin stress distribution and magnitude reflect the complexmechanical behavior of the windings under overload con-ditions. These findings provide key guidance for the designand maintenance of converter transformers under overloadconditions[15]-[16].Therefore, to further enhance the performance, reliabil-ity and economy of the flexible DC transmission systemfor offshore wind power, and to support the developmentand construction of offshore wind power and contribute tothe realization of China’s dual carbon goals, in-depth re-search on the thermal characteristics and overload capacityof offshore converter transformers can improve the opera-tional efficiency and reliability of converter transformers,and also ensure the efficient transmission of wind powerand the guarantee of power quality. This is of great prac-tical significance and urgency for promoting the rapid de-velopment of the offshore wind power industry.2. Theoretical ResearchTo simulate the thermal and flow fields within a trans-former, this study uses Fluent, a numerical calculationsoftware based on the finite volume method. The phys-ical foundation of this method is detailed below. Beforenumerical computation, the computational domain is di-vided into several control volumes. Each mesh point issurrounded by a control volume ∆V , the smallest geomet-ric unit for applying control equations. The 2D structuredmesh used in this study is shown in the figure below. Inthe figure, P represents the grid node under study and itssurrounding control volume. The boundaries of this con-trol volume are denoted as n, w, s, and e, with horizontaland vertical widths of ∆x and ∆y, respectively. N, W, S,and E represent the grid nodes adjacent to P and theirsurrounding control volumes.Discretizing the conservative control equations of the fi-nite volume method on each mesh yields:∂(ρφ)∂τ+∂(ρuφ)∂x+∂(ρvφ)∂y=∂∂x(Γ∂φ∂x) +∂∂y(Γ∂φ∂y) + S (1)The equation can be divided into four parts, representingthe sum of the rate of change of a general variable φ withtime, and the convective outflow equals the sum of thediffusive inflow and the increase from internal sources. Asthis study focuses on steady-state results, the first termon the left, the partial derivative with respect to time, iszero. u and v denote the velocity components of φ in thex and y directions, Γ is the diffusion coefficient of φ, andS is the source term. Integrating the differential equationover each mesh gives:Figure 1. Two-dimensional structural mesh∆V∂(ρuφ)∂x+∆V∂(ρvφ)∂y=∆V∂∂x(Γ∂φ∂x)+∆V∂∂y(Γ∂φ∂y) +∆VS(2)Since ∆x1 = ∆x2 = ∆x, ∆y1 = ∆y2 = ∆y,∆V = ∆x∆y the above equation can be expanded as:[(ρuφA)e − (ρuφA)w] + [(ρvφA)n − (ρvφA)x]=ïÅΓA∂φ∂xãe−ÅΓA∂φ∂xãvò+ïÅΓA∂φ∂yãn−ÅΓA∂φ∂yãxò+S∆x∆y(3)Where the convection term and diffusion term are rep-resented by the convection flow rate and diffusion quan-tity at the control volume boundary, A represents thelength of the control volume boundary, and the subscriptse, w, n, and s pass through the eastern, western, northern,and southern boundaries, respectively. And Aw = Ae =∆x, An = As = ∆y. These quantities can be further rep-resented by interpolating adjacent nodes in the difference-in-center format:(ρuφA)e = (ρu)eAeφE + φP2(4)(ρuφA)w = (ρu)wAwφW + φP2(5)(ρvφA)n = (ρv)nAnφN + φP2(6)(ρvφA)s = (ρv)sAsφS + φP2(7)ÅΓA∂φ∂xãe= ΓeAeïφE − φP∆x2ò(8)ÅΓA∂φ∂xãw= ΓwAwïφP − φW∆x1ò(9)ÅΓA∂φ∂xãn= ΓnAnïφN − φP∆y1ò(10)ÅΓA∂φ∂xãs= ΓsAsïφP − φS∆y2ò(11)3Fi = (ρu)iAi or Fj = (ρv)jAjDi =ΓiAi∆xior Dj =ΓjAj∆yj(12)where i takes w and e, and j takes n and s. Finishing isavailable:ïFe2(φE + φP ) −Fw2(φW + φP )ò+ïFn2(φN + φP )−Fs2(φS + φP )ò= [De (φE − φP ) − Dw (φP − φW )]+ [Dn (φN − φP ) − Ds (φP − φS)] + SV(13)Based on the above equation, it is sorted out according tothe general variable φ to obtain:ïÅDe +Fe2ã+ÅDw −Fw2ã+ÅDn +Fn2ã+ÅDs −Fs2ãòφP =ÅDe −Fe2ãφE +ÅDw +Fw2ãφW+ÅDn −Fn2ãφN +ÅDs +Fs2ãφS + SV(14)The α = D± F2 coefficient of the variable of the normalizedtreatment is written:αP φP = αEφE + αW φW + αN φN + αSφSαP= αE + αW + αN + αS + FE − FW + FN− FS − SP(15)Write the discrete equation for all control node columns,and solve the system of equations according to the initialconditions to obtain the quantity to be solved.3. Material Properties and Finite Element Simu-lationTo solve the temperature and flow fields of a 2D model us-ing Fluent, it is essential to first specify the materials andtheir physical properties within the computational domainand accurately calculate the losses of heat-generating com-ponents.3.1 Transformer Oil Physical ParametersThe oil-immersed transformer uses mineral oil as the cool-ing medium, and its physical properties, such as density ρ,specific heat capacity Cp, thermal conductivity γ, and dy-namic viscosity, µ, will change with the change of temper-ature, affecting its heat transfer efficiency and heat dissi-pation effect. Therefore, the following laws of transformeroil physical parameters with temperature are summarizedand set accordingly in the simulation model, which can im-prove the calculation accuracy of thermal field steady-statesimulation.a) DensityBased on the density of transformer oil measured at5 K (5◦C) intervals within the temperature range of278.15 K (5◦C) to 373.15 K (100◦C), the density as afunction of temperature is shown in Fig. 2 below. Itcan be seen from the figure that the density of trans-former oil is approximately negatively linearly cor-related with temperature, and the density decreaseswith the increase of temperature.ρ(T) = 1093−0.826T +3.612×10−4T2Äkg · m−3ä(16)Figure 2. The Relationship Between Density and Temper-atureAccording to the known data, the function relation-ship between density and temperature is obtained asfollows, where ρ the transformer oil density is thetransformer oil density and T is the oil tempera-ture, which is only valid in the temperature range of278.15 − 373.15 K.b) Specific heat capacitySpecific heat capacity is a commonly used physicalquantity in thermodynamics, which refers to the en-ergy absorbed or dissipated by a unit temperature ofa unit mass of a substance rising or falling, and canbe used to characterize the ability of the substanceto absorb heat or dissipate heat. The specific heatcapacity-temperature curve is shown in Fig. 3 usingthe specific heat capacity of the transformer oil corre-sponding to each 5 K interval in 278.15 − 373.15 K.Cp(T) = 455.9+5.191T −1.522×10−3T2(J · kg−1· K−1) (17)From the curve, it can be seen that the two are ap-proximately positively linearly correlated, and the spe-cific heat capacity of transformer oil increases with theincrease of temperature. After the function fitting,the functional relationship between the specific heatcapacity and the temperature is obtained as follows,where Cp is the specific heat capacity of transformeroil. It is also noted that the equation holds only in thetemperature range of 278.15 − 373.15 K.c) Thermal conductivityThermal conductivity characterizes the thermal con-ductivity of a material. The higher the thermal con-ductivity, the better the thermal conductivity of thematerial. According to the thermal conductivity ofthe transformer oil corresponding to each interval of 54Figure 3. The Relationship Between Specific Heat Capac-ity and TemperatureFigure 4. The Relationship Between Thermal Conductiv-ity and TemperatureK in 278.15 − 373.15 K, the curve of thermal conduc-tivity with temperature as shown in Fig. 4 below isobtained.The thermal conductivity of transformer oil decreasesapproximately linearly as the temperature rises. Therelationship between thermal conductivity and tem-perature is fitted exponentially to obtain the func-tional relationship described in the following equation.In the following formula, is the thermal conductivityof transformer oil. This formula holds only when thetemperature is in the range of 278.15 373.15 K.γ(T) = 0.1538 − 7.645 × 10−5T(W · m−1· K−1) (18)3.2 Solid Domain Material Characteristics andHeat Source SettingThe main materials used in the solid domain are siliconsteel sheet, copper and cellulose, and their physical prop-erties fluctuate very little in the temperature range of273.15 − 373.15 K, which can be regarded as constant inthe simulation calculation:ρfe = 7550( kg/m3)Cpfe= 446( J · kg−1· K−1)γfe = 51.9( W · m−1· K−1)ρcu = 8978( kg/m3)Cpcu= 381( J · kg−1· K−1)γcu = 387.6( W · m−1· K−1)ρisl = 1400( kg/m3)Cpisl= 1600( J · kg−1· K−1)γisl = 0.15( W · m−1· K−1)Among them, the subscripts Fe, Cu and ISL representthe iron core, copper wire, and insulating paper composedof the above materials, respectively.The winding is composed of two parts, copper wire andinsulating paper, when calculating the calorific value perunit volume of low-voltage and high-voltage windings, itis necessary to consider the influence of insulating paper,and multiply the heat source per unit volume of the copperconductor by the area ratio of the copper conductor to thewire cake in the two-dimensional model, so as to obtainthe equivalent unit volume heat source of the wire cake.In addition, the cushion block between the wire cake andthe wire cake is not conducive to the heat dissipation of thewinding, and the equivalent volume heat source needs tobe adjusted according to the coverage area, and finally theheat flux density of each wire cake of the low-voltage andhigh-voltage windings is 247.4 kW/m3 and 181.6 kW/m3,respectively.3.3 Boundary Condition Setting and Model Se-lectionThe interaction between the fluid and the wall is the keyto the coupling heat transfer problem, and the appropriateboundary conditions and initial conditions can not onlymeet the thermophysical requirements but also improvethe stability of the calculation. According to the actualsituation of the temperature rise test, the ambient tem-perature was set to 293.15 K in the simulation. All solidsurfaces in contact with the oil are non-slip, the outer sur-face of the oil tank and radiator is set to convective heattransfer, and the thermal boundary conditions of the restof the solid surfaces are coupled heat transfer. In orderto ensure the convergence and stability of the calculation,two criteria are used to determine that the temperaturefield and flow field in the transformer reach a steady state,one is that the residuals of these equations are within theallowable range: the residuals of the continuity and ve-locity equations are less than 10−3, and the residuals ofthe energy equations are less than 10−6; Another criterionis that the area-weighted average temperature fluctuationof the low-voltage winding is less than 0.5◦C in 1000 stepiterations.The proper selection of the mathematical model shouldfirst judge the type of oil flow in the transformer, and themain judgment is based on the Reynolds number. Usu-ally, the Reynolds number less than 2300 is laminar flow,otherwise it is considered turbulence. For ON-type trans-formers, the oil flow velocity is very low (oil flow inlet ve-5locity less than 0.1 m/s ), and the kinematic viscosity ishigh, resulting in a low Reynolds number for the flow. Inthe two-dimensional model established in this paper, theReynolds number is estimated to be about 31 based onthe temperature, flow velocity, and channel width of theoil inlet, so the laminar flow model is adopted. In additionto this, in order to facilitate the calculation of fast con-vergence, the pressure solver chooses PRESTO based onstaggered volume control.3.4 Model Simulation ResultsTaking the DF-80000/220 transformer as an example, themodel information is shown in Table 1. Among them, ”230/√3kV ” refers to the rated phase voltage of the high-voltage winding (Y-connection), and ” 35 kV ” refers tothe rated line voltage of the low-voltage winding ( ∆-connection). After running 15,000 steps in Fluent, thesteady-state convergence result was obtained. In the sim-ulation model, no heat source load is applied to the corepart, and the equivalent heat source power of eddy cur-rent loss is set for the top and bottom wire cakes of thehigh and low voltage windings. The cooling method ofthe transformer follows the IEC 60076-7 standard, wherethe acronym ONAF (Oil Natural Air Forced) describesthe cooling system characterized by natural oil circulationcombined with forced air cooling via fans.Table 1Transformer Model InformationTransformermodelCoolingmethodRated voltage/kVRatedcapacity/kVADF- 80000/220 ONAF 230/√3/35 80000Figure 5 visualizes the operational thermal profile: (a)presents the full transformer with temperature gradients,revealing hotspots at the core-stack junction and upperwindings; (b) zooms into the high-voltage winding, wherethe peak temperature at the top terminal correlates withcurrent concentration in the terminal assembly. As can beseen from Fig.5, the hot spot temperature of the trans-former is 108.1◦C, which appears at the top of the low-voltage winding, and the maximum temperature of thehigh-voltage winding is 97.88◦C, which appears in thehigh-voltage winding top line cake. The internal tempera-ture distribution and hot spot position of the transformerwinding are different from those of the previous two, whichis analyzed to be caused by the large eddy current loss ofthe wire cake at the top of the winding. In the vicinityof the oil baffle inside the winding, the temperature dis-tribution also presents a more obvious local extreme phe-nomenon.Figure 6 visualizes the oil flow dynamics: (a) presentsthe full transformer with velocity gradients, highlightinghigh-velocity channels at the oil inlet and low-velocity re-circulation zones near the corelamination interface; (b)zooms into the high-voltage winding region, where thepeak flow velocity at the winding entrance corresponds tothe structural design of the internal oil ducts. The maxi-mum oil flow rate inside the transformer is 0.102 m/s, andFigure 5. Transformer Temperature Distribution CloudMapFigure 6. Cloud Map of Transformer Oil Flow VelocityDistributionthe maximum oil flow rate of the high-voltage winding is0.095 m/s, which appears at the internal oil baffle.3.5 Simulation Model and Solution Process ofConverter Transformer Temperature Field(1) Analysis of harmonic influence on the temperaturefield of the converter transformer and study on cop-per shielding effectThe finite element analysis software is used to calculatethe temperature of the converter transformer, and theJoule heat obtained in the magnetic field is used as thethermal load of the temperature field analysis, whichis applied to the transformer winding and its oil tank,and structural parts, respectively. At the same time,the changes of the hot spot temperature of the con-verter transformer winding, the hot spot temperatureof the oil tank wall, and the hot spot temperature ofthe clamp before and after the installation of the cop-6Table 2Thermal Properties of Converter Transformer Structural PartsComponent Material PermeabilityThermal conductivityW/ (m · ◦C)Specific heat capacityJ/ (kg ·◦C)Density (kg/m3)Core 27ZH100 B-H curve 21 m · ◦C 490 kg · ◦C 7650 kg/m3Winding Copper - 338 381 8978Oil tank A3 Steel B-H curve 50 485 7800Clamping Nonmag-netic steel- 50 502 8030per shield under the harmonic condition are analyzed.Table 2 shows the thermal properties of the convertertransformer core, winding, oil tank, and clamp.The converter valve generally uses a 12 -pulse valvegroup. Due to the rapid conversion of the on-off valveduring the working process of the converter valve,many harmonics will be generated, which have a signif-icant impact on the quality of the power supply. Sincethe 12-pulse converter valve group is composed of two6-pulse converters in series, it is generally studied byanalyzing the 6-pulse converter valve as an example.The function of the converter determines that manyharmonics will be generated during the commutationprocess. The types of harmonics can be roughly di-vided into three categories: characteristic harmonics,non-characteristic harmonics, and conduction harmon-ics.For the 12 -pulse rectifier, the 6 × (2 K − 1) ± 1 har-monics cancel each other due to the equal amplitudeof each harmonic component of the Y/y and Y/d con-verter transformers and the same phase of the 12 K+1harmonics. Therefore, there are only characteristicharmonics in the 6-pulse harmonics, of which 6 K + 1is a positive-sequence characteristic wave and 6 K − 1is a negative-sequence characteristic wave. Therefore,there are only 12 K + 1 harmonics on the AC side ofthe 12 -pulse converter.In the process of engineering operation, there is a cer-tain gap between the operation of DC transmissionproject and the theoretical simulation state. There-fore, there are other ripples accompanied by charac-teristic harmonics, which are called non-characteristicharmonics. Such harmonics are often caused by non-ideal conditions. For example, the trigger pulse pe-riod is not absolutely equal, the bus voltage is notstrictly symmetrical or the commutation reactance isunbalanced, which may lead to the generation of non-characteristic harmonics. Due to the many and com-plex causes of non-characteristic harmonics, and in theactual equipment manufacturing process, manufactur-ers will specifically design to maximize the suppres-sion of non-characteristic harmonics, so that the im-pact of non-characteristic harmonics in the DC trans-mission process is not obvious. The analysis of non-characteristic harmonics often adopts the method ofignoring other causes and analyzing a certain cause.(2) Field-circuit coupling model of converter transformerThe single capacity of the ultra-high voltage convertertransformer is large, so the stray loss caused by theleakage magnetic field is becoming more serious, andit will undoubtedly increase the stray loss caused bythe leakage magnetic field in the case of DC bias orserious harmonics. Therefore, this chapter will carryout finite element simulation calculation on the hotspot temperature of converter transformer winding, oiltank wall and clamp under harmonic conditions, andcompare it with the temperature after adding coppershielding.Fig. 7 is a 1/2 converter transformer three-dimensionalmodel diagram based on the converter transformermodel ZZDFPZ-412300/750-200 provided by thetransformer company. Based on the parameters ofthe transformer experimental model, the transformermodel is simplified. Due to the symmetry, half ofthe three-dimensional physical model and equivalentcircuit model are established by MAGNET software,which is the field-circuit coupling model, as shown inFig.8.Figure 7. 1/2 Structure Model Diagram of ConverterTransformer(3) Solution processAccording to the finite element simulation model es-tablished above, the corresponding material propertiesare loaded into the physical model, and the accuracysuitable for this simulation is selected for subdivision.The corresponding subdivision results are shown inFig.9. According to the field-circuit coupling method,the physical model of the transformer is coupled withthe circuit model, and the relevant simulation analy-sis is carried out. A sinusoidal AC voltage source isadded to the primary side of the circuit model, andthe equivalent simulation calculation is performed onthe working conditions under harmonics. The initialtemperature of the environment was set to 30◦C.7Figure 8. Field-Circuit Coupling ModelFigure 9. Meshing Diagram of the ModelCompared with the general transformer, the structure ofthe converter transformer is more complex, and its interiorhas a variety of media and nonlinear materials. Therefore,this chapter uses MagNet/ThermNet electromagnetic fieldfinite element analysis software. According to the symme-try of the converter transformer structure and the char-acteristics of the electromagnetic distribution, the calcula-tion model of the converter transformer is simplified andassumed as follows:(1) Because the converter transformer is a symmetricalstructure, so the calculation reduces the calculationtime to take the model of the whole transformer 1/2structure, and the inner side of the symmetrical sur-face is set to a symmetrical boundary.(2) Ignoring the DC component of the low-voltage valveside winding, the total ampere turns of the grid sidewinding and the valve side winding are balanced afterconsidering the influence of the high-order harmoniccurrent.(3) The core silicon steel sheets and components of theconverter transformer are processed according to thenonlinear material of the non-magnetic steel, ignoringthe hysteresis effect of the ferromagnetic material andbeing isotropic.(4) Ignore the eddy current in the core, and the influenceof lead current and displacement current on the leakagemagnetic field.According to the above solution process, the core loss ofthe converter transformer in MagNet under no-load condi-tion is 166 kW and the load loss is 1050 kW. Fig. 10, Fig.11 and Fig. 12 show the unshielded temperature of theconverter transformer and the temperature distribution ofthe tank wall and the clamp under rated conditions.Figure 10. The Overall Temperature Distribution CloudDiagram of the TransformerFigure 11. Temperature Distribution Cloud Diagram ofCore and WindingAs shown in Fig.10, Fig. 11 and Fig.12, before the mag-netic shielding is not installed, the hot spot temperatureof the winding can reach 82.77◦C, and the hot spot tem-perature of the core can reach 74.92◦C. The eddy currentdensity of the fuel tank is concentrated at the hot spot ofthe winding corresponding to the rear wall of the fuel tank,reaching 84.72◦C. The clamp is located in the area wherethe leakage magnetic field of the transformer is strong, andthe size is relatively small compared with other structuralparts. It is easy to induce a large eddy current loss in itslocal area. The highest temperature rise of the clamp isat the central column of the iron core, because this is a8Figure 12. Temperature Distribution Cloud Diagram ofFuel Tank Wall and Clamphigh magnetic flux leakage area, and the eddy current lossis relatively large, so the temperature rise here is higher,forming a local hot spot, and at this time the hot spottemperature of the clamp also reached 77.52◦C.The heat resistance grade of oil-immersed transformersis grade A, and the insulation materials used in the trans-former have a certain heat resistance life. At this time,the hot spot temperature of the oil tank wall and the hotspot temperature of the clamp will form local overheating.Therefore, this local overheating will cause insulation ag-ing, threatening the safe use and life of the transformer,and it must be improved. Electromagnetic shielding gen-erally refers to the shielding device made of a copper plate(or an aluminum plate), and the installation of electromag-netic shielding in the fuel tank is one of the main methodscommonly used in engineering to reduce the eddy currentloss caused by magnetic flux leakage on the fuel tank. Un-der the action of the magnetic flux of the leakage magneticfield, an eddy current will be induced on the surface ofthe copper plate. The magnetic field generated by theeddy current is just opposite to the direction of the leak-age magnetic field and cancels each other out, so that theleakage magnetic flux entering the transformer tank is re-duced, so as to achieve the purpose of reducing the eddycurrent loss and magnetic flux density of the transformertank. In view of the above problems, this paper adds a4mm thick copper shield in the calculation.Figure 13. Copper Shielding Position Structure DiagramAfter adding copper shielding in the simulation, the tem-perature field of the current transformer under rated loadis simulated to verify the influence of copper shielding onhigh temperature. Fig. 14 and Fig. 15 are shown as thecore, winding temperature cloud map, fuel tank wall, andclamp temperature cloud map after the installation of thecopper shield.Figure 14. Cloud Map of Core and Winding TemperatureDistributionFigure 15. Cloud Map of Temperature Distribution on theFuel Tank Wall and ClampsAfter the installation of 4 mm thick copper shield, fromFig.15, the hot spot temperature of the fuel tank dropsto 60.52◦C, and the hot spot temperature of the clampdrops to 64.01◦C. The calculated temperature rise con-forms to the temperature rise limit of Class A insulatingmaterial. Therefore, the copper shields installed in thefollowing parts of this section are all 4 mm thick.4. Thermal Rise Calculation Considering Accu-racy and Real-Time RequirementsThe thermal circuit model method, while fast and simple,has lower accuracy due to parameter errors from simplifiedheat transfer representations. In contrast, the steady-statesimulation method offers high accuracy and detailed physi-cal field distributions but is computationally intensive andtime-consuming, requiring significant computer resourcesand making it less practical for on-site use. To reconcile theneed for both accuracy and real-time performance, a field-circuit coupling method is proposed. This method refinesthe thermal circuit model parameters based on simulationresults, enabling precise hotspot temperature calculations.For the field-circuit coupling model, the first step is toidentify the coupling parameters. These parameters arecategorized into five classes, as shown in Fig.16. Name-plate data, structural data, and winding DC resistance canbe obtained from routine transformer tests. Temperature-rise test data, used to simplify heat dissipation resistance9Figure 16. Parameters Required for the Hot Path Model Methodcalculations, are derived from temperature-rise tests; ifthese tests are unavailable, relevant data such as the num-ber and height of coils in different windings and the out-er/inner diameters of windings can be used as alterna-tives. When the transformer tap position is fixed, thesedata remain unchanged for each calculation. Initial valuedata, which affect the speed of the thermal circuit modelmethod, can be roughly estimated due to the method’sfast computation speed. Operating data, which vary withthe transformer’s operating state, directly impact calcula-tion accuracy. Ambient temperature and load current canbe monitored in real-time, while top oil temperature andhotspot coefficients require precise assignment.For transformers with online top-oil-temperature mon-itoring, real-time top-oil-temperature data is accessible.However, installing temperature sensors inside transform-ers demands high design standards for internal structures,and most transformers lack these sensors. Retrofittingin-service transformers with sensors is more challengingand costly than installing them during design or manufac-turing. The hot-spot coefficient lacks a precise definitionformula. Load guidelines suggest a hot-spot coefficient of1.3 for medium and large transformers, yet this approachoverlooks the specific structure and operating conditionsof transformers, potentially compromising the accuracy ofhot-spot temperature calculations. steady-state simulationcan model the steady thermal field of transformers underany operating conditions, allowing for the calculation ofthe top-oil temperature and hot-spot coefficient. Based onthis, the coupling parameters of the thermal circuit modeland steady-state simulation are identified as the top-oiltemperature and hot-spot coefficient.The core steps of the coupled calculation model are asfollows:1. Use steady-state simulation to model the opera-tion of the transformer under typical load currents and am-bient temperatures. Collect data on top-oil temperature,bottom-oil temperature, hot-spot temperature, and aver-age winding temperature under different operating con-ditions to calculate the hot-spot coefficient and form adatabase.2. Analyze the database to determine the rela-tionship between top-oil temperature, hot-spot coefficient,load ratio, and ambient temperature. Develop formulas forcalculating top-oil temperature and hot-spot coefficient un-der any load and ambient temperature conditions.3. Dur-ing field operation of the transformer, calculate the top-oil temperature and hot-spot coefficient based on actualoperating conditions and input them into the thermal cir-cuit model. This enables quick estimation of the hot-spottemperature at steady-state and supports simulation cal-culations. The following Fig. 17 summarizes the aboveapproach. Taking the SFZ8-31500/110 transformer as anexample, the first two steps are described in detail.(1) The general provisions of power transformers stipu-late that the maximum ambient temperature of powertransformer operation shall not exceed 40◦C, the min-imum ambient temperature of indoor transformer op-eration shall not be less than −5◦C, and the minimumambient temperature of outdoor transformer shall notbe less than −25◦C. Considering that users are moreconcerned about the change of the internal tempera-ture of the transformer at high temperatures, whenthe ambient temperature is very low, the temperaturerise of the windings is small even at high load rates,so the ambient temperature range of steady-state sim-ulation is set at 5◦C ∼ 40◦C (simulated every 5◦C ).Generally, the economic load rate of the transformeris 0.75 ∼ 0.85, when the transformer needs to bearthe overload, the load rate should not exceed 1.2, con-sidering that some in-service transformers have a longoperating life and the carrying capacity is reduced, therange of load rate selected in the steady-state simula-tion is 0.4 ∼ 1.2 (every 0.2 simulation). Since the hot10Table 3Top Oil Temperature and Hot Spot Coefficient of Transformers Under Different Operating ConditionsLoad rate Ambient temperature 0.4 0.6 0.8 1.0 1.25◦CTop layer oil temperature/◦C27.18 30.85 38.11 47.10 55.03Hot Spot Coefficient 1.29 1.31 1.26 1.17 1.1610◦CTop layer oiltemperature/ ◦C30.31 35.90 42.05 49.94 57.85Hot Spot Coefficient 1.19 1.15 1.18 1.18 1.1515◦CTop layer oiltemperature/ ◦C33.97 39.00 46.41 53.72 62.39Hot Spot Coefficient 0.99 1.19 1.11 1.09 1.1320◦CTop oil temperature /◦C 37.99 43.60 49.82 57.30 65.43Hot Spot Coefficient 1.05 1.07 1.10 1.10 1.1625◦CTop oil temperature/ ◦C 41.53 47.25 53.54 61.29 70.30Hot Spot Coefficient 1.00 1.03 1.08 1.08 1.1430◦CTop oil temperature/ ◦C 46.39 51.36 57.78 65.42 74.36Hot Spot Coefficient 0.84 1.02 1.06 1.09 1.1135◦CTop layer oiltemperature/ ◦C50.95 55.42 61.90 69.89 78.08Hot Spot Coefficient 0.76 1.02 1.06 1.08 1.1440◦CTop layer oiltemperature/ ◦C55.17 60.05 66.45 73.49 83.19Hot Spot Coefficient 0.80 0.96 1.04 1.11 1.14Figure 17. Coupling Calculation Flowcircuit model method needs to input the top oil tem-perature and hot spot coefficient of the current op-erating state obtained by the steady-state simulationmethod, the following Table 3 can be obtained by col-lating these data.(2) In order to obtain the top oil temperature and hotspot coefficient of the transformer under any operat-ing state, it is necessary to analyze the data obtainedunder typical operating conditions. The load loss isproportional to the square of the load factor, so thevariation curve of the top oil temperature with thesquare of the ambient temperature and the load rateis respectively made, as shown in Fig. 18 below.The top oil temperature increases with the increase ofthe square of the ambient temperature and the load rate,respectively, and shows a strong linear relationship, so themultiple linear regression method is used to analyze thechange trend of the top oil temperature under any operat-ing state. Multiple linear regression is a kind of regressionanalysis method, which is often used to study the relation-ship between dependent variables and multiple indepen-dent variables and has been widely used in various fields.A multiple linear regression equation is established basedon the number of dependent variables, as shown in (19).f(x) = a0 + a1x1 + a2x22 (19)where x1 and x2 represent the ambient temperature andload rate, respectively, with the help of statistical analysissoftware SPSS, the estimated values of parameters a0, a1and a2 can be obtained through stepwise regression, soas to obtain the expression of the top oil temperature, asshown in the following ().Ttop-oil = 19.51 + 0.8x1 + 21.76x22 (20)In order to evaluate the effect of the regression model, theequation was tested for goodness-of-fit R2 and significanceF.R2 is 0.997, which is very close to 1, and the F-valuefalls in the rejection domain, which is very significant, sothe equation has a good linear regression effect.The relationship between the hot spot coefficient andthe ambient temperature and load rate is shown in Fig. 19below, and the change of the hot spot coefficient is morecomplex than that of the top oil temperature. Overall,the hot spot coefficient is negatively correlated with the11(a) The VariationRelationship of Top Layer OilTemperature and AmbientTemperature Under DifferentLoading Rates(b) The VariationRelationship of the Top LayerOil Temperature and theSquare of the Load RateUnder DifferentEnvironmental TemperaturesFigure 18. The Variation Law of the Top Layer Oil Tem-perature of the Transformer Under Different OperatingConditionsambient temperature and positively correlated with theload rate, which is a nonlinear problem. If the nonlinearregression method is to be adopted, the difficulty lies indetermining the nonlinear regression equation, consideringthat the change of the hot spot coefficient is approximatelylinear, and the linear fitting method is used to determinethe expression.(a) The Relationship Betweenthe Hot Spot Coefficient andthe Variation of AmbientTemperature(b) The Relationship Betweenthe Hot Spot Coefficient andthe Square of the Load RateFigure 19. The Variation Law of the Transformer Hot SpotCoefficient Under Different Operating ConditionsFirstly, based on Fig.19(b) above, the hot spot coeffi-cient H curve at different ambient temperatures is linearlyfitted, and the expression is obtained as follows.H = −0.20x2 + 1.40x1 (x1 = 5◦C)H = −0.017x2 + 1.18x1 (x1 = 10◦C)H = 0.084x2 + 1.04x1 (x1 = 15◦C)H = 0.13x2 + 0.99x1 (x1 = 20◦C)H = 0.16x2 + 0.93x1 (x1 = 25◦C)H = 0.31x2 + 0.78x1 (x1 = 30◦C)H = 0.41x2 + 0.68x1 (x1 = 35◦C)H = 0.42x2 + 0.67x1 (x1 = 40◦C)The slope and intercept of the equation at ambient tem-perature of 20◦C are taken as the initial slope and initialintercept of the hot spot coefficient prediction equation,and the average value of the difference between the slopeof the adjacent equation and the average value of the dif-ference between the intercept are taken as the increase anddecrease constants of the slope and intercept of the predic-tion equation, respectively, and the prediction equation isobtained:H =ï0.13 +0.089 (x1 − 20)5òx2 +ï0.99 −0.10 (x1 − 20)5ò(21)Finishing type can get the following (22):H = 1.40 − 0.02x1 − 0.22x2 + 0.018x1x2 (22)The goodness-of-fit test of the equation shows that R2 is0.823, and the predicted hotspot coefficient value of theequation is less than 0.1, so the coupled calculation modelhas good prediction accuracy.The proposed field-path coupling model is used to cal-culate the average oil temperature, the average windingtemperature, the top oil temperature and the hot spot tem-perature of a transformer under the operating conditionsof temperature rise test conditions, and the calculation re-sults are compared with the temperature rise test results,as follows.The results are shown in the following table, where thedefinition of the average oil temperature in the tempera-ture rise test value is the same as that of the previous two,and the average temperature value of the winding is theaverage value of the high-voltage winding and the averagetemperature value of the low-voltage winding. From theresults in the table, it can be seen that the error of thecalculated value of the field-path coupling model and thetemperature rise test value is within 5◦C, which can meetthe actual engineering requirements.According to the thickness of the transformer wire andthe rated capacity, the hot spot coefficient H = 1.2 is de-termined, and the hot spot temperature value is 101.68◦Caccording to the standard recommendation method. Thesimulation results show that the hot spot temperature ofthe transformer appears at the #1-line cake, that is, the#1 optical fiber temperature measurement point, so thetemperature value of 115.0◦C is used as the temperaturerise test value of the transformer hot spot temperaturefor comparison. According to Table 4 below, the abso-lute error between the hot spot temperature value andthe temperature rise test value calculated by the field-pathcoupling model is 0.25◦C, while the error of the standardrecommendation method is 14.32◦C. The model has highcalculation accuracy.5. ConclusionsThis paper deeply probes into the thermal characteristicsand overload capacity of converter transformers in offshorewind power flexible DC transmission systems. Two mainconclusions are drawn:(1) By using Fluent to solve the 2D temperature and flowfields of the transformer, we studied the temperature-dependent variations in transformer oil’s properties,12Table 4Calculation Results of Test and Field-Path Coupling MethodAmount of contrast Calculated value/◦CTest values /◦C Absolute error/◦CRelative error/%Average oil temperature 49.80 49.65 0.15 0.30Top layer oil temperature 65.26 64.90 0.36 0.55Average temperature ofthe windings75.74 75.60 0.14 0.19Hot spot temperature 115.25 / / /including density, specific heat capacity, thermal con-ductivity, and dynamic viscosity. These findings en-hanced the precision of thermal field simulations. De-tailed descriptions of solid domain material propertiesand heat source setups were provided, covering thephysical properties of silicon steel, copper, and cel-lulose, as well as the heat flux density calculationsfor each low and high-voltage winding segment. Re-garding boundary conditions and model selection, af-ter considering the interaction between fluid and wall,suitable conditions and a laminar flow model for theoil flow within the transformer were chosen. Takingthe DF-80000/220 transformer as an example, the in-ternal temperature and oil flow velocity distributionswere obtained. It was found that the hotspot temper-ature appears at the top of the low-voltage winding,the highest temperature of the high-voltage windingis in the top coil, and the maximum internal oil flowvelocity occurs at the internal baffle.(2) A field-circuit coupled calculation method is proposed.By analyzing the coupling parameters of the ther-mal circuit model and steady-state simulation, andrefining the model parameters based on simulationresults, the hot-spot temperature can be accuratelycalculated. Through steady-state simulation of thetransformer’s operation under typical load currentsand ambient temperatures, a database of top-oil tem-peratures, bottom-oil temperatures, hot-spot temper-atures, and average winding temperatures was formed,along with the calculation of the hot-spot coefficient.Based on the database, the variation laws of top-oiltemperature and hot-spot coefficient with load ratioand ambient temperature were analyzed, leading to thedevelopment of formulas for calculating these param-eters under any load and ambient temperature condi-tions. Finally, the calculated values of the field-circuitcoupled model show an error of less than 5◦C com-pared to the temperature-rise test values, meeting thepractical engineering requirements. The absolute er-ror of the calculated hot-spot temperature comparedto the test value is 0.25◦C, which is smaller than thatof the standard recommended method, indicating ahigher calculation accuracy.Funding5500-202319103A-1-1-ZN Research on Key Technologiesof Medium-Frequency Convergence DC Transmission forLarge-Capacity Offshore Wind Power.AcknowledgmentsThank you for the great assistance provided by TBEAHengyang Transformer Co., Ltd.References[1] X. Zhou, Y. Luo, L. Zhu, J. Bai, T. Tian, B. Liu, Y. Xu, andW. Zhao, “Analysis of Fine Fault Electrothermal Characteris-tics of Converter Transformer Reduced-Scale Model,” Energies,vol. 17, no. 5, 2024.[2] Y. Wang, K. Liu, M. Lin, H. Tang, X. Li, and G. Wu, “Analysisof electrical–thermal-stress characteristics for eccentric contactstrip in the valve-side bushing of converter transformer,” HighVoltage, vol. 10, no. 1, pp. 106–115, 2024.[3] J. Peiyu, Z. Zhanlong, D. Zijian, W. Yongye, X. Rui, D. Jun, andP. Zhicheng, “Research on distribution characteristics of vibra-tion signals of ±500 kV HVDC converter transformer windingbased on load test,” International Journal of Electrical Powerand Energy Systems, vol. 132, p. 107200, 2021.[4] P. Huang, T. Shen, Z. Liu, R. Dian, X. Wanlun, and D. Wang,“Thermal characteristics analysis of medium frequency trans-former under multiple working conditions,” Thermal Science,vol. 28, no. 1B, pp. 599–609, 2024.[5] Z. Zhou, C. Luo, F. Zhang, J. Zhang, X. Yang, P. Yu,and M. Liao, “Thermal Management in 500 kV Oil-ImmersedConverter Transformers: Synergistic Investigation of CriticalParameters Through Simulation and Experiment,” Energies,vol. 18, no. 9, p. 2270, 2025.[6] J. Peiyu, Z. Zhanlong, D. Zijian, Y. Yu, P. Zhicheng, Y. Fanghui,and Q. Menghao, “Transient-steady state vibration character-istics and influencing factors under no-load closing conditionsof converter transformers,” International Journal of ElectricalPower and Energy Systems, vol. 155, p. 109497, 2024. [7] Y. Guangyuan, L. Xingyuan, F. Ming, and L. Kuan, “Researchon the Calculation Method of Overload Capacity of ConverterTransformer,” Transformer, vol. 52, no. 03, pp. 16–20, 2015. (inChinese). [9] have studied the factors affecting the overload ca-pacity of the converter transformer and, through param-eter research, demonstrated the specific impact of thesefactors on the transformer’s overload capacity, providing abasis for the safe operation, fault diagnosis, aging research,1and cooling scheme design of the converter transformer.Reference [10] considered the impact of the load signalof the converter transformer on its voice signal character-istics and selected the converter transformer of an 800 kVconverter station as the research object. It collected faultsignals including voice signals and current signals underoverload conditions (such as DC bias) and constructed asample library through historical playback. By introduc-ing the load signal segmentation diagnosis interval, a jointfeature vector was formed to improve the accuracy of faultdiagnosis. The operation process of the converter trans-former was divided into different load intervals, enablingthe separate diagnosis of core faults and winding faults, ef-fectively overcoming the problem of overlapping core andwinding faults and improving the accuracy of fault identi-fication.Reference [11] detailly analyzed the operational capacityof the converter transformer under different overload con-ditions, including continuous overload, hour-level overload,and other states, and proposed corresponding calculationmodels and methods for each state. Under the continu-ous overload state, the transformer environment was builtaccording to the designed wiring method, and the opera-tional capacity data of the transformer under continuousoverload conditions were collected and compared with thecalculated values by the algorithm. The results showedthat when the error was within ±0.02p.u., the proposedalgorithm met the calculation accuracy requirements. Sta-tistical results indicated that when the transformer’s op-erating environment temperature did not reach 25◦C, theoperational capacity remained unchanged under continu-ous overload conditions; as the temperature increased, theoperational capacity gradually decreased, and there wasa linear relationship between the two. Under the hour-level overload state, different initial load rates (1.05p.u.,1.15p.u., 1.25p.u.) were used as analysis conditions, andthe hour-level overload capacity was calculated using theproposed algorithm. The results showed that under dif-ferent initial load rates, when the temperature remainedconstant, the overload capacity was positively correlatedwith the duration; when the initial load rate and over-load capacity were the same, as the temperature increased,the duration gradually decreased. Under three initial loadrate conditions, the overload capacity decreases as the ini-tial overload rate increases, and the duration will also beshortened.Reference [12] conducted an in-depth study on the vibra-tion characteristics of ±800 kV converter transformers un-der overload conditions. Through full-load thermal stabil-ity tests, important information such as vibration, voltage,and current under different load conditions was collected,and features such as vibration amplitude, vibration spec-trum, main frequency, vibration power ratio in differentfrequency bands, vibration power entropy, and odd-evenharmonic ratio were analyzed to evaluate the vibrationstate. Under overload conditions, the vibration amplitudeof the converter transformer significantly increases, mainlydue to the electromagnetic force generated by the load cur-rent in the windings. Theoretical analysis shows that theelectromagnetic force is proportional to the square of theload current, so the vibration amplitude increases quadrat-ically with the increase in the load rate. The vibrationpower ratio in different frequency bands changes, reflectingthe shift of the vibration source from the core to the wind-ings. The vibration power ratio in the low-frequency band(0-400 Hz) decreases from light load to medium load butincreases from medium load to heavy load, while the op-posite occurs in the high-frequency band. Under overloadconditions, the vibration power entropy decreases, indicat-ing a reduction in the complexity of the vibration signal.The odd-even harmonic ratio decreases with the increasein the load rate under overload conditions, which is relatedto the operating state of the filter.Reference [13] analyzed the temperature distribution lawof the windings of ±800 kV converter transformers underthe influence of different harmonic currents through a two-dimensional refined simulation model. It was pointed outthat as the load rate increases, the vibration amplitude ofthe converter transformer significantly increases, mainlydue to the electromagnetic force generated by the loadcurrent in the windings. The vibration frequency of theconverter transformer gradually shifts from 200 Hz to 300Hz or 400 Hz, indicating that under overload conditions,the vibration of the windings gradually replaces the vibra-tion of the core as the dominant vibration source. In addi-tion, the temperature rise caused by harmonic currents in-creases the hot spot temperature of the windings, therebyaffecting the mechanical performance and stress distribu-tion of the windings. High-frequency harmonic currentscause the equivalent resistance of the windings to gradu-ally increase, intensifying the losses and further raising thetemperature of the windings. Under overload conditions,the stress distribution and temperature distribution of thewindings become more complex, and the coupling effect ofharmonic currents and temperature rise needs to be com-prehensively considered. The final research shows that asthe content and frequency of harmonic currents increase,the hot spot temperature and stress of the windings signif-icantly increase. The proposed winding stress calculationmodel can accurately reflect the influence of harmonic cur-rents and temperature rise on the stress of the windings,providing important technical guidance for the design andmaintenance of converter transformers.Reference [14] studied the stress distribution characteris-tics of the windings of ±800 kV converter transformers un-der the influence of harmonic currents through simulation,revealing the thermal characteristics and stress changes ofthe transformer under overload conditions. The researchshows that harmonic currents cause the temperature ofthe windings to rise, with uneven temperature distribu-tion, and the hot spots are mainly concentrated in theupper part of the windings. Under 250 Hz harmonics, asthe harmonic current content increases from 0% to 20%,the hot spot temperature of the grid side winding risesfrom 87.2◦C to 99.2◦C, and that of the valve side risesfrom 98.1◦C to 108.7◦C; under 650 Hz harmonics, thetemperature rise of the grid side hot spot is more signif-icant. At the same time, the stress distribution of the2windings is affected by temperature and shifts towards theoil channels and the center area of the windings, with themaximum stress increasing in a power function relation-ship with the harmonic current content. The research alsoshows that the temperature rise caused by harmonic cur-rents increases the equivalent resistance of the windings,intensifying losses and temperature rise, and the changesin stress distribution and magnitude reflect the complexmechanical behavior of the windings under overload con-ditions. These findings provide key guidance for the designand maintenance of converter transformers under overloadconditions [15]- [16].Therefore, to further enhance the performance, reliabil-ity and economy of the flexible DC transmission systemfor offshore wind power, and to support the developmentand construction of offshore wind power and contribute tothe realization of China’s dual carbon goals, in-depth re-search on the thermal characteristics and overload capacityof offshore converter transformers can improve the opera-tional efficiency and reliability of converter transformers,and also ensure the efficient transmission of wind powerand the guarantee of power quality. This is of great prac-tical significance and urgency for promoting the rapid de-velopment of the offshore wind power industry.2. Theoretical ResearchTo simulate the thermal and flow fields within a trans-former, this study uses Fluent, a numerical calculationsoftware based on the finite volume method. The phys-ical foundation of this method is detailed below. Beforenumerical computation, the computational domain is di-vided into several control volumes. Each mesh point issurrounded by a control volume ∆V , the smallest geomet-ric unit for applying control equations. The 2D structuredmesh used in this study is shown in the figure below. Inthe figure, P represents the grid node under study and itssurrounding control volume. The boundaries of this con-trol volume are denoted as n, w, s, and e, with horizontaland vertical widths of ∆x and ∆y, respectively. N, W, S,and E represent the grid nodes adjacent to P and theirsurrounding control volumes.Discretizing the conservative control equations of the fi-nite volume method on each mesh yields:∂(ρφ)∂τ+∂(ρuφ)∂x+∂(ρvφ)∂y=∂∂x(Γ∂φ∂x) +∂∂y(Γ∂φ∂y) + S (1)The equation can be divided into four parts, representingthe sum of the rate of change of a general variable φ withtime, and the convective outflow equals the sum of thediffusive inflow and the increase from internal sources. Asthis study focuses on steady-state results, the first termon the left, the partial derivative with respect to time, iszero. u and v denote the velocity components of φ in thex and y directions, Γ is the diffusion coefficient of φ, andS is the source term. Integrating the differential equationover each mesh gives:Figure 1. Two-dimensional structural mesh∆V∂(ρuφ)∂x+∆V∂(ρvφ)∂y=∆V∂∂x(Γ∂φ∂x)+∆V∂∂y(Γ∂φ∂y) +∆VS(2)Since ∆x1 = ∆x2 = ∆x, ∆y1 = ∆y2 = ∆y,∆V = ∆x∆y the above equation can be expanded as:[(ρuφA)e − (ρuφA)w] + [(ρvφA)n − (ρvφA)x]=ïÅΓA∂φ∂xãe−ÅΓA∂φ∂xãvò+ïÅΓA∂φ∂yãn−ÅΓA∂φ∂yãxò+S∆x∆y(3)Where the convection term and diffusion term are rep-resented by the convection flow rate and diffusion quan-tity at the control volume boundary, A represents thelength of the control volume boundary, and the subscriptse, w, n, and s pass through the eastern, western, northern,and southern boundaries, respectively. And Aw = Ae =∆x, An = As = ∆y. These quantities can be further rep-resented by interpolating adjacent nodes in the difference-in-center format:(ρuφA)e = (ρu)eAeφE + φP2(4)(ρuφA)w = (ρu)wAwφW + φP2(5)(ρvφA)n = (ρv)nAnφN + φP2(6)(ρvφA)s = (ρv)sAsφS + φP2(7)ÅΓA∂φ∂xãe= ΓeAeïφE − φP∆x2ò(8)ÅΓA∂φ∂xãw= ΓwAwïφP − φW∆x1ò(9)ÅΓA∂φ∂xãn= ΓnAnïφN − φP∆y1ò(10)ÅΓA∂φ∂xãs= ΓsAsïφP − φS∆y2ò(11)3Fi = (ρu)iAi or Fj = (ρv)jAjDi =ΓiAi∆xior Dj =ΓjAj∆yj(12)where i takes w and e, and j takes n and s. Finishing isavailable:ïFe2(φE + φP ) −Fw2(φW + φP )ò+ïFn2(φN + φP )−Fs2(φS + φP )ò= [De (φE − φP ) − Dw (φP − φW )]+ [Dn (φN − φP ) − Ds (φP − φS)] + SV(13)Based on the above equation, it is sorted out according tothe general variable φ to obtain:ïÅDe +Fe2ã+ÅDw −Fw2ã+ÅDn +Fn2ã+ÅDs −Fs2ãòφP =ÅDe −Fe2ãφE +ÅDw +Fw2ãφW+ÅDn −Fn2ãφN +ÅDs +Fs2ãφS + SV(14)The α = D± F2 coefficient of the variable of the normalizedtreatment is written:αP φP = αEφE + αW φW + αN φN + αSφSαP= αE + αW + αN + αS + FE − FW + FN− FS − SP(15)Write the discrete equation for all control node columns,and solve the system of equations according to the initialconditions to obtain the quantity to be solved.3. Material Properties and Finite Element Simu-lationTo solve the temperature and flow fields of a 2D model us-ing Fluent, it is essential to first specify the materials andtheir physical properties within the computational domainand accurately calculate the losses of heat-generating com-ponents.3.1 Transformer Oil Physical ParametersThe oil-immersed transformer uses mineral oil as the cool-ing medium, and its physical properties, such as density ρ,specific heat capacity Cp, thermal conductivity γ, and dy-namic viscosity, µ, will change with the change of temper-ature, affecting its heat transfer efficiency and heat dissi-pation effect. Therefore, the following laws of transformeroil physical parameters with temperature are summarizedand set accordingly in the simulation model, which can im-prove the calculation accuracy of thermal field steady-statesimulation.a) DensityBased on the density of transformer oil measured at5 K (5◦C) intervals within the temperature range of278.15 K (5◦C) to 373.15 K (100◦C), the density as afunction of temperature is shown in Fig. 2 below. Itcan be seen from the figure that the density of trans-former oil is approximately negatively linearly cor-related with temperature, and the density decreaseswith the increase of temperature.ρ(T) = 1093−0.826T +3.612×10−4T2Äkg · m−3ä(16)Figure 2. The Relationship Between Density and Temper-atureAccording to the known data, the function relation-ship between density and temperature is obtained asfollows, where ρ the transformer oil density is thetransformer oil density and T is the oil tempera-ture, which is only valid in the temperature range of278.15 − 373.15 K.b) Specific heat capacitySpecific heat capacity is a commonly used physicalquantity in thermodynamics, which refers to the en-ergy absorbed or dissipated by a unit temperature ofa unit mass of a substance rising or falling, and canbe used to characterize the ability of the substanceto absorb heat or dissipate heat. The specific heatcapacity-temperature curve is shown in Fig. 3 usingthe specific heat capacity of the transformer oil corre-sponding to each 5 K interval in 278.15 − 373.15 K.Cp(T) = 455.9+5.191T −1.522×10−3T2(J · kg−1· K−1) (17)From the curve, it can be seen that the two are ap-proximately positively linearly correlated, and the spe-cific heat capacity of transformer oil increases with theincrease of temperature. After the function fitting,the functional relationship between the specific heatcapacity and the temperature is obtained as follows,where Cp is the specific heat capacity of transformeroil. It is also noted that the equation holds only in thetemperature range of 278.15 − 373.15 K.c) Thermal conductivityThermal conductivity characterizes the thermal con-ductivity of a material. The higher the thermal con-ductivity, the better the thermal conductivity of thematerial. According to the thermal conductivity ofthe transformer oil corresponding to each interval of 54Figure 3. The Relationship Between Specific Heat Capac-ity and TemperatureFigure 4. The Relationship Between Thermal Conductiv-ity and TemperatureK in 278.15 − 373.15 K, the curve of thermal conduc-tivity with temperature as shown in Fig. 4 below isobtained.The thermal conductivity of transformer oil decreasesapproximately linearly as the temperature rises. Therelationship between thermal conductivity and tem-perature is fitted exponentially to obtain the func-tional relationship described in the following equation.In the following formula, is the thermal conductivityof transformer oil. This formula holds only when thetemperature is in the range of 278.15 373.15 K.γ(T) = 0.1538 − 7.645 × 10−5T(W · m−1· K−1) (18)3.2 Solid Domain Material Characteristics andHeat Source SettingThe main materials used in the solid domain are siliconsteel sheet, copper and cellulose, and their physical prop-erties fluctuate very little in the temperature range of273.15 − 373.15 K, which can be regarded as constant inthe simulation calculation:ρfe = 7550( kg/m3)Cpfe= 446( J · kg−1· K−1)γfe = 51.9( W · m−1· K−1)ρcu = 8978( kg/m3)Cpcu= 381( J · kg−1· K−1)γcu = 387.6( W · m−1· K−1)ρisl = 1400( kg/m3)Cpisl= 1600( J · kg−1· K−1)γisl = 0.15( W · m−1· K−1)Among them, the subscripts Fe, Cu and ISL representthe iron core, copper wire, and insulating paper composedof the above materials, respectively.The winding is composed of two parts, copper wire andinsulating paper, when calculating the calorific value perunit volume of low-voltage and high-voltage windings, itis necessary to consider the influence of insulating paper,and multiply the heat source per unit volume of the copperconductor by the area ratio of the copper conductor to thewire cake in the two-dimensional model, so as to obtainthe equivalent unit volume heat source of the wire cake.In addition, the cushion block between the wire cake andthe wire cake is not conducive to the heat dissipation of thewinding, and the equivalent volume heat source needs tobe adjusted according to the coverage area, and finally theheat flux density of each wire cake of the low-voltage andhigh-voltage windings is 247.4 kW/m3 and 181.6 kW/m3,respectively.3.3 Boundary Condition Setting and Model Se-lectionThe interaction between the fluid and the wall is the keyto the coupling heat transfer problem, and the appropriateboundary conditions and initial conditions can not onlymeet the thermophysical requirements but also improvethe stability of the calculation. According to the actualsituation of the temperature rise test, the ambient tem-perature was set to 293.15 K in the simulation. All solidsurfaces in contact with the oil are non-slip, the outer sur-face of the oil tank and radiator is set to convective heattransfer, and the thermal boundary conditions of the restof the solid surfaces are coupled heat transfer. In orderto ensure the convergence and stability of the calculation,two criteria are used to determine that the temperaturefield and flow field in the transformer reach a steady state,one is that the residuals of these equations are within theallowable range: the residuals of the continuity and ve-locity equations are less than 10−3, and the residuals ofthe energy equations are less than 10−6; Another criterionis that the area-weighted average temperature fluctuationof the low-voltage winding is less than 0.5◦C in 1000 stepiterations.The proper selection of the mathematical model shouldfirst judge the type of oil flow in the transformer, and themain judgment is based on the Reynolds number. Usu-ally, the Reynolds number less than 2300 is laminar flow,otherwise it is considered turbulence. For ON-type trans-formers, the oil flow velocity is very low (oil flow inlet ve-5locity less than 0.1 m/s ), and the kinematic viscosity ishigh, resulting in a low Reynolds number for the flow. Inthe two-dimensional model established in this paper, theReynolds number is estimated to be about 31 based onthe temperature, flow velocity, and channel width of theoil inlet, so the laminar flow model is adopted. In additionto this, in order to facilitate the calculation of fast con-vergence, the pressure solver chooses PRESTO based onstaggered volume control.3.4 Model Simulation ResultsTaking the DF-80000/220 transformer as an example, themodel information is shown in Table 1. Among them, ”230/√3kV ” refers to the rated phase voltage of the high-voltage winding (Y-connection), and ” 35 kV ” refers tothe rated line voltage of the low-voltage winding ( ∆-connection). After running 15,000 steps in Fluent, thesteady-state convergence result was obtained. In the sim-ulation model, no heat source load is applied to the corepart, and the equivalent heat source power of eddy cur-rent loss is set for the top and bottom wire cakes of thehigh and low voltage windings. The cooling method ofthe transformer follows the IEC 60076-7 standard, wherethe acronym ONAF (Oil Natural Air Forced) describesthe cooling system characterized by natural oil circulationcombined with forced air cooling via fans.Table 1Transformer Model InformationTransformermodelCoolingmethodRated voltage/kVRatedcapacity/kVADF- 80000/220 ONAF 230/√3/35 80000Figure 5 visualizes the operational thermal profile: (a)presents the full transformer with temperature gradients,revealing hotspots at the core-stack junction and upperwindings; (b) zooms into the high-voltage winding, wherethe peak temperature at the top terminal correlates withcurrent concentration in the terminal assembly. As can beseen from Fig.5, the hot spot temperature of the trans-former is 108.1◦C, which appears at the top of the low-voltage winding, and the maximum temperature of thehigh-voltage winding is 97.88◦C, which appears in thehigh-voltage winding top line cake. The internal tempera-ture distribution and hot spot position of the transformerwinding are different from those of the previous two, whichis analyzed to be caused by the large eddy current loss ofthe wire cake at the top of the winding. In the vicinityof the oil baffle inside the winding, the temperature dis-tribution also presents a more obvious local extreme phe-nomenon.Figure 6 visualizes the oil flow dynamics: (a) presentsthe full transformer with velocity gradients, highlightinghigh-velocity channels at the oil inlet and low-velocity re-circulation zones near the corelamination interface; (b)zooms into the high-voltage winding region, where thepeak flow velocity at the winding entrance corresponds tothe structural design of the internal oil ducts. The maxi-mum oil flow rate inside the transformer is 0.102 m/s, andFigure 5. Transformer Temperature Distribution CloudMapFigure 6. Cloud Map of Transformer Oil Flow VelocityDistributionthe maximum oil flow rate of the high-voltage winding is0.095 m/s, which appears at the internal oil baffle.3.5 Simulation Model and Solution Process ofConverter Transformer Temperature Field(1) Analysis of harmonic influence on the temperaturefield of the converter transformer and study on cop-per shielding effectThe finite element analysis software is used to calculatethe temperature of the converter transformer, and theJoule heat obtained in the magnetic field is used as thethermal load of the temperature field analysis, whichis applied to the transformer winding and its oil tank,and structural parts, respectively. At the same time,the changes of the hot spot temperature of the con-verter transformer winding, the hot spot temperatureof the oil tank wall, and the hot spot temperature ofthe clamp before and after the installation of the cop-6Table 2Thermal Properties of Converter Transformer Structural PartsComponent Material PermeabilityThermal conductivityW/ (m · ◦C)Specific heat capacityJ/ (kg ·◦C)Density (kg/m3)Core 27ZH100 B-H curve 21 m · ◦C 490 kg · ◦C 7650 kg/m3Winding Copper - 338 381 8978Oil tank A3 Steel B-H curve 50 485 7800Clamping Nonmag-netic steel- 50 502 8030per shield under the harmonic condition are analyzed.Table 2 shows the thermal properties of the convertertransformer core, winding, oil tank, and clamp.The converter valve generally uses a 12 -pulse valvegroup. Due to the rapid conversion of the on-off valveduring the working process of the converter valve,many harmonics will be generated, which have a signif-icant impact on the quality of the power supply. Sincethe 12-pulse converter valve group is composed of two6-pulse converters in series, it is generally studied byanalyzing the 6-pulse converter valve as an example.The function of the converter determines that manyharmonics will be generated during the commutationprocess. The types of harmonics can be roughly di-vided into three categories: characteristic harmonics,non-characteristic harmonics, and conduction harmon-ics.For the 12 -pulse rectifier, the 6 × (2 K − 1) ± 1 har-monics cancel each other due to the equal amplitudeof each harmonic component of the Y/y and Y/d con-verter transformers and the same phase of the 12 K+1harmonics. Therefore, there are only characteristicharmonics in the 6-pulse harmonics, of which 6 K + 1is a positive-sequence characteristic wave and 6 K − 1is a negative-sequence characteristic wave. Therefore,there are only 12 K + 1 harmonics on the AC side ofthe 12 -pulse converter.In the process of engineering operation, there is a cer-tain gap between the operation of DC transmissionproject and the theoretical simulation state. There-fore, there are other ripples accompanied by charac-teristic harmonics, which are called non-characteristicharmonics. Such harmonics are often caused by non-ideal conditions. For example, the trigger pulse pe-riod is not absolutely equal, the bus voltage is notstrictly symmetrical or the commutation reactance isunbalanced, which may lead to the generation of non-characteristic harmonics. Due to the many and com-plex causes of non-characteristic harmonics, and in theactual equipment manufacturing process, manufactur-ers will specifically design to maximize the suppres-sion of non-characteristic harmonics, so that the im-pact of non-characteristic harmonics in the DC trans-mission process is not obvious. The analysis of non-characteristic harmonics often adopts the method ofignoring other causes and analyzing a certain cause.(2) Field-circuit coupling model of converter transformerThe single capacity of the ultra-high voltage convertertransformer is large, so the stray loss caused by theleakage magnetic field is becoming more serious, andit will undoubtedly increase the stray loss caused bythe leakage magnetic field in the case of DC bias orserious harmonics. Therefore, this chapter will carryout finite element simulation calculation on the hotspot temperature of converter transformer winding, oiltank wall and clamp under harmonic conditions, andcompare it with the temperature after adding coppershielding.Fig. 7 is a 1/2 converter transformer three-dimensionalmodel diagram based on the converter transformermodel ZZDFPZ-412300/750-200 provided by thetransformer company. Based on the parameters ofthe transformer experimental model, the transformermodel is simplified. Due to the symmetry, half ofthe three-dimensional physical model and equivalentcircuit model are established by MAGNET software,which is the field-circuit coupling model, as shown inFig.8.Figure 7. 1/2 Structure Model Diagram of ConverterTransformer(3) Solution processAccording to the finite element simulation model es-tablished above, the corresponding material propertiesare loaded into the physical model, and the accuracysuitable for this simulation is selected for subdivision.The corresponding subdivision results are shown inFig.9. According to the field-circuit coupling method,the physical model of the transformer is coupled withthe circuit model, and the relevant simulation analy-sis is carried out. A sinusoidal AC voltage source isadded to the primary side of the circuit model, andthe equivalent simulation calculation is performed onthe working conditions under harmonics. The initialtemperature of the environment was set to 30◦C.7Figure 8. Field-Circuit Coupling ModelFigure 9. Meshing Diagram of the ModelCompared with the general transformer, the structure ofthe converter transformer is more complex, and its interiorhas a variety of media and nonlinear materials. Therefore,this chapter uses MagNet/ThermNet electromagnetic fieldfinite element analysis software. According to the symme-try of the converter transformer structure and the char-acteristics of the electromagnetic distribution, the calcula-tion model of the converter transformer is simplified andassumed as follows:(1) Because the converter transformer is a symmetricalstructure, so the calculation reduces the calculationtime to take the model of the whole transformer 1/2structure, and the inner side of the symmetrical sur-face is set to a symmetrical boundary.(2) Ignoring the DC component of the low-voltage valveside winding, the total ampere turns of the grid sidewinding and the valve side winding are balanced afterconsidering the influence of the high-order harmoniccurrent.(3) The core silicon steel sheets and components of theconverter transformer are processed according to thenonlinear material of the non-magnetic steel, ignoringthe hysteresis effect of the ferromagnetic material andbeing isotropic.(4) Ignore the eddy current in the core, and the influenceof lead current and displacement current on the leakagemagnetic field.According to the above solution process, the core loss ofthe converter transformer in MagNet under no-load condi-tion is 166 kW and the load loss is 1050 kW. Fig. 10, Fig.11 and Fig. 12 show the unshielded temperature of theconverter transformer and the temperature distribution ofthe tank wall and the clamp under rated conditions.Figure 10. The Overall Temperature Distribution CloudDiagram of the TransformerFigure 11. Temperature Distribution Cloud Diagram ofCore and WindingAs shown in Fig.10, Fig. 11 and Fig.12, before the mag-netic shielding is not installed, the hot spot temperatureof the winding can reach 82.77◦C, and the hot spot tem-perature of the core can reach 74.92◦C. The eddy currentdensity of the fuel tank is concentrated at the hot spot ofthe winding corresponding to the rear wall of the fuel tank,reaching 84.72◦C. The clamp is located in the area wherethe leakage magnetic field of the transformer is strong, andthe size is relatively small compared with other structuralparts. It is easy to induce a large eddy current loss in itslocal area. The highest temperature rise of the clamp isat the central column of the iron core, because this is a8Figure 12. Temperature Distribution Cloud Diagram ofFuel Tank Wall and Clamphigh magnetic flux leakage area, and the eddy current lossis relatively large, so the temperature rise here is higher,forming a local hot spot, and at this time the hot spottemperature of the clamp also reached 77.52◦C.The heat resistance grade of oil-immersed transformersis grade A, and the insulation materials used in the trans-former have a certain heat resistance life. At this time,the hot spot temperature of the oil tank wall and the hotspot temperature of the clamp will form local overheating.Therefore, this local overheating will cause insulation ag-ing, threatening the safe use and life of the transformer,and it must be improved. Electromagnetic shielding gen-erally refers to the shielding device made of a copper plate(or an aluminum plate), and the installation of electromag-netic shielding in the fuel tank is one of the main methodscommonly used in engineering to reduce the eddy currentloss caused by magnetic flux leakage on the fuel tank. Un-der the action of the magnetic flux of the leakage magneticfield, an eddy current will be induced on the surface ofthe copper plate. The magnetic field generated by theeddy current is just opposite to the direction of the leak-age magnetic field and cancels each other out, so that theleakage magnetic flux entering the transformer tank is re-duced, so as to achieve the purpose of reducing the eddycurrent loss and magnetic flux density of the transformertank. In view of the above problems, this paper adds a4mm thick copper shield in the calculation.Figure 13. Copper Shielding Position Structure DiagramAfter adding copper shielding in the simulation, the tem-perature field of the current transformer under rated loadis simulated to verify the influence of copper shielding onhigh temperature. Fig. 14 and Fig. 15 are shown as thecore, winding temperature cloud map, fuel tank wall, andclamp temperature cloud map after the installation of thecopper shield.Figure 14. Cloud Map of Core and Winding TemperatureDistributionFigure 15. Cloud Map of Temperature Distribution on theFuel Tank Wall and ClampsAfter the installation of 4 mm thick copper shield, fromFig.15, the hot spot temperature of the fuel tank dropsto 60.52◦C, and the hot spot temperature of the clampdrops to 64.01◦C. The calculated temperature rise con-forms to the temperature rise limit of Class A insulatingmaterial. Therefore, the copper shields installed in thefollowing parts of this section are all 4 mm thick.4. Thermal Rise Calculation Considering Accu-racy and Real-Time RequirementsThe thermal circuit model method, while fast and simple,has lower accuracy due to parameter errors from simplifiedheat transfer representations. In contrast, the steady-statesimulation method offers high accuracy and detailed physi-cal field distributions but is computationally intensive andtime-consuming, requiring significant computer resourcesand making it less practical for on-site use. To reconcile theneed for both accuracy and real-time performance, a field-circuit coupling method is proposed. This method refinesthe thermal circuit model parameters based on simulationresults, enabling precise hotspot temperature calculations.For the field-circuit coupling model, the first step is toidentify the coupling parameters. These parameters arecategorized into five classes, as shown in Fig.16. Name-plate data, structural data, and winding DC resistance canbe obtained from routine transformer tests. Temperature-rise test data, used to simplify heat dissipation resistance9Figure 16. Parameters Required for the Hot Path Model Methodcalculations, are derived from temperature-rise tests; ifthese tests are unavailable, relevant data such as the num-ber and height of coils in different windings and the out-er/inner diameters of windings can be used as alterna-tives. When the transformer tap position is fixed, thesedata remain unchanged for each calculation. Initial valuedata, which affect the speed of the thermal circuit modelmethod, can be roughly estimated due to the method’sfast computation speed. Operating data, which vary withthe transformer’s operating state, directly impact calcula-tion accuracy. Ambient temperature and load current canbe monitored in real-time, while top oil temperature andhotspot coefficients require precise assignment.For transformers with online top-oil-temperature mon-itoring, real-time top-oil-temperature data is accessible.However, installing temperature sensors inside transform-ers demands high design standards for internal structures,and most transformers lack these sensors. Retrofittingin-service transformers with sensors is more challengingand costly than installing them during design or manufac-turing. The hot-spot coefficient lacks a precise definitionformula. Load guidelines suggest a hot-spot coefficient of1.3 for medium and large transformers, yet this approachoverlooks the specific structure and operating conditionsof transformers, potentially compromising the accuracy ofhot-spot temperature calculations. steady-state simulationcan model the steady thermal field of transformers underany operating conditions, allowing for the calculation ofthe top-oil temperature and hot-spot coefficient. Based onthis, the coupling parameters of the thermal circuit modeland steady-state simulation are identified as the top-oiltemperature and hot-spot coefficient.The core steps of the coupled calculation model are asfollows:1. Use steady-state simulation to model the opera-tion of the transformer under typical load currents and am-bient temperatures. Collect data on top-oil temperature,bottom-oil temperature, hot-spot temperature, and aver-age winding temperature under different operating con-ditions to calculate the hot-spot coefficient and form adatabase.2. Analyze the database to determine the rela-tionship between top-oil temperature, hot-spot coefficient,load ratio, and ambient temperature. Develop formulas forcalculating top-oil temperature and hot-spot coefficient un-der any load and ambient temperature conditions.3. Dur-ing field operation of the transformer, calculate the top-oil temperature and hot-spot coefficient based on actualoperating conditions and input them into the thermal cir-cuit model. This enables quick estimation of the hot-spottemperature at steady-state and supports simulation cal-culations. The following Fig. 17 summarizes the aboveapproach. Taking the SFZ8-31500/110 transformer as anexample, the first two steps are described in detail.(1) The general provisions of power transformers stipu-late that the maximum ambient temperature of powertransformer operation shall not exceed 40◦C, the min-imum ambient temperature of indoor transformer op-eration shall not be less than −5◦C, and the minimumambient temperature of outdoor transformer shall notbe less than −25◦C. Considering that users are moreconcerned about the change of the internal tempera-ture of the transformer at high temperatures, whenthe ambient temperature is very low, the temperaturerise of the windings is small even at high load rates,so the ambient temperature range of steady-state sim-ulation is set at 5◦C ∼ 40◦C (simulated every 5◦C ).Generally, the economic load rate of the transformeris 0.75 ∼ 0.85, when the transformer needs to bearthe overload, the load rate should not exceed 1.2, con-sidering that some in-service transformers have a longoperating life and the carrying capacity is reduced, therange of load rate selected in the steady-state simula-tion is 0.4 ∼ 1.2 (every 0.2 simulation). Since the hot10Table 3Top Oil Temperature and Hot Spot Coefficient of Transformers Under Different Operating ConditionsLoad rate Ambient temperature 0.4 0.6 0.8 1.0 1.25◦CTop layer oil temperature/◦C27.18 30.85 38.11 47.10 55.03Hot Spot Coefficient 1.29 1.31 1.26 1.17 1.1610◦CTop layer oiltemperature/ ◦C30.31 35.90 42.05 49.94 57.85Hot Spot Coefficient 1.19 1.15 1.18 1.18 1.1515◦CTop layer oiltemperature/ ◦C33.97 39.00 46.41 53.72 62.39Hot Spot Coefficient 0.99 1.19 1.11 1.09 1.1320◦CTop oil temperature /◦C 37.99 43.60 49.82 57.30 65.43Hot Spot Coefficient 1.05 1.07 1.10 1.10 1.1625◦CTop oil temperature/ ◦C 41.53 47.25 53.54 61.29 70.30Hot Spot Coefficient 1.00 1.03 1.08 1.08 1.1430◦CTop oil temperature/ ◦C 46.39 51.36 57.78 65.42 74.36Hot Spot Coefficient 0.84 1.02 1.06 1.09 1.1135◦CTop layer oiltemperature/ ◦C50.95 55.42 61.90 69.89 78.08Hot Spot Coefficient 0.76 1.02 1.06 1.08 1.1440◦CTop layer oiltemperature/ ◦C55.17 60.05 66.45 73.49 83.19Hot Spot Coefficient 0.80 0.96 1.04 1.11 1.14Figure 17. Coupling Calculation Flowcircuit model method needs to input the top oil tem-perature and hot spot coefficient of the current op-erating state obtained by the steady-state simulationmethod, the following Table 3 can be obtained by col-lating these data.(2) In order to obtain the top oil temperature and hotspot coefficient of the transformer under any operat-ing state, it is necessary to analyze the data obtainedunder typical operating conditions. The load loss isproportional to the square of the load factor, so thevariation curve of the top oil temperature with thesquare of the ambient temperature and the load rateis respectively made, as shown in Fig. 18 below.The top oil temperature increases with the increase ofthe square of the ambient temperature and the load rate,respectively, and shows a strong linear relationship, so themultiple linear regression method is used to analyze thechange trend of the top oil temperature under any operat-ing state. Multiple linear regression is a kind of regressionanalysis method, which is often used to study the relation-ship between dependent variables and multiple indepen-dent variables and has been widely used in various fields.A multiple linear regression equation is established basedon the number of dependent variables, as shown in (19).f(x) = a0 + a1x1 + a2x22 (19)where x1 and x2 represent the ambient temperature andload rate, respectively, with the help of statistical analysissoftware SPSS, the estimated values of parameters a0, a1and a2 can be obtained through stepwise regression, soas to obtain the expression of the top oil temperature, asshown in the following ().Ttop-oil = 19.51 + 0.8x1 + 21.76x22 (20)In order to evaluate the effect of the regression model, theequation was tested for goodness-of-fit R2 and significanceF.R2 is 0.997, which is very close to 1, and the F-valuefalls in the rejection domain, which is very significant, sothe equation has a good linear regression effect.The relationship between the hot spot coefficient andthe ambient temperature and load rate is shown in Fig. 19below, and the change of the hot spot coefficient is morecomplex than that of the top oil temperature. Overall,the hot spot coefficient is negatively correlated with the11(a) The VariationRelationship of Top Layer OilTemperature and AmbientTemperature Under DifferentLoading Rates(b) The VariationRelationship of the Top LayerOil Temperature and theSquare of the Load RateUnder DifferentEnvironmental TemperaturesFigure 18. The Variation Law of the Top Layer Oil Tem-perature of the Transformer Under Different OperatingConditionsambient temperature and positively correlated with theload rate, which is a nonlinear problem. If the nonlinearregression method is to be adopted, the difficulty lies indetermining the nonlinear regression equation, consideringthat the change of the hot spot coefficient is approximatelylinear, and the linear fitting method is used to determinethe expression.(a) The Relationship Betweenthe Hot Spot Coefficient andthe Variation of AmbientTemperature(b) The Relationship Betweenthe Hot Spot Coefficient andthe Square of the Load RateFigure 19. The Variation Law of the Transformer Hot SpotCoefficient Under Different Operating ConditionsFirstly, based on Fig.19(b) above, the hot spot coeffi-cient H curve at different ambient temperatures is linearlyfitted, and the expression is obtained as follows.H = −0.20x2 + 1.40x1 (x1 = 5◦C)H = −0.017x2 + 1.18x1 (x1 = 10◦C)H = 0.084x2 + 1.04x1 (x1 = 15◦C)H = 0.13x2 + 0.99x1 (x1 = 20◦C)H = 0.16x2 + 0.93x1 (x1 = 25◦C)H = 0.31x2 + 0.78x1 (x1 = 30◦C)H = 0.41x2 + 0.68x1 (x1 = 35◦C)H = 0.42x2 + 0.67x1 (x1 = 40◦C)The slope and intercept of the equation at ambient tem-perature of 20◦C are taken as the initial slope and initialintercept of the hot spot coefficient prediction equation,and the average value of the difference between the slopeof the adjacent equation and the average value of the dif-ference between the intercept are taken as the increase anddecrease constants of the slope and intercept of the predic-tion equation, respectively, and the prediction equation isobtained:H =ï0.13 +0.089 (x1 − 20)5òx2 +ï0.99 −0.10 (x1 − 20)5ò(21)Finishing type can get the following (22):H = 1.40 − 0.02x1 − 0.22x2 + 0.018x1x2 (22)The goodness-of-fit test of the equation shows that R2 is0.823, and the predicted hotspot coefficient value of theequation is less than 0.1, so the coupled calculation modelhas good prediction accuracy.The proposed field-path coupling model is used to cal-culate the average oil temperature, the average windingtemperature, the top oil temperature and the hot spot tem-perature of a transformer under the operating conditionsof temperature rise test conditions, and the calculation re-sults are compared with the temperature rise test results,as follows.The results are shown in the following table, where thedefinition of the average oil temperature in the tempera-ture rise test value is the same as that of the previous two,and the average temperature value of the winding is theaverage value of the high-voltage winding and the averagetemperature value of the low-voltage winding. From theresults in the table, it can be seen that the error of thecalculated value of the field-path coupling model and thetemperature rise test value is within 5◦C, which can meetthe actual engineering requirements.According to the thickness of the transformer wire andthe rated capacity, the hot spot coefficient H = 1.2 is de-termined, and the hot spot temperature value is 101.68◦Caccording to the standard recommendation method. Thesimulation results show that the hot spot temperature ofthe transformer appears at the #1-line cake, that is, the#1 optical fiber temperature measurement point, so thetemperature value of 115.0◦C is used as the temperaturerise test value of the transformer hot spot temperaturefor comparison. According to Table 4 below, the abso-lute error between the hot spot temperature value andthe temperature rise test value calculated by the field-pathcoupling model is 0.25◦C, while the error of the standardrecommendation method is 14.32◦C. The model has highcalculation accuracy.5. ConclusionsThis paper deeply probes into the thermal characteristicsand overload capacity of converter transformers in offshorewind power flexible DC transmission systems. Two mainconclusions are drawn:(1) By using Fluent to solve the 2D temperature and flowfields of the transformer, we studied the temperature-dependent variations in transformer oil’s properties,12Table 4Calculation Results of Test and Field-Path Coupling MethodAmount of contrast Calculated value/◦CTest values /◦C Absolute error/◦CRelative error/%Average oil temperature 49.80 49.65 0.15 0.30Top layer oil temperature 65.26 64.90 0.36 0.55Average temperature ofthe windings75.74 75.60 0.14 0.19Hot spot temperature 115.25 / / /including density, specific heat capacity, thermal con-ductivity, and dynamic viscosity. These findings en-hanced the precision of thermal field simulations. De-tailed descriptions of solid domain material propertiesand heat source setups were provided, covering thephysical properties of silicon steel, copper, and cel-lulose, as well as the heat flux density calculationsfor each low and high-voltage winding segment. Re-garding boundary conditions and model selection, af-ter considering the interaction between fluid and wall,suitable conditions and a laminar flow model for theoil flow within the transformer were chosen. Takingthe DF-80000/220 transformer as an example, the in-ternal temperature and oil flow velocity distributionswere obtained. It was found that the hotspot temper-ature appears at the top of the low-voltage winding,the highest temperature of the high-voltage windingis in the top coil, and the maximum internal oil flowvelocity occurs at the internal baffle.(2) A field-circuit coupled calculation method is proposed.By analyzing the coupling parameters of the ther-mal circuit model and steady-state simulation, andrefining the model parameters based on simulationresults, the hot-spot temperature can be accuratelycalculated. Through steady-state simulation of thetransformer’s operation under typical load currentsand ambient temperatures, a database of top-oil tem-peratures, bottom-oil temperatures, hot-spot temper-atures, and average winding temperatures was formed,along with the calculation of the hot-spot coefficient.Based on the database, the variation laws of top-oiltemperature and hot-spot coefficient with load ratioand ambient temperature were analyzed, leading to thedevelopment of formulas for calculating these param-eters under any load and ambient temperature condi-tions. Finally, the calculated values of the field-circuitcoupled model show an error of less than 5◦C com-pared to the temperature-rise test values, meeting thepractical engineering requirements. The absolute er-ror of the calculated hot-spot temperature comparedto the test value is 0.25◦C, which is smaller than thatof the standard recommended method, indicating ahigher calculation accuracy.Funding5500-202319103A-1-1-ZN Research on Key Technologiesof Medium-Frequency Convergence DC Transmission forLarge-Capacity Offshore Wind Power.AcknowledgmentsThank you for the great assistance provided by TBEAHengyang Transformer Co., Ltd.References[1] X. Zhou, Y. Luo, L. Zhu, J. Bai, T. Tian, B. Liu, Y. Xu, andW. Zhao, “Analysis of Fine Fault Electrothermal Characteris-tics of Converter Transformer Reduced-Scale Model,” Energies,vol. 17, no. 5, 2024.[2] Y. Wang, K. Liu, M. Lin, H. Tang, X. Li, and G. Wu, “Analysisof electrical–thermal-stress characteristics for eccentric contactstrip in the valve-side bushing of converter transformer,” HighVoltage, vol. 10, no. 1, pp. 106–115, 2024.[3] J. Peiyu, Z. Zhanlong, D. Zijian, W. Yongye, X. Rui, D. Jun, andP. Zhicheng, “Research on distribution characteristics of vibra-tion signals of ±500 kV HVDC converter transformer windingbased on load test,” International Journal of Electrical Powerand Energy Systems, vol. 132, p. 107200, 2021.[4] P. Huang, T. Shen, Z. Liu, R. Dian, X. Wanlun, and D. Wang,“Thermal characteristics analysis of medium frequency trans-former under multiple working conditions,” Thermal Science,vol. 28, no. 1B, pp. 599–609, 2024.[5] Z. Zhou, C. Luo, F. Zhang, J. Zhang, X. Yang, P. Yu,and M. Liao, “Thermal Management in 500 kV Oil-ImmersedConverter Transformers: Synergistic Investigation of CriticalParameters Through Simulation and Experiment,” Energies,vol. 18, no. 9, p. 2270, 2025.[6] J. Peiyu, Z. Zhanlong, D. Zijian, Y. Yu, P. Zhicheng, Y. Fanghui,and Q. Menghao, “Transient-steady state vibration character-istics and influencing factors under no-load closing conditionsof converter transformers,” International Journal of ElectricalPower and Energy Systems, vol. 155, p. 109497, 2024.[7] Y. Guangyuan, L. Xingyuan, F. Ming, and L. Kuan, “Researchon the Calculation Method of Overload Capacity of ConverterTransformer,” Transformer, vol. 52, no. 03, pp. 16–20, 2015. (inChinese).[8] W. Jian, W. Yi, X. Zhangmin, X. Xiaofu, and O. Jinxin, “Co-operative overload control strategy of power grid transformerconsidering dynamic security margin of transformer in emer-gencies,” International Journal of Electrical Power and EnergySystems, vol. 140, p. 108098, 2022.[9] “Thermal Overload Protection of Power Transformers,” Waterand Energy Abstracts, vol. 18, no. 2, pp. 57–57, 2008.13[10] H. Li, Q. Yao, and X. Li, “Voiceprint Fault Diagnosis ofConverter Transformer under Load Influence Based on Multi-Strategy Improved Mel-Frequency Spectrum Coefficient andTemporal Convolutional Network,” Sensors, vol. 24, no. 3,p. 757, 2024.[11] L. Dong, “Analysis of temperature rise characteristics and cal-culation of overload capacity of converter transformer,” ElectricPower Equipment Management, no. 01, pp. 194–195, 201, 2021.CNKI:SUN:DSGL.0.2021-01-081.[12] Q. Menghao, Y. Fanghui, Y. Yuan, J. Peiyu, W. Liming, andZ. Linjie, “Vibration characteristics of ±800 kV converter trans-formers part II: Under load conditions,” International Journalof Electrical Power and Energy Systems, vol. 159, p. 110026,2024.[13] X. Jing, H. Jian, Z. Ning, L. Ruijin, F. Yun, L. Wenlong, andC. Huanchao, “Simulation study on converter transformer wind-ings stress characteristics under harmonic current and tempera-ture rise effect,” International Journal of Electrical Power andEnergy Systems, vol. 165, p. 110505, 2025.[14] W. Hao, Z. Li, S. Youliang, and Z. Liang, “Research on theinfluence mechanism of harmonic components on the noise dis-tribution characteristics of converter transformers,” Interna-tional Journal of Electrical Power and Energy Systems, vol. 160,p. 110095, 2024.[15] A. Irshad and A. Z. J. Nadeem, “An Intelligent Technique forthe Health Assessment of Power Transformer Using ThermalImaging,” International Journal of Power and Energy Systems,vol. 41, no. 1, pp. 48–57, 2021.[16] S. A. Mehdi, “Flux-Based Transformer Model with Inter-TurnFault Considering Saturation Effect,” International Journal ofPower and Energy Systems, vol. 40, no. 1, pp. 1–8, 2020.
Important Links:
Go Back
