Flux: Transformers xxx Philippe Wendling info@tianyuantech.com Create,,Design, sg Engineer! www.magsoft-flux.com www.cedrat.com
Possible analysis Modeling any type of industrial transformers: three-phase, single-phase, auto transformer, reactors.. Simulating classical tests: Analyzing No-load Short-circuit i Inrush current Iron losses Stray losses Joule losses Magnetizing reactance Performing thermal and mechanical analysis Multiphysics (3 rd party tools) References ABB, Alstom, Electricité De France (EDF), Federal Mogul, General Electric, Hydro Quebec, Iskra Stikala, Sh Schneider Electric, Trafomec, Trasfor, Transrail, VATech, Westinghouse 2
Transformers Geometry: Direct Input Import Full or reduced model ¼th 3-phase transformer 3
Physical domain in Flux Steady state AC magnetic: Flux: Transformers and Coils common tests (short circuit, open circuit, rated conditions) Single Frequency/Harmonic Transient Magnetic: common tests (short circuit, open circuit, rated conditions) Full signal Steady state thermal : thermal behavior 4
An example: HV transformer 150 MVA - 132 kv / 14.1 kv Flux Model: (courtesy of WTC) Flux: Transformers and Coils The Electric Circuit V1 HV_1 LV_1 R1 V2 HV_2 LV_2 R2 V3 HV_3 LV_3 R3 5
Flux: Transformers and Coils Transformer Flux region Description Core, Shunts: Laminated Tank frames: δ<<sheet thickness Shunt for fastening: thin sheet thickness Conductive parts with eddy current Windings, Bus bars, current sources, no eddy currents Magnetic non conductive volume region Surface impedance (face region) Thin conducting surface region Solid conductor volume region Coil conductor volume region or non meshed coils µr µr, ρ µr, ρ thickness µr, ρ Coil component Number of turns 6
Modeling of laminated magnetic core Allows reducing the eddy current losses in Flux Problem of dimensional disproportion (sheet length compared to the sheet thickness) Need to simplify the model 7
Equivalent macroscopic model Simplifying i by homogenization i the block of insulated laminations is replaced by a homogeneous block takes into consideration anisotropy, saturation and eddy currents technique Ongoing PhD work taking into account forbidden current loops (paper) User version Lamination available in Flux 3D permits the modeling of the ferromagnetic material by means of the Analytical anisotropic saturation 8
Windings definitions iti 1) Non-meshed coils Fast computation Independent from the mesh 2) Meshed coils : Coil conductor volume region Simplification of the representation as an homogeneous volume region (if thin wires and many turns) 3) Meshed coils : representing every conductor (only for specific studies) 9
Real transformer model Transformer model parameters 10
Flux - Transformer See how it works! 11
Open Circuit it Open Circuit Test Case (No Load) Magnetizing current in the primary Saturated core Neglected leakages V1 HV_1 LV_1 R1 R>>1 I=0A V2 HV_2 LV_2 R2 V3 HV_3 LV_3 R3 12
Open Circuit it Color shades of B Arrows of B Joule losses on the tank: 10 W Energy on the domain: 73 Joules Magnetizing reactance Iron losses on the core (Bertotti): 416 Joules 13
Open Circuit it Flux Computes Results Current in each primary phase Magnetic energy E on the domain Magnetizing current Reactive power/phase E=1/2*L*I² Qtot=2*E*ω Q=Qtot/3 X_1=Q/(I_1)² Magnetizing reactance Xm1, Xm2 Magnetic flux density in core + Bertotti tti coefficients i Iron Losses 14
Principle Magnetizing current neglected Core non saturated low flux density Large flux leakage Short-circuit it test t simulation V1 HV_1 LV_1 R1 R<<1 U=0 V2 HV_2 LV_2 R2 V3 HV_3 LV_3 R3 15
Short-circuit it test t simulation Color shades of B Arrows of B Joule losses on the tank: 1395 W Stray losses Energy on the domain: 1024 Joules Leakage Reactance Laplace forces Joule losses in the windings 16
Short-circuit it test t simulation Flux computes Voltage in each primary phase Magnetic energy E on the domain R1, R2, I1, I2 Radial magnetic induction Stray losses density Short-circuit voltages Results Reactive power/phase p E=1/2*L*I² Qtot=2*E*ω Q=Qtot/3 X_1=Q/(I_1)² Leakage reactance X1, X2 Pj=3*R1*I1²+3*R2*I2² Joule losses in the winding Eddy current losses in the winding Total Stray losses 17
Stray losses Flux leakage ~Eddy current in conductive parts ~Joule losses - «Stray losses» In Flux use of surface impedance region Short-circuit it test t simulation 18
Eddy current losses in the winding Short-circuit it test t simulation Losses per conductor per winding linked to radial magnetic induction Brad In Flux: export on 2D grid of B in the coil use formula P( eddy) 1 b sinh( a / δ ) sin( a / δ ) 2 a sinh( b / δ ) sin( b / δ ) + 2 cosh( a / ) + cos( a / ) Brad σ μ δ δ δ δ cosh( b / δ ) + cos( b / δ ) b 2 = Bax o This methods refer to : Calculation lation of Extra losses in shell transformers s windings, T.Ngneugueu, IEEE, 1988. 19
Laplace forces analysis Definition df(t)=pvec(j,b) = F1+F2(t) with F1 = 1/2Re(JxB*) and F2(t) = cos(2wt).f21+sin(2wt).f22 Display color shades or arrows of Laplace force density on coils DF Laplace/DV = Component F1 (Fundamental) DF Laplace/DV 2w = Pulsating component F2(t) (double frequency) Compute total force Integral of the above quantities in all coils 20
Export Joule losses from short-circuit simulation Thermal analysis of heating For example the Joule losses on the tank Define a Steady State Thermal application Use of thin conducting region with ihexchange and thermal source Create a spatial parameter for import Imported losses will be used as heat source 21
Example Eddy Currents Computation of eddy currents in tank Surface Impedance formulation 22
Power Transformer A three-phase h transformer with an air core reactor inside id of the tank was considered as the application of this analysis 23
Objectives Calculate eddy current losses in the clamping plate, tank and electromagnetic shielding of a power transformer using FLUX3D Analyze the effects of electromagnetic shielding and magnetic shunts on the eddy current loss reduction in the transformer tank 24
Surface Impedance Method The 3D Time-Harmonic Magnetodynamic Formulation was used in this analysis This formulation takes into account the currents induced in the conducting regions (eddy currents) and also considers the skin effects and the proximity effects in the conducting regions. Some devices such as clamping plate, bus bars of transformers and shielding are mainly made up of sheet or line type parts of thin air-gaps. Modeling these parts using traditional finite volume elements available in 3D software is tiresome, and even impossible. Moreover, the skin effect in ferromagnetic materials increases the difficulties of meshing eddy current problems in under sinusoidal conditions. 25
Surface Impedance Method An alternative to this difficulty of meshing the thin regions is the use special shell elements for the modeling of magnetic or thin conducting regions, and surface impedance elements for the modeling of conducting regions having a strong skin depth Special surface elements, using the concept of surface impedance, which describe the surface of the conducting region, allow the exponential decay to be taken into account. They also allow the magnetic field to only be calculated on the surface and outside 26
Power Transformer Description The tank and the clamping plates are made of mild steel (modeled by Surface Impedance Method - SIM) The core and the magnetic shunts are made of silicon-steel laminations The tank wall (side A) was modeled considering three cases: No Shielding Aluminum Electromagnetic Shielding (modeled by SIM) Magnetic Shunts 27
FLUX-3D Geometry Electromagnetic Shielding 28
FLUX-3D Geometry Magnetic Shunts 29
FLUX-3D Coupled Circuit it Electrical circuit feeding the active part of the transformer Electrical circuit coupled to the winding of the air core reactor 30
FLUX-3D Mesh 31
RESULTS 32
Magnetic Field Distribution ib ti in the Oil No Shielding There is only tangential ti component of the magnetic field in the tank walls (modeled by Surface Impedance) 33
Magnetic Field Distribution ib ti in the Oil Aluminum Electromagnetic Shielding There is only tangential component of the magnetic field in the tank walls and Electromagnetic Shielding (modeled by Surface Impedance) 34
Magnetic Field Distribution ib ti in the Oil Magnetic Shunts The magnetic flux tends to pass through the shunts 35
Eddy Current Losses in the Transformer Tank No Shielding The eddy current losses in the tank are larger in this first case 36
Eddy Current Losses in the Transformer Tank Aluminum Electromagnetic Shielding The eddy current losses in the tank are reduced in this second case 37
Eddy Current Losses in the Transformer Tank Magnetic Shunts The tank wall protected by the magnetic shunts has a loss concentration bigger than the tank wall protected by the aluminum electromagnetic shielding 38
Thermal Image of the Tank Wall with Magnetic Shunts One can see the presence of hot spots in position behind the magnetic shunts (red region). This shows that the magnetic shunts concentrate ce the eddy current losses at the top of shunts 39
Transformer winding HV winding Leg A Leg B The winding on leg A and B are parallel connected. LV winding has 2 layers for each leg and 2 layers are series connected with each other. LV winding 40
Eddy Current Losses in Coils 1 54 HV TAP HV HV TAP HV Section1 to section 54 are series. Section55 to section 108 are series. Then, upper and lower part are parallel connected. Each section is consist with 9-turn continuously transposed conductors (CTC). 55 HV leg HV A TAP TAP HV HV 108 CTC Single section 41
FLUX MODEL Axisymmetric i Just take 3 sections of HV winding and 1 section of LV winding. core 8571.9 A for this area 1004.9 /2 A for this area 42
External circuit it LV HV 43
Current density - hv DC 60Hz 44
Current density - lv DC 60 Hz 45
Joule Losses vs. Frequency on HV 46
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