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A link between EMTP-RV and FLUX3D for transformer energization studies S. Dennetière, Y. Guillot, J. Mahseredjian, M. Rioual Abstract-- This paper presents a programmed link between the electromagnetic transients program EMTP-RV and the finite element field solver FLUX3D. The model created in FLUX3D is driven from simulation designs in EMTP-RV. The test cases presented in this paper demonstrate that the coupling method is numerically robust and with sufficient accuracy. This approach benefits fr
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  A link between EMTP-RV and FLUX3D for transformer energization studies S. Dennetière, Y. Guillot, J. Mahseredjian, M. Rioual Abstract-- This paper presents a programmed link betweenthe electromagnetic transients program EMTP-RV and the finiteelement field solver FLUX3D. The model created in FLUX3D isdriven from simulation designs in EMTP-RV. The test casespresented in this paper demonstrate that the coupling method isnumerically robust and with sufficient accuracy. This approachbenefits from EMTP advantages in modeling large scalenetworks and from field solver advantages for detailedrepresentation of power transformer iron cores.Keywords: EMTP, FLUX3D, interface, switching transients,transformer transients I. I  NTRODUCTION   T He R&D Division of EDF performs since 1996 studies ontransformer energizations, from the determination of  palliative solutions for auxiliary transformers of power plantsafter a partial or total collapse of the network, to the reductionof stresses when energizing transformers of wind farms or those on hydraulic pumped-storage plants.The energization of an unloaded power transformer mayhave undesirable effects on power quality and may damagethe transformer.For those purposes, the modelling of the transformer is akey issue, especially the phenomena involved in the iron coreduring energization. The transient modeling of transformer energization requires an accurate nonlinear model of themagnetic material and a detailed representation of theelectrical network as presented in[1]-[3].  In most EMTP studies involving the energization of transformers, the transformer models are based on uncoupledsingle-phase units, to which a hysteretic model is added, inorder to take into account the losses in the iron core (eddycurrent and iron losses). This model is also very useful for therepresentation of winding copper losses and can be efficientlyused in EMTP statistical studies. It is however limited by thefact that it does provide a detailed representation of the ironcore, from its geometrical and magnetic characteristics andtherefore does not represent the coupling effect with highaccuracy. Such a limitation will not affect simulation results insome cases, but may have a significant impact in other cases,depending on the connection type of the transformer windings.A detailed representation of the iron core is needed tomodel the behavior of flux paths and saturation effects insidethe core, the flow of fluxes inside and outside the transformer,especially in the case of five limb transformers. Thisrepresentation is also useful to estimate the mechanicalstresses generated by the flow of fault and inrush currentsinside the transformer.A field solver based on the finite element method (FEM)can accurately take into account the material nonlinearity,winding connections and material anisotropy. However, fieldsolvers do not provide the variety of power systemcomponents needed for a large power network simulation withcontrol systems, surge arresters and multiphase transmissionlines. This paper is based on the idea of coupling (interfacing)two different modeling and computation approaches for agiven simulation case and thus achieving higher precision asrequired. The interface applications are FLUX3D and EMTP-RV.II. C OUPLING ELECTRICAL CIRCUIT AND MAGNETIC FIELDSOLVERS  There are two different approaches for combining thesolutions of field equations and circuit equations.The first approach consists in developing a program thatsolves simultaneously field equations and circuit equations.The magnetic equations are solved using a formulation withthe magnetic potential vector. The coupling is obtained by theconductor current expressed in terms of current density andflux linkage found from the potential vector (see[4], [6]-[8]). The time-dependant differential system resulting fromcoupling is solved with step-by-step numerical integration. Totake into account the magnetic and electric nonlinearities, a Newton-Raphson iterative procedure is used. This approach isdisadvantaged for the simulation of complex and large power networks since it provides a limited number of network component models and is inherently less efficient for classicalnetwork models. S. Dennetière, Y. Guillot and M. Rioual are with Electricité de France,Clamart, France. (e-mail of corresponding author:sebastien.dennetiere@edf.fr) The second approach consists on interfacing separatespecialized codes for optimizing performance and precision,and for benefiting from investments in established andvalidated libraries.This paper is based on the second approach: it presents andtests a DLL (Dynamic Link Library) based interface betweenthe Electromagnetic Transient Program EMTP-RV and thefield program FLUX3D. J. Mahseredjian is with École Polytechnique de Montréal, Canada. Presented at the International Conference on Power SystemsTransients (IPST’07) in Lyon, France on June 4-7, 2007  Simulation variables are exchanged between the field andcircuit models with a one time-step delay. This principle is notnew and is similar to[9]and[10].The interest of this paper  lies in the fact that this connection is general: not only currentsand voltages can be exchanged between the field solver andEMTP but also switching times, fluxes and mechanical forces.The paper is also contributing a programmed interface withFLUX3D and EMTP-RV applications.IV. T HE EMTP   /   FLUX3D   I  NTERFACE    A. Basic principles A DLL based interface has been chosen to couple EMTP-RV with FLUX3D. EMTP-RV drives the complete simulationthrough the EMTP-RV graphical user interface (Fig. 2). V km   FLUX 3DEMTP-RV Extra data : ã   Internal forces ã   Internal fluxesSimulation Data : ã   Time ã   Simulation flag I km   III. S IMULATION OF POWER TRANSFORMER TRANSIENTS    A. Network modeling in FLUX3D A 3D finite element method coupled to circuit equations is presented in[5].In[7]it is proposed to generalize this method for the case of solid conductors. The proposed formulationtakes into account multiple connected electrical circuits for nonlinear solid conductors. To deal with magnetic saturationthe Newton-Raphson procedure is used along with a prediction procedure.An example of power transformer energization with circuitequations is presented in.The Wye/Delta transformer isconnected to a Thevenin equivalent circuit.Fig. 1 Fig. 1 Finite element method coupled to circuit equations in FLUX3D The number of circuit (power) components is limited.  B. Transformer modeling in EMTP  Two types of transformer models are available in EMTP:3-phase transformer model based on uncoupled single phaseunits and 3-phase transformer model with internal coupling.The representation of single-phase N-winding transformers for steady-state and transient studies is straightforward[11]. Three-phase transformer models are usually based on the physical concept of representing windings as mutuallycoupled coils. The impedance or admittance matrices of thecoupled coils can be easily derived from commonly availabletest data[12].The models can be used for many types of studies as long as the frequencies are low enough so that thecapacitances in the transformer can be ignored.Studies of energization of unloaded transformers for power restoration purposes require detailed models that account for the behavior of flux paths, saturation effects inside the coreand forces inside transformers. Transformer models in EMTPare not suitable for these studies. DLLinterface V sourceI source    +   EMTPNetwork       +        +   Fig. 2 Coupling principle for each phase of transformer  A FLUX3D coil is represented in EMTP by a controlledcurrent source connected between two nodes. At each time- point EMTP solves the network equations and finds unknownvoltages. The branch voltages of controlled currentsources are sent to FLUX3D. EMTP also sends the timevariable. The controlled voltage sources are updated at thisstep with values and a FEM simulation is performed. Atthe end of the simulation currents flowing in each coil areavailable on EMTP side in addition to extra data such as tank temperatures, internal fluxes and internal forces. The interfaceenables to simulate transformers with any number of phases. km V km VA flag signal transmitted using EMTP control blocks toFLUX3D enables or disables this communication process.EMTP calls the field program only when it is required: atevery time-point, at every n th time-point or when a certainuser-defined condition is reached. An example of conditioncould be the value of flux derivative exceeding a giventhreshold. The overall interface is designed to optimizecomputational speed.  B. Time-step delay The approach presented above introduces a time-step delay between field calculations and the EMTP side solution. Thecurrent injected in the EMTP network at time t  has beencalculated in FLUX3D at t-  ∆ t  . Experiments indicate that thisapproach is acceptable in most of cases. Although it will notgive the exact solution, the error can be minimized byselecting smaller time-steps. As explained in[13]such aninterfacing method is not fully accurate, but numerical  stability is preserved. Satisfactory results are obtained withsmaller time-steps, which can be 10 times smaller than thetime-step size required for simultaneous solution capablesolvers[9]. The transformer modelled in FLUX3D is a 400/225 kVtransformer, 600 MVA, 5 limbs, YnD11. The B(H)characteristic of the magnetic circuit is nonlinear. A first order finite element mesh of 12,000 nodes is used. A view of theFLUX3D model is presented in (the mesh of themagnetic circuit and coils).The computational burden is also strongly related to the performance of the FLUX3D software.Fig. 4 Fig. 4 Representation of the magnetic circuit and coils in FLUX3D C. Switching times and floating nodes Initially the interface has been developed to simulatesimultaneous switching events in phases a, b and c. In realityswitching events are not simultaneous: the coupling principle presented in is only valid for the 1-phase or 3-phaseuncoupled cases. When a 3–phase coupled transformer isenergized, the first switching event produces magnetizationinside the transformer and generates induced voltages on open phase poles of breakers. These induced voltages have asignificant impact on over-voltages that appear when the open poles of breakers close. To take into account this statement theabove interface has been modified as follows, for each coil:Fig. 2Fig. 2 ã    before switching: the coil simulated in FLUX3D ismodelled in EMTP as a voltage source. The inducedvoltage between the two nodes of this coil iscalculated at each time-point by the field programand transmitted to EMTP. The current flowing in thiscoil is zero, this data is transmitted to the field program.As shown in an electrical circuit is coupled to thetransformer model in FLUX3D. This circuit contains 3 voltagesources controlled by EMTP as follow : ã   after switching: the coil is modelled as a currentsource in EMTP. Data is now transmitted as in V. T EST CASES    A. Validation on a simple case The objective of the first test case is to validate thecoupling method. This case consists in simulating theenergization of a 3-phase transformer connected to an RLimpedance and a voltage source. The 3 phases are energizedsimultaneously. presents the circuit in EMTP-RV.Fig. 3 Fig. 3 First test case in EMTP-RV Fig. 3Fig. 5 Fig. 5 Description of the electrical circuit in FLUX3D ã   V 1 (t)=V transfo a (t) ã   V 2 (t)=V transfo b (t) ã   V 3 (t)=V transfo c (t)The FLUX3D transformer model is represented in the GUI by a 3-phase block. The control pin is used to activate thefield calculation (always activated in this case, C1>0). Internalfluxes and forces are available through a bundle connection.By clicking on this block users can fill a form to specifysimulation options of the field solver and internal measuresthat will become available through bundle pins.This EMTP/FLUX3D simulation is validated with aFLUX3D simulation in which circuit equations are solvedsimultaneously with field equations. This circuit used for validation is presented in.RL1a, RL1b and RL1c inare defined inFias R1-L2, R2-L3, R3-L4.Fig. 1g. 1The phase a inrush current is presented in.Currentvalues calculated by FLUX3D alone (circuit equations aresolved simultaneously with field equations) are comparedagainst those calculated by the EMTP/FLUX3D interfacescheme. Maximum relative error is 3% with  ∆ t  =0.5 ms. Theerror is due to the one time-step delay between EMTPsolutions and field calculations. The error increases when thevalue of the network impedance increases.Fig. 6  Phases a-b-cclose at t=0s c 1 C1    +  AC1343kV /_-90+10m,15mH RL1+  CtrlFLUX3Dtransformer modelMes Force_MTBXForce_MTBYForce_MTBZ scope scp1 scope scp2 scope scp3cbaVtransfo    00.0050.010.0150.020.0250.030.0350.040100200300400500600700time (s)    C  u  r  r  e  n   t   (   A   )   Fig. 6 Inrush currents, solved with FLUX3D (solid) and FLUX3D/EMTP(dashed line) Magnetic induction in the transformer is available at eachtime-point during the EMTP/FLUX3D simulation.  B. Real case, EHV 400 kV network  A high-level view of the selected test case is shown in. The test case studies the energization of a 600 MVAautotransformer through a 180 km long line. This targettransformer, modeled in FLUX3D, is the same than the one presented in the first test case.Fig.7 Fig. 7 Single line diagram of the industrial case 900 MWGenerator 3x360 MVAstep-uptransformer 2x29 MVAauxiliarytransformer overheadline of 180 km600 MVAautotransformer FLUX3D model     1   2  +  12 236/6.8    +  CtrlMes PQ     +  cba      + The methodology applied to model the rest of the network is explained in[1].The generator at the sending end is a900 MW machine, which is modeled as an ideal source behindits substransient reactance.The long line is modeled using pi-sections. The number of PI cells has been chosen in order to represent correctly theexact impedance under the 4th harmonic which is theresonance frequency of this network. Step-up and auxiliarytransformers are modeled by a set of one-phase transformerswhere the leakage reactances, the copper and core losses andthe saturation are taken into account. The time-step for thistest case is 0.1 ms. It has been chosen to correctly representover-voltages due to harmonic inrush currents.Switching times are: t=15.8 ms on phase a, t=0 ms on phase b, t=10.2 ms on phase c.This EMTP/FLUX3D simulation is compared against anEMTP simulation in which the autotransformer is modeled bya set of 3 one-phase transformers. This is a classical model of one-phase transformer with nonlinear magnetization branch.The method of modeling used in this EMTP simulation is presented in[1]and has been validated by on site tests.Voltages at the breaker are shown in,and. Even if coupling between phases is not modeled in theEMTP autotransformer model, the EMTP/FLUX3D coupled-scheme results are very close to the results obtained with thesimple EMTP modeling.Fig. 8 Fig. 8 Phase-a voltage, EMTP/FLUX3D solution (solid line) and EMTPsolution (dashed line) Fig. 9 Fig. 9 Phase-b voltage, EMTP/FLUX3D solution (solid line) and EMTPsolution (dashed line) Fig.10  00.020.040.060.080.1-505x 10 5 time (s)    V  o   l   t  a  g  e   (   V   )   00.020.040.060.080.1-6-4-20246x 10 5 time (s)    V  o   l   t  a  g  e   (   V   )  
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