Transformer Modelling Looking Inside to Access the Key Data. Stefan Tenbohlen, University of Stuttgart, Germany

Transcription

1 Transformer Modelling Looking Inside to Access the Key Data Stefan Tenbohlen, University of Stuttgart, Germany 1www.ieh.uni 1. Introduction 2. Winding Modelling by Lumped Elements 3. 3D Electromagnetic Field Simulation 4. Thermal-hydraulic Modelling by CFD 5. Conclusion

2 Introduction New requirements and utilization modes require a higher degree of knowledge about internal behaviour of power transformers Most of internal electrical and thermal values are not accessible directly Modelling can be the access key to these data Validation of modelling tools is absolutely necessary! Modelling of Voltage Distribution Electric Field Magnetic Circuit Transient interaction with grid Oil flow and Thermal Distribution Hot Spot 2

3 Winding Modelling by Lumped Elements Descretization of large HV structures into smaller units V H Based on geometry information calculation of lumped elements Detailed winding modelling enables calculation of - Frequency response - Internal voltage distribution Re i Valid up to several 100 khz 1 MHz for detailed models Most accepted modelling technique C i K i L i Rp i Rs i L ij Discretization Unit I Earth Z E 3

4 Validation of Lumped Elements Model If simulation model doesn t meet accuracy requirements: Possibility to optimize lumped parameters by genetic algorithms on the basis of measurement data Iterative Parameter Adaption Winding with Geometry Information Lumped Element Estimation Comparison f Measurement 4

5 Transfer Function based on Lumped Elements Modelled Winding Geometry Optimized Simulation Result Source: Rahimpour, Tenbohlen: Experimental and theoretical investigation of disc space variation in real high-voltage windings using transfer function method, IET Electr. Power Appl., 2010, Vol. 4, Iss. 6, pp

6 3D Electromagnetic Field Simulation Tool example: CST Microwave Studio Suite Uses Finite Integration Technique (FIT): - Universal spatial discretization scheme for integral form of Maxwell s equations - Ranging from electrostatic field to high frequency For Power Transformer Modelling: Frequency range up to several MHz High model complexity allowed 6

7 Example: Simulation of Winding End-to-End Transfer Function (TF) Continous disc winding: 60 discs, 9 turns per disc Input data: Geometry and material information (CAD) Simulation and measurement of end-to-end frequency response (@ 50 Ohm) TF(f) in db 90 cm f in MHz 7

8 Thermal-hydraulic Modelling with CFD CFD (Computational Fluid Dynamics) is comparable to the Finite-Volume Method The flow area is discretized into many small sub volumes (meshing) Within each of these elements, the governing Navier-Stokes equations are solved (Conservation of mass and momentum) After solution all flow quantities within the modelled domain are known and accessible With knowledge of oil flow the thermal distribution can be calculated based on loss matrix and heat transport equation Oil Duct Oil duct Disc Disc Section of a discretized disc type winding geometry 8

9 Hydraulic Modelling with Computational Fluid Dynamics (CFD) Conservation of Mass: d r r dv = v da dt ρ ρ CV Bounds CV Conservation of Momentum: of 0 ( stationary case) Mass change within CV = inflow - outflow of mass through all bounding surfaces d dt CV r ρ v dv = Bounds ρ of CV r r r v v da Change of Momentum within CV = inflow - outflow of momentum through all bounding surfaces + surface forces at the bounds of CV (e.g. shear forces) + body forces caused by gravity etc. + = Bounds Control Volume (CV) within Fluid Domain These two sets of equations are called Navier Stokes Equations. They are the fundamental law of all fluid flows! Within each of these elements, the governing Navier-Stokes Equations are formulated This leads to an nonlinear system of coupled equations This equation system is solved numerically in an iterative process After solution all flow quantities within the modelled domain are known = Fluid Flow r r ( f + p) da + f ρ dv = 0 ( stationary case) of A CV CV B 9

10 Validation by Pressure Drop Measurement Pressure drop over a whole zigzag section between two washers Hydraulic model of winding Pressure drop in Pa Measurement Simulation Flowrate in l/min The deviation over the whole section is quiet low Source: Tenbohlen, Weinläder, Wittmaack: Prediction of the Oil Flow and Temperature Distribution in Power Transformers by CFD, CIGRE Session 2010, Paris, France, paper No. A

11 Hydraulic Simulation Investigated section Velocity distribution Washer 11

12 Hydraulic Simulation Oil Flow between Discs Separation eddies are blocking the horizontal ducts 12

13 Simulation - Velocity Distribution washer Streamlines at 1 l/min Oil washer Streamlines at 20 l/min Oil Oil Oil For higher flowrates, separation eddies are blocking the lower ducts 13

14 Velocity Distribution at Different Flowrates Oil Disc Disc Disc Disc Disc Disc Disc Oil Scanning line for the velocity Non-uniform flow distribution for higher flowrates 14

15 Thermal-Hydraulic Simulation Temperature distribution Velocity distribution Losses at 4 A/mm 2 are impressed

16 Conclusion Detailed modelling of electromagnetic and thermal behaviour of power transformers is possible Simulation tools have to be validated by means of real measurements With the aid of appropriate models extensive parameter studies can be performed in order to improve design and operation of power transformers 16