The voltage on the valve side windings of the converter transformer is non-sinusoidal, which contains many high-order harmonic components. To calculate the nonlinear electric field distribution under the non-sinusoidal voltage, the harmonic-balanced decomposition finite element method (HBDFEM) is proposed in this paper. By using the fixed-point method, the finite element stiffness matrix of each iteration is decomposed according to the harmonic order, by which the memory consumption can be remarkably reduced. To verify the effectiveness of the proposed algorithm, a typical model of the oil-paper insulation structure is taken for instance, and the results obtained by the HBDFEM is compared with two algorithms, the traditional HBFEM and the time step method. The calculation results show that the HBDFEM can effectively reduce the computation cost for the nonlinear electric field problems with the non-sinusoidal periodic voltage. And it can be applied to analyze the compound electric field problems of the actual converter transformer. The electric field distribution of a ±500 kV converter transformer is calculated and analyzed considering the nonlinear relationship between the electric field and the medium conductivity.
ZhaoW.J., HVDC Engineering Technology, China Electric Power Press, Beijing, 2004, pp. 318–325.
2.
LvX.D.ChenS.K.FangZ.Q., Analysis on characteristics of electric field at ends of valve-side winding in converter transformer, Transformer35 (1998), 15–20, doi:10.19487/j.cnki.1001-8425.1998.06.005.
3.
ChenQ.G.ZhangJ.GaoY., Analysis of complex electrical field on valve side winding of converter transformer, High Voltage34 (2008), 484–488, doi:10.13336/j.1003-6520.hve.2008.03.031.
4.
ChatterjeeS.PradhanA.K.DalaiS., Reducing frequency domain spectroscopy measurement time for condition monitoring of transformer oil-paper insulation using non-sinusoidal excitations, IET Science, Measurement Technology11 (2017), 204–212, doi:10.1049/iet-smt.2016.0264.
5.
DuB.X.ZhuW.B.ZhangJ.G., Surface and interface charge accumulation and decay of oil-paper insulation under DC voltage, IEEE Transactions on Dielectrics and Electrical Insulation24 (2017), 939–946, doi:10.1109/TDEI.2017.006153.
6.
ChiarielloA.G.FormisanoA.LeddaF., Analytical representation of 3D magnetic surfaces, International Journal of Applied Electromagnetics and Mechanics54 (2017), 627–645, doi:10.3233/JAE-170003.
7.
SuB.SunX.ChenL., Thermal modeling and analysis of bearingless permanent magnet synchronous motors, International Journal of Applied Electromagnetics and Mechanics56 (2017), 1–16, doi:10.3233/JAE-170112.
8.
QiB.WeiZ.LiC.R., The Phenomena and characteristics of oil-paper insulation surface discharge under ac and dc voltage, Transactions of China Electro Technical Society31 (2016), 59–67, doi:10.19595/j.cnki.1000-6753.tces.2016.10.007.
9.
XieD.X.YaoY.Y.BaiB.D.Finite Element Analysis of 3D Eddy Current Field, Machinery Industry Press, Beijing, 2001, pp. 81–98.
10.
BiroO. and PreisK., An efficient time domain method for nonlinear periodic eddy current problems, IEEE Transactions on Magnetics42 (2006), 695–698, doi:10.1109/TMAG.2006.871666.
11.
ZhaoX.J.LiL.ChengZ.G., Analysis of the dc bias phenomenon in transformers based on harmonic-balanced finite element method, Proceedings of the CSEE30 (2010), 103–108, doi:10.13334/j.0258-8013.pcsee.2010.21.019.
12.
YamadaS. and BesshoK., Harmonic field calculation by the combination of finite element analysis and harmonic balance method, IEEE Transactions on Magnetics24 (1988), 2588–2590, doi:10.1109/20.92182.
13.
CaiC.WangJ.HuM., Electromagnetic properties of cylinder permanent magnet eddy current coupling, International Journal of Applied Electromagnetics and Mechanics54 (2017), 655–671, doi:10.3233/JAE-170006.
14.
BachingerF.LangerU. and SchöberlJ., Efficient solvers for nonlinear time-periodic eddy current problems, Computing and Visualization Science9 (2004), 197–207, doi:10.1007/s00791-006-0023-z.
15.
HantilaF.I.PredaG. and VasiliuM., Polarization method for static field, IEEE Transactions on Magnetics36 (2000), 672–675, doi:10.1109/20.877538.
16.
AusserhoferS.BiroO. and PreisK., An efficient harmonic balance method for nonlinear eddy-current problems, IEEE Transactions on Magnetics43 (2007), 1229–1232, doi:10.1109/TMAG.2006.890961.
17.
AusserhoferS.BiroO. and PreisK., A strategy to improve the convergence of the fixed-point method for nonlinear eddy current problems, IEEE Transactions on Magnetics44 (2008), 1282–1285, doi:10.1109/TMAG.2007.916012.
18.
DlalaE. and ArkkioA., Analysis of the convergence of the fixed-point method used for solving nonlinear rotational magnetic field problems, IEEE Transactions on Magnetics44 (2008), 473–478, doi:10.1109/TMAG.2007.914888.
19.
LiuG.LiL.ZhaoX.J., Analysis of nonlinear electric field of oil-paper insulation under ac-dc hybrid voltage by fixed point method combined with fem in frequency domain, Proceedings of the CSEE32 (2012), 154–161+5, doi:10.13334/j.0258-8013.pcsee.2012.01.021.
20.
HouseH.A. and MelcherJ.R., Electromagnetic Field and Electromagnetic Energy, Higher Education Press, Beijing, 1992, pp. 9–26.
21.
ZhaoX.J.GuanD.W.ZhongY.T., The improved fixed-point harmonic-balanced method for nonlinear eddy current prombles, Transactions of China Electro Technical Society32 (2017), 214–221, doi:10.19595/j.cnki.1000-6753.tces.2017.01.024.
22.
KoczkaG.AuberhoferS.BiroO., Optimal convergence of the fixed-point method for nonlinear eddy current problems, IEEE Transactions on Magnetics45 (2009), 948–951, doi:10.1109/TMAG.2009.2012477.
23.
YangF.Y. and XuZ., Typical transient responses in hvdc transmission system, Transactions of china electro technical society20 (2005), 45–52, doi:10.19595/j.cnki.1000-6753.tces.2005.03.009.
24.
TakahashiE.ShirasakaY., Analysis of an ansisotropic nonlinear electric field with a discussion of dielectric tests for converter transformers and smoothing reactors, IEEE Transactions on Power Delivery9 (1994), 1480–1486, doi:10.1109/61.311221.
25.
LiJ.B. and XieD.X., Adaptive FE analysis of nonlinear and aniotropic DC electric field in converter transformer for DC transmission, Transformer44 (2007), 13–16, doi:10.19487/j.cnki.1001-8425.2007.12.004.
